info
large_stringlengths 120
50k
| question
large_stringlengths 504
10.4k
| avg@8_qwen3_4b_instruct_2507
float64 0
0.88
|
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{"tests": "{\"inputs\": [\"6\\n2 7 1 8 2 8\", \"3\\n1 4 1\", \"3\\n1 10 100\", \"2\\n1 1\", \"4\\n1 2 3 4\", \"6\\n2 7 2 8 2 8\", \"3\\n-1 1 1\", \"3\\n0 4 1\", \"3\\n2 10 100\", \"4\\n2 2 3 4\", \"6\\n4 7 2 8 2 8\", \"3\\n0 1 1\", \"3\\n0 10 100\", \"4\\n0 2 3 4\", \"6\\n6 7 2 8 2 8\", \"3\\n0 11 100\", \"4\\n0 2 3 7\", \"6\\n6 7 0 8 2 8\", \"3\\n-1 1 0\", \"3\\n0 11 101\", \"6\\n6 7 0 8 2 5\", \"3\\n-1 0 0\", \"3\\n0 11 111\", \"6\\n6 7 0 8 2 9\", \"3\\n-1 -1 0\", \"3\\n0 14 111\", \"6\\n6 7 0 8 3 9\", \"3\\n-1 -2 0\", \"3\\n0 14 011\", \"6\\n6 7 0 8 4 9\", \"3\\n-1 0 -1\", \"3\\n0 14 010\", \"6\\n6 7 0 8 6 9\", \"3\\n-1 -1 -1\", \"3\\n0 28 010\", \"6\\n5 7 0 8 6 9\", \"3\\n0 -1 -1\", \"3\\n1 28 010\", \"6\\n5 7 0 0 6 9\", \"3\\n0 -1 -2\", \"6\\n4 7 0 0 6 9\", \"3\\n0 0 -2\", \"6\\n4 7 0 -1 6 9\", \"3\\n0 1 -2\", \"6\\n4 7 0 -1 6 4\", \"3\\n1 1 -2\", \"3\\n1 1 -3\", \"3\\n1 0 -3\", \"3\\n1 0 -5\", \"3\\n0 0 -5\", \"3\\n0 0 0\", \"3\\n0 0 1\", \"3\\n0 1 0\", \"3\\n1 1 0\", \"3\\n1 2 0\", \"3\\n0 1 2\", \"3\\n0 0 2\", \"3\\n0 -1 2\", \"3\\n0 -1 3\", \"3\\n0 -1 1\", \"3\\n0 -1 0\", \"3\\n1 -1 0\", \"3\\n1 -2 0\", \"3\\n0 -2 0\", \"3\\n0 -3 0\", \"3\\n1 -3 0\", \"3\\n1 -3 -1\", \"3\\n1 -5 0\", \"3\\n1 -8 0\", \"3\\n1 -16 0\", \"3\\n0 -16 0\", \"3\\n1 -16 1\", \"3\\n1 -10 0\", \"3\\n1 -15 0\", \"3\\n2 -5 0\", \"3\\n2 -5 -1\", \"3\\n3 -5 -1\", \"3\\n3 -8 -1\", \"3\\n3 -4 -1\", \"3\\n3 -4 0\", \"3\\n1 -4 -1\", \"3\\n1 -4 -2\", \"3\\n1 -3 -2\", \"3\\n1 -6 0\", \"3\\n2 -6 0\", \"6\\n2 7 1 8 4 8\", \"3\\n1 2 1\", \"3\\n1 7 100\", \"2\\n0 0\", \"6\\n2 7 2 12 2 8\", \"3\\n0 4 2\", \"3\\n2 10 110\", \"4\\n2 2 0 4\", \"6\\n4 7 2 8 2 10\", \"3\\n0 -1 5\", \"3\\n0 10 101\", \"6\\n3 7 2 8 2 8\", \"3\\n0 2 1\", \"3\\n0 18 100\", \"4\\n-1 2 3 7\", \"6\\n6 7 0 8 0 8\", \"3\\n-1 1 -1\", \"3\\n0 22 101\", \"6\\n6 7 0 8 3 5\", \"3\\n-2 1 0\"], \"outputs\": [\"Yes\", \"Yes\", \"Yes\", \"No\", \"No\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\"]}", "source": "primeintellect"}
|
We have a sequence of length N, a = (a_1, a_2, ..., a_N). Each a_i is a positive integer.
Snuke's objective is to permute the element in a so that the following condition is satisfied:
* For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.
Determine whether Snuke can achieve his objective.
Constraints
* 2 ≤ N ≤ 10^5
* a_i is an integer.
* 1 ≤ a_i ≤ 10^9
Input
Input is given from Standard Input in the following format:
N
a_1 a_2 ... a_N
Output
If Snuke can achieve his objective, print `Yes`; otherwise, print `No`.
Examples
Input
3
1 10 100
Output
Yes
Input
4
1 2 3 4
Output
No
Input
3
1 4 1
Output
Yes
Input
2
1 1
Output
No
Input
6
2 7 1 8 2 8
Output
Yes
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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\"2\\n\", \"110\\n\", \"122\\n\", \"238\\n\", \"2\\n\", \"162\\n\", \"194\\n\", \"52\\n\", \"32\\n\", \"218\\n\", \"218\\n\", \"200\\n\", \"32\\n\", \"122\\n\", \"130\\n\", \"272\\n\", \"102\\n\", \"102\\n\", \"56\\n\", \"110\\n\", \"200\\n\", \"212\\n\", \"56\\n\", \"194\\n\", \"92\\n\", \"194\\n\", \"62\\n\"]}", "source": "primeintellect"}
|
There is a tree T with N vertices, numbered 1 through N. For each 1 ≤ i ≤ N - 1, the i-th edge connects vertices a_i and b_i.
Snuke is constructing a directed graph T' by arbitrarily assigning direction to each edge in T. (There are 2^{N - 1} different ways to construct T'.)
For a fixed T', we will define d(s,\ t) for each 1 ≤ s,\ t ≤ N, as follows:
* d(s,\ t) = (The number of edges that must be traversed against the assigned direction when traveling from vertex s to vertex t)
In particular, d(s,\ s) = 0 for each 1 ≤ s ≤ N. Also note that, in general, d(s,\ t) ≠ d(t,\ s).
We will further define D as the following:
3d2f3f88e8fa23f065c04cd175c14ebf.png
Snuke is constructing T' so that D will be the minimum possible value. How many different ways are there to construct T' so that D will be the minimum possible value, modulo 10^9 + 7?
Constraints
* 2 ≤ N ≤ 1000
* 1 ≤ a_i,\ b_i ≤ N
* The given graph is a tree.
Input
The input is given from Standard Input in the following format:
N
a_1 b_1
a_2 b_2
:
a_{N - 1} b_{N - 1}
Output
Print the number of the different ways to construct T' so that D will be the minimum possible value, modulo 10^9 + 7.
Examples
Input
4
1 2
1 3
1 4
Output
2
Input
4
1 2
2 3
3 4
Output
6
Input
6
1 2
1 3
1 4
2 5
2 6
Output
14
Input
10
2 4
2 5
8 3
10 7
1 6
2 8
9 5
8 6
10 6
Output
102
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 5\\n0W 1W\\n0W 2W\\n0W 2E\\n0E 1E\\n1E 2E\\naabbccdee\\n-\\n-\\n-\\n-\\nbbaadeecc\\n3 3\\n0E 1W\\n1E 2W\\n2E 0W\\naabb\\nbbcc\\naa\\nbbbb\\ncc\\naaaa\\n3 4\\n0E 1W\\n0E 2E\\n1E 2W\\n2E 0W\\nababab\\n-\\n-\\naaabbb\\n-\\n-\\n0 0\", \"3 5\\n0W 1W\\n0W 2W\\n0W 2E\\n0E 1E\\n1E 2E\\naabbcdcee\\n-\\n-\\n-\\n-\\nbbaadeecc\\n3 3\\n0E 1W\\n1E 2W\\n2E 0W\\naabb\\nbbcc\\naa\\nbbbb\\ncc\\naaaa\\n3 4\\n0E 1W\\n0E 2E\\n1E 2W\\n2E 0W\\nababab\\n-\\n-\\naaabbb\\n-\\n-\\n0 0\", \"3 5\\n0W 1W\\n0W 2W\\n0W 2E\\n0E 1E\\n1E 2E\\naabbccdee\\n-\\n-\\n-\\n-\\nbbaadeecc\\n3 3\\n0E 1W\\n0E 2W\\n2E 0W\\naabb\\nbbcc\\naa\\nbbbb\\ncc\\naaaa\\n3 4\\n0E 1W\\n0E 2E\\n1E 2W\\n2E 0W\\nababab\\n-\\n-\\naaabbb\\n-\\n-\\n0 0\", \"3 5\\n0W 1W\\n0W 2W\\n0W 2E\\n0E 1E\\n1E 2E\\naabbccdee\\n-\\n-\\n-\\n-\\nbbaadeecc\\n3 3\\n0E 2W\\n1E 2W\\n2E 0W\\naabb\\nbbcc\\naa\\nbbbb\\ncc\\naaaa\\n3 4\\n0E 1W\\n0E 2E\\n1E 2W\\n2E 0W\\nababab\\n-\\n-\\naaabbb\\n-\\n-\\n0 0\", \"3 5\\n0W 1W\\n0W 2W\\n0W 2E\\n0E 1E\\n1E 2E\\neecdcbbaa\\n-\\n-\\n-\\n-\\nbbaadeecc\\n3 3\\n0E 1W\\n1E 2W\\n2E 0W\\naabb\\nbbcc\\naa\\nbbbb\\ncc\\naaaa\\n3 4\\n0E 1W\\n0E 2E\\n1E 2W\\n2E 0W\\nababab\\n-\\n-\\naaabbb\\n-\\n-\\n0 0\", \"3 5\\n0W 1W\\n0W 2W\\n0W 2E\\n0E 1E\\n1E 2E\\neecdcbbaa\\n-\\n-\\n-\\n-\\nbbaadeecc\\n3 3\\n0E 1W\\n1E 2W\\n2E 0W\\naabb\\nbbcc\\naa\\nbbbb\\ncc\\naaaa\\n3 4\\n0E 1W\\n0E 2E\\n1E 2W\\n2E 0W\\nababab\\n-\\n-\\nbbbaaa\\n-\\n-\\n0 0\", \"3 5\\n0W 1W\\n0W 2W\\n0W 2E\\n0E 1E\\n1E 2E\\naabbccdee\\n-\\n-\\n-\\n-\\nbbaadeecc\\n3 3\\n0E 1W\\n0E 2W\\n2E 0W\\naabb\\nbbcc\\naa\\nbbbb\\ncc\\naaaa\\n3 4\\n0E 1W\\n0E 2E\\n1D 2W\\n2E 0W\\nbababa\\n-\\n-\\naaabbb\\n-\\n-\\n0 0\", \"3 5\\n0W 1W\\n0W 2W\\n0W 2E\\n0E 1E\\n1E 2E\\neecdcbbaa\\n-\\n-\\n-\\n-\\nbbaadeecc\\n3 3\\n0E 1W\\n1E 2W\\n2E 0W\\naabb\\nbbcc\\naa\\nbbbb\\ncc\\naaaa\\n3 4\\n0E 1W\\n0E 2E\\n1E 2W\\n2E 0W\\nbaabab\\n-\\n-\\nbbbaaa\\n-\\n-\\n0 0\", \"3 5\\n0W 1W\\n0W 2W\\n1W 2E\\n0E 1E\\n1E 2E\\neecdcbbaa\\n-\\n-\\n-\\n-\\ncceedaabb\\n3 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|
In the good old Hachioji railroad station located in the west of Tokyo, there are several parking lines, and lots of freight trains come and go every day.
All freight trains travel at night, so these trains containing various types of cars are settled in your parking lines early in the morning. Then, during the daytime, you must reorganize cars in these trains according to the request of the railroad clients, so that every line contains the “right” train, i.e. the right number of cars of the right types, in the right order.
As shown in Figure 7, all parking lines run in the East-West direction. There are exchange lines connecting them through which you can move cars. An exchange line connects two ends of different parking lines. Note that an end of a parking line can be connected to many ends of other lines. Also note that an exchange line may connect the East-end of a parking line and the West-end of another.
<image>
Cars of the same type are not discriminated between each other. The cars are symmetric, so directions of cars don’t matter either.
You can divide a train at an arbitrary position to make two sub-trains and move one of them through an exchange line connected to the end of its side. Alternatively, you may move a whole train as is without dividing it. Anyway, when a (sub-) train arrives at the destination parking line and the line already has another train in it, they are coupled to form a longer train.
Your superautomatic train organization system can do these without any help of locomotive engines. Due to the limitation of the system, trains cannot stay on exchange lines; when you start moving a (sub-) train, it must arrive at the destination parking line before moving another train.
In what follows, a letter represents a car type and a train is expressed as a sequence of letters. For example in Figure 8, from an initial state having a train "aabbccdee" on line 0 and no trains on other lines, you can make "bbaadeecc" on line 2 with the four moves shown in the figure.
<image>
To cut the cost out, your boss wants to minimize the number of (sub-) train movements. For example, in the case of Figure 8, the number of movements is 4 and this is the minimum.
Given the configurations of the train cars in the morning (arrival state) and evening (departure state), your job is to write a program to find the optimal train reconfiguration plan.
Input
The input consists of one or more datasets. A dataset has the following format:
x y
p1 P1 q1 Q1
p2 P2 q2 Q2
.
.
.
py Py qy Qy
s0
s1
.
.
.
sx-1
t0
t1
.
.
.
tx-1
x is the number of parking lines, which are numbered from 0 to x-1. y is the number of exchange lines. Then y lines of the exchange line data follow, each describing two ends connected by the exchange line; pi and qi are integers between 0 and x - 1 which indicate parking line numbers, and Pi and Qi are either "E" (East) or "W" (West) which indicate the ends of the parking lines.
Then x lines of the arrival (initial) configuration data, s0, ... , sx-1, and x lines of the departure (target) configuration data, t0, ... tx-1, follow. Each of these lines contains one or more lowercase letters "a", "b", ..., "z", which indicate types of cars of the train in the corresponding parking line, in west to east order, or alternatively, a single "-" when the parking line is empty.
You may assume that x does not exceed 4, the total number of cars contained in all the trains does not exceed 10, and every parking line has sufficient length to park all the cars.
You may also assume that each dataset has at least one solution and that the minimum number of moves is between one and six, inclusive.
Two zeros in a line indicate the end of the input.
Output
For each dataset, output the number of moves for an optimal reconfiguration plan, in a separate line.
Example
Input
3 5
0W 1W
0W 2W
0W 2E
0E 1E
1E 2E
aabbccdee
-
-
-
-
bbaadeecc
3 3
0E 1W
1E 2W
2E 0W
aabb
bbcc
aa
bbbb
cc
aaaa
3 4
0E 1W
0E 2E
1E 2W
2E 0W
ababab
-
-
aaabbb
-
-
0 0
Output
4
2
5
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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\"00000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000111111111\\n10000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000011111111\\n01010101010101010101010101010101010101010101010101010101010101010100010101010101010101010101010101010101010101010101010101010101\\n#\"], \"outputs\": [\"yes\\nyes\\nno\", \"yes\\nyes\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nyes\\nno\\n\", \"yes\\nyes\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nyes\\nno\\n\", \"yes\\nyes\\nno\\n\", \"yes\\nyes\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nyes\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nyes\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nyes\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nno\\nno\\n\", \"yes\\nyes\\nno\\n\"]}", "source": "primeintellect"}
|
Problem Statement
Let's consider operations on monochrome images that consist of hexagonal pixels, each of which is colored in either black or white. Because of the shape of pixels, each of them has exactly six neighbors (e.g. pixels that share an edge with it.)
"Filtering" is an operation to determine the color of a pixel from the colors of itself and its six neighbors. Examples of filterings are shown below.
Example 1: Color a pixel in white when all of its neighboring pixels are white. Otherwise the color will not change.
<image>
Performing this operation on all the pixels simultaneously results in "noise canceling," which removes isolated black pixels.
Example 2: Color a pixel in white when its all neighboring pixels are black. Otherwise the color will not change.
<image>
Performing this operation on all the pixels simultaneously results in "edge detection," which leaves only the edges of filled areas.
Example 3: Color a pixel with the color of the pixel just below it, ignoring any other neighbors.
<image>
Performing this operation on all the pixels simultaneously results in "shifting up" the whole image by one pixel.
Applying some filter, such as "noise canceling" and "edge detection," twice to any image yields the exactly same result as if they were applied only once. We call such filters idempotent. The "shifting up" filter is not idempotent since every repeated application shifts the image up by one pixel.
Your task is to determine whether the given filter is idempotent or not.
Input
The input consists of multiple datasets. The number of dataset is less than $100$. Each dataset is a string representing a filter and has the following format (without spaces between digits).
> $c_0c_1\cdots{}c_{127}$
$c_i$ is either '0' (represents black) or '1' (represents white), which indicates the output of the filter for a pixel when the binary representation of the pixel and its neighboring six pixels is $i$. The mapping from the pixels to the bits is as following:
<image>
and the binary representation $i$ is defined as $i = \sum_{j=0}^6{\mathit{bit}_j \times 2^j}$, where $\mathit{bit}_j$ is $0$ or $1$ if the corresponding pixel is in black or white, respectively. Note that the filter is applied on the center pixel, denoted as bit 3.
The input ends with a line that contains only a single "#".
Output
For each dataset, print "yes" in a line if the given filter is idempotent, or "no" otherwise (quotes are for clarity).
Sample Input
00000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000111111111
10000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000011111111
01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
Output for the Sample Input
yes
yes
no
Example
Input
00000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000111111111
10000000111111110000000011111111000000001111111100000000111111110000000011111111000000001111111100000000111111110000000011111111
01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
#
Output
yes
yes
no
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3\\n1 2\\n1 3\\n2 3\\n1\\n1 3\", \"3\\n1 2\\n1 3\\n2 3\\n1\\n1 2\", \"3\\n1 2\\n1 3\\n3 3\\n1\\n1 2\", \"3\\n2 2\\n1 3\\n2 1\\n2\\n2 3\", \"3\\n1 2\\n1 3\\n2 3\\n2\\n2 3\", \"3\\n2 2\\n1 3\\n3 3\\n1\\n1 2\", \"3\\n2 2\\n1 3\\n3 3\\n1\\n1 4\", \"3\\n2 2\\n1 3\\n2 3\\n1\\n1 4\", \"3\\n1 2\\n1 1\\n2 3\\n1\\n1 3\", \"3\\n2 2\\n1 3\\n2 3\\n1\\n1 8\", \"3\\n1 1\\n1 1\\n2 3\\n1\\n1 3\", \"3\\n1 1\\n2 1\\n2 3\\n1\\n1 3\", \"3\\n1 2\\n1 3\\n3 3\\n1\\n1 4\", \"3\\n2 2\\n1 3\\n2 1\\n1\\n1 8\", \"3\\n1 2\\n1 1\\n3 3\\n1\\n1 2\", \"3\\n1 2\\n1 3\\n3 3\\n1\\n1 3\", \"3\\n2 2\\n1 3\\n2 1\\n1\\n1 7\", \"3\\n2 2\\n1 3\\n3 3\\n1\\n1 8\", \"3\\n2 2\\n1 3\\n2 1\\n1\\n1 4\", \"3\\n1 2\\n2 3\\n3 3\\n1\\n1 2\", \"3\\n2 2\\n2 3\\n1 3\\n1\\n1 4\", \"3\\n1 1\\n2 1\\n1 3\\n1\\n1 3\", \"3\\n2 1\\n1 3\\n3 3\\n1\\n1 8\", \"3\\n1 1\\n2 1\\n1 3\\n1\\n1 1\", \"3\\n3 2\\n1 3\\n3 3\\n1\\n1 4\", \"3\\n2 2\\n1 1\\n2 3\\n1\\n1 3\", \"3\\n1 1\\n2 2\\n2 3\\n1\\n1 3\", \"3\\n3 2\\n1 3\\n3 3\\n1\\n1 2\", \"3\\n2 2\\n1 3\\n3 3\\n1\\n1 6\", \"3\\n2 1\\n1 3\\n3 3\\n1\\n1 15\", \"3\\n2 1\\n2 3\\n3 3\\n1\\n1 15\", \"3\\n2 2\\n1 3\\n2 3\\n1\\n1 2\", \"3\\n3 3\\n1 3\\n3 3\\n1\\n1 4\", \"3\\n1 2\\n1 3\\n2 3\\n1\\n2 3\", \"3\\n2 2\\n1 3\\n3 3\\n1\\n1 3\", \"3\\n1 1\\n2 1\\n1 3\\n1\\n2 1\", \"3\\n1 2\\n2 2\\n2 3\\n1\\n1 3\", \"3\\n2 2\\n1 3\\n2 3\\n1\\n2 3\", \"3\\n1 2\\n2 2\\n2 3\\n1\\n1 4\", \"3\\n2 3\\n1 3\\n3 3\\n1\\n1 8\", \"3\\n2 1\\n2 2\\n2 3\\n1\\n1 3\", \"3\\n2 1\\n1 3\\n2 3\\n1\\n1 2\", \"3\\n1 2\\n1 3\\n3 3\\n1\\n2 3\", \"3\\n2 2\\n1 3\\n2 3\\n1\\n1 3\", \"3\\n2 2\\n1 3\\n2 1\\n1\\n2 3\", \"3\\n2 3\\n1 3\\n3 3\\n1\\n1 2\", \"3\\n2 1\\n1 3\\n3 3\\n1\\n1 4\", \"3\\n2 2\\n1 3\\n2 1\\n1\\n1 2\", \"3\\n1 2\\n1 1\\n1 3\\n1\\n1 2\", \"3\\n2 2\\n1 3\\n2 1\\n1\\n1 3\", \"3\\n1 1\\n2 2\\n1 3\\n1\\n1 1\", \"3\\n2 3\\n1 3\\n3 3\\n1\\n1 16\", \"3\\n2 2\\n1 3\\n2 1\\n1\\n2 2\", \"3\\n2 3\\n1 3\\n3 3\\n1\\n2 16\", \"3\\n3 2\\n1 3\\n2 1\\n1\\n2 2\", \"3\\n1 1\\n1 3\\n2 3\\n1\\n2 3\", \"3\\n1 3\\n2 3\\n3 3\\n1\\n1 2\", \"3\\n2 2\\n1 2\\n2 3\\n1\\n1 4\", \"3\\n1 1\\n2 1\\n2 3\\n1\\n2 3\", \"3\\n1 2\\n1 3\\n3 3\\n1\\n2 4\", \"3\\n1 2\\n2 3\\n3 3\\n1\\n1 3\", \"3\\n2 2\\n2 3\\n1 3\\n1\\n1 2\", \"3\\n3 2\\n1 3\\n3 3\\n1\\n2 4\", \"3\\n2 2\\n2 1\\n2 3\\n1\\n1 3\", \"3\\n3 1\\n2 2\\n2 3\\n1\\n1 3\", \"3\\n1 1\\n1 3\\n2 3\\n2\\n2 3\", \"3\\n2 2\\n1 3\\n3 3\\n1\\n1 15\", \"3\\n2 2\\n3 3\\n1 3\\n1\\n1 4\", \"3\\n3 2\\n1 3\\n3 3\\n1\\n1 3\", \"3\\n2 1\\n2 2\\n2 3\\n1\\n1 6\", \"3\\n2 2\\n2 3\\n2 1\\n1\\n1 3\", \"3\\n2 3\\n1 3\\n3 3\\n1\\n1 4\", \"3\\n2 1\\n1 3\\n3 3\\n1\\n1 5\", \"3\\n1 2\\n1 1\\n1 3\\n1\\n1 1\", \"3\\n1 1\\n2 2\\n1 1\\n1\\n1 1\", \"3\\n2 1\\n1 3\\n2 3\\n2\\n2 3\", \"3\\n2 2\\n1 2\\n3 3\\n1\\n1 15\", \"3\\n2 3\\n1 2\\n3 3\\n1\\n1 4\", \"3\\n1 2\\n1 1\\n1 3\\n1\\n2 1\", \"3\\n2 1\\n1 3\\n3 3\\n2\\n2 3\", \"3\\n2 2\\n1 2\\n3 3\\n1\\n1 4\", \"3\\n1 2\\n1 1\\n2 3\\n1\\n1 2\", \"3\\n2 2\\n1 3\\n3 3\\n1\\n1 5\", \"3\\n1 2\\n2 2\\n2 2\\n1\\n1 4\", \"3\\n2 1\\n1 3\\n2 2\\n1\\n1 2\", \"3\\n1 2\\n1 1\\n1 3\\n1\\n1 3\", \"3\\n2 2\\n2 1\\n1 3\\n1\\n1 2\", \"3\\n2 2\\n3 3\\n1 3\\n1\\n1 2\", \"3\\n2 3\\n1 2\\n3 3\\n1\\n1 2\", \"3\\n1 2\\n2 2\\n2 2\\n1\\n1 5\", \"3\\n2 3\\n3 3\\n1 3\\n1\\n1 2\", \"3\\n2 3\\n1 1\\n3 3\\n1\\n1 2\", \"3\\n2 2\\n1 3\\n2 3\\n1\\n1 11\", \"3\\n2 2\\n1 3\\n3 2\\n1\\n1 8\", \"3\\n2 2\\n2 3\\n1 3\\n1\\n1 3\", \"3\\n2 1\\n2 3\\n3 3\\n1\\n2 15\", \"3\\n2 3\\n1 3\\n3 3\\n1\\n1 3\", \"3\\n1 2\\n2 2\\n2 3\\n1\\n1 5\", \"3\\n2 3\\n1 2\\n3 3\\n1\\n1 8\", \"3\\n2 1\\n1 3\\n2 2\\n1\\n1 3\", \"3\\n2 1\\n1 3\\n3 3\\n1\\n1 2\"], \"outputs\": [\"2\", \"2\\n\", \"1\\n\", \"1\\n1\\n\", \"2\\n2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"2\\n2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\"]}", "source": "primeintellect"}
|
C: Namo .. Cut
problem
-Defeat the mysterious giant jellyfish, codenamed "Nari"-
"Nari" has a very strong vitality, so if you don't keep cutting quickly, it will be revived in a blink of an eye. We are making trial and error every day to find out how to cut "Nari" efficiently. In the process, you needed the help of a programmer.
"Na ◯ ri" can be represented by a connected undirected graph consisting of N vertices and N edges. From now on, suppose each vertex is named with a different number from 1 to N.
We ask Q questions about "Nari". I want you to create a program that answers all of them.
Questions have numbers from 1 to Q, and each question is structured as follows:
* Question i specifies two vertices a_i and b_i. Answer the minimum number of edges that need to be deleted in order to unlink a_i and b_i.
Here, the fact that the vertices u and v are unconnected means that there is no route that can go back and forth between u and v.
Input format
N
u_1 v_1
u_2 v_2
...
u_N v_N
Q
a_1 b_1
a_2 b_2
...
a_Q b_Q
All inputs are integers.
The number of vertices N is given in the first line. The i-th line of the following N lines is given the numbers u_i and v_i of the two vertices connected by the i-th edge, separated by blanks.
Then the number of questions Q is given. The i-th line of the following Q lines is given the numbers a_i and b_i of the two vertices specified in the i-th question, separated by blanks.
Constraint
* 3 \ leq N \ leq 100,000
* 1 \ leq Q \ leq 100,000
* There are no self-loops or multiple edges in the graph
* 1 \ leq a_i, b_i \ leq N and a_i \ neq b_i (1 \ leq i \ leq Q)
Output format
The output consists of Q lines. On line i, output an integer that represents the minimum number of edges that need to be deleted in order to unlink a_i and b_i.
Input example 1
3
1 2
13
twenty three
1
13
Output example 1
2
Input example 2
7
1 2
1 6
3 5
twenty five
5 4
14
3 7
3
twenty four
3 1
6 7
Output example 2
2
1
1
Example
Input
3
1 2
1 3
2 3
1
1 3
Output
2
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4\\n4 3 2 1\", \"5\\n1 5 3 4 2\", \"4\\n8 3 2 1\", \"5\\n0 5 3 4 2\", \"5\\n0 5 3 1 2\", \"5\\n1 8 3 4 2\", \"5\\n0 9 3 1 2\", \"5\\n1 8 3 4 0\", \"5\\n0 15 3 1 2\", \"5\\n1 5 3 8 2\", \"5\\n0 5 6 4 2\", \"5\\n0 5 3 1 4\", \"5\\n0 19 3 1 2\", \"4\\n3 5 2 1\", \"5\\n0 5 6 4 3\", \"5\\n0 12 3 1 4\", \"5\\n0 17 3 1 4\", \"4\\n4 0 2 1\", \"5\\n0 17 3 1 8\", \"5\\n0 17 2 1 6\", \"5\\n0 23 2 1 4\", \"5\\n0 17 2 1 9\", \"5\\n0 28 3 1 5\", \"5\\n0 23 3 1 5\", \"4\\n0 3 2 1\", \"5\\n0 8 3 1 2\", \"5\\n0 18 3 1 4\", \"5\\n0 26 3 1 10\", \"5\\n0 26 3 1 19\", \"5\\n0 7 6 1 5\", \"5\\n1 6 3 4 2\", \"5\\n0 17 3 1 13\", \"5\\n0 23 3 1 8\", \"5\\n0 28 3 1 7\", \"5\\n0 4 3 2 8\", \"5\\n0 5 12 4 6\", \"5\\n0 28 3 2 7\", \"5\\n0 5 23 4 6\", \"5\\n0 26 6 2 19\", \"5\\n0 5 23 4 10\", \"5\\n0 48 6 2 19\", \"5\\n0 3 23 4 10\", \"5\\n0 48 9 2 11\", \"5\\n0 48 9 2 17\", \"5\\n0 23 3 1 19\", \"5\\n0 42 3 1 10\", \"5\\n0 32 3 1 19\", \"5\\n0 5 17 4 6\", \"5\\n0 47 5 2 7\", \"5\\n0 34 6 2 19\", \"5\\n0 48 9 2 1\", \"5\\n0 25 9 2 11\", \"5\\n0 54 3 1 10\", \"4\\n6 25 1 2\", \"5\\n0 26 11 2 9\", \"5\\n0 5 40 3 10\", \"5\\n0 48 9 4 1\", \"5\\n1 26 11 2 9\", \"5\\n0 5 40 3 14\", \"5\\n1 25 13 2 11\", \"5\\n0 48 3 1 17\", \"5\\n0 42 2 1 26\", \"5\\n0 26 6 2 15\", \"5\\n0 48 6 2 33\", \"5\\n0 48 9 4 19\", \"5\\n0 91 9 2 11\", \"5\\n0 68 3 1 10\", \"5\\n0 47 5 1 7\", \"5\\n0 5 68 4 10\", \"5\\n0 91 14 2 11\", \"5\\n0 68 3 2 10\", \"5\\n0 94 5 1 7\", \"5\\n0 26 5 4 9\", \"5\\n0 46 9 3 1\", \"5\\n0 65 3 2 4\", \"5\\n0 91 14 3 11\", \"4\\n4 5 2 1\", \"4\\n11 3 2 1\", \"5\\n0 12 3 1 2\", \"4\\n6 5 2 1\", \"5\\n0 10 3 1 4\", \"5\\n0 17 2 1 4\", \"4\\n4 3 1 2\", \"5\\n1 10 3 4 2\", \"5\\n1 8 3 7 0\", \"5\\n0 15 3 1 4\", \"5\\n0 12 2 1 4\", \"5\\n0 10 3 1 7\", \"5\\n1 11 3 4 2\", \"5\\n1 8 3 6 0\", \"5\\n0 15 3 1 5\", \"5\\n0 13 3 1 8\", \"5\\n1 8 5 7 0\", \"5\\n1 8 4 7 0\", \"5\\n0 23 3 1 10\", \"5\\n1 7 3 4 2\", \"5\\n0 5 12 4 2\", \"5\\n0 7 3 1 4\", \"4\\n6 7 2 1\", \"4\\n6 3 1 2\", \"5\\n1 15 3 7 0\", \"5\\n0 15 6 1 4\"], \"outputs\": [\"10\", \"7\", \"14\\n\", \"7\\n\", \"12\\n\", \"10\\n\", \"16\\n\", \"9\\n\", \"22\\n\", \"17\\n\", \"19\\n\", \"11\\n\", \"26\\n\", \"13\\n\", \"21\\n\", \"18\\n\", \"23\\n\", \"5\\n\", \"27\\n\", \"25\\n\", \"29\\n\", \"28\\n\", \"35\\n\", \"30\\n\", \"4\\n\", \"15\\n\", \"24\\n\", \"38\\n\", \"47\\n\", \"20\\n\", \"8\\n\", \"32\\n\", \"33\\n\", \"37\\n\", \"6\\n\", \"31\\n\", \"39\\n\", \"42\\n\", \"49\\n\", \"46\\n\", \"71\\n\", \"41\\n\", \"63\\n\", \"69\\n\", \"44\\n\", \"54\\n\", \"53\\n\", \"36\\n\", \"58\\n\", \"57\\n\", \"60\\n\", \"40\\n\", \"66\\n\", \"34\\n\", \"50\\n\", \"61\\n\", \"62\\n\", \"52\\n\", \"65\\n\", \"55\\n\", \"67\\n\", \"70\\n\", \"45\\n\", \"85\\n\", \"75\\n\", \"106\\n\", \"80\\n\", \"56\\n\", \"91\\n\", \"120\\n\", \"82\\n\", \"103\\n\", \"43\\n\", \"59\\n\", \"73\\n\", \"122\\n\", \"14\\n\", \"17\\n\", \"19\\n\", \"14\\n\", \"16\\n\", \"23\\n\", \"12\\n\", \"12\\n\", \"9\\n\", \"21\\n\", \"18\\n\", \"19\\n\", \"13\\n\", \"9\\n\", \"22\\n\", \"23\\n\", \"9\\n\", \"9\\n\", \"35\\n\", \"9\\n\", \"25\\n\", \"13\\n\", \"18\\n\", \"14\\n\", \"16\\n\", \"27\\n\"]}", "source": "primeintellect"}
|
You are given $n$ integers $w_i (i = 0, 1, ..., n-1)$ to be sorted in ascending order. You can swap two integers $w_i$ and $w_j$. Each swap operation has a cost, which is the sum of the two integers $w_i + w_j$. You can perform the operations any number of times.
Write a program which reports the minimal total cost to sort the given integers.
Constraints
* $1 \leq n \leq 1,000$
* $0 \leq w_i\leq 10^4$
* $w_i$ are all different
Input
In the first line, an integer $n$ is given. In the second line, $n$ integers $w_i (i = 0, 1, 2, ... n-1)$ separated by space characters are given.
Output
Print the minimal cost in a line.
Examples
Input
5
1 5 3 4 2
Output
7
Input
4
4 3 2 1
Output
10
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"14\\n1 0\\n1 1\\n1 2\\n2 1\\n0 0\\n0 1\\n0 2\\n0 3\\n3 3\\n4\\n5\\n6\\n7\\n8\", \"14\\n1 0\\n1 1\\n1 2\\n2 1\\n0 0\\n0 1\\n1 2\\n0 3\\n3 3\\n4\\n5\\n6\\n7\\n8\", \"14\\n1 0\\n1 1\\n1 2\\n2 1\\n0 0\\n0 1\\n0 2\\n0 6\\n3 3\\n4\\n5\\n6\\n7\\n8\", \"14\\n1 0\\n1 1\\n2 2\\n2 1\\n0 0\\n0 1\\n0 2\\n0 6\\n3 3\\n4\\n5\\n6\\n7\\n8\", \"14\\n1 0\\n1 1\\n1 2\\n2 1\\n0 0\\n0 1\\n0 2\\n0 3\\n3 3\\n4\\n5\\n6\\n7\\n7\", \"14\\n1 0\\n1 1\\n1 2\\n2 1\\n0 0\\n0 1\\n1 2\\n0 3\\n3 3\\n4\\n5\\n5\\n7\\n8\", \"14\\n1 0\\n1 1\\n1 2\\n2 1\\n0 0\\n0 1\\n0 2\\n0 6\\n3 1\\n4\\n5\\n6\\n7\\n8\", \"14\\n1 0\\n1 1\\n2 2\\n2 1\\n0 0\\n0 1\\n0 2\\n0 6\\n3 3\\n4\\n4\\n6\\n7\\n8\", \"14\\n1 0\\n1 1\\n1 2\\n2 1\\n0 0\\n0 1\\n1 2\\n0 3\\n3 3\\n4\\n5\\n6\\n7\\n7\", \"14\\n1 0\\n1 1\\n1 2\\n2 1\\n0 1\\n0 1\\n1 2\\n0 3\\n3 3\\n4\\n5\\n5\\n7\\n8\", \"14\\n1 0\\n1 1\\n1 2\\n2 1\\n0 0\\n0 1\\n0 2\\n0 2\\n3 1\\n4\\n5\\n6\\n7\\n8\", \"14\\n1 0\\n1 1\\n1 2\\n2 1\\n0 0\\n0 0\\n0 2\\n0 2\\n3 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|
A state with $n$ flags of ON or OFF can be represented by a sequence of bits where $0, 1, ..., n-1$ -th flag corresponds to 1 (ON) or 0 (OFF). The state can be managed by the corresponding decimal integer, because the sequence of bits is a binary representation where each bit is 0 or 1.
Given a sequence of bits with 64 flags which represent a state, perform the following operations. Note that each flag of the bits is initialized by OFF.
* test(i): Print 1 if $i$-th flag is ON, otherwise 0
* set(i): Set $i$-th flag to ON
* clear(i): Set $i$-th flag to OFF
* flip(i): Inverse $i$-th flag
* all: Print 1 if all flags are ON, otherwise 0
* any: Print 1 if at least one flag is ON, otherwise 0
* none: Print 1 if all flags are OFF, otherwise 0
* count: Print the number of ON flags
* val: Print the decimal value of the state
Constraints
* $1 \leq q \leq 200,000$
* $0 \leq i < 64$
Input
The input is given in the following format.
$q$
$query_1$
$query_2$
:
$query_q$
Each query $query_i$ is given in the following format:
0 $i$
or
1 $i$
or
2 $i$
or
3 $i$
or
4
or
5
or
6
or
7
or
8
The first digit 0, 1,...,8 represents the operation test(i), set(i), clear(i), flip(i), all, any, none, count or val respectively.
Output
Print the result in a line for each test, all, any, none, count and val operation.
Example
Input
14
1 0
1 1
1 2
2 1
0 0
0 1
0 2
0 3
3 3
4
5
6
7
8
Output
1
0
1
0
0
1
0
3
13
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
Petr has just bought a new car. He's just arrived at the most known Petersburg's petrol station to refuel it when he suddenly discovered that the petrol tank is secured with a combination lock! The lock has a scale of 360 degrees and a pointer which initially points at zero:
<image>
Petr called his car dealer, who instructed him to rotate the lock's wheel exactly n times. The i-th rotation should be a_i degrees, either clockwise or counterclockwise, and after all n rotations the pointer should again point at zero.
This confused Petr a little bit as he isn't sure which rotations should be done clockwise and which should be done counterclockwise. As there are many possible ways of rotating the lock, help him and find out whether there exists at least one, such that after all n rotations the pointer will point at zero again.
Input
The first line contains one integer n (1 ≤ n ≤ 15) — the number of rotations.
Each of the following n lines contains one integer a_i (1 ≤ a_i ≤ 180) — the angle of the i-th rotation in degrees.
Output
If it is possible to do all the rotations so that the pointer will point at zero after all of them are performed, print a single word "YES". Otherwise, print "NO". Petr will probably buy a new car in this case.
You can print each letter in any case (upper or lower).
Examples
Input
3
10
20
30
Output
YES
Input
3
10
10
10
Output
NO
Input
3
120
120
120
Output
YES
Note
In the first example, we can achieve our goal by applying the first and the second rotation clockwise, and performing the third rotation counterclockwise.
In the second example, it's impossible to perform the rotations in order to make the pointer point at zero in the end.
In the third example, Petr can do all three rotations clockwise. In this case, the whole wheel will be rotated by 360 degrees clockwise and the pointer will point at zero again.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
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3\\n10 5\\n\", \"7 7\\n4 1\\n7 5\\n3 7\\n4 2\\n1 3\\n1 4\\n5 3\\n\", \"10 10\\n1 5\\n9 6\\n4 10\\n1 9\\n8 6\\n1 7\\n3 2\\n5 7\\n4 3\\n10 5\\n\", \"7 7\\n4 1\\n7 5\\n3 7\\n4 2\\n2 3\\n1 4\\n5 3\\n\", \"10 10\\n1 3\\n9 6\\n4 5\\n1 9\\n8 5\\n9 7\\n3 1\\n5 7\\n5 3\\n10 5\\n\", \"4 5\\n1 2\\n2 3\\n3 3\\n4 1\\n1 3\\n\", \"10 10\\n4 3\\n6 8\\n5 3\\n8 1\\n2 9\\n7 8\\n9 6\\n10 2\\n9 3\\n6 3\\n\", \"10 10\\n6 8\\n9 10\\n10 1\\n2 10\\n10 7\\n3 1\\n8 2\\n2 1\\n4 1\\n5 10\\n\", \"10 10\\n9 2\\n8 4\\n2 10\\n7 8\\n8 6\\n9 3\\n2 6\\n7 1\\n7 4\\n5 4\\n\", \"7 7\\n4 7\\n7 6\\n1 5\\n3 2\\n5 6\\n7 1\\n2 4\\n\", \"10 10\\n1 3\\n9 6\\n4 5\\n1 9\\n8 6\\n9 7\\n3 2\\n5 7\\n5 3\\n10 7\\n\", \"7 7\\n4 1\\n7 5\\n4 7\\n4 4\\n1 3\\n6 4\\n5 3\\n\", \"10 10\\n1 3\\n9 6\\n4 5\\n1 9\\n2 6\\n1 7\\n3 2\\n5 7\\n4 3\\n10 5\\n\", \"7 7\\n4 1\\n7 5\\n3 7\\n4 2\\n1 3\\n1 4\\n5 4\\n\", \"7 7\\n4 1\\n7 5\\n5 1\\n4 2\\n2 3\\n1 4\\n5 3\\n\", \"10 10\\n4 3\\n6 8\\n5 3\\n8 1\\n2 9\\n9 8\\n9 6\\n10 2\\n9 3\\n6 3\\n\", \"10 10\\n1 3\\n9 6\\n4 5\\n1 9\\n8 6\\n9 7\\n3 2\\n5 7\\n9 3\\n10 7\\n\", \"10 10\\n1 6\\n9 6\\n4 5\\n1 9\\n2 6\\n1 7\\n3 2\\n5 7\\n4 3\\n10 5\\n\", \"10 10\\n1 3\\n9 6\\n4 5\\n1 9\\n8 6\\n9 7\\n3 3\\n5 7\\n9 3\\n10 7\\n\", \"10 10\\n4 3\\n6 8\\n5 3\\n8 1\\n2 9\\n4 8\\n3 6\\n10 2\\n9 3\\n6 3\\n\", \"10 10\\n1 3\\n9 6\\n4 1\\n1 9\\n8 6\\n9 7\\n3 3\\n5 7\\n9 3\\n10 7\\n\", \"10 10\\n1 3\\n9 6\\n4 1\\n1 9\\n8 6\\n9 7\\n3 3\\n5 7\\n9 4\\n10 7\\n\", \"10 10\\n2 1\\n3 4\\n7 1\\n4 10\\n6 1\\n8 4\\n9 1\\n6 8\\n1 8\\n3 6\\n\", \"4 5\\n1 2\\n2 3\\n3 4\\n4 2\\n1 3\\n\", \"10 10\\n3 4\\n3 5\\n2 9\\n5 1\\n7 3\\n3 2\\n3 10\\n8 3\\n6 3\\n5 10\\n\", \"7 7\\n4 7\\n7 2\\n3 5\\n3 2\\n5 6\\n7 1\\n2 4\\n\", \"10 10\\n1 3\\n9 6\\n4 5\\n1 9\\n8 6\\n9 7\\n3 2\\n5 7\\n5 3\\n10 1\\n\", \"10 10\\n3 4\\n3 5\\n8 10\\n5 1\\n7 3\\n3 2\\n3 10\\n8 3\\n6 3\\n4 10\\n\", \"4 5\\n1 2\\n4 2\\n3 4\\n4 1\\n1 3\\n\", \"10 10\\n1 3\\n9 6\\n4 5\\n1 9\\n8 6\\n1 7\\n3 3\\n5 7\\n4 3\\n10 5\\n\", \"10 10\\n1 5\\n9 6\\n4 5\\n1 8\\n8 6\\n1 7\\n3 2\\n5 7\\n4 3\\n10 5\\n\", \"10 10\\n1 5\\n9 6\\n4 10\\n1 9\\n8 7\\n1 7\\n3 2\\n5 7\\n4 3\\n10 5\\n\", \"7 7\\n4 1\\n7 5\\n3 7\\n4 2\\n2 5\\n1 4\\n5 3\\n\", \"10 10\\n9 2\\n8 4\\n2 10\\n7 8\\n8 6\\n9 3\\n3 6\\n7 1\\n7 4\\n5 4\\n\", \"7 7\\n4 1\\n7 5\\n5 7\\n4 2\\n1 3\\n1 4\\n5 4\\n\", \"10 10\\n4 3\\n6 8\\n5 3\\n8 1\\n2 9\\n9 8\\n9 6\\n10 2\\n8 3\\n6 3\\n\", \"20 10\\n1 3\\n9 6\\n4 5\\n1 9\\n8 6\\n9 7\\n3 2\\n5 7\\n9 3\\n10 7\\n\", \"10 10\\n2 1\\n3 6\\n7 1\\n4 10\\n6 1\\n8 4\\n9 1\\n6 8\\n1 8\\n3 6\\n\", \"4 5\\n1 2\\n2 3\\n3 4\\n4 2\\n2 3\\n\", \"20 10\\n3 4\\n3 5\\n8 10\\n5 1\\n7 3\\n3 2\\n3 10\\n8 3\\n6 3\\n4 10\\n\", \"7 7\\n2 1\\n7 5\\n4 7\\n4 2\\n1 3\\n6 5\\n5 3\\n\", \"4 5\\n1 1\\n4 2\\n3 4\\n4 1\\n1 3\\n\", \"10 10\\n1 5\\n9 6\\n4 5\\n1 8\\n8 6\\n1 10\\n3 2\\n5 7\\n4 3\\n10 5\\n\", \"15 10\\n1 5\\n9 6\\n4 10\\n1 9\\n8 7\\n1 7\\n3 2\\n5 7\\n4 3\\n10 5\\n\", \"10 10\\n1 2\\n8 4\\n2 10\\n7 8\\n8 6\\n9 3\\n3 6\\n7 1\\n7 4\\n5 4\\n\", \"20 10\\n1 3\\n9 6\\n4 5\\n2 9\\n8 6\\n9 7\\n3 2\\n5 7\\n9 3\\n10 7\\n\", \"7 5\\n1 2\\n2 3\\n3 4\\n4 2\\n2 3\\n\", \"7 7\\n2 1\\n7 5\\n4 7\\n4 2\\n1 3\\n4 5\\n5 3\\n\", \"19 10\\n1 5\\n9 6\\n4 5\\n1 8\\n8 6\\n1 10\\n3 2\\n5 7\\n4 3\\n10 5\\n\", \"15 10\\n1 5\\n9 6\\n4 10\\n1 9\\n8 7\\n1 7\\n3 2\\n5 7\\n4 5\\n10 5\\n\", \"10 10\\n1 2\\n8 4\\n2 10\\n7 8\\n8 6\\n9 3\\n6 6\\n7 1\\n7 4\\n5 4\\n\", \"20 10\\n1 3\\n1 6\\n4 5\\n2 9\\n8 6\\n9 7\\n3 2\\n5 7\\n9 3\\n10 7\\n\", \"7 7\\n2 1\\n7 5\\n7 7\\n4 2\\n1 3\\n4 5\\n5 3\\n\"], \"outputs\": [\"YES\\n10100\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n0100111\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n0001010\", \"NO\\n\", \"YES\\n0010101000\", \"NO\\n\", \"NO\\n\", \"YES\\n1011000\", \"NO\\n\", \"YES\\n0001110\\n\", \"YES\\n1011000\\n\", \"YES\\n1001010110\\n\", \"YES\\n0010111\\n\", \"YES\\n1110010111\\n\", \"YES\\n0011101\\n\", \"YES\\n1011001000\\n\", \"YES\\n1001011100\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n1011000\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n1011000\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n1110010111\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n0010111\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n0011101\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\"]}", "source": "primeintellect"}
|
You are given a connected undirected graph consisting of n vertices and m edges. There are no self-loops or multiple edges in the given graph.
You have to direct its edges in such a way that the obtained directed graph does not contain any paths of length two or greater (where the length of path is denoted as the number of traversed edges).
Input
The first line contains two integer numbers n and m (2 ≤ n ≤ 2 ⋅ 10^5, n - 1 ≤ m ≤ 2 ⋅ 10^5) — the number of vertices and edges, respectively.
The following m lines contain edges: edge i is given as a pair of vertices u_i, v_i (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i). There are no multiple edges in the given graph, i. e. for each pair (u_i, v_i) there are no other pairs (u_i, v_i) and (v_i, u_i) in the list of edges. It is also guaranteed that the given graph is connected (there is a path between any pair of vertex in the given graph).
Output
If it is impossible to direct edges of the given graph in such a way that the obtained directed graph does not contain paths of length at least two, print "NO" in the first line.
Otherwise print "YES" in the first line, and then print any suitable orientation of edges: a binary string (the string consisting only of '0' and '1') of length m. The i-th element of this string should be '0' if the i-th edge of the graph should be directed from u_i to v_i, and '1' otherwise. Edges are numbered in the order they are given in the input.
Example
Input
6 5
1 5
2 1
1 4
3 1
6 1
Output
YES
10100
Note
The picture corresponding to the first example: <image>
And one of possible answers: <image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"(()((\\n\", \"(()())\\n\", \")(\\n\", \"()()()()()()()(\\n\", \"()\\n\", \"())((\\n\", \"))()((\\n\", \"(())(\\n\", \")))(((\\n\", \"(()()(\\n\", \"()))((\\n\", \"()(()(\\n\", \"((()()))()()()(\\n\", \"()(((\\n\", \"(())))\\n\", \"()()()()))()(((\\n\", \"()()()())(()(((\\n\", \")())(\\n\", \"((()(())()()()(\\n\", \")(()(())()()()(\\n\", \"()()()())(()(()\\n\", \"(()))\\n\", \"((()))\\n\", \"((()(())()))()(\\n\", \"()(())\\n\", \"((()()))()()))(\\n\", \")((()(\\n\", \"(()(()\\n\", \"))()()())(()(()\\n\", \"((()()\\n\", \"()()))())(()(((\\n\", \"))(()(\\n\", \"()())(\\n\", \"((()()))((())))\\n\", \"()((()\\n\", \")(()(())()()())\\n\", \"()()))())((((((\\n\", \"((()()))((()))(\\n\", \"(((((())()))()(\\n\", \"((())())((()))(\\n\", \"()))((())())(((\\n\", \"()()))()((()(((\\n\", \"(()))())((()))(\\n\", \"((()((()()))))(\\n\", \"()))((())()))((\\n\", \"()))))()((()(((\\n\", \"()))((()(()))((\\n\", \"()))))()((())((\\n\", \"(()))(()((()))(\\n\", \"(()))(()((())))\\n\", \"))))((()(()))((\\n\", \")()((\\n\", \")(((()\\n\", \"((()()))()((()(\\n\", \"()((()())(()(((\\n\", \")(()(())()()))(\\n\", \"()()()())((((()\\n\", \"((()(())()))(((\\n\", \"()))()()))()(((\\n\", \"((\\n\", \"))\\n\", \"))((((\\n\", \"(())((\\n\", \"((()(\\n\", \"(((())\\n\", \"())(((\\n\", \"(()(((\\n\", \"((()((\\n\", \"()(()\\n\", \"())()(\\n\", \"()()((\\n\", \"(()))(\\n\", \"()((((\\n\", \"((())(\\n\", \"()()(\\n\", \"((((((\\n\", \")(()(\\n\", \")))((\\n\", \")(((((\\n\", \"(())()\\n\", \"((((()\\n\", \"((()((()()))()(\\n\", \"))))((\\n\", \"(()()\\n\", \")()()(\\n\", \")((((\\n\", \")())))\\n\", \"(((()(\\n\", \")()(((\\n\", \"(((()\\n\", \"())))\\n\", \"))(((\\n\"], \"outputs\": [\"1\\n2\\n1 3 \", \"1\\n4\\n1 2 5 6 \", \"0\", \"1\\n8\\n1 3 5 7 8 10 12 14 \", \"1\\n2\\n1 2 \", \"1\\n2\\n1 3\\n\", \"1\\n2\\n3 4\\n\", \"1\\n4\\n1 2 3 4\\n\", \"0\\n\", \"1\\n4\\n1 2 3 5\\n\", \"1\\n2\\n1 4\\n\", \"1\\n2\\n1 5\\n\", \"1\\n8\\n1 2 3 5 8 10 12 14\\n\", \"1\\n2\\n1 2\\n\", \"1\\n4\\n1 2 5 6\\n\", \"1\\n8\\n1 3 5 7 8 9 10 12\\n\", \"1\\n6\\n1 3 5 8 9 12\\n\", \"1\\n2\\n2 4\\n\", \"1\\n10\\n1 2 3 5 6 7 8 10 12 14\\n\", \"1\\n8\\n2 3 5 6 8 10 12 14\\n\", \"1\\n8\\n1 3 5 7 8 9 12 15\\n\", \"1\\n4\\n1 2 4 5\\n\", \"1\\n6\\n1 2 3 4 5 6\\n\", \"1\\n10\\n1 2 3 5 6 8 10 11 12 14\\n\", \"1\\n4\\n1 3 5 6\\n\", \"1\\n8\\n1 2 3 5 10 12 13 14\\n\", \"1\\n2\\n2 5\\n\", \"1\\n4\\n1 2 3 6\\n\", \"1\\n6\\n3 5 7 9 12 15\\n\", \"1\\n4\\n1 2 4 6\\n\", \"1\\n6\\n1 3 7 8 9 12\\n\", \"1\\n2\\n3 5\\n\", \"1\\n4\\n1 3 4 5\\n\", \"1\\n8\\n1 2 3 5 12 13 14 15\\n\", \"1\\n2\\n1 6\\n\", \"1\\n8\\n2 3 5 6 10 12 14 15\\n\", \"1\\n4\\n1 3 8 9\\n\", \"1\\n8\\n1 2 3 5 8 12 13 14\\n\", \"1\\n12\\n1 2 3 4 5 6 7 8 10 11 12 14\\n\", \"1\\n8\\n1 2 3 6 8 12 13 14\\n\", \"1\\n8\\n1 5 6 7 8 9 11 12\\n\", \"1\\n4\\n1 3 8 12\\n\", \"1\\n6\\n1 2 6 12 13 14\\n\", \"1\\n12\\n1 2 3 5 6 7 8 10 11 12 13 14\\n\", \"1\\n8\\n1 5 6 7 9 11 12 13\\n\", \"1\\n4\\n1 7 8 12\\n\", \"1\\n8\\n1 5 6 7 8 11 12 13\\n\", \"1\\n4\\n1 7 12 13\\n\", \"1\\n8\\n1 2 6 7 8 12 13 14\\n\", \"1\\n8\\n1 2 6 7 12 13 14 15\\n\", \"1\\n6\\n5 6 7 11 12 13\\n\", \"1\\n2\\n2 3\\n\", \"1\\n2\\n2 6\\n\", \"1\\n8\\n1 2 3 5 7 8 10 14\\n\", \"1\\n8\\n1 3 4 5 6 8 9 12\\n\", \"1\\n8\\n2 3 5 6 10 12 13 14\\n\", \"1\\n6\\n1 3 5 8 9 15\\n\", \"1\\n10\\n1 2 3 5 6 7 8 10 11 12\\n\", \"1\\n6\\n1 5 7 9 10 12\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n4\\n1 2 3 4\\n\", \"1\\n2\\n1 4\\n\", \"1\\n4\\n1 2 5 6\\n\", \"1\\n2\\n1 3\\n\", \"1\\n2\\n1 3\\n\", \"1\\n2\\n1 4\\n\", \"1\\n2\\n1 5\\n\", \"1\\n2\\n1 5\\n\", \"1\\n2\\n1 4\\n\", \"1\\n4\\n1 2 4 5\\n\", \"1\\n2\\n1 2\\n\", \"1\\n4\\n1 2 4 5\\n\", \"1\\n2\\n1 4\\n\", \"0\\n\", \"1\\n2\\n2 4\\n\", \"0\\n\", \"0\\n\", \"1\\n4\\n1 2 4 6\\n\", \"1\\n2\\n1 6\\n\", \"1\\n10\\n1 2 3 5 6 8 10 11 12 14\\n\", \"0\\n\", \"1\\n4\\n1 2 3 5\\n\", \"1\\n2\\n2 5\\n\", \"0\\n\", \"1\\n2\\n2 6\\n\", \"1\\n2\\n1 5\\n\", \"1\\n2\\n2 3\\n\", \"1\\n2\\n1 5\\n\", \"1\\n2\\n1 5\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Now that Kuroni has reached 10 years old, he is a big boy and doesn't like arrays of integers as presents anymore. This year he wants a Bracket sequence as a Birthday present. More specifically, he wants a bracket sequence so complex that no matter how hard he tries, he will not be able to remove a simple subsequence!
We say that a string formed by n characters '(' or ')' is simple if its length n is even and positive, its first n/2 characters are '(', and its last n/2 characters are ')'. For example, the strings () and (()) are simple, while the strings )( and ()() are not simple.
Kuroni will be given a string formed by characters '(' and ')' (the given string is not necessarily simple). An operation consists of choosing a subsequence of the characters of the string that forms a simple string and removing all the characters of this subsequence from the string. Note that this subsequence doesn't have to be continuous. For example, he can apply the operation to the string ')()(()))', to choose a subsequence of bold characters, as it forms a simple string '(())', delete these bold characters from the string and to get '))()'.
Kuroni has to perform the minimum possible number of operations on the string, in such a way that no more operations can be performed on the remaining string. The resulting string does not have to be empty.
Since the given string is too large, Kuroni is unable to figure out how to minimize the number of operations. Can you help him do it instead?
A sequence of characters a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters.
Input
The only line of input contains a string s (1 ≤ |s| ≤ 1000) formed by characters '(' and ')', where |s| is the length of s.
Output
In the first line, print an integer k — the minimum number of operations you have to apply. Then, print 2k lines describing the operations in the following format:
For each operation, print a line containing an integer m — the number of characters in the subsequence you will remove.
Then, print a line containing m integers 1 ≤ a_1 < a_2 < ... < a_m — the indices of the characters you will remove. All integers must be less than or equal to the length of the current string, and the corresponding subsequence must form a simple string.
If there are multiple valid sequences of operations with the smallest k, you may print any of them.
Examples
Input
(()((
Output
1
2
1 3
Input
)(
Output
0
Input
(()())
Output
1
4
1 2 5 6
Note
In the first sample, the string is '(()(('. The operation described corresponds to deleting the bolded subsequence. The resulting string is '(((', and no more operations can be performed on it. Another valid answer is choosing indices 2 and 3, which results in the same final string.
In the second sample, it is already impossible to perform any operations.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\n1 2\\n\", \"5\\n8 4 2 0 1\\n\", \"2\\n1 1\\n\", \"5\\n0 0 0 0 35\\n\", \"36\\n110 7 51 3 36 69 30 7 122 22 11 96 98 17 133 44 38 75 7 10 4 3 68 50 43 25 4 29 42 36 11 7 36 12 75 1\\n\", \"10\\n7758 19921 15137 1138 90104 17467 82544 55151 3999 6781\\n\", \"100\\n4364 698 1003 1128 1513 39 4339 969 7452 3415 1154 1635 6649 136 1442 50 834 1680 107 978 983 3176 4017 1692 1113 1504 1118 396 1975 2053 2366 3022 3007 167 610 4649 14659 2331 4565 318 7232 204 7131 6122 2885 5748 1998 3833 6799 4219 8454 8698 4964 1736 1554 1665 2425 4227 1967 534 2719 80 2865 652 1920 1577 658 1165 3222 1222 1238 560 12018 768 7144 2701 501 2520 9194 8052 13092 7366 2733 6050 2914 1740 5467 546 2947 186 1789 2658 2150 19 1854 1489 7590 990 296 1647\\n\", \"39\\n79 194 29 36 51 363 57 446 559 28 41 34 98 168 555 26 111 97 167 121 749 21 719 20 207 217 226 63 168 248 478 1231 399 518 291 14 741 149 97\\n\", \"2\\n300000 0\\n\", \"100\\n9 0 2 8 3 6 55 1 11 12 3 8 32 18 38 16 0 27 6 3 3 4 25 2 0 0 7 3 6 16 10 26 5 4 2 38 13 1 7 4 14 8 1 9 5 26 4 8 1 11 3 4 18 2 6 11 5 6 13 9 1 1 1 2 27 0 25 3 2 6 9 5 3 17 17 2 5 1 15 41 2 2 4 4 22 64 10 31 17 7 0 0 3 5 17 20 5 1 1 4\\n\", \"5\\n24348 15401 19543 206086 34622\\n\", \"2\\n0 1\\n\", \"2\\n184931 115069\\n\", \"36\\n110 7 51 3 36 69 30 7 122 22 11 96 98 17 133 44 38 75 7 10 4 3 68 50 43 26 4 29 42 36 11 7 36 12 75 1\\n\", \"10\\n7758 19921 15137 1138 90104 17467 82544 55151 3999 6249\\n\", \"39\\n79 194 29 36 51 363 57 446 559 28 41 34 98 168 555 26 110 97 167 121 749 21 719 20 207 217 226 63 168 248 478 1231 399 518 291 14 741 149 97\\n\", \"100\\n9 0 2 8 3 6 55 1 11 12 3 8 32 18 38 16 0 27 6 3 3 4 25 2 0 0 7 3 6 16 10 26 5 4 2 38 13 1 7 1 14 8 1 9 5 26 4 8 1 11 3 4 18 2 6 11 5 6 13 9 1 1 1 2 27 0 25 3 2 6 9 5 3 17 17 2 5 1 15 41 2 2 4 4 22 64 10 31 17 7 0 0 3 5 17 20 5 1 1 4\\n\", \"2\\n2 1\\n\", \"2\\n1 0\\n\", \"5\\n8 4 4 0 1\\n\", \"5\\n0 0 1 0 35\\n\", \"36\\n110 7 51 3 36 69 30 7 122 22 11 96 98 17 133 44 38 75 7 10 4 3 68 50 43 26 4 29 42 36 11 7 36 19 75 1\\n\", \"10\\n7758 15465 15137 1138 90104 17467 82544 55151 3999 6249\\n\", \"39\\n79 194 29 36 51 363 57 446 559 28 41 34 98 4 555 26 110 97 167 121 749 21 719 20 207 217 226 63 168 248 478 1231 399 518 291 14 741 149 97\\n\", \"100\\n9 0 2 8 3 6 55 1 11 12 3 8 32 18 38 16 0 27 6 3 3 4 25 2 0 0 7 3 6 16 10 26 5 4 2 38 13 1 7 1 14 8 1 9 5 26 4 8 1 11 3 4 18 2 6 11 5 6 13 9 1 1 1 2 27 0 25 3 2 6 9 5 3 17 17 2 5 1 15 41 2 2 4 4 22 64 10 31 17 7 0 0 3 5 17 20 5 1 2 4\\n\", \"2\\n2 2\\n\", \"5\\n8 4 3 0 1\\n\", \"5\\n0 0 1 0 22\\n\", \"36\\n110 7 51 3 36 69 30 7 122 36 11 96 98 17 133 44 38 75 7 10 4 3 68 50 43 26 4 29 42 36 11 7 36 19 75 1\\n\", \"10\\n7758 15465 15137 1138 90104 17467 7218 55151 3999 6249\\n\", \"39\\n79 194 29 36 51 363 57 446 559 28 40 34 98 4 555 26 110 97 167 121 749 21 719 20 207 217 226 63 168 248 478 1231 399 518 291 14 741 149 97\\n\", \"100\\n9 0 2 8 3 6 55 1 11 12 3 8 32 18 38 16 0 27 6 3 3 4 25 2 0 0 7 3 6 16 10 26 5 4 2 38 13 1 7 1 14 8 1 9 5 26 4 8 1 11 3 4 18 2 3 11 5 6 13 9 1 1 1 2 27 0 25 3 2 6 9 5 3 17 17 2 5 1 15 41 2 2 4 4 22 64 10 31 17 7 0 0 3 5 17 20 5 1 2 4\\n\", \"2\\n2 3\\n\", \"2\\n4 1\\n\", \"5\\n8 4 3 1 1\\n\", \"36\\n110 7 51 3 36 69 30 7 122 36 11 96 98 17 76 44 38 75 7 10 4 3 68 50 43 26 4 29 42 36 11 7 36 19 75 1\\n\", \"10\\n7758 15465 2476 1138 90104 17467 7218 55151 3999 6249\\n\", \"39\\n79 194 29 40 51 363 57 446 559 28 40 34 98 4 555 26 110 97 167 121 749 21 719 20 207 217 226 63 168 248 478 1231 399 518 291 14 741 149 97\\n\", \"100\\n9 0 2 8 3 6 55 1 11 12 3 8 4 18 38 16 0 27 6 3 3 4 25 2 0 0 7 3 6 16 10 26 5 4 2 38 13 1 7 1 14 8 1 9 5 26 4 8 1 11 3 4 18 2 3 11 5 6 13 9 1 1 1 2 27 0 25 3 2 6 9 5 3 17 17 2 5 1 15 41 2 2 4 4 22 64 10 31 17 7 0 0 3 5 17 20 5 1 2 4\\n\", \"2\\n4 3\\n\", \"2\\n4 2\\n\", \"5\\n8 4 0 1 1\\n\", \"36\\n110 7 51 3 36 69 30 7 122 36 11 96 98 17 76 44 38 75 7 10 4 3 68 50 43 26 4 29 42 36 11 7 36 19 75 0\\n\", \"10\\n7758 15465 2476 1138 90104 17467 7218 72818 3999 6249\\n\", \"39\\n79 194 29 40 51 363 57 446 559 28 40 34 98 4 555 26 110 97 167 121 749 21 719 20 207 184 226 63 168 248 478 1231 399 518 291 14 741 149 97\\n\", \"100\\n9 0 2 8 3 6 55 1 11 12 3 8 4 18 38 16 0 27 6 3 3 4 25 2 0 0 7 3 6 16 10 26 5 4 2 38 13 1 7 0 14 8 1 9 5 26 4 8 1 11 3 4 18 2 3 11 5 6 13 9 1 1 1 2 27 0 25 3 2 6 9 5 3 17 17 2 5 1 15 41 2 2 4 4 22 64 10 31 17 7 0 0 3 5 17 20 5 1 2 4\\n\", \"2\\n8 2\\n\", \"5\\n8 4 0 2 1\\n\", \"36\\n110 7 51 3 36 69 30 7 122 36 11 96 98 17 76 44 38 75 7 10 4 3 68 50 43 26 4 29 42 45 11 7 36 19 75 0\\n\", \"10\\n7758 15465 2476 1138 90104 17467 7218 72818 3999 6274\\n\", \"39\\n79 194 28 40 51 363 57 446 559 28 40 34 98 4 555 26 110 97 167 121 749 21 719 20 207 184 226 63 168 248 478 1231 399 518 291 14 741 149 97\\n\", \"100\\n9 0 2 8 3 6 55 1 11 12 3 8 4 18 38 16 0 27 6 3 3 4 25 2 0 0 7 3 6 16 10 26 5 4 2 38 13 1 7 0 14 8 1 9 5 26 4 8 1 11 3 4 18 2 3 11 5 6 13 9 1 1 1 2 27 0 25 3 2 6 9 5 3 17 17 0 5 1 15 41 2 2 4 4 22 64 10 31 17 7 0 0 3 5 17 20 5 1 2 4\\n\", \"2\\n1 3\\n\", \"2\\n8 4\\n\", \"5\\n8 1 0 2 1\\n\", \"36\\n010 7 51 3 36 69 30 7 122 36 11 96 98 17 76 44 38 75 7 10 4 3 68 50 43 26 4 29 42 45 11 7 36 19 75 0\\n\", \"10\\n7758 15465 2476 1138 90104 17467 7218 94259 3999 6274\\n\", \"39\\n79 194 28 40 51 363 57 446 559 28 40 34 98 4 503 26 110 97 167 121 749 21 719 20 207 184 226 63 168 248 478 1231 399 518 291 14 741 149 97\\n\", \"100\\n9 0 2 8 3 6 55 1 11 12 3 8 4 18 38 16 0 27 6 3 3 4 25 2 0 0 7 3 6 16 10 26 5 4 2 38 13 1 7 0 14 8 1 9 5 26 4 8 1 11 3 4 18 2 3 11 5 6 13 9 1 1 1 2 27 0 25 3 2 6 9 5 3 16 17 0 5 1 15 41 2 2 4 4 22 64 10 31 17 7 0 0 3 5 17 20 5 1 2 4\\n\", \"2\\n4 4\\n\", \"36\\n010 7 51 3 36 69 30 7 122 36 11 96 98 17 76 44 38 75 7 10 4 3 68 50 43 26 4 29 42 77 11 7 36 19 75 0\\n\", \"39\\n79 194 28 40 51 363 57 446 559 28 40 34 98 4 503 26 111 97 167 121 749 21 719 20 207 184 226 63 168 248 478 1231 399 518 291 14 741 149 97\\n\", \"2\\n2 0\\n\", \"2\\n3 0\\n\", \"2\\n0 3\\n\"], \"outputs\": [\"3\\n\", \"801604029\\n\", \"1\\n\", \"0\\n\", \"420723999\\n\", \"663099907\\n\", \"301328767\\n\", \"918301015\\n\", \"0\\n\", \"241327503\\n\", \"788526601\\n\", \"0\\n\", \"244559876\\n\", \"436384350\\n\", \"217539815\\n\", \"782251506\\n\", \"303418924\\n\", \"3\\n\", \"0\\n\", \"887976517\\n\", \"545314799\\n\", \"101294486\\n\", \"700652635\\n\", \"944249001\\n\", \"754583581\\n\", \"8\\n\", \"31419769\\n\", \"939686190\\n\", \"974453244\\n\", \"84581656\\n\", \"316198985\\n\", \"230206020\\n\", \"499122194\\n\", \"15\\n\", \"460157510\\n\", \"35715792\\n\", \"698445289\\n\", \"276950653\\n\", \"799009427\\n\", \"665496310\\n\", \"36\\n\", \"934200297\\n\", \"365388672\\n\", \"179205393\\n\", \"585732294\\n\", \"275802614\\n\", \"665496802\\n\", \"801604029\\n\", \"341583446\\n\", \"120227225\\n\", \"143220396\\n\", \"277829212\\n\", \"7\\n\", \"199651149\\n\", \"291996592\\n\", \"399795430\\n\", \"133103953\\n\", \"127706559\\n\", \"126425588\\n\", \"332748267\\n\", \"642561515\\n\", \"394186241\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Slime and his n friends are at a party. Slime has designed a game for his friends to play.
At the beginning of the game, the i-th player has a_i biscuits. At each second, Slime will choose a biscuit randomly uniformly among all a_1 + a_2 + … + a_n biscuits, and the owner of this biscuit will give it to a random uniform player among n-1 players except himself. The game stops when one person will have all the biscuits.
As the host of the party, Slime wants to know the expected value of the time that the game will last, to hold the next activity on time.
For convenience, as the answer can be represented as a rational number p/q for coprime p and q, you need to find the value of (p ⋅ q^{-1})mod 998 244 353. You can prove that qmod 998 244 353 ≠ 0.
Input
The first line contains one integer n\ (2≤ n≤ 100 000): the number of people playing the game.
The second line contains n non-negative integers a_1,a_2,...,a_n\ (1≤ a_1+a_2+...+a_n≤ 300 000), where a_i represents the number of biscuits the i-th person own at the beginning.
Output
Print one integer: the expected value of the time that the game will last, modulo 998 244 353.
Examples
Input
2
1 1
Output
1
Input
2
1 2
Output
3
Input
5
0 0 0 0 35
Output
0
Input
5
8 4 2 0 1
Output
801604029
Note
For the first example, in the first second, the probability that player 1 will give the player 2 a biscuit is 1/2, and the probability that player 2 will give the player 1 a biscuit is 1/2. But anyway, the game will stop after exactly 1 second because only one player will occupy all biscuits after 1 second, so the answer is 1.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 5 4 3 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n3\\n5 3 4\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 5 4 3 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n3\\n10 1 5\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 7 4 3 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n3\\n10 1 8\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 7 8 3 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n3\\n5 3 8\\n\", \"6\\n5\\n5 3 7 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 9 8 3 2\\n3\\n0 1 2\\n5\\n5 4 3 5 5\\n\", \"6\\n5\\n6 3 4 4 4\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 5 4 6 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 5 4\\n5\\n5 9 8 3 2\\n3\\n1 1 2\\n2\\n5 4 3 5 5\\n\", \"6\\n5\\n5 3 4 4 9\\n3\\n1 1 1\\n5\\n4 4 3 5 4\\n5\\n5 9 8 3 2\\n3\\n1 1 2\\n2\\n5 4 3 5 5\\n\", \"6\\n5\\n6 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 5 4 3 2\\n3\\n1 1 1\\n5\\n5 4 3 5 5\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 0 4 4\\n5\\n9 7 4 3 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"6\\n5\\n6 3 4 4 4\\n3\\n0 1 1\\n5\\n4 4 3 4 4\\n5\\n5 5 4 3 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"6\\n5\\n5 3 7 4 5\\n3\\n1 1 1\\n5\\n4 4 3 8 4\\n5\\n5 9 8 3 2\\n3\\n0 1 2\\n5\\n5 4 3 5 5\\n\", \"6\\n5\\n6 3 5 4 4\\n3\\n1 0 1\\n5\\n4 4 3 4 4\\n5\\n5 5 4 6 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"6\\n5\\n6 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 5 4 3 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n3\\n20 1 8\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 9 8 3 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n3\\n20 1 3\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 9 8 3 2\\n3\\n0 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n3\\n20 0 3\\n\", \"1\\n3\\n17 1 5\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 0 4 4\\n5\\n5 7 4 3 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"6\\n5\\n6 3 4 4 4\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 5 4 3 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n3\\n20 1 14\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 9 8 3 2\\n3\\n1 1 2\\n2\\n5 4 3 5 5\\n\", \"1\\n3\\n20 1 2\\n\", \"1\\n3\\n20 -1 3\\n\", \"1\\n3\\n9 3 8\\n\", \"1\\n3\\n17 1 2\\n\", \"1\\n3\\n29 1 14\\n\", \"6\\n5\\n5 3 7 4 5\\n3\\n1 1 1\\n5\\n3 4 3 4 4\\n5\\n5 9 8 3 2\\n3\\n0 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n2\\n20 -1 3\\n\", \"1\\n3\\n16 3 8\\n\", \"6\\n5\\n6 3 5 4 4\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 5 4 6 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n3\\n29 1 12\\n\", \"1\\n2\\n20 -1 5\\n\", \"1\\n3\\n16 3 0\\n\", \"6\\n5\\n6 2 5 4 4\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 5 4 6 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n3\\n24 1 12\\n\", \"1\\n2\\n40 -1 5\\n\", \"1\\n3\\n18 3 0\\n\", \"1\\n3\\n24 2 12\\n\", \"1\\n2\\n40 -2 5\\n\", \"1\\n3\\n46 2 12\\n\", \"1\\n2\\n40 -1 9\\n\", \"1\\n3\\n46 2 19\\n\", \"1\\n2\\n40 0 9\\n\", \"1\\n3\\n46 2 5\\n\", \"1\\n2\\n40 0 16\\n\", \"1\\n3\\n46 0 5\\n\", \"1\\n2\\n17 0 16\\n\", \"1\\n3\\n39 0 5\\n\", \"1\\n2\\n17 0 15\\n\", \"1\\n3\\n39 1 5\\n\", \"1\\n3\\n39 1 4\\n\", \"1\\n3\\n39 1 0\\n\", \"1\\n3\\n39 1 -1\\n\", \"1\\n3\\n34 1 -1\\n\", \"1\\n3\\n4 3 4\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 5 6 3 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 7 8 3 2\\n3\\n1 1 2\\n5\\n5 2 3 5 5\\n\", \"6\\n5\\n5 3 6 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 9 8 3 2\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n3\\n1 1 2\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n3 4 3 4 4\\n5\\n5 9 8 3 2\\n3\\n0 1 2\\n5\\n5 4 3 5 5\\n\", \"1\\n3\\n20 0 1\\n\", \"1\\n3\\n0 3 8\\n\", \"1\\n3\\n17 2 5\\n\", \"1\\n3\\n20 0 14\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 5 4\\n5\\n5 9 8 3 2\\n3\\n1 1 2\\n2\\n5 1 3 5 5\\n\", \"1\\n3\\n20 1 0\\n\", \"6\\n5\\n5 3 7 4 5\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 9 8 3 2\\n3\\n0 1 2\\n5\\n5 4 0 5 5\\n\", \"1\\n3\\n20 -1 5\\n\", \"1\\n3\\n17 0 2\\n\", \"6\\n5\\n6 3 4 4 4\\n3\\n1 1 1\\n5\\n4 4 3 4 4\\n5\\n5 5 4 6 0\\n3\\n1 1 2\\n5\\n5 4 3 5 5\\n\", \"6\\n5\\n5 3 4 4 5\\n3\\n1 1 1\\n5\\n4 4 3 5 4\\n5\\n5 9 8 3 2\\n3\\n1 1 2\\n2\\n9 4 3 5 5\\n\", \"1\\n2\\n20 0 3\\n\", \"1\\n3\\n16 3 5\\n\", \"1\\n3\\n42 1 12\\n\", \"6\\n5\\n5 3 4 1 9\\n3\\n1 1 1\\n5\\n4 4 3 5 4\\n5\\n5 9 8 3 2\\n3\\n1 1 2\\n2\\n5 4 3 5 5\\n\", \"1\\n2\\n20 -1 10\\n\", \"1\\n3\\n16 2 0\\n\", \"1\\n3\\n24 0 12\\n\", \"1\\n2\\n73 -1 5\\n\", \"1\\n3\\n18 1 0\\n\", \"1\\n3\\n19 0 12\\n\", \"1\\n2\\n40 -3 5\\n\", \"1\\n2\\n40 -1 18\\n\", \"1\\n3\\n51 2 19\\n\", \"1\\n3\\n86 2 5\\n\", \"1\\n2\\n40 -1 16\\n\", \"1\\n3\\n87 0 5\\n\", \"1\\n3\\n5 0 5\\n\", \"1\\n3\\n39 1 3\\n\"], \"outputs\": [\"1\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n\", \"1\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n\", \"1\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n\", \"1\\n-1\\n2\\n3\\n3\\n1\\n\", \"3\\n\", \"3\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n-1\\n2\\n4\\n3\\n1\\n\", \"1\\n-1\\n4\\n2\\n3\\n1\\n\", \"5\\n-1\\n4\\n2\\n3\\n1\\n\", \"1\\n-1\\n2\\n2\\n-1\\n1\\n\", \"1\\n-1\\n2\\n1\\n3\\n1\\n\", \"1\\n2\\n2\\n2\\n3\\n1\\n\", \"3\\n-1\\n4\\n2\\n3\\n1\\n\", \"1\\n1\\n2\\n4\\n3\\n1\\n\", \"1\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n\", \"1\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n\", \"1\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n\", \"1\\n\", \"1\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n\", \"1\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n\", \"1\\n\", \"1\\n-1\\n2\\n4\\n3\\n1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n-1\\n2\\n4\\n3\\n1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n-1\\n2\\n3\\n3\\n1\\n\", \"1\\n-1\\n2\\n3\\n3\\n1\\n\", \"3\\n-1\\n2\\n2\\n3\\n1\\n\", \"3\\n\", \"1\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"1\\n-1\\n4\\n2\\n3\\n1\\n\", \"1\\n\", \"3\\n-1\\n2\\n2\\n3\\n1\\n\", \"1\\n\", \"1\\n\", \"1\\n-1\\n2\\n4\\n3\\n1\\n\", \"1\\n-1\\n4\\n2\\n3\\n1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"5\\n-1\\n4\\n2\\n3\\n1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\"]}", "source": "primeintellect"}
|
There are n piranhas with sizes a_1, a_2, …, a_n in the aquarium. Piranhas are numbered from left to right in order they live in the aquarium.
Scientists of the Berland State University want to find if there is dominant piranha in the aquarium. The piranha is called dominant if it can eat all the other piranhas in the aquarium (except itself, of course). Other piranhas will do nothing while the dominant piranha will eat them.
Because the aquarium is pretty narrow and long, the piranha can eat only one of the adjacent piranhas during one move. Piranha can do as many moves as it needs (or as it can). More precisely:
* The piranha i can eat the piranha i-1 if the piranha i-1 exists and a_{i - 1} < a_i.
* The piranha i can eat the piranha i+1 if the piranha i+1 exists and a_{i + 1} < a_i.
When the piranha i eats some piranha, its size increases by one (a_i becomes a_i + 1).
Your task is to find any dominant piranha in the aquarium or determine if there are no such piranhas.
Note that you have to find any (exactly one) dominant piranha, you don't have to find all of them.
For example, if a = [5, 3, 4, 4, 5], then the third piranha can be dominant. Consider the sequence of its moves:
* The piranha eats the second piranha and a becomes [5, \underline{5}, 4, 5] (the underlined piranha is our candidate).
* The piranha eats the third piranha and a becomes [5, \underline{6}, 5].
* The piranha eats the first piranha and a becomes [\underline{7}, 5].
* The piranha eats the second piranha and a becomes [\underline{8}].
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.
The first line of the test case contains one integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of piranhas in the aquarium. The second line of the test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9), where a_i is the size of the i-th piranha.
It is guaranteed that the sum of n does not exceed 3 ⋅ 10^5 (∑ n ≤ 3 ⋅ 10^5).
Output
For each test case, print the answer: -1 if there are no dominant piranhas in the aquarium or index of any dominant piranha otherwise. If there are several answers, you can print any.
Example
Input
6
5
5 3 4 4 5
3
1 1 1
5
4 4 3 4 4
5
5 5 4 3 2
3
1 1 2
5
5 4 3 5 5
Output
3
-1
4
3
3
1
Note
The first test case of the example is described in the problem statement.
In the second test case of the example, there are no dominant piranhas in the aquarium.
In the third test case of the example, the fourth piranha can firstly eat the piranha to the left and the aquarium becomes [4, 4, 5, 4], then it can eat any other piranha in the aquarium.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
As a teacher, Riko Hakozaki often needs to help her students with problems from various subjects. Today, she is asked a programming task which goes as follows.
You are given an undirected complete graph with n nodes, where some edges are pre-assigned with a positive weight while the rest aren't. You need to assign all unassigned edges with non-negative weights so that in the resulting fully-assigned complete graph the [XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) sum of all weights would be equal to 0.
Define the ugliness of a fully-assigned complete graph the weight of its [minimum spanning tree](https://en.wikipedia.org/wiki/Minimum_spanning_tree), where the weight of a spanning tree equals the sum of weights of its edges. You need to assign the weights so that the ugliness of the resulting graph is as small as possible.
As a reminder, an undirected complete graph with n nodes contains all edges (u, v) with 1 ≤ u < v ≤ n; such a graph has (n(n-1))/(2) edges.
She is not sure how to solve this problem, so she asks you to solve it for her.
Input
The first line contains two integers n and m (2 ≤ n ≤ 2 ⋅ 10^5, 0 ≤ m ≤ min(2 ⋅ 10^5, (n(n-1))/(2) - 1)) — the number of nodes and the number of pre-assigned edges. The inputs are given so that there is at least one unassigned edge.
The i-th of the following m lines contains three integers u_i, v_i, and w_i (1 ≤ u_i, v_i ≤ n, u ≠ v, 1 ≤ w_i < 2^{30}), representing the edge from u_i to v_i has been pre-assigned with the weight w_i. No edge appears in the input more than once.
Output
Print on one line one integer — the minimum ugliness among all weight assignments with XOR sum equal to 0.
Examples
Input
4 4
2 1 14
1 4 14
3 2 15
4 3 8
Output
15
Input
6 6
3 6 4
2 4 1
4 5 7
3 4 10
3 5 1
5 2 15
Output
0
Input
5 6
2 3 11
5 3 7
1 4 10
2 4 14
4 3 8
2 5 6
Output
6
Note
The following image showcases the first test case. The black weights are pre-assigned from the statement, the red weights are assigned by us, and the minimum spanning tree is denoted by the blue edges.
<image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
This is an interactive problem.
Little Dormi was faced with an awkward problem at the carnival: he has to guess the edges of an unweighted tree of n nodes! The nodes of the tree are numbered from 1 to n.
The game master only allows him to ask one type of question:
* Little Dormi picks a node r (1 ≤ r ≤ n), and the game master will reply with an array d_1, d_2, …, d_n, where d_i is the length of the shortest path from node r to i, for all 1 ≤ i ≤ n.
Additionally, to make the game unfair challenge Little Dormi the game master will allow at most ⌈n/2⌉ questions, where ⌈ x ⌉ denotes the smallest integer greater than or equal to x.
Faced with the stomach-churning possibility of not being able to guess the tree, Little Dormi needs your help to devise a winning strategy!
Note that the game master creates the tree before the game starts, and does not change it during the game.
Input
The first line of input contains the integer n (2 ≤ n ≤ 2 000), the number of nodes in the tree.
You will then begin interaction.
Output
When your program has found the tree, first output a line consisting of a single "!" followed by n-1 lines each with two space separated integers a and b, denoting an edge connecting nodes a and b (1 ≤ a, b ≤ n). Once you are done, terminate your program normally immediately after flushing the output stream.
You may output the edges in any order and an edge (a,b) is considered the same as an edge (b,a). Answering is not considered as a query.
Interaction
After taking input, you may make at most ⌈n/2⌉ queries. Each query is made in the format "? r", where r is an integer 1 ≤ r ≤ n that denotes the node you want to pick for that query.
You will then receive n space separated integers d_1, d_2, …, d_n, where d_i is the length of the shortest path from node r to i, followed by a newline.
After printing a query do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:
* fflush(stdout) or cout.flush() in C++;
* System.out.flush() in Java;
* flush(output) in Pascal;
* stdout.flush() in Python;
* see documentation for other languages.
If at any point you make an invalid query or try to make more than ⌈ n/2 ⌉ queries, the interaction will terminate immediately and you will receive a Wrong Answer verdict.
Hacks
To hack a solution, use the following format.
The first line contains the integer n (2 ≤ n ≤ 2 000).
The next n−1 lines contain two integers u and v (1 ≤ u,v ≤ n) denoting an edge between u and v (u ≠ v). These n-1 edges must form a tree.
Examples
Input
4
0 1 2 2
1 0 1 1
Output
? 1
? 2
!
4 2
1 2
2 3
Input
5
2 2 1 1 0
Output
? 5
!
4 5
3 5
2 4
1 3
Note
Here is the tree from the first example.
<image>
Notice that the edges can be output in any order.
Additionally, here are the answers for querying every single node in example 1:
* 1: [0,1,2,2]
* 2: [1,0,1,1]
* 3: [2,1,0,2]
* 4: [2,1,2,0]
Below is the tree from the second example interaction.
<image>
Lastly, here are the answers for querying every single node in example 2:
* 1: [0,4,1,3,2]
* 2: [4,0,3,1,2]
* 3: [1,3,0,2,1]
* 4: [3,1,2,0,1]
* 5: [2,2,1,1,0]
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"10 2\\nXXBXXWXXXX\\n\", \"3 2\\nXXX\\n\", \"4 2\\nXXXX\\n\", \"4 2\\nXXBW\\n\", \"2 1\\nWB\\n\", \"128 100\\nXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\\n\", \"25 7\\nXWBXWBXWXWBWXBWWXBWXXXXBB\\n\", \"1 1\\nX\\n\", \"2 1\\nXW\\n\", \"20 6\\nXXBXBXXBWWWWXWWXBBBW\\n\", \"100 3\\nXXXXXWXXXXBXXWXXBXXBXXXXXXXXXXXXXXXXWWXXWXXWXXXXWWXXXXXWXXXXBWXXXXWXBXXXWXXXBWXXWXXXWXXXXWWWXXXXXWXX\\n\", \"100 21\\nXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\\n\", \"3 1\\nWBX\\n\", \"100 20\\nWWXWWXXXXBBXWBXXXXWXXWXXXXXXXBBXXXXXXXWWXXWXXXXBWBXXXXXXXXXXWXWXXXXWXXXWXXWXXXXBXBXXBXXXXXWBXWBXXXXB\\n\", \"20 5\\nXBBXXXXXXXBWWXBWBWWX\\n\", \"3 2\\nXWW\\n\", \"20 7\\nBWXBXBWWXXBBXBBWXWBW\\n\", \"300 200\\nWXWWWWXWWBXXXBWWXXXWBWWXXWXXXXWWXXXWXXXXWWWXWBWXWWXWXBWXWWWWBWBBWWWWXWXXXXWWXBXWXWWWWWXXXXXWBXWBXWWWWXXXWXBWXBWXWXXXWXWXXWWXXWXWWWWWXWXWWXWWXXWXWXWWXWXXXXWWWXWWWXXWWWBXXWXWWWXWBWXWWXWWXXXWWXXXWXWXXBWXXXBBWWWXXXXWWXWWXWXWWWWWWWXXWXXWWWWBWWWBWWWWXBXWWWWXXXXWXXXXWBXBXWWWXBWXWXXXWXXXXWWXXWXWWXWBXWXBXWWW\\n\", \"100 20\\nWXWXWWBWBBXXXWWBBXXWBWWWWXXBWXXBXXBXXBXXWXXXXWBBWWWBXWWBXWXWWBXXWXWXWWXXWWWXXXBXBWXWXBXXXWXXWWXWWBWW\\n\", \"17 3\\nBBBWXXWBXBXWXBXBW\\n\", \"2 1\\nBW\\n\", \"256 100\\nXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\\n\", \"2 2\\nXX\\n\", \"100 25\\nBXWWXWBWWWWWBXBBWXWWXBBWBWWWWWWWXWXWXXXWWWXXXXBXBBXWXWWXBBXWBXWXWXXXXXWBBXWXXWXWWWBXXWBXWWXBWWBXBXXB\\n\", \"3 1\\nWWW\\n\", \"10 3\\nXBXBXWXBXW\\n\", \"101 18\\nWXXBXXWXXXXXXXXXXXXBBXXBBXXWXBXXBXXXXXXXXBXXXXWBBBXWXXWXWXWXWXWXBXBXXXXXWBXXWXBXXXXXXWXBBXXXXWWXXBWBW\\n\", \"4 2\\nXBXW\\n\", \"4 1\\nXXXX\\n\", \"100 1\\nWBWWWXWWWXWBWXWXWXXWWBWBXWWBBWWWXXWBWWBWWXWWXBBBWBWWWWXBWWWWWXXWWWWBBBWBBBWWWXWWXWBWWBWWWBWWWBWXXWXX\\n\", \"100 1\\nXWXWXWWXXWWXWXXWWXXBXBXWWXXXXWBWWXWXWWXBXWXBWXWWWBWXXWXBBXWXWXWWBXXWBBBWWWXXXWBWXWXWBWBWBWXXWXBXXWWX\\n\", \"10 1\\nXXXWXBXBXX\\n\", \"20 4\\nWWWWXWBXBBXWWXWXBWWW\\n\", \"300 7\\nXXWXWWXXWWWBBXXXWWBWBWXWWWXXWBXXBXWWXXXWXWXBXWBWWWXBBWBXBXWXWBBBBXWBXWBBBXBXXXXBWXXXWBBXWXXBBWBBXBBXWXBXWBWXBWXXXXWXBWBBWXWXWXWWBWWWXXWWBBBXBXBWXBXXWWWBWWWBXWWXXWXWBWWWBWWWXXBBWXWXWXXWXXXXBWBXXBXBBBXBBWWXWBBXXWBBXBBXXBWXXWBWWBXWXXWWXXBXBWBWXWBBBWXXWXXWBWBBXWWBBWXXXBBWWXXXXBBBBBBWWBBWBWBXXWWXXBWXWWBB\\n\", \"3 1\\nXBW\\n\", \"4 1\\nXXXW\\n\", \"100 20\\nWBBXWBBWWWXBXWWWWWBBBWWBWWBWWWWXWXXBWWBWXWBBXWBWBXWXWXWWBWWWBBXWWBXBBBWBXXWWBXXWWXWXWXBBBWXXWWBWBWXW\\n\", \"4 1\\nXXWW\\n\", \"20 1\\nXBBBWBXXBWXWWWBWWXXW\\n\", \"2 1\\nWX\\n\", \"3 1\\nXBX\\n\", \"20 2\\nXXXBXWBBBBWXWWWXWWXB\\n\", \"20 3\\nBWWWWWXBWXXXXBBWBBWX\\n\", \"10 3\\nBXBWBWWWWX\\n\", \"10 3\\nWWXBWXXWWW\\n\", \"1 2\\nX\\n\", \"100 15\\nXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\\n\", \"20 1\\nXBBXXXXXXXBWWXBWBWWX\\n\", \"256 101\\nXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\\n\", \"100 2\\nXWXWXWWXXWWXWXXWWXXBXBXWWXXXXWBWWXWXWWXBXWXBWXWWWBWXXWXBBXWXWXWWBXXWBBBWWWXXXWBWXWXWBWBWBWXXWXBXXWWX\\n\", \"10 2\\nXXXWXBXBXX\\n\", \"300 5\\nXXWXWWXXWWWBBXXXWWBWBWXWWWXXWBXXBXWWXXXWXWXBXWBWWWXBBWBXBXWXWBBBBXWBXWBBBXBXXXXBWXXXWBBXWXXBBWBBXBBXWXBXWBWXBWXXXXWXBWBBWXWXWXWWBWWWXXWWBBBXBXBWXBXXWWWBWWWBXWWXXWXWBWWWBWWWXXBBWXWXWXXWXXXXBWBXXBXBBBXBBWWXWBBXXWBBXBBXXBWXXWBWWBXWXXWWXXBXBWBWXWBBBWXXWXXWBWBBXWWBBWXXXBBWWXXXXBBBBBBWWBBWBWBXXWWXXBWXWWBB\\n\", \"4 2\\nXXXW\\n\", \"20 1\\nBWWWWWXBWXXXXBBWBBWX\\n\", \"10 2\\nXXBXBXWXXX\\n\", \"300 4\\nXXWXWWXXWWWBBXXXWWBWBWXWWWXXWBXXBXWWXXXWXWXBXWBWWWXBBWBXBXWXWBBBBXWBXWBBBXBXXXXBWXXXWBBXWXXBBWBBXBBXWXBXWBWXBWXXXXWXBWBBWXWXWXWWBWWWXXWWBBBXBXBWXBXXWWWBWWWBXWWXXWXWBWWWBWWWXXBBWXWXWXXWXXXXBWBXXBXBBBXBBWWXWBBXXWBBXBBXXBWXXWBWWBXWXXWWXXBXBWBWXWBBBWXXWXXWBWBBXWWBBWXXXBBWWXXXXBBBBBBWWBBWBWBXXWWXXBWXWWBB\\n\", \"4 1\\nWXWX\\n\", \"300 4\\nXXWXWWXXWWWBBXXXWXBWBWXWWWXXWBXXBXWWXXXWXWXBXWBWWWXBBWBXBXWXWBBBBXWBXWBBBXBXXXXBWXXXWBBXWXXBBWBBXBBXWXBXWBWXBWXXXXWXBWBBWXWWWXWWBWWWXXWWBBBXBXBWXBXXWWWBWWWBXWWXXWXWBWWWBWWWXXBBWXWXWXXWXXXXBWBXXBXBBBXBBWWXWBBXXWBBXBBXXBWXXWBWWBXWXXWWXXBXBWBWXWBBBWXXWXXWBWBBXWWBBWXXXBBWWXXXXBBBBBBWWBBWBWBXXWWXXBWXWWBB\\n\", \"300 4\\nBBWWXWBXXWWXXBWBWBBWWBBBBBBXXXXWWBBXXXWBBWWXBBWBWXXWXXWBBBWXWBWBXBXXWWXXWXBWWBWXXWBXXBBXBBWXXBBWXWWBBXBBBXBXXBWBXXXXWXXWXWXWBBXXWWWBWWWBWXWXXWWXBWWWBWWWXXBXWBXBXBBBWWXXWWWBWWXWWWXWBBWBXWXXXXWBXWBWXBXWXBBXBBWBBXXWXBBWXXXWBXXXXBXBBBWXBWXBBBBWXWXBXBWBBXWWWBWXBXWXWXXXWWXBXXBWXXWWWXWBWBXWXXXBBWWWXXWWXWXX\\n\", \"100 21\\nXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXWXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX\\n\", \"256 100\\nXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXWXXXXXXXXXXX\\n\", \"100 1\\nBXWWXWBWWWWWBXBBWXWWXBBWBWWWWWWWXWXWXXXWWWXXXXBXBBXWXWWXBBXWBXWXWXXXXXWBBXWXXWXWWWBXXWBXWWXBWWBXBXXB\\n\", \"20 7\\nWBWXWBBXBBXXWWBXBXWB\\n\", \"300 200\\nWXWWWWXWWBXXXBWWXXXWBWWXXWXXXXWWXXXWXXXXWWWXWBWXWWBWXBWXWWWWBWBBWWWWXWXXXXWWXBXWXWWWWWXXXXXWBXWBXWWWWXXXWXBWXBWXWXXXWXWXXWWXXWXWWWWWXWXWWXWWXXWXWXWWXWXXXXWWWXWWWXXWWWBXXWXWWWXWBWXWWXWWXXXWWXXXWXWXXBWXXXBBWWWXXXXWWXWWXWXWWWWWWWXXWXXWWWWBWWWBWWWWXBXWWWWXXXXWXXXXWBXBXWWWXXWXWXXXWXXXXWWXXWXWWXWBXWXBXWWW\\n\", \"100 36\\nWXWXWWBWBBXXXWWBBXXWBWWWWXXBWXXBXXBXXBXXWXXXXWBBWWWBXWWBXWXWWBXXWXWXWWXXWWWXXXBXBWXWXBXXXWXXWWXWWBWW\\n\", \"100 25\\nBXWWXWBWWWWWBXBBWXWWXBBWBWWWWWWWXWXWXXXWWWXXXXBXBBXXXWWXBBXWBXWXWXXXXXWBBXWXXWXWWWBXXWBXWWXBWWBXBXXB\\n\", \"1 1\\nWWW\\n\", \"4 1\\nWWXX\\n\", \"10 3\\nXWWWWBWBXB\\n\", \"100 36\\nWXWXWWBWBBXXXWWBBXXWBWWWWXXBWXXBXXBXXBXXWXXXXWBBWWWBXWWBXWXWWBXXWXWXWWXXWWWXXXBXBWXWXBXXXWXXWWXWWBWX\\n\", \"100 49\\nBXWWXWBWWWWWBXBBWXWWXBBWBWWWWWWWXWXWXXXWWWXXXXBXBBXXXWWXBBXWBXWXWXXXXXWBBXWXXWXWWWBXXWBXWWXBWWBXBXXB\\n\", \"1 1\\nWVW\\n\", \"4 2\\nXXWX\\n\", \"10 3\\nXWWWWBWBWB\\n\", \"100 18\\nWXWXWWBWBBXXXWWBBXXWBWWWWXXBWXXBXXBXXBXXWXXXXWBBWWWBXWWBXWXWWBXXWXWXWWXXWWWXXXBXBWXWXBXXXWXXWWXWWBWX\\n\", \"100 93\\nBXWWXWBWWWWWBXBBWXWWXBBWBWWWWWWWXWXWXXXWWWXXXXBXBBXXXWWXBBXWBXWXWXXXXXWBBXWXXWXWWWBXXWBXWWXBWWBXBXXB\\n\", \"1 1\\nWVV\\n\", \"4 3\\nXXWX\\n\", \"10 1\\nXWWWWBWBWB\\n\", \"100 18\\nXWBWWXWWXXWXXXBXWXWBXBXXXWWWXXWWXWXWXXBWWXWXBWWXBWWWBBWXXXXWXXBXXBXXBXXWBXXWWWWBWXXBBWWXXXBBWBWWXWXW\\n\", \"100 22\\nBXWWXWBWWWWWBXBBWXWWXBBWBWWWWWWWXWXWXXXWWWXXXXBXBBXXXWWXBBXWBXWXWXXXXXWBBXWXXWXWWWBXXWBXWWXBWWBXBXXB\\n\", \"10 2\\nXWWWWBWBWB\\n\", \"10 2\\nXWWWWBXBWB\\n\", \"100 35\\nWWXWWXXXXBBXWBXXXXWXXWXXXXXXXBBXXXXXXXWWXXWXXXXBWBXXXXXXXXXXWXWXXXXWXXXWXXWXXXXBXBXXBXXXXXWBXWBXXXXB\\n\", \"20 5\\nXWWBWBXWWBXXXXXXXBBX\\n\", \"6 7\\nBWXBXBWWXXBBXBBWXWBW\\n\", \"300 200\\nWWWXBXWXBWXWWXWXXWWXXXXWXXXWXWBXWWWXBXBWXXXXWXXXXWWWWXBXWWWWBWWWBWWWWXXWXXWWWWWWWXWXWWXWWXXXXWWWBBXXXWBXXWXWXXXWWXXXWWXWWXWBWXWWWXWXXBWWWXXWWWXWWWXXXXWXWWXWXWXXWWXWWXWXWWWWWXWXXWWXXWXWXXXWXWBXWBXWXXXWWWWXBWXBWXXXXXWWWWWXWXBXWWXXXXWXWWWWBBWBWWWWXWBXWXWWXWBWXWWWXXXXWXXXWWXXXXWXXWWBWXXXWWBXXXBWWXWWWWXW\\n\", \"100 31\\nWXWXWWBWBBXXXWWBBXXWBWWWWXXBWXXBXXBXXBXXWXXXXWBBWWWBXWWBXWXWWBXXWXWXWWXXWWWXXXBXBWXWXBXXXWXXWWXWWBWW\\n\"], \"outputs\": [\"166\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"10\\n\", \"951778854\\n\", \"135234318\\n\", \"1\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"28\\n\", \"1\\n\", \"817953325\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"1\\n\", \"11\\n\", \"1048576\\n\", \"23240159\\n\", \"126\\n\", \"8\\n\", \"469056403\\n\", \"2\\n\", \"7\\n\", \"0\\n\", \"3\\n\", \"64\\n\", \"0\\n\", \"2\\n\", \"128\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"671329881\\n\", \"1024\\n\", \"740588372\\n\", \"23240159\\n\", \"51\\n\", \"887988879\\n\", \"1\\n\", \"64\\n\", \"88\\n\", \"210016448\\n\", \"2\\n\", \"131852167\\n\", \"867456188\\n\", \"592781947\\n\", \"974340363\\n\", \"438952513\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
The Little Elephant has found a ragged old black-and-white string s on the attic.
The characters of string s are numbered from the left to the right from 1 to |s|, where |s| is the length of the string. Let's denote the i-th character of string s as si. As the string is black-and-white, each character of the string is either letter "B", or letter "W". Unfortunately, the string is very old and some characters are damaged. The damaged positions are denoted as "X".
The Little Elephant in determined to restore the string and hang it on the wall. For that he needs to replace each character "X" by a "B" or a "W". The string must look good on the wall, so it must be beautiful. The Little Elephant considers a string beautiful if it has two non-intersecting substrings of a given length k, such that the left one fully consists of characters "B", and the right one fully consists of characters "W". More formally, there are four integers a, b, c, d (1 ≤ a ≤ b < c ≤ d ≤ |s|; b - a + 1 = d - c + 1 = k) such that si = "B" (a ≤ i ≤ b) and sj = "W" (c ≤ j ≤ d).
Help the Little Elephant find the number of different beautiful strings he can obtain from string s. Two strings are considered different if there is such position, where the character in the first string differs from the corresponding character in the second string. If this string doesn't contain characters «X» and it is already beautiful — the answer is 1.
As the answer can be rather large, print it modulo 1000000007 (109 + 7).
Input
The first line contains two space-separated integers n and k (1 ≤ k ≤ n ≤ 106). The second line contains string s. String s has length n and only consists of characters "W", "B" and "X".
Output
On a single line print an integer — the answer to the problem modulo 1000000007 (109 + 7).
Examples
Input
3 2
XXX
Output
0
Input
4 2
XXXX
Output
1
Input
10 2
XXBXXWXXXX
Output
166
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4 2\\n\", \"3 3\\n\", \"100 100\\n\", \"1 2\\n\", \"10 100\\n\", \"1 34\\n\", \"1 100\\n\", \"90 100\\n\", \"1 4\\n\", \"89 89\\n\", \"6 4\\n\", \"1 98\\n\", \"99 3\\n\", \"1 1\\n\", \"46 2\\n\", \"84 27\\n\", \"5 5\\n\", \"76 48\\n\", \"2 1\\n\", \"56 98\\n\", \"100 90\\n\", \"18 94\\n\", \"100 1\\n\", \"100 101\\n\", \"2 2\\n\", \"0 100\\n\", \"1 32\\n\", \"1 110\\n\", \"22 100\\n\", \"1 7\\n\", \"89 36\\n\", \"2 4\\n\", \"1 188\\n\", \"53 3\\n\", \"8 2\\n\", \"83 2\\n\", \"168 27\\n\", \"6 5\\n\", \"31 48\\n\", \"2 0\\n\", \"56 106\\n\", \"110 90\\n\", \"18 99\\n\", \"101 1\\n\", \"4 1\\n\", \"3 5\\n\", \"100 001\\n\", \"1 3\\n\", \"1 0\\n\", \"0 101\\n\", \"22 000\\n\", \"0 7\\n\", \"89 42\\n\", \"0 4\\n\", \"1 359\\n\", \"78 3\\n\", \"8 3\\n\", \"142 2\\n\", \"168 12\\n\", \"2 5\\n\", \"45 48\\n\", \"112 106\\n\", \"010 90\\n\", \"18 8\\n\", \"101 2\\n\", \"3 1\\n\", \"3 10\\n\", \"100 011\\n\", \"1 6\\n\", \"0 001\\n\", \"0 3\\n\", \"89 33\\n\", \"-1 4\\n\", \"1 442\\n\", \"54 3\\n\", \"6 3\\n\", \"147 2\\n\", \"279 12\\n\", \"2 6\\n\", \"45 38\\n\", \"112 176\\n\", \"010 162\\n\", \"22 8\\n\", \"101 4\\n\", \"3 2\\n\", \"1 10\\n\", \"110 001\\n\", \"1 5\\n\", \"0 010\\n\", \"3 000\\n\", \"9 33\\n\", \"0 2\\n\", \"1 852\\n\", \"20 3\\n\", \"6 2\\n\", \"188 2\\n\", \"374 12\\n\", \"3 6\\n\", \"45 19\\n\", \"136 176\\n\", \"011 162\\n\", \"22 13\\n\", \"101 0\\n\", \"3 4\\n\", \"1 19\\n\", \"010 001\\n\", \"4 000\\n\", \"9 34\\n\", \"1 430\\n\", \"20 0\\n\", \"-1 5\\n\", \"188 0\\n\", \"259 12\\n\", \"3 7\\n\", \"45 37\\n\", \"136 10\\n\", \"001 162\\n\", \"33 13\\n\", \"100 0\\n\", \"2 7\\n\", \"0 19\\n\", \"010 101\\n\", \"1 011\\n\"], \"outputs\": [\"BGBGBB\\n\", \"GBGBGB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGB\\n\", \"GBG\\n\", \"GBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGG\\n\", \"GBGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGB\\n\", \"BGBGBGBGBB\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GB\\n\", \"BGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBGBGB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBG\\n\", \"GBGB\\n\", \"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBBBBBB\\n\", \"BGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGG\\n\", \"BB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBBB\\n\", \"GBGBGBGG\\n\", \"BGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGG\\n\", \"B\\n\", \"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BBBBBBBBBBBBBBBBBBBBBB\\n\", \"GGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBBBBB\\n\", \"BGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBB\\n\", \"GBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBBBBBBBBBB\\n\", \"BGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBB\\n\", \"GBGBGBGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGGGGG\\n\", \"G\\n\", \"GGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GGGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBBB\\n\", \"BGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGB\\n\", \"GBGGGGGGGGG\\n\", \"BGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGGGG\\n\", \"GGGGGGGGGG\\n\", \"BBB\\n\", \"GBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBBBBBBBBBBBBBBBBB\\n\", \"BGBGBBBB\\n\", \"BGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBB\\n\", \"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBG\\n\", \"GBGGGGGGGGGGGGGGGGGG\\n\", \"BGBBBBBBBBB\\n\", \"BBBB\\n\", \"GBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BBBBBBBBBBBBBBBBBBBB\\n\", \"GGGGGG\\n\", \"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGBGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBB\\n\", \"BGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"BGBGBGBGBGBGBGBGBGBGBGBGBGBBBBBBBBBBBBBBBBBBBB\\n\", \"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\\n\", \"GBGBGGGGG\\n\", \"GGGGGGGGGGGGGGGGGGG\\n\", \"GBGBGBGBGBGBGBGBGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\\n\", \"GBGGGGGGGGGG\\n\"]}", "source": "primeintellect"}
|
There are n boys and m girls studying in the class. They should stand in a line so that boys and girls alternated there as much as possible. Let's assume that positions in the line are indexed from left to right by numbers from 1 to n + m. Then the number of integers i (1 ≤ i < n + m) such that positions with indexes i and i + 1 contain children of different genders (position i has a girl and position i + 1 has a boy or vice versa) must be as large as possible.
Help the children and tell them how to form the line.
Input
The single line of the input contains two integers n and m (1 ≤ n, m ≤ 100), separated by a space.
Output
Print a line of n + m characters. Print on the i-th position of the line character "B", if the i-th position of your arrangement should have a boy and "G", if it should have a girl.
Of course, the number of characters "B" should equal n and the number of characters "G" should equal m. If there are multiple optimal solutions, print any of them.
Examples
Input
3 3
Output
GBGBGB
Input
4 2
Output
BGBGBB
Note
In the first sample another possible answer is BGBGBG.
In the second sample answer BBGBGB is also optimal.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\n\", \"3\\n\", \"1\\n\", \"11\\n\", \"0\\n\", \"17\\n\", \"18855321\\n\", \"34609610\\n\", \"25\\n\", \"9\\n\", \"40000000\\n\", \"17464436\\n\", \"38450759\\n\", \"395938\\n\", \"39099999\\n\", \"8\\n\", \"4\\n\", \"30426905\\n\", \"7\\n\", \"17082858\\n\", \"46341\\n\", \"46340\\n\", \"39999996\\n\", \"6\\n\", \"12823666\\n\", \"39999999\\n\", \"5\\n\", \"5626785\\n\", \"22578061\\n\", \"3766137\\n\", \"13\\n\", \"19863843\\n\", \"24562258\\n\", \"17590047\\n\", \"33146037\\n\", \"2870141\\n\", \"10\\n\", \"14\\n\", \"25329968\\n\", \"39999997\\n\", \"31975828\\n\", \"31988776\\n\", \"31416948\\n\", \"39268638\\n\", \"614109\\n\", \"24483528\\n\", \"39999998\\n\", \"15012490\\n\", \"3107977\\n\", \"2346673\\n\", \"34714265\\n\", \"12\\n\", \"15\\n\", \"16\\n\", \"1059264\\n\", \"743404\\n\", \"22\\n\", \"18712741\\n\", \"19\\n\", \"18\\n\", \"28793983\\n\", \"23224290\\n\", \"99745\\n\", \"35202758\\n\", \"29\\n\", \"12297368\\n\", \"28479\\n\", \"6339\\n\", \"14358961\\n\", \"8046391\\n\", \"21458941\\n\", \"290175\\n\", \"23635292\\n\", \"5753398\\n\", \"20\\n\", \"15059571\\n\", \"6489939\\n\", \"15765759\\n\", \"2702862\\n\", \"1116491\\n\", \"5376403\\n\", \"27801925\\n\", \"12940822\\n\", \"333126\\n\", \"32480774\\n\", \"39328213\\n\", \"14730633\\n\", \"1391775\\n\", \"867315\\n\", \"24\\n\", \"28\\n\", \"561480\\n\", \"1379091\\n\", \"31\\n\", \"4756040\\n\", \"32\\n\", \"26\\n\", \"9699318\\n\", \"11303201\\n\", \"44610\\n\", \"7174193\\n\", \"11125829\\n\", \"8284\\n\", \"2901\\n\", \"4008032\\n\", \"2043829\\n\", \"30131997\\n\", \"310519\\n\", \"13942423\\n\", \"2216663\\n\", \"33\\n\", \"28327088\\n\", \"8381907\\n\", \"28084809\\n\", \"2007849\\n\", \"1118477\\n\", \"3630257\\n\", \"12750347\\n\", \"410223\\n\", \"34348875\\n\", \"28556748\\n\", \"8702249\\n\", \"2294898\\n\", \"419940\\n\", \"42\\n\", \"34\\n\", \"796661\\n\", \"2220203\\n\", \"55\\n\", \"3850788\\n\", \"23\\n\", \"37\\n\", \"7229468\\n\", \"3005575\\n\", \"41095\\n\"], \"outputs\": [\"8\\n\", \"16\\n\", \"4\\n\", \"60\\n\", \"1\\n\", \"96\\n\", \"106661800\\n\", \"195781516\\n\", \"140\\n\", \"48\\n\", \"226274168\\n\", \"98793768\\n\", \"217510336\\n\", \"2239760\\n\", \"221182992\\n\", \"44\\n\", \"20\\n\", \"172120564\\n\", \"36\\n\", \"96635236\\n\", \"262144\\n\", \"262136\\n\", \"226274144\\n\", \"32\\n\", \"72541608\\n\", \"226274164\\n\", \"28\\n\", \"31829900\\n\", \"127720800\\n\", \"21304488\\n\", \"72\\n\", \"112366864\\n\", \"138945112\\n\", \"99504332\\n\", \"187502300\\n\", \"16235968\\n\", \"56\\n\", \"76\\n\", \"143287936\\n\", \"226274152\\n\", \"180882596\\n\", \"180955840\\n\", \"177721092\\n\", \"222136960\\n\", \"3473924\\n\", \"138499748\\n\", \"226274156\\n\", \"84923464\\n\", \"17581372\\n\", \"13274784\\n\", \"196373536\\n\", \"64\\n\", \"84\\n\", \"88\\n\", \"5992100\\n\", \"4205328\\n\", \"124\\n\", \"105855248\\n\", \"104\\n\", \"100\\n\", \"162883364\\n\", \"131376420\\n\", \"564240\\n\", \"199136868\\n\", \"164\\n\", \"69564416\\n\", \"161100\\n\", \"35856\\n\", \"81226548\\n\", \"45517260\\n\", \"121390100\\n\", \"1641476\\n\", \"133701400\\n\", \"32546132\\n\", \"112\\n\", \"85189796\\n\", \"36712636\\n\", \"89184600\\n\", \"15289696\\n\", \"6315824\\n\", \"30413528\\n\", \"157271436\\n\", \"73204340\\n\", \"1884444\\n\", \"183739004\\n\", \"222473968\\n\", \"83329040\\n\", \"7873068\\n\", \"4906272\\n\", \"132\\n\", \"156\\n\", \"3176208\\n\", \"7801316\\n\", \"172\\n\", \"26904224\\n\", \"180\\n\", \"144\\n\", \"54867628\\n\", \"63940560\\n\", \"252352\\n\", \"40583364\\n\", \"62937192\\n\", \"46860\\n\", \"16408\\n\", \"22672852\\n\", \"11561640\\n\", \"170452312\\n\", \"1756560\\n\", \"78870252\\n\", \"12539336\\n\", \"184\\n\", \"160242208\\n\", \"47415224\\n\", \"158871668\\n\", \"11358108\\n\", \"6327060\\n\", \"20535832\\n\", \"72126852\\n\", \"2320568\\n\", \"194306576\\n\", \"161541360\\n\", \"49227352\\n\", \"12981900\\n\", \"2375536\\n\", \"236\\n\", \"192\\n\", \"4506592\\n\", \"12559364\\n\", \"308\\n\", \"21783344\\n\", \"128\\n\", \"208\\n\", \"40896044\\n\", \"17002096\\n\", \"232468\\n\"]}", "source": "primeintellect"}
|
Imagine you have an infinite 2D plane with Cartesian coordinate system. Some of the integral points are blocked, and others are not. Two integral points A and B on the plane are 4-connected if and only if:
* the Euclidean distance between A and B is one unit and neither A nor B is blocked;
* or there is some integral point C, such that A is 4-connected with C, and C is 4-connected with B.
Let's assume that the plane doesn't contain blocked points. Consider all the integral points of the plane whose Euclidean distance from the origin is no more than n, we'll name these points special. Chubby Yang wants to get the following property: no special point is 4-connected to some non-special point. To get the property she can pick some integral points of the plane and make them blocked. What is the minimum number of points she needs to pick?
Input
The first line contains an integer n (0 ≤ n ≤ 4·107).
Output
Print a single integer — the minimum number of points that should be blocked.
Examples
Input
1
Output
4
Input
2
Output
8
Input
3
Output
16
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"9\\n-1 6 -1 2 -1 4 7 -1 2\\n\", \"5\\n-1 -1 -1 -1 -1\\n\", \"7\\n-1 -1 4 5 1 2 3\\n\", \"9\\n8 6 4 2 1 4 7 10 2\\n\", \"3\\n-1 1 -1\\n\", \"4\\n45 -1 41 -1\\n\", \"1\\n-1\\n\", \"5\\n40 -1 44 46 48\\n\", \"6\\n43 40 37 34 -1 -1\\n\", \"7\\n-1 2 4 -1 4 1 5\\n\", \"19\\n23 26 -1 -1 35 38 41 -1 -1 -1 53 -1 59 62 6 7 8 9 -1\\n\", \"6\\n-1 2 6 -1 -1 6\\n\", \"16\\n3 8 13 18 23 -1 -1 -1 43 48 53 45 -1 -1 -1 -1\\n\", \"13\\n25 24 23 22 24 27 -1 33 -1 2 2 2 -1\\n\", \"12\\n-1 17 -1 54 -1 64 -1 74 79 84 -1 94\\n\", \"8\\n-1 12 14 16 18 20 -1 -1\\n\", \"13\\n2 -1 3 1 3 1 -1 1 3 -1 -1 1 1\\n\", \"5\\n-1 40 42 -1 46\\n\", \"2\\n1000000000 -1\\n\", \"14\\n-1 5 3 -1 -1 31 31 31 -1 31 -1 -1 4 7\\n\", \"3\\n-1 1000000000 999999999\\n\", \"7\\n32 33 34 -1 -1 37 38\\n\", \"1\\n1000000000\\n\", \"10\\n29 27 -1 23 42 -1 -1 45 -1 -1\\n\", \"3\\n39 42 -1\\n\", \"15\\n-1 28 -1 32 34 26 -1 26 -1 -1 26 26 26 -1 -1\\n\", \"3\\n1000000000 999999999 1000000000\\n\", \"17\\n-1 -1 -1 -1 64 68 72 -1 45 46 47 48 49 50 51 52 53\\n\", \"3\\n-1 1 1000000000\\n\", \"2\\n-1 1000000000\\n\", \"3\\n999999999 -1 1000000000\\n\", \"1\\n1\\n\", \"2\\n1000000000 1000000000\\n\", \"3\\n999999999 1000000000 -1\\n\", \"7\\n11 8 5 -1 -1 -1 -1\\n\", \"3\\n-1 1 2\\n\", \"2\\n-1 21\\n\", \"8\\n-1 -1 1 7 -1 9 5 2\\n\", \"11\\n9 21 17 13 -1 -1 -1 -1 -1 -1 -1\\n\", \"3\\n-1 1000000000 -1\\n\", \"6\\n-1 6 1 -1 -1 -1\\n\", \"1\\n65\\n\", \"20\\n-1 32 37 -1 -1 -1 57 -1 -1 40 31 33 -1 -1 39 47 43 -1 35 32\\n\", \"5\\n-1 1 7 -1 5\\n\", \"18\\n21 19 -1 -1 -1 48 50 -1 54 -1 5 1 -1 -1 -1 37 36 35\\n\", \"9\\n42 39 36 33 -1 -1 -1 34 39\\n\", \"2\\n-1 -1\\n\", \"5\\n49 -1 44 46 48\\n\", \"7\\n-1 1 4 -1 4 1 5\\n\", \"13\\n25 24 23 12 24 27 -1 33 -1 2 2 2 -1\\n\", \"13\\n2 -1 3 1 3 1 -2 1 3 -1 -1 1 1\\n\", \"2\\n0000000000 -1\\n\", \"6\\n43 42 37 34 -1 -1\\n\", \"6\\n-1 1 6 -1 -1 6\\n\", \"12\\n-1 17 -1 54 -1 64 -1 74 41 84 -1 94\\n\", \"8\\n-1 12 14 16 9 20 -1 -1\\n\", \"14\\n-1 5 3 -1 -1 31 31 31 -1 31 -1 -1 4 2\\n\", \"3\\n-1 1000010000 999999999\\n\", \"1\\n1000000100\\n\", \"10\\n29 33 -1 23 42 -1 -1 45 -1 -1\\n\", \"3\\n5 42 -1\\n\", \"3\\n1000000000 1499407202 1000000000\\n\", \"17\\n-1 -1 -1 -1 64 39 72 -1 45 46 47 48 49 50 51 52 53\\n\", \"3\\n-2 1 1000000000\\n\", \"2\\n-1 1010000000\\n\", \"1\\n-2\\n\", \"2\\n-1 14\\n\", \"11\\n7 21 17 13 -1 -1 -1 -1 -1 -1 -1\\n\", \"1\\n45\\n\", \"5\\n-1 1 7 -1 2\\n\", \"2\\n-1 -2\\n\", \"9\\n-1 6 -1 4 -1 4 7 -1 2\\n\", \"9\\n8 6 2 2 1 4 7 10 2\\n\", \"5\\n49 -1 44 46 2\\n\", \"7\\n-1 1 4 -1 1 1 5\\n\", \"6\\n-1 1 6 -1 -1 3\\n\", \"8\\n-1 12 2 16 9 20 -1 -1\\n\", \"3\\n-1 1000010000 1814015438\\n\", \"1\\n1000001100\\n\", \"10\\n29 33 -1 23 38 -1 -1 45 -1 -1\\n\", \"3\\n5 29 -1\\n\", \"17\\n-1 -1 -1 -1 64 62 72 -1 45 46 47 48 49 50 51 52 53\\n\", \"3\\n-2 1 1000010000\\n\", \"2\\n-1 1010000100\\n\", \"1\\n-4\\n\", \"2\\n-1 10\\n\", \"11\\n7 21 17 13 -1 -1 -1 -1 -1 -1 0\\n\", \"1\\n37\\n\", \"5\\n-1 1 4 -1 2\\n\", \"2\\n-1 0\\n\", \"9\\n3 6 2 2 1 4 7 10 2\\n\", \"5\\n49 -1 44 46 3\\n\", \"6\\n-1 1 6 -1 -1 5\\n\"], \"outputs\": [\"3\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"1\\n\", \"6\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"3\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"5\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"4\\n\", \"6\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"3\\n\", \"4\\n\", \"3\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"3\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"4\\n\", \"3\\n\", \"3\\n\"]}", "source": "primeintellect"}
|
Polycarpus develops an interesting theory about the interrelation of arithmetic progressions with just everything in the world. His current idea is that the population of the capital of Berland changes over time like an arithmetic progression. Well, or like multiple arithmetic progressions.
Polycarpus believes that if he writes out the population of the capital for several consecutive years in the sequence a1, a2, ..., an, then it is convenient to consider the array as several arithmetic progressions, written one after the other. For example, sequence (8, 6, 4, 2, 1, 4, 7, 10, 2) can be considered as a sequence of three arithmetic progressions (8, 6, 4, 2), (1, 4, 7, 10) and (2), which are written one after another.
Unfortunately, Polycarpus may not have all the data for the n consecutive years (a census of the population doesn't occur every year, after all). For this reason, some values of ai may be unknown. Such values are represented by number -1.
For a given sequence a = (a1, a2, ..., an), which consists of positive integers and values -1, find the minimum number of arithmetic progressions Polycarpus needs to get a. To get a, the progressions need to be written down one after the other. Values -1 may correspond to an arbitrary positive integer and the values ai > 0 must be equal to the corresponding elements of sought consecutive record of the progressions.
Let us remind you that a finite sequence c is called an arithmetic progression if the difference ci + 1 - ci of any two consecutive elements in it is constant. By definition, any sequence of length 1 is an arithmetic progression.
Input
The first line of the input contains integer n (1 ≤ n ≤ 2·105) — the number of elements in the sequence. The second line contains integer values a1, a2, ..., an separated by a space (1 ≤ ai ≤ 109 or ai = - 1).
Output
Print the minimum number of arithmetic progressions that you need to write one after another to get sequence a. The positions marked as -1 in a can be represented by any positive integers.
Examples
Input
9
8 6 4 2 1 4 7 10 2
Output
3
Input
9
-1 6 -1 2 -1 4 7 -1 2
Output
3
Input
5
-1 -1 -1 -1 -1
Output
1
Input
7
-1 -1 4 5 1 2 3
Output
2
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 1 1 1\\n\", \"2 2 1 2\\n\", \"50 50 50 50\\n\", \"49 49 4 1\\n\", \"48 50 12 11\\n\", \"5 7 1 10\\n\", \"1 50 50 50\\n\", \"5 7 1 4\\n\", \"32 4 17 3\\n\", \"1 50 1 50\\n\", \"50 1 1 1\\n\", \"32 31 10 9\\n\", \"5 7 4 1\\n\", \"49 49 3 3\\n\", \"50 49 1 2\\n\", \"50 48 3 1\\n\", \"50 1 1 50\\n\", \"5 7 10 10\\n\", \"1 1 1 1\\n\", \"49 50 11 12\\n\", \"50 50 87 50\\n\", \"48 46 12 11\\n\", \"49 85 4 1\\n\", \"5 7 0 10\\n\", \"2 50 50 50\\n\", \"5 7 2 4\\n\", \"32 4 13 3\\n\", \"2 50 1 50\\n\", \"50 1 0 1\\n\", \"32 52 10 9\\n\", \"5 7 4 2\\n\", \"49 49 3 2\\n\", \"50 49 1 1\\n\", \"50 48 5 1\\n\", \"50 1 1 80\\n\", \"5 14 10 10\\n\", \"1 1 2 1\\n\", \"49 50 11 3\\n\", \"2 1 1 2\\n\", \"2 4 1 2\\n\", \"50 50 87 41\\n\", \"49 39 4 1\\n\", \"39 46 12 11\\n\", \"5 7 0 5\\n\", \"2 50 50 27\\n\", \"5 7 4 4\\n\", \"32 4 3 3\\n\", \"2 36 1 50\\n\", \"50 1 0 2\\n\", \"32 52 9 9\\n\", \"5 7 4 3\\n\", \"49 87 3 2\\n\", \"50 85 1 1\\n\", \"50 41 5 1\\n\", \"50 1 1 93\\n\", \"5 14 1 10\\n\", \"1 1 0 1\\n\", \"49 50 21 3\\n\", \"2 1 2 2\\n\", \"2 7 1 2\\n\", \"70 50 87 41\\n\", \"49 39 5 1\\n\", \"39 12 12 11\\n\", \"8 7 0 5\\n\", \"2 50 64 27\\n\", \"5 7 5 4\\n\", \"32 5 3 3\\n\", \"2 52 1 50\\n\", \"50 1 0 4\\n\", \"32 5 9 9\\n\", \"7 7 4 4\\n\", \"49 9 3 2\\n\", \"50 34 1 1\\n\", \"50 41 7 1\\n\", \"50 1 0 93\\n\", \"5 14 1 11\\n\", \"1 1 0 2\\n\", \"49 50 33 3\\n\", \"2 1 2 4\\n\", \"2 8 1 2\\n\", \"115 50 87 41\\n\", \"34 39 5 1\\n\", \"39 23 12 11\\n\", \"8 14 0 5\\n\", \"2 50 95 27\\n\", \"1 7 2 4\\n\", \"32 10 3 3\\n\", \"2 47 1 50\\n\", \"99 1 0 4\\n\", \"32 5 5 9\\n\", \"7 9 4 4\\n\", \"49 4 3 2\\n\", \"50 12 1 1\\n\", \"50 41 9 1\\n\", \"50 1 1 121\\n\", \"5 14 1 7\\n\", \"0 1 0 2\\n\", \"41 50 33 3\\n\", \"2 2 2 4\\n\", \"4 8 1 2\\n\", \"115 93 87 41\\n\", \"34 39 9 1\\n\"], \"outputs\": [\"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\"]}", "source": "primeintellect"}
|
Two players play a simple game. Each player is provided with a box with balls. First player's box contains exactly n1 balls and second player's box contains exactly n2 balls. In one move first player can take from 1 to k1 balls from his box and throw them away. Similarly, the second player can take from 1 to k2 balls from his box in his move. Players alternate turns and the first player starts the game. The one who can't make a move loses. Your task is to determine who wins if both players play optimally.
Input
The first line contains four integers n1, n2, k1, k2. All numbers in the input are from 1 to 50.
This problem doesn't have subproblems. You will get 3 points for the correct submission.
Output
Output "First" if the first player wins and "Second" otherwise.
Examples
Input
2 2 1 2
Output
Second
Input
2 1 1 1
Output
First
Note
Consider the first sample test. Each player has a box with 2 balls. The first player draws a single ball from his box in one move and the second player can either take 1 or 2 balls from his box in one move. No matter how the first player acts, the second player can always win if he plays wisely.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"1 1 5 5\\n\", \"-157778763 218978790 976692563 591093088\\n\", \"-1 -4 1 4\\n\", \"-999999999 -1000000000 -1 0\\n\", \"1000000000 1000000000 1000000000 1000000000\\n\", \"-2 -3 -2 1\\n\", \"-1000000000 -999999999 1000000000 999999999\\n\", \"0 -1 0 1\\n\", \"-999999999 -999999999 999999999 999999999\\n\", \"-946749893 -687257665 -539044455 -443568671\\n\", \"-26644507 -867720841 975594569 264730225\\n\", \"309857887 -687373066 663986893 403321752\\n\", \"-2 -2 -2 0\\n\", \"0 -2 0 2\\n\", \"0 -1 2 1\\n\", \"-2 -2 2 2\\n\", \"-999999999 -1000000000 999999999 1000000000\\n\", \"-330513944 -970064382 500608496 369852884\\n\", \"0 -3 0 3\\n\", \"0 0 2 2\\n\", \"-946749893 -687257666 -539044455 -443568670\\n\", \"-330513944 -970064383 500608496 369852885\\n\", \"-1000000000 -1000000000 1000000000 1000000000\\n\", \"0 -1 2 3\\n\", \"-999999999 -999999999 -1 -1\\n\", \"309857887 -687373065 663986893 403321751\\n\", \"-482406510 -512306895 412844236 -168036049\\n\", 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\"-26644507 -867720842 975594569 278686966\\n\", \"-471257905 -685885153 782342299 446545709\\n\", \"-537640548 -254017711 62355638 535162001\\n\", \"-26644507 -867720841 975594569 661552343\\n\", \"309857887 -687373065 663986893 432941331\\n\", \"-282631127 33834653 -234317741 590897073\\n\", \"-26644507 -707437992 975594569 278686966\\n\", \"-834861468 -254017711 62355638 535162001\\n\", \"-22488177 -867720841 975594569 661552343\\n\", \"309857887 -687373065 663986893 823249837\\n\", \"-345682807 -999999999 999999999 999999999\\n\", \"-26644507 -867720841 975594569 253312317\\n\", \"309857887 -687373066 388880807 403321752\\n\", \"-330513944 -970064382 612008854 369852884\\n\", \"0 -5 0 3\\n\", \"-946749893 -687257666 -162979065 -443568670\\n\", \"-755075199 -999999999 -1 -1\\n\", \"309857887 -687373065 663986893 295122503\\n\", \"-482406510 -218941148 412844236 -168036050\\n\", \"-157778763 377786815 976692563 591093087\\n\", \"-766179411 33834652 -234317741 925065546\\n\", 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|
Developing tools for creation of locations maps for turn-based fights in a new game, Petya faced the following problem.
A field map consists of hexagonal cells. Since locations sizes are going to be big, a game designer wants to have a tool for quick filling of a field part with identical enemy units. This action will look like following: a game designer will select a rectangular area on the map, and each cell whose center belongs to the selected rectangle will be filled with the enemy unit.
More formally, if a game designer selected cells having coordinates (x1, y1) and (x2, y2), where x1 ≤ x2 and y1 ≤ y2, then all cells having center coordinates (x, y) such that x1 ≤ x ≤ x2 and y1 ≤ y ≤ y2 will be filled. Orthogonal coordinates system is set up so that one of cell sides is parallel to OX axis, all hexagon centers have integer coordinates and for each integer x there are cells having center with such x coordinate and for each integer y there are cells having center with such y coordinate. It is guaranteed that difference x2 - x1 is divisible by 2.
Working on the problem Petya decided that before painting selected units he wants to output number of units that will be painted on the map.
Help him implement counting of these units before painting.
<image>
Input
The only line of input contains four integers x1, y1, x2, y2 ( - 109 ≤ x1 ≤ x2 ≤ 109, - 109 ≤ y1 ≤ y2 ≤ 109) — the coordinates of the centers of two cells.
Output
Output one integer — the number of cells to be filled.
Examples
Input
1 1 5 5
Output
13
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
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2\\n552 9\\n852 193\\n943 383\\n878 716\\n770 1598\\n536 240\\n28 757\\n\", \"10 1000 24 381\\n131 197\\n303 53\\n528 0\\n546 0\\n726 57\\n792 76\\n917 187\\n755 1675\\n220 895\\n124 796\\n\", \"10 1000 787 576\\n-209 73\\n-20 24\\n216 7\\n287 34\\n312 967\\n288 976\\n99 999\\n-138 1010\\n-220 853\\n-193 734\\n\", \"10 1000 22 255\\n70 171\\n272 88\\n328 47\\n740 55\\n850 868\\n550 999\\n448 996\\n371 980\\n302 954\\n18 718\\n\"], \"outputs\": [\"5.0000000000\\n\", \"1.5000000000\\n\", \"2.6246719160\\n\", \"2.0760668149\\n\", \"1.2030330437\\n\", \"3.9215686275\\n\", \"1.6778523490\\n\", \"3.9215686275\\n\", \"798.0000000000\\n\", \"334.1250000000\\n\", \"814.9000000000\\n\", \"252.0000000000\\n\", \"3.0000000000\\n\", \"10.2500000000\\n\", \"3.1264023359\\n\", \"1787.2500000000\\n\", \"8.5946721130\\n\", \"353.6500000000\\n\", \"899.3333333333\\n\", \"2.2574889399\\n\", \"5.0000000000\\n\", \"218.5714285714\\n\", \"2.5000000000\\n\", \"4.5000000000\\n\", \"1.3850415512\\n\", \"3.9130609854\\n\", \"2.1733990074\\n\", \"447.8750000000\\n\", \"3.8197492879\\n\", \"9.2241153342\\n\", \"6.6238787879\\n\", \"5.0000000000\\n\", \"5.6450159450\\n\", \"1.5000000000\\n\", \"28.3139682540\\n\", \"219.7500000000\\n\", \"22.0000000000\\n\", \"2.3474178404\\n\", \"0.5\\n\", \"2.6246719160104988\\n\", \"2.0760668149089367\\n\", \"3.9215686274509802\\n\", \"1.6778523489932886\\n\", \"252.0\\n\", \"3.0\\n\", \"899.3333333333334\\n\", \"2.257488939885022\\n\", \"218.57142857142858\\n\", \"2.5\\n\", \"28.89097744360902\\n\", \"3.9130609854308513\\n\", \"2.17339900739208\\n\", \"3.819749287922867\\n\", \"9.224115334207077\\n\", \"5.0\\n\", \"5.6475604742380305\\n\", \"28.313968253968255\\n\", \"219.75\\n\", \"2.041759318085557\\n\", \"39.15401069518717\\n\", \"4.0\\n\", \"9.233289646133683\\n\", \"0.3333333333333333\\n\", \"9.176963056232754\\n\", \"3.9215686274509802\\n\", \"0.5\\n\", \"2.6246719160104988\\n\", \"3.9215686274509802\\n\", \"3.0\\n\", \"2.257488939885022\\n\", \"218.57142857142858\\n\", \"28.89097744360902\\n\", \"2.17339900739208\\n\", \"5.0\\n\", \"5.6475604742380305\\n\", \"28.313968253968255\\n\", \"2.6246719160104988\\n\", \"2.041759318085557\\n\", \"39.15401069518717\\n\", \"3.0\\n\", \"2.257488939885022\\n\", \"218.57142857142858\\n\", \"4.0\\n\", \"28.89097744360902\\n\", \"2.17339900739208\\n\", \"9.233289646133683\\n\", \"5.0\\n\", \"28.313968253968255\\n\", \"2.6246719160104988\\n\", \"2.041759318085557\\n\", \"39.15401069518717\\n\"]}", "source": "primeintellect"}
|
And while Mishka is enjoying her trip...
Chris is a little brown bear. No one knows, where and when he met Mishka, but for a long time they are together (excluding her current trip). However, best friends are important too. John is Chris' best friend.
Once walking with his friend, John gave Chris the following problem:
At the infinite horizontal road of width w, bounded by lines y = 0 and y = w, there is a bus moving, presented as a convex polygon of n vertices. The bus moves continuously with a constant speed of v in a straight Ox line in direction of decreasing x coordinates, thus in time only x coordinates of its points are changing. Formally, after time t each of x coordinates of its points will be decreased by vt.
There is a pedestrian in the point (0, 0), who can move only by a vertical pedestrian crossing, presented as a segment connecting points (0, 0) and (0, w) with any speed not exceeding u. Thus the pedestrian can move only in a straight line Oy in any direction with any speed not exceeding u and not leaving the road borders. The pedestrian can instantly change his speed, thus, for example, he can stop instantly.
Please look at the sample note picture for better understanding.
We consider the pedestrian is hit by the bus, if at any moment the point he is located in lies strictly inside the bus polygon (this means that if the point lies on the polygon vertex or on its edge, the pedestrian is not hit by the bus).
You are given the bus position at the moment 0. Please help Chris determine minimum amount of time the pedestrian needs to cross the road and reach the point (0, w) and not to be hit by the bus.
Input
The first line of the input contains four integers n, w, v, u (3 ≤ n ≤ 10 000, 1 ≤ w ≤ 109, 1 ≤ v, u ≤ 1000) — the number of the bus polygon vertices, road width, bus speed and pedestrian speed respectively.
The next n lines describes polygon vertices in counter-clockwise order. i-th of them contains pair of integers xi and yi ( - 109 ≤ xi ≤ 109, 0 ≤ yi ≤ w) — coordinates of i-th polygon point. It is guaranteed that the polygon is non-degenerate.
Output
Print the single real t — the time the pedestrian needs to croos the road and not to be hit by the bus. The answer is considered correct if its relative or absolute error doesn't exceed 10 - 6.
Example
Input
5 5 1 2
1 2
3 1
4 3
3 4
1 4
Output
5.0000000000
Note
Following image describes initial position in the first sample case:
<image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"BUVTYZFQSNRIWOXXGJLKACPEMDH\\n\", \"ABCDEFGHIJKLMNOPQRSGTUVWXYZ\\n\", \"MKBGVNDJRAWUEHFSYLIZCOPTXKQ\\n\", \"ABACDEFGHIJKLMNOPQRSTUVWXYZ\\n\", \"BACDEFGHIJKLMNOPQRSTUVWXYZA\\n\", \"BADSLHIYGMZJQKTCOPRVUXFWENN\\n\", \"HVDEBKMJTLKQORNWCZSGXYIPUAF\\n\", \"UNGHFQRCIPBZTEOAYJXLDMSKNWV\\n\", \"TEGXHBUVZDPAMIJFQYCWRKSTNLO\\n\", \"MIDLBEUAGTNPYKFWHVSRJOXCZMQ\\n\", \"RFKNZXHAIMVBWEBPTCSYOLJGDQU\\n\", \"ABCDEFGHIJKLMNOPQRSTUVWXYZX\\n\", \"ABCDEFGHIJKLMZYXWVUTSRQPONA\\n\", \"YOFJVQSWBUZENPCXGQTHMDKAILR\\n\", \"BMVFGRNDOWTILZVHAKCQSXYEJUP\\n\", \"HIDCLZUTPOQGEXFASJNYBVRMDKW\\n\", \"LCFNHUQWXBPOSJMYTGKDAZVREIF\\n\", \"AHGZCRJTKPMQUNBWSIYLDXEHFVO\\n\", \"ABCDEFGHIJKLMNOPQRSTUVWXYZG\\n\", \"MKNTKOBFLJSXWQPVUERDHIACYGZ\\n\", \"ZWFIRJNXVKHOUSTQBLEGYMAPIDC\\n\", \"XZTMCRBONHFIUVPKWSDLJQGAHYE\\n\", \"GYCUAXSBNAWFIJPDQVETKZOMLHR\\n\", \"CNHIKJWRLPXTQZVUGYDMBAOEFHS\\n\", \"ABCDEFGHIJKLMNOPQRSTUVWXYZA\\n\", \"ABCDEFGHIJKLMNOPQRSTUVWXAYZ\\n\", \"UTEDBZRVWLOFUASHCYIPXGJMKNQ\\n\", 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\"UQDGJLOYSCTPBEWBVMIAHXZNKFR\\n\", \"ABCTEFGHIJKLMNOPQRSDUVWXYZX\\n\", \"ANOPQRSTUVWXYZMLKJIHGFEDCBA\\n\", \"RLIAKDMHTQGXCPNEZUBWSQVJFOY\\n\", \"HIDCLZUTPOQGXEFASJNYBVRMDKW\\n\", \"CDIPAMYGELBQTSUOHKVXNJRIFWZ\\n\", \"XZTMCRBONQFIUVPKWSDLJHGAHYE\\n\", \"SHFEOABMDYGUVZQTXPLRWJKIHNC\\n\", \"KTEDBZRVWLOFUASHCYIPXGJMUNQ\\n\", \"XQVBTCNIRFPLOHAYDUMKWEJSXZG\\n\", \"BETRFOVLPCMWKHTXSGUDQYJAZIN\\n\", \"QWERTYUIOPASDBGHJKLZXCVFNMQ\\n\", \"PJFCVBQTYIEMASLGNDZHKRXJWOU\\n\", \"EOKRAQMVWZFNHPBUGIJWYTLSDCX\\n\", \"ABCBDEFGHISKLMNOPQRJTUVWXYZ\\n\", \"TZXIPMVQANOSFYLWRKBCHJEDGTU\\n\", \"FKSBTQIPGRNXLZWCDELJUHOVMAY\\n\", \"TBNAPCWKYVMEZOSQXUFRGLJTDHI\\n\", \"ZYXWVUTGSRQPONMLKJIHGFEDCBA\\n\", \"ZYXWVUTSRQPONMLAJIHGFEDCABK\\n\", \"UNGHFSRCIXBZTEOAYJPLDMQKNWV\\n\", \"WKDMRVBYNJSAFEXGQOPTUZLCDIH\\n\", \"XZQMCRBONTFIUVPKWSDLJHGAHYE\\n\", \"SIFEOABMDYGUVZQTXPLRWJKIHNC\\n\", \"QNUMJGXPIYCHSAUFOLWVRZBDETK\\n\", \"XQVBTCNIRFXLOHAYDUMKWEJSPZG\\n\", \"NIZAJYQDUGSXTHKWMCPLVOFRTEB\\n\", \"QWKRTYUIOPASDBGHJELZXCVFNMQ\\n\", \"ZYXWVUTJRQPONMLKSIHGFEDBCBA\\n\", \"FKSBTQIPGRNXLZWCDEMJUHOVMAY\\n\", \"TYXWVUZGSRQPONMLKJIHGFEDCBA\\n\", \"UNGHFBRCIXSZTEOAYJPLDMQKNWV\\n\", \"SJFEOABMDYGUVZQTXPLRWJKIHNC\\n\", \"XQVBTCNIRFHLOXAYDUMKWEJSPZG\\n\", \"NIZAJYQDUGBXTHKWMCPLVOFRTES\\n\", \"QWKRTYUIOPASDLGHJEBZXCVFNMQ\\n\", \"VWNKQMDLPJYAOETZSXICRBFHGNU\\n\", \"XQVBTCNIRFHGOXAYDUMKWEJSPZL\\n\", \"AWKRTYUIOPQSDLGHJEBZXCVFNMQ\\n\", \"ZWNKQMDLPJYAOETVSXICRBFHGNU\\n\", \"AWKRTYUIOPQEDLGHJSBZXCVFNMQ\\n\", \"UNGHFBRCIXSVTEOAYJPLDMQKNWZ\\n\", \"AWKRTCUIOPQEDLGHJSBZXYVFNMQ\\n\", \"UNGHFPRCIXSVTEOAYJBLDMQKNWZ\\n\", \"UNGHFPRCIXSVTEOLYJBADMQKNWZ\\n\", \"ZYXWVUTSRQPONMLKJIHGFEDCABA\\n\", \"AZYXWVUTSRQPONMLKJIHGFEDCAB\\n\", \"UNGHFQRCIPBZTEXAYJOLDMSKNWV\\n\", \"XZYXWVUTSRQPONMLKJIHGFEDCBA\\n\", \"OMVFGRNDBWTILZVHAKCQSXYEJUP\\n\", \"WKDMRVBYNJSAFXEGQOPTUZLCDIH\\n\", \"LCFNHUQWXBPOSJIYTGKDAZVREMF\\n\", \"GZYXWVUTSRQPONMLKJIHGFEDCBA\\n\", \"UTEDBZRXWLOFUASHCYIPVGJMKNQ\\n\", \"BYNRHKXGSMDOPUVEJAIQCTLFMWZ\\n\", \"GDXSJEWKMUZYAHOLPFRINCTBVQX\\n\", \"ZYXWVUTSRQPONMLKJIGHGFEDCBA\\n\", \"BETRFOVLPIMWKHAXSGUDQYJTZCN\\n\", \"BHDMEPCAKLJGXOWIRNSQFZYTVUB\\n\", \"QMNBVCXZLKJHGFDSAPOIUYTREWQ\\n\", \"EMGIFDZKBCVRYLTWOASXHNUQPJN\\n\", \"ZYXWVUTSRQPONMLKJIHGFEDBCBA\\n\", \"UBGDEJHCTKRWLYFSONAQVMPIXZT\\n\", \"FKABTQIPGRNXLZWCDELJUHOVMSY\\n\", \"BUVTYZFQSNXIWOXRGJLKACPEMDH\\n\", \"QKXTPOCZILYSNHEUWARJDFVGBKM\\n\", \"VWNKQMDLXJYAOETZBPICRSFHGNU\\n\", \"OLNTSKRWCYQFJIMAPDGVUBHXZET\\n\", \"MIDLGEUABTNPYKFWVHSRJOXCZMQ\\n\", \"FJLBATRSQWHPVNIOZGMKXXUECYD\\n\", \"NFLGVEZQHXYAWSUDDPMKOJRCTIB\\n\", \"NNEWFXUVRPOCTIQJZMGYKHLSDAB\\n\", \"NNEWFXUVRPOCTKQJZMGYIHLSDAB\\n\", \"TEGXHBUVZDPAMIJFQYCWRKSSNLO\\n\", \"BBCDEFGHIJKLMNOPQRSTUVWXYZA\\n\", \"QIFKYWPXHTJMSCVNEZDOABRGLUU\\n\", \"DYCEUXXKMGZOINVPHFQSRTABLJW\\n\"], \"outputs\": [\"Impossible\\n\", \"ABCDEFGHIJKLM\\nZYXWVUTSRQPON\\n\", \"MKBGVNDJRAWUE\\nQXTPOCZILYSFH\\n\", \"OPQRSTUVWXYZA\\nNMLKJIHGFEDCB\\n\", \"ACDEFGHIJKLMN\\nBZYXWVUTSRQPO\\n\", \"Impossible\\n\", \"IPUAFHVDEBKMJ\\nYXGSZCWNROQLT\\n\", \"UNGHFQRCIPBZT\\nVWKSMDLXJYAOE\\n\", \"OTEGXHBUVZDPA\\nLNSKRWCYQFJIM\\n\", \"MIDLBEUAGTNPY\\nQZCXOJRSVHWFK\\n\", \"RFKNZXHAIMVBW\\nUQDGJLOYSCTPE\\n\", \"MNOPQRSTUVWXY\\nLKJIHGFEDCBAZ\\n\", \"ABCDEFGHIJKLM\\nNOPQRSTUVWXYZ\\n\", \"LRYOFJVQSWBUZ\\nIAKDMHTGXCPNE\\n\", \"YEJUPBMVFGRND\\nXSQCKAHZLITWO\\n\", \"HIDCLZUTPOQGE\\nWKMRVBYNJSAFX\\n\", \"CFNHUQWXBPOSJ\\nLIERVZADKGTYM\\n\", \"OAHGZCRJTKPMQ\\nVFEXDLYISWBNU\\n\", \"DEFGHIJKLMNOP\\nCBAZYXWVUTSRQ\\n\", \"ERDHIACYGZMKN\\nUVPQWXSJLFBOT\\n\", \"WFIRJNXVKHOUS\\nZCDPAMYGELBQT\\n\", \"CRBONHFIUVPKW\\nMTZXEYAGQJLDS\\n\", \"ZOMLHRGYCUAXS\\nKTEVQDPJIFWNB\\n\", \"NHIKJWRLPXTQZ\\nCSFEOABMDYGUV\\n\", \"ABCDEFGHIJKLM\\nZYXWVUTSRQPON\\n\", \"ZABCDEFGHIJKL\\nYXWVUTSRQPONM\\n\", \"XGJMKNQUTEDBZ\\nPIYCHSAFOLWVR\\n\", \"NYBZWMFLTCQIA\\nRHKXGSDOPUVEJ\\n\", \"GXQVBTCNIRFPL\\nDSJEWKMUZYAHO\\n\", \"Impossible\\n\", \"UVWXYZABCDEFG\\nTSRQPONMLKJIH\\n\", \"LMNOPQRSTUVWY\\nKJIHGFEDCBAZX\\n\", \"SHBGLRJAMDUIP\\nTXFQKNEVZOYWC\\n\", \"OURNQJWMIXCLG\\nHPTYBFAZKEVDS\\n\", \"BETRFOVLPCMWK\\nNIZJYQDUGSXAH\\n\", \"BUVTYZFQSNRIW\\nHDMEPCAKLJGXO\\n\", \"QWERTYUIOPASD\\nMNBVCXZLKJHGF\\n\", \"OWJXRKHZDNGLS\\nUPFCVBQTYIEMA\\n\", \"QGZEMFKWLUHOV\\nBANDRYIPCTJXS\\n\", \"NMGIFDZKBCVRY\\nJPQUEHXSAOWTL\\n\", \"Impossible\\n\", \"XCDSLTYWJIGUB\\nEOKRAQMVZFNHP\\n\", \"PQRSTUVWXYZAB\\nONMLKJIHGFEDC\\n\", \"CPFJBHINOWVLA\\nEXKDSQYZRMUTG\\n\", \"TGDEJHCBKRWLY\\nUZXIPMVQANOSF\\n\", \"KFYAMVOHUJLED\\nSBTQIPGRNXZWC\\n\", \"Impossible\\n\", \"DTJLGRFUXQSOZ\\nHIBNAPCWKYVME\\n\", \"QKXTPOCZILYSF\\nMBGVNDJRAWUEH\\n\", \"UVWXYZKBACDEF\\nTSRQPONMLJIHG\\n\", \"Impossible\\n\", \"UNGHFSRCIPBZT\\nVWKQMDLXJYAOE\\n\", \"NTSKRWCYQFJIM\\nLOEGXHBUVZDPA\\n\", \"MIDLGEUABTNPY\\nQZCXOJRSVHWFK\\n\", \"QDGJLOYSCTPBE\\nURFKNZXHAIMVW\\n\", \"MNOPQRSDUVWXY\\nLKJIHGFETCBAZ\\n\", \"ANOPQRSTUVWXY\\nBCDEFGHIJKLMZ\\n\", \"IAKDMHTQGXCPN\\nLRYOFJVSWBUZE\\n\", \"HIDCLZUTPOQGX\\nWKMRVBYNJSAFE\\n\", \"CDIPAMYGELBQT\\nZWFRJNXVKHOUS\\n\", \"FIUVPKWSDLJHG\\nQNOBRCMTZXEYA\\n\", \"SHFEOABMDYGUV\\nCNIKJWRLPXTQZ\\n\", \"ZRVWLOFUASHCY\\nBDETKQNMJGXPI\\n\", \"GXQVBTCNIRFPL\\nZSJEWKMUDYAHO\\n\", \"JAZINBETRFOVL\\nYQDUGSXHKWMCP\\n\", \"QWERTYUIOPASD\\nMNFVCXZLKJHGB\\n\", \"UPJFCVBQTYIEM\\nOWXRKHZDNGLSA\\n\", \"OKRAQMVWZFNHP\\nEXCDSLTYJIGUB\\n\", \"PQRJTUVWXYZAB\\nONMLKSIHGFEDC\\n\", \"TZXIPMVQANOSF\\nUGDEJHCBKRWLY\\n\", \"SBTQIPGRNXLZW\\nKFYAMVOHUJEDC\\n\", \"ITBNAPCWKYVME\\nHDJLGRFUXQSOZ\\n\", \"YXWVUTGSRQPON\\nZABCDEFHIJKLM\\n\", \"SRQPONMLAJIHG\\nTUVWXYZKBCDEF\\n\", \"UNGHFSRCIXBZT\\nVWKQMDLPJYAOE\\n\", \"WKDMRVBYNJSAF\\nHICLZUTPOQGXE\\n\", \"FIUVPKWSDLJHG\\nTNOBRCMQZXEYA\\n\", \"CSIFEOABMDYGU\\nNHKJWRLPXTQZV\\n\", \"BDETKQNUMJGXP\\nZRVWLOFASHCYI\\n\", \"KWEJSPZGXQVBT\\nMUDYAHOLFRINC\\n\", \"YQDUGSXTHKWMC\\nJAZINBERFOVLP\\n\", \"QWKRTYUIOPASD\\nMNFVCXZLEJHGB\\n\", \"ONMLKSIHGFEDB\\nPQRJTUVWXYZAC\\n\", \"GRNXLZWCDEMJU\\nPIQTBSKFYAVOH\\n\", \"YXWVUZGSRQPON\\nTABCDEFHIJKLM\\n\", \"UNGHFBRCIXSZT\\nVWKQMDLPJYAOE\\n\", \"NCSJFEOABMDYG\\nHIKWRLPXTQZVU\\n\", \"EJSPZGXQVBTCN\\nWKMUDYAOLHFRI\\n\", \"YQDUGBXTHKWMC\\nJAZINSERFOVLP\\n\", \"QWKRTYUIOPASD\\nMNFVCXZBEJHGL\\n\", \"WNKQMDLPJYAOE\\nVUGHFBRCIXSZT\\n\", \"EJSPZLXQVBTCN\\nWKMUDYAOGHFRI\\n\", \"YUIOPQSDLGHJE\\nTRKWAMNFVCXZB\\n\", \"WNKQMDLPJYAOE\\nZUGHFBRCIXSVT\\n\", \"YUIOPQEDLGHJS\\nTRKWAMNFVCXZB\\n\", \"UNGHFBRCIXSVT\\nZWKQMDLPJYAOE\\n\", \"CUIOPQEDLGHJS\\nTRKWAMNFVYXZB\\n\", \"UNGHFPRCIXSVT\\nZWKQMDLBJYAOE\\n\", \"UNGHFPRCIXSVT\\nZWKQMDABJYLOE\\n\", \"NMLKJIHGFEDCA\\nOPQRSTUVWXYZB\\n\", \"AZYXWVUTSRQPO\\nBCDEFGHIJKLMN\\n\", \"UNGHFQRCIPBZT\\nVWKSMDLOJYAXE\\n\", \"KJIHGFEDCBAXZ\\nLMNOPQRSTUVWY\\n\", \"YEJUPOMVFGRND\\nXSQCKAHZLITWB\\n\", \"WKDMRVBYNJSAF\\nHICLZUTPOQGEX\\n\", \"CFNHUQWXBPOSJ\\nLMERVZADKGTYI\\n\", \"CBAGZYXWVUTSR\\nDEFHIJKLMNOPQ\\n\", \"VGJMKNQUTEDBZ\\nPIYCHSAFOLWXR\\n\", \"HKXGSMDOPUVEJ\\nRNYBZWFLTCQIA\\n\", \"DXSJEWKMUZYAH\\nGQVBTCNIRFPLO\\n\", \"TSRQPONMLKJIG\\nUVWXYZABCDEFH\\n\", \"BETRFOVLPIMWK\\nNCZJYQDUGSXAH\\n\", \"BHDMEPCAKLJGX\\nUVTYZFQSNRIWO\\n\", \"QMNBVCXZLKJHG\\nWERTYUIOPASDF\\n\", \"RYLTWOASXHNUQ\\nVCBKZDFIGMEJP\\n\", \"ONMLKJIHGFEDB\\nPQRSTUVWXYZAC\\n\", \"EJHCTKRWLYFSO\\nDGBUZXIPMVQAN\\n\", \"ABTQIPGRNXLZW\\nKFYSMVOHUJEDC\\n\", \"HBUVTYZFQSNXI\\nDMEPCAKLJGROW\\n\", \"QKXTPOCZILYSN\\nMBGVFDJRAWUEH\\n\", \"WNKQMDLXJYAOE\\nVUGHFSRCIPBZT\\n\", \"NTSKRWCYQFJIM\\nLOEZXHBUVGDPA\\n\", \"MIDLGEUABTNPY\\nQZCXOJRSHVWFK\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\", \"Impossible\\n\"]}", "source": "primeintellect"}
|
Let’s define a grid to be a set of tiles with 2 rows and 13 columns. Each tile has an English letter written in it. The letters don't have to be unique: there might be two or more tiles with the same letter written on them. Here is an example of a grid:
ABCDEFGHIJKLM
NOPQRSTUVWXYZ
We say that two tiles are adjacent if they share a side or a corner. In the example grid above, the tile with the letter 'A' is adjacent only to the tiles with letters 'B', 'N', and 'O'. A tile is not adjacent to itself.
A sequence of tiles is called a path if each tile in the sequence is adjacent to the tile which follows it (except for the last tile in the sequence, which of course has no successor). In this example, "ABC" is a path, and so is "KXWIHIJK". "MAB" is not a path because 'M' is not adjacent to 'A'. A single tile can be used more than once by a path (though the tile cannot occupy two consecutive places in the path because no tile is adjacent to itself).
You’re given a string s which consists of 27 upper-case English letters. Each English letter occurs at least once in s. Find a grid that contains a path whose tiles, viewed in the order that the path visits them, form the string s. If there’s no solution, print "Impossible" (without the quotes).
Input
The only line of the input contains the string s, consisting of 27 upper-case English letters. Each English letter occurs at least once in s.
Output
Output two lines, each consisting of 13 upper-case English characters, representing the rows of the grid. If there are multiple solutions, print any of them. If there is no solution print "Impossible".
Examples
Input
ABCDEFGHIJKLMNOPQRSGTUVWXYZ
Output
YXWVUTGHIJKLM
ZABCDEFSRQPON
Input
BUVTYZFQSNRIWOXXGJLKACPEMDH
Output
Impossible
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"xxxxxx\\nxxxxxx\\n\", \"tinkoff\\nzscoder\\n\", \"ioi\\nimo\\n\", \"bcdef\\nabbbc\\n\", \"z\\ny\\n\", \"reddit\\nabcdef\\n\", \"abc\\naaa\\n\", \"y\\nz\\n\", \"cbxz\\naaaa\\n\", \"fedcb\\nabbbc\\n\", \"reddit\\nbbcdef\\n\", \"cba\\naaa\\n\", \"bbxz\\naaaa\\n\", \"xxxxxw\\nxxxxxx\\n\", \"tinkogf\\nzscoder\\n\", \"ioj\\nimo\\n\", \"feddb\\nabbbc\\n\", \"bbxz\\nbaaa\\n\", \"xxxxxw\\nxxyxxx\\n\", \"thnkogf\\nzscoder\\n\", \"bbxy\\nbaba\\n\", \"xxyxxw\\nxxzxxx\\n\", \"ffoknht\\nzscoder\\n\", \"xxyxxv\\nxxzxxx\\n\", \"ffojnht\\nzscoder\\n\", \"cddff\\nbbbca\\n\", \"cdeff\\nbbbca\\n\", \"baxx\\nbaab\\n\", \"xvxyxx\\nxxzxyw\\n\", \"ffedc\\nbbbba\\n\", \"xvxyxx\\nxyzxyw\\n\", \"jjr\\njom\\n\", \"tredch\\nbfbdeb\\n\", \"axax\\naaab\\n\", \"jjr\\njnm\\n\", \"tidder\\nbbcdef\\n\", \"ipj\\nimo\\n\", \"feddb\\nacbbb\\n\", \"tidder\\nfedcbb\\n\", \"bbxy\\nbaaa\\n\", \"xxyxxw\\nxxyxxx\\n\", \"fgoknht\\nzscoder\\n\", \"ipj\\nomi\\n\", \"feddb\\nbbbca\\n\", \"reddit\\nbfcdeb\\n\", \"iqj\\nomi\\n\", \"ffddb\\nbbbca\\n\", \"reddht\\nbfcdeb\\n\", \"bbxy\\nabab\\n\", \"irj\\nomi\\n\", \"bddff\\nbbbca\\n\", \"reddht\\nbedcfb\\n\", \"bbxy\\nbaab\\n\", \"xxyxvx\\nxxzxxx\\n\", \"ffnjnht\\nzscoder\\n\", \"irj\\nmoi\\n\", \"rddeht\\nbedcfb\\n\", \"bbxx\\nbaab\\n\", \"xvxyxx\\nxxzxxx\\n\", \"ffnjnht\\nzscoeer\\n\", \"irj\\niom\\n\", \"rddeht\\nbfcdeb\\n\", \"xvxyxx\\nxxzxxw\\n\", \"ffnhnjt\\nzscoeer\\n\", \"ijr\\niom\\n\", \"ffedc\\nbbbca\\n\", \"hddert\\nbfcdeb\\n\", \"aaxx\\nbaab\\n\", \"tjnhnff\\nzscoeer\\n\", \"ijr\\njom\\n\", \"hddert\\nbfbdeb\\n\", \"xaxa\\nbaab\\n\", \"tjnhnff\\nzseocer\\n\", \"jir\\njom\\n\", \"ffedc\\nbbaba\\n\", \"treddh\\nbfbdeb\\n\", \"axax\\nbaab\\n\", \"tjnhnff\\nzseober\\n\", \"ffedc\\nbbbbb\\n\", \"tjnhnff\\nreboesz\\n\"], \"outputs\": [\"xxxxxx\\n\", \"fzfsirk\\n\", \"ioi\\n\", \"bccdb\\n\", \"z\\n\", \"dfdeed\\n\", \"aab\\n\", \"y\\n\", \"abac\\n\", \"bccdb\", \"dfdeed\", \"aab\", \"abab\", \"wxxxxx\", \"fzgsirk\", \"ioj\", \"bdcdb\", \"bbab\", \"wyxxxx\", \"fzgshrk\", \"bbbb\", \"wzxxxx\", \"fzfshrk\", \"vzxxxx\", \"fzfshrj\", \"ccdbd\", \"ccdbe\", \"abbb\", \"vzxyxx\", \"cbdbe\", \"vzxyxy\", \"joj\", \"cfdeed\", \"abaa\", \"jnj\", \"dfdeed\", \"ioj\", \"bdcdb\", \"dfdeed\", \"bbab\", \"wyxxxx\", \"fzgshrk\", \"ioj\", \"bdcdb\", \"dfdeed\", \"ioj\", \"bdcdb\", \"dfdeed\", \"bbbb\", \"ioj\", \"bdcdb\", \"dfdeed\", \"bbbb\", \"vzxxxx\", \"fzfshrj\", \"ioj\", \"dfdeed\", \"bbbb\", \"vzxxxx\", \"fzfshrj\", \"ioj\", \"dfdeed\", \"vzxxxx\", \"fzfshrj\", \"ioj\", \"ccdbe\", \"dfdeed\", \"abab\", \"fzfshrj\", \"ioj\", \"dfdeed\", \"abab\", \"fzfshrj\", \"ioj\", \"cbdbe\", \"dfdeed\", \"abab\", \"fzfshrj\", \"cbdbe\", \"fzfshrj\"]}", "source": "primeintellect"}
|
Oleg the client and Igor the analyst are good friends. However, sometimes they argue over little things. Recently, they started a new company, but they are having trouble finding a name for the company.
To settle this problem, they've decided to play a game. The company name will consist of n letters. Oleg and Igor each have a set of n letters (which might contain multiple copies of the same letter, the sets can be different). Initially, the company name is denoted by n question marks. Oleg and Igor takes turns to play the game, Oleg moves first. In each turn, a player can choose one of the letters c in his set and replace any of the question marks with c. Then, a copy of the letter c is removed from his set. The game ends when all the question marks has been replaced by some letter.
For example, suppose Oleg has the set of letters {i, o, i} and Igor has the set of letters {i, m, o}. One possible game is as follows :
Initially, the company name is ???.
Oleg replaces the second question mark with 'i'. The company name becomes ?i?. The set of letters Oleg have now is {i, o}.
Igor replaces the third question mark with 'o'. The company name becomes ?io. The set of letters Igor have now is {i, m}.
Finally, Oleg replaces the first question mark with 'o'. The company name becomes oio. The set of letters Oleg have now is {i}.
In the end, the company name is oio.
Oleg wants the company name to be as lexicographically small as possible while Igor wants the company name to be as lexicographically large as possible. What will be the company name if Oleg and Igor always play optimally?
A string s = s1s2...sm is called lexicographically smaller than a string t = t1t2...tm (where s ≠ t) if si < ti where i is the smallest index such that si ≠ ti. (so sj = tj for all j < i)
Input
The first line of input contains a string s of length n (1 ≤ n ≤ 3·105). All characters of the string are lowercase English letters. This string denotes the set of letters Oleg has initially.
The second line of input contains a string t of length n. All characters of the string are lowercase English letters. This string denotes the set of letters Igor has initially.
Output
The output should contain a string of n lowercase English letters, denoting the company name if Oleg and Igor plays optimally.
Examples
Input
tinkoff
zscoder
Output
fzfsirk
Input
xxxxxx
xxxxxx
Output
xxxxxx
Input
ioi
imo
Output
ioi
Note
One way to play optimally in the first sample is as follows :
* Initially, the company name is ???????.
* Oleg replaces the first question mark with 'f'. The company name becomes f??????.
* Igor replaces the second question mark with 'z'. The company name becomes fz?????.
* Oleg replaces the third question mark with 'f'. The company name becomes fzf????.
* Igor replaces the fourth question mark with 's'. The company name becomes fzfs???.
* Oleg replaces the fifth question mark with 'i'. The company name becomes fzfsi??.
* Igor replaces the sixth question mark with 'r'. The company name becomes fzfsir?.
* Oleg replaces the seventh question mark with 'k'. The company name becomes fzfsirk.
For the second sample, no matter how they play, the company name will always be xxxxxx.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4\\n3 7 5 2\\n\", \"5\\n3 6 9 12 15\\n\", \"6\\n58376259 643910770 5887448 757703054 544067926 902981667\\n\", \"5\\n585325539 365329221 412106895 291882089 564718673\\n\", \"7\\n941492387 72235422 449924898 783332532 378192988 592684636 147499872\\n\", \"1\\n1\\n\", \"16\\n985629174 189232688 48695377 692426437 952164554 243460498 173956955 210310239 237322183 96515847 678847559 682240199 498792552 208770488 736004147 176573082\\n\", \"1\\n1000000000\\n\", \"19\\n519879446 764655030 680293934 914539062 744988123 317088317 653721289 239862203 605157354 943428394 261437390 821695238 312192823 432992892 547139308 408916833 829654733 223751525 672158759\\n\", \"17\\n458679894 912524637 347508634 863280107 226481104 787939275 48953130 553494227 458256339 673787326 353107999 298575751 436592642 233596921 957974470 254020999 707869688\\n\", \"2\\n500000004 500000003\\n\", \"4\\n702209411 496813081 673102149 561219907\\n\", \"18\\n341796022 486073481 86513380 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\"7\\n909477052 72235422 491411672 508549203 614166628 836405597 147499872\\n\", \"16\\n999398008 189232688 48695377 692426437 632347651 84418761 79338975 210310239 237322183 96515847 678847559 682240199 498792552 208770488 197289383 263328967\\n\", \"2\\n402863513 30174005\\n\", \"4\\n323946631 44343710 673102149 502163887\\n\", \"3\\n31553688 1068026867 1004891379\\n\", \"4\\n6 2 1 0\\n\", \"5\\n364246207 365329221 405727045 386979084 938186731\\n\", \"7\\n909477052 72235422 491411672 875801315 614166628 836405597 147499872\\n\", \"16\\n999398008 189232688 48695377 692426437 632347651 84418761 79338975 210310239 237322183 96515847 678847559 682240199 498792552 286178843 197289383 263328967\\n\", \"2\\n402863513 22591375\\n\", \"4\\n323946631 44343710 673102149 823893227\\n\", \"5\\n3 6 9 7 23\\n\", \"4\\n6 7 2 0\\n\", \"4\\n6 7 3 0\\n\", \"5\\n364246207 365329221 337523407 386979084 938186731\\n\", \"5\\n5 6 17 0 39\\n\"], \"outputs\": [\"\\n1000000006\\n\", \"\\n36\\n\", \"\\n676517605\\n\", \"\\n974257995\\n\", \"\\n328894634\\n\", \"\\n1\\n\", \"\\n347261016\\n\", \"\\n1000000000\\n\", \"\\n265109293\\n\", \"\\n769845668\\n\", \"\\n0\\n\", \"\\n317278572\\n\", \"\\n773499683\\n\", \"\\n996365563\\n\", \"398120187\\n\", \"715219974\\n\", \"2\\n\", \"631106102\\n\", \"319418291\\n\", \"907728994\\n\", \"62357268\\n\", \"39410582\\n\", \"722101345\\n\", \"1\\n\", \"44\\n\", \"248953211\\n\", \"616086665\\n\", \"4\\n\", \"319476823\\n\", \"902863516\\n\", \"27035989\\n\", \"304886733\\n\", \"1000000005\\n\", \"682893929\\n\", \"717203247\\n\", \"8\\n\", \"232720938\\n\", \"197915687\\n\", \"506377213\\n\", \"380040553\\n\", \"46\\n\", \"604011687\\n\", \"481229607\\n\", \"0\\n\", \"572597394\\n\", \"433712313\\n\", \"514826639\\n\", \"229529046\\n\", \"62\\n\", \"977479745\\n\", \"449214272\\n\", \"33882630\\n\", \"422228640\\n\", \"828803963\\n\", \"873190783\\n\", \"7\\n\", \"78\\n\", \"490701046\\n\", \"47651464\\n\", \"433037518\\n\", \"450541183\\n\", \"162716036\\n\", \"5\\n\", \"113887014\\n\", \"959709487\\n\", \"505792986\\n\", \"425454888\\n\", \"128811843\\n\", \"44\\n\", \"1\\n\", \"2\\n\", \"977479745\\n\", \"78\\n\"]}", "source": "primeintellect"}
|
Karen has just arrived at school, and she has a math test today!
<image>
The test is about basic addition and subtraction. Unfortunately, the teachers were too busy writing tasks for Codeforces rounds, and had no time to make an actual test. So, they just put one question in the test that is worth all the points.
There are n integers written on a row. Karen must alternately add and subtract each pair of adjacent integers, and write down the sums or differences on the next row. She must repeat this process on the values on the next row, and so on, until only one integer remains. The first operation should be addition.
Note that, if she ended the previous row by adding the integers, she should start the next row by subtracting, and vice versa.
The teachers will simply look at the last integer, and then if it is correct, Karen gets a perfect score, otherwise, she gets a zero for the test.
Karen has studied well for this test, but she is scared that she might make a mistake somewhere and it will cause her final answer to be wrong. If the process is followed, what number can she expect to be written on the last row?
Since this number can be quite large, output only the non-negative remainder after dividing it by 109 + 7.
Input
The first line of input contains a single integer n (1 ≤ n ≤ 200000), the number of numbers written on the first row.
The next line contains n integers. Specifically, the i-th one among these is ai (1 ≤ ai ≤ 109), the i-th number on the first row.
Output
Output a single integer on a line by itself, the number on the final row after performing the process above.
Since this number can be quite large, print only the non-negative remainder after dividing it by 109 + 7.
Examples
Input
5
3 6 9 12 15
Output
36
Input
4
3 7 5 2
Output
1000000006
Note
In the first test case, the numbers written on the first row are 3, 6, 9, 12 and 15.
Karen performs the operations as follows:
<image>
The non-negative remainder after dividing the final number by 109 + 7 is still 36, so this is the correct output.
In the second test case, the numbers written on the first row are 3, 7, 5 and 2.
Karen performs the operations as follows:
<image>
The non-negative remainder after dividing the final number by 109 + 7 is 109 + 6, so this is the correct output.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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1\\nqb4crj 1\\n\", \"4\\n4 0\\n3 1\\n1 1\\n2 1\\n\", \"4\\n4 1\\n1 0\\n3 1\\nmod9zl 0\\n\", \"3\\n2 1\\n1 0\\n3 0\\n\", \"2\\n01 0\\n02 1\\n\", \"3\\n1 1\\n7ph5fw 1\\ntfxz1j 1\\n\", \"1\\nxzp9ni 1\\n\", \"1\\nsd84r7 1\\n\", \"2\\n1 0\\n2 1\\n\", \"6\\n1 1\\n3 0\\n2 1\\n6 1\\n4 0\\n5 0\\n\", \"3\\ngdm5ri 1\\n1 1\\n2 1\\n\", \"3\\ncxbbpd 1\\n3 1\\n1 1\\n\", \"2\\n1 1\\nvinxur 1\\n\", \"6\\n6slonw 1\\nptk9mc 1\\n57a4nq 0\\nhiq2f7 1\\n2 0\\nc0gtv3 0\\n\", \"5\\n3 1\\n5 0\\n4 1\\n1 1\\n2 0\\n\", \"3\\naf2f6j 1\\nmjni5l 1\\njvyxgc 1\\n\", \"5\\n1 0\\n4 1\\n3 0\\nlog9cm 1\\nu5m0ls 1\\n\", \"3\\n3 1\\n1 0\\n2 1\\n\", \"2\\n1 0\\n2 1\\n\", \"4\\n9f4aoa 1\\n4 0\\nf4m1ec 1\\nqyr2h6 1\\n\", \"4\\n2 0\\n3 0\\n1 1\\n4 1\\n\", \"5\\n5 1\\nz9zr7d 0\\ne8rwo4 1\\nrfpjp6 0\\ngz6dhj 0\\n\", \"2\\n2 0\\njkwekx 1\\n\", \"4\\nyi9ta0 1\\nmeljgm 0\\nf7bqon 0\\n5bbvun 0\\n\", \"3\\norwsz0 1\\nmbt097 1\\n3 1\\n\", \"4\\n0la3gu 0\\nzhrmyb 1\\n3iprc0 0\\n3 0\\n\", \"4\\n1wp56i 1\\n2 1\\n1 0\\n6m76jb 1\\n\", \"3\\n3 0\\n26mp5s 0\\n1 1\\n\", \"5\\n2 0\\n1 1\\nq4hyeg 1\\n5 0\\n4 1\\n\", \"5\\n5 0\\n4 0\\n5nvzu4 1\\nvkpzzk 1\\nzamzcz 1\\n\", \"4\\n4 0\\n1 0\\n2 0\\nizfotg 1\\n\", \"3\\n1 1\\n3 1\\n2 1\\n\", \"6\\n1 1\\n3 0\\n2 1\\n6 1\\n4 0\\n5 0\\n\", \"4\\n3 1\\n4 1\\n1 0\\n2 0\\n\", \"4\\nuilh9a 0\\n4lxxh9 1\\nkqdpzy 1\\nn1d7hd 1\\n\", \"1\\n1 1\\n\", \"3\\n3 1\\n1 0\\n2 1\\n\", \"5\\n3 1\\n4 0\\nejo0a4 1\\ngqzdbk 0\\n1 1\\n\", \"1\\n1 0\\n\", \"2\\n1qe46n 1\\n1 1\\n\", \"6\\n5 0\\n2 0\\ncbhvyf 1\\nl1z5mg 0\\nwkwhby 1\\nx7fdh9 1\\n\", \"2\\n1 0\\n2 1\\n\", \"6\\nc3py3h 0\\n2 1\\n4 0\\n3 0\\n1 1\\n5 1\\n\", \"4\\nkgw83p 0\\np3p3ch 0\\n4 1\\n0te9lv 0\\n\", \"5\\n5sbtul 1\\n2 1\\n8i2duz 0\\n5 1\\n4b85z6 0\\n\", \"3\\n3 1\\n1 0\\n2 1\\n\", \"2\\n1 0\\n2 0\\n\", \"2\\n1 1\\ng5jlzp 1\\n\", \"3\\nunw560 1\\n0iswxk 0\\ndonjp9 1\\n\", \"6\\nhmpfsz 1\\n6 0\\n5 1\\n4 0\\n1 0\\n3 1\\n\", \"4\\n4 1\\n1 1\\n3 1\\n2 0\\n\", \"2\\n1 0\\nxdkh5a 1\\n\", \"6\\n1 1\\n3 0\\n2 1\\n6 1\\n4 0\\n5 0\\n\", \"3\\n1 1\\nc9qyld 1\\n3 1\\n\", \"6\\n1t68ks 1\\npkbj1g 1\\n5 0\\n5pw8wm 1\\n1 0\\n4 0\\n\", \"2\\n1 0\\n2 1\\n\", \"3\\n2 1\\n1 0\\n3 0\\n\", \"5\\n73s1nt 1\\nsbngv2 0\\n4n3qri 1\\nbyhzp8 1\\nadpjs4 0\\n\", \"2\\n1 1\\n2 1\\n\", \"2\\n1 0\\n2 1\\n\", \"5\\n2 0\\n3 1\\n4 0\\n1 1\\n5 1\\n\", \"5\\n5 0\\nts7a1c 0\\n4 1\\n1 1\\n2 1\\n\", \"4\\n4 0\\npa613p 1\\nuuizq7 1\\n2 0\\n\", \"2\\n17dgbb 0\\n2 1\\n\", \"6\\np1wjw9 1\\nueksby 0\\nu1ixfc 1\\nj3lk2e 1\\n36iskv 0\\n9imqi1 0\\n\", \"2\\nkfsipl 0\\n1jj1ol 0\\n\", \"4\\n4 1\\nwgh8s0 1\\n1 0\\n2 1\\n\", \"3\\n2 1\\n1 0\\nomitxh 1\\n\", \"3\\n2 1\\n1 0\\n3 0\\n\", \"3\\n1 1\\nnwfzx2 1\\n7g8t6z 1\\n\", \"3\\nqmf7iz 1\\ndiwdce 1\\n1 1\\n\", \"6\\n4 1\\n410jiy 1\\n1 0\\n6 -1\\nxc98l2 1\\n5 0\\n\", \"3\\n2 1\\n3 0\\nhs9j9t 0\\n\", \"6\\n5 1\\n6 0\\nxhfzge 0\\n3 1\\n0 0\\n1n9mqv 1\\n\", \"3\\n3 1\\n1 0\\n4 1\\n\", \"5\\nw0g96a 1\\nv99tdj 0\\nmywrle 0\\nweh22w 1\\n9hywt4 0\\n\", \"6\\n5 1\\nuf6mdr 0\\n4 1\\noclx1h 0\\n7l3kg1 1\\nq25te0 0\\n\", \"3\\nbwo0pe 1\\nbt50pa 1\\n2tx68t 1\\n\", \"5\\n949pnr 1\\n9sxhcr 0\\n5 0\\nx8srx3 1\\ncl7ppd 1\\n\", \"5\\n3 1\\n5 0\\n4 1\\n2 1\\n2 0\\n\", \"4\\n3 0\\niipymv 1\\nvak5db 1\\n2ktczv 1\\n\", \"3\\nt0dfz3 0\\n5 0\\n1 1\\n\", \"3\\n1 1\\n1 0\\n2 1\\n\", \"3\\n2 0\\nuv8c54 2\\n508bb0 1\\n\", \"4\\n2 1\\n7 1\\n1 0\\n3 1\\n\", \"1\\nabbde7 1\\n\", \"3\\n2 1\\n3 2\\n1 1\\n\", \"4\\nhex0ur 1\\n2 1\\n3 0\\n2 1\\n\", \"4\\n2kk04q 0\\nkdktuk 1\\nc4i5k8 1\\nawaock 0\\n\", \"3\\n3 1\\n1 0\\n3 1\\n\", \"2\\n1 0\\n4 1\\n\", \"6\\n0zluka 0\\nqp7q8l 1\\nwglqu8 1\\n9i7kta 0\\nnwf3m8 0\\n3 1\\n\", \"3\\n3 1\\n1 0\\n2 2\\n\", \"3\\n2 1\\n1 0\\n5 0\\n\", \"4\\n1 0\\nsc7czx 0\\nfr4033 0\\n3 0\\n\", \"4\\n4 0\\n3 1\\n1 0\\n2 0\\n\", \"4\\n4i2i2a 0\\n4 1\\npf618n 1\\n6xlnmh 1\\n\", \"1\\nprzvln -1\\n\", \"4\\ny9144q -1\\n3 1\\n2 1\\ns0bdnf 0\\n\", \"5\\npuusew 1\\npvoy4h 0\\nwdzx4r 0\\n1z84cx 0\\nozsuvc 0\\n\", \"5\\no8gja7 1\\np7cqxy 1\\n3qrp34 0\\nh93m07 1\\n2 0\\n\", \"5\\n3 1\\n5 0\\n4 1\\n1 1\\n3 0\\n\", \"5\\n5 0\\n12qcjd 1\\nuthzbz 0\\nb3670z 0\\nl1u93o 1\\n\", \"5\\n4 1\\nhvrhea 0\\naio11n 0\\n2 1\\n3 1\\n\", \"4\\nwpteku 1\\n1 0\\n4 1\\n73xpqz 1\\n\", \"4\\n4 1\\n1 1\\n3 0\\n2 0\\n\", \"3\\nt4hdos 0\\ndhje0g 0\\n4 0\\n\"], \"outputs\": [\"4\\nmove 3 1\\nmove 01 3\\nmove 2extra 4\\nmove 99 5\\n\", \"3\\nmove 1 3\\nmove 2 1\\nmove 3 2\\n\", \"5\\nmove 1 3\\nmove 11 1\\nmove 111 4\\nmove 1111 2\\nmove 11111 5\\n\", \"2\\nmove zwfnx2 2\\nmove 7g8t6z 3\\n\", \"2\\nmove qmf7iz 2\\nmove djwdce 3\\n\", \"4\\nmove 4 2\\nmove 1 4\\nmove 410jiy 1\\nmove xc98l2 3\\n\", \"1\\nmove hs9j9t 1\\n\", \"4\\nmove 5 2\\nmove 1 4\\nmove 1n9mqv 1\\nmove xhfzge 5\\n\", \"3\\nmove 3 4\\nmove 1 3\\nmove 4 1\\n\", \"5\\nmove w0g96a 1\\nmove v99tdi 3\\nmove mywrle 4\\nmove weh22w 2\\nmove 9hywt4 5\\n\", \"6\\nmove 4 1\\nmove 5 2\\nmove 7l3kg1 3\\nmove oclx1h 4\\nmove q25te0 5\\nmove rdm6fu 6\\n\", \"3\\nmove bxo0pe 1\\nmove bt50pa 2\\nmove 2tx68t 3\\n\", \"5\\nmove 5 1\\nmove 949pnr 2\\nmove 9sxhcr 5\\nmove x8srx3 3\\nmove cl7ppd 4\\n\", \"3\\nmove 4 6\\nmove 2 4\\nmove 6 2\\n\", \"4\\nmove 3 4\\nmove iipymv 1\\nmove vakd5b 2\\nmove 2ktczv 3\\n\", \"1\\nmove t0dfz3 2\\n\", \"3\\nmove 3 4\\nmove 1 3\\nmove 4 1\\n\", \"3\\nmove 2 3\\nmove uv8c54 1\\nmove 508bb0 2\\n\", \"3\\nmove 4 5\\nmove 1 4\\nmove 5 1\\n\", \"1\\nmove abbdf7 1\\n\", \"0\\n\", \"3\\nmove 4 1\\nmove 3 4\\nmove hex0ur 3\\n\", \"4\\nmove 2kk04q 3\\nmove kdktvk 1\\nmove c4i5k8 2\\nmove awaock 4\\n\", \"3\\nmove 3 4\\nmove 1 3\\nmove 4 1\\n\", \"3\\nmove 1 3\\nmove 2 1\\nmove 3 2\\n\", \"5\\nmove qp7q8l 1\\nmove wglqu8 2\\nmove 0zluka 4\\nmove 9i7kta 5\\nmove nwf8m3 6\\n\", \"3\\nmove 3 4\\nmove 1 3\\nmove 4 1\\n\", \"3\\nmove 2 4\\nmove 1 2\\nmove 4 1\\n\", \"3\\nmove 1 2\\nmove fr4033 1\\nmove sc7czx 4\\n\", \"5\\nmove 1 5\\nmove 4 1\\nmove 2 4\\nmove 3 2\\nmove 5 3\\n\", \"4\\nmove 4 1\\nmove 4i2i2a 4\\nmove pf618n 2\\nmove lx6nmh 3\\n\", \"1\\nmove przvln 1\\n\", \"3\\nmove 3 1\\nmove s0bdnf 3\\nmove y9144q 4\\n\", \"5\\nmove puusew 1\\nmove pvoy4h 2\\nmove wdzx4r 3\\nmove 1z84cx 4\\nmove ozsuvd 5\\n\", \"5\\nmove 2 4\\nmove 7ajg8o 1\\nmove p7cqxy 2\\nmove 3qrp34 5\\nmove h93m07 3\\n\", \"3\\nmove 4 6\\nmove 2 4\\nmove 6 2\\n\", \"4\\nmove 12qcjd 1\\nmove uthzbz 3\\nmove b3670z 4\\nmove l2u93o 2\\n\", \"3\\nmove 4 1\\nmove aio11n 4\\nmove hvshea 5\\n\", \"4\\nmove 4 2\\nmove 1 4\\nmove 73xpqz 1\\nmove xpteku 3\\n\", \"3\\nmove 4 5\\nmove 2 4\\nmove 5 2\\n\", \"2\\nmove t4hdos 1\\nmove dhje0g 2\\n\", \"4\\nmove 4 1\\nmove u9do88 2\\nmove 787at9 3\\nmove fcud6k 4\\n\", \"6\\nmove 5 1\\nmove 2 4\\nmove 3 5\\nmove 6qb4ia 2\\nmove w9h0pv 3\\nmove q92z4i 6\\n\", \"3\\nmove 2 5\\nmove 4 2\\nmove 5 4\\n\", \"4\\nmove 2 3\\nmove mqbjos 4\\nmove 6mhijg 1\\nmove 6wum8y 2\\n\", \"4\\nmove 5 3\\nmove eik3kw 4\\nmove zoonoj 5\\nmove ivzfie 6\\n\", \"3\\nmove 4 2\\nmove 3 4\\nmove 2y4agr 3\\n\", \"3\\nmove 4 5\\nmove 2 4\\nmove 5 2\\n\", \"0\\n\", \"5\\nmove 4 1\\nmove 2 3\\nmove setddt 2\\nmove 5sn77g 4\\nmove bz16cb 5\\n\", \"4\\nmove 3 2\\nmove noidnv 3\\nmove x3xiiz 4\\nmove 1lfa9v 5\\n\", \"3\\nmove n3pmj8 2\\nmove 2alui6 3\\nmove e7lf4u 1\\n\", \"3\\nmove 1 2\\nmove 6a2egk 1\\nmove dr1lp8 3\\n\", \"5\\nmove 5 1\\nmove 3 4\\nmove wje9ts 2\\nmove kytn5q 3\\nmove 7frk8z 5\\n\", \"5\\nmove 1 5\\nmove 3 1\\nmove 2 3\\nmove 4 2\\nmove 5 4\\n\", \"3\\nmove 2x7a4g 1\\nmove 27lqe6 2\\nmove zfo3sp 3\\n\", \"3\\nmove 3 7\\nmove 6 3\\nmove 7 6\\n\", \"4\\nmove 3 4\\nmove q4b449 1\\nmove cjg1x2 2\\nmove e878er 3\\n\", \"2\\nmove iy1dq6 2\\nmove wy6i6o 4\\n\", \"3\\nmove 1 3\\nmove 2 1\\nmove 3 2\\n\", \"2\\nmove 2 4\\nmove g6ugrm 2\\n\", \"5\\nmove 1 5\\nmove 4 1\\nmove 2 4\\nmove 3 2\\nmove 5 3\\n\", \"4\\nmove 3 1\\nmove v04v6j 2\\nmove 1o0bp2 3\\nmove 9tn379 4\\n\", \"3\\nmove 2 5\\nmove 4 2\\nmove 5 4\\n\", \"3\\nmove 1 3\\nmove 2 1\\nmove 3 2\\n\", \"5\\nmove 1 4\\nmove 2 5\\nmove p2gcxf 1\\nmove wfyoiq 2\\nmove zjw3vg 3\\n\", \"3\\nmove 2 4\\nmove x2miqh 2\\nmove 1rq643 5\\n\", \"2\\nmove o9z069 1\\nmove 5hools 2\\n\", \"3\\nmove 2 6\\nmove 5 2\\nmove 6 5\\n\", \"16\\nmove 16 1\\nmove 18 2\\nmove 5 10\\nmove 6 12\\nmove 1pon1p 3\\nmove e14bkx 4\\nmove php8vy 5\\nmove sfms2u 6\\nmove d9stsx 13\\nmove f2548d 14\\nmove jvpwuo 15\\nmove keeona 16\\nmove sbklx4 18\\nmove wzf4eb 19\\nmove yszsig 20\\nmove yyf4q2 7\\n\", \"2\\nmove 4 2\\nmove d1cks2 4\\n\", \"1\\nmove t6kdte 1\\n\", \"3\\nmove 4 5\\nmove 2 4\\nmove 5 2\\n\", \"3\\nmove 4 5\\nmove 1 4\\nmove 5 1\\n\", \"3\\nmove 2 5\\nmove 4 2\\nmove 5 4\\n\", \"0\\n\", \"3\\nmove 4 5\\nmove 1 4\\nmove 5 1\\n\", \"2\\nmove joa6mr 1\\nmove 5xzjm4 2\\n\", \"3\\nmove z1nwrd 1\\nmove t0xrja 2\\nmove 106qy1 3\\n\", \"5\\nmove 1 5\\nmove 4 1\\nmove 2 4\\nmove 3 2\\nmove 5 3\\n\", \"3\\nmove 1 4\\nmove yumiqt 1\\nmove t19jus 2\\n\", \"2\\nmove 9afh0z 1\\nmove 0qcaht 2\\n\", \"3\\nmove 4 5\\nmove 1 4\\nmove 5 1\\n\", \"4\\nmove 1 4\\nmove y0wnwz 1\\nmove 0totai 2\\nmove ym8xwz 3\\n\", \"5\\nmove 5 3\\nmove 2 4\\nmove 6 2\\nmove 7igwk9 5\\nmove dx2yu0 6\\n\", \"3\\nmove 4 2\\nmove 3 4\\nmove 4soxj3 3\\n\", \"4\\nmove 1 4\\nmove 2 5\\nmove h015vv 1\\nmove 9w2keb 2\\n\", \"3\\nmove j9rnac 1\\nmove oetwfz 2\\nmove d6n3ww 3\\n\", \"3\\nmove r2qlj2 1\\nmove t8wf1y 2\\nmove igids8 3\\n\", \"0\\n\", \"2\\nmove yzzyab 1\\nmove 728oq0 2\\n\", \"3\\nmove 3 4\\nmove 1 3\\nmove 4 1\\n\", \"4\\nmove 1h3t85 1\\nmove rf2ikt 4\\nmove 3vhl6e 2\\nmove 5l3oka 6\\n\", \"2\\nmove vsyajx 3\\nmove 783b38 5\\n\", \"1\\nmove i19lnk 1\\n\", \"3\\nmove 4 2\\nmove m5nhux 4\\nmove ogvgi7 5\\n\", \"5\\nmove 1 5\\nmove 3 1\\nmove 2 3\\nmove 4 2\\nmove 5 4\\n\", \"2\\nmove 3 2\\nmove av5vex 3\\n\", \"4\\nmove ir7oz8 1\\nmove vj4v5t 2\\nmove kwkahb 3\\nmove j5s8o1 4\\n\", \"4\\nmove ynagvf 1\\nmove ojz4mm 2\\nmove dovec3 4\\nmove nc1jye 5\\n\", \"4\\nmove 1 2\\nmove 3 1\\nmove 3a5ad1 3\\nmove nj94jx 4\\n\", \"5\\nmove 5 3\\nmove 1 4\\nmove wrrcmu 1\\nmove 3r4wqz 5\\nmove p4tuyt 6\\n\", \"5\\nmove 1 5\\nmove 4 1\\nmove 2 4\\nmove 3 2\\nmove 5 3\\n\", \"3\\nmove 2 6\\nmove 5 2\\nmove 6 5\\n\", \"2\\nmove c8p28p 1\\nmove vk4gdf 3\\n\", \"2\\nmove qvw4ow 2\\nmove ne0ng9 4\\n\", \"1\\nmove 01 1\\n\", \"5\\nmove 1 5\\nmove 3 1\\nmove 2 3\\nmove 4 2\\nmove 5 4\\n\", \"0\\n\", \"4\\nmove 3 1\\nmove 2 3\\nmove 4 2\\nmove cvfl8i 4\\n\", \"2\\nmove dbif39 1\\nmove e8dkf8 2\\n\", \"3\\nmove 3 1\\nmove scrn8k 2\\nmove ycvm9s 3\\n\", \"5\\nmove 1 3\\nmove 2 4\\nmove 0jc7xb 1\\nmove 1m7l9s 5\\nmove 9xzkau 2\\n\", \"3\\nmove 2 6\\nmove 5 2\\nmove 6 5\\n\", \"3\\nmove 4 6\\nmove 2 4\\nmove 6 2\\n\", \"2\\nmove qy2kmc 1\\nmove qb4crj 2\\n\", \"0\\n\", \"4\\nmove 3 2\\nmove 1 3\\nmove 4 1\\nmove mod9zl 4\\n\", \"3\\nmove 2 4\\nmove 1 2\\nmove 4 1\\n\", \"2\\nmove 02 1\\nmove 01 2\\n\", \"2\\nmove 7ph5fw 2\\nmove tfxz1j 3\\n\", \"1\\nmove xzp9ni 1\\n\", \"1\\nmove sd84r7 1\\n\", \"3\\nmove 1 3\\nmove 2 1\\nmove 3 2\\n\", \"3\\nmove 3 7\\nmove 6 3\\nmove 7 6\\n\", \"1\\nmove gdm5ri 3\\n\", \"1\\nmove cxbbpd 2\\n\", \"1\\nmove vinxur 2\\n\", \"6\\nmove 2 4\\nmove 6slonw 1\\nmove ptk9mc 2\\nmove 57a4nq 5\\nmove hiq2f7 3\\nmove c0gtv3 6\\n\", \"3\\nmove 4 6\\nmove 2 4\\nmove 6 2\\n\", \"3\\nmove af2f6j 1\\nmove mjni5l 2\\nmove jvyxgc 3\\n\", \"5\\nmove 4 2\\nmove 1 4\\nmove 3 5\\nmove log9cm 1\\nmove u5m0ls 3\\n\", \"3\\nmove 3 4\\nmove 1 3\\nmove 4 1\\n\", \"3\\nmove 1 3\\nmove 2 1\\nmove 3 2\\n\", \"3\\nmove 9f4aoa 1\\nmove f4m1ec 2\\nmove qyr2h6 3\\n\", \"3\\nmove 2 5\\nmove 4 2\\nmove 5 4\\n\", \"5\\nmove 5 1\\nmove e8rwo4 2\\nmove gz6dhj 3\\nmove rfpjp6 4\\nmove z9zr7d 5\\n\", \"1\\nmove jkwekx 1\\n\", \"4\\nmove yi9ta0 1\\nmove meljgm 2\\nmove f7bqon 3\\nmove 5bbvun 4\\n\", \"2\\nmove orwsz0 1\\nmove mbt097 2\\n\", \"3\\nmove zhrmyb 1\\nmove 0la3gu 2\\nmove 3iprc0 4\\n\", \"3\\nmove 1 4\\nmove 1wp56i 1\\nmove 6m76jb 3\\n\", \"1\\nmove 26mp5s 2\\n\", \"3\\nmove 4 3\\nmove 2 4\\nmove q4hyeg 2\\n\", \"3\\nmove 5nvzu4 1\\nmove vkpzzk 2\\nmove zamzcz 3\\n\", \"2\\nmove 1 3\\nmove izfotg 1\\n\", \"0\\n\", \"3\\nmove 3 7\\nmove 6 3\\nmove 7 6\\n\", \"5\\nmove 1 5\\nmove 3 1\\nmove 2 3\\nmove 4 2\\nmove 5 4\\n\", \"4\\nmove uilh9a 4\\nmove 4lxxh9 1\\nmove kqdpzy 2\\nmove n1d7hd 3\\n\", \"0\\n\", \"3\\nmove 3 4\\nmove 1 3\\nmove 4 1\\n\", \"2\\nmove ejo0a4 2\\nmove gqzdbk 5\\n\", \"0\\n\", \"1\\nmove 1qe46n 2\\n\", \"5\\nmove 2 4\\nmove cbhvyf 1\\nmove l1z5mg 6\\nmove wkwhby 2\\nmove x7fdh9 3\\n\", \"3\\nmove 1 3\\nmove 2 1\\nmove 3 2\\n\", \"3\\nmove 3 6\\nmove 5 3\\nmove c3py3h 5\\n\", \"4\\nmove 4 1\\nmove kgw83p 2\\nmove p3p3ch 3\\nmove 0te9lv 4\\n\", \"4\\nmove 5 1\\nmove 5sbtul 3\\nmove 8i2duz 4\\nmove 4b85z6 5\\n\", \"3\\nmove 3 4\\nmove 1 3\\nmove 4 1\\n\", \"0\\n\", \"1\\nmove g5jlzp 2\\n\", \"3\\nmove donjp9 1\\nmove unw560 2\\nmove 0iswxk 3\\n\", \"3\\nmove 5 2\\nmove 1 5\\nmove hmpfsz 1\\n\", \"3\\nmove 4 5\\nmove 2 4\\nmove 5 2\\n\", \"2\\nmove 1 2\\nmove xdkh5a 1\\n\", \"3\\nmove 3 7\\nmove 6 3\\nmove 7 6\\n\", \"1\\nmove c9qyld 2\\n\", \"4\\nmove 1 6\\nmove 1t68ks 1\\nmove pkbj1g 2\\nmove 5pw8wm 3\\n\", \"3\\nmove 1 3\\nmove 2 1\\nmove 3 2\\n\", \"3\\nmove 2 4\\nmove 1 2\\nmove 4 1\\n\", \"5\\nmove 73s1nt 1\\nmove sbngv2 4\\nmove 4n3qri 2\\nmove byhzp8 3\\nmove adpjs4 5\\n\", \"0\\n\", \"3\\nmove 1 3\\nmove 2 1\\nmove 3 2\\n\", \"3\\nmove 2 6\\nmove 5 2\\nmove 6 5\\n\", \"2\\nmove 4 3\\nmove ts7a1c 4\\n\", \"3\\nmove 2 3\\nmove pa613p 1\\nmove uuizq7 2\\n\", \"2\\nmove 2 1\\nmove 17dgbb 2\\n\", \"6\\nmove p1wjw9 1\\nmove u1ixfc 2\\nmove j3lk2e 3\\nmove ueksby 4\\nmove 36iskv 5\\nmove 9imqi1 6\\n\", \"2\\nmove kfsipl 1\\nmove 1jj1ol 2\\n\", \"3\\nmove 4 3\\nmove 1 4\\nmove wgh8s0 1\\n\", \"2\\nmove 1 3\\nmove omitxh 1\\n\", \"3\\nmove 2 4\\nmove 1 2\\nmove 4 1\\n\", \"2\\nmove 7g8t6z 2\\nmove nwfzx2 3\\n\", \"2\\nmove diwdce 2\\nmove qmf7iz 3\\n\", \"4\\nmove 4 2\\nmove 1 4\\nmove 410jiy 1\\nmove xc98l2 3\\n\", \"2\\nmove 2 1\\nmove hs9j9t 2\\n\", \"4\\nmove 5 1\\nmove 1n9mqv 2\\nmove 0 4\\nmove xhfzge 5\\n\", \"3\\nmove 3 2\\nmove 1 3\\nmove 4 1\\n\", \"5\\nmove w0g96a 1\\nmove weh22w 2\\nmove 9hywt4 3\\nmove mywrle 4\\nmove v99tdj 5\\n\", \"6\\nmove 4 1\\nmove 5 2\\nmove 7l3kg1 3\\nmove oclx1h 4\\nmove q25te0 5\\nmove uf6mdr 6\\n\", \"3\\nmove 2tx68t 1\\nmove bt50pa 2\\nmove bwo0pe 3\\n\", \"4\\nmove 949pnr 1\\nmove cl7ppd 2\\nmove x8srx3 3\\nmove 9sxhcr 4\\n\", \"2\\nmove 4 1\\nmove 2 4\\n\", \"4\\nmove 3 4\\nmove 2ktczv 1\\nmove iipymv 2\\nmove vak5db 3\\n\", \"2\\nmove 5 2\\nmove t0dfz3 3\\n\", \"1\\nmove 1 3\\n\", \"2\\nmove 508bb0 1\\nmove uv8c54 3\\n\", \"2\\nmove 1 4\\nmove 7 1\\n\", \"1\\nmove abbde7 1\\n\", \"0\\n\", \"1\\nmove hex0ur 1\\n\", \"4\\nmove c4i5k8 1\\nmove kdktuk 2\\nmove 2kk04q 3\\nmove awaock 4\\n\", \"2\\nmove 1 2\\nmove 3 1\\n\", \"2\\nmove 1 2\\nmove 4 1\\n\", \"5\\nmove qp7q8l 1\\nmove wglqu8 2\\nmove 0zluka 4\\nmove 9i7kta 5\\nmove nwf3m8 6\\n\", \"3\\nmove 3 4\\nmove 1 3\\nmove 4 1\\n\", \"3\\nmove 1 3\\nmove 2 1\\nmove 5 2\\n\", \"2\\nmove fr4033 2\\nmove sc7czx 4\\n\", \"3\\nmove 3 5\\nmove 1 3\\nmove 5 1\\n\", \"4\\nmove 4 1\\nmove 6xlnmh 2\\nmove pf618n 3\\nmove 4i2i2a 4\\n\", \"1\\nmove przvln 1\\n\", \"3\\nmove 3 1\\nmove s0bdnf 3\\nmove y9144q 4\\n\", \"5\\nmove puusew 1\\nmove 1z84cx 2\\nmove ozsuvc 3\\nmove pvoy4h 4\\nmove wdzx4r 5\\n\", \"5\\nmove 2 4\\nmove h93m07 1\\nmove o8gja7 2\\nmove p7cqxy 3\\nmove 3qrp34 5\\n\", \"2\\nmove 4 2\\nmove 3 4\\n\", \"4\\nmove 12qcjd 1\\nmove l1u93o 2\\nmove b3670z 3\\nmove uthzbz 4\\n\", \"3\\nmove 4 1\\nmove aio11n 4\\nmove hvrhea 5\\n\", \"4\\nmove 4 2\\nmove 1 4\\nmove 73xpqz 1\\nmove wpteku 3\\n\", \"3\\nmove 4 5\\nmove 2 4\\nmove 5 2\\n\", \"3\\nmove 4 1\\nmove dhje0g 2\\nmove t4hdos 3\\n\"]}", "source": "primeintellect"}
|
The All-Berland National Olympiad in Informatics has just ended! Now Vladimir wants to upload the contest from the Olympiad as a gym to a popular Codehorses website.
Unfortunately, the archive with Olympiad's data is a mess. For example, the files with tests are named arbitrary without any logic.
Vladimir wants to rename the files with tests so that their names are distinct integers starting from 1 without any gaps, namely, "1", "2", ..., "n', where n is the total number of tests.
Some of the files contain tests from statements (examples), while others contain regular tests. It is possible that there are no examples, and it is possible that all tests are examples. Vladimir wants to rename the files so that the examples are the first several tests, all all the next files contain regular tests only.
The only operation Vladimir can perform is the "move" command. Vladimir wants to write a script file, each of the lines in which is "move file_1 file_2", that means that the file "file_1" is to be renamed to "file_2". If there is a file "file_2" at the moment of this line being run, then this file is to be rewritten. After the line "move file_1 file_2" the file "file_1" doesn't exist, but there is a file "file_2" with content equal to the content of "file_1" before the "move" command.
Help Vladimir to write the script file with the minimum possible number of lines so that after this script is run:
* all examples are the first several tests having filenames "1", "2", ..., "e", where e is the total number of examples;
* all other files contain regular tests with filenames "e + 1", "e + 2", ..., "n", where n is the total number of all tests.
Input
The first line contains single integer n (1 ≤ n ≤ 105) — the number of files with tests.
n lines follow, each describing a file with test. Each line has a form of "name_i type_i", where "name_i" is the filename, and "type_i" equals "1", if the i-th file contains an example test, and "0" if it contains a regular test. Filenames of each file are strings of digits and small English letters with length from 1 to 6 characters. The filenames are guaranteed to be distinct.
Output
In the first line print the minimum number of lines in Vladimir's script file.
After that print the script file, each line should be "move file_1 file_2", where "file_1" is an existing at the moment of this line being run filename, and "file_2" — is a string of digits and small English letters with length from 1 to 6.
Examples
Input
5
01 0
2 1
2extra 0
3 1
99 0
Output
4
move 3 1
move 01 5
move 2extra 4
move 99 3
Input
2
1 0
2 1
Output
3
move 1 3
move 2 1
move 3 2
Input
5
1 0
11 1
111 0
1111 1
11111 0
Output
5
move 1 5
move 11 1
move 1111 2
move 111 4
move 11111 3
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"tictictactac\\n\", \"bbaabaabbb\\n\", \"technocup\\n\", \"fabbbhgedd\\n\", \"abbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaab\\n\", \"hcdhgcchbdhbeagdcfedgcbaffebgcbcccadeefacbhefgeadfgchabgeebegahfgegahbddedfhffeadcedadgfbeebhgfahhfb\\n\", \"khjcoijiicdkdianmdolmadobdkcmgifdnffddnjehhbldlkjffknficdcmokfacioiegjedbmadjioomdacbodcajcmonmnlabo\\n\", \"bababbdaee\\n\", \"cbbbbcaaca\\n\", \"gaejllebhn\\n\", \"eaaebccaeacdecaedcaabbbdeebccdcdaabeeaeeaddbaabdccebecebbbbedbdcbbbbbbecbaddcddcccdcbbadbecddecedbba\\n\", \"difhjdjbcdjedhiegagdejkbjfcdcdagdijdjajecbheiabfbjdgjdecfhdkgdbkcgcgakkiiggfkgcfadkjhiijkjacgejfhjge\\n\", \"bbababaaababaabbbbbabbbbbbaaabbabaaaaabbbbbaaaabbbbabaabaabababbbabbabbabaaababbabbababaaaaabaaaabbb\\n\", \"cadbcdddda\\n\", \"kpsaloedscghjeaqadfhmlibjepjafdomkkorinrpakondtnrnknbqarbejcenrlsbfgdbsdmkpphbkdnbitjfcofsjibssmmlll\\n\", \"aaabbbaaaabbbbaaabbbbbaabbbbaaababbaaabbbbaaabbbbababbbbaaabbbbaaabbbbbaabbbbaaabbbbaaabbbb\\n\", \"ibledofnibedebifmnjdoaijeghajecbkjaebbkofnacceaodiifbhgkihkibddneeiemacodeafeaiiiaoajhmkjffbmmiehebhokfklhbkeoanoajdedjdlkbhenidclagggfhhhldfleccgmjbkhaginlhabkabagikalccndciokabfaebjkndf\\n\", \"abbacba\\n\", \"jkeaagakbifeaechkifkdghcjcgighidcgdccfbdbcackfgaebkddabgijkhjkaffkabacekdkjekeccegbecbkecbgbgcacgdackcdfjefaifgbigahkbedidfhjbikejdhejcgideaeejdcegeeccaefbddejkbdkfagfcdjbikbidfggkidcdcic\\n\", \"faabbhgedd\\n\", \"abbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbbaababbaaab\\n\", \"hcdhgdchbdhbeagdcfedgcbaffebgcbcccadeefacbhefgeadfgchabgeebegahfgegahbddedfhffeadcedadgfbeebhgfahhfb\\n\", \"khjcoijiicdkdianmdolmadobdkcmgifdnffdcnjehhbldlkjffknficdcmokfacioiegjedbmadjioomdacbodcajcmonmnlabo\\n\", \"bcbbbcaaca\\n\", \"abbdeceddcebdabbcdcccddcddabcebbbbbbcdbdebbbbecebeccdbaabddaeeaeebaadcdccbeedbbbaacdeacedcaeaccbeaae\\n\", \"egjhfjegcajkjiihjkdafcgkfggiikkagcgckbdgkdhfcedjgdjbfbaiehbcejajdjidgadcdcfjbkjedgageihdejdcbjdjhfid\\n\", \"bbababaaababaabbbbbabbbbbbaaabbabaaaaabbbbbaaaabbbbabaabaabababbbabbabbabaaababbabbababaabaabaaaabbb\\n\", \"ibledofnibedebifmnjdoaijeghajecbkjaebbkofnacceaodiifbhgkihkibddneeiemacodeafeaiiiaoajhmkjffbmmiehebhokfklhbkeoanoajdedjdlkbhenidclagggfhhhldfleccgmjbkhaginlhabkabagikalccndcjokabfaebjkndf\\n\", \"jkeaagakbifeaechkifkdghcjcgighidcgdccgbdbcackfgaebkddabgijkhjkaffkabacekdkjekeccegbecbkecbgbgcacgdackcdfjefaifgbigahkbedidfhjbikejdhejcgideaeejdcefeeccaefbddejkbdkfagfcdjbikbidfggkidcdcic\\n\", \"catcatcitcit\\n\", \"bbbaabaabb\\n\", \"egjhfjegcajkjiihjkdafcgkfggiikkagcgckbcgkdhfcedjgdjbfbaiehbcejajdjidgadcdcfjbkjedgageihdejdcbjdjhfid\\n\", \"abcabbb\\n\", \"jkeaagakbifeaechkifkdghcjcgighidcgdccgbdbcackfgaebkddabgijkhjkaffkacacekdkjekeccegbecbkecbgbgcacgdackcdfjefaifgbigahkbedidfhjbikejdhejcgideaeejdcefeeccaefbddejkbdkfagfbdjbikbidfggkidcdcic\\n\", \"batcatcitcit\\n\", \"obalnmnomcjacdobcadmooijdambdejgeioicafjomcdcifnkffjkldlbhhejncdffndfigmckdbodamlodmnaidkdciijiocjhk\\n\", \"dgjhfjegcajkjiihjkdafcgkfggiikkagcgckbcgkdhfcedjgdjbfbaiehbcejajdjidgadcdcfjbkjedgageihdejdcbjdjhfid\\n\", \"cbbbababbbbaaabbbbaabbabbaaabbbbaaabbbbababbbbaaabbbbaaabbabaaabbbbaabbbbbaaabbbbaaaabbbaaa\\n\", \"ibledofnibedebifmnjdoaijeghajecbkjaebbkofnacceaodiifbhgkihkibddneeiemacodeafeaiiiboajhmkjffbmmiehebhokfklhbkeoanoajdedjdlkbhenidclagggfhhhldfleccgmjbkhaginlhabkabagikalccndcjokabfaebjkndf\\n\", \"batcatciscit\\n\", \"eeadbbabab\\n\", \"nhbelljeag\\n\", \"addddcbdac\\n\", \"kpsaloedscghjeaqadfhmlibiepjafdomkkorinrpakondtnrnknbqarbejcenrlsbfgdbsdmkpphbkdnbitjfcofsjibssmmlll\\n\", \"aaabbbaaaabbbbaaabbbbbaabbbbaaababbaaabbbbaaabbbbababbbbaaabbbbaaabbabbaabbbbaaabbbbababbbb\\n\", \"abcabba\\n\", \"oechntcup\\n\", \"faagbhbedd\\n\", \"bfhhafghbeebfgdadecdaeffhfdeddbhagegfhagebeegbahcgfdaegfehbcafeedacccbcgbeffabcgdefcdgaebhdbhcdghdch\\n\", \"obalnmnomcjacdobcadmooijdambdejgeioicafkomcdcifnkffjkldlbhhejncdffndfigmckdbodamlodmnaidkdciijiocjhk\\n\", \"eeadbaabab\\n\", \"acaacbbbcb\\n\", \"nhaelljeag\\n\", \"abbdeceddcebdabbcdcccddcddabcebbbbbbcdbdebbbbecebeccdbaabddaeebeebaadcdccbeedbabaacdeacedcaeaccbeaae\\n\", \"bbababaaababaabbbbbabbbbbbaaaababaaaaabbbbbaaaabbbbabaabaabababbbabbabbabaaababbabbababaabaabaaaabbb\\n\", \"addddbcdac\\n\", \"kpsaloedscghjeaqadfhmlibiepjafdomkkorinrpakondtnrnknaqarbejcenrlsbfgdbsdmkpphbkdnbitjfcofsjibssmmlll\\n\", \"bbbbababbbbaaabbbbaabbabbaaabbbbaaabbbbababbbbaaabbbbaaabbabaaabbbbaabbbbbaaabbbbaaaabbbaaa\\n\", \"fdnkjbeafbakojcdncclakigabakbahlnigahkbjmgccelfdlhhhfgggalcdinehbkldjdedjaonaoekbhlkfkohbeheimmbffjkmhjaoaiiiaefaedocameieenddbikhikghbfiidoaeccanfokbbeajkbcejahgejiaodjnmfibedebinfodelbi\\n\", \"bbbaabbabb\\n\", \"oehcntcup\\n\", \"faagbhbedc\\n\", \"hcdhgdchbdhbeagdcfedgcbaffebgcbcccadeefacbhefgeadfgchabgeebegahfgegahbddedfhffeadcedbdgfbeebhgfahhfb\\n\", \"edadbaabab\\n\", \"bcbabcaacb\\n\", \"niaelljeag\\n\", \"eaaebccaeacdecaedcaababdeebccdcdaabeebeeaddbaabdccebecebbbbedbdcbbbbbbecbaddcddcccdcbbadbecddecedbba\\n\", \"bbababaaababaabbbbbabbbbbbaaaababaaaaabbbbbaaaabbbbabaabbabaaabbbabbabbabaaababbabbababaabaabaaaabbb\\n\", \"adddebcdac\\n\", \"kpsaloedscghjeaqadfhmlibiepjafdomkkorinrpakondtnrnknaqarbejcenrlsbfgdbsdmkpphbkdnbiujfcofsjibssmmlll\\n\", \"bbbacba\\n\", \"jkeaagakbifeaechkifkcghcjcgighidcgdccgbdbcackfgaebkddabgijkhjkaffkacacekdkjekeccegbecbkecbgbgcacgdackcdfjefaifgbigahkbedidfhjbikejdhejcgideaeejdcefeeccaefbddejkbdkfagfbdjbikbidfggkidcdcic\\n\", \"bbbaabbaab\\n\", \"puctncheo\\n\", \"hcdhgdchbdhbeagdcfedgcbaffebgcbcccadeefadbhefgeadfgchabgeebegahfgegahbddedfhffeadcedbdgfbeebhgfahhfb\\n\", \"khjcoijiicdkdianmdolmadobdkcmgifdnffdcnjehhbldlkjffknficdcmojfacioiegjedbmadjioomdacbodcajcmonmnlabo\\n\", \"edadbaabbb\\n\", \"bcbcbaaacb\\n\", \"giaelljean\\n\"], \"outputs\": [\"0.333333333333333\\n\", \"0.100000000000000\\n\", \"1.000000000000000\\n\", \"1.000000000000000\\n\", \"0.000000000000000\\n\", \"0.450000000000000\\n\", \"0.960000000000000\\n\", \"1.000000000000000\\n\", \"0.800000000000000\\n\", \"1.000000000000000\\n\", \"0.080000000000000\\n\", \"0.840000000000000\\n\", \"0.000000000000000\\n\", \"0.800000000000000\\n\", \"1.000000000000000\\n\", \"0.000000000000000\\n\", \"0.786096256684492\\n\", \"1.000000000000000\\n\", \"0.438502673796791\\n\", \"1.0\\n\", \"0.02197802197802198\\n\", \"0.47\\n\", \"0.96\\n\", \"0.8\\n\", \"0.08\\n\", \"0.84\\n\", \"0.0\\n\", \"0.7807486631016043\\n\", \"0.44919786096256686\\n\", \"0.3333333333333333\\n\", \"0.1\\n\", \"0.82\\n\", \"0.7142857142857143\\n\", \"0.44385026737967914\\n\", \"0.5833333333333334\\n\", \"0.98\\n\", \"0.81\\n\", \"0.03296703296703297\\n\", \"0.7914438502673797\\n\", \"0.6666666666666666\\n\", \"1.0\\n\", \"1.0\\n\", \"0.8\\n\", \"1.0\\n\", \"0.0\\n\", \"1.0\\n\", \"1.0\\n\", \"1.0\\n\", \"0.47\\n\", \"0.96\\n\", \"1.0\\n\", \"0.8\\n\", \"1.0\\n\", \"0.08\\n\", \"0.0\\n\", \"0.8\\n\", \"1.0\\n\", \"0.0\\n\", \"0.7807486631016043\\n\", \"0.1\\n\", \"1.0\\n\", \"1.0\\n\", \"0.47\\n\", \"1.0\\n\", \"0.8\\n\", \"1.0\\n\", \"0.08\\n\", \"0.0\\n\", \"1.0\\n\", \"1.0\\n\", \"0.7142857142857143\\n\", \"0.44385026737967914\\n\", \"0.1\\n\", \"1.0\\n\", \"0.47\\n\", \"0.98\\n\", \"1.0\\n\", \"0.8\\n\", \"1.0\\n\"]}", "source": "primeintellect"}
|
Vasya and Kolya play a game with a string, using the following rules. Initially, Kolya creates a string s, consisting of small English letters, and uniformly at random chooses an integer k from a segment [0, len(s) - 1]. He tells Vasya this string s, and then shifts it k letters to the left, i. e. creates a new string t = sk + 1sk + 2... sns1s2... sk. Vasya does not know the integer k nor the string t, but he wants to guess the integer k. To do this, he asks Kolya to tell him the first letter of the new string, and then, after he sees it, open one more letter on some position, which Vasya can choose.
Vasya understands, that he can't guarantee that he will win, but he wants to know the probability of winning, if he plays optimally. He wants you to compute this probability.
Note that Vasya wants to know the value of k uniquely, it means, that if there are at least two cyclic shifts of s that fit the information Vasya knowns, Vasya loses. Of course, at any moment of the game Vasya wants to maximize the probability of his win.
Input
The only string contains the string s of length l (3 ≤ l ≤ 5000), consisting of small English letters only.
Output
Print the only number — the answer for the problem. You answer is considered correct, if its absolute or relative error does not exceed 10 - 6.
Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>
Examples
Input
technocup
Output
1.000000000000000
Input
tictictactac
Output
0.333333333333333
Input
bbaabaabbb
Output
0.100000000000000
Note
In the first example Vasya can always open the second letter after opening the first letter, and the cyclic shift is always determined uniquely.
In the second example if the first opened letter of t is "t" or "c", then Vasya can't guess the shift by opening only one other letter. On the other hand, if the first letter is "i" or "a", then he can open the fourth letter and determine the shift uniquely.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"8 3\\n4 5 7 8 3 1 2 6\", \"5 1\\n5 4 3 2 1\", \"4 2\\n4 2 3 1\", \"4 4\\n4 2 3 1\", \"5 2\\n5 4 3 2 1\", \"4 1\\n4 2 3 1\", \"8 2\\n4 5 7 8 3 1 2 6\", \"4 2\\n4 3 2 1\", \"8 6\\n4 5 7 8 3 1 2 6\", \"8 5\\n4 5 7 8 3 1 2 6\", \"8 1\\n4 5 7 8 3 1 2 6\", \"8 4\\n4 5 7 8 3 1 2 6\", \"4 3\\n4 1 3 2\", \"5 4\\n4 5 3 2 1\", \"4 2\\n4 1 3 2\", \"4 3\\n3 2 4 1\", \"4 3\\n4 2 3 1\", \"4 5\\n4 2 3 1\", \"5 4\\n5 4 3 2 1\", \"4 10\\n4 2 3 1\", \"4 11\\n4 2 3 1\", \"4 13\\n4 2 3 1\", \"4 12\\n4 2 3 1\", \"4 21\\n4 2 3 1\", \"4 16\\n4 2 3 1\", \"4 34\\n4 2 3 1\", \"4 24\\n4 2 3 1\", \"4 47\\n4 2 3 1\", \"4 27\\n4 2 3 1\", \"5 5\\n5 4 3 2 1\", \"4 36\\n4 2 3 1\", \"4 19\\n4 2 3 1\", \"5 3\\n5 4 3 2 1\", \"4 8\\n4 2 3 1\", \"4 65\\n4 2 3 1\", \"4 6\\n4 2 3 1\", \"4 39\\n4 2 3 1\", \"4 43\\n4 2 3 1\", \"8 7\\n4 5 7 8 3 1 2 6\", \"4 45\\n4 2 3 1\", \"4 83\\n4 2 3 1\", \"4 48\\n4 2 3 1\", \"4 30\\n4 2 3 1\", \"4 63\\n4 2 3 1\", \"4 17\\n4 2 3 1\", \"4 4\\n4 3 2 1\", \"4 15\\n4 2 3 1\", \"4 33\\n4 2 3 1\", \"4 4\\n4 1 3 2\", \"4 9\\n4 2 3 1\", \"4 25\\n4 2 3 1\", \"4 28\\n4 2 3 1\", \"4 7\\n4 2 3 1\", \"8 9\\n4 5 7 8 3 1 2 6\", \"4 71\\n4 2 3 1\", \"4 20\\n4 2 3 1\", \"4 134\\n4 2 3 1\", \"4 35\\n4 2 3 1\", \"4 23\\n4 2 3 1\", \"4 5\\n4 1 3 2\", \"4 3\\n4 3 2 1\", \"4 234\\n4 2 3 1\", \"5 5\\n4 5 3 2 1\", \"4 5\\n4 3 2 1\", \"4 50\\n4 2 3 1\", \"4 89\\n4 2 3 1\", \"4 59\\n4 2 3 1\", \"4 61\\n4 2 3 1\", \"4 130\\n4 2 3 1\", \"4 22\\n4 2 3 1\", \"4 32\\n4 2 3 1\", \"4 14\\n4 2 3 1\", \"4 18\\n4 2 3 1\", \"4 6\\n4 3 2 1\", \"4 56\\n4 2 3 1\", \"4 1\\n4 1 3 2\", \"4 272\\n4 2 3 1\", \"4 79\\n4 2 3 1\", \"4 60\\n4 2 3 1\", \"4 31\\n4 2 3 1\", \"4 70\\n4 2 3 1\", \"4 123\\n4 2 3 1\", \"4 95\\n4 2 3 1\", \"4 7\\n4 3 2 1\", \"4 74\\n4 2 3 1\", \"4 29\\n4 2 3 1\", \"4 133\\n4 2 3 1\", \"4 4\\n3 2 4 1\", \"4 41\\n4 2 3 1\", \"4 178\\n4 2 3 1\", \"4 101\\n4 2 3 1\", \"4 1\\n4 2 3 1\", \"4 3\\n4 2 3 1\", \"4 5\\n4 2 3 1\", \"4 9\\n4 2 3 1\", \"4 7\\n4 2 3 1\", \"4 18\\n4 2 3 1\", \"4 6\\n4 2 3 1\", \"5 2\\n5 4 3 2 1\", \"4 8\\n4 2 3 1\", \"4 11\\n4 2 3 1\", \"4 10\\n4 2 3 1\", \"4 14\\n4 2 3 1\"], \"outputs\": [\"1\\n2\\n6\\n7\\n5\\n3\\n4\\n8\", \"1\\n2\\n3\\n4\\n5\", \"2\\n1\\n4\\n3\", \"4\\n2\\n3\\n1\\n\", \"5\\n4\\n3\\n2\\n1\\n\", \"1\\n2\\n3\\n4\\n\", \"1\\n2\\n3\\n6\\n5\\n4\\n7\\n8\\n\", \"4\\n3\\n2\\n1\\n\", \"4\\n5\\n7\\n8\\n3\\n1\\n2\\n6\\n\", \"4\\n5\\n6\\n8\\n3\\n1\\n2\\n7\\n\", \"1\\n2\\n3\\n4\\n5\\n6\\n7\\n8\\n\", \"1\\n5\\n6\\n7\\n4\\n2\\n3\\n8\\n\", \"4\\n1\\n3\\n2\\n\", \"4\\n5\\n3\\n2\\n1\\n\", \"2\\n1\\n4\\n3\\n\", \"3\\n2\\n4\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"5\\n4\\n3\\n2\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"5\\n4\\n3\\n2\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"5\\n4\\n3\\n2\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n5\\n7\\n8\\n3\\n1\\n2\\n6\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n3\\n2\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n1\\n3\\n2\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n5\\n7\\n8\\n3\\n1\\n2\\n6\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n1\\n3\\n2\\n\", \"4\\n3\\n2\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n5\\n3\\n2\\n1\\n\", \"4\\n3\\n2\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n3\\n2\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"1\\n2\\n3\\n4\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n3\\n2\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"3\\n2\\n4\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"1\\n2\\n3\\n4\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"5\\n4\\n3\\n2\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\", \"4\\n2\\n3\\n1\\n\"]}", "source": "primeintellect"}
|
You are given a permutation P_1 ... P_N of the set {1, 2, ..., N}.
You can apply the following operation to this permutation, any number of times (possibly zero):
* Choose two indices i,j (1 ≦ i < j ≦ N), such that j - i ≧ K and |P_i - P_j| = 1. Then, swap the values of P_i and P_j.
Among all permutations that can be obtained by applying this operation to the given permutation, find the lexicographically smallest one.
Constraints
* 2≦N≦500,000
* 1≦K≦N-1
* P is a permutation of the set {1, 2, ..., N}.
Input
The input is given from Standard Input in the following format:
N K
P_1 P_2 ... P_N
Output
Print the lexicographically smallest permutation that can be obtained.
Examples
Input
4 2
4 2 3 1
Output
2
1
4
3
Input
5 1
5 4 3 2 1
Output
1
2
3
4
5
Input
8 3
4 5 7 8 3 1 2 6
Output
1
2
6
7
5
3
4
8
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 6\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 14\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 22\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 6\\n90 11\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 0\\n5 2\\n0 1 1 90 30 22\\n-3 0\\n3 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 21\\n90 6\\n55 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 0\\n1 3\\n0 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 3\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 21\\n90 6\\n179 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n1 1\\n1 2\\n4 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n142 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 21\\n133 6\\n55 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n4 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 10 45\\n-3 0\\n2 -2\\n16 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 15\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 21\\n133 6\\n55 6\\n2 1\\n1 1\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n4 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 9\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 10 45\\n-2 0\\n2 -2\\n16 6\\n0 0\", \"6 3\\n1 1\\n1 3\\n4 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n151 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 9 45\\n-3 0\\n2 -2\\n3 7\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 6\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 -1\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-2 0\\n2 -2\\n45 6\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n4 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 6\\n90 11\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 2\\n3 -4\\n-3 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 113 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n83 11\\n90 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 32 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 0\\n4 2\\n0 1 1 90 30 22\\n-3 0\\n3 -4\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n2 4\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n4 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 1\\n5 2\\n0 1 1 90 30 15\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 3\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 21\\n90 6\\n55 6\\n2 1\\n1 3\\n7 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n0 2\\n5 3\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 21\\n90 6\\n179 6\\n2 1\\n1 3\\n1 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n31 21\\n133 6\\n55 6\\n2 1\\n1 1\\n5 2\\n0 1 1 113 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 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-4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 14\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 59 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 22\\n-3 0\\n3 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 14\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 4\\n0 1 1 90 59 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 3\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 0\\n5 2\\n0 1 1 90 30 22\\n-3 0\\n3 -4\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 3\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n4 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 0\\n5 2\\n0 1 1 90 5 22\\n-3 0\\n3 -4\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n1 1\\n1 2\\n4 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n10 6\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 0\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 1\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n0 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 22\\n-3 0\\n2 -2\\n37 2\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 1\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 14\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 4\\n0 1 1 90 59 45\\n-4 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 -1\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 0\\n4 2\\n0 1 1 90 30 22\\n-3 0\\n3 -4\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 3\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 1 45\\n3 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n4 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 10 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 40\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 40\\n-3 1\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n2 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n0 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 4\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 22\\n-3 0\\n2 -2\\n37 2\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 14\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n143 6\\n135 6\\n2 1\\n1 3\\n5 4\\n0 1 1 90 59 45\\n-4 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 0\\n4 2\\n0 1 1 90 30 13\\n-3 0\\n3 -4\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 0\\n5 3\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 1 45\\n3 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n1 1\\n1 2\\n4 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n142 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 9 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 4\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 1\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 22\\n-3 0\\n2 -2\\n37 2\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 14\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n143 6\\n99 6\\n2 1\\n1 3\\n5 4\\n0 1 1 90 59 45\\n-4 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 0\\n5 3\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 1 45\\n3 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 6\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n4 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 10 45\\n-2 0\\n2 -2\\n16 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 4\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 15\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n1 1\\n1 3\\n4 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n142 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 9 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 4\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 1\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 22\\n-3 0\\n1 -2\\n37 2\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n2 4\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 15\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n1 1\\n1 3\\n4 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n151 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 9 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n2 4\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n4 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 15\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n1 1\\n1 3\\n4 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n151 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 9 45\\n-3 0\\n2 -2\\n37 7\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n2 4\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n4 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 8\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 156 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 39 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n3 2\\n0 1 1 90 30 22\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 53\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 0\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n58 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 22\\n-3 0\\n3 -1\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 14\\n3 -4\\n-3 0\\n0 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 4\\n0 1 1 90 59 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 0\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 0\\n5 2\\n0 1 1 90 30 22\\n-3 0\\n3 -4\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 3\\n1 2\\n1 2\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-4 0\\n2 -2\\n45 21\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 3\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 0\\n5 2\\n0 1 1 90 5 22\\n-3 0\\n3 -4\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n10 6\\n90 6\\n132 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 0\\n2 1\\n1 3\\n5 0\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 16\\n3 -4\\n-3 0\\n2 -3\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 1\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 8\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n0 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n37 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 2\\n1 1 1 90 30 16\\n3 -4\\n-1 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 22\\n-3 0\\n2 -2\\n37 2\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 87 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 1\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 3\\n1 5\\n-2 3\\n1 1 1 90 30 14\\n3 -7\\n-3 0\\n2 -2\\n45 11\\n90 6\\n135 6\\n2 1\\n1 3\\n5 4\\n0 1 1 90 59 45\\n-4 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 2\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 21\\n90 6\\n55 6\\n2 1\\n1 3\\n7 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n0 2\\n5 3\\n1 2\\n1 5\\n-2 3\\n1 1 1 90 30 45\\n3 -4\\n-3 0\\n2 -2\\n45 21\\n90 6\\n179 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 0\\n2 -2\\n45 6\\n0 0\", \"6 3\\n2 1\\n1 2\\n5 0\\n1 3\\n1 5\\n-2 4\\n1 1 1 90 30 9\\n3 -4\\n-3 0\\n2 -2\\n45 11\\n90 6\\n36 6\\n2 1\\n1 3\\n5 2\\n0 1 1 90 30 45\\n-3 -1\\n2 -2\\n37 6\\n0 0\"], \"outputs\": [\"5 6\\nNA\", \"6\\nNA\\n\", \"2 6\\nNA\\n\", \"2\\nNA\\n\", \"2\\n2\\n\", \"1 2 5 6\\nNA\\n\", \"1 2 5\\nNA\\n\", \"2\\n1 2\\n\", \"1 2 4 5\\nNA\\n\", \"1 2\\nNA\\n\", \"1 2 4 5 6\\nNA\\n\", \"1\\nNA\\n\", \"1 2 4\\nNA\\n\", \"1 2 5\\n2\\n\", \"6\\n2\\n\", \"1 2 4\\n1\\n\", \"1 5\\n2\\n\", \"1\\n2\\n\", \"5 6\\nNA\\n\", \"1 5 6\\nNA\\n\", \"2 5 6\\nNA\\n\", \"2 4 6\\nNA\\n\", \"2 5\\nNA\\n\", \"5\\nNA\\n\", \"5\\n1 2\\n\", \"6\\n1 2\\n\", \"1 4 5\\nNA\\n\", \"1 2 4 5 6\\n2\\n\", \"1\\n1\\n\", \"6\\n1\\n\", \"3 5 6\\n1\\n\", \"1 5 6\\n2\\n\", \"1 3 5 6\\n1\\n\", \"1 2 3 4 5\\nNA\\n\", \"2 6\\nNA\\n\", \"2 6\\nNA\\n\", \"6\\nNA\\n\", \"2 6\\nNA\\n\", \"2\\nNA\\n\", \"2\\n2\\n\", \"6\\nNA\\n\", \"2 6\\nNA\\n\", \"6\\nNA\\n\", \"1 2 5\\nNA\\n\", \"2\\n1 2\\n\", \"6\\nNA\\n\", \"1 2 5\\nNA\\n\", \"2\\n1 2\\n\", \"6\\nNA\\n\", \"1 2 5\\nNA\\n\", \"6\\nNA\\n\", \"2\\nNA\\n\", \"2 6\\nNA\\n\", \"2\\nNA\\n\", \"2\\nNA\\n\", \"6\\nNA\\n\", \"2 6\\nNA\\n\", \"1 2 5\\nNA\\n\", \"2\\n1 2\\n\", \"6\\nNA\\n\", \"1 2 5\\nNA\\n\", \"6\\nNA\\n\", \"2 6\\nNA\\n\", \"2\\nNA\\n\", \"2\\nNA\\n\", \"6\\nNA\\n\", \"2\\n1 2\\n\", \"6\\nNA\\n\", \"1\\nNA\\n\", \"2\\nNA\\n\", \"6\\nNA\\n\", \"6\\nNA\\n\", \"1 2 5\\n2\\n\", \"6\\n2\\n\", \"1\\nNA\\n\", \"2\\nNA\\n\", \"6\\n2\\n\", \"1\\nNA\\n\", \"6\\n2\\n\", \"1\\nNA\\n\", \"6\\n2\\n\", \"2 6\\nNA\\n\", \"2\\nNA\\n\", \"2\\n2\\n\", \"6\\nNA\\n\", \"2\\nNA\\n\", \"2\\n2\\n\", \"2 6\\nNA\\n\", \"2\\n1 2\\n\", \"6\\nNA\\n\", \"2\\n1 2\\n\", \"6\\nNA\\n\", \"2\\nNA\\n\", \"2 6\\nNA\\n\", \"2\\nNA\\n\", \"5\\nNA\\n\", \"6\\nNA\\n\", \"2 6\\nNA\\n\", \"1 2 4 5\\nNA\\n\", \"1 2 4 5 6\\nNA\\n\", \"1 2 5\\nNA\\n\"]}", "source": "primeintellect"}
|
I decided to move and decided to leave this place. There is nothing wrong with this land itself, but there is only one thing to worry about. It's a plum tree planted in the garden. I was looking forward to this plum blooming every year. After leaving here, the fun of spring will be reduced by one. Wouldn't the scent of my plums just take the wind and reach the new house to entertain spring?
There are three flowers that symbolize spring in Japan. There are three, plum, peach, and cherry blossom. In addition to my plum blossoms, the scent of these flowers will reach my new address. However, I would like to live in the house where only the scent of my plums arrives the most days.
<image>
As shown in the figure, the scent of flowers spreads in a fan shape, and the area is determined by the direction and strength of the wind. The sector spreads symmetrically around the direction w of the wind, and has a region whose radius is the strength of the wind a. The angle d at which the scent spreads is determined by the type of flower, but the direction and strength of the wind varies from day to day. However, on the same day, the direction and strength of the wind is the same everywhere.
At hand, I have data on the positions of plums, peaches, and cherry blossoms other than my plums, the angle at which the scent spreads for each type of flower, and the candidate homes to move to. In addition, there are data on the direction and strength of the wind for several days. The positions of plums, peaches, cherry trees and houses other than my plums are shown in coordinates with the position of my plums as the origin.
Let's use these data to write a program to find the house with the most days when only my plum scent arrives. Because I'm a talented programmer!
input
The input consists of multiple datasets. The end of the input is indicated by two lines of zeros. Each dataset is given in the following format:
H R
hx1 hy1
hx2 hy2
::
hxH hyH
U M S du dm ds
ux1 uy1
ux2 uy2
::
uxU uyU
mx1 my1
mx2 my2
::
mxM myM
sx1 sy1
sx2 sy2
::
sxS syS
w1 a1
w2 a2
::
wR aR
The numbers given on each line are separated by a single space.
The first line gives the number of candidate homes to move to H (1 ≤ H ≤ 100) and the number of wind records R (1 ≤ R ≤ 100). The following line H is given the location of the new house. hxi and hyi are integers between -1000 and 1000 that indicate the x and y coordinates of the i-th house.
In the next line, the number U of plum trees other than my plum and the number of peach / cherry trees M, S, and the angles du, dm, and ds that spread the scent of plum / peach / cherry are given. The range of U, M, and S is 0 or more and 10 or less. The unit of angle is degrees, which is an integer greater than or equal to 1 and less than 180. The following U line gives the position of the plum tree other than my plum, the following M line gives the position of the peach tree, and the following S line gives the position of the cherry tree. uxi and uyi, mxi and myi, sxi and syi are integers between -1000 and 1000, indicating the x and y coordinates of the i-th plum, peach, and cherry tree, respectively.
The following R line is given a record of the wind. wi (0 ≤ wi <360) and ai (0 <ai ≤ 100) are integers representing the direction and strength of the wind on day i. The direction of the wind is expressed as an angle measured counterclockwise from the positive direction of the x-axis, and the unit is degrees.
The input may be considered to satisfy the following conditions.
* All coordinates entered shall be different.
* There is nothing but my plum at the origin.
* For any flower, there is no house within 0.001 distance from the boundary of the area where the scent of the flower reaches.
The number of datasets does not exceed 50.
output
For each dataset, print the numbers of all the houses with the most days that only my plum scent arrives on one line in ascending order. Separate the house numbers with a single space. Do not print whitespace at the end of the line.
However, for any house, if there is no day when only the scent of my plum blossoms arrives, it will be output as NA.
Example
Input
6 3
2 1
1 2
5 2
1 3
1 5
-2 3
1 1 1 90 30 45
3 -4
-3 0
2 -2
45 6
90 6
135 6
2 1
1 3
5 2
0 1 1 90 30 45
-3 0
2 -2
45 6
0 0
Output
5 6
NA
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"None\", \"ABRACADABRA\\nECADADABRBCRDARA\\nUPWJCIRUCAXIIRGL\\nSBQNYBSBZDFNEV\", \"Nnne\", \"ABRACADAARA\\nECADADABRBCRDARA\\nUPWJCIRUCAXIIRGL\\nSBQNYBSBZDFNEV\", \"DBRACAAAARA\\nECADADBBRBCRDARA\\nLCRIIXACURIGJWPU\\nSBQNYBSBZDFOEV\", \"DBRACAAAARA\\nECADADBBRBBRDARA\\nLCRIIXACURIGJWPU\\nSBQNYBSBFDZOEU\", \"DBRACAAA@RA\\nECADADBBRBBRDARA\\nLCRIIXACURIGJWPU\\nSBQNYBSBFDZOEU\", \"CARBR@AA?CB\\nABRDRBSBAACADACD\\nLDRTIXAWURIHKCOI\\nBBDDYRTBDNZOUQ\", \"AD?BB>ARCBQ\\nCBBDQARCBEB@ADRA\\nOVKRMDAESKVVHKXI\\nZBARNTWBBCYCOQ\", \"A>?BR@BQ@BD\\nBSDACBFQERB@CBBA\\nIVXVOCJHEAJURKMR\\nBA@CQXAYNSYTBP\", \"Nnnd\", \"ABRACADAARA\\nECADADABRBCRDARA\\nLGRIIXACURICJWPU\\nSBQNYBSBZDFNEV\", \"Nond\", \"ABRACADAARA\\nECADADABRBCRDARA\\nLCRIIXACURIGJWPU\\nSBQNYBSBZDFNEV\", \"Npnd\", \"ABRACADAARA\\nECADADABRBCRDARA\\nLCRIIXACURIGJWPU\\nSBQNYBSBZDFOEV\", \"Npne\", \"ABRACADAARA\\nECADADBBRBCRDARA\\nLCRIIXACURIGJWPU\\nSBQNYBSBZDFOEV\", \"enpN\", \"dnpN\", \"DBRACAAAARA\\nECADADBBRBBRDARA\\nLCRIIXACURIGJWPU\\nSBQNYBSBZDFOEV\", \"dnoN\", \"DBRACAAAARA\\nECADADBBRBBRDARA\\nLCRIIXACURIGJWPU\\nSBQNYBSBFDZOEV\", \"dooN\", \"donN\", \"Nnod\", \"DBRACAAA@RA\\nECADADBBRBBRDARA\\nUPWJGIRUCAXIIRCL\\nSBQNYBSBFDZOEU\", \"dnnN\", \"DBRACAAA@RA\\nECADADBBRBBRDARA\\nUPWJGIRUCAXIIRCL\\nSBQNYBSBEDZOEU\", \"dnnO\", \"DBRACAAA@RA\\nECADADBBRBBRDARA\\nUPWJGIRUCAXIIRCL\\nSBQNYBSBEDZNEU\", \"dmnO\", \"DBRACAAA@RA\\nARADRBBRBBDADACE\\nUPWJGIRUCAXIIRCL\\nSBQNYBSBEDZNEU\", \"dmmO\", \"DBRACAAA@RA\\nAARDRBBRBBDADACE\\nUPWJGIRUCAXIIRCL\\nSBQNYBSBEDZNEU\", \"dOmm\", \"DBRACAAA@RA\\nECADADBBRBBRDRAA\\nUPWJGIRUCAXIIRCL\\nSBQNYBSBEDZNEU\", \"dPmm\", \"DBRACAAA@RA\\nECADADBBRBBRDRAA\\nUOWJGIRUCAXIIRCL\\nSBQNYBSBEDZNEU\", \"mmOd\", \"DBRAC@AA@RA\\nECADADBBRBBRDRAA\\nUOWJGIRUCAXIIRCL\\nSBQNYBSBEDZNEU\", \"mmNd\", \"DBRAC@AA@RA\\nECADADBBRBBRDRAA\\nUOWJGIRUCAXIIRCL\\nRBQNYBSBEDZNEU\", \"dNmm\", \"DBRAC@AA@RA\\nECADADBBRBBRDRAA\\nUOWJGIRUCAXIIRCL\\nUENZDEBSBYNQBR\", \"cNmm\", \"DBRAC@AA@RA\\nECADADBBRCBRDRAA\\nUOWJGIRUCAXIIRCL\\nUENZDEBSBYNQBR\", \"mmNc\", \"DBRAC@AA@RA\\nECADADBBRCBRDRAA\\nUOWKGIRUCAXIIRCL\\nUENZDEBSBYNQBR\", \"cmNm\", \"DBRAC@AA@RA\\nAARDRBCRBBDADACE\\nUOWKGIRUCAXIIRCL\\nUENZDEBSBYNQBR\", \"mnNc\", \"DBRAC@AA@RA\\nABRDRBCRBBDADACE\\nUOWKGIRUCAXIIRCL\\nUENZDEBSBYNQBR\", \"cnNm\", \"DBRAC@AA@RA\\nABRDRBCRBBDADACE\\nLCRIIXACURIGKWOU\\nUENZDEBSBYNQBR\", \"bnNm\", \"DBRAR@AA@CA\\nABRDRBCRBBDADACE\\nLCRIIXACURIGKWOU\\nUENZDEBSBYNQBR\", \"nbNm\", \"DBRAR@AA@CB\\nABRDRBCRBBDADACE\\nLCRIIXACURIGKWOU\\nUENZDEBSBYNQBR\", \"nbMm\", \"DBRAR@AA@CB\\nABRDRBCRBBCADACE\\nLCRIIXACURIGKWOU\\nUENZDEBSBYNQBR\", \"nbLm\", \"DARBR@AA@CB\\nABRDRBCRBBCADACE\\nLCRIIXACURIGKWOU\\nUENZDEBSBYNQBR\", \"ncLm\", \"BC@AA@RBRAD\\nABRDRBCRBBCADACE\\nLCRIIXACURIGKWOU\\nUENZDEBSBYNQBR\", \"mLcn\", \"BC@AA@RBRAD\\nABRDRBRCBBCADACE\\nLCRIIXACURIGKWOU\\nUENZDEBSBYNQBR\", \"lLcn\", \"BC@AA@RBRAD\\nABRDRBRCBBCADACE\\nLCRIIXACURIGKWOT\\nUENZDEBSBYNQBR\", \"lKcn\", \"BC@AA@RBRAC\\nABRDRBRCBBCADACE\\nLCRIIXACURIGKWOT\\nUENZDEBSBYNQBR\", \"lKnc\", \"BC@AA@RBRAC\\nECADACBBCRBRDRBA\\nLCRIIXACURIGKWOT\\nUENZDEBSBYNQBR\", \"nKlc\", \"BC@AA@RBRAC\\nECADACBBCRBRDRBA\\nLCRIIXACURIGKWOT\\nUENZDEBTBYNQBR\", \"nKlb\", \"BC@AA@RBRAC\\nECADACBBCRBRDRBA\\nLCRIIXACURIGKWOT\\nEUNZDEBTBYNQBR\", \"nKla\", \"BC@AA@RBRAC\\nECADACABCRBRDRBA\\nLCRIIXACURIGKWOT\\nEUNZDEBTBYNQBR\", \"aKln\", \"BC@AA@RBRAC\\nDCADACABCRBRDRBA\\nLCRIIXACURIGKWOT\\nEUNZDEBTBYNQBR\", \"aLln\", \"BC@AA@RBRAC\\nDCADACABCRBRDRBA\\nLCRIIXACURIGKWOT\\nEUNZNEBTBYDQBR\", \"bLln\", \"BC@AA@RBRAC\\nDCADACABCRBRDRBA\\nLCRIIXACURIGKWOT\\nDUNZNEBTBYDQBR\", \"nlLb\", \"BC@AA@RBRAC\\nDCADACABCRBRDRBA\\nTOWKGIRUCAXIIRCL\\nDUNZNEBTBYDQBR\", \"olLb\", \"BC@AA@RBRAC\\nDCADACABCSBRDRBA\\nTOWKGIRUCAXIIRCL\\nDUNZNEBTBYDQBR\", \"olLa\", \"CARBR@AA@CB\\nDCADACABCSBRDRBA\\nTOWKGIRUCAXIIRCL\\nDUNZNEBTBYDQBR\", \"nlLa\", \"CARBR@AA@CB\\nDBADACABCSBRDRBA\\nTOWKGIRUCAXIIRCL\\nDUNZNEBTBYDQBR\", \"nlKa\", \"CARBR@AA@CB\\nDBADACABCSBRDRBA\\nLCRIIXACURIGKWOT\\nDUNZNEBTBYDQBR\", \"mlKa\", \"CARBR@AA@CB\\nABRDRBSCBACADABD\\nLCRIIXACURIGKWOT\\nDUNZNEBTBYDQBR\", \"aKlm\", \"CARBR@AA@CB\\nABRDRBSCBACADACD\\nLCRIIXACURIGKWOT\\nDUNZNEBTBYDQBR\", \"aJlm\", \"CARBR@AA@CB\\nABRDRBSCAACADACD\\nLCRIIXACURIGKWOT\\nDUNZNEBTBYDQBR\", \"`Jlm\"], \"outputs\": [\"None\", \"5\\n0\", \"0\\n\", \"4\\n0\\n\", \"3\\n0\\n\", \"3\\n1\\n\", \"2\\n1\\n\", \"2\\n2\\n\", \"4\\n1\\n\", \"1\\n1\\n\", \"0\\n\", \"4\\n0\\n\", \"0\\n\", \"4\\n0\\n\", \"0\\n\", \"4\\n0\\n\", \"0\\n\", \"4\\n0\\n\", \"0\\n\", \"0\\n\", \"3\\n0\\n\", \"0\\n\", \"3\\n0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"3\\n1\\n\", \"0\\n\", \"3\\n1\\n\", \"0\\n\", \"3\\n1\\n\", \"0\\n\", \"3\\n1\\n\", \"0\\n\", \"3\\n1\\n\", \"0\\n\", \"3\\n1\\n\", \"0\\n\", \"3\\n1\\n\", \"0\\n\", \"3\\n1\\n\", \"0\\n\", \"3\\n1\\n\", \"0\\n\", \"3\\n1\\n\", \"0\\n\", \"3\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\", \"2\\n1\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
problem
Given two strings, find the longest of the strings contained in both strings and write a program that answers that length.
Here, the string s included in the string t means that s appears consecutively in t. An empty string, that is, a string of length 0, is included in any string. For example, the string ABRACADABRA contains the following strings: ABRA, RAC, D, ACADABRA, ABRACADABRA, the empty string, etc. On the other hand, the string ABRACADABRA does not contain the following strings: ABRC, RAA, BA , K etc.
input
The input consists of multiple datasets. Each dataset is given in the following format.
The input consists of two lines, the first line is given the first string and the second line is given the second string. The strings consist of uppercase letters and each string is 1 in length. More than 4000 and less.
Of the scoring data, for 30% of the points, the length of each character string is 1 or more and 50 or less.
The end of input is indicated by EOF. The number of datasets does not exceed 10.
output
Outputs the length of the longest string contained in both of the two strings given for each dataset on one line.
Examples
Input
ABRACADABRA
ECADADABRBCRDARA
UPWJCIRUCAXIIRGL
SBQNYBSBZDFNEV
Output
5
0
Input
None
Output
None
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\n1 2\", \"2\\n0 2\", \"2\\n-1 4\", \"2\\n0 4\", \"2\\n0 1\", \"2\\n1 0\", \"2\\n0 7\", \"2\\n-1 2\", \"2\\n2 0\", \"2\\n-1 10\", \"2\\n-2 2\", \"2\\n2 -1\", \"2\\n-2 4\", \"2\\n4 -1\", \"2\\n-2 8\", \"2\\n4 0\", \"2\\n-2 5\", \"2\\n5 0\", \"2\\n1 1\", \"2\\n2 2\", \"2\\n2 4\", \"2\\n4 4\", \"2\\n0 0\", \"2\\n1 4\", \"2\\n0 3\", \"2\\n0 -2\", \"2\\n2 1\", \"2\\n2 8\", \"2\\n0 8\", \"2\\n0 10\", \"2\\n-4 2\", \"2\\n-2 3\", \"2\\n4 1\", \"2\\n-3 8\", \"2\\n3 0\", \"2\\n3 2\", \"2\\n2 7\", \"2\\n4 2\", \"2\\n1 5\", \"2\\n5 1\", \"2\\n8 1\", \"2\\n2 3\", \"2\\n1 8\", \"2\\n1 10\", \"2\\n6 2\", \"2\\n0 9\", \"2\\n3 1\", \"2\\n3 4\", \"2\\n1 7\", \"2\\n6 0\", \"2\\n1 6\", \"2\\n6 1\", \"2\\n4 3\", \"2\\n4 8\", \"2\\n1 13\", \"2\\n-2 0\", \"2\\n1 9\", \"2\\n2 -2\", \"2\\n3 5\", \"2\\n1 15\", \"2\\n6 -1\", \"2\\n2 6\", \"2\\n7 1\", \"2\\n12 0\", \"2\\n7 8\", \"2\\n0 13\", \"2\\n2 9\", \"2\\n2 -4\", \"2\\n10 0\", \"2\\n0 15\", \"2\\n4 -2\", \"2\\n7 0\", \"2\\n21 0\", \"2\\n7 9\", \"2\\n2 15\", \"2\\n4 -4\", \"2\\n10 -1\", \"2\\n0 11\", \"2\\n14 0\", \"2\\n34 0\", \"2\\n5 9\", \"2\\n4 15\", \"2\\n0 -4\", \"2\\n10 -2\", \"2\\n14 -1\", \"2\\n24 0\", \"2\\n7 18\", \"2\\n4 10\", \"2\\n13 -2\", \"2\\n24 1\", \"2\\n7 36\", \"2\\n5 10\", \"2\\n15 1\", \"2\\n13 36\", \"2\\n5 3\", \"2\\n19 1\", \"2\\n13 38\", \"2\\n1 3\", \"2\\n19 0\", \"2\\n13 26\", \"2\\n38 0\"], \"outputs\": [\"First\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"Second\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"Second\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"First\\n\", \"Second\\n\"]}", "source": "primeintellect"}
|
Problem statement
There is a positive integer sequence $ a_1, a_2, \ ldots, a_N $ of length $ N $.
Consider the following game, which uses this sequence and is played by $ 2 $ players on the play and the play.
* Alternately select one of the following operations for the first move and the second move.
* Select a positive term in the sequence for $ 1 $ and decrement its value by $ 1 $.
* When all terms in the sequence are positive, decrement the values of all terms by $ 1 $.
The one who cannot operate first is the loser.
When $ 2 $ players act optimally, ask for the first move or the second move.
Constraint
* $ 1 \ leq N \ leq 2 \ times 10 ^ 5 $
* $ 1 \ leq a_i \ leq 10 ^ 9 $
* All inputs are integers
* * *
input
Input is given from standard input in the following format.
$ N $
$ a_1 $ $ a_2 $ $ ... $ $ a_N $
output
Output `First` when the first move wins, and output` Second` when the second move wins.
* * *
Input example 1
2
1 2
Output example 1
First
The first move has to reduce the value of the $ 1 $ term by $ 1 $ first, and then the second move has to reduce the value of the $ 2 $ term by $ 1 $.
If the first move then decrements the value of the $ 2 $ term by $ 1 $, the value of all terms in the sequence will be $ 0 $, and the second move will not be able to perform any operations.
* * *
Input example 2
Five
3 1 4 1 5
Output example 2
Second
* * *
Input example 3
8
2 4 8 16 32 64 128 256
Output example 3
Second
* * *
Input example 4
3
999999999 1000000000 1000000000
Output example 4
First
Example
Input
2
1 2
Output
First
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3\\n0 3\\n1 3\\n3 8\\n\", \"3\\n1 3\\n2 4\\n5 7\\n\", \"1\\n0 1000000000000000000\\n\", \"3\\n1 3\\n2 4\\n3 7\\n\", \"1\\n1 1000000000000000000\\n\", \"3\\n0 3\\n1 1\\n3 8\\n\", \"3\\n1 3\\n2 4\\n3 14\\n\", \"3\\n1 5\\n2 4\\n3 14\\n\", \"3\\n0 3\\n2 3\\n3 8\\n\", \"3\\n1 1\\n2 4\\n5 7\\n\", \"3\\n1 3\\n2 7\\n3 7\\n\", \"3\\n1 3\\n2 4\\n3 23\\n\", \"3\\n0 3\\n2 3\\n3 7\\n\", \"3\\n0 1\\n2 4\\n5 7\\n\", \"3\\n1 3\\n1 7\\n3 7\\n\", \"3\\n1 3\\n1 4\\n3 23\\n\", \"3\\n0 3\\n2 3\\n5 7\\n\", \"3\\n1 4\\n1 7\\n3 7\\n\", \"3\\n0 0\\n2 3\\n5 7\\n\", \"3\\n1 4\\n1 7\\n0 7\\n\", \"3\\n0 4\\n1 7\\n0 7\\n\", \"3\\n0 3\\n2 3\\n3 9\\n\", \"3\\n1 3\\n2 4\\n5 13\\n\", \"3\\n2 3\\n2 4\\n3 7\\n\", \"1\\n2 1000000000000000000\\n\", \"3\\n0 3\\n1 1\\n3 5\\n\", \"3\\n1 3\\n1 4\\n3 14\\n\", \"3\\n1 5\\n2 4\\n0 14\\n\", \"3\\n0 3\\n2 3\\n3 5\\n\", \"3\\n2 3\\n2 7\\n3 7\\n\", \"3\\n1 3\\n2 4\\n3 8\\n\", \"3\\n1 3\\n1 5\\n3 7\\n\", \"3\\n1 3\\n1 4\\n1 23\\n\", \"3\\n0 3\\n2 3\\n2 7\\n\", \"3\\n0 0\\n2 4\\n6 10\\n\", \"3\\n1 4\\n1 3\\n0 7\\n\", \"3\\n0 4\\n1 8\\n0 7\\n\", \"3\\n0 1\\n2 3\\n3 9\\n\", \"3\\n2 3\\n2 4\\n5 13\\n\", \"3\\n2 3\\n2 4\\n3 6\\n\", \"1\\n3 1000000000000000000\\n\", \"3\\n0 3\\n1 1\\n4 5\\n\", \"3\\n1 3\\n1 4\\n0 14\\n\", \"3\\n0 5\\n2 4\\n0 14\\n\", \"3\\n1 3\\n0 4\\n3 8\\n\", \"3\\n1 3\\n1 4\\n3 7\\n\", \"3\\n1 3\\n1 6\\n1 23\\n\", \"3\\n0 4\\n1 3\\n0 7\\n\", \"3\\n0 4\\n1 8\\n1 7\\n\", \"3\\n0 1\\n2 3\\n2 9\\n\", \"3\\n0 3\\n2 4\\n5 13\\n\", \"3\\n2 2\\n2 4\\n3 6\\n\", \"3\\n2 3\\n2 8\\n3 3\\n\", \"3\\n1 3\\n1 4\\n3 8\\n\", \"3\\n1 3\\n1 6\\n1 41\\n\", \"3\\n0 7\\n1 8\\n1 7\\n\", \"3\\n0 3\\n2 4\\n5 19\\n\", \"3\\n2 2\\n2 2\\n3 6\\n\", \"3\\n0 3\\n2 4\\n0 14\\n\", \"3\\n1 3\\n1 4\\n5 8\\n\", \"3\\n1 5\\n1 6\\n1 41\\n\", \"3\\n0 1\\n3 5\\n3 7\\n\", \"3\\n0 4\\n1 9\\n0 7\\n\", \"3\\n0 8\\n1 8\\n1 7\\n\", \"3\\n1 1\\n3 3\\n2 9\\n\", \"3\\n0 3\\n2 4\\n5 29\\n\", \"3\\n0 3\\n2 4\\n0 8\\n\", \"3\\n1 5\\n2 6\\n1 41\\n\", \"3\\n0 1\\n2 4\\n6 7\\n\", \"3\\n0 0\\n2 4\\n6 7\\n\", \"3\\n0 1\\n2 5\\n6 7\\n\", \"3\\n0 0\\n2 3\\n5 9\\n\", \"3\\n0 3\\n1 3\\n3 5\\n\", \"3\\n2 3\\n2 8\\n3 7\\n\", \"3\\n0 1\\n3 5\\n6 7\\n\", \"3\\n0 3\\n1 4\\n0 14\\n\", \"3\\n0 3\\n1 3\\n3 7\\n\", \"3\\n1 3\\n0 4\\n3 7\\n\", \"3\\n0 0\\n3 5\\n6 7\\n\", \"3\\n0 4\\n1 6\\n0 7\\n\", \"3\\n1 1\\n2 3\\n2 9\\n\", \"3\\n1 3\\n0 3\\n3 7\\n\", \"3\\n1 2\\n2 2\\n3 6\\n\", \"3\\n2 3\\n0 3\\n3 7\\n\", \"3\\n0 1\\n3 5\\n4 7\\n\"], \"outputs\": [\"6 2 1\\n\", \"5 2 0\\n\", \"1000000000000000001\\n\", \"4 2 1 \\n\", \"1000000000000000000 \\n\", \"7 2 0 \\n\", \"11 2 1 \\n\", \"10 2 2 \\n\", \"7 1 1 \\n\", \"7 0 0 \\n\", \"1 5 1 \\n\", \"20 2 1 \\n\", \"6 1 1 \\n\", \"8 0 0 \\n\", \"0 6 1 \\n\", \"19 3 1 \\n\", \"5 2 0 \\n\", \"0 5 2 \\n\", \"6 0 0 \\n\", \"1 3 4 \\n\", \"0 4 4 \\n\", \"8 1 1 \\n\", \"11 2 0 \\n\", \"3 2 1 \\n\", \"999999999999999999 \\n\", \"4 2 0 \\n\", \"10 3 1 \\n\", \"10 2 3 \\n\", \"4 1 1 \\n\", \"0 5 1 \\n\", \"5 2 1 \\n\", \"2 4 1 \\n\", \"19 1 3 \\n\", \"6 0 2 \\n\", \"9 0 0 \\n\", \"4 1 3 \\n\", \"1 4 4 \\n\", \"9 1 0 \\n\", \"10 2 0 \\n\", \"2 2 1 \\n\", \"999999999999999998 \\n\", \"5 1 0 \\n\", \"11 1 3 \\n\", \"9 3 3 \\n\", \"5 3 1 \\n\", \"3 3 1 \\n\", \"17 3 3 \\n\", \"3 2 3 \\n\", \"2 3 4 \\n\", \"8 2 0 \\n\", \"12 2 0 \\n\", \"2 3 0 \\n\", \"5 1 1 \\n\", \"4 3 1 \\n\", \"35 3 3 \\n\", \"2 0 7 \\n\", \"18 2 0 \\n\", \"4 1 0 \\n\", \"10 3 2 \\n\", \"5 3 0 \\n\", \"35 1 5 \\n\", \"4 3 0 \\n\", \"2 4 4 \\n\", \"1 1 7 \\n\", \"8 1 0 \\n\", \"28 2 0 \\n\", \"4 3 2 \\n\", \"35 2 4 \\n\", \"7 0 0 \\n\", \"6 0 0 \\n\", \"8 0 0 \\n\", \"8 0 0 \\n\", \"3 2 1 \\n\", \"1 5 1 \\n\", \"7 0 0 \\n\", \"10 2 3 \\n\", \"5 2 1 \\n\", \"4 3 1 \\n\", \"6 0 0 \\n\", \"1 3 4 \\n\", \"7 2 0 \\n\", \"5 2 1 \\n\", \"5 1 0 \\n\", \"6 1 1 \\n\", \"5 2 0 \\n\"]}", "source": "primeintellect"}
|
You are given n segments on a coordinate line; each endpoint of every segment has integer coordinates. Some segments can degenerate to points. Segments can intersect with each other, be nested in each other or even coincide.
Your task is the following: for every k ∈ [1..n], calculate the number of points with integer coordinates such that the number of segments that cover these points equals k. A segment with endpoints l_i and r_i covers point x if and only if l_i ≤ x ≤ r_i.
Input
The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of segments.
The next n lines contain segments. The i-th line contains a pair of integers l_i, r_i (0 ≤ l_i ≤ r_i ≤ 10^{18}) — the endpoints of the i-th segment.
Output
Print n space separated integers cnt_1, cnt_2, ..., cnt_n, where cnt_i is equal to the number of points such that the number of segments that cover these points equals to i.
Examples
Input
3
0 3
1 3
3 8
Output
6 2 1
Input
3
1 3
2 4
5 7
Output
5 2 0
Note
The picture describing the first example:
<image>
Points with coordinates [0, 4, 5, 6, 7, 8] are covered by one segment, points [1, 2] are covered by two segments and point [3] is covered by three segments.
The picture describing the second example:
<image>
Points [1, 4, 5, 6, 7] are covered by one segment, points [2, 3] are covered by two segments and there are no points covered by three segments.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
{"tests": "{\"inputs\": [\"9\\n4 8 10 12 15 18 33 44 81\\n\", \"6\\n3 6 9 18 36 108\\n\", \"2\\n7 17\\n\", \"4\\n3 5 7 105\\n\", \"13\\n2 12 60 300 900 6300 44100 176400 352800 705600 3528000 21168000 148176000\\n\", \"11\\n2 6 15 35 77 143 221 323 437 667 899\\n\", \"4\\n2 3 5 30\\n\", \"27\\n5 10 29 58 116 174 2297 4594 9188 18376 36752 43643 415757 831514 1663028 2494542 6236355 12472710 22450878 44901756 47396298 68344938 114906990 229813980 306418640 612837280 919255920\\n\", \"4\\n3 7 14 99\\n\", \"4\\n30 34 57 115\\n\", \"14\\n122501 245002 367503 735006 1225010 4287535 8575070 21437675 42875350 85750700 171501400 343002800 531654340 823206720\\n\", \"4\\n3 7 13 273\\n\", \"9\\n2 3 5 7 9 11 13 17 9699690\\n\", \"2\\n4 6\\n\", \"6\\n2 3 5 7 11 2310\\n\", \"25\\n2 4 8 10 25 50 100 107903 215806 431612 863224 1726448 3452896 4316120 8632240 17264480 21580600 32370900 64741800 86322400 172644800 193362176 302128400 604256800 841824100\\n\", \"2\\n2 4\\n\", \"22\\n2 4 8 16 32 96 288 576 1728 3456 10368 20736 62208 186624 559872 1119744 3359232 10077696 30233088 90699264 181398528 544195584\\n\", \"27\\n17 34 68 85 170 340 510 1020 1105 22621 45242 90484 113105 226210 452420 565525 2284721 11423605 15993047 47979141 79965235 114236050 124981025 199969640 299954460 599908920 999848200\\n\", \"4\\n14 15 35 39\\n\", \"21\\n2 1637 8185 16370 32740 49110 98220 106405 532025 671170 1225010 5267543 10535086 21070172 42140344 63210516 94815774 189631548 379263096 568894644 632105160\\n\", \"36\\n3 41 82 123 174 216 432 864 1080 1228 2149 4298 8596 11052 22104 33156 35919 71838 179595 359190 431028 862056 994680 1315440 1753920 3507840 7015680 10523520 21047040 26500200 53000400 106000800 132501000 176668000 353336000 530004000\\n\", \"5\\n3 4 5 7 420\\n\", \"5\\n11 18 33 44 81\\n\", \"6\\n5 11 18 33 44 81\\n\", \"29\\n2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216 33554432 67108864 134217728 268435456 536870912\\n\", \"5\\n2 3 210 485 707\\n\", \"8\\n2 3 5 14 33 65 119 187\\n\", \"29\\n2 4 8 16 24 449 898 1796 3592 5388 16613 33226 66452 132904 199356 398712 689664 1375736 2751472 3439340 6878680 13757360 27514720 52277968 86671368 132501000 265002000 530004000 795006000\\n\", \"4\\n2 3 4 9\\n\", \"4\\n3 5 6 105\\n\", \"4\\n2 4 8 16\\n\", \"5\\n2 6 9 10 81\\n\", \"4\\n23 247 299 703\\n\", \"8\\n3 7 16 18 36 57 84 90\\n\", \"23\\n5 10 149 298 397 794 1588 3176 6352 12704 20644 30966 61932 103220 118306 208600 312900 625800 1225010 13107607 249044533 498089066 917532490\\n\", \"7\\n7 38 690 717 11165 75361 104117\\n\", \"9\\n2 3 4 5 7 9 25 49 210\\n\", \"5\\n2 3 5 7 210\\n\", \"7\\n2 6 15 35 77 85 143\\n\", \"4\\n7 12 24 77\\n\", \"30\\n5 10 14 28 42 3709 7418 11127 14836 29672 44508 55635 74180 148360 222540 445080 778890 1557780 2039646 5778997 11557994 23115988 46231976 92463952 138695928 208043892 312065838 624131676 832175568 928038930\\n\", \"4\\n2 3 4 6\\n\", \"27\\n13 26 52 104 208 221 442 884 1105 4211 12633 25266 63165 126330 130541 261082 522164 1044328 1305410 1697033 12426661 37279983 111839949 223679898 298239864 385226491 721239025\\n\", \"24\\n13 26 52 104 130 260 520 728 1105 238529 477058 954116 1908232 3816464 4293522 6440283 12880566 20274965 40549930 60824895 121649790 243299580 263574545 527149090\\n\", \"5\\n3 5 7 11 1155\\n\", \"30\\n3 5 15 30 55 77 154 231 462 770 1540 2310 4569 13707 41121 123363 246726 424917 662505 1987515 5962545 7950060 15900120 23850180 35775270 71550540 132501000 265002000 397503000 795006000\\n\", \"21\\n2 6 18 54 216 432 1296 5184 10368 31104 124416 248832 746496 1492992 2985984 5971968 17915904 53747712 107495424 214990848 644972544\\n\", \"4\\n3 4 9 12\\n\", \"13\\n2 12 60 300 900 6300 85523 176400 352800 705600 3528000 21168000 148176000\\n\", \"27\\n5 10 29 87 116 174 2297 4594 9188 18376 36752 43643 415757 831514 1663028 2494542 6236355 12472710 22450878 44901756 47396298 68344938 114906990 229813980 306418640 612837280 919255920\\n\", \"11\\n2 6 15 35 77 143 221 323 843 667 899\\n\", \"4\\n3 7 18 99\\n\", \"4\\n30 34 57 221\\n\", \"14\\n84707 245002 367503 735006 1225010 4287535 8575070 21437675 42875350 85750700 171501400 343002800 531654340 823206720\\n\", \"4\\n3 7 17 273\\n\", \"9\\n2 3 5 7 9 11 13 17 10277292\\n\", \"2\\n4 3\\n\", \"6\\n2 3 2 7 11 2310\\n\", \"25\\n2 4 8 10 48 50 100 107903 215806 431612 863224 1726448 3452896 4316120 8632240 17264480 21580600 32370900 64741800 86322400 172644800 193362176 302128400 604256800 841824100\\n\", \"2\\n2 1\\n\", \"22\\n2 4 8 16 32 96 498 576 1728 3456 10368 20736 62208 186624 559872 1119744 3359232 10077696 30233088 90699264 181398528 544195584\\n\", \"27\\n17 34 68 85 170 340 510 1020 1105 22621 45242 90484 113105 226210 452420 565525 2284721 11423605 15993047 47979141 79965235 114236050 124981025 199969640 299954460 67384097 999848200\\n\", \"4\\n14 15 19 39\\n\", \"21\\n2 1637 8185 16370 32740 49110 179962 106405 532025 671170 1225010 5267543 10535086 21070172 42140344 63210516 94815774 189631548 379263096 568894644 632105160\\n\", \"36\\n3 41 82 123 174 216 432 864 1080 1228 2149 4298 8596 11052 22104 33156 35919 71838 179595 359190 431028 862056 994680 1315440 1753920 3507840 3303585 10523520 21047040 26500200 53000400 106000800 132501000 176668000 353336000 530004000\\n\", \"5\\n3 5 5 7 420\\n\", \"6\\n5 11 18 42 44 81\\n\", \"29\\n2 4 8 8 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576 2097152 4194304 8388608 16777216 33554432 67108864 134217728 268435456 536870912\\n\", \"5\\n2 3 210 485 1171\\n\", \"8\\n2 3 5 14 33 65 93 187\\n\", \"29\\n2 4 8 16 24 449 898 1796 3592 5388 16613 33226 66452 132904 199356 398712 689664 469139 2751472 3439340 6878680 13757360 27514720 52277968 86671368 132501000 265002000 530004000 795006000\\n\", \"4\\n1 3 4 9\\n\", \"4\\n1 5 6 105\\n\", \"4\\n2 3 8 16\\n\", \"4\\n23 182 299 703\\n\", \"8\\n3 7 9 18 36 57 84 90\\n\", \"23\\n5 10 126 298 397 794 1588 3176 6352 12704 20644 30966 61932 103220 118306 208600 312900 625800 1225010 13107607 249044533 498089066 917532490\\n\", \"7\\n7 32 690 717 11165 75361 104117\\n\", \"9\\n2 3 4 8 7 9 25 49 210\\n\", \"7\\n1 6 15 35 77 85 143\\n\", \"4\\n7 20 24 77\\n\", \"30\\n5 10 14 28 77 3709 7418 11127 14836 29672 44508 55635 74180 148360 222540 445080 778890 1557780 2039646 5778997 11557994 23115988 46231976 92463952 138695928 208043892 312065838 624131676 832175568 928038930\\n\", \"4\\n3 3 4 6\\n\", \"27\\n13 26 52 104 208 221 442 884 1105 4211 3504 25266 63165 126330 130541 261082 522164 1044328 1305410 1697033 12426661 37279983 111839949 223679898 298239864 385226491 721239025\\n\", \"24\\n13 26 52 104 130 260 520 728 1105 182569 477058 954116 1908232 3816464 4293522 6440283 12880566 20274965 40549930 60824895 121649790 243299580 263574545 527149090\\n\", \"5\\n3 5 3 11 1155\\n\", \"30\\n3 5 15 30 55 77 154 231 462 770 1540 2310 4569 13707 41121 123363 246726 285446 662505 1987515 5962545 7950060 15900120 23850180 35775270 71550540 132501000 265002000 397503000 795006000\\n\", \"21\\n2 6 18 54 216 432 1296 5184 10368 31104 124416 248832 781343 1492992 2985984 5971968 17915904 53747712 107495424 214990848 644972544\\n\", \"4\\n3 4 5 12\\n\", \"9\\n4 8 10 12 15 3 33 44 81\\n\", \"6\\n3 6 9 18 36 50\\n\", \"2\\n1 17\\n\", \"13\\n2 12 60 300 1042 6300 85523 176400 352800 705600 3528000 21168000 148176000\\n\", \"11\\n2 6 15 35 77 76 221 323 843 667 899\\n\", \"27\\n5 10 29 87 116 174 2297 4594 9188 18376 36752 43643 415757 831514 1663028 2494542 6236355 12472710 22450878 44901756 47396298 68344938 47401585 229813980 306418640 612837280 919255920\\n\", \"4\\n3 7 15 99\\n\", \"4\\n30 7 57 221\\n\", \"14\\n84707 245002 367503 735006 1225010 4287535 8575070 21437675 42875350 36111749 171501400 343002800 531654340 823206720\\n\", \"4\\n1 7 17 273\\n\", \"9\\n2 3 5 7 9 11 13 17 6818890\\n\"], \"outputs\": [\"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\"]}", "source": "primeintellect"}
|
Dima the hamster enjoys nibbling different things: cages, sticks, bad problemsetters and even trees!
Recently he found a binary search tree and instinctively nibbled all of its edges, hence messing up the vertices. Dima knows that if Andrew, who has been thoroughly assembling the tree for a long time, comes home and sees his creation demolished, he'll get extremely upset.
To not let that happen, Dima has to recover the binary search tree. Luckily, he noticed that any two vertices connected by a direct edge had their greatest common divisor value exceed 1.
Help Dima construct such a binary search tree or determine that it's impossible. The definition and properties of a binary search tree can be found [here.](https://en.wikipedia.org/wiki/Binary_search_tree)
Input
The first line contains the number of vertices n (2 ≤ n ≤ 700).
The second line features n distinct integers a_i (2 ≤ a_i ≤ 10^9) — the values of vertices in ascending order.
Output
If it is possible to reassemble the binary search tree, such that the greatest common divisor of any two vertices connected by the edge is greater than 1, print "Yes" (quotes for clarity).
Otherwise, print "No" (quotes for clarity).
Examples
Input
6
3 6 9 18 36 108
Output
Yes
Input
2
7 17
Output
No
Input
9
4 8 10 12 15 18 33 44 81
Output
Yes
Note
The picture below illustrates one of the possible trees for the first example.
<image>
The picture below illustrates one of the possible trees for the third example.
<image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5 5\\n0 1 2 4 5\\n1 2 3 4 5\\n4\\n2\\n3\\n5\\n4\\n\", \"5 3\\n0 1 2 2 0\\n1 2 2 3 2\\n5\\n3\\n2\\n4\\n5\\n1\\n\", \"5 3\\n0 1 2 2 1\\n1 3 2 3 2\\n5\\n4\\n2\\n3\\n5\\n1\\n\", \"5 5\\n0 0 1 1 2\\n1 2 2 3 2\\n2\\n2\\n3\\n\", \"5 3\\n0 0 1 1 2\\n1 2 2 3 2\\n2\\n2\\n3\\n\", \"10 5\\n0 1 1 0 3 1 3 0 2 0\\n5 4 3 4 3 4 1 2 3 3\\n10\\n1\\n2\\n8\\n7\\n3\\n9\\n6\\n5\\n10\\n4\\n\", \"10 10\\n2 0 3 5 6 1 9 4 7 8\\n9 2 5 7 1 6 4 10 8 3\\n5\\n9\\n5\\n4\\n10\\n7\\n\", \"10 5\\n1 2 0 4 2 4 1 3 4 4\\n2 4 4 3 5 1 1 4 4 2\\n10\\n1\\n8\\n2\\n9\\n10\\n3\\n5\\n4\\n6\\n7\\n\", \"10 5\\n3 1 4 3 4 2 3 1 0 1\\n2 5 3 5 2 5 4 4 1 4\\n5\\n4\\n2\\n10\\n7\\n1\\n\", \"20 5\\n0 1 418 1718 2027 0 1 2 2 1 433 227 0 1 0 2 0 114 1 1329\\n4 5 4 2 4 1 3 1 2 4 5 1 5 2 3 5 3 2 3 4\\n10\\n20\\n12\\n11\\n18\\n5\\n3\\n4\\n9\\n16\\n8\\n\", \"20 20\\n10 13 3 14 17 19 0 7 16 5 9 8 12 2 18 6 11 4 15 1\\n20 8 17 11 2 10 12 4 19 7 6 3 1 18 16 5 14 13 9 15\\n15\\n9\\n15\\n6\\n5\\n13\\n2\\n19\\n4\\n11\\n17\\n12\\n1\\n10\\n18\\n16\\n\", \"10 5\\n1 0 1 4 2 4 4 0 1 1\\n4 4 4 5 2 1 4 2 3 5\\n5\\n1\\n6\\n3\\n2\\n7\\n\", \"20 8\\n1 17 10 12 13 7 14 9 16 15 6 3 11 18 19 8 4 2 0 5\\n8 6 3 4 4 8 5 8 3 7 4 2 4 5 7 1 4 6 4 1\\n8\\n13\\n17\\n20\\n11\\n3\\n16\\n2\\n4\\n\", \"10 10\\n8 5 1 3 9 2 7 0 6 4\\n6 4 8 2 7 9 5 1 10 3\\n10\\n9\\n2\\n1\\n7\\n5\\n6\\n8\\n3\\n10\\n4\\n\", \"20 5\\n6 3 8 0 0 2 7 5 7 1059 9 4 9 3457 1 3 8 988 6 8\\n1 4 2 3 2 2 4 1 1 5 1 5 1 3 1 5 2 5 3 4\\n10\\n3\\n11\\n12\\n19\\n18\\n10\\n17\\n13\\n8\\n14\\n\", \"10 5\\n9 7 8 0 1 4 5 2 6 3\\n5 5 4 4 2 2 1 3 4 5\\n5\\n9\\n6\\n10\\n5\\n1\\n\", \"1 1\\n0\\n1\\n1\\n1\\n\", \"20 20\\n0 0 3 2 1 2 2 3 2 2 1 1 0 3 0 0 1 1 1 3\\n15 1 20 13 6 12 16 8 3 14 10 5 18 17 4 9 2 11 7 19\\n20\\n2\\n10\\n7\\n4\\n6\\n5\\n14\\n8\\n9\\n18\\n13\\n11\\n19\\n1\\n16\\n20\\n17\\n12\\n15\\n3\\n\", \"10 5\\n5 1 9 7 3 2 8 0 6 4\\n1 1 1 5 4 3 2 5 2 4\\n10\\n9\\n3\\n5\\n7\\n10\\n6\\n1\\n4\\n2\\n8\\n\", \"5 5\\n0 0 1 1 2\\n1 2 2 5 2\\n2\\n2\\n3\\n\", \"5 3\\n0 0 1 1 4\\n1 2 2 3 2\\n2\\n2\\n3\\n\", \"20 5\\n0 1 418 1718 2027 0 1 2 2 1 433 227 0 1 0 2 0 114 1 1329\\n4 5 4 1 4 1 3 1 2 4 5 1 5 2 3 5 3 2 3 4\\n10\\n20\\n12\\n11\\n18\\n5\\n3\\n4\\n9\\n16\\n8\\n\", \"20 20\\n10 13 3 14 17 19 0 8 16 5 9 8 12 2 18 6 11 4 15 1\\n20 8 17 11 2 10 12 4 19 7 6 3 1 18 16 5 14 13 9 15\\n15\\n9\\n15\\n6\\n5\\n13\\n2\\n19\\n4\\n11\\n17\\n12\\n1\\n10\\n18\\n16\\n\", \"10 5\\n1 0 1 4 2 4 4 1 1 1\\n4 4 4 5 2 1 4 2 3 5\\n5\\n1\\n6\\n3\\n2\\n7\\n\", \"20 8\\n1 17 10 12 13 7 14 9 16 15 6 3 11 18 19 8 4 2 0 5\\n8 6 3 4 4 8 5 8 3 7 4 2 4 5 14 1 4 6 4 1\\n8\\n13\\n17\\n20\\n11\\n3\\n16\\n2\\n4\\n\", \"20 5\\n6 3 8 0 0 2 7 5 7 1059 9 4 1 3457 1 3 8 988 6 8\\n1 4 2 3 2 2 4 1 1 5 1 5 1 3 1 5 2 5 3 4\\n10\\n3\\n11\\n12\\n19\\n18\\n10\\n17\\n13\\n8\\n14\\n\", \"10 5\\n5 1 9 7 3 2 8 0 6 4\\n1 2 1 5 4 3 2 5 2 4\\n10\\n9\\n3\\n5\\n7\\n10\\n6\\n1\\n4\\n2\\n8\\n\", \"5 5\\n0 1 2 4 5\\n1 2 3 4 1\\n4\\n2\\n3\\n5\\n4\\n\", \"10 5\\n0 1 1 0 3 1 3 0 2 0\\n5 4 3 4 3 4 1 2 2 3\\n10\\n1\\n2\\n8\\n7\\n3\\n9\\n6\\n5\\n10\\n4\\n\", \"10 10\\n2 0 3 5 6 1 9 4 7 8\\n9 2 5 7 1 6 4 10 8 3\\n5\\n9\\n1\\n4\\n10\\n7\\n\", \"10 5\\n1 2 0 4 2 4 1 3 4 4\\n2 4 4 3 3 1 1 4 4 2\\n10\\n1\\n8\\n2\\n9\\n10\\n3\\n5\\n4\\n6\\n7\\n\", \"10 5\\n3 1 4 3 4 2 3 1 0 1\\n2 5 3 5 2 5 4 4 2 4\\n5\\n4\\n2\\n10\\n7\\n1\\n\", \"10 5\\n1 0 1 4 2 4 4 0 1 1\\n4 4 4 4 2 1 4 2 3 5\\n5\\n1\\n6\\n3\\n2\\n7\\n\", \"10 10\\n8 5 1 3 9 2 7 0 6 4\\n6 4 8 2 7 9 8 1 10 3\\n10\\n9\\n2\\n1\\n7\\n5\\n6\\n8\\n3\\n10\\n4\\n\", \"5 3\\n0 1 2 4 0\\n1 2 2 3 2\\n5\\n3\\n2\\n4\\n5\\n1\\n\", \"5 3\\n0 1 0 2 1\\n1 3 2 3 2\\n5\\n4\\n2\\n3\\n5\\n1\\n\", \"10 5\\n5 1 15 7 3 0 8 0 6 4\\n1 2 1 5 4 3 2 5 2 4\\n10\\n9\\n3\\n5\\n7\\n10\\n6\\n1\\n4\\n2\\n8\\n\", \"10 10\\n2 0 6 5 6 1 9 4 7 8\\n9 2 5 7 1 6 4 10 8 3\\n5\\n9\\n1\\n4\\n10\\n7\\n\", \"20 5\\n0 1 418 1718 2027 0 1 2 2 1 433 227 0 1 0 2 0 114 1 1329\\n4 5 2 2 4 1 3 1 2 4 5 1 5 2 3 5 3 2 3 4\\n10\\n20\\n12\\n11\\n18\\n5\\n3\\n4\\n13\\n16\\n8\\n\", \"10 10\\n8 5 1 3 9 2 7 0 6 4\\n6 4 9 2 7 9 8 1 10 3\\n10\\n9\\n2\\n1\\n7\\n5\\n6\\n8\\n3\\n10\\n4\\n\", \"5 3\\n0 2 2 4 0\\n1 2 2 3 2\\n5\\n3\\n2\\n4\\n5\\n1\\n\", \"10 5\\n2 1 15 5 3 2 8 0 7 5\\n1 2 1 5 4 3 2 5 2 4\\n10\\n9\\n3\\n5\\n7\\n10\\n6\\n1\\n4\\n2\\n8\\n\", \"20 20\\n10 13 3 14 17 19 0 8 16 5 9 8 12 2 18 6 11 4 15 1\\n16 8 17 11 2 10 12 4 19 7 6 3 1 18 16 5 14 13 9 15\\n15\\n9\\n15\\n6\\n5\\n13\\n2\\n19\\n4\\n11\\n17\\n12\\n1\\n10\\n18\\n16\\n\", \"10 5\\n5 1 15 7 3 2 8 0 6 4\\n1 2 1 5 4 3 2 5 2 4\\n10\\n9\\n3\\n5\\n7\\n10\\n6\\n1\\n4\\n2\\n8\\n\", \"20 20\\n10 13 3 14 4 19 0 8 16 5 9 8 12 2 18 6 11 4 15 1\\n16 8 17 11 2 10 12 4 19 7 6 3 1 18 16 5 14 13 9 15\\n15\\n9\\n15\\n6\\n5\\n13\\n2\\n19\\n4\\n11\\n17\\n12\\n1\\n10\\n18\\n16\\n\", \"10 5\\n5 1 15 7 3 2 8 0 7 4\\n1 2 1 5 4 3 2 5 2 4\\n10\\n9\\n3\\n5\\n7\\n10\\n6\\n1\\n4\\n2\\n8\\n\", \"10 5\\n5 1 15 5 3 2 8 0 7 4\\n1 2 1 5 4 3 2 5 2 4\\n10\\n9\\n3\\n5\\n7\\n10\\n6\\n1\\n4\\n2\\n8\\n\", \"20 5\\n0 1 418 1718 2027 0 1 2 2 1 433 227 0 1 0 2 0 114 1 1329\\n4 5 2 2 4 1 3 1 2 4 5 1 5 2 3 5 3 2 3 4\\n10\\n20\\n12\\n11\\n18\\n5\\n3\\n4\\n9\\n16\\n8\\n\", \"20 5\\n6 3 8 0 0 2 7 5 7 1059 9 4 9 3457 1 3 8 988 6 8\\n1 4 2 3 2 2 4 1 1 5 1 5 1 3 1 5 2 5 3 4\\n10\\n3\\n11\\n12\\n19\\n18\\n7\\n17\\n13\\n8\\n14\\n\", \"10 5\\n5 1 11 7 3 2 8 0 6 4\\n1 1 1 5 4 3 2 5 2 4\\n10\\n9\\n3\\n5\\n7\\n10\\n6\\n1\\n4\\n2\\n8\\n\", \"5 5\\n0 1 2 4 0\\n1 2 3 4 5\\n4\\n2\\n3\\n5\\n4\\n\", \"5 5\\n0 0 1 1 2\\n1 2 1 5 2\\n2\\n2\\n3\\n\", \"20 5\\n0 1 418 1718 2027 0 1 2 2 1 433 227 0 1 0 2 0 114 1 1329\\n4 5 4 1 4 1 3 1 2 4 5 1 4 2 3 5 3 2 3 4\\n10\\n20\\n12\\n11\\n18\\n5\\n3\\n4\\n9\\n16\\n8\\n\", \"20 5\\n6 3 8 0 0 2 7 5 7 1059 9 4 1 3457 1 3 8 988 6 8\\n1 4 2 3 2 2 4 1 2 5 1 5 1 3 1 5 2 5 3 4\\n10\\n3\\n11\\n12\\n19\\n18\\n10\\n17\\n13\\n8\\n14\\n\", \"20 20\\n10 13 3 14 17 19 0 8 16 5 9 8 12 2 32 6 11 4 15 1\\n16 8 17 11 2 10 12 4 19 7 6 3 1 18 16 5 14 13 9 15\\n15\\n9\\n15\\n6\\n5\\n13\\n2\\n19\\n4\\n11\\n17\\n12\\n1\\n10\\n18\\n16\\n\", \"10 5\\n5 1 15 5 3 2 8 0 7 5\\n1 2 1 5 4 3 2 5 2 4\\n10\\n9\\n3\\n5\\n7\\n10\\n6\\n1\\n4\\n2\\n8\\n\", \"5 5\\n0 1 2 4 0\\n1 2 1 4 5\\n4\\n2\\n3\\n5\\n4\\n\", \"5 3\\n0 1 0 2 0\\n1 3 2 3 2\\n5\\n4\\n2\\n3\\n5\\n1\\n\", \"5 5\\n0 0 0 1 2\\n1 2 1 5 2\\n2\\n2\\n3\\n\", \"20 5\\n0 1 418 1718 2027 0 1 2 2 1 433 84 0 1 0 2 0 114 1 1329\\n4 5 4 1 4 1 3 1 2 4 5 1 4 2 3 5 3 2 3 4\\n10\\n20\\n12\\n11\\n18\\n5\\n3\\n4\\n9\\n16\\n8\\n\", \"20 5\\n12 3 8 0 0 2 7 5 7 1059 9 4 1 3457 1 3 8 988 6 8\\n1 4 2 3 2 2 4 1 2 5 1 5 1 3 1 5 2 5 3 4\\n10\\n3\\n11\\n12\\n19\\n18\\n10\\n17\\n13\\n8\\n14\\n\", \"10 10\\n2 0 6 5 0 1 9 4 7 8\\n9 2 5 7 1 6 4 10 8 3\\n5\\n9\\n1\\n4\\n10\\n7\\n\", \"5 5\\n0 1 2 4 0\\n1 2 1 5 5\\n4\\n2\\n3\\n5\\n4\\n\", \"5 3\\n0 0 2 4 0\\n1 2 2 3 2\\n5\\n3\\n2\\n4\\n5\\n1\\n\", \"20 5\\n12 3 8 0 0 2 7 5 7 1059 9 4 1 3457 1 3 8 988 6 8\\n1 4 2 3 2 2 4 1 2 4 1 5 1 3 1 5 2 5 3 4\\n10\\n3\\n11\\n12\\n19\\n18\\n10\\n17\\n13\\n8\\n14\\n\", \"5 3\\n0 0 0 4 0\\n1 2 2 3 2\\n5\\n3\\n2\\n4\\n5\\n1\\n\", \"20 5\\n12 3 8 0 1 2 7 5 7 1059 9 4 1 3457 1 3 8 988 6 8\\n1 4 2 3 2 2 4 1 2 4 1 5 1 3 1 5 2 5 3 4\\n10\\n3\\n11\\n12\\n19\\n18\\n10\\n17\\n13\\n8\\n14\\n\"], \"outputs\": [\"1\\n1\\n1\\n1\\n\", \"3\\n1\\n1\\n1\\n0\\n\", \"3\\n2\\n2\\n1\\n0\\n\", \"3\\n3\\n\", \"3\\n3\\n\", \"4\\n4\\n2\\n2\\n2\\n2\\n1\\n1\\n1\\n0\\n\", \"7\\n6\\n5\\n5\\n5\\n\", \"3\\n3\\n3\\n3\\n3\\n0\\n0\\n0\\n0\\n0\\n\", \"5\\n5\\n5\\n5\\n3\\n\", \"3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n2\\n\", \"16\\n16\\n16\\n16\\n12\\n12\\n12\\n12\\n9\\n9\\n8\\n8\\n5\\n4\\n4\\n\", \"3\\n3\\n3\\n2\\n2\\n\", \"4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\", \"6\\n5\\n5\\n5\\n5\\n2\\n0\\n0\\n0\\n0\\n\", \"5\\n5\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n3\\n1\\n1\\n\", \"0\\n\", \"4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n2\\n2\\n2\\n2\\n2\\n2\\n2\\n2\\n2\\n1\\n0\\n0\\n\", \"4\\n4\\n3\\n3\\n3\\n2\\n2\\n2\\n1\\n0\\n\", \"3\\n3\\n\", \"2\\n2\\n\", \"3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n2\\n\", \"7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n5\\n4\\n4\\n\", \"3\\n3\\n3\\n0\\n0\\n\", \"4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\", \"5\\n5\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n3\\n3\\n3\\n2\\n2\\n2\\n1\\n0\\n\", \"1\\n1\\n1\\n1\\n\", \"4\\n4\\n4\\n3\\n3\\n2\\n1\\n1\\n1\\n0\\n\", \"7\\n2\\n2\\n2\\n2\\n\", \"3\\n3\\n3\\n3\\n3\\n0\\n0\\n0\\n0\\n0\\n\", \"3\\n3\\n3\\n3\\n3\\n\", \"3\\n3\\n3\\n2\\n2\\n\", \"6\\n5\\n5\\n5\\n5\\n2\\n0\\n0\\n0\\n0\\n\", \"2\\n1\\n1\\n1\\n0\\n\", \"2\\n2\\n2\\n1\\n0\\n\", \"2\\n2\\n2\\n2\\n2\\n2\\n2\\n2\\n1\\n0\\n\", \"3\\n2\\n2\\n2\\n2\\n\", \"3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n\", \"2\\n2\\n2\\n2\\n2\\n2\\n0\\n0\\n0\\n0\\n\", \"1\\n1\\n1\\n1\\n0\\n\", \"4\\n4\\n3\\n3\\n3\\n3\\n2\\n2\\n1\\n0\\n\", \"7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n5\\n4\\n4\\n\", \"4\\n4\\n3\\n3\\n3\\n2\\n2\\n2\\n1\\n0\\n\", \"7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n5\\n4\\n4\\n\", \"4\\n4\\n3\\n3\\n3\\n2\\n2\\n2\\n1\\n0\\n\", \"4\\n4\\n3\\n3\\n3\\n2\\n2\\n2\\n1\\n0\\n\", \"3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n2\\n\", \"5\\n5\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\", \"4\\n4\\n3\\n3\\n3\\n2\\n2\\n2\\n1\\n0\\n\", \"1\\n1\\n1\\n1\\n\", \"3\\n3\\n\", \"3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n2\\n\", \"5\\n5\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\", \"7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n7\\n5\\n4\\n4\\n\", \"4\\n4\\n3\\n3\\n3\\n2\\n2\\n2\\n1\\n0\\n\", \"1\\n1\\n1\\n1\\n\", \"2\\n1\\n1\\n1\\n0\\n\", \"3\\n3\\n\", \"3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n3\\n2\\n\", \"5\\n5\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\", \"3\\n2\\n2\\n2\\n2\\n\", \"1\\n1\\n1\\n1\\n\", \"1\\n1\\n1\\n1\\n0\\n\", \"5\\n5\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\", \"1\\n1\\n1\\n1\\n0\\n\", \"5\\n5\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n4\\n\"]}", "source": "primeintellect"}
|
There are n students and m clubs in a college. The clubs are numbered from 1 to m. Each student has a potential p_i and is a member of the club with index c_i. Initially, each student is a member of exactly one club. A technical fest starts in the college, and it will run for the next d days. There is a coding competition every day in the technical fest.
Every day, in the morning, exactly one student of the college leaves their club. Once a student leaves their club, they will never join any club again. Every day, in the afternoon, the director of the college will select one student from each club (in case some club has no members, nobody is selected from that club) to form a team for this day's coding competition. The strength of a team is the mex of potentials of the students in the team. The director wants to know the maximum possible strength of the team for each of the coming d days. Thus, every day the director chooses such team, that the team strength is maximized.
The mex of the multiset S is the smallest non-negative integer that is not present in S. For example, the mex of the \{0, 1, 1, 2, 4, 5, 9\} is 3, the mex of \{1, 2, 3\} is 0 and the mex of ∅ (empty set) is 0.
Input
The first line contains two integers n and m (1 ≤ m ≤ n ≤ 5000), the number of students and the number of clubs in college.
The second line contains n integers p_1, p_2, …, p_n (0 ≤ p_i < 5000), where p_i is the potential of the i-th student.
The third line contains n integers c_1, c_2, …, c_n (1 ≤ c_i ≤ m), which means that i-th student is initially a member of the club with index c_i.
The fourth line contains an integer d (1 ≤ d ≤ n), number of days for which the director wants to know the maximum possible strength of the team.
Each of the next d lines contains an integer k_i (1 ≤ k_i ≤ n), which means that k_i-th student lefts their club on the i-th day. It is guaranteed, that the k_i-th student has not left their club earlier.
Output
For each of the d days, print the maximum possible strength of the team on that day.
Examples
Input
5 3
0 1 2 2 0
1 2 2 3 2
5
3
2
4
5
1
Output
3
1
1
1
0
Input
5 3
0 1 2 2 1
1 3 2 3 2
5
4
2
3
5
1
Output
3
2
2
1
0
Input
5 5
0 1 2 4 5
1 2 3 4 5
4
2
3
5
4
Output
1
1
1
1
Note
Consider the first example:
On the first day, student 3 leaves their club. Now, the remaining students are 1, 2, 4 and 5. We can select students 1, 2 and 4 to get maximum possible strength, which is 3. Note, that we can't select students 1, 2 and 5, as students 2 and 5 belong to the same club. Also, we can't select students 1, 3 and 4, since student 3 has left their club.
On the second day, student 2 leaves their club. Now, the remaining students are 1, 4 and 5. We can select students 1, 4 and 5 to get maximum possible strength, which is 1.
On the third day, the remaining students are 1 and 5. We can select students 1 and 5 to get maximum possible strength, which is 1.
On the fourth day, the remaining student is 1. We can select student 1 to get maximum possible strength, which is 1.
On the fifth day, no club has students and so the maximum possible strength is 0.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4\\n0 1 2 1\\n3 2 1 1\\n\", \"7\\n2 5 1 5 3 4 3\\n2 4 3 5 6 5 1\\n\", \"1\\n0\\n0\\n\", \"10\\n6 3 0 5 4 5 5 5 8 5\\n3 8 2 9 5 4 1 0 3 6\\n\", \"5\\n1 4 2 1 3\\n3 3 1 0 1\\n\", \"5\\n2 1 3 0 4\\n1 0 3 2 3\\n\", \"4\\n1 2 1 1\\n1 3 0 2\\n\", \"3\\n2 0 0\\n1 0 2\\n\", \"4\\n1 1 0 3\\n2 0 2 2\\n\", \"3\\n0 1 1\\n0 1 0\\n\", \"2\\n1 1\\n0 1\\n\", \"3\\n2 0 0\\n2 2 0\\n\", \"2\\n0 0\\n1 1\\n\", \"4\\n1 2 3 2\\n3 0 1 0\\n\", \"6\\n0 2 1 5 1 4\\n0 0 3 0 5 1\\n\", \"5\\n1 3 1 2 3\\n1 4 2 0 4\\n\", \"10\\n6 3 0 5 4 5 5 4 8 5\\n3 8 2 9 5 4 1 0 3 6\\n\", \"5\\n1 4 2 1 3\\n3 3 0 0 1\\n\", \"5\\n2 1 3 0 4\\n1 0 3 1 3\\n\", \"4\\n1 2 0 1\\n1 3 0 2\\n\", \"3\\n0 1 0\\n0 1 0\\n\", \"2\\n0 1\\n0 1\\n\", \"3\\n1 0 0\\n2 2 0\\n\", \"2\\n1 0\\n1 1\\n\", \"4\\n0 2 3 2\\n3 0 1 0\\n\", \"5\\n1 3 1 3 3\\n1 4 2 0 4\\n\", \"4\\n0 0 2 1\\n3 2 1 1\\n\", \"7\\n2 5 1 5 3 4 1\\n2 4 3 5 6 5 1\\n\", \"4\\n1 2 0 1\\n2 3 0 2\\n\", \"3\\n1 1 0\\n0 1 0\\n\", \"2\\n2 0\\n1 1\\n\", \"4\\n0 2 3 2\\n3 0 0 0\\n\", \"5\\n2 3 1 3 3\\n1 4 2 0 4\\n\", \"4\\n0 1 2 1\\n3 3 1 1\\n\", \"7\\n2 5 1 5 3 4 1\\n1 4 3 5 6 5 1\\n\", \"3\\n1 2 0\\n0 1 0\\n\", \"4\\n0 2 3 2\\n1 0 1 0\\n\", \"5\\n2 3 1 3 3\\n1 4 0 0 4\\n\", \"4\\n0 2 2 1\\n3 3 1 1\\n\", \"3\\n0 2 0\\n0 1 0\\n\", \"4\\n0 2 3 2\\n1 0 0 0\\n\", \"4\\n0 3 2 1\\n3 3 1 1\\n\", \"7\\n2 5 1 5 3 4 1\\n1 1 3 5 6 5 2\\n\", \"3\\n0 2 0\\n0 0 0\\n\", \"4\\n0 3 2 1\\n3 3 2 1\\n\", \"7\\n2 5 1 5 3 4 1\\n0 1 3 5 6 5 2\\n\", \"7\\n2 5 1 0 3 5 1\\n0 1 3 5 6 5 2\\n\", \"7\\n2 5 1 0 2 5 1\\n0 1 3 5 6 5 2\\n\", \"7\\n2 5 1 0 2 5 1\\n0 1 3 5 6 3 2\\n\", \"7\\n2 5 1 0 2 5 2\\n0 1 3 5 6 3 2\\n\", \"7\\n2 5 0 0 2 5 2\\n0 1 3 5 6 3 2\\n\", \"7\\n0 5 0 0 2 5 2\\n0 1 3 5 6 3 2\\n\", \"7\\n0 5 0 0 2 5 2\\n0 1 3 5 6 0 2\\n\", \"7\\n0 0 0 0 2 5 2\\n0 1 3 5 6 0 2\\n\", \"10\\n6 3 0 5 6 5 5 5 8 5\\n3 8 2 9 5 4 1 0 3 6\\n\", \"5\\n1 3 2 1 3\\n3 3 1 0 1\\n\", \"5\\n2 1 3 0 4\\n1 0 1 2 3\\n\", \"4\\n1 2 1 1\\n1 3 0 1\\n\", \"4\\n1 1 0 2\\n2 0 2 2\\n\", \"3\\n1 0 0\\n1 2 0\\n\", \"6\\n0 0 1 5 1 4\\n0 0 3 0 5 1\\n\", \"5\\n1 3 2 2 3\\n1 4 2 0 4\\n\", \"4\\n0 1 2 1\\n2 2 1 1\\n\", \"7\\n2 5 1 5 3 4 6\\n2 4 3 5 6 5 1\\n\", \"10\\n6 3 0 5 4 5 5 4 8 5\\n3 4 2 9 5 4 1 0 3 6\\n\", \"5\\n1 4 3 1 3\\n3 3 0 0 1\\n\", \"5\\n1 1 3 0 4\\n1 0 3 1 3\\n\", \"4\\n1 2 1 1\\n2 3 0 2\\n\", \"5\\n1 3 0 3 3\\n1 4 2 0 4\\n\", \"7\\n2 5 1 5 3 4 0\\n2 4 3 5 6 5 1\\n\", \"3\\n2 1 0\\n0 1 0\\n\", \"7\\n2 5 1 5 3 0 1\\n1 4 3 5 6 5 1\\n\", \"3\\n1 2 1\\n0 1 0\\n\", \"5\\n2 3 1 3 3\\n1 1 0 0 4\\n\", \"4\\n0 2 2 1\\n3 3 1 0\\n\", \"7\\n2 5 1 5 1 4 1\\n1 4 3 5 6 5 2\\n\", \"4\\n0 2 3 3\\n1 0 0 1\\n\", \"4\\n0 3 0 1\\n3 3 1 1\\n\", \"2\\n0 1\\n0 0\\n\", \"7\\n2 5 1 5 3 4 1\\n1 4 3 5 6 5 2\\n\", \"4\\n0 2 3 3\\n1 0 0 0\\n\", \"7\\n2 5 1 5 3 5 1\\n0 1 3 5 6 5 2\\n\", \"3\\n0 1 1\\n0 0 0\\n\", \"2\\n0 0\\n1 0\\n\", \"4\\n1 2 3 2\\n3 0 1 1\\n\", \"3\\n0 0 0\\n0 1 0\\n\", \"4\\n0 2 3 2\\n3 1 0 0\\n\", \"5\\n0 3 1 3 3\\n1 4 2 0 4\\n\", \"7\\n2 5 1 5 3 4 1\\n1 0 3 5 6 5 2\\n\"], \"outputs\": [\"1 0 0 2 \", \"0 0 0 1 0 2 4 \", \"0 \", \"0 1 0 0 0 4 6 7 1 8 \", \"1 0 0 2 1 \", \"0 1 0 1 2 \", \"0 0 1 2 \", \"0 0 2 \", \"1 3 2 1 \", \"0 1 2 \", \"0 1 \", \"1 0 2 \", \"1 1 \", \"0 2 0 2 \", \"0 1 1 0 1 1 \", \"0 0 0 2 4 \", \"0 1 0 0 0 4 6 6 1 8\\n\", \"1 0 0 1 1\\n\", \"0 1 1 1 0\\n\", \"0 0 0 2\\n\", \"0 1 1\\n\", \"0 0\\n\", \"0 0 2\\n\", \"0 1\\n\", \"0 1 0 2\\n\", \"0 0 0 3 4\\n\", \"1 1 0 0\\n\", \"0 0 0 1 0 2 2\\n\", \"0 0 0 3\\n\", \"1 1 1\\n\", \"1 1\\n\", \"0 1 3 2\\n\", \"1 0 0 3 4\\n\", \"1 0 1 2\\n\", \"0 1 0 2 1 5 2\\n\", \"1 0 0\\n\", \"0 2 0 3\\n\", \"1 2 1 3 4\\n\", \"1 1 1 2\\n\", \"0 0 0\\n\", \"0 2 0 2\\n\", \"1 0 1 0\\n\", \"0 0 0 1 1 5 2\\n\", \"0 2 0\\n\", \"1 1 1 0\\n\", \"0 0 0 1 1 4 2\\n\", \"0 0 0 0 1 1 2\\n\", \"0 0 0 0 0 1 2\\n\", \"0 0 0 0 3 1 4\\n\", \"0 0 0 0 3 1 5\\n\", \"0 0 0 1 1 1 5\\n\", \"0 0 1 3 0 1 1\\n\", \"0 0 0 1 0 1 1\\n\", \"0 0 1 2 0 1 1\\n\", \"0 1 0 0 2 4 6 7 1 8\\n\", \"1 1 0 2 4\\n\", \"0 1 0 1 0\\n\", \"0 2 2 2\\n\", \"1 3 2 0\\n\", \"0 0 1\\n\", \"0 0 0 0 1 1\\n\", \"0 0 1 2 4\\n\", \"1 2 0 3\\n\", \"0 0 0 1 0 2 0\\n\", \"0 2 0 0 0 6 7 7 1 9\\n\", \"1 0 1 1 1\\n\", \"1 2 1 1 2\\n\", \"0 0 1 3\\n\", \"0 0 0 2 4\\n\", \"0 0 0 1 0 2 1\\n\", \"0 1 0\\n\", \"0 1 0 2 1 1 2\\n\", \"1 0 1\\n\", \"1 3 1 4 4\\n\", \"0 1 1 2\\n\", \"0 0 0 1 2 1 6\\n\", \"0 2 0 0\\n\", \"1 0 3 0\\n\", \"0 1\\n\", \"0 0 0 1 0 2 2\\n\", \"0 2 0 3\\n\", \"0 0 0 1 1 5 2\\n\", \"0 1 1\\n\", \"0 1\\n\", \"0 2 0 3\\n\", \"0 0 1\\n\", \"0 1 0 2\\n\", \"0 0 0 2 4\\n\", \"0 0 0 1 1 4 2\\n\"]}", "source": "primeintellect"}
|
You are given two arrays a and b, both of length n. All elements of both arrays are from 0 to n-1.
You can reorder elements of the array b (if you want, you may leave the order of elements as it is). After that, let array c be the array of length n, the i-th element of this array is c_i = (a_i + b_i) \% n, where x \% y is x modulo y.
Your task is to reorder elements of the array b to obtain the lexicographically minimum possible array c.
Array x of length n is lexicographically less than array y of length n, if there exists such i (1 ≤ i ≤ n), that x_i < y_i, and for any j (1 ≤ j < i) x_j = y_j.
Input
The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a, b and c.
The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i < n), where a_i is the i-th element of a.
The third line of the input contains n integers b_1, b_2, ..., b_n (0 ≤ b_i < n), where b_i is the i-th element of b.
Output
Print the lexicographically minimum possible array c. Recall that your task is to reorder elements of the array b and obtain the lexicographically minimum possible array c, where the i-th element of c is c_i = (a_i + b_i) \% n.
Examples
Input
4
0 1 2 1
3 2 1 1
Output
1 0 0 2
Input
7
2 5 1 5 3 4 3
2 4 3 5 6 5 1
Output
0 0 0 1 0 2 4
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
{"tests": "{\"inputs\": [\"5\\nAABBB\\n\", \"3\\nAAA\\n\", \"7\\nAAABABB\\n\", \"3\\nABA\\n\", \"7\\nBBABAAA\\n\", \"7\\nBAAAABB\\n\", \"5\\nBBBBA\\n\", \"7\\nABABAAB\\n\", \"7\\nBBAAABA\\n\", \"3\\nBBB\\n\", \"5\\nABBAA\\n\", \"5\\nABBBA\\n\", \"7\\nBAAAAAB\\n\", \"7\\nAAAAAAA\\n\", \"3\\nBAA\\n\", \"3\\nAAB\\n\", \"7\\nBBAAAAB\\n\", \"3\\nBBA\\n\", \"3\\nBAB\\n\", \"7\\nABBAAAB\\n\", \"7\\nBBABAAB\\n\", \"3\\nABB\\n\", \"7\\nAABBABB\\n\", \"7\\nAAAAABB\\n\", \"7\\nBBAAABB\\n\", \"5\\nABBBB\\n\", \"7\\nABAAABB\\n\", \"7\\nABBAABA\\n\", \"7\\nAABAABA\\n\", \"7\\nAABAAAA\\n\", \"7\\nAAABBBB\\n\", \"7\\nBBBAAAB\\n\", \"7\\nBBAAAAA\\n\", \"7\\nBAABABB\\n\", \"7\\nBBAABAB\\n\", \"7\\nBBABABA\\n\", \"5\\nBBABA\\n\", \"7\\nABAAABA\\n\", \"7\\nABBABBA\\n\", \"7\\nABAABAA\\n\", \"7\\nBABABAB\\n\", \"7\\nBBAABAA\\n\", \"7\\nBBABABB\\n\", \"7\\nBBBABAB\\n\", \"7\\nABABABB\\n\", \"5\\nABABB\\n\", \"7\\nABBAABB\\n\", \"7\\nBBBABBB\\n\", \"7\\nBAABAAB\\n\", \"7\\nBBBABBA\\n\", \"7\\nBAABBAB\\n\", \"7\\nBAAABAB\\n\", \"7\\nBAAABBB\\n\", \"7\\nBABABBB\\n\", \"7\\nABBBAAB\\n\", \"7\\nBABBABB\\n\", \"7\\nABBAAAA\\n\", \"7\\nAABBABA\\n\", \"7\\nAAAABBA\\n\", \"5\\nABBAB\\n\", \"7\\nAAABBAB\\n\", \"7\\nBBBAAAA\\n\", \"7\\nAAABAAB\\n\", \"7\\nABAABBB\\n\", \"7\\nAABABBA\\n\", \"7\\nABAAAAA\\n\", \"7\\nAABAABB\\n\", \"7\\nBAABABA\\n\", \"7\\nBABBAAB\\n\", \"7\\nBABAAAB\\n\", \"7\\nABBABAB\\n\", \"7\\nBBABBAB\\n\", \"7\\nBABAABB\\n\", \"5\\nBABBA\\n\", \"7\\nABABBAA\\n\", \"7\\nAAAABAA\\n\", \"7\\nABABABA\\n\", \"7\\nBBBAABA\\n\", \"7\\nABAAAAB\\n\", \"7\\nAABABAB\\n\", \"7\\nAAAABAB\\n\", \"7\\nBABAAAA\\n\", \"7\\nABABBBB\\n\", \"5\\nBABAA\\n\", \"7\\nABBBABA\\n\", \"7\\nAAAAAAB\\n\", \"7\\nBABAABA\\n\", \"5\\nAABAA\\n\", \"7\\nBAAAAAA\\n\", \"7\\nABAABAB\\n\", \"7\\nAAAAABA\\n\", \"7\\nBAAAABA\\n\", \"5\\nBAABB\\n\", \"7\\nAABBAAB\\n\", \"7\\nBAABBBA\\n\", \"7\\nABABBAB\\n\", \"7\\nABBBABB\\n\", \"7\\nBAAABAA\\n\", \"5\\nBBAAA\\n\", \"7\\nABABBBA\\n\", \"5\\nABABA\\n\", \"7\\nAABAAAB\\n\", \"7\\nBBAABBA\\n\"], \"outputs\": [\"6\\n\", \"3\\n\", \"15\\n\", \"1\\n\", \"15\\n\", \"12\\n\", \"6\\n\", \"14\\n\", \"13\\n\", \"3\\n\", \"5\\n\", \"4\\n\", \"11\\n\", \"21\\n\", \"1\\n\", \"1\\n\", \"12\\n\", \"1\\n\", \"1\\n\", \"12\\n\", \"14\\n\", \"1\\n\", \"14\\n\", \"15\\n\", \"13\\n\", \"6\\n\", \"13\\n\", \"13\\n\", \"14\\n\", \"15\\n\", \"15\\n\", \"13\\n\", \"15\\n\", \"14\\n\", \"14\\n\", \"15\\n\", \"6\\n\", \"13\\n\", \"13\\n\", \"14\\n\", \"15\\n\", \"14\\n\", \"15\\n\", \"15\\n\", \"15\\n\", \"6\\n\", \"13\\n\", \"15\\n\", \"13\\n\", \"14\\n\", \"13\\n\", \"13\\n\", \"13\\n\", \"15\\n\", \"12\\n\", \"14\\n\", \"14\\n\", \"14\\n\", \"14\\n\", \"5\\n\", \"14\\n\", \"15\\n\", \"14\\n\", \"14\\n\", \"14\\n\", \"15\\n\", \"14\\n\", \"14\\n\", \"13\\n\", \"13\\n\", \"14\\n\", \"14\\n\", \"14\\n\", \"5\\n\", \"14\\n\", \"15\\n\", \"15\\n\", \"14\\n\", \"12\\n\", \"15\\n\", \"15\\n\", \"15\\n\", \"15\\n\", \"6\\n\", \"13\\n\", \"15\\n\", \"14\\n\", \"6\\n\", \"15\\n\", \"14\\n\", \"15\\n\", \"12\\n\", \"5\\n\", \"13\\n\", \"12\\n\", \"14\\n\", \"13\\n\", \"13\\n\", \"6\\n\", \"13\\n\", \"6\\n\", \"13\\n\", \"13\\n\"]}", "source": "primeintellect"}
|
The string t_1t_2 ... t_k is good if each letter of this string belongs to at least one palindrome of length greater than 1.
A palindrome is a string that reads the same backward as forward. For example, the strings A, BAB, ABBA, BAABBBAAB are palindromes, but the strings AB, ABBBAA, BBBA are not.
Here are some examples of good strings:
* t = AABBB (letters t_1, t_2 belong to palindrome t_1 ... t_2 and letters t_3, t_4, t_5 belong to palindrome t_3 ... t_5);
* t = ABAA (letters t_1, t_2, t_3 belong to palindrome t_1 ... t_3 and letter t_4 belongs to palindrome t_3 ... t_4);
* t = AAAAA (all letters belong to palindrome t_1 ... t_5);
You are given a string s of length n, consisting of only letters A and B.
You have to calculate the number of good substrings of string s.
Input
The first line contains one integer n (1 ≤ n ≤ 3 ⋅ 10^5) — the length of the string s.
The second line contains the string s, consisting of letters A and B.
Output
Print one integer — the number of good substrings of string s.
Examples
Input
5
AABBB
Output
6
Input
3
AAA
Output
3
Input
7
AAABABB
Output
15
Note
In the first test case there are six good substrings: s_1 ... s_2, s_1 ... s_4, s_1 ... s_5, s_3 ... s_4, s_3 ... s_5 and s_4 ... s_5.
In the second test case there are three good substrings: s_1 ... s_2, s_1 ... s_3 and s_2 ... s_3.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5\\n01110\\n10010\\n10001\\n10011\\n11110\\n\", \"3\\n000\\n000\\n000\\n\", \"10\\n1111100000\\n0010100000\\n0110111000\\n0000001000\\n1011001010\\n0010100001\\n0010111000\\n0011001010\\n0000110010\\n0000001100\\n\", \"10\\n1101010101\\n1110101010\\n0111010101\\n1011101010\\n0101110101\\n1010111010\\n0101011101\\n1010101110\\n0101010111\\n1010101011\\n\", \"2\\n11\\n11\\n\", \"1\\n0\\n\", \"10\\n1100011000\\n0000101000\\n1001000011\\n0000100010\\n1101010011\\n1100100101\\n1000011101\\n1001110011\\n1110111100\\n1000111100\\n\", \"3\\n001\\n100\\n101\\n\", \"6\\n110000\\n000010\\n001011\\n011011\\n100001\\n111000\\n\", \"10\\n0000000000\\n0000110000\\n1001000000\\n1000011110\\n1011111101\\n1011110011\\n1011000111\\n1011000001\\n1111000010\\n0000111110\\n\", \"3\\n011\\n110\\n001\\n\", \"10\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n\", \"4\\n1001\\n0000\\n1001\\n0110\\n\", \"10\\n1100111010\\n1000011011\\n0110000000\\n1001111011\\n0011011010\\n1100001001\\n0011010110\\n1100011110\\n0000101011\\n1110101011\\n\", \"5\\n01010\\n01101\\n11110\\n00111\\n10100\\n\", \"6\\n100000\\n010000\\n001000\\n000100\\n000000\\n000001\\n\", \"2\\n00\\n00\\n\", \"2\\n11\\n00\\n\", \"2\\n10\\n00\\n\", \"1\\n1\\n\", \"4\\n0000\\n0111\\n0001\\n0001\\n\", \"7\\n0000010\\n0100101\\n0010011\\n0111111\\n0100000\\n0110010\\n0000101\\n\", \"2\\n11\\n10\\n\", \"3\\n000\\n000\\n010\\n\", \"10\\n1111100000\\n0010100000\\n0110111000\\n0000001000\\n1011001010\\n0010100001\\n0010111000\\n0011001011\\n0000110010\\n0000001100\\n\", \"10\\n1101010101\\n1110101010\\n0111010101\\n1011101010\\n0101010101\\n1010111010\\n0101011101\\n1010101110\\n0101010111\\n1010101011\\n\", \"10\\n1100011000\\n0000101000\\n1001000011\\n0000100010\\n1101010011\\n1100100101\\n1000011101\\n1001110001\\n1110111100\\n1000111100\\n\", \"3\\n011\\n100\\n101\\n\", \"6\\n110100\\n000010\\n001011\\n011011\\n100001\\n111000\\n\", \"10\\n0000000000\\n0000110000\\n1001000000\\n1000011110\\n1011111101\\n1011110011\\n1011000111\\n1011000001\\n1111000010\\n0001111110\\n\", \"3\\n001\\n110\\n001\\n\", \"4\\n1001\\n0000\\n1001\\n0100\\n\", \"10\\n1100111010\\n1000011011\\n0110000000\\n1001111011\\n0001011010\\n1100001001\\n0011010110\\n1100011110\\n0000101011\\n1110101011\\n\", \"5\\n01010\\n01100\\n11110\\n00111\\n10100\\n\", \"6\\n100000\\n010000\\n001000\\n000000\\n000000\\n000001\\n\", \"7\\n0000010\\n0100111\\n0010011\\n0111111\\n0100000\\n0110010\\n0000101\\n\", \"10\\n1111100000\\n0010100000\\n0100111000\\n0000001000\\n1011001010\\n0010100001\\n0010111000\\n0011001011\\n0000110010\\n0000001100\\n\", \"10\\n1101010101\\n1110101010\\n0111010101\\n1011101010\\n0101010101\\n1010111010\\n0101011101\\n1010101110\\n0101010101\\n1010101011\\n\", \"10\\n1100011000\\n0000101000\\n1001000011\\n0000100010\\n1101010011\\n1100100101\\n1000011101\\n1001110001\\n1111111100\\n1000111100\\n\", \"3\\n011\\n000\\n101\\n\", \"3\\n001\\n110\\n101\\n\", \"4\\n1001\\n0000\\n1011\\n0100\\n\", \"10\\n1100111010\\n1000011011\\n0110000000\\n1001111011\\n0001011010\\n1100001001\\n0011010110\\n1100011110\\n0000101011\\n1110101010\\n\", \"5\\n11010\\n01100\\n11110\\n00111\\n10100\\n\", \"6\\n100000\\n010000\\n001000\\n000000\\n000000\\n001001\\n\", \"10\\n1111100000\\n0010100000\\n0100111000\\n0000001000\\n1011001010\\n0010100001\\n0010111000\\n0111001011\\n0000110010\\n0000001100\\n\", \"10\\n1101010101\\n1110101010\\n0111010101\\n1011101010\\n0101010101\\n1010111010\\n0101011101\\n1010101010\\n0101010101\\n1010101011\\n\", \"10\\n1100111010\\n1000011011\\n0110000000\\n1001111011\\n0001011010\\n1000001001\\n0011010110\\n1100011110\\n0000101011\\n1110101010\\n\", \"5\\n11010\\n01100\\n11110\\n00111\\n10101\\n\", \"10\\n1111100000\\n0010100000\\n0100111000\\n0000001000\\n1011001010\\n0010100001\\n0010111000\\n0111001011\\n0000110000\\n0000001100\\n\", \"10\\n1101011101\\n1110101010\\n0111010101\\n1011101010\\n0101010101\\n1010111010\\n0101011101\\n1010101010\\n0101010101\\n1010101011\\n\", \"10\\n1100011000\\n0000101000\\n1001000011\\n0000100010\\n1101010010\\n1100100101\\n1000011101\\n1001111001\\n1111111100\\n1000111100\\n\", \"10\\n0000000000\\n0000110000\\n1001000000\\n0000011110\\n1011111101\\n1011110011\\n1011000111\\n1010010001\\n1111000010\\n0001111110\\n\", \"4\\n1001\\n0000\\n1011\\n0010\\n\", \"10\\n1100111010\\n1000011011\\n0110000000\\n1001111011\\n0001011010\\n1000101001\\n0011010110\\n1100011110\\n0000101011\\n1110101010\\n\", \"5\\n11010\\n01100\\n11111\\n00111\\n10101\\n\", \"10\\n0000000000\\n1000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n\", \"4\\n0000\\n0101\\n0001\\n0001\\n\", \"5\\n01110\\n10010\\n10001\\n10011\\n11111\\n\", \"3\\n001\\n000\\n010\\n\", \"6\\n110100\\n000011\\n001011\\n011011\\n100001\\n111000\\n\", \"10\\n0000000000\\n0000110000\\n1001000000\\n1000011110\\n1011111101\\n1011110011\\n1011000111\\n1010000001\\n1111000010\\n0001111110\\n\", \"10\\n0000000000\\n1000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000000\\n0000010000\\n0000000000\\n\", \"4\\n0100\\n0111\\n0001\\n0001\\n\", \"7\\n0000010\\n0100111\\n0010011\\n0111111\\n0100010\\n0110010\\n0000101\\n\", \"5\\n01110\\n10010\\n10011\\n10011\\n11111\\n\", \"3\\n001\\n001\\n010\\n\", \"10\\n1100011000\\n0000101000\\n1001000011\\n0000100010\\n1101010011\\n1100100101\\n1000011101\\n1001111001\\n1111111100\\n1000111100\\n\", \"3\\n001\\n000\\n101\\n\", \"6\\n110100\\n000011\\n001011\\n011011\\n100000\\n111000\\n\", \"10\\n0000000000\\n0000110000\\n1001000000\\n1000011110\\n1011111101\\n1011110011\\n1011000111\\n1010010001\\n1111000010\\n0001111110\\n\", \"3\\n001\\n010\\n001\\n\", \"10\\n0000000000\\n1000000000\\n0000000000\\n0000000000\\n0000000000\\n0000000100\\n0000000000\\n0000000000\\n0000010000\\n0000000000\\n\", \"4\\n1001\\n0000\\n1011\\n0000\\n\", \"6\\n100000\\n010000\\n001000\\n000000\\n000000\\n000101\\n\", \"4\\n0100\\n0111\\n0001\\n0000\\n\", \"7\\n0000010\\n0100111\\n0010011\\n0111101\\n0100010\\n0110010\\n0000101\\n\", \"5\\n01110\\n10010\\n10111\\n10011\\n11111\\n\", \"3\\n001\\n001\\n011\\n\", \"3\\n001\\n000\\n100\\n\", \"6\\n110100\\n000011\\n001011\\n011011\\n100010\\n111000\\n\", \"3\\n001\\n010\\n000\\n\", \"10\\n0000000000\\n1000000000\\n0000000000\\n0000000010\\n0000000000\\n0000000100\\n0000000000\\n0000000000\\n0000010000\\n0000000000\\n\"], \"outputs\": [\"4\\n\", \"0\\n\", \"20\\n\", \"100\\n\", \"4\\n\", \"0\\n\", \"40\\n\", \"8\\n\", \"13\\n\", \"20\\n\", \"5\\n\", \"0\\n\", \"10\\n\", \"75\\n\", \"22\\n\", \"5\\n\", \"0\\n\", \"2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"19\\n\", \"3\\n\", \"3\\n\", \"23\\n\", \"99\\n\", \"41\\n\", \"5\\n\", \"14\\n\", \"21\\n\", \"6\\n\", \"11\\n\", \"74\\n\", \"19\\n\", \"4\\n\", \"20\\n\", \"22\\n\", \"98\\n\", \"40\\n\", \"8\\n\", \"7\\n\", \"12\\n\", \"73\\n\", \"18\\n\", \"9\\n\", \"25\\n\", \"97\\n\", \"70\\n\", \"17\\n\", \"24\\n\", \"90\\n\", \"44\\n\", \"26\\n\", \"10\\n\", \"67\\n\", \"16\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"6\\n\", \"11\\n\", \"20\\n\", \"8\\n\", \"4\\n\", \"21\\n\", \"6\\n\", \"3\\n\", \"41\\n\", \"7\\n\", \"12\\n\", \"23\\n\", \"5\\n\", \"11\\n\", \"11\\n\", \"7\\n\", \"5\\n\", \"22\\n\", \"7\\n\", \"4\\n\", \"6\\n\", \"11\\n\", \"4\\n\", \"14\\n\"]}", "source": "primeintellect"}
|
After years of hard work scientists invented an absolutely new e-reader display. The new display has a larger resolution, consumes less energy and its production is cheaper. And besides, one can bend it. The only inconvenience is highly unusual management. For that very reason the developers decided to leave the e-readers' software to programmers.
The display is represented by n × n square of pixels, each of which can be either black or white. The display rows are numbered with integers from 1 to n upside down, the columns are numbered with integers from 1 to n from the left to the right. The display can perform commands like "x, y". When a traditional display fulfills such command, it simply inverts a color of (x, y), where x is the row number and y is the column number. But in our new display every pixel that belongs to at least one of the segments (x, x) - (x, y) and (y, y) - (x, y) (both ends of both segments are included) inverts a color.
For example, if initially a display 5 × 5 in size is absolutely white, then the sequence of commands (1, 4), (3, 5), (5, 1), (3, 3) leads to the following changes:
<image>
You are an e-reader software programmer and you should calculate minimal number of commands needed to display the picture. You can regard all display pixels as initially white.
Input
The first line contains number n (1 ≤ n ≤ 2000).
Next n lines contain n characters each: the description of the picture that needs to be shown. "0" represents the white color and "1" represents the black color.
Output
Print one integer z — the least number of commands needed to display the picture.
Examples
Input
5
01110
10010
10001
10011
11110
Output
4
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4 0\\n\", \"3 2\\n\", \"1337 42\\n\", \"3 3\\n\", \"4 5\\n\", \"4 3\\n\", \"3000 3000\\n\", \"200000 200000\\n\", \"200000 1000\\n\", \"3000 0\\n\", \"2 1\\n\", \"3 0\\n\", \"4 4\\n\", \"3000 42\\n\", \"4 1\\n\", \"200000 199999\\n\", \"4 6\\n\", \"200000 199998\\n\", \"200000 3393\\n\", \"1 0\\n\", \"3 1\\n\", \"1500 1000\\n\", \"2 0\\n\", \"200000 19999900000\\n\", \"3000 4498500\\n\", \"4 2\\n\", \"3000 3713\\n\", \"3000 2999\\n\", \"200000 0\\n\", \"200000 800000\\n\", \"3000 1337\\n\", \"200000 100000\\n\", \"200000 1\\n\", \"200000 100\\n\", \"4 7\\n\", \"200000 132521\\n\", \"30875 1000\\n\", \"2094 0\\n\", \"6 0\\n\", \"7 4\\n\", \"3000 78\\n\", \"5 0\\n\", \"200000 89177\\n\", \"200000 3093\\n\", \"7 0\\n\", \"5764 3713\\n\", \"4632 2999\\n\", \"2591 1337\\n\", \"200000 110\\n\", \"6 1\\n\", \"2488 42\\n\", \"8 7\\n\", \"4307 1000\\n\", \"4001 0\\n\", \"11 4\\n\", \"3000 92\\n\", \"10 0\\n\", \"124271 89177\\n\", \"200000 3883\\n\", \"9 0\\n\", \"4632 4364\\n\", \"2591 2525\\n\", \"11 1\\n\", \"3543 42\\n\", \"8 2\\n\", \"4307 0000\\n\", \"945 0\\n\", \"15 4\\n\", \"5213 92\\n\", \"42569 3883\\n\", \"12 0\\n\", \"2591 1733\\n\", \"436 3000\\n\", \"49226 199999\\n\", \"3 4\\n\", \"354 1000\\n\", \"200000 26492691161\\n\", \"1179 4498500\\n\", \"200000 666153\\n\", \"3 6\\n\", \"436 4882\\n\", \"114218 132521\\n\", \"49226 334171\\n\", \"354 1100\\n\", \"1179 2209383\\n\", \"1097 3713\\n\", \"200000 1275699\\n\", \"0 2\\n\", \"230 4882\\n\", \"71056 132521\\n\", \"6365 334171\\n\", \"36980 89177\\n\", \"99 1100\\n\", \"1179 1231488\\n\", \"404 3713\\n\", \"4632 5442\\n\"], \"outputs\": [\"24\\n\", \"6\\n\", \"807905441\\n\", \"0\\n\", \"0\\n\", \"8\\n\", \"0\\n\", \"0\\n\", \"13181387\\n\", \"201761277\\n\", \"4\\n\", \"6\\n\", \"0\\n\", \"281860640\\n\", \"288\\n\", \"400000\\n\", \"0\\n\", \"508670650\\n\", \"259194802\\n\", \"1\\n\", \"36\\n\", \"229881914\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"168\\n\", \"0\\n\", \"6000\\n\", \"638474417\\n\", \"0\\n\", \"729468301\\n\", \"668585001\\n\", \"466559115\\n\", \"431967939\\n\", \"0\\n\", \"660798392\\n\", \"45848221\\n\", \"552437276\\n\", \"720\\n\", \"126420\\n\", \"784900207\\n\", \"120\\n\", \"773611800\\n\", \"395522989\\n\", \"5040\\n\", \"709890387\\n\", \"654932331\\n\", \"320382228\\n\", \"824308468\\n\", \"21600\\n\", \"329482299\\n\", \"16\\n\", \"261523254\\n\", \"846183233\\n\", \"220309611\\n\", \"748741394\\n\", \"3628800\\n\", \"535280058\\n\", \"959684298\\n\", \"362880\\n\", \"39004266\\n\", \"536532666\\n\", \"397870588\\n\", \"128587371\\n\", \"10725120\\n\", \"406193428\\n\", \"32030240\\n\", \"292464441\\n\", \"728186961\\n\", \"175008997\\n\", \"479001600\\n\", \"865597061\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Calculate the number of ways to place n rooks on n × n chessboard so that both following conditions are met:
* each empty cell is under attack;
* exactly k pairs of rooks attack each other.
An empty cell is under attack if there is at least one rook in the same row or at least one rook in the same column. Two rooks attack each other if they share the same row or column, and there are no other rooks between them. For example, there are only two pairs of rooks that attack each other in the following picture:
<image> One of the ways to place the rooks for n = 3 and k = 2
Two ways to place the rooks are considered different if there exists at least one cell which is empty in one of the ways but contains a rook in another way.
The answer might be large, so print it modulo 998244353.
Input
The only line of the input contains two integers n and k (1 ≤ n ≤ 200000; 0 ≤ k ≤ (n(n - 1))/(2)).
Output
Print one integer — the number of ways to place the rooks, taken modulo 998244353.
Examples
Input
3 2
Output
6
Input
3 3
Output
0
Input
4 0
Output
24
Input
1337 42
Output
807905441
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"1\\n1\\n\", \"6\\n6 5 4 3 2 1\\n\", \"4\\n3 1 2 4\\n\", \"44\\n1 32 3 18 5 41 27 26 9 10 11 31 13 14 19 35 17 4 22 40 21 15 24 23 44 8 7 43 29 30 37 2 33 34 28 36 12 38 39 20 6 42 16 25\\n\", \"51\\n51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1\\n\", \"52\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52\\n\", \"3\\n3 2 1\\n\", \"46\\n1 2 3 16 5 19 7 8 9 35 11 26 13 14 15 29 17 18 6 20 21 22 23 24 25 12 27 28 4 46 31 32 33 34 45 36 37 38 10 40 41 42 43 44 39 30\\n\", \"43\\n25 43 38 35 39 5 2 42 40 34 13 32 31 24 36 28 27 18 33 15 16 4 21 20 19 29 7 23 30 14 26 12 11 37 9 8 17 6 41 1 3 10 22\\n\", \"45\\n39 44 12 42 17 8 27 38 37 36 35 24 33 32 31 34 41 15 45 28 10 30 23 22 21 20 19 18 13 16 29 14 26 43 11 40 9 1 7 6 5 4 3 2 25\\n\", \"41\\n12 1 35 38 7 26 17 20 33 24 23 13 19 28 36 27 21 4 3 22 39 30 2 40 15 14 25 16 10 6 34 31 32 8 9 41 5 37 11 18 29\\n\", \"20\\n1 6 15 9 18 17 7 8 3 19 2 13 11 12 14 4 5 20 16 10\\n\", \"43\\n22 10 3 1 41 6 17 8 9 37 11 12 26 14 30 23 7 29 19 20 21 4 16 15 33 18 27 28 36 24 31 32 13 34 40 42 2 5 39 35 38 43 25\\n\", \"51\\n3 1 25 43 51 27 6 13 33 32 8 7 28 36 14 49 50 4 10 39 41 26 2 16 40 34 23 42 29 45 15 48 47 22 5 46 11 18 38 35 44 12 20 24 21 9 17 31 30 37 19\\n\", \"31\\n1 20 14 5 11 26 23 15 22 4 6 12 19 9 2 10 7 21 31 16 24 25 27 8 30 13 29 3 28 17 18\\n\", \"51\\n47 48 49 50 51 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46\\n\", \"22\\n9 17 5 15 10 1 21 11 18 14 3 16 13 6 8 22 2 7 4 19 20 12\\n\", \"30\\n15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14\\n\", \"40\\n5 40 6 27 39 37 17 34 3 30 28 13 12 8 11 10 31 4 1 16 38 22 29 35 33 23 7 9 24 14 18 26 19 21 15 36 2 20 32 25\\n\", \"21\\n7 8 20 6 14 3 19 9 2 4 16 5 13 10 15 11 17 21 18 1 12\\n\", \"40\\n30 31 32 33 34 35 36 37 38 39 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29\\n\", \"49\\n49 48 47 36 45 44 43 42 41 40 39 38 25 46 32 34 33 35 31 30 29 28 27 26 37 24 23 22 21 20 19 18 17 16 10 14 13 12 11 15 9 8 7 4 5 6 3 2 1\\n\", \"50\\n50 49 48 47 30 45 44 43 10 41 40 39 38 37 36 35 4 33 32 31 46 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 8 9 42 7 6 5 34 3 2 1\\n\", \"52\\n25 35 4 36 19 31 44 37 47 9 41 3 14 5 45 22 32 39 12 46 1 30 8 34 2 51 42 50 13 49 28 10 16 29 26 21 27 6 24 40 17 18 23 43 52 48 20 7 33 11 38 15\\n\", \"49\\n14 48 47 19 45 32 43 42 41 40 16 44 37 36 35 34 33 38 39 30 29 28 15 26 25 24 23 22 21 20 49 18 31 17 27 46 13 12 11 10 6 8 7 9 5 4 3 2 1\\n\", \"10\\n8 9 10 1 2 3 4 5 6 7\\n\", \"52\\n1 30 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 41 2 31 32 33 34 35 36 37 38 39 40 29 42 43 44 45 46 47 48 49 50 51 52\\n\", \"51\\n51 50 16 48 47 46 45 44 43 42 41 40 39 38 37 33 35 34 36 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 49 15 14 13 12 11 10 4 8 7 6 5 9 3 2 1\\n\", \"46\\n30 39 44 43 42 41 40 10 38 37 36 45 34 33 32 31 46 4 28 27 12 25 24 23 22 21 20 6 18 17 29 15 14 13 26 11 35 9 8 7 19 5 16 3 2 1\\n\", \"50\\n43 40 28 32 50 29 45 49 2 5 23 7 31 35 38 4 16 8 20 33 13 39 9 17 18 37 42 25 14 41 10 27 3 48 26 19 47 24 21 6 11 34 30 22 44 46 1 12 36 15\\n\", \"41\\n29 18 11 37 5 41 9 8 32 31 34 6 10 16 25 14 15 40 2 30 39 22 3 4 21 27 36 28 19 13 23 24 33 20 17 26 7 38 35 1 12\\n\", \"48\\n1 38 3 4 5 6 7 8 9 10 11 25 13 14 15 16 31 18 19 20 46 22 23 37 12 26 27 48 29 30 17 32 33 34 35 36 24 2 39 40 41 42 43 44 45 21 47 28\\n\", \"44\\n44 27 31 21 7 18 38 9 12 14 35 33 24 39 10 17 28 22 34 15 3 30 29 11 2 16 1 19 36 37 42 5 6 25 26 40 43 20 8 13 32 23 41 4\\n\", \"33\\n8 28 16 3 17 5 13 4 15 14 20 31 2 11 9 30 29 25 12 10 1 26 7 32 6 21 24 23 22 27 33 18 19\\n\", \"43\\n38 23 26 18 14 41 30 31 4 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30 47 48 49 50\\n\", \"49\\n1 2 3 6 5 4 7 8 9 15 11 12 13 14 10 16 17 18 19 20 21 22 23 24 37 26 27 28 29 30 31 35 33 34 32 46 25 38 39 40 41 42 43 44 45 36 47 48 49\\n\", \"51\\n1 2 3 9 5 6 7 8 4 10 11 12 13 14 15 49 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 36 34 35 33 37 38 39 40 41 42 43 44 45 46 47 48 16 50 51\\n\", \"20\\n20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19\\n\", \"47\\n47 46 45 42 43 22 39 40 4 38 6 36 35 34 33 32 16 30 31 28 27 26 25 24 23 44 21 20 19 18 17 29 15 14 13 12 11 10 9 8 7 37 5 41 3 2 1\\n\", \"52\\n52 51 50 49 48 47 46 45 44 43 42 29 40 39 38 37 36 35 34 33 32 31 2 41 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 30 1\\n\", \"47\\n1 2 3 41 5 37 7 8 9 10 11 12 13 14 15 29 17 18 19 20 21 44 23 24 25 26 27 28 31 30 16 32 33 34 35 36 6 38 4 40 39 22 43 42 45 46 47\\n\", \"44\\n44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1\\n\", \"40\\n23 40 35 27 26 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9 35 16 5 10 34 41 24 30 19 3 42 31 28 44 26 12 21 20 43 23 15 22 11 18\\n\", \"52\\n21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20\\n\", \"50\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50\\n\", \"2\\n1 2\\n\"], \"outputs\": [\"0\\n\", \"4\\n3 1 1 4\\n3 1 1 4\\n3 1 1 4\\n3 2 2 2\\n\", \"2\\n3 1 2 1\\n2 1 3\\n\", \"37\\n4 1 1 10 32\\n3 2 23 19\\n3 2 34 8\\n3 1 24 19\\n3 1 32 11\\n3 1 13 30\\n3 1 2 41\\n3 1 18 25\\n3 1 7 36\\n3 1 14 29\\n3 2 27 15\\n3 1 1 42\\n3 3 14 27\\n3 1 15 28\\n3 1 20 23\\n3 1 1 42\\n3 1 5 38\\n3 2 6 36\\n3 1 21 22\\n3 1 28 15\\n3 1 21 22\\n3 4 16 24\\n3 2 36 6\\n3 6 16 22\\n3 3 8 33\\n3 2 19 23\\n3 2 2 40\\n3 8 21 15\\n3 5 30 9\\n3 9 10 25\\n3 3 22 19\\n2 2 42\\n3 6 22 16\\n3 16 11 17\\n3 2 6 36\\n3 9 27 8\\n2 8 36\\n\", \"1\\n51 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n\", \"0\\n\", \"1\\n3 1 1 1\\n\", \"20\\n4 3 1 11 31\\n3 1 12 33\\n3 1 32 13\\n3 2 40 4\\n4 4 1 28 13\\n3 1 12 33\\n2 6 40\\n3 1 31 14\\n3 1 13 32\\n2 3 43\\n3 1 5 40\\n3 3 18 25\\n3 19 7 20\\n3 5 1 40\\n3 1 39 6\\n3 6 13 27\\n3 4 23 19\\n3 2 4 40\\n2 3 43\\n3 12 25 9\\n\", \"43\\n2 39 4\\n3 1 10 32\\n4 32 9 1 1\\n5 1 1 1 23 17\\n6 24 15 1 1 1 1\\n7 1 1 1 1 1 30 8\\n8 26 11 1 1 1 1 1 1\\n9 1 1 1 1 1 1 1 9 27\\n10 34 1 1 1 1 1 1 1 1 1\\n11 1 1 1 1 1 1 1 1 1 3 31\\n12 29 4 1 1 1 1 1 1 1 1 1 1\\n12 1 1 1 1 1 1 1 1 1 1 1 32\\n14 12 19 1 1 1 1 1 1 1 1 1 1 1 1\\n15 1 1 1 1 1 1 1 1 1 1 1 1 1 17 13\\n16 21 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 27\\n18 8 19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17 9\\n20 3 22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 24\\n22 22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n23 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 15\\n24 16 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n25 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 5\\n26 9 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n27 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16 2\\n28 13 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16\\n30 1 14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n31 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 13\\n32 10 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n32 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12\\n34 1 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n35 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 1\\n36 5 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n37 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4\\n37 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n39 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3\\n39 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n41 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2\\n41 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n42 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\\n43 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"40\\n3 1 7 37\\n3 1 1 43\\n3 1 5 39\\n3 1 19 25\\n3 1 13 31\\n3 1 26 18\\n3 1 14 30\\n3 1 25 19\\n3 1 33 11\\n3 1 30 14\\n3 2 2 41\\n3 1 11 33\\n3 1 1 43\\n3 1 1 43\\n3 1 3 41\\n3 1 41 3\\n3 3 30 12\\n3 1 25 19\\n3 1 32 12\\n3 2 19 24\\n3 1 1 43\\n3 1 9 35\\n3 2 2 41\\n3 2 35 8\\n3 4 8 33\\n3 2 15 28\\n3 6 4 35\\n3 10 2 33\\n3 6 8 31\\n3 2 2 41\\n3 5 24 16\\n3 1 1 43\\n3 1 1 43\\n3 1 34 10\\n3 6 2 37\\n3 2 35 8\\n2 8 37\\n3 7 26 12\\n4 12 4 10 19\\n2 33 12\\n\", \"37\\n3 1 38 2\\n3 1 7 33\\n3 1 5 35\\n3 1 2 38\\n3 1 37 3\\n3 1 28 12\\n3 1 34 6\\n3 2 29 10\\n3 1 7 33\\n3 2 4 35\\n3 1 34 6\\n3 1 17 23\\n3 1 1 39\\n3 1 35 5\\n3 3 28 10\\n3 2 18 21\\n3 3 5 33\\n3 1 26 14\\n3 1 1 39\\n3 1 25 15\\n3 1 5 35\\n3 2 3 36\\n3 2 35 4\\n3 1 28 12\\n3 1 22 18\\n3 5 3 33\\n4 1 4 25 11\\n3 3 13 25\\n3 2 6 33\\n3 3 13 25\\n4 1 8 19 13\\n3 5 17 19\\n2 7 34\\n3 11 1 29\\n3 8 8 25\\n3 13 12 16\\n2 16 25\\n\", \"15\\n4 1 1 15 3\\n3 1 10 9\\n3 1 8 11\\n3 1 2 17\\n3 1 4 15\\n3 1 11 8\\n3 1 7 12\\n3 2 13 5\\n3 1 16 3\\n2 3 17\\n3 4 7 9\\n4 3 6 4 7\\n2 7 13\\n3 1 2 17\\n2 7 13\\n\", \"33\\n3 1 20 22\\n3 1 23 19\\n4 1 1 30 11\\n3 1 41 1\\n4 2 1 8 32\\n3 1 40 2\\n4 2 1 16 24\\n3 1 30 12\\n3 1 3 39\\n3 4 6 33\\n3 2 25 16\\n3 2 19 22\\n3 1 30 12\\n3 5 34 4\\n4 2 2 4 35\\n3 3 18 22\\n3 3 27 13\\n3 1 6 36\\n3 1 17 25\\n3 1 30 12\\n3 1 32 10\\n2 8 35\\n3 2 9 32\\n3 2 11 30\\n2 1 42\\n3 1 37 5\\n3 1 4 38\\n3 4 24 15\\n3 4 26 13\\n3 13 24 6\\n2 6 37\\n4 2 4 5 32\\n2 41 2\\n\", \"49\\n3 1 22 28\\n3 1 7 43\\n3 1 1 49\\n3 1 11 39\\n3 1 15 35\\n3 1 45 5\\n3 1 34 16\\n3 1 8 42\\n4 1 1 41 8\\n3 2 6 43\\n3 1 24 26\\n3 1 34 16\\n3 1 26 24\\n3 1 38 12\\n2 1 50\\n3 2 33 16\\n3 2 16 33\\n3 1 33 17\\n3 1 43 7\\n3 2 42 7\\n3 2 10 39\\n3 1 19 31\\n3 2 35 14\\n3 1 26 24\\n3 1 31 19\\n3 1 45 5\\n2 5 46\\n3 1 25 25\\n3 3 27 21\\n3 2 10 39\\n3 3 12 36\\n3 2 23 26\\n3 1 47 3\\n4 3 1 1 46\\n3 1 26 24\\n3 10 32 9\\n3 4 26 21\\n3 1 1 49\\n3 4 4 43\\n3 11 1 39\\n3 4 27 20\\n3 8 26 17\\n3 11 19 21\\n3 2 25 24\\n2 12 39\\n3 12 6 33\\n2 2 49\\n3 11 20 20\\n2 40 11\\n\", \"30\\n3 1 14 16\\n4 12 17 1 1\\n5 1 1 1 12 16\\n6 21 6 1 1 1 1\\n7 1 1 1 1 1 6 20\\n8 4 21 1 1 1 1 1 1\\n9 1 1 1 1 1 1 1 7 17\\n10 15 8 1 1 1 1 1 1 1 1\\n11 1 1 1 1 1 1 1 1 1 1 21\\n12 14 7 1 1 1 1 1 1 1 1 1 1\\n13 1 1 1 1 1 1 1 1 1 1 1 5 15\\n14 8 11 1 1 1 1 1 1 1 1 1 1 1 1\\n15 1 1 1 1 1 1 1 1 1 1 1 1 1 6 12\\n16 2 15 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 11\\n18 6 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 13\\n20 4 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 3\\n22 3 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10\\n24 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n25 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 6\\n25 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n27 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1\\n28 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n29 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1\\n30 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\\n31 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"1\\n2 5 46\\n\", \"18\\n3 1 14 7\\n3 1 12 9\\n3 1 18 3\\n4 1 2 13 6\\n3 1 5 16\\n3 1 16 5\\n3 1 14 7\\n3 4 3 15\\n3 1 4 17\\n3 1 6 15\\n3 1 17 4\\n2 2 20\\n3 4 1 17\\n3 6 6 10\\n3 1 12 9\\n2 9 13\\n3 4 5 13\\n2 13 9\\n\", \"1\\n2 16 14\\n\", \"36\\n3 1 17 22\\n4 1 1 15 23\\n3 1 26 13\\n3 1 15 24\\n3 1 27 12\\n3 1 22 17\\n3 1 2 37\\n3 1 11 28\\n3 2 35 3\\n3 1 15 24\\n3 1 27 12\\n3 1 37 2\\n3 2 34 4\\n3 2 23 15\\n2 2 38\\n3 1 31 8\\n3 1 19 20\\n3 2 14 24\\n3 1 31 8\\n3 1 3 36\\n3 1 20 19\\n3 6 30 4\\n2 1 39\\n3 3 9 28\\n3 2 17 21\\n3 1 20 19\\n2 2 38\\n3 3 25 12\\n3 2 1 37\\n3 9 3 28\\n3 2 5 33\\n3 4 18 18\\n3 11 15 14\\n3 1 6 33\\n3 14 19 7\\n2 26 14\\n\", \"21\\n2 19 2\\n3 1 10 10\\n4 16 3 1 1\\n5 1 1 1 3 15\\n6 1 16 1 1 1 1\\n7 1 1 1 1 1 12 4\\n8 12 3 1 1 1 1 1 1\\n9 1 1 1 1 1 1 1 1 13\\n10 3 10 1 1 1 1 1 1 1 1\\n11 1 1 1 1 1 1 1 1 1 3 9\\n12 1 10 1 1 1 1 1 1 1 1 1 1\\n13 1 1 1 1 1 1 1 1 1 1 1 4 6\\n14 4 5 1 1 1 1 1 1 1 1 1 1 1 1\\n15 1 1 1 1 1 1 1 1 1 1 1 1 1 6 2\\n16 2 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6\\n17 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2\\n20 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\\n21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"1\\n2 11 29\\n\", \"49\\n2 48 1\\n2 1 48\\n4 46 1 1 1\\n5 1 1 1 44 2\\n5 45 1 1 1 1\\n7 1 1 1 1 1 1 43\\n8 42 1 1 1 1 1 1 1\\n8 1 1 1 1 1 1 1 42\\n10 40 1 1 1 1 1 1 1 1 1\\n11 1 1 1 1 1 1 1 1 1 35 5\\n12 3 36 1 1 1 1 1 1 1 1 1 1\\n12 1 1 1 1 1 1 1 1 1 1 1 38\\n14 36 1 1 1 1 1 1 1 1 1 1 1 1 1\\n14 1 1 1 1 1 1 1 1 1 1 1 1 1 36\\n15 35 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 34\\n18 32 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n18 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 32\\n20 30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 30\\n22 28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 28\\n24 26 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 26\\n26 12 13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n27 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 13\\n28 22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 22\\n30 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20\\n32 18 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n33 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 3\\n34 1 16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n34 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16\\n35 15 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n37 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 9\\n38 9 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n39 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 1\\n40 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n40 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10\\n42 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n42 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8\\n44 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n44 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6\\n46 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n47 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3\\n48 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n48 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\\n49 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"48\\n3 1 1 48\\n3 1 1 48\\n3 1 17 32\\n3 1 1 48\\n3 1 1 48\\n3 1 1 48\\n3 1 1 48\\n3 1 1 48\\n3 1 1 48\\n3 1 1 48\\n3 1 1 48\\n3 1 1 48\\n3 2 2 46\\n3 1 1 48\\n3 1 20 29\\n3 1 1 48\\n3 1 34 15\\n3 1 1 48\\n3 1 36 13\\n3 2 19 29\\n3 2 2 46\\n3 2 2 46\\n3 2 2 46\\n3 2 2 46\\n3 2 2 46\\n3 2 2 46\\n3 1 16 33\\n3 1 1 48\\n3 1 1 48\\n3 1 1 48\\n3 3 29 18\\n3 1 1 48\\n3 2 2 46\\n3 2 2 46\\n3 2 2 46\\n3 2 2 46\\n3 4 4 42\\n3 4 4 42\\n3 4 4 42\\n3 4 4 42\\n4 2 4 4 40\\n3 4 4 42\\n3 8 8 34\\n3 8 8 34\\n3 8 10 32\\n3 16 16 18\\n3 2 16 32\\n2 48 2\\n\", \"47\\n3 1 38 13\\n3 1 29 22\\n3 1 31 20\\n3 1 8 43\\n3 1 11 40\\n4 1 1 12 38\\n3 1 5 46\\n3 2 41 9\\n3 2 46 4\\n3 1 29 22\\n3 1 8 43\\n3 2 45 5\\n3 1 20 31\\n3 1 4 47\\n3 1 46 5\\n3 1 26 25\\n3 3 41 8\\n3 2 44 6\\n3 1 29 22\\n4 1 7 4 40\\n3 1 20 31\\n3 1 40 11\\n3 4 26 22\\n3 1 35 16\\n3 1 46 5\\n3 1 47 4\\n3 4 38 10\\n3 2 18 32\\n3 4 19 29\\n3 1 17 34\\n3 1 25 26\\n3 1 35 16\\n3 6 25 21\\n3 2 6 44\\n3 2 11 39\\n3 8 9 35\\n3 1 14 37\\n3 1 10 41\\n3 1 38 13\\n3 8 15 29\\n2 2 50\\n3 13 19 20\\n2 8 44\\n3 12 14 26\\n3 2 1 49\\n3 37 12 3\\n2 3 49\\n\", \"49\\n2 48 1\\n2 1 48\\n4 46 1 1 1\\n4 1 1 1 46\\n6 44 1 1 1 1 1\\n7 1 1 1 1 1 41 3\\n8 1 42 1 1 1 1 1 1\\n8 1 1 1 1 1 1 1 42\\n9 41 1 1 1 1 1 1 1 1\\n10 1 1 1 1 1 1 1 1 1 40\\n12 38 1 1 1 1 1 1 1 1 1 1 1\\n12 1 1 1 1 1 1 1 1 1 1 1 38\\n14 36 1 1 1 1 1 1 1 1 1 1 1 1 1\\n15 1 1 1 1 1 1 1 1 1 1 1 1 1 1 35\\n16 21 14 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 23 11\\n18 21 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 31 1\\n20 5 26 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 24 6\\n22 28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 28\\n24 26 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 26\\n26 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n26 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 24\\n28 2 21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n29 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20 2\\n30 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20\\n32 1 18 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n33 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 13\\n34 9 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n34 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16\\n36 14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n36 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 14\\n38 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n39 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11\\n39 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n41 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 1\\n42 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n42 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8\\n44 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n45 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5\\n46 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n47 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2\\n48 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n48 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\\n49 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"1\\n2 3 7\\n\", \"7\\n4 1 1 39 11\\n3 11 27 14\\n3 1 13 38\\n2 26 26\\n3 12 10 30\\n3 2 28 22\\n2 22 30\\n\", \"51\\n2 50 1\\n2 1 50\\n4 48 1 1 1\\n5 1 1 1 43 5\\n6 3 44 1 1 1 1\\n6 1 1 1 1 1 46\\n8 44 1 1 1 1 1 1 1\\n8 1 1 1 1 1 1 1 44\\n9 43 1 1 1 1 1 1 1 1\\n10 1 1 1 1 1 1 1 1 1 42\\n12 40 1 1 1 1 1 1 1 1 1 1 1\\n12 1 1 1 1 1 1 1 1 1 1 1 40\\n14 38 1 1 1 1 1 1 1 1 1 1 1 1 1\\n14 1 1 1 1 1 1 1 1 1 1 1 1 1 38\\n16 36 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 33\\n18 31 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n18 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 34\\n20 32 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 32\\n22 30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 30\\n24 28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 28\\n26 26 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n26 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 26\\n28 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 24\\n30 22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 22\\n32 20 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n32 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20\\n34 15 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n35 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 16\\n36 16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n37 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15\\n38 14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n38 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 14\\n40 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n40 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12\\n42 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n42 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10\\n44 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n44 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8\\n46 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n46 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6\\n48 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n48 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4\\n49 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n50 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\\n51 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"41\\n3 1 30 15\\n3 1 1 44\\n3 1 32 13\\n3 1 1 44\\n3 1 1 44\\n3 1 1 44\\n3 1 14 31\\n3 1 36 9\\n3 1 34 11\\n3 2 2 42\\n3 1 1 44\\n3 2 32 12\\n3 1 5 40\\n3 4 11 31\\n3 2 20 24\\n3 3 6 37\\n3 2 3 41\\n3 1 19 26\\n3 1 1 44\\n3 1 24 21\\n3 1 1 44\\n3 1 27 18\\n3 2 32 12\\n3 2 24 20\\n3 2 28 16\\n3 7 14 25\\n3 1 1 44\\n4 1 1 30 14\\n3 12 28 6\\n3 5 14 27\\n3 1 1 44\\n3 1 24 21\\n4 3 1 1 41\\n3 1 1 44\\n3 1 11 34\\n3 2 25 19\\n3 2 5 39\\n3 4 15 27\\n2 20 26\\n4 3 5 7 31\\n3 1 42 3\\n\", \"46\\n3 1 26 23\\n3 1 10 39\\n3 1 29 20\\n3 1 33 16\\n3 1 3 46\\n3 1 38 11\\n3 1 42 7\\n3 1 12 37\\n3 1 46 3\\n3 3 7 40\\n2 1 49\\n3 1 11 38\\n3 2 2 46\\n3 1 41 8\\n3 2 41 7\\n3 1 40 9\\n3 5 28 17\\n3 1 22 27\\n3 1 20 29\\n3 6 9 35\\n3 1 35 14\\n2 1 49\\n4 2 1 10 37\\n3 2 23 25\\n3 1 4 45\\n3 1 20 29\\n3 1 9 40\\n3 1 4 45\\n3 1 16 33\\n3 3 33 14\\n3 1 9 40\\n3 5 26 19\\n3 3 26 21\\n4 2 4 1 43\\n3 3 11 36\\n3 6 11 33\\n3 12 31 7\\n2 7 43\\n3 5 17 28\\n3 3 2 45\\n3 23 6 21\\n3 10 6 34\\n2 1 49\\n3 4 29 17\\n3 17 2 31\\n2 31 19\\n\", \"41\\n2 39 2\\n3 1 20 20\\n4 3 36 1 1\\n5 1 1 1 1 37\\n6 20 17 1 1 1 1\\n7 1 1 1 1 1 7 29\\n8 21 14 1 1 1 1 1 1\\n9 1 1 1 1 1 1 1 10 24\\n10 32 1 1 1 1 1 1 1 1 1\\n11 1 1 1 1 1 1 1 1 1 4 28\\n12 25 6 1 1 1 1 1 1 1 1 1 1\\n13 1 1 1 1 1 1 1 1 1 1 1 28 2\\n14 20 9 1 1 1 1 1 1 1 1 1 1 1 1\\n15 1 1 1 1 1 1 1 1 1 1 1 1 1 18 10\\n15 27 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 25 1\\n18 14 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 19\\n20 14 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 18\\n22 14 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 20\\n24 3 16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n25 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 17\\n26 10 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n27 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8 8\\n28 11 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n29 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 12\\n30 3 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n31 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 5\\n32 8 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n32 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10\\n34 4 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n35 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 3\\n36 4 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n37 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1\\n38 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n38 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4\\n40 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n40 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\\n41 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"16\\n4 1 1 22 24\\n3 1 32 15\\n3 1 26 21\\n3 1 34 13\\n3 2 11 35\\n3 7 26 15\\n4 2 1 14 31\\n3 1 42 5\\n3 1 22 25\\n3 1 11 36\\n3 2 11 35\\n3 2 33 13\\n3 1 28 19\\n3 1 30 17\\n4 23 12 5 8\\n2 25 23\\n\", \"38\\n3 1 36 7\\n3 1 33 10\\n3 2 24 18\\n3 1 28 15\\n3 1 20 23\\n3 1 22 21\\n3 1 36 7\\n3 2 36 6\\n3 2 10 32\\n3 1 33 10\\n3 2 21 21\\n3 1 34 9\\n3 1 17 26\\n3 1 2 41\\n3 2 18 24\\n3 1 6 37\\n3 1 7 36\\n3 1 31 12\\n3 7 24 13\\n3 3 16 25\\n3 1 1 42\\n3 2 29 13\\n3 2 22 20\\n3 10 1 33\\n3 1 4 39\\n3 4 21 19\\n2 3 41\\n3 11 16 17\\n3 1 16 27\\n3 1 13 30\\n3 13 23 8\\n3 3 26 15\\n3 1 36 7\\n2 7 37\\n3 14 13 17\\n3 17 5 22\\n4 2 3 17 22\\n2 42 2\\n\", \"29\\n3 1 22 10\\n3 1 20 12\\n3 1 8 24\\n3 1 28 4\\n3 1 27 5\\n3 1 9 23\\n3 1 13 19\\n3 1 8 24\\n3 1 1 31\\n3 2 8 23\\n3 1 1 31\\n3 1 30 2\\n3 2 27 4\\n2 4 29\\n3 1 14 18\\n3 3 3 27\\n4 2 3 15 13\\n3 1 24 8\\n3 1 30 2\\n3 7 2 24\\n3 1 1 31\\n3 1 18 14\\n3 1 29 3\\n3 3 2 28\\n4 9 2 9 13\\n3 8 5 20\\n3 3 2 28\\n3 6 9 18\\n2 18 15\\n\", \"39\\n3 1 37 5\\n3 1 36 6\\n3 1 38 4\\n3 1 36 6\\n3 1 19 23\\n3 1 36 6\\n3 1 1 41\\n3 1 16 26\\n3 1 23 19\\n3 2 10 31\\n3 1 7 35\\n3 1 4 38\\n4 2 1 12 28\\n3 3 9 31\\n3 3 8 32\\n3 1 35 7\\n3 2 5 36\\n3 1 22 20\\n3 1 9 33\\n3 1 27 15\\n3 1 33 9\\n3 1 34 8\\n3 1 4 38\\n3 3 36 4\\n3 2 24 17\\n3 2 15 26\\n3 2 10 31\\n3 2 19 22\\n3 1 3 39\\n3 6 19 18\\n3 1 19 23\\n3 3 37 3\\n3 1 11 31\\n3 1 35 7\\n3 7 10 26\\n3 4 16 23\\n3 2 4 37\\n3 17 9 17\\n2 11 32\\n\", \"26\\n2 1 47\\n3 1 22 25\\n3 1 7 40\\n3 1 39 8\\n3 1 3 44\\n3 4 16 28\\n3 2 26 20\\n3 1 33 14\\n3 1 22 25\\n3 1 27 20\\n3 1 22 25\\n3 6 23 19\\n2 1 47\\n3 4 1 43\\n2 1 47\\n3 3 19 26\\n3 5 31 12\\n3 2 31 15\\n3 1 1 46\\n3 1 12 35\\n3 1 37 10\\n3 1 41 6\\n3 8 17 23\\n3 15 15 18\\n3 5 21 22\\n2 35 13\\n\", \"41\\n2 31 10\\n3 1 32 8\\n4 24 15 1 1\\n4 1 1 1 38\\n6 35 2 1 1 1 1\\n7 1 1 1 1 1 26 10\\n8 3 32 1 1 1 1 1 1\\n9 1 1 1 1 1 1 1 30 4\\n10 12 21 1 1 1 1 1 1 1 1\\n11 1 1 1 1 1 1 1 1 1 19 13\\n12 24 7 1 1 1 1 1 1 1 1 1 1\\n13 1 1 1 1 1 1 1 1 1 1 1 17 13\\n14 13 16 1 1 1 1 1 1 1 1 1 1 1 1\\n15 1 1 1 1 1 1 1 1 1 1 1 1 1 4 24\\n16 9 18 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 23\\n18 8 17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 14 10\\n20 15 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 21 1\\n22 16 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n23 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6 14\\n24 1 18 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n25 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 3\\n26 5 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n27 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6 10\\n28 12 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n29 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 7\\n30 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n30 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12\\n32 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n33 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8 2\\n34 5 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n35 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 3\\n36 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n37 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 2\\n38 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n38 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4\\n40 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n40 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\\n41 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"1\\n2 1 1\\n\", \"34\\n3 1 33 6\\n3 1 30 9\\n3 1 23 16\\n3 1 6 33\\n3 1 21 18\\n3 1 30 9\\n3 1 28 11\\n3 2 31 7\\n3 1 28 11\\n3 1 10 29\\n3 2 4 34\\n3 1 2 37\\n3 1 16 23\\n3 1 35 4\\n3 1 3 36\\n3 2 22 16\\n3 1 28 11\\n3 4 23 13\\n3 1 4 35\\n3 1 21 18\\n3 1 33 6\\n4 2 2 5 31\\n3 1 32 7\\n3 5 26 9\\n3 3 11 26\\n3 5 5 30\\n3 4 20 16\\n2 6 34\\n3 2 11 27\\n2 3 37\\n3 6 26 8\\n3 1 26 13\\n2 20 20\\n3 3 3 34\\n\", \"1\\n2 2 29\\n\", \"29\\n3 1 21 10\\n3 1 14 17\\n3 1 5 26\\n3 1 23 8\\n3 2 6 24\\n3 1 9 22\\n3 1 4 27\\n3 1 19 12\\n3 1 6 25\\n3 1 6 25\\n3 1 1 30\\n3 1 3 28\\n3 1 19 12\\n3 1 8 23\\n2 3 29\\n3 1 24 7\\n3 2 11 19\\n3 1 25 6\\n2 6 26\\n3 1 11 20\\n3 2 1 29\\n3 3 18 11\\n3 1 7 24\\n2 3 29\\n3 5 11 16\\n4 1 8 16 7\\n3 7 7 18\\n3 1 17 14\\n2 30 2\\n\", \"1\\n2 20 30\\n\", \"12\\n4 3 1 29 17\\n2 1 49\\n3 7 39 4\\n4 4 1 13 32\\n3 1 42 7\\n3 1 37 12\\n2 3 47\\n3 1 33 16\\n3 1 15 34\\n2 4 46\\n3 6 4 40\\n2 40 10\\n\", \"18\\n4 3 1 1 44\\n2 1 48\\n3 3 42 4\\n4 4 1 4 40\\n3 1 39 9\\n2 5 44\\n3 4 9 36\\n3 1 21 27\\n3 3 35 11\\n3 1 30 18\\n3 4 6 39\\n3 1 2 46\\n3 1 41 7\\n3 4 3 42\\n3 4 8 37\\n3 2 31 16\\n3 4 12 33\\n2 45 4\\n\", \"11\\n4 3 1 4 43\\n2 1 50\\n3 6 41 4\\n4 4 1 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7\\n42 1 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n43 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 2\\n43 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n45 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3\\n46 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n46 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\\n47 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"49\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 13 38\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 12 39\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 1 50\\n3 1 29 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1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n31 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15\\n32 3 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n33 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 13\\n33 13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n34 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 12\\n35 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n37 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9\\n37 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n39 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7\\n40 2 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n41 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5\\n42 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n43 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3\\n44 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n44 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\\n45 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"0\\n\", \"34\\n3 1 37 4\\n3 1 27 14\\n3 1 5 36\\n3 1 1 40\\n3 1 30 11\\n3 1 37 4\\n3 1 3 38\\n3 2 37 3\\n2 3 39\\n3 1 1 40\\n3 1 28 13\\n3 1 1 40\\n3 1 35 6\\n3 1 21 20\\n4 1 1 12 28\\n3 1 38 3\\n3 2 24 16\\n3 2 18 22\\n3 2 13 27\\n3 2 28 12\\n3 4 8 30\\n3 1 16 25\\n2 2 40\\n4 1 1 30 10\\n2 1 41\\n3 2 1 39\\n3 1 26 15\\n2 4 38\\n3 2 2 38\\n3 2 2 38\\n3 3 1 38\\n3 4 26 12\\n3 4 4 34\\n3 5 29 8\\n\", \"45\\n3 1 21 26\\n3 1 14 33\\n3 1 1 46\\n3 1 1 46\\n3 1 1 46\\n3 1 1 46\\n3 1 12 35\\n3 1 14 33\\n3 1 23 24\\n3 1 1 46\\n3 1 1 46\\n3 1 1 46\\n3 1 37 10\\n4 1 1 26 20\\n3 1 1 46\\n3 1 33 14\\n3 1 1 46\\n3 1 8 39\\n4 1 2 34 11\\n3 2 2 44\\n3 1 15 32\\n3 2 2 44\\n3 2 12 34\\n3 1 1 46\\n3 1 1 46\\n3 1 16 31\\n3 1 1 46\\n3 1 1 46\\n3 2 37 9\\n3 3 19 26\\n3 2 2 44\\n3 4 9 35\\n3 4 5 39\\n2 2 46\\n3 2 2 44\\n3 3 4 41\\n3 2 25 21\\n3 10 13 25\\n3 5 4 39\\n3 2 2 44\\n3 4 12 32\\n3 7 30 11\\n3 3 33 12\\n3 32 9 7\\n2 16 32\\n\", \"1\\n52 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \\n\", \"38\\n3 1 4 37\\n3 1 26 15\\n3 1 33 8\\n3 1 15 26\\n3 1 39 2\\n3 2 7 33\\n3 1 25 16\\n3 1 24 17\\n3 1 34 7\\n3 1 29 12\\n3 1 20 21\\n3 1 20 21\\n3 1 27 14\\n3 1 25 16\\n3 1 19 22\\n3 1 28 13\\n3 1 38 3\\n3 3 9 30\\n3 3 31 8\\n3 1 36 5\\n3 1 36 5\\n3 2 38 2\\n3 2 14 26\\n3 1 15 26\\n3 2 15 25\\n3 2 23 17\\n3 1 7 34\\n3 3 14 25\\n2 1 41\\n3 2 35 5\\n3 5 3 34\\n3 2 17 23\\n3 15 17 10\\n3 2 16 24\\n3 1 23 18\\n3 1 21 20\\n3 27 13 2\\n2 12 30\\n\", \"45\\n2 15 30\\n3 1 38 6\\n4 20 23 1 1\\n5 1 1 1 19 23\\n6 16 25 1 1 1 1\\n7 1 1 1 1 1 22 18\\n8 10 29 1 1 1 1 1 1\\n9 1 1 1 1 1 1 1 33 5\\n10 9 28 1 1 1 1 1 1 1 1\\n11 1 1 1 1 1 1 1 1 1 3 33\\n12 17 18 1 1 1 1 1 1 1 1 1 1\\n13 1 1 1 1 1 1 1 1 1 1 1 28 6\\n14 8 25 1 1 1 1 1 1 1 1 1 1 1 1\\n15 1 1 1 1 1 1 1 1 1 1 1 1 1 8 24\\n16 20 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n17 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 16 14\\n18 20 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n19 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 24 4\\n20 16 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 19\\n22 24 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n23 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 21\\n24 22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n25 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15 7\\n26 15 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n27 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 9\\n28 10 9 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n29 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 7 11\\n30 9 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n31 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 11\\n32 1 14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n33 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 10\\n34 12 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n35 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 8 4\\n36 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n36 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10\\n38 4 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n39 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4\\n40 6 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n40 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 6\\n41 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n43 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3\\n44 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n44 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\\n45 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"1\\n2 32 20\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
You are given a deck of n cards numbered from 1 to n (not necessarily in this order in the deck). You have to sort the deck by repeating the following operation.
* Choose 2 ≤ k ≤ n and split the deck in k nonempty contiguous parts D_1, D_2,..., D_k (D_1 contains the first |D_1| cards of the deck, D_2 contains the following |D_2| cards and so on). Then reverse the order of the parts, transforming the deck into D_k, D_{k-1}, ..., D_2, D_1 (so, the first |D_k| cards of the new deck are D_k, the following |D_{k-1}| cards are D_{k-1} and so on). The internal order of each packet of cards D_i is unchanged by the operation.
You have to obtain a sorted deck (i.e., a deck where the first card is 1, the second is 2 and so on) performing at most n operations. It can be proven that it is always possible to sort the deck performing at most n operations.
Examples of operation: The following are three examples of valid operations (on three decks with different sizes).
* If the deck is [3 6 2 1 4 5 7] (so 3 is the first card and 7 is the last card), we may apply the operation with k=4 and D_1=[3 6], D_2=[2 1 4], D_3=[5], D_4=[7]. Doing so, the deck becomes [7 5 2 1 4 3 6].
* If the deck is [3 1 2], we may apply the operation with k=3 and D_1=[3], D_2=[1], D_3=[2]. Doing so, the deck becomes [2 1 3].
* If the deck is [5 1 2 4 3 6], we may apply the operation with k=2 and D_1=[5 1], D_2=[2 4 3 6]. Doing so, the deck becomes [2 4 3 6 5 1].
Input
The first line of the input contains one integer n (1≤ n≤ 52) — the number of cards in the deck.
The second line contains n integers c_1, c_2, ..., c_n — the cards in the deck. The first card is c_1, the second is c_2 and so on.
It is guaranteed that for all i=1,...,n there is exactly one j∈\{1,...,n\} such that c_j = i.
Output
On the first line, print the number q of operations you perform (it must hold 0≤ q≤ n).
Then, print q lines, each describing one operation.
To describe an operation, print on a single line the number k of parts you are going to split the deck in, followed by the size of the k parts: |D_1|, |D_2|, ... , |D_k|.
It must hold 2≤ k≤ n, and |D_i|≥ 1 for all i=1,...,k, and |D_1|+|D_2|+⋅⋅⋅ + |D_k| = n.
It can be proven that it is always possible to sort the deck performing at most n operations. If there are several ways to sort the deck you can output any of them.
Examples
Input
4
3 1 2 4
Output
2
3 1 2 1
2 1 3
Input
6
6 5 4 3 2 1
Output
1
6 1 1 1 1 1 1
Input
1
1
Output
0
Note
Explanation of the first testcase: Initially the deck is [3 1 2 4].
* The first operation splits the deck as [(3) (1 2) (4)] and then transforms it into [4 1 2 3].
* The second operation splits the deck as [(4) (1 2 3)] and then transforms it into [1 2 3 4].
Explanation of the second testcase: Initially the deck is [6 5 4 3 2 1].
* The first (and only) operation splits the deck as [(6) (5) (4) (3) (2) (1)] and then transforms it into [1 2 3 4 5 6].
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
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{"tests": "{\"inputs\": [\"60 3\\n2012-03-16 16:15:25: Disk size is\\n2012-03-16 16:15:25: Network failute\\n2012-03-16 16:16:29: Cant write varlog\\n2012-03-16 16:16:42: Unable to start process\\n2012-03-16 16:16:43: Disk size is too small\\n2012-03-16 16:16:53: Timeout detected\\n\", \"2 2\\n2012-03-16 23:59:59:Disk size is too sm\\n2012-03-17 00:00:00:Network failute dete\\n2012-03-17 00:00:01:Cant write varlogmysq\\n\", \"1 2\\n2012-03-16 23:59:59:Disk size\\n2012-03-17 00:00:00: Network\\n2012-03-17 00:00:01:Cant write varlog\\n\", \"2 3\\n2012-02-20 16:15:00: Dis\\n2012-03-16 16:15:01: Net\\n2012-03-16 16:15:02: Cant write varlog\\n2012-03-16 16:15:02: Unable to start process\\n2012-03-16 16:16:43: Dis\\n2012-03-16 16:16:53: Timeout detected\\n\", \"2 4\\n2012-02-20 16:15:00: Dis\\n2012-03-16 16:15:01: Net\\n2012-03-16 16:15:02: Cant write varlog\\n2012-03-16 16:15:02: Unable to start process\\n2012-03-16 16:16:43: Dis\\n2012-03-16 16:16:53: Timeout detected\\n\", \"10 30\\n2012-02-03 10:01:10: qQsNeHR.BLmZVMsESEKKDvqcQHHzBeddbKiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"2 3\\n2012-02-20 16:15:00: Dis\\n2012-03-16 16:15:01: Net\\n2012-03-16 16:15:02: Cant write warlog\\n2012-03-16 16:15:02: Unable to start process\\n2012-03-16 16:16:43: Dis\\n2012-03-16 16:16:53: Timeout detected\\n\", \"10 30\\n2012-02-03 10:01:10: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbKiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"60 3\\n2012-03-16 16:15:25: Disk size is\\n2012-03-16 16:15:25: Network failute\\n2012-03-16 16:16:29: Cant write varlog\\n2012-03-16 16:16:42: Unable to start process\\n2012-03-16 16:16:43: Diks size is too small\\n2012-03-16 16:16:53: Timeout detected\\n\", \"2 2\\n2012-03-16 23:59:59:Disk size\\n2012-03-17 00:00:00: Network\\n2012-03-17 00:00:01:Cant write varlog\\n\", \"2 3\\n2012-02-20 16:15:00: Dis\\n2012-03-16 16:15:01: Net\\n2012-03-16 16:15:02: Cant write warlog\\n2012-03-16 16:15:02: Unable ot start process\\n2012-03-16 16:16:43: Dis\\n2012-03-16 16:16:53: Timeout detected\\n\", \"10 30\\n2012-02-03 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbKiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"10 30\\n2012-02-03 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbLiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"10 30\\n2012-02-04 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbLiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"5 30\\n2012-02-04 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbLiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"10 13\\n2012-02-03 10:01:10: qQsNeHR.BLmZVMsESEKKDvqcQHHzBeddbKiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"2 2\\n2012-03-16 23:59:59:Disk size is too rm\\n2012-03-17 00:00:00:Network failute dete\\n2012-03-17 00:00:01:Cant write varlogmysq\\n\", \"1 3\\n2012-03-16 23:59:59:Disk size\\n2012-03-17 00:00:00: Network\\n2012-03-17 00:00:01:Cant write varlog\\n\", \"2 3\\n2012-02-20 16:15:00: Dis\\n2012-03-16 16:15:01: Net\\n2012-03-16 16:15:02: Cant write warlog\\n2012-03-16 16:15:02: Unable tp start process\\n2012-03-16 16:16:43: Dis\\n2012-03-16 16:16:53: Timeout detected\\n\", \"60 3\\n2012-03-16 16:15:25: Disk size is\\n2012-03-16 16:15:25: Network etuliaf\\n2012-03-16 16:16:29: Cant write varlog\\n2012-03-16 16:16:42: Unable to start process\\n2012-03-16 16:16:43: Diks size is too small\\n2012-03-16 16:16:53: Timeout detected\\n\", \"4 2\\n2012-03-16 23:59:59:Disk size\\n2012-03-17 00:00:00: Network\\n2012-03-17 00:00:01:Cant write varlog\\n\", \"1 30\\n2012-02-03 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbKiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"10 30\\n2012-02-03 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbLiIb,aDQmBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"10 30\\n2012-02-04 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbLiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBYXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"10 13\\n2012-02-03 10:01:10: qQsNeHR.BLmZVMsESEKKDvqcQHHzBeddbKwIb,aDQnBKNtdcvititpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"2 2\\n2012-03-16 23:59:59:Disk size is too rm\\n2012-03-17 00:00:00:Network failtue dete\\n2012-03-17 00:00:01:Cant write varlogmysq\\n\", \"1 3\\n2012-03-16 23:59:59:Disk size\\n2012-03-18 00:00:00: Network\\n2012-03-17 00:00:01:Cant write varlog\\n\", \"60 3\\n2012-03-16 16:15:25: Disk size is\\n2012-03-16 16:15:25: Network etuliaf\\n2012-03-16 16:16:29: Cant etirw varlog\\n2012-03-16 16:16:42: Unable to start process\\n2012-03-16 16:16:43: Diks size is too small\\n2012-03-16 16:16:53: Timeout detected\\n\", \"4 2\\n2012-03-16 23:59:59:Disk size\\n2012-03-17 00:00:00: Network\\n2012-03-17 00:00t01:Can: write varlog\\n\", \"10 30\\n2012-02-03 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbLiIb,aDQmBKNtdcviIwtpUDGVFSh.Lx,FPBZXdSrsSDZttJDgx!mSovndGiqHlCwCFAHy\\n\", \"10 30\\n2012-02-04 10:11:00: qQsNeHR.BLmZVMsEREKKDuqcQHHzBeddbLiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBYXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"10 13\\n2012-02-03 10:01:10: yHAFCwClHqiGdnvoSm!xgDJItZDSsrSdXZBPF,xL.hSFVGDUptitivcdtNKBnQDa,bIwKbddeBzHHQcqvDKKESEsMVZmLB.RHeNsQq\\n\", \"2 2\\n2012-03-16 23:59:59:Disk size is oot rm\\n2012-03-17 00:00:00:Network failtue dete\\n2012-03-17 00:00:01:Cant write varlogmysq\\n\", \"1 3\\n2012-03-16 23:59:59:Disk size\\n2012-03-17 00:00:00: Netrowk\\n2012-03-17 00:00:01:Cant write varlog\\n\", \"4 2\\n2012-03-16 23:59:59:Disk size\\n2012-03-17 00:00:00: Network\\n2012-03-17 00:00t01:Can: etirw varlog\\n\", \"20 30\\n2012-02-03 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbLiIb,aDQmBKNtdcviIwtpUDGVFSh.Lx,FPBZXdSrsSDZttJDgx!mSovndGiqHlCwCFAHy\\n\", \"10 30\\n2012-02-04 10:11:00: qQsNeHR.BLmZVMsEREKKDuqcQHHzBeddbLiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBYXdSrsSDZtIJDgx!mSovneGiqHlCwCFAHy\\n\", \"10 4\\n2012-02-03 10:01:10: yHAFCwClHqiGdnvoSm!xgDJItZDSsrSdXZBPF,xL.hSFVGDUptitivcdtNKBnQDa,bIwKbddeBzHHQcqvDKKESEsMVZmLB.RHeNsQq\\n\", \"4 2\\n2012-03-16 23:59:59:Disk size\\n2012-03-17 00:00:00: Network\\n2012-03-17 00:00t01:Can: esirw varlog\\n\", \"20 52\\n2012-02-03 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbLiIb,aDQmBKNtdcviIwtpUDGVFSh.Lx,FPBZXdSrsSDZttJDgx!mSovndGiqHlCwCFAHy\\n\", \"1 30\\n2012-02-04 10:11:00: qQsNeHR.BLmZVMsEREKKDuqcQHHzBeddbLiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBYXdSrsSDZtIJDgx!mSovneGiqHlCwCFAHy\\n\", \"10 4\\n2012-02-03 10:01:10: yHAFCwClHqiGdnvoSm!xgDJItZDSsrSdXZBPF,xL.hSFVGDUptitivcdtMKBnQDa,bIwKbddeBzHHQcqvDKKESEsMVZmLB.RHeNsQq\\n\", \"20 52\\n2012-02-03 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbLiIb,aDQmBKNtdcviIwtpUDGVFSh.Lx,FPBZXdSrsSDZttJDgx!mSnvndGiqHlCwCFAHy\\n\", \"1 30\\n2012-02-04 10:10:01: qQsNeHR.BLmZVMsEREKKDuqcQHHzBeddbLiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBYXdSrsSDZtIJDgx!mSovneGiqHlCwCFAHy\\n\", \"10 4\\n2012-02-03 10:01:10: yH!FCwClHqiGdnvoSmAxgDJItZDSsrSdXZBPF,xL.hSFVGDUptitivcdtMKBnQDa,bIwKbddeBzHHQcqvDKKESEsMVZmLB.RHeNsQq\\n\", \"20 52\\n2012-02-03 10:12:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbLiIb,aDQmBKNtdcviIwtpUDGVFSh.Lx,FPBZXdSrsSDZttJDgx!mSnvndGiqHlCwCFAHy\\n\", \"10 4\\n2012-02-03 10:02:10: yH!FCwClHqiGdnvoSmAxgDJItZDSsrSdXZBPF,xL.hSFVGDUptitivcdtMKBnQDa,bIwKbddeBzHHQcqvDKKESEsMVZmLB.RHeNsQq\\n\", \"20 52\\n2012-02-03 10:11:00: yHAFCwClHqiGdnvnSm!xgDJttZDSsrSdXZBPF,xL.hSFVGDUptwIivcdtNKBmQDa,bIiLbddeBzHHQcquDKKESEsMVZmLB.RHeNsQq\\n\", \"10 4\\n2012-02-03 10:02:10: yH!FCwClHqiGdnvoSmAxgDJItZDSsrSdXZBPF,xL.hSFVGDUptitivcdtMKBnQDa,bIwKbddeBzHHQcqvqKKESEsMVZmLB.RHeNsQD\\n\", \"10 32\\n2012-02-03 10:01:10: qQsNeHR.BLmZVMsESEKKDvqcQHHzBeddbKiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"60 3\\n2012-03-16 16:15:25: Disk size is\\n2012-03-16 16:15:25: Network failute\\n2012-03-16 16:16:29: Cant write vbrlog\\n2012-03-16 16:16:42: Unable to start process\\n2012-03-16 16:16:43: Disk size is too small\\n2012-03-16 16:16:53: Timeout detected\\n\", \"2 2\\n2012-03-16 23:59:59:Disk size js too sm\\n2012-03-17 00:00:00:Network failute dete\\n2012-03-17 00:00:01:Cant write varlogmysq\\n\", \"2 3\\n2012-02-20 16:15:00: Dis\\n2012-03-16 16:15:02: Net\\n2012-03-16 16:15:02: Cant write warlog\\n2012-03-16 16:15:02: Unable to start process\\n2012-03-16 16:16:43: Dis\\n2012-03-16 16:16:53: Timeout detected\\n\", \"10 30\\n2012-02-04 10:01:10: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbKiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"60 3\\n2012-03-16 16:15:25: Disk size is\\n2012-03-16 16:15:25: Network failute\\n2012-03-16 16:16:29: Cant write varlog\\n2012-03-16 16:16:42: Unable to start process\\n2012-03-16 16:16:43: Diks size is too small\\n2012-03-16 16:16:53: Timfout detected\\n\", \"10 25\\n2012-02-03 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbKiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\", \"6 30\\n2012-02-03 10:11:00: qQsNeHR.BLmZVMsESEKKDuqcQHHzBeddbLiIb,aDQnBKNtdcvitwtpUDGVFSh.Lx,FPBZXdSrsSDZtIJDgx!mSovndGiqHlCwCFAHy\\n\"], \"outputs\": [\"2012-03-16 16:16:43\\n\", \"2012-03-17 00:00:00\\n\", \"-1\\n\", \"2012-03-16 16:15:02\\n\", \"-1\\n\", \"-1\\n\", \"2012-03-16 16:15:02\\n\", \"-1\\n\", \"2012-03-16 16:16:43\\n\", \"2012-03-17 00:00:00\\n\", \"2012-03-16 16:15:02\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2012-03-17 00:00:00\\n\", \"-1\\n\", \"2012-03-16 16:15:02\\n\", \"2012-03-16 16:16:43\\n\", \"2012-03-17 00:00:00\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2012-03-17 00:00:00\\n\", \"-1\\n\", \"2012-03-16 16:16:43\\n\", \"2012-03-17 00:00:00\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2012-03-17 00:00:00\\n\", \"-1\\n\", \"2012-03-17 00:00:00\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2012-03-17 00:00:00\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2012-03-16 16:16:43\\n\", \"2012-03-17 00:00:00\\n\", \"2012-03-16 16:15:02\\n\", \"-1\\n\", \"2012-03-16 16:16:43\\n\", \"-1\\n\", \"-1\\n\"]}", "source": "primeintellect"}
|
You've got a list of program warning logs. Each record of a log stream is a string in this format:
"2012-MM-DD HH:MM:SS:MESSAGE" (without the quotes).
String "MESSAGE" consists of spaces, uppercase and lowercase English letters and characters "!", ".", ",", "?". String "2012-MM-DD" determines a correct date in the year of 2012. String "HH:MM:SS" determines a correct time in the 24 hour format.
The described record of a log stream means that at a certain time the record has got some program warning (string "MESSAGE" contains the warning's description).
Your task is to print the first moment of time, when the number of warnings for the last n seconds was not less than m.
Input
The first line of the input contains two space-separated integers n and m (1 ≤ n, m ≤ 10000).
The second and the remaining lines of the input represent the log stream. The second line of the input contains the first record of the log stream, the third line contains the second record and so on. Each record of the log stream has the above described format. All records are given in the chronological order, that is, the warning records are given in the order, in which the warnings appeared in the program.
It is guaranteed that the log has at least one record. It is guaranteed that the total length of all lines of the log stream doesn't exceed 5·106 (in particular, this means that the length of some line does not exceed 5·106 characters). It is guaranteed that all given dates and times are correct, and the string 'MESSAGE" in all records is non-empty.
Output
If there is no sought moment of time, print -1. Otherwise print a string in the format "2012-MM-DD HH:MM:SS" (without the quotes) — the first moment of time when the number of warnings for the last n seconds got no less than m.
Examples
Input
60 3
2012-03-16 16:15:25: Disk size is
2012-03-16 16:15:25: Network failute
2012-03-16 16:16:29: Cant write varlog
2012-03-16 16:16:42: Unable to start process
2012-03-16 16:16:43: Disk size is too small
2012-03-16 16:16:53: Timeout detected
Output
2012-03-16 16:16:43
Input
1 2
2012-03-16 23:59:59:Disk size
2012-03-17 00:00:00: Network
2012-03-17 00:00:01:Cant write varlog
Output
-1
Input
2 2
2012-03-16 23:59:59:Disk size is too sm
2012-03-17 00:00:00:Network failute dete
2012-03-17 00:00:01:Cant write varlogmysq
Output
2012-03-17 00:00:00
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"8\\n\", \"1\\n\", \"2\\n\", \"10154\\n\", \"19000881\\n\", \"6\\n\", \"18\\n\", \"3\\n\", \"947039074\\n\", \"19000883\\n\", \"10\\n\", \"945070564\\n\", \"15\\n\", \"987719184\\n\", \"956726760\\n\", \"16\\n\", \"12\\n\", \"1000000000\\n\", \"992187002\\n\", \"987719182\\n\", \"951352336\\n\", \"956726762\\n\", \"954377448\\n\", \"19000882\\n\", \"992313002\\n\", \"13\\n\", \"23\\n\", \"957097968\\n\", \"19000880\\n\", \"26\\n\", \"250\\n\", \"987656328\\n\", \"989983296\\n\", \"246\\n\", \"25\\n\", \"959140898\\n\", \"21\\n\", \"988850914\\n\", \"200\\n\", \"200702\\n\", \"22\\n\", \"951352334\\n\", \"24\\n\", \"947900944\\n\", \"248\\n\", \"28\\n\", \"200705\\n\", \"7\\n\", \"200706\\n\", \"992313000\\n\", \"53\\n\", \"200704\\n\", \"247\\n\", \"959140900\\n\", \"200703\\n\", \"999999999\\n\", \"945070562\\n\", \"992187000\\n\", \"19\\n\", \"52\\n\", \"999999998\\n\", \"954377450\\n\", \"947039076\\n\", \"11\\n\", \"940219568\\n\", \"988850916\\n\", \"17\\n\", \"10155\\n\", \"5\\n\", \"4\\n\", \"957097970\\n\", \"27\\n\", \"9\\n\", \"989983294\\n\", \"987656330\\n\", \"10153\\n\", \"14\\n\", \"940219570\\n\", \"249\\n\", \"20\\n\", \"947900942\\n\", \"8350\\n\", \"27668680\\n\", \"252780602\\n\", \"24737876\\n\", \"739939498\\n\", \"39\\n\", \"1000000001\\n\", \"857211966\\n\", \"7115716\\n\", \"928459748\\n\", \"32\\n\", \"31567404\\n\", \"6186813\\n\", \"35\\n\", \"418\\n\", \"395\\n\", \"40\\n\", \"145\\n\", \"68366\\n\", \"994763104\\n\", \"44\\n\", \"210145775\\n\", \"353\\n\", \"49\\n\", \"85102\\n\", \"391714\\n\", \"77\\n\", \"82669\\n\", \"45\\n\", \"297888\\n\", \"458695092\\n\", \"803689731\\n\", \"38\\n\", \"198694268\\n\", \"106364792\\n\", \"31\\n\", \"4836\\n\", \"29\\n\", \"33\\n\", \"242706161\\n\", \"679940574\\n\", \"17913\\n\", \"142\\n\", \"37\\n\", \"55\\n\", \"42\\n\", \"10273\\n\", \"39191243\\n\", \"168713196\\n\", \"6762337\\n\", \"968737171\\n\", \"30\\n\", \"0000000001\\n\", \"430139251\\n\", \"10697442\\n\", \"63\\n\", \"36836900\\n\", \"5508411\\n\", \"54\\n\", \"621\\n\", \"647\\n\", \"41\\n\", \"403\\n\", \"132540\\n\", \"429806024\\n\", \"100\\n\", \"251695843\\n\"], \"outputs\": [\"Petya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Petya\\n\", \"Petya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Petya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\", \"Vasya\\n\"]}", "source": "primeintellect"}
|
Vasya and Petya wrote down all integers from 1 to n to play the "powers" game (n can be quite large; however, Vasya and Petya are not confused by this fact).
Players choose numbers in turn (Vasya chooses first). If some number x is chosen at the current turn, it is forbidden to choose x or all of its other positive integer powers (that is, x2, x3, ...) at the next turns. For instance, if the number 9 is chosen at the first turn, one cannot choose 9 or 81 later, while it is still allowed to choose 3 or 27. The one who cannot make a move loses.
Who wins if both Vasya and Petya play optimally?
Input
Input contains single integer n (1 ≤ n ≤ 109).
Output
Print the name of the winner — "Vasya" or "Petya" (without quotes).
Examples
Input
1
Output
Vasya
Input
2
Output
Petya
Input
8
Output
Petya
Note
In the first sample Vasya will choose 1 and win immediately.
In the second sample no matter which number Vasya chooses during his first turn, Petya can choose the remaining number and win.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 4 6 8 10\\n\", \"18 13 91 64 22\\n\", \"31 38 47 26 13\\n\", \"65 46 3 77 81\\n\", \"94 21 36 89 20\\n\", \"12 39 3 50 84\\n\", \"75 82 48 95 12\\n\", \"46 68 3 0 51\\n\", \"1 1 2 6 4\\n\", \"50 27 17 31 89\\n\", \"42 9 59 19 24\\n\", \"74 21 36 68 80\\n\", \"50 87 29 81 21\\n\", \"0 74 25 35 48\\n\", \"41 85 14 43 23\\n\", \"3 26 69 33 18\\n\", \"14 63 14 25 18\\n\", \"32 36 80 54 48\\n\", \"12 31 47 31 84\\n\", \"0 0 0 0 0\\n\", \"1 1 2 7 4\\n\", \"1 0 2 7 4\\n\", \"1 1 1 7 4\\n\", \"67 66 69 96 92\\n\", \"51 19 70 5 78\\n\", \"79 2 93 92 16\\n\", \"81 26 69 0 84\\n\", \"28 49 58 47 54\\n\", \"2 2 3 14 8\\n\", \"51 56 14 99 21\\n\", \"81 67 58 8 51\\n\", \"94 28 3 29 9\\n\", \"71 61 47 9 19\\n\", \"60 92 82 71 53\\n\", \"1 2 2 7 4\\n\", \"1 1 3 7 4\\n\", \"100 100 100 100 100\\n\", \"52 43 80 14 79\\n\", \"19 84 69 57 55\\n\", \"14 13 91 64 22\\n\", \"31 38 59 26 13\\n\", \"65 58 3 77 81\\n\", \"46 13 3 0 51\\n\", \"50 27 20 31 89\\n\", \"37 9 59 19 24\\n\", \"32 63 80 54 48\\n\", \"64 66 69 96 92\\n\", \"28 49 58 63 54\\n\", \"60 120 82 71 53\\n\", \"100 110 100 100 100\\n\", \"19 84 71 57 55\\n\", \"100 110 100 110 100\\n\", \"94 10 36 89 20\\n\", \"12 39 3 68 84\\n\", \"75 155 48 95 12\\n\", \"1 1 2 3 4\\n\", \"74 3 36 68 80\\n\", \"50 87 29 14 21\\n\", \"0 74 25 35 85\\n\", \"80 85 14 43 23\\n\", \"3 26 69 9 18\\n\", \"14 63 22 25 18\\n\", \"20 31 47 31 84\\n\", \"0 0 0 1 0\\n\", \"1 1 2 7 8\\n\", \"1 0 2 10 4\\n\", \"1 1 1 7 0\\n\", \"51 19 49 5 78\\n\", \"79 2 93 92 23\\n\", \"81 51 69 0 84\\n\", \"2 3 3 14 8\\n\", \"35 56 14 99 21\\n\", \"81 67 58 9 51\\n\", \"94 28 3 55 9\\n\", \"71 98 47 9 19\\n\", \"1 2 2 7 8\\n\", \"1 1 3 9 4\\n\", \"46 43 80 14 79\\n\", \"1 4 6 8 10\\n\", \"14 13 23 64 22\\n\", \"31 40 59 26 13\\n\", \"90 58 3 77 81\\n\", \"94 10 36 84 20\\n\", \"12 39 3 68 59\\n\", \"57 155 48 95 12\\n\", \"46 21 3 0 51\\n\", \"1 1 2 0 4\\n\", \"50 49 20 31 89\\n\", \"37 9 59 19 32\\n\", \"80 3 36 68 80\\n\", \"50 87 29 14 39\\n\", \"80 138 14 43 23\\n\", \"3 26 69 9 34\\n\", \"14 63 22 25 6\\n\", \"32 63 157 54 48\\n\", \"20 31 47 31 11\\n\", \"0 1 0 1 0\\n\", \"2 1 2 7 8\\n\", \"1 1 2 10 4\\n\", \"2 1 1 7 0\\n\", \"64 84 69 96 92\\n\", \"51 19 49 3 78\\n\", \"79 2 124 92 23\\n\", \"117 51 69 0 84\\n\", \"28 49 80 63 54\\n\", \"2 3 3 18 8\\n\", \"35 56 14 53 21\\n\", \"70 67 58 9 51\\n\", \"122 28 3 55 9\\n\", \"71 147 47 9 19\\n\", \"60 28 82 71 53\\n\", \"1 2 0 7 8\\n\", \"1 1 3 6 4\\n\", \"46 43 80 7 79\\n\", \"19 84 71 57 69\\n\", \"1 4 6 8 14\\n\", \"14 18 23 64 22\\n\", \"31 40 67 26 13\\n\", \"90 58 3 140 81\\n\", \"94 10 36 84 15\\n\", \"12 39 3 68 26\\n\", \"57 47 48 95 12\\n\", \"46 21 3 0 89\\n\", \"1 1 0 0 4\\n\", \"71 49 20 31 89\\n\", \"37 9 18 19 32\\n\", \"80 3 36 120 80\\n\", \"50 87 34 14 39\\n\", \"80 95 14 43 23\\n\", \"3 51 69 9 34\\n\", \"14 63 22 10 6\\n\", \"32 63 157 33 48\\n\", \"20 31 47 31 16\\n\", \"0 1 0 0 0\\n\", \"2 1 3 7 8\\n\", \"2 1 2 10 4\\n\", \"2 1 1 0 0\\n\", \"64 134 69 96 92\\n\", \"51 19 49 3 59\\n\"], \"outputs\": [\"1\\n\", \"5\\n\", \"3\\n\", \"1\\n\", \"5\\n\", \"1\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"2\\n\", \"9\\n\", \"5\\n\", \"0\\n\", \"5\\n\", \"3\\n\", \"3\\n\", \"7\\n\", \"4\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"13\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"6\\n\", \"1\\n\", \"5\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"10\\n\", \"1\\n\", \"1\\n\", \"14\\n\", \"2\\n\", \"8\\n\", \"5\\n\", \"3\\n\", \"1\\n\", \"0\\n\", \"4\\n\", \"2\\n\", \"7\\n\", \"13\\n\", \"9\\n\", \"10\\n\", \"14\\n\", \"8\\n\", \"15\\n\", \"5\\n\", \"1\\n\", \"3\\n\", \"0\\n\", \"3\\n\", \"2\\n\", \"0\\n\", \"5\\n\", \"1\\n\", \"3\\n\", \"4\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"5\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"5\\n\", \"3\\n\", \"1\\n\", \"5\\n\", \"1\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"5\\n\", \"1\\n\", \"1\\n\", \"7\\n\", \"2\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"13\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"9\\n\", \"1\\n\", \"5\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"10\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"8\\n\", \"1\\n\", \"5\\n\", \"3\\n\", \"1\\n\", \"3\\n\", \"1\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"5\\n\", \"1\\n\", \"1\\n\", \"4\\n\", \"4\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"13\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Salve, mi amice.
Et tu quidem de lapis philosophorum. Barba non facit philosophum. Labor omnia vincit. Non potest creatio ex nihilo. Necesse est partibus.
Rp:
I Aqua Fortis
I Aqua Regia
II Amalgama
VII Minium
IV Vitriol
Misce in vitro et æstus, et nil admirari. Festina lente, et nulla tenaci invia est via.
Fac et spera,
Vale,
Nicolas Flamel
Input
The first line of input contains several space-separated integers ai (0 ≤ ai ≤ 100).
Output
Print a single integer.
Examples
Input
2 4 6 8 10
Output
1
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"6 7\\n1 2 1\\n3 2 5\\n2 4 2\\n2 5 2\\n2 6 9\\n5 4 3\\n4 3 4\\n\", \"3 3\\n1 2 1\\n2 3 1\\n3 1 1\\n\", \"3 3\\n1 2 1\\n2 3 2\\n3 1 3\\n\", \"6 7\\n1 2 1\\n1 5 1\\n5 2 3\\n2 3 3\\n3 4 4\\n1 6 1\\n6 2 3\\n\", \"3 6\\n1 2 1\\n2 3 1\\n3 1 1\\n2 1 2\\n3 2 4\\n1 3 3\\n\", \"2 2\\n1 2 1\\n2 1 2\\n\", \"4 3\\n1 2 1\\n2 3 1\\n3 4 2\\n\", \"4 3\\n1 2 1\\n3 4 1\\n2 1 2\\n\", \"5 5\\n1 2 3\\n1 3 3\\n2 3 4\\n3 4 4\\n4 5 5\\n\", \"4 12\\n1 2 2\\n2 1 2\\n1 3 1\\n3 1 1\\n1 4 1\\n4 1 1\\n2 3 1\\n3 2 1\\n2 4 1\\n4 2 1\\n3 4 2\\n4 3 2\\n\", \"5 8\\n1 2 1\\n2 3 1\\n3 4 1\\n4 5 1\\n1 5 1\\n1 3 2\\n2 4 2\\n3 5 3\\n\", \"3 4\\n1 2 1\\n2 1 2\\n2 3 2\\n3 1 3\\n\", \"3 3\\n1 2 1\\n1 3 2\\n3 2 3\\n\", \"6 7\\n1 2 1\\n1 1 1\\n5 2 3\\n2 3 3\\n3 4 4\\n1 6 1\\n6 2 3\\n\", \"3 6\\n1 2 1\\n2 3 1\\n3 1 2\\n2 1 2\\n3 2 4\\n1 3 3\\n\", \"2 2\\n2 2 1\\n2 1 2\\n\", \"4 3\\n1 3 1\\n3 4 1\\n2 1 2\\n\", \"6 7\\n1 2 1\\n3 2 5\\n2 4 0\\n2 5 2\\n2 6 9\\n5 4 3\\n4 3 4\\n\", \"6 7\\n1 2 2\\n3 2 5\\n2 4 0\\n2 5 2\\n2 6 9\\n5 4 3\\n4 3 4\\n\", \"5 12\\n1 2 2\\n2 1 2\\n1 3 1\\n3 1 1\\n1 4 1\\n4 1 1\\n2 3 1\\n3 2 1\\n2 4 1\\n4 2 1\\n3 4 2\\n4 3 2\\n\", \"8 8\\n1 2 1\\n2 3 1\\n3 4 1\\n4 5 1\\n1 5 1\\n1 3 2\\n2 4 2\\n3 5 3\\n\", \"3 3\\n1 2 0\\n1 3 2\\n3 2 3\\n\", \"5 3\\n1 2 1\\n2 3 2\\n3 1 3\\n\", \"6 7\\n1 2 1\\n1 1 1\\n5 2 3\\n2 3 3\\n3 4 5\\n1 6 1\\n6 2 3\\n\", \"3 6\\n1 2 1\\n2 3 1\\n3 1 2\\n2 1 2\\n3 2 7\\n1 3 3\\n\", \"4 3\\n1 3 1\\n3 4 1\\n4 1 2\\n\", \"5 12\\n1 2 2\\n2 1 2\\n1 3 1\\n3 1 1\\n2 4 1\\n4 1 1\\n2 3 1\\n3 2 1\\n2 4 1\\n4 2 1\\n3 4 2\\n4 3 2\\n\", \"8 8\\n1 2 1\\n2 3 1\\n3 4 1\\n4 5 1\\n1 5 1\\n1 3 2\\n2 4 3\\n3 5 3\\n\", \"3 3\\n1 2 0\\n1 3 2\\n3 1 3\\n\", \"5 3\\n1 2 1\\n1 3 2\\n3 1 3\\n\", \"4 3\\n2 3 1\\n3 4 1\\n4 1 2\\n\", \"5 3\\n1 2 1\\n1 3 2\\n2 1 3\\n\", \"5 3\\n1 2 1\\n2 3 2\\n2 1 3\\n\", \"5 3\\n1 2 1\\n2 3 4\\n2 1 3\\n\", \"5 3\\n1 2 2\\n2 3 4\\n2 1 3\\n\", \"5 3\\n1 4 2\\n2 3 4\\n2 1 3\\n\", \"5 3\\n1 4 2\\n2 3 4\\n2 2 3\\n\", \"5 3\\n1 4 2\\n2 3 3\\n2 2 3\\n\", \"6 7\\n1 2 1\\n1 5 1\\n5 2 3\\n2 3 3\\n3 4 4\\n1 6 1\\n5 2 3\\n\", \"4 3\\n1 2 1\\n2 3 1\\n2 4 2\\n\", \"4 3\\n1 2 1\\n3 4 1\\n2 2 2\\n\", \"5 5\\n1 2 3\\n1 3 3\\n2 3 4\\n3 4 4\\n4 3 5\\n\", \"4 12\\n1 2 2\\n2 1 2\\n1 3 2\\n3 1 1\\n1 4 1\\n4 1 1\\n2 3 1\\n3 2 1\\n2 4 1\\n4 2 1\\n3 4 2\\n4 3 2\\n\", \"6 7\\n1 2 1\\n3 2 5\\n2 4 2\\n2 5 2\\n2 6 3\\n5 4 3\\n4 3 4\\n\", \"6 7\\n1 2 1\\n1 1 1\\n5 2 3\\n2 3 3\\n3 4 4\\n1 3 1\\n6 2 3\\n\", \"3 6\\n1 2 1\\n2 3 1\\n3 1 2\\n2 1 1\\n3 2 4\\n1 3 3\\n\", \"10 12\\n1 2 2\\n2 1 2\\n1 3 1\\n3 1 1\\n1 4 1\\n4 1 1\\n2 3 1\\n3 2 1\\n2 4 1\\n4 2 1\\n3 4 2\\n4 3 2\\n\", \"8 8\\n1 2 1\\n2 3 1\\n3 4 1\\n4 5 1\\n1 5 1\\n1 3 2\\n2 6 2\\n3 5 3\\n\", \"3 3\\n1 2 0\\n1 3 2\\n3 2 4\\n\", \"6 7\\n1 2 1\\n3 2 5\\n2 4 0\\n2 5 2\\n1 6 9\\n5 4 3\\n4 3 4\\n\", \"6 7\\n1 2 1\\n1 1 1\\n5 2 3\\n2 3 1\\n3 4 5\\n1 6 1\\n6 2 3\\n\", \"5 12\\n1 2 2\\n2 1 2\\n1 3 1\\n3 1 1\\n2 4 1\\n4 1 1\\n2 3 1\\n3 3 1\\n2 4 1\\n4 2 1\\n3 4 2\\n4 3 2\\n\", \"3 3\\n1 2 0\\n1 2 2\\n3 2 3\\n\"], \"outputs\": [\"6\\n\", \"1\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"3\\n\", \"4\\n\", \"2\\n\", \"1\\n\", \"6\\n\", \"5\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"3\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"3\\n\", \"2\\n\", \"2\\n\", \"3\\n\", \"2\\n\", \"5\\n\", \"3\\n\", \"4\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"5\\n\", \"2\\n\", \"2\\n\", \"1\\n\"]}", "source": "primeintellect"}
|
Pashmak's homework is a problem about graphs. Although he always tries to do his homework completely, he can't solve this problem. As you know, he's really weak at graph theory; so try to help him in solving the problem.
You are given a weighted directed graph with n vertices and m edges. You need to find a path (perhaps, non-simple) with maximum number of edges, such that the weights of the edges increase along the path. In other words, each edge of the path must have strictly greater weight than the previous edge in the path.
Help Pashmak, print the number of edges in the required path.
Input
The first line contains two integers n, m (2 ≤ n ≤ 3·105; 1 ≤ m ≤ min(n·(n - 1), 3·105)). Then, m lines follows. The i-th line contains three space separated integers: ui, vi, wi (1 ≤ ui, vi ≤ n; 1 ≤ wi ≤ 105) which indicates that there's a directed edge with weight wi from vertex ui to vertex vi.
It's guaranteed that the graph doesn't contain self-loops and multiple edges.
Output
Print a single integer — the answer to the problem.
Examples
Input
3 3
1 2 1
2 3 1
3 1 1
Output
1
Input
3 3
1 2 1
2 3 2
3 1 3
Output
3
Input
6 7
1 2 1
3 2 5
2 4 2
2 5 2
2 6 9
5 4 3
4 3 4
Output
6
Note
In the first sample the maximum trail can be any of this trails: <image>.
In the second sample the maximum trail is <image>.
In the third sample the maximum trail is <image>.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4 6\\n1 2\\n1 4\\n2 3\\n2 4\\n3 2\\n3 4\\n\", \"4 5\\n1 2\\n1 3\\n1 4\\n2 3\\n2 4\\n\", \"7 13\\n6 1\\n7 2\\n3 7\\n6 5\\n3 6\\n7 4\\n3 5\\n4 1\\n3 1\\n1 5\\n1 6\\n6 2\\n2 4\\n\", \"8 12\\n6 1\\n7 5\\n2 5\\n4 1\\n6 3\\n4 3\\n5 7\\n1 3\\n5 2\\n2 7\\n4 6\\n7 2\\n\", \"10 10\\n10 6\\n9 4\\n7 8\\n1 5\\n3 10\\n2 1\\n4 9\\n5 2\\n10 3\\n6 3\\n\", \"10 4\\n7 4\\n6 8\\n2 3\\n3 8\\n\", \"2 1\\n1 2\\n\", \"5 3\\n4 2\\n2 1\\n5 4\\n\", \"10 4\\n8 4\\n9 8\\n2 8\\n8 1\\n\", \"6 7\\n5 4\\n3 1\\n4 2\\n2 1\\n5 2\\n2 3\\n2 6\\n\", \"8 7\\n6 3\\n2 4\\n3 7\\n8 2\\n4 8\\n7 6\\n3 2\\n\", \"7 8\\n4 6\\n2 1\\n2 5\\n7 4\\n7 1\\n7 2\\n1 4\\n2 4\\n\", \"9 10\\n6 4\\n7 5\\n9 3\\n7 6\\n4 8\\n4 2\\n9 8\\n1 3\\n5 1\\n4 7\\n\", \"8 5\\n3 1\\n7 5\\n2 5\\n8 6\\n1 3\\n\", \"5 7\\n4 3\\n2 5\\n2 1\\n3 2\\n1 3\\n3 4\\n1 4\\n\", \"3 6\\n1 2\\n1 3\\n2 1\\n2 3\\n3 1\\n3 2\\n\", \"5 4\\n2 5\\n4 3\\n5 2\\n5 1\\n\", \"4 6\\n1 2\\n1 3\\n1 4\\n2 3\\n2 4\\n3 4\\n\", \"7 7\\n7 3\\n5 4\\n4 7\\n5 7\\n6 3\\n5 6\\n3 4\\n\", \"9 5\\n5 8\\n7 4\\n7 2\\n9 8\\n9 5\\n\", \"7 13\\n6 1\\n7 2\\n3 7\\n6 5\\n3 6\\n7 4\\n3 5\\n4 1\\n3 1\\n1 5\\n1 6\\n4 2\\n2 4\\n\", \"10 10\\n10 6\\n9 4\\n7 8\\n1 4\\n3 10\\n2 1\\n4 9\\n5 2\\n10 3\\n6 3\\n\", \"10 4\\n7 4\\n6 7\\n2 3\\n3 8\\n\", \"8 7\\n6 3\\n2 4\\n3 3\\n8 2\\n4 8\\n7 6\\n3 2\\n\", \"8 5\\n3 1\\n7 5\\n2 5\\n8 2\\n1 3\\n\", \"3 6\\n1 2\\n1 2\\n2 1\\n2 3\\n3 1\\n3 2\\n\", \"10 10\\n10 6\\n9 4\\n7 8\\n1 4\\n6 10\\n2 1\\n1 9\\n5 1\\n10 3\\n6 3\\n\", \"7 8\\n4 6\\n3 1\\n2 5\\n7 4\\n7 1\\n7 2\\n1 4\\n2 4\\n\", \"9 10\\n6 4\\n7 7\\n9 3\\n7 6\\n4 8\\n4 2\\n9 8\\n1 3\\n5 1\\n4 7\\n\", \"5 7\\n4 3\\n2 3\\n2 1\\n3 2\\n1 3\\n3 4\\n1 4\\n\", \"4 6\\n1 2\\n1 3\\n1 4\\n2 4\\n2 4\\n3 4\\n\", \"9 5\\n5 8\\n8 4\\n7 2\\n9 8\\n9 5\\n\", \"4 6\\n1 3\\n1 4\\n2 3\\n2 4\\n3 2\\n3 4\\n\", \"7 13\\n6 1\\n7 2\\n3 7\\n6 5\\n3 6\\n7 4\\n3 7\\n4 1\\n3 1\\n1 5\\n1 6\\n4 2\\n2 4\\n\", \"10 10\\n10 6\\n9 4\\n7 8\\n1 4\\n3 10\\n2 1\\n4 9\\n5 1\\n10 3\\n6 3\\n\", \"10 4\\n7 4\\n6 7\\n2 3\\n3 1\\n\", \"8 7\\n6 3\\n2 6\\n3 3\\n8 2\\n4 8\\n7 6\\n3 2\\n\", \"7 8\\n4 6\\n3 1\\n2 5\\n7 4\\n3 1\\n7 2\\n1 4\\n2 4\\n\", \"9 10\\n6 4\\n7 8\\n9 3\\n7 6\\n4 8\\n4 2\\n9 8\\n1 3\\n5 1\\n4 7\\n\", \"9 5\\n5 8\\n8 6\\n7 2\\n9 8\\n9 5\\n\", \"4 6\\n1 3\\n1 4\\n2 3\\n2 4\\n1 2\\n3 4\\n\", \"10 10\\n10 6\\n9 4\\n7 9\\n1 4\\n3 10\\n2 1\\n4 9\\n5 1\\n10 3\\n6 3\\n\", \"10 4\\n7 4\\n6 7\\n1 3\\n3 1\\n\", \"7 8\\n4 6\\n3 1\\n2 6\\n7 4\\n3 1\\n7 2\\n1 4\\n2 4\\n\", \"7 8\\n2 6\\n3 1\\n2 6\\n7 4\\n3 1\\n7 2\\n1 4\\n2 4\\n\", \"10 10\\n3 6\\n9 4\\n7 8\\n1 5\\n3 10\\n2 1\\n4 9\\n5 2\\n10 3\\n6 3\\n\", \"8 7\\n6 3\\n2 4\\n3 7\\n8 2\\n4 8\\n5 6\\n3 2\\n\", \"7 8\\n4 6\\n2 1\\n2 5\\n7 4\\n7 1\\n5 2\\n1 4\\n2 4\\n\", \"9 10\\n6 4\\n7 5\\n9 3\\n7 6\\n4 8\\n4 2\\n9 8\\n1 3\\n5 1\\n4 6\\n\", \"3 6\\n1 1\\n1 3\\n2 1\\n2 3\\n3 1\\n3 2\\n\", \"5 4\\n2 5\\n4 3\\n3 2\\n5 1\\n\", \"17 5\\n5 8\\n7 4\\n7 2\\n9 8\\n9 5\\n\", \"4 6\\n2 2\\n1 4\\n2 3\\n2 4\\n3 2\\n3 4\\n\", \"4 5\\n1 2\\n1 3\\n1 4\\n1 3\\n2 4\\n\", \"7 13\\n6 1\\n7 2\\n3 7\\n6 5\\n3 6\\n7 4\\n3 4\\n4 1\\n3 1\\n1 5\\n1 6\\n4 2\\n2 4\\n\", \"5 7\\n4 3\\n2 3\\n2 1\\n3 2\\n1 5\\n3 4\\n1 4\\n\", \"4 6\\n1 1\\n1 4\\n2 3\\n2 4\\n3 2\\n3 4\\n\", \"10 10\\n10 6\\n9 4\\n7 8\\n1 4\\n6 10\\n2 1\\n4 9\\n5 1\\n10 3\\n6 3\\n\", \"10 4\\n7 4\\n6 7\\n2 3\\n5 1\\n\", \"7 8\\n4 6\\n3 1\\n2 5\\n7 4\\n3 1\\n3 2\\n1 4\\n2 4\\n\", \"16 5\\n5 8\\n8 6\\n7 2\\n9 8\\n9 5\\n\", \"10 10\\n10 6\\n9 4\\n7 4\\n1 4\\n3 10\\n2 1\\n4 9\\n5 1\\n10 3\\n6 3\\n\", \"10 4\\n7 4\\n6 7\\n1 3\\n2 1\\n\", \"7 8\\n4 6\\n3 1\\n2 6\\n7 4\\n6 1\\n7 2\\n1 4\\n2 4\\n\", \"10 10\\n3 6\\n9 4\\n7 8\\n1 5\\n3 10\\n3 1\\n4 9\\n5 2\\n10 3\\n6 3\\n\", \"8 7\\n6 5\\n2 4\\n3 7\\n8 2\\n4 8\\n5 6\\n3 2\\n\", \"7 8\\n4 6\\n2 1\\n3 5\\n7 4\\n7 1\\n5 2\\n1 4\\n2 4\\n\", \"13 10\\n6 4\\n7 5\\n9 3\\n7 6\\n4 8\\n4 2\\n9 8\\n1 3\\n5 1\\n4 6\\n\", \"3 6\\n2 1\\n1 3\\n2 1\\n2 3\\n3 1\\n3 2\\n\", \"5 4\\n2 5\\n1 3\\n3 2\\n5 1\\n\", \"5 7\\n4 3\\n2 3\\n2 1\\n3 2\\n1 5\\n4 4\\n1 4\\n\", \"10 4\\n7 4\\n6 7\\n2 3\\n2 1\\n\", \"13 10\\n6 4\\n7 5\\n9 3\\n7 6\\n4 8\\n4 2\\n9 8\\n1 4\\n5 1\\n4 6\\n\", \"5 4\\n2 5\\n1 4\\n3 2\\n5 1\\n\", \"10 4\\n7 5\\n6 7\\n2 3\\n2 1\\n\", \"7 13\\n6 1\\n7 2\\n1 7\\n6 5\\n3 6\\n7 4\\n3 5\\n4 1\\n3 1\\n1 5\\n1 6\\n6 2\\n2 4\\n\", \"8 12\\n6 1\\n7 5\\n2 5\\n4 1\\n6 3\\n6 3\\n5 7\\n1 3\\n5 2\\n2 7\\n4 6\\n7 2\\n\", \"10 10\\n10 5\\n9 4\\n7 8\\n1 5\\n3 10\\n2 1\\n4 9\\n5 2\\n10 3\\n6 3\\n\", \"10 4\\n7 4\\n10 8\\n2 3\\n3 8\\n\", \"5 3\\n4 2\\n2 1\\n1 4\\n\", \"10 4\\n8 4\\n9 6\\n2 8\\n8 1\\n\", \"6 7\\n5 4\\n3 1\\n4 2\\n2 1\\n5 2\\n2 3\\n3 6\\n\", \"8 7\\n6 3\\n2 4\\n3 7\\n8 2\\n4 8\\n7 4\\n3 2\\n\"], \"outputs\": [\"4\", \"3\", \"7\", \"6\", \"9\", \"4\", \"1\", \"3\", \"4\", \"5\", \"6\", \"5\", \"9\", \"5\", \"5\", \"3\", \"4\", \"3\", \"5\", \"4\", \"7\\n\", \"9\\n\", \"4\\n\", \"6\\n\", \"5\\n\", \"3\\n\", \"8\\n\", \"6\\n\", \"9\\n\", \"4\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"7\\n\", \"9\\n\", \"4\\n\", \"6\\n\", \"6\\n\", \"9\\n\", \"4\\n\", \"3\\n\", \"9\\n\", \"4\\n\", \"5\\n\", \"5\\n\", \"9\\n\", \"7\\n\", \"6\\n\", \"9\\n\", \"3\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"3\\n\", \"7\\n\", \"5\\n\", \"4\\n\", \"9\\n\", \"4\\n\", \"6\\n\", \"4\\n\", \"9\\n\", \"4\\n\", \"6\\n\", \"9\\n\", \"7\\n\", \"6\\n\", \"9\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"4\\n\", \"9\\n\", \"4\\n\", \"4\\n\", \"7\\n\", \"6\\n\", \"9\\n\", \"4\\n\", \"3\\n\", \"4\\n\", \"5\\n\", \"6\\n\"]}", "source": "primeintellect"}
|
Shuseki Kingdom is the world's leading nation for innovation and technology. There are n cities in the kingdom, numbered from 1 to n.
Thanks to Mr. Kitayuta's research, it has finally become possible to construct teleportation pipes between two cities. A teleportation pipe will connect two cities unidirectionally, that is, a teleportation pipe from city x to city y cannot be used to travel from city y to city x. The transportation within each city is extremely developed, therefore if a pipe from city x to city y and a pipe from city y to city z are both constructed, people will be able to travel from city x to city z instantly.
Mr. Kitayuta is also involved in national politics. He considers that the transportation between the m pairs of city (ai, bi) (1 ≤ i ≤ m) is important. He is planning to construct teleportation pipes so that for each important pair (ai, bi), it will be possible to travel from city ai to city bi by using one or more teleportation pipes (but not necessarily from city bi to city ai). Find the minimum number of teleportation pipes that need to be constructed. So far, no teleportation pipe has been constructed, and there is no other effective transportation between cities.
Input
The first line contains two space-separated integers n and m (2 ≤ n ≤ 105, 1 ≤ m ≤ 105), denoting the number of the cities in Shuseki Kingdom and the number of the important pairs, respectively.
The following m lines describe the important pairs. The i-th of them (1 ≤ i ≤ m) contains two space-separated integers ai and bi (1 ≤ ai, bi ≤ n, ai ≠ bi), denoting that it must be possible to travel from city ai to city bi by using one or more teleportation pipes (but not necessarily from city bi to city ai). It is guaranteed that all pairs (ai, bi) are distinct.
Output
Print the minimum required number of teleportation pipes to fulfill Mr. Kitayuta's purpose.
Examples
Input
4 5
1 2
1 3
1 4
2 3
2 4
Output
3
Input
4 6
1 2
1 4
2 3
2 4
3 2
3 4
Output
4
Note
For the first sample, one of the optimal ways to construct pipes is shown in the image below:
<image>
For the second sample, one of the optimal ways is shown below:
<image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4 4\\n1 2 1\\n2 3 1\\n3 4 0\\n4 1 0\\n\", \"3 0\\n\", \"4 4\\n1 2 1\\n2 3 1\\n3 4 0\\n4 1 1\\n\", \"4 4\\n1 2 0\\n2 3 0\\n2 4 0\\n3 4 0\\n\", \"6 6\\n1 2 0\\n2 3 1\\n3 4 0\\n4 5 1\\n5 6 0\\n6 1 1\\n\", \"5 5\\n1 2 0\\n2 3 0\\n3 4 0\\n4 5 0\\n1 5 0\\n\", \"9 2\\n1 2 0\\n2 3 0\\n\", \"28567 13\\n28079 24675 1\\n18409 26720 1\\n980 10815 1\\n20794 16571 1\\n7376 19861 1\\n11146 706 1\\n4255 16391 1\\n27376 18263 1\\n10019 28444 1\\n6574 28053 1\\n5036 16610 1\\n3543 7122 1\\n512 9554 1\\n\", \"100 3\\n1 2 0\\n2 3 0\\n3 1 0\\n\", \"4 3\\n2 3 0\\n3 4 0\\n2 4 0\\n\", \"100000 0\\n\", \"6 6\\n1 2 0\\n2 3 1\\n3 4 1\\n4 5 1\\n5 6 0\\n6 1 1\\n\", \"5 5\\n1 4 0\\n2 3 0\\n3 4 0\\n4 5 0\\n1 5 0\\n\", \"9 2\\n1 2 0\\n2 6 0\\n\", \"100 3\\n1 2 0\\n2 3 0\\n4 1 0\\n\", \"2 0\\n\", \"4 0\\n\", \"7 4\\n2 2 1\\n2 3 0\\n3 4 0\\n1 1 1\\n\", \"28567 13\\n28079 24675 1\\n18409 26720 1\\n980 10815 1\\n20794 16571 1\\n7376 19861 1\\n10805 706 1\\n4255 16391 1\\n27376 18263 1\\n10019 28444 1\\n6574 28053 1\\n5036 16610 1\\n3543 7122 1\\n512 9554 1\\n\", \"100 3\\n1 2 0\\n1 3 0\\n3 1 0\\n\", \"4 3\\n1 3 0\\n3 4 0\\n2 4 0\\n\", \"4 4\\n1 2 1\\n2 3 0\\n3 4 0\\n4 1 1\\n\", \"6 6\\n1 2 0\\n2 3 1\\n3 4 1\\n4 5 1\\n5 3 0\\n6 1 1\\n\", \"5 5\\n1 4 0\\n2 3 0\\n3 4 0\\n5 5 0\\n1 5 0\\n\", \"7 4\\n1 2 1\\n2 3 0\\n3 4 0\\n4 1 1\\n\", \"6 6\\n1 2 0\\n2 3 1\\n3 4 1\\n4 5 1\\n6 3 0\\n6 1 1\\n\", \"1 0\\n\", \"7 4\\n1 2 1\\n2 3 0\\n3 4 0\\n1 1 1\\n\", \"4 4\\n1 2 0\\n2 2 0\\n2 4 0\\n3 4 0\\n\", \"5 5\\n1 2 0\\n2 3 1\\n3 4 0\\n4 5 0\\n1 5 0\\n\", \"9 2\\n1 2 0\\n2 2 0\\n\", \"4 3\\n2 1 0\\n3 4 0\\n2 4 0\\n\", \"4 4\\n1 2 1\\n2 3 1\\n3 4 0\\n4 2 0\\n\", \"5 0\\n\", \"100 3\\n1 2 0\\n2 3 0\\n6 1 0\\n\", \"4 3\\n1 3 0\\n3 4 0\\n2 3 0\\n\", \"4 4\\n1 2 1\\n2 3 0\\n3 4 1\\n4 1 1\\n\", \"6 6\\n1 2 0\\n2 3 1\\n3 4 1\\n4 5 1\\n5 3 0\\n6 1 0\\n\", \"6 6\\n1 2 1\\n2 3 1\\n3 4 1\\n4 5 1\\n6 3 0\\n6 1 1\\n\", \"4 4\\n1 2 0\\n2 2 0\\n2 3 0\\n3 4 0\\n\", \"5 5\\n1 2 0\\n2 3 1\\n3 4 0\\n4 5 1\\n1 5 0\\n\", \"28567 13\\n28079 24675 1\\n18409 26720 1\\n980 12226 1\\n20794 16571 1\\n7376 19861 1\\n10805 706 1\\n4255 16391 1\\n27376 18263 1\\n10019 28444 1\\n6574 28053 1\\n5036 16610 1\\n3543 7122 1\\n512 9554 1\\n\", \"100 3\\n1 2 0\\n1 3 0\\n5 1 0\\n\", \"4 3\\n2 1 0\\n3 2 0\\n2 4 0\\n\", \"4 4\\n1 2 1\\n3 3 1\\n3 4 0\\n4 2 0\\n\", \"6 6\\n1 2 1\\n2 3 1\\n3 4 1\\n4 5 1\\n5 3 0\\n6 1 0\\n\", \"6 6\\n1 2 1\\n2 3 1\\n3 4 1\\n4 5 1\\n6 4 0\\n6 1 1\\n\", \"5 5\\n1 2 0\\n2 4 1\\n3 4 0\\n4 5 1\\n1 5 0\\n\", \"28567 13\\n28079 24675 1\\n18409 26720 1\\n980 21698 1\\n20794 16571 1\\n7376 19861 1\\n10805 706 1\\n4255 16391 1\\n27376 18263 1\\n10019 28444 1\\n6574 28053 1\\n5036 16610 1\\n3543 7122 1\\n512 9554 1\\n\", \"4 4\\n1 2 1\\n3 3 1\\n3 4 1\\n4 2 0\\n\", \"6 6\\n1 4 1\\n2 3 1\\n3 4 1\\n4 5 1\\n6 4 0\\n6 1 1\\n\", \"5 5\\n1 2 0\\n3 4 1\\n3 4 0\\n4 5 1\\n1 5 0\\n\", \"28567 13\\n28079 24675 1\\n18409 26720 1\\n980 21698 1\\n20794 16571 1\\n7376 19861 1\\n10805 706 1\\n4255 16391 1\\n27376 18263 1\\n10019 28444 1\\n6574 28053 1\\n5036 16610 1\\n5332 7122 1\\n512 9554 1\\n\", \"28567 13\\n28079 24675 1\\n18409 26720 1\\n980 21698 1\\n20794 16571 1\\n7376 19861 1\\n3303 706 1\\n4255 16391 1\\n27376 18263 1\\n10019 28444 1\\n6574 28053 1\\n5036 16610 1\\n5332 7122 1\\n512 9554 1\\n\", \"28567 13\\n28079 24675 1\\n18409 26720 1\\n1015 21698 1\\n20794 16571 1\\n7376 19861 1\\n3303 706 1\\n4255 16391 1\\n27376 18263 1\\n10019 28444 1\\n6574 28053 1\\n5036 16610 1\\n5332 7122 1\\n512 9554 1\\n\", \"28567 13\\n28079 24675 1\\n18409 26720 1\\n1015 21698 1\\n20794 16571 1\\n7376 19861 1\\n3433 706 1\\n4255 16391 1\\n27376 18263 1\\n10019 28444 1\\n6574 28053 1\\n5036 16610 1\\n5332 7122 1\\n512 9554 1\\n\", \"6 6\\n1 2 0\\n2 5 1\\n3 4 0\\n4 5 1\\n5 6 0\\n6 1 1\\n\", \"5 5\\n1 2 0\\n2 3 0\\n3 2 0\\n4 5 0\\n1 5 0\\n\", \"9 2\\n1 2 0\\n2 4 0\\n\", \"5 5\\n1 4 0\\n2 3 0\\n3 2 0\\n4 5 0\\n1 5 0\\n\", \"9 2\\n1 4 0\\n2 6 0\\n\", \"4 3\\n1 3 1\\n3 4 0\\n2 4 0\\n\", \"5 5\\n1 4 1\\n2 3 0\\n3 4 0\\n5 5 0\\n1 5 0\\n\"], \"outputs\": [\"1\", \"4\", \"0\", \"0\", \"0\", \"0\", \"64\", \"928433852\", \"0\", \"0\", \"303861760\", \"1\\n\", \"0\", \"64\\n\", \"873523211\\n\", \"2\\n\", \"8\\n\", \"16\\n\", \"928433852\\n\", \"747046415\\n\", \"1\\n\", \"1\\n\", \"0\", \"0\", \"8\\n\", \"1\\n\", \"1\\n\", \"8\\n\", \"0\", \"1\\n\", \"0\", \"1\\n\", \"1\\n\", \"16\\n\", \"873523211\\n\", \"1\\n\", \"0\", \"0\", \"0\", \"0\", \"0\", \"928433852\\n\", \"873523211\\n\", \"1\\n\", \"1\\n\", \"0\", \"0\", \"1\\n\", \"928433852\\n\", \"1\\n\", \"0\", \"0\", \"928433852\\n\", \"928433852\\n\", \"928433852\\n\", \"928433852\\n\", \"1\\n\", \"1\\n\", \"64\\n\", \"0\", \"64\\n\", \"1\\n\", \"0\"]}", "source": "primeintellect"}
|
There are many anime that are about "love triangles": Alice loves Bob, and Charlie loves Bob as well, but Alice hates Charlie. You are thinking about an anime which has n characters. The characters are labeled from 1 to n. Every pair of two characters can either mutually love each other or mutually hate each other (there is no neutral state).
You hate love triangles (A-B are in love and B-C are in love, but A-C hate each other), and you also hate it when nobody is in love. So, considering any three characters, you will be happy if exactly one pair is in love (A and B love each other, and C hates both A and B), or if all three pairs are in love (A loves B, B loves C, C loves A).
You are given a list of m known relationships in the anime. You know for sure that certain pairs love each other, and certain pairs hate each other. You're wondering how many ways you can fill in the remaining relationships so you are happy with every triangle. Two ways are considered different if two characters are in love in one way but hate each other in the other. Print this count modulo 1 000 000 007.
Input
The first line of input will contain two integers n, m (3 ≤ n ≤ 100 000, 0 ≤ m ≤ 100 000).
The next m lines will contain the description of the known relationships. The i-th line will contain three integers ai, bi, ci. If ci is 1, then ai and bi are in love, otherwise, they hate each other (1 ≤ ai, bi ≤ n, ai ≠ bi, <image>).
Each pair of people will be described no more than once.
Output
Print a single integer equal to the number of ways to fill in the remaining pairs so that you are happy with every triangle modulo 1 000 000 007.
Examples
Input
3 0
Output
4
Input
4 4
1 2 1
2 3 1
3 4 0
4 1 0
Output
1
Input
4 4
1 2 1
2 3 1
3 4 0
4 1 1
Output
0
Note
In the first sample, the four ways are to:
* Make everyone love each other
* Make 1 and 2 love each other, and 3 hate 1 and 2 (symmetrically, we get 3 ways from this).
In the second sample, the only possible solution is to make 1 and 3 love each other and 2 and 4 hate each other.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 2 1\\n1 1\\n2 1 1\\n\", \"4 3 2\\n1 2 3 4\\n2 1 5\\n3 4 2\\n\", \"10 5 5\\n45 45 12 67 32 6 125 33 89 100\\n6 3 78\\n1 2 23\\n5 7 17\\n9 2 90\\n4 8 39\\n\", \"16 12 2\\n215685056 606689499 786509392 322681480 170763622 255981931 402020260 580776290 525819654 50248606 830314959 223078821 851769718 76817680 251067040 491418559\\n14 4 951819487\\n4 2 770897556\\n\", \"18 18 17\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n7 2 554462987\\n2 4 444921228\\n4 6 157507820\\n6 10 900032432\\n10 9 888093209\\n9 17 115896460\\n17 5 904317029\\n5 12 581655689\\n12 3 743717743\\n3 13 692735618\\n13 11 607064833\\n11 18 677893322\\n18 1 909539256\\n1 14 619680883\\n14 15 933580266\\n15 8 932409037\\n8 16 555252931\\n\", \"1 1 0\\n1000000000\\n\", \"15 15 14\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n2 6 57661\\n6 15 67617\\n15 10 81652\\n10 1 16278\\n1 14 3009\\n14 11 33687\\n11 3 62989\\n3 9 96410\\n9 13 91302\\n13 5 86368\\n5 12 2182\\n12 4 16546\\n4 8 12851\\n8 7 26224\\n\", \"18 18 3\\n759507857 606098930 900220927 233055471 218518255 171579924 442155777 996213891 751779343 197968566 990617245 159772960 717293019 848554997 726485601 13147425 265922263 562203963\\n13 4 408141884\\n3 2 213428327\\n10 17 126413702\\n\", \"14 14 13\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n6 4 4\\n4 8 6\\n8 3 6\\n3 12 1\\n12 14 5\\n14 2 4\\n2 10 5\\n10 1 2\\n1 9 4\\n9 7 8\\n7 13 1\\n13 11 5\\n11 5 1\\n\", \"4 2 0\\n1 2 3 2\\n\", \"5 4 1\\n1000000000 500000000 1 1000000000 1000000000\\n3 5 700000000\\n\", \"5 5 5\\n3 3 3 3 3\\n3 4 6\\n4 1 2\\n1 5 7\\n5 2 4\\n2 3 5\\n\", \"15 15 14\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n7 11 6827\\n11 5 7756\\n5 14 6186\\n14 8 1460\\n8 13 1620\\n13 9 1232\\n9 15 7361\\n15 3 2850\\n3 4 4479\\n4 2 6756\\n2 6 3449\\n6 10 8684\\n10 1 6984\\n1 12 2948\\n\", \"17 17 16\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n11 7 231657830\\n7 5 232292501\\n5 8 231939378\\n8 4 224957214\\n4 12 229241817\\n12 1 231562923\\n1 3 226465387\\n3 16 230627405\\n16 10 229220153\\n10 9 228646517\\n9 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13582102\\n8 14 510800814\\n14 3 880706849\\n\", \"7 1 21\\n15 11 13 13 15 8 5\\n4 1 14\\n7 2 5\\n3 2 11\\n6 4 19\\n3 1 12\\n1 3 9\\n3 6 12\\n2 5 10\\n5 7 14\\n2 6 5\\n5 2 19\\n7 5 9\\n4 2 19\\n5 1 6\\n6 2 7\\n1 4 6\\n2 4 15\\n7 4 10\\n2 7 19\\n4 5 14\\n6 7 8\\n\", \"18 18 17\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n2 1 34349196\\n1 8 40123769\\n8 9 52139422\\n9 15 10987402\\n15 16 61786095\\n16 12 77282765\\n12 4 18495873\\n4 11 85323692\\n11 10 28529557\\n10 5 53623688\\n5 18 40093687\\n18 3 67739085\\n3 14 68785388\\n14 6 65567931\\n6 17 48915166\\n17 7 4911634\\n7 13 70519650\\n\", \"2 2 1\\n1 1\\n2 1 2\\n\", \"4 3 2\\n1 2 3 4\\n2 1 5\\n3 4 0\\n\", \"10 5 5\\n45 45 12 67 32 6 125 29 89 100\\n6 3 78\\n1 2 23\\n5 7 17\\n9 2 90\\n2 8 39\\n\", \"18 18 17\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n7 2 554462987\\n2 4 444921228\\n4 6 157507820\\n9 10 900032432\\n10 9 888093209\\n9 17 115896460\\n17 5 904317029\\n5 12 64075203\\n12 3 743717743\\n3 13 692735618\\n13 11 607064833\\n11 18 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645116094 328898380 458939277 646488701 699003763 666873084 991845119 532882957 385678203\\n\", \"18 18 17\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n4 17 510748572\\n17 10 696685757\\n10 15 176207942\\n15 1 126069679\\n1 2 837682033\\n2 12 436383858\\n12 9 267569422\\n9 16 881873714\\n16 11 992321262\\n11 6 259423529\\n6 5 263222337\\n5 18 697008445\\n18 13 962557222\\n13 7 790468460\\n7 8 13582102\\n8 14 510800814\\n14 3 880706849\\n\", \"2 2 1\\n0 1\\n2 1 2\\n\", \"4 3 2\\n1 2 3 4\\n2 1 4\\n3 4 0\\n\", \"18 18 17\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n7 2 72234689\\n2 4 444921228\\n4 6 157507820\\n9 10 900032432\\n10 9 888093209\\n9 17 115896460\\n17 5 904317029\\n5 12 64075203\\n12 3 743717743\\n3 13 692735618\\n13 11 607064833\\n11 18 677893322\\n18 1 909539256\\n1 14 619680883\\n14 15 933580266\\n15 8 932409037\\n8 16 555252931\\n\", \"14 14 13\\n0 0 0 0 0 0 0 0 0 1 0 0 0 0\\n6 4 4\\n4 8 6\\n8 3 6\\n3 12 1\\n12 14 5\\n14 2 4\\n2 10 7\\n10 1 2\\n1 9 4\\n9 7 8\\n7 13 2\\n13 11 5\\n11 5 1\\n\", \"17 17 16\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n11 7 261657114\\n7 5 232292501\\n5 8 231939378\\n8 4 224957214\\n7 12 229241817\\n12 1 231562923\\n1 3 226465387\\n3 16 230627405\\n16 10 229220153\\n10 9 228646517\\n9 2 230321133\\n2 17 232190045\\n17 6 229133406\\n6 15 227156658\\n1 13 228664795\\n13 14 228903543\\n\", \"7 4 3\\n2 6 13 5 7 1 5\\n6 1 0\\n2 5 3\\n4 4 8\\n\", \"18 18 0\\n115005244 38190165 126325576 724501685 765839937 1273580106 596662787 415309843 853044850 645116094 328898380 458939277 331388275 699003763 666873084 991845119 532882957 385678203\\n\", \"18 18 17\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\\n7 17 510748572\\n17 10 696685757\\n10 15 176207942\\n15 1 126069679\\n1 2 837682033\\n2 12 436383858\\n12 9 267569422\\n9 16 881873714\\n16 11 992321262\\n11 6 259423529\\n6 5 263222337\\n5 18 697008445\\n18 13 962557222\\n13 7 790468460\\n7 8 13582102\\n8 14 510800814\\n14 3 880706849\\n\", \"18 2 4\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0\\n18 2 5\\n7 8 3\\n1 8 2\\n6 4 1\\n\", \"16 1 2\\n210848946 606689499 786509392 322681480 170763622 255981931 402020260 580776290 525819654 50248606 830314959 223078821 851769718 76817680 251067040 491418559\\n14 4 951819487\\n4 2 770897556\\n\", \"18 2 4\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0\\n18 2 5\\n7 8 3\\n1 8 2\\n6 4 1\\n\", \"7 1 21\\n15 11 13 13 15 8 5\\n4 1 14\\n7 2 5\\n3 2 11\\n6 4 19\\n3 1 12\\n1 3 9\\n3 6 12\\n2 5 10\\n5 7 14\\n2 6 5\\n5 2 19\\n7 5 9\\n4 2 19\\n5 1 6\\n6 2 7\\n1 4 6\\n2 4 15\\n7 4 10\\n2 7 19\\n4 6 14\\n6 7 8\\n\", \"16 1 2\\n210848946 606689499 786509392 322681480 170763622 255981931 402020260 580776290 525819654 50248606 830314959 223078821 851769718 76817680 251067040 731477354\\n14 4 951819487\\n4 2 770897556\\n\", \"7 1 21\\n15 11 13 13 15 8 5\\n4 1 14\\n7 2 5\\n3 2 11\\n6 4 19\\n3 1 12\\n1 3 9\\n3 6 12\\n2 5 10\\n5 7 14\\n2 6 5\\n5 2 19\\n7 5 9\\n4 2 19\\n5 1 6\\n6 3 7\\n1 4 6\\n2 4 15\\n7 4 10\\n2 7 19\\n4 6 14\\n6 7 8\\n\"], \"outputs\": [\"3\", \"12\", \"516\", \"7704583505\", \"11218760743\", \"1000000000\", \"654776\", \"10309080327\", \"52\", \"5\", \"3700000001\", \"37\", \"68592\", \"3672980705\", \"403\", \"6\", \"40\", \"18\", \"4858815472\", \"17000000000\", \"516\", \"3699356001\", \"8720611720\", \"9763298061\", \"9031649747\", \"15\", \"852211284\", \"521\\n\", \"851769718\\n\", \"10701180257\\n\", \"689552\\n\", \"53\\n\", \"6\\n\", \"35\\n\", \"73956\\n\", \"3702979989\\n\", \"603\\n\", \"40\\n\", \"4892309078\\n\", \"16000000000\\n\", \"516\\n\", \"2883948837\\n\", \"10380193387\\n\", \"9288209474\\n\", \"15\\n\", \"829174000\\n\", \"4\\n\", \"12\\n\", \"517\\n\", \"9801147825\\n\", \"631891\\n\", \"54\\n\", \"9\\n\", \"3476514602\\n\", \"38\\n\", \"10264185771\\n\", \"9303311997\\n\", \"3\\n\", \"11\\n\", \"9318919527\\n\", \"56\\n\", \"3247272785\\n\", \"34\\n\", \"9949085345\\n\", \"9163660216\\n\", \"6\\n\", \"851769718\\n\", \"6\\n\", \"15\\n\", \"851769718\\n\", \"15\\n\"]}", "source": "primeintellect"}
|
When Kefa came to the restaurant and sat at a table, the waiter immediately brought him the menu. There were n dishes. Kefa knows that he needs exactly m dishes. But at that, he doesn't want to order the same dish twice to taste as many dishes as possible.
Kefa knows that the i-th dish gives him ai units of satisfaction. But some dishes do not go well together and some dishes go very well together. Kefa set to himself k rules of eating food of the following type — if he eats dish x exactly before dish y (there should be no other dishes between x and y), then his satisfaction level raises by c.
Of course, our parrot wants to get some maximal possible satisfaction from going to the restaurant. Help him in this hard task!
Input
The first line of the input contains three space-separated numbers, n, m and k (1 ≤ m ≤ n ≤ 18, 0 ≤ k ≤ n * (n - 1)) — the number of dishes on the menu, the number of portions Kefa needs to eat to get full and the number of eating rules.
The second line contains n space-separated numbers ai, (0 ≤ ai ≤ 109) — the satisfaction he gets from the i-th dish.
Next k lines contain the rules. The i-th rule is described by the three numbers xi, yi and ci (1 ≤ xi, yi ≤ n, 0 ≤ ci ≤ 109). That means that if you eat dish xi right before dish yi, then the Kefa's satisfaction increases by ci. It is guaranteed that there are no such pairs of indexes i and j (1 ≤ i < j ≤ k), that xi = xj and yi = yj.
Output
In the single line of the output print the maximum satisfaction that Kefa can get from going to the restaurant.
Examples
Input
2 2 1
1 1
2 1 1
Output
3
Input
4 3 2
1 2 3 4
2 1 5
3 4 2
Output
12
Note
In the first sample it is best to first eat the second dish, then the first one. Then we get one unit of satisfaction for each dish and plus one more for the rule.
In the second test the fitting sequences of choice are 4 2 1 or 2 1 4. In both cases we get satisfaction 7 for dishes and also, if we fulfill rule 1, we get an additional satisfaction 5.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5 5\\n4 2\\n3 5\\n4 5\\n5 1\\n1 2\\n\", \"4 6\\n1 2\\n1 3\\n1 4\\n2 3\\n2 4\\n3 4\\n\", \"4 2\\n1 3\\n3 4\\n\", \"3 1\\n1 2\\n\", \"3 1\\n1 3\\n\", \"400 1\\n1 400\\n\", \"3 0\\n\", \"20 1\\n20 1\\n\", \"3 3\\n1 2\\n2 3\\n3 1\\n\", \"5 4\\n1 2\\n3 2\\n3 4\\n5 4\\n\", \"3 2\\n2 3\\n3 1\\n\", \"381 0\\n\", \"2 1\\n1 2\\n\", \"100 1\\n100 1\\n\", \"4 5\\n1 3\\n2 1\\n3 4\\n4 2\\n2 3\\n\", \"4 1\\n1 4\\n\", \"20 0\\n\", \"5 5\\n2 5\\n1 2\\n1 4\\n1 3\\n3 2\\n\", \"21 1\\n21 1\\n\", \"2 0\\n\", \"6 1\\n1 2\\n\", \"4 2\\n1 3\\n1 4\\n\", \"5 5\\n4 5\\n1 2\\n2 4\\n1 3\\n3 2\\n\", \"6 1\\n1 3\\n\", \"6 0\\n\", \"100 1\\n100 2\\n\", \"26 0\\n\", \"10 5\\n2 5\\n1 2\\n1 4\\n1 3\\n3 2\\n\", \"4 2\\n1 3\\n2 4\\n\", \"6 1\\n1 5\\n\", \"17 0\\n\", \"101 1\\n100 1\\n\", \"4 1\\n1 2\\n\", \"22 0\\n\", \"5 5\\n2 5\\n1 2\\n2 4\\n1 3\\n3 2\\n\", \"21 1\\n12 1\\n\", \"4 0\\n\", \"4 2\\n1 3\\n3 2\\n\", \"9 0\\n\", \"110 1\\n100 2\\n\", \"4 2\\n2 3\\n1 4\\n\", \"4 1\\n1 3\\n\", \"16 0\\n\", \"8 0\\n\", \"29 0\\n\", \"5 2\\n2 3\\n3 1\\n\", \"39 0\\n\", \"6 1\\n1 6\\n\", \"6 1\\n2 3\\n\", \"6 1\\n2 5\\n\", \"14 0\\n\", \"4 2\\n1 2\\n1 4\\n\", \"101 1\\n100 2\\n\", \"22 1\\n12 1\\n\", \"5 0\\n\", \"111 1\\n100 2\\n\", \"12 0\\n\", \"25 0\\n\", \"10 0\\n\", \"9 1\\n2 5\\n\", \"111 1\\n110 2\\n\", \"111 1\\n010 2\\n\", \"7 0\\n\", \"20 1\\n20 2\\n\"], \"outputs\": [\"3\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"2\\n\", \"2\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"4\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"2\\n\", \"2\\n\", \"-1\\n\", \"2\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"3\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\"]}", "source": "primeintellect"}
|
In Absurdistan, there are n towns (numbered 1 through n) and m bidirectional railways. There is also an absurdly simple road network — for each pair of different towns x and y, there is a bidirectional road between towns x and y if and only if there is no railway between them. Travelling to a different town using one railway or one road always takes exactly one hour.
A train and a bus leave town 1 at the same time. They both have the same destination, town n, and don't make any stops on the way (but they can wait in town n). The train can move only along railways and the bus can move only along roads.
You've been asked to plan out routes for the vehicles; each route can use any road/railway multiple times. One of the most important aspects to consider is safety — in order to avoid accidents at railway crossings, the train and the bus must not arrive at the same town (except town n) simultaneously.
Under these constraints, what is the minimum number of hours needed for both vehicles to reach town n (the maximum of arrival times of the bus and the train)? Note, that bus and train are not required to arrive to the town n at the same moment of time, but are allowed to do so.
Input
The first line of the input contains two integers n and m (2 ≤ n ≤ 400, 0 ≤ m ≤ n(n - 1) / 2) — the number of towns and the number of railways respectively.
Each of the next m lines contains two integers u and v, denoting a railway between towns u and v (1 ≤ u, v ≤ n, u ≠ v).
You may assume that there is at most one railway connecting any two towns.
Output
Output one integer — the smallest possible time of the later vehicle's arrival in town n. If it's impossible for at least one of the vehicles to reach town n, output - 1.
Examples
Input
4 2
1 3
3 4
Output
2
Input
4 6
1 2
1 3
1 4
2 3
2 4
3 4
Output
-1
Input
5 5
4 2
3 5
4 5
5 1
1 2
Output
3
Note
In the first sample, the train can take the route <image> and the bus can take the route <image>. Note that they can arrive at town 4 at the same time.
In the second sample, Absurdistan is ruled by railwaymen. There are no roads, so there's no way for the bus to reach town 4.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"glo?yto?e??an?\\nor\\n\", \"??c?????\\nabcab\\n\", \"winlose???winl???w??\\nwin\\n\", \"ww?ww\\nw\\n\", \"xznxr\\nxznxr\\n\", \"????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????\\nrcmcscoffidfyaeeanevbcfloxrhzxnitikwyidszzgmvicjupbfzhlbkzjbyidpdaeagaanokohwofzvfsvmcwvrqkvgbwnxomajvotbpzqgiyifngpnfvmtsoovrstzhtkeqamskzdmspvihochmajwkdoeozqpkdoxffhokosfqnaqshxbsfnkjsbbkxhrzgqhufq\\n\", \"???a??????a??b?a??a????aabc??a???a?????ab???????b????????????????ab?a?????a????a??a??????b??cb?????????????b?????c????a??????????b????c????????ca?b???????c??bc????????a?b??b??a??cc?b???????a??a?ab?a?ca?a???????c????????b????b?c\\nabaab\\n\", \"a???????bc\\nabcabc\\n\", \"t?t?t?xnu?\\ntstx\\n\", \"zubxnxnxnxn?xixiox?oxinoxnox?xnoxxnox?xnoxixxnox?oxii?xnoxiin?noxixnoxiox?noxixxnox?noxxnoxi?xnoxinn\\nxnoxi\\n\", \"a????ab\\nabab\\n\", \"qjcenuvdsn?ytytyt?yrznaaqeol?tyttyty?ycfaiphfmo?qpvtmhk?xzfr?tytytytytyty?oeqotyt?tyjhdhjtyt?tyyewxh\\ntytyty\\n\", \"hacking????????????????????????hackingisfun\\nhackingisfunhackingisfun\\n\", \"pe????????????petooh\\npetoohpetooh\\n\", \"cb???????a\\ncbacba\\n\", \"????b?b\\nabab\\n\", \"youdontgiveup????????????????????????????????????youyoudontgiveupdoyo?youyoudontgiveupdoyou\\nyoudontgiveupdoyouyoudontgiveupdoyou\\n\", \"????ufu\\nfufu\\n\", \"emnd?t??m?gd?t?p?s??m?dp??t???m?????m?d?ydo????????i??u?d??dp??h??d?tdp???cj?dm?dpxf?hsf??rdmt?pu?tw\\ndmtdp\\n\", \"a\\nb\\n\", \"??????c???\\nabcabc\\n\", \"p??p??????\\numpq\\n\", \"?????\\nn\\n\", \"????????baaab\\naaabaaab\\n\", \"ddddd\\nd\\n\", \"a???????abcax\\naxabcax\\n\", \"irsdljdahusytoclelxidaaiaiaicaiaiaiaiiaiaiyyexmohdwmeyycaiaiaitclluaiaiaiznxweleaiaiaiixdwehyruhizbc\\naiaiai\\n\", \"wnfbhg?dkhdbh?hdmfjkcunzbh?hdbjjrbh?hddmh?zubhgh?qbjbhghdpwr?bhghdfjnjf?qbhghdqq?qebhgh?umvbhghdivvj\\nbhghd\\n\", \"??????????????????????????\\nabacaba\\n\", \"baaab????????\\nbaaabaaa\\n\", \"wv?ww\\nw\\n\", \"rxnzx\\nxznxr\\n\", \"????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????\\nrcmcscoffidfyaeeanevbcfloxrhzxnitikwyddszzgmvicjupbfzhlbkzjbyidpdaeagaanokohwofzvfsvmcwvrqkvgbwnxomajvotbpzqgiyifngpnfvmtsoovrstzhtkeqamskzimspvihochmajwkdoeozqpkdoxffhokosfqnaqshxbsfnkjsbbkxhrzgqhufq\\n\", \"???a??????a??b?a??a????aabc??a???a?????ab???????b????????????????ab?a?????a????a??a??????b??cb?????????????b?????c????a??????????b????c????????ca?b???????c??bc????????a?b??b??a??cc?b???????a??a?ab?a?ca?a???????c????????b????b?c\\nabaac\\n\", \"hxweyyt?tytjhdhjyt?tytoqeo?ytytytytytyt?rfzx?khmtvpq?omfhpiafcy?ytyttyt?loeqaanzry?tytyty?nsdvunecjq\\ntytyty\\n\", \"????b?b\\nbaba\\n\", \"emnd?t??m?gd?t?p?s??m?dp??t???m?????m?d?ydo????????i??u?d??dp??h??d?tdp???cj?dm?dpxf?hsf??rdmt?pu?tw\\ncmtdp\\n\", \"?na??e?oty?olg\\nro\\n\", \"hxweyyt?tytjhdhjyt?tytoqep?ytytytytytyt?rfzx?khmtvpq?omfhpiafcy?ytyttyt?loeqaanzry?tytyty?nsdvunecjq\\nytytyt\\n\", \"a???????bc\\naccabc\\n\", \"t?t?t?xnu?\\ntstw\\n\", \"zubxnxnxnxn?xixiox?oxinoxnox?xnoxxnox?xnoxixxnox?oxii?xnoxiin?noxixnoxiox?noxixxnox?noxxnoxi?xnoxinn\\nixonx\\n\", \"pe????????????petooh\\npetooopetohh\\n\", \"cb???????a\\ncbacbb\\n\", \"youdontgiveup?????????????????????????????u??????youyoudontgiveupdoyo?youyo?dontgiveupdoyou\\nyoudontgiveupdoyouyoudontgiveupdoyou\\n\", \"????ufu\\nfvfu\\n\", \"a\\nc\\n\", \"??????c???\\naacbbc\\n\", \"p??p??????\\nulpq\\n\", \"?????\\nm\\n\", \"ddddd\\ne\\n\", \"wnfbhg?dkhdbh?hdmfjkcunzbh?hdbjjrbh?hddmh?zubhgh?qbjbhghdpwr?bhghdfjnjf?qbhghdqq?qebhgh?umvbhghdivvj\\ndhghb\\n\", \"baaab????????\\nbaabbaaa\\n\", \"?na??e?oty?olg\\nor\\n\", \"??b?????\\nabcab\\n\", \"winlose???winl???w??\\nniw\\n\", \"wv?ww\\nx\\n\", \"rxnzx\\nxxnzr\\n\", \"????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????\\nqfuhqgzrhxkbbsjknfsbxhsqanqfsokohffxodkpqzoeodkwjamhcohivpsmizksmaqekthztsrvoostmvfnpgnfiyigqzpbtovjamoxnwbgvkqrvwcmvsfvzfowhokonaagaeadpdiybjzkblhzfbpujcivmgzzsddywkitinxzhrxolfcbvenaeeayfdiffocscmcr\\n\", \"a???????bc\\nccaabc\\n\", \"t?t??txnu?\\ntstw\\n\", \"zubxnxnxnxn?xixiox?oxinoxnox?xnoxxnox?xnoxixxnox?oxih?xnoxiin?noxixnoxiox?noxixxnox?noxxnoxi?xnoxinn\\nixonx\\n\", \"hxweyyt?tytjhdhjyt?tytoqep?ytytytytytyt?rfzx?khmtvpq?omfhpiafcy?ytyttyt?loeqaanzry?tytyty?nsdvunecjq\\ntytyty\\n\", \"pe????????????petoph\\npetooopetohh\\n\", \"cb???????a\\nbcacbb\\n\", \"youeontgiveup?????????????????????????????u??????youyoudontgiveupdoyo?youyo?dontgiveupdoyou\\nyoudontgiveupdoyouyoudontgiveupdoyou\\n\", \"???u?fu\\nfvfu\\n\", \"wt?up?tmdr??fsh?fxpd?md?jc???pdt?d??h??pd??d?u??i????????ody?d?m?????m???t??pd?m??s?p?t?dg?m??t?dnme\\ncmtdp\\n\", \"??????p??p\\nulpq\\n\", \"ddded\\ne\\n\", \"wnfbhg?dkhdbh?hdmfjkcunzbh?hdbjjrbh?hddmh?zubhgh?qbjbhghdpvr?bhghdfjnjf?qbhghdqq?qebhgh?umvbhghdivvj\\ndhghb\\n\", \"baaab????????\\nbaacbaaa\\n\", \"winlose???winl???w??\\nniv\\n\", \"ww?ww\\nx\\n\", \"rxnzx\\nxynzr\\n\", \"a???????bc\\ncbaacc\\n\", \"t?t??txnu?\\ntstv\\n\", \"zubxnxnxnxn?xixiox?oxinoxnox?xnoxxnox?xnoxixxnox?oxih?xnoxiin?noxixnoxiox?noxixxnox?noxxnoxi?xnoxinn\\nioxnx\\n\", \"pe????????????petoph\\nhhotepoootep\\n\", \"cb???????a\\nbcacba\\n\", \"???u?fu\\nufvf\\n\", \"p??p??????\\nqplu\\n\", \"ddded\\nd\\n\", \"wnfbbg?dkhdbh?hdmfjkcunzbh?hdbjjrbh?hddmh?zubhgh?qhjbhghdpvr?bhghdfjnjf?qbhghdqq?qebhgh?umvbhghdivvj\\ndhghb\\n\", \"baaab????????\\nbaacbaab\\n\", \"glo?yto?e??an?\\nro\\n\", \"winlose???winl???w??\\noiv\\n\", \"ww?ww\\nv\\n\", \"xznxr\\nxynzr\\n\", \"t?t??tynu?\\ntstv\\n\", \"zubxnxnxnxn?xixiox?oxinoxnox?xnoxxnox?xnoxixxnox?oxih?xnoxiin?noxixnoxiox?noxixxnox?noxxnoxi?xnoxinn\\nioxny\\n\"], \"outputs\": [\"3\", \"2\", \"5\", \"5\", \"1\", \"1\", \"55\", \"2\", \"1\", \"13\", \"2\", \"9\", \"2\", \"2\", \"2\", \"2\", \"2\", \"2\", \"11\", \"0\", \"2\", \"2\", \"5\", \"2\", \"5\", \"2\", \"6\", \"10\", \"5\", \"2\", \"4\\n\", \"0\\n\", \"1\\n\", \"34\\n\", \"6\\n\", \"2\\n\", \"5\\n\", \"3\\n\", \"9\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"5\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"6\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"4\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"4\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"1\\n\", \"0\\n\", \"1\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Berland has a long and glorious history. To increase awareness about it among younger citizens, King of Berland decided to compose an anthem.
Though there are lots and lots of victories in history of Berland, there is the one that stand out the most. King wants to mention it in the anthem as many times as possible.
He has already composed major part of the anthem and now just needs to fill in some letters. King asked you to help him with this work.
The anthem is the string s of no more than 105 small Latin letters and question marks. The most glorious victory is the string t of no more than 105 small Latin letters. You should replace all the question marks with small Latin letters in such a way that the number of occurrences of string t in string s is maximal.
Note that the occurrences of string t in s can overlap. Check the third example for clarification.
Input
The first line contains string of small Latin letters and question marks s (1 ≤ |s| ≤ 105).
The second line contains string of small Latin letters t (1 ≤ |t| ≤ 105).
Product of lengths of strings |s|·|t| won't exceed 107.
Output
Output the maximum number of occurrences of string t you can achieve by replacing all the question marks in string s with small Latin letters.
Examples
Input
winlose???winl???w??
win
Output
5
Input
glo?yto?e??an?
or
Output
3
Input
??c?????
abcab
Output
2
Note
In the first example the resulting string s is "winlosewinwinlwinwin"
In the second example the resulting string s is "glorytoreorand". The last letter of the string can be arbitrary.
In the third example occurrences of string t are overlapping. String s with maximal number of occurrences of t is "abcabcab".
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"12\\n\", \"4\\n\", \"3\\n\", \"998\\n\", \"69\\n\", \"9\\n\", \"1000\\n\", \"5\\n\", \"10\\n\", \"8\\n\", \"994\\n\", \"100\\n\", \"423\\n\", \"999\\n\", \"997\\n\", \"57\\n\", \"34\\n\", \"13\\n\", \"6\\n\", \"876\\n\", \"995\\n\", \"29\\n\", \"24\\n\", \"11\\n\", \"996\\n\", \"17\\n\", \"1120\\n\", \"16\\n\", \"1010\\n\", \"7\\n\", \"1200\\n\", \"110\\n\", \"685\\n\", \"359\\n\", \"1764\\n\", \"52\\n\", \"26\\n\", \"1729\\n\", \"109\\n\", \"47\\n\", \"28\\n\", \"524\\n\", \"27\\n\", \"22\\n\", \"19\\n\", \"744\\n\", \"14\\n\", \"1041\\n\", \"597\\n\", \"345\\n\", \"66\\n\", \"51\\n\", \"977\\n\", \"20\\n\", \"39\\n\", \"660\\n\", \"33\\n\", \"406\\n\", \"23\\n\", \"1285\\n\", \"297\\n\", \"258\\n\", \"102\\n\", \"62\\n\", \"48\\n\", \"21\\n\", \"32\\n\", \"201\\n\", \"18\\n\", \"208\\n\", \"38\\n\", \"1962\\n\", \"473\\n\", \"357\\n\", \"112\\n\", \"31\\n\", \"42\\n\", \"58\\n\", \"331\\n\", \"215\\n\", \"63\\n\", \"396\\n\", \"495\\n\", \"121\\n\", \"25\\n\", \"36\\n\", \"101\\n\", \"129\\n\", \"67\\n\", \"35\\n\", \"169\\n\", \"383\\n\", \"237\\n\", \"56\\n\", \"111\\n\", \"46\\n\", \"83\\n\", \"30\\n\", \"133\\n\", \"446\\n\", \"68\\n\", \"55\\n\", \"40\\n\", \"123\\n\", \"94\\n\", \"463\\n\", \"120\\n\", \"85\\n\", \"50\\n\", \"151\\n\", \"170\\n\", \"834\\n\", \"216\\n\", \"174\\n\", \"53\\n\", \"281\\n\", \"45\\n\", \"773\\n\", \"234\\n\", \"272\\n\", \"15\\n\", \"78\\n\", \"1402\\n\", \"302\\n\", \"149\\n\"], \"outputs\": [\"5 7\\n\", \"1 3\\n\", \"1 2\\n\", \"497 501\\n\", \"34 35\\n\", \"4 5\\n\", \"499 501\\n\", \"2 3\\n\", \"3 7\\n\", \"3 5\\n\", \"495 499\\n\", \"49 51\\n\", \"211 212\\n\", \"499 500\\n\", \"498 499\\n\", \"28 29\\n\", \"15 19\\n\", \"6 7\\n\", \"1 5\\n\", \"437 439\\n\", \"497 498\\n\", \"14 15\\n\", \"11 13\\n\", \"5 6\\n\", \"497 499\\n\", \"8 9\\n\", \"559 561\\n\", \"7 9\\n\", \"503 507\\n\", \"3 4\\n\", \"599 601\\n\", \"53 57\\n\", \"342 343\\n\", \"179 180\\n\", \"881 883\\n\", \"25 27\\n\", \"11 15\\n\", \"864 865\\n\", \"54 55\\n\", \"23 24\\n\", \"13 15\\n\", \"261 263\\n\", \"13 14\\n\", \"9 13\\n\", \"9 10\\n\", \"371 373\\n\", \"5 9\\n\", \"520 521\\n\", \"298 299\\n\", \"172 173\\n\", \"31 35\\n\", \"25 26\\n\", \"488 489\\n\", \"9 11\\n\", \"19 20\\n\", \"329 331\\n\", \"16 17\\n\", \"201 205\\n\", \"11 12\\n\", \"642 643\\n\", \"148 149\\n\", \"127 131\\n\", \"49 53\\n\", \"29 33\\n\", \"23 25\\n\", \"10 11\\n\", \"15 17\\n\", \"100 101\\n\", \"7 11\\n\", \"103 105\\n\", \"17 21\\n\", \"979 983\\n\", \"236 237\\n\", \"178 179\\n\", \"55 57\\n\", \"15 16\\n\", \"19 23\\n\", \"27 31\\n\", \"165 166\\n\", \"107 108\\n\", \"31 32\\n\", \"197 199\\n\", \"247 248\\n\", \"60 61\\n\", \"12 13\\n\", \"17 19\\n\", \"50 51\\n\", \"64 65\\n\", \"33 34\\n\", \"17 18\\n\", \"84 85\\n\", \"191 192\\n\", \"118 119\\n\", \"27 29\\n\", \"55 56\\n\", \"21 25\\n\", \"41 42\\n\", \"13 17\\n\", \"66 67\\n\", \"221 225\\n\", \"33 35\\n\", \"27 28\\n\", \"19 21\\n\", \"61 62\\n\", \"45 49\\n\", \"231 232\\n\", \"59 61\\n\", \"42 43\\n\", \"23 27\\n\", \"75 76\\n\", \"83 87\\n\", \"415 419\\n\", \"107 109\\n\", \"85 89\\n\", \"26 27\\n\", \"140 141\\n\", \"22 23\\n\", \"386 387\\n\", \"115 119\\n\", \"135 137\\n\", \"7 8\\n\", \"37 41\\n\", \"699 703\\n\", \"149 153\\n\", \"74 75\\n\"]}", "source": "primeintellect"}
|
Petya is a big fan of mathematics, especially its part related to fractions. Recently he learned that a fraction <image> is called proper iff its numerator is smaller than its denominator (a < b) and that the fraction is called irreducible if its numerator and its denominator are coprime (they do not have positive common divisors except 1).
During his free time, Petya thinks about proper irreducible fractions and converts them to decimals using the calculator. One day he mistakenly pressed addition button ( + ) instead of division button (÷) and got sum of numerator and denominator that was equal to n instead of the expected decimal notation.
Petya wanted to restore the original fraction, but soon he realized that it might not be done uniquely. That's why he decided to determine maximum possible proper irreducible fraction <image> such that sum of its numerator and denominator equals n. Help Petya deal with this problem.
Input
In the only line of input there is an integer n (3 ≤ n ≤ 1000), the sum of numerator and denominator of the fraction.
Output
Output two space-separated positive integers a and b, numerator and denominator of the maximum possible proper irreducible fraction satisfying the given sum.
Examples
Input
3
Output
1 2
Input
4
Output
1 3
Input
12
Output
5 7
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3 5\\n0 2\\n2 4\\n3 5\\n\", \"3 7\\n0 4\\n2 5\\n6 7\\n\", \"50 10\\n0 2\\n0 2\\n0 6\\n1 9\\n1 3\\n1 2\\n1 6\\n1 1\\n1 1\\n2 7\\n2 6\\n2 4\\n3 9\\n3 8\\n3 8\\n3 8\\n3 6\\n3 4\\n3 7\\n3 4\\n3 6\\n3 5\\n4 8\\n5 5\\n5 7\\n6 7\\n6 6\\n7 7\\n7 7\\n7 7\\n7 8\\n7 8\\n8 8\\n8 8\\n8 9\\n8 8\\n8 9\\n9 9\\n9 9\\n9 9\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n\", \"30 40\\n0 0\\n4 8\\n5 17\\n7 32\\n7 16\\n8 16\\n10 19\\n12 22\\n12 27\\n13 21\\n13 28\\n13 36\\n14 28\\n14 18\\n18 21\\n21 26\\n21 36\\n22 38\\n23 32\\n24 30\\n26 35\\n29 32\\n29 32\\n31 34\\n31 31\\n33 33\\n33 35\\n35 40\\n38 38\\n40 40\\n\", \"3 8\\n0 0\\n1 8\\n2 8\\n\", \"70 100\\n0 99\\n1 87\\n1 94\\n1 4\\n2 72\\n3 39\\n3 69\\n4 78\\n5 85\\n7 14\\n8 59\\n12 69\\n14 15\\n14 76\\n17 17\\n19 53\\n19 57\\n19 21\\n21 35\\n21 83\\n24 52\\n24 33\\n27 66\\n27 97\\n30 62\\n30 74\\n30 64\\n32 63\\n35 49\\n37 60\\n40 99\\n40 71\\n41 83\\n42 66\\n42 46\\n45 83\\n51 76\\n53 69\\n54 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99\\n92 92\\n98 99\\n100 100\\n\", \"70 10\\n0 4\\n0 4\\n0 8\\n0 9\\n0 1\\n0 5\\n0 7\\n1 3\\n1 8\\n1 8\\n1 10\\n1 9\\n1 6\\n1 2\\n1 3\\n1 2\\n2 6\\n2 5\\n2 4\\n2 3\\n2 10\\n2 2\\n2 6\\n2 2\\n3 10\\n4 7\\n3 7\\n3 4\\n3 7\\n3 4\\n3 8\\n3 4\\n3 10\\n3 5\\n3 3\\n3 7\\n4 8\\n4 8\\n4 9\\n4 6\\n5 7\\n5 10\\n5 7\\n5 8\\n5 5\\n6 8\\n6 9\\n6 10\\n6 6\\n6 9\\n6 7\\n7 8\\n7 9\\n7 10\\n7 10\\n8 8\\n8 8\\n8 9\\n8 10\\n9 10\\n9 9\\n9 10\\n9 10\\n9 9\\n9 9\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n\", \"10 40\\n0 21\\n1 19\\n4 33\\n6 26\\n8 39\\n15 15\\n20 24\\n27 13\\n29 39\\n37 40\\n\", \"50 100\\n0 95\\n1 100\\n1 38\\n2 82\\n5 35\\n7 71\\n8 53\\n11 49\\n15 27\\n17 84\\n17 75\\n18 99\\n18 43\\n18 69\\n21 89\\n27 60\\n27 29\\n38 62\\n38 77\\n39 83\\n40 66\\n48 80\\n48 100\\n50 51\\n50 61\\n53 77\\n53 63\\n55 58\\n56 68\\n60 82\\n62 95\\n66 74\\n67 83\\n69 88\\n69 81\\n69 88\\n69 98\\n70 91\\n70 76\\n71 90\\n72 99\\n81 99\\n85 87\\n88 57\\n88 93\\n90 97\\n90 97\\n92 98\\n98 99\\n100 100\\n\", \"50 40\\n0 9\\n1 26\\n1 27\\n2 33\\n2 5\\n3 30\\n4 28\\n5 31\\n5 27\\n5 29\\n7 36\\n8 32\\n8 13\\n9 24\\n9 10\\n10 30\\n11 26\\n11 22\\n11 40\\n11 31\\n12 26\\n13 25\\n14 32\\n17 19\\n21 29\\n22 36\\n24 27\\n25 39\\n25 27\\n27 32\\n27 29\\n27 39\\n27 29\\n28 38\\n30 38\\n32 40\\n32 38\\n33 33\\n33 40\\n34 35\\n34 34\\n34 38\\n34 38\\n35 37\\n36 39\\n36 39\\n37 37\\n38 40\\n39 39\\n40 40\\n\", \"30 10\\n0 7\\n1 2\\n0 2\\n1 4\\n1 4\\n1 3\\n2 2\\n2 4\\n2 6\\n2 9\\n2 2\\n3 5\\n3 8\\n4 8\\n4 5\\n4 6\\n5 6\\n5 7\\n6 6\\n6 9\\n6 7\\n6 9\\n7 7\\n7 7\\n8 8\\n8 8\\n9 9\\n9 9\\n10 10\\n10 10\\n\", \"70 40\\n1 34\\n1 16\\n3 33\\n4 36\\n4 22\\n5 9\\n5 9\\n7 16\\n8 26\\n9 29\\n9 25\\n10 15\\n10 22\\n10 29\\n10 20\\n11 27\\n11 26\\n11 12\\n12 19\\n13 21\\n14 31\\n14 36\\n15 34\\n15 37\\n16 21\\n17 31\\n18 22\\n20 27\\n20 32\\n20 20\\n20 29\\n21 29\\n21 34\\n21 30\\n22 40\\n23 23\\n23 28\\n24 29\\n25 38\\n26 35\\n27 37\\n28 39\\n28 33\\n28 40\\n28 33\\n29 31\\n29 33\\n30 38\\n30 36\\n30 30\\n30 38\\n31 37\\n31 35\\n31 32\\n31 36\\n33 39\\n33 40\\n35 38\\n36 38\\n37 38\\n37 40\\n38 39\\n38 40\\n38 39\\n39 39\\n39 40\\n40 40\\n40 40\\n40 40\\n40 40\\n\", \"50 10\\n0 2\\n0 2\\n0 6\\n1 9\\n1 3\\n1 2\\n1 6\\n1 1\\n1 1\\n2 7\\n2 6\\n2 4\\n3 9\\n3 8\\n3 8\\n6 8\\n3 6\\n3 4\\n3 7\\n3 4\\n3 6\\n3 10\\n4 6\\n5 9\\n5 5\\n6 7\\n6 10\\n7 8\\n7 7\\n7 7\\n7 7\\n7 10\\n8 8\\n8 8\\n8 10\\n8 8\\n8 8\\n9 10\\n9 10\\n9 10\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n10 10\\n\", \"70 100\\n0 99\\n1 87\\n1 94\\n1 4\\n2 72\\n3 39\\n3 69\\n4 78\\n5 85\\n7 14\\n8 59\\n12 69\\n14 15\\n14 76\\n17 17\\n19 53\\n19 57\\n19 21\\n21 5\\n21 83\\n24 52\\n24 33\\n27 66\\n27 97\\n30 62\\n30 74\\n30 64\\n32 63\\n35 49\\n37 60\\n40 99\\n40 71\\n41 83\\n42 66\\n42 46\\n45 83\\n51 76\\n53 69\\n54 82\\n54 96\\n54 88\\n55 91\\n56 88\\n58 62\\n62 87\\n64 80\\n67 90\\n67 69\\n68 92\\n72 93\\n74 93\\n77 79\\n77 91\\n78 97\\n78 98\\n81 85\\n81 83\\n81 83\\n84 85\\n86 88\\n89 94\\n89 100\\n92 97\\n96 96\\n97 98\\n97 100\\n99 100\\n100 100\\n100 100\\n100 100\\n\"], \"outputs\": [\"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", \"NO\\n\", \"YES\\n\", 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|
Pig is visiting a friend.
Pig's house is located at point 0, and his friend's house is located at point m on an axis.
Pig can use teleports to move along the axis.
To use a teleport, Pig should come to a certain point (where the teleport is located) and choose where to move: for each teleport there is the rightmost point it can move Pig to, this point is known as the limit of the teleport.
Formally, a teleport located at point x with limit y can move Pig from point x to any point within the segment [x; y], including the bounds.
<image>
Determine if Pig can visit the friend using teleports only, or he should use his car.
Input
The first line contains two integers n and m (1 ≤ n ≤ 100, 1 ≤ m ≤ 100) — the number of teleports and the location of the friend's house.
The next n lines contain information about teleports.
The i-th of these lines contains two integers ai and bi (0 ≤ ai ≤ bi ≤ m), where ai is the location of the i-th teleport, and bi is its limit.
It is guaranteed that ai ≥ ai - 1 for every i (2 ≤ i ≤ n).
Output
Print "YES" if there is a path from Pig's house to his friend's house that uses only teleports, and "NO" otherwise.
You can print each letter in arbitrary case (upper or lower).
Examples
Input
3 5
0 2
2 4
3 5
Output
YES
Input
3 7
0 4
2 5
6 7
Output
NO
Note
The first example is shown on the picture below:
<image>
Pig can use the first teleport from his house (point 0) to reach point 2, then using the second teleport go from point 2 to point 3, then using the third teleport go from point 3 to point 5, where his friend lives.
The second example is shown on the picture below:
<image>
You can see that there is no path from Pig's house to his friend's house that uses only teleports.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
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hard\\nmymaoi hard\\n\", \"31\\npevkjopz soft\\nsmqei hard\\nxhfmuqua soft\\ngtmbnvn hard\\nkdvztv soft\\ncziuxm hard\\ngdswd hard\\nnawkigiz soft\\neehdplwt hard\\nizhivjj soft\\ntvnkqkc hard\\nwefwgi hard\\nuxczrz hard\\njdqudhgp soft\\nhmyzqb soft\\nwwlc soft\\ndsax soft\\nslefe soft\\nahfitc hard\\nlztbmai soft\\nzcatg soft\\nhwlubzmy soft\\njkbl soft\\nbfdfh soft\\nzshdiuce hard\\neobyco soft\\nckg hard\\nahcwzw soft\\nvtaujlke soft\\niwfdcik hard\\nitb soft\\n\", \"17\\nqojmshqd soft\\ncwbg hard\\nxomz soft\\nymxfk soft\\nusledpbg hard\\nhaaw hard\\nimwjce soft\\naioff soft\\nsumpqbzx soft\\nzffbvrq hard\\nqosengs soft\\nkbori soft\\nkxsnrkc soft\\nwzsxh hard\\nisibmmg soft\\nhrfnj soft\\nhdaavekw soft\\n\", \"1\\ncamembert soft\\n\", \"21\\nazjrptg hard\\nynvyfw hard\\ncpoe hard\\njqbglg hard\\nsqh hard\\nynya hard\\naldaolkg soft\\ndrf hard\\nesdsm hard\\nfjyua hard\\nvzlnckg hard\\nyxjfqjd hard\\nvkyay hard\\nebhhke hard\\nmsibo hard\\nvvmkenyh hard\\nxzk hard\\nlggl hard\\nvrb hard\\niep hard\\nrsseijey hard\\n\", \"18\\nbcvyeeap soft\\nubb hard\\nsrbb hard\\nemcmg hard\\nmelqan hard\\nuenps soft\\ncpyminr hard\\ndpx soft\\nglkj hard\\nmsozshuy soft\\nxnvrcozn soft\\ntftctb soft\\ncija hard\\ngxl hard\\npjoja soft\\ndhzze hard\\niyvl soft\\nctrszg hard\\n\", \"42\\nquxukow soft\\nwcn soft\\npbwg soft\\nlrp hard\\nphdvfz soft\\nidkvymji soft\\nobq soft\\nyhx soft\\nijygw soft\\nztzz soft\\nuwdhnwu soft\\ndgnuuej hard\\nhntyyzr soft\\nqxf hard\\nztg soft\\nhnpq soft\\nuhznu soft\\nitelgl hard\\nggceadhw hard\\nrxq soft\\nkznmshem hard\\nlri hard\\ndalh soft\\ngyzzuht hard\\nzvx soft\\nbjffln soft\\nwnjwrvi hard\\nxudeknru hard\\nmql soft\\ninoddzbf hard\\npdg soft\\ngtfk soft\\nhyv soft\\nxkv soft\\nwajqepw soft\\ndgc soft\\nsefwhuoa soft\\nbliirvj soft\\nhqea soft\\nped soft\\nyjgwc soft\\natlyha soft\\n\", \"32\\nauhwslzn soft\\nkpq hard\\neukw soft\\nsinenrsz soft\\najuoe soft\\ngapj soft\\nuyuhqv hard\\nifldxi hard\\npgy soft\\njnjhh hard\\nbyswtu soft\\nhdr hard\\njamqcp hard\\nmrknxch soft\\nghktedrf hard\\nutley hard\\nreinr hard\\nvbhk hard\\neuft soft\\nxspriqy soft\\ntrooa soft\\nuylbj soft\\nkgt soft\\nlhc hard\\nrwxhlux soft\\nsuoku soft\\ndhhoae soft\\nlisv soft\\nwlco hard\\nbhmptm soft\\nualppum soft\\nlpxizrhr soft\\n\", \"18\\nzpvpfze soft\\nsdlnere soft\\nkwkvgz soft\\nzla soft\\ndxlx hard\\nkpmnsooq soft\\nlomen soft\\nvywn soft\\nwfrc hard\\nmiash soft\\nkrbjwpyw hard\\ngpeksveq soft\\njhbfqs soft\\nkfncick hard\\nnwkqbsv soft\\nlywaxy soft\\nhbxh soft\\nbba hard\\n\", \"1\\nprovolone hard\\n\", \"2\\nmuenster soft\\nasiago hard\\n\", \"4\\nemmental hard\\nfeta soft\\ngoat soft\\nroquefort hard\\n\", \"17\\ngewvfeq soft\\noaximz hard\\nxkfscel soft\\nnbxdbggw soft\\ngxgsscq hard\\nmqbu hard\\nbtpzl soft\\npsv soft\\niov soft\\nhliudz soft\\nbmiu soft\\nqqegoe hard\\nvfq soft\\nmgx soft\\nawjthx hard\\nonjmhee soft\\nxoarup soft\\n\", \"1\\ncamemcert soft\\n\", \"21\\nazjrptg hard\\nynwyfw hard\\ncpoe hard\\njqbglg hard\\nsqh hard\\nynya hard\\naldaolkg soft\\ndrf hard\\nesdsm hard\\nfjyua hard\\nvzlnckg hard\\nyxjfqjd hard\\nvkyay hard\\nebhhke hard\\nmsibo hard\\nvvmkenyh hard\\nxzk hard\\nlggl hard\\nvrb hard\\niep hard\\nrsseijey hard\\n\", \"42\\nquxukow soft\\nwcn soft\\npbwg soft\\nlrp hard\\npgdvfz soft\\nidkvymji soft\\nobq soft\\nyhx soft\\nijygw soft\\nztzz soft\\nuwdhnwu soft\\ndgnuuej hard\\nhntyyzr soft\\nqxf hard\\nztg soft\\nhnpq soft\\nuhznu soft\\nitelgl hard\\nggceadhw hard\\nrxq soft\\nkznmshem hard\\nlri hard\\ndalh soft\\ngyzzuht hard\\nzvx soft\\nbjffln soft\\nwnjwrvi hard\\nxudeknru hard\\nmql soft\\ninoddzbf hard\\npdg soft\\ngtfk soft\\nhyv soft\\nxkv soft\\nwajqepw soft\\ndgc soft\\nsefwhuoa soft\\nbliirvj soft\\nhqea soft\\nped soft\\nyjgwc soft\\natlyha soft\\n\", \"2\\nmuentter soft\\nasiago hard\\n\", \"6\\nparmesan hard\\nemmental hard\\nedam hard\\ncolby hard\\ngruyere hard\\nogaisa hard\\n\", \"9\\nbrie soft\\ncamembert soft\\nfeta soft\\ngoat soft\\nluenster soft\\nasiago hard\\ncheddar hard\\ngouda hard\\nswiss hard\\n\", \"18\\nbcvyeeap soft\\nubb hard\\nsrbb hard\\nemcmg hard\\nmelqan hard\\nuenps soft\\ncpyminr hard\\ndpx soft\\nglkj hard\\nmsozshuy soft\\nxnvrcozn soft\\ntftctb soft\\ncija hard\\ngxl hard\\npjajo soft\\ndhzze hard\\niyvl soft\\nctrszg hard\\n\", \"18\\nzpvpfze soft\\nsdlnere soft\\nkwkvgz soft\\nzla soft\\ndxlx hard\\nkpmnsooq soft\\nlomen soft\\nvywn soft\\nwfrc hard\\nmiash soft\\nkrbjwpyw hard\\ngpeksveq soft\\njhbfqr soft\\nkfncick hard\\nnwkqbsv soft\\nlywaxy soft\\nhbxh soft\\nbba hard\\n\", \"21\\nazjrptg hard\\nynwyfw hard\\ncpoe hard\\njqbglg hard\\nsqh hard\\nynya hard\\naldaolkg soft\\ndrf hard\\nesdsm hard\\nfjxua hard\\nvzlnckg hard\\nyxjfqjd hard\\nvkyay hard\\nebhhke hard\\nmsibo hard\\nvvmkenyh hard\\nxzk hard\\nlggl hard\\nvrb hard\\niep hard\\nrsseijey hard\\n\", \"18\\nbcvyeeap soft\\nubb hard\\nsrbb hard\\nemcmg hard\\nmelqan hard\\nuenps soft\\ncpyminr hard\\ndpx soft\\nglkj hard\\nmsozshuy soft\\nxnvrcozn soft\\ntftctb soft\\ncija hard\\ngxl hard\\npjaoj soft\\ndhzze hard\\niyvl soft\\nctrszg hard\\n\", \"42\\nquxukow soft\\nwcn soft\\npbwg soft\\nlrp hard\\npgdvfz soft\\nidkvymji soft\\nobq soft\\nyhx soft\\nijygw soft\\nztzz soft\\nuwdhnwu soft\\ndgnuuej hard\\nhntyyzr soft\\nqxf hard\\nztg soft\\nhnpq soft\\nuhznu soft\\nitelgl hard\\nggceadhw hard\\nrxq soft\\nkznmshem hard\\nlri hard\\ndalh soft\\ngyzzuht hard\\nzvx soft\\nbjffln soft\\nwnjwrvi hard\\nxudeknru hard\\nmql soft\\ninoddzbf hard\\npdg soft\\ngtfk soft\\nhyv soft\\nxkv soft\\nwajqepw soft\\ndgc soft\\nsefwhuoa soft\\nbliirvj soft\\nhqea soft\\ndep soft\\nyjgwc soft\\natlyha soft\\n\", \"18\\nzpvpfze soft\\nsdlnere soft\\nkwkvgz soft\\nzla soft\\ndxlx hard\\nkpmnsooq soft\\nlomen soft\\nvywo soft\\nwfrc hard\\nmiash soft\\nkrbjwpyw hard\\ngpeksveq soft\\njhbfqr soft\\nkfncick hard\\nnwkqbsv soft\\nlywaxy soft\\nhbxh soft\\nbba hard\\n\", \"2\\nrettneum soft\\nasiago hard\\n\", \"18\\nbcvyeebp soft\\nubb hard\\nsrbb hard\\nemcmg hard\\nmelqan hard\\nuenps soft\\ncpyminr hard\\ndpx soft\\nglkj hard\\nmsozshuy soft\\nxnvrcozn soft\\ntftctb soft\\ncija hard\\ngxl hard\\npjaoj soft\\ndhzze hard\\niyvl soft\\nctrszg hard\\n\", \"18\\nzpvpfze soft\\nsdlnere soft\\nkwkvgz soft\\nzla soft\\ndxlx hard\\nkpmnsooq soft\\nlomen soft\\nvywo soft\\nwfrc hard\\nmiash soft\\nkrbjwpyw hard\\ngpeksveq soft\\njhbfqr soft\\nkfncick hard\\nnwkqbsv soft\\nkywaxy soft\\nhbxh soft\\nbba hard\\n\", \"18\\nzpvpfze soft\\nsdlnere soft\\nkwkvgz soft\\nzla soft\\ndxlx hard\\nkpmnsooq soft\\nlomen soft\\nvywo soft\\nwfrc hard\\nmiash soft\\nkrbjwpyw hard\\ngpeksveq soft\\njhbfqr soft\\nkfncick hard\\nmwkqbsv soft\\nkywaxy soft\\nhbxh soft\\nbba hard\\n\", \"18\\nzpvpfze soft\\nsdlnere soft\\nkwkvgz soft\\nzla soft\\ndxlx hard\\nkpmnsooq soft\\nlomen soft\\nvywo soft\\nwfrc hard\\nmiash soft\\nkrbjwpyw hard\\ngpeksveq soft\\njhbfqr soft\\njfncick hard\\nmwkqbsv soft\\nkywaxy soft\\nhbxh soft\\nbba hard\\n\", \"17\\ngewvfeq soft\\noaximz hard\\nxkfscel soft\\nnbxdbggw soft\\ngxgsscq hard\\nmqbu hard\\nbtpzl soft\\nvsp soft\\niov soft\\nhliudz soft\\nbmiu soft\\nqqegoe hard\\nufq soft\\nmgx soft\\nawjthx hard\\nonjmhee soft\\nxoarup soft\\n\", \"27\\ndbilglfh hard\\niecrbay hard\\ncpunhmf hard\\nszvvz soft\\nqsbg hard\\nvdzexx hard\\naiuvj soft\\nfuccez hard\\ndvscmzd hard\\ngps soft\\ndev hard\\nnwlfdh soft\\nnrlglw soft\\nypff hard\\nwig hard\\njvgtfo hard\\nzyp soft\\ncpgbws soft\\nxjsyjgi hard\\nizizf hard\\nizrwozx hard\\nwau hard\\ngqz hard\\nffqa hard\\nnajmkxn soft\\nvqtw hard\\nmymaoi hard\\n\", \"31\\npevkjopz soft\\nsmqei hard\\nxhfmuqua soft\\ngtmbnvn hard\\nkdvztv soft\\ncziuxm hard\\ngdswd hard\\nnawkigiz soft\\neehdplwt hard\\nizhivjj soft\\ntvnkqkc hard\\nwefwgi hard\\nuxczrz hard\\njdqudhgp soft\\nhmyzqb soft\\nwwlc soft\\nesax soft\\nslefe soft\\nahfitc hard\\nlztbmai soft\\nzcatg soft\\nhwlubzmy soft\\njkbl soft\\nbfdfh soft\\nzshdiuce hard\\neobyco soft\\nckg hard\\nahcwzw soft\\nvtaujlke soft\\niwfdcik hard\\nitb soft\\n\", \"17\\nqojmshqd soft\\ncwbg hard\\nxomz soft\\nymxfk soft\\nusledpbg hard\\nhaaw hard\\nimwjce soft\\naioff soft\\nsumpqbzx soft\\nzffbvrq hard\\nqosemgs soft\\nkbori soft\\nkxsnrkc soft\\nwzsxh hard\\nisibmmg soft\\nhrfnj soft\\nhdaavekw soft\\n\", \"1\\ntrebmemac soft\\n\", \"21\\nazjrptg hard\\nynvyfw hard\\ncpoe hard\\njqbglg hard\\nsqh hard\\nynya hard\\naldaolkg soft\\ndrf hard\\nesdsm hard\\nfjyua hard\\nvzlnckg hard\\nyxjfqjd hard\\nyaykv hard\\nebhhke hard\\nmsibo hard\\nvvmkenyh hard\\nxzk hard\\nlggl hard\\nvrb hard\\niep hard\\nrsseijey hard\\n\", \"18\\npaeeyvcb soft\\nubb hard\\nsrbb hard\\nemcmg hard\\nmelqan hard\\nuenps soft\\ncpyminr hard\\ndpx soft\\nglkj hard\\nmsozshuy soft\\nxnvrcozn soft\\ntftctb soft\\ncija hard\\ngxl hard\\npjoja soft\\ndhzze hard\\niyvl soft\\nctrszg hard\\n\", \"42\\nquxukow soft\\nwcn soft\\npbwg soft\\nlrp hard\\nphdvfz soft\\nidkvymji soft\\nobq soft\\nyhx soft\\nijygw soft\\nztzz soft\\nuwdhnwu soft\\ndgnuuej hard\\nhntyyzr soft\\nqxf hard\\nztg soft\\nhnpq soft\\nuhznu soft\\nitelgl hard\\nggceadhw hard\\nrxq soft\\nkznmshem hard\\nlri hard\\ndalh soft\\ngyzzuht hard\\nzvx soft\\nnlffjb soft\\nwnjwrvi hard\\nxudeknru hard\\nmql soft\\ninoddzbf hard\\npdg soft\\ngtfk soft\\nhyv soft\\nxkv soft\\nwajqepw soft\\ndgc soft\\nsefwhuoa soft\\nbliirvj soft\\nhqea soft\\nped soft\\nyjgwc soft\\natlyha soft\\n\", \"1\\nprouolone hard\\n\", \"2\\nretsneum soft\\nasiago hard\\n\", \"4\\nemmental hard\\nfeta soft\\ntaog soft\\nroquefort hard\\n\", \"1\\ncrmemceat soft\\n\", \"18\\nbcvyeeap soft\\nubb hard\\nsrbb hard\\nemcmg hard\\nlelqan hard\\nuenps soft\\ncpyminr hard\\ndpx soft\\nglkj hard\\nmsozshuy soft\\nxnvrcozn soft\\ntftctb soft\\ncija hard\\ngxl hard\\npjajo soft\\ndhzze hard\\niyvl soft\\nctrszg hard\\n\", \"18\\nzpvpfze soft\\nsdlnere soft\\nkwkvgz soft\\nzla soft\\ndxlx hard\\nkpmnsooq soft\\nkomen soft\\nvywn soft\\nwfrc hard\\nmiash soft\\nkrbjwpyw hard\\ngpeksveq soft\\njhbfqr soft\\nkfncick hard\\nnwkqbsv soft\\nlywaxy soft\\nhbxh soft\\nbba hard\\n\", \"2\\nmventter soft\\nasiago hard\\n\", \"42\\nquxukow soft\\nwcn soft\\npbwg soft\\nlrp hard\\npgdvfz soft\\nidkvymji soft\\nobq soft\\nyhx soft\\nijygw soft\\nztzz soft\\nuwdhnwu soft\\ndgnuuej hard\\nhntyyzr soft\\nqxf hard\\nztg soft\\nhnpq soft\\nuhznu soft\\niselgl hard\\nggceadhw hard\\nrxq soft\\nkznmshem hard\\nlri hard\\ndalh soft\\ngyzzuht hard\\nzvx soft\\nbjffln soft\\nwnjwrvi hard\\nxudeknru hard\\nmql soft\\ninoddzbf hard\\npdg soft\\ngtfk soft\\nhyv soft\\nxkv soft\\nwajqepw soft\\ndgc soft\\nsefwhuoa soft\\nbliirvj soft\\nhqea soft\\ndep soft\\nyjgwc soft\\natlyha soft\\n\", \"18\\nzpvpfze soft\\nsdlneqe soft\\nkwkvgz soft\\nzla soft\\ndxlx hard\\nkpmnsooq soft\\nlomen soft\\nvywo soft\\nwfrc hard\\nmiash soft\\nkrbjwpyw hard\\ngpeksveq soft\\njhbfqr soft\\nkfncick hard\\nnwkqbsv soft\\nkywaxy soft\\nhbxh soft\\nbba hard\\n\", \"18\\nzpvpfze soft\\nsdlnere soft\\nkwkvgz soft\\nzla soft\\ndxlx hard\\nkpmnsooq soft\\nlomen soft\\nvywo soft\\nwfrc hard\\nmiash soft\\nkrbjwqyw hard\\ngpeksveq soft\\njhbfqr soft\\nkfncick hard\\nmwkqbsv soft\\nkywaxy soft\\nhbxh soft\\nbba hard\\n\", \"18\\nzpvpfze soft\\nsdlnere soft\\nkwkvgz soft\\nzla soft\\ndxlx hard\\nkpmnsooq soft\\nlomen soft\\nvywo soft\\nwfrc hard\\nmiash soft\\nkrbjwpyw hard\\ngpeksveq soft\\njhbfqr soft\\njfmcick hard\\nmwkqbsv soft\\nkywaxy soft\\nhbxh soft\\nbba hard\\n\", \"17\\ngewvfeq soft\\noaximz hard\\nxkfscel soft\\nnbxdbggw soft\\ngxgsscq hard\\nmqbu hard\\nbtpzl soft\\nvsp soft\\nvoi soft\\nhliudz soft\\nbmiu soft\\nqqegoe hard\\nufq soft\\nmgx soft\\nawjthx hard\\nonjmhee soft\\nxoarup soft\\n\", \"27\\ndbilglfh hard\\niecrbay hard\\ncpunhmf hard\\nszvvz soft\\nqsbg hard\\nvdzexx hard\\naiuvj soft\\nfuccez hard\\ndvscmzd hard\\ngps soft\\ndev hard\\nnwlfdh soft\\nnrlglw soft\\nypff hard\\nwih hard\\njvgtfo hard\\nzyp soft\\ncpgbws soft\\nxjsyjgi hard\\nizizf hard\\nizrwozx hard\\nwau hard\\ngqz hard\\nffqa hard\\nnajmkxn soft\\nvqtw hard\\nmymaoi hard\\n\", \"31\\npevkjopz soft\\nsmqei hard\\nxhfmuqua soft\\ngtmbnvn hard\\nkdvytv soft\\ncziuxm hard\\ngdswd hard\\nnawkigiz soft\\neehdplwt hard\\nizhivjj soft\\ntvnkqkc hard\\nwefwgi hard\\nuxczrz hard\\njdqudhgp soft\\nhmyzqb soft\\nwwlc soft\\nesax soft\\nslefe soft\\nahfitc hard\\nlztbmai soft\\nzcatg soft\\nhwlubzmy soft\\njkbl soft\\nbfdfh soft\\nzshdiuce hard\\neobyco soft\\nckg hard\\nahcwzw soft\\nvtaujlke soft\\niwfdcik hard\\nitb soft\\n\", \"17\\nqojmshqd soft\\ncwbg hard\\nxomz soft\\nymxfk soft\\nusledpbg hard\\nhaaw hard\\nimwjce soft\\naioff soft\\nsumpqbzx soft\\nzffbvrq hard\\nqosemgs soft\\nlbori soft\\nkxsnrkc soft\\nwzsxh hard\\nisibmmg soft\\nhrfnj soft\\nhdaavekw soft\\n\", \"1\\nrtebmemac soft\\n\", \"18\\npaeeyvcb soft\\nubb hard\\nsrbb hard\\nemcmg hard\\nmelqan hard\\nuenps soft\\ncpyminr hard\\ndpx soft\\nglkj hard\\nmsozshuy soft\\nxnvrcozn soft\\ntftctb soft\\ncija hard\\ngxl hard\\npjoja soft\\ndhzze hard\\niyvl soft\\nrtcszg hard\\n\", \"42\\nquxukow soft\\nwcn soft\\npbwg soft\\nlrp hard\\nphdvfz soft\\nidkvymji soft\\nobq soft\\nyhx soft\\nijygw soft\\nztzz soft\\nuwdhnwu soft\\ndgnuuej hard\\nhntyyzr soft\\nqxf hard\\nztg soft\\nhnpq soft\\nuhznu soft\\nitelgl hard\\nggceadhw hard\\nrxq soft\\nkznmshem hard\\nlri hard\\ndalh soft\\ngyzzuht hard\\nzvx soft\\nnlffjb soft\\nwnjwrvi hard\\nxudeknru hard\\nmql soft\\ninoddzbf hard\\npdg soft\\ngtfk soft\\nhyv soft\\nxkv soft\\nwajqepw soft\\ndgc soft\\nsefwhuoa soft\\nbliirvj soft\\nhqea soft\\nped soft\\ncwgjy soft\\natlyha soft\\n\", \"4\\nlatnemme hard\\nfeta soft\\ntaog soft\\nroquefort hard\\n\", \"1\\ntaecmemrc soft\\n\", \"18\\nzpvpfze soft\\nsdlnere soft\\nkwkvgz soft\\nzla soft\\ndxlx hard\\nkpmnsooq soft\\nlomen soft\\nvywo soft\\nwfrc hard\\nmiash soft\\nkrbjwpyw hard\\ngpeksveq soft\\njhbfqr soft\\njfmcick hard\\nmwkqbsv soft\\nkywaxy soft\\nhbxh soft\\nabb hard\\n\", \"31\\npevkjopz soft\\nsmqei hard\\nxhfmuqua soft\\ngtmbnvn hard\\nkdvytv soft\\ncziuxm hard\\ngdswd hard\\nnawkigiz soft\\neehdplwt hard\\nizhivjj soft\\ntvnkqkc hard\\nwefwgi hard\\nuxczrz hard\\njdqudhgp soft\\nhmyzqb soft\\nwwlc soft\\nesax soft\\nslefe soft\\nahfitc hard\\nlztbmai soft\\nzcatg soft\\nhwlubzmy soft\\njkbl soft\\nbfdfh soft\\nzrhdiuce hard\\neobyco soft\\nckg hard\\nahcwzw soft\\nvtaujlke soft\\niwfdcik hard\\nitb soft\\n\", \"1\\nrtebemmac soft\\n\", \"42\\nquxukow soft\\nwcn soft\\npbwg soft\\nlrp hard\\nphdvfz soft\\nidkvymji soft\\nobq soft\\nyhx soft\\nijygw soft\\nztzz soft\\nuwdhnwu soft\\ndgnuuej hard\\nhntyyzr soft\\nqxf hard\\nztg soft\\nhnpq soft\\nuhznu soft\\nitelgl hard\\nggceadhw hard\\nrxq soft\\nkznmshem hard\\nlri hard\\ndalh soft\\ngyzzuht hard\\nzvx soft\\nnkffjb soft\\nwnjwrvi hard\\nxudeknru hard\\nmql soft\\ninoddzbf hard\\npdg soft\\ngtfk soft\\nhyv soft\\nxkv soft\\nwajqepw soft\\ndgc soft\\nsefwhuoa soft\\nbliirvj soft\\nhqea soft\\nped soft\\ncwgjy soft\\natlyha soft\\n\", \"42\\nquxukow soft\\nwcn soft\\npbwg soft\\nlrp hard\\nphdvfz soft\\nidkvymji soft\\nobq soft\\nyhx soft\\nijygw soft\\nztzz soft\\nuwdhnwu soft\\ndgnuuej hard\\nrzyytnh soft\\nqxf hard\\nztg soft\\nhnpq soft\\nuhznu soft\\nitelgl hard\\nggceadhw hard\\nrxq soft\\nkznmshem hard\\nlri hard\\ndalh soft\\ngyzzuht hard\\nzvx soft\\nnkffjb soft\\nwnjwrvi hard\\nxudeknru hard\\nmql soft\\ninoddzbf hard\\npdg soft\\ngtfk soft\\nhyv soft\\nxkv soft\\nwajqepw soft\\ndgc soft\\nsefwhuoa soft\\nbliirvj soft\\nhqea soft\\nped soft\\ncwgjy soft\\natlyha soft\\n\", \"42\\nquxukow soft\\nwcn soft\\npbwg soft\\nlrp hard\\nphdvfz soft\\nidkvymji soft\\nobq soft\\nyhx soft\\nijygw soft\\nztzz soft\\nuwdhnwu soft\\ndgnuuej hard\\nrzyytnh soft\\nqxf hard\\nzgt soft\\nhnpq soft\\nuhznu soft\\nitelgl hard\\nggceadhw hard\\nrxq soft\\nkznmshem hard\\nlri hard\\ndalh soft\\ngyzzuht hard\\nzvx soft\\nnkffjb soft\\nwnjwrvi hard\\nxudeknru hard\\nmql soft\\ninoddzbf hard\\npdg soft\\ngtfk soft\\nhyv soft\\nxkv soft\\nwajqepw soft\\ndgc soft\\nsefwhuoa soft\\nbliirvj soft\\nhqea soft\\nped soft\\ncwgjy soft\\natlyha soft\\n\", \"17\\ngewvfeq soft\\noayimz hard\\nxkfscel soft\\nnbxdbggw soft\\ngxgsscq hard\\nmqbu hard\\nbtpzl soft\\npsv soft\\niov soft\\nhliudz soft\\nbmiu soft\\nqqegoe hard\\nufq soft\\nmgx soft\\nawjthx hard\\nonjmhee soft\\nxoarup soft\\n\", \"27\\ndbilglfh hard\\niecrbay hard\\ncpunhmf hard\\nszvvz soft\\nqsbg hard\\nvdzexx hard\\nbiuvj soft\\nfuccez hard\\ndvscmzd hard\\ngps soft\\ndev hard\\nnwlfdh soft\\nnrlglw soft\\nypff hard\\nwig hard\\njvgtfo hard\\nzyp soft\\ncpgbws soft\\nxjsyjgi hard\\nizizf hard\\nizrwozx hard\\nwau hard\\ngzq hard\\nffqa hard\\nnajmkxn soft\\nvqtw hard\\nmymaoi hard\\n\", \"31\\npevkjopz soft\\nsmqei hard\\nxhfmuqua soft\\ngtmbnvn hard\\nkdvztv soft\\ncziuxm hard\\ngdswd hard\\nnawkigiz soft\\neehdplwt hard\\nizhivjj soft\\ntvnkqkc hard\\nwefwgi hard\\nuxczrz hard\\njdqudhgp soft\\nbqzymh soft\\nwwlc soft\\ndsax soft\\nslefe soft\\nahfitc hard\\nlztbmai soft\\nzcatg soft\\nhwlubzmy soft\\njkbl soft\\nbfdfh soft\\nzshdiuce hard\\neobyco soft\\nckg hard\\nahcwzw soft\\nvtaujlke soft\\niwfdcik hard\\nitb soft\\n\", \"21\\nazjrptg hard\\nynvyfw hard\\ncppe hard\\njqbglg hard\\nsqh hard\\nynya hard\\naldaolkg soft\\ndrf hard\\nesdsm hard\\nfjyua hard\\nvzlnckg hard\\nyxjfqjd hard\\nvkyay hard\\nebhhke hard\\nmsibo hard\\nvvmkenyh hard\\nxzk hard\\nlggl hard\\nvrb hard\\niep hard\\nrsseijey hard\\n\", \"18\\nbcvyeeap soft\\nubb hard\\nsrbb hard\\nemcmg hard\\nmelqan hard\\nuenpt soft\\ncpyminr hard\\ndpx soft\\nglkj hard\\nmsozshuy soft\\nxnvrcozn soft\\ntftctb soft\\ncija hard\\ngxl hard\\npjoja soft\\ndhzze hard\\niyvl soft\\nctrszg hard\\n\", \"18\\nzpvpfze soft\\nsdlnere soft\\nkwkvgz soft\\nzla soft\\ndylx hard\\nkpmnsooq soft\\nlomen soft\\nvywn soft\\nwfrc hard\\nmiash soft\\nkrbjwpyw hard\\ngpeksveq soft\\njhbfqs soft\\nkfncick hard\\nnwkqbsv soft\\nlywaxy soft\\nhbxh soft\\nbba hard\\n\", \"1\\nprovoloen hard\\n\", \"6\\nparmesan hard\\nemmental hard\\nedam hard\\ncolay hard\\ngruyere hard\\nasiago hard\\n\"], \"outputs\": [\"4\\n\", \"3\\n\", \"5\\n\", \"5\\n\", \"7\\n\", \"7\\n\", \"5\\n\", \"1\\n\", \"7\\n\", \"5\\n\", \"8\\n\", \"7\\n\", \"5\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"5\\n\", \"1\\n\", \"7\\n\", \"8\\n\", \"2\\n\", \"4\\n\", \"3\\n\", \"5\\n\", \"5\\n\", \"7\\n\", \"5\\n\", \"8\\n\", \"5\\n\", \"2\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"7\\n\", \"7\\n\", \"5\\n\", \"1\\n\", \"7\\n\", \"5\\n\", \"8\\n\", \"1\\n\", \"2\\n\", \"2\\n\", \"1\\n\", \"5\\n\", \"5\\n\", \"2\\n\", \"8\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"5\\n\", \"7\\n\", \"7\\n\", \"5\\n\", \"1\\n\", \"5\\n\", \"8\\n\", \"2\\n\", \"1\\n\", \"5\\n\", \"7\\n\", \"1\\n\", \"8\\n\", \"8\\n\", \"8\\n\", \"5\\n\", \"7\\n\", \"7\\n\", \"7\\n\", \"5\\n\", \"5\\n\", \"1\\n\", \"4\\n\"]}", "source": "primeintellect"}
|
Not to be confused with [chessboard](https://en.wikipedia.org/wiki/Chessboard).
<image>
Input
The first line of input contains a single integer N (1 ≤ N ≤ 100) — the number of cheeses you have.
The next N lines describe the cheeses you have. Each line contains two space-separated strings: the name of the cheese and its type. The name is a string of lowercase English letters between 1 and 10 characters long. The type is either "soft" or "hard. All cheese names are distinct.
Output
Output a single number.
Examples
Input
9
brie soft
camembert soft
feta soft
goat soft
muenster soft
asiago hard
cheddar hard
gouda hard
swiss hard
Output
3
Input
6
parmesan hard
emmental hard
edam hard
colby hard
gruyere hard
asiago hard
Output
4
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5\\n5\\n14\\n76\\n67\\n40\\n\\nSAMPLE\", \"100\\n402\\n409\\n278\\n29\\n268\\n874\\n527\\n617\\n727\\n485\\n616\\n724\\n660\\n190\\n286\\n562\\n270\\n21\\n75\\n625\\n1\\n122\\n579\\n89\\n764\\n679\\n145\\n847\\n405\\n419\\n728\\n29\\n126\\n494\\n216\\n760\\n662\\n660\\n651\\n902\\n7\\n202\\n192\\n194\\n908\\n876\\n214\\n915\\n711\\n445\\n422\\n989\\n651\\n406\\n492\\n712\\n866\\n762\\n5\\n488\\n888\\n791\\n957\\n406\\n7\\n669\\n881\\n871\\n457\\n975\\n666\\n278\\n219\\n176\\n778\\n12\\n886\\n145\\n598\\n762\\n404\\n550\\n180\\n154\\n474\\n528\\n489\\n744\\n64\\n82\\n941\\n877\\n526\\n658\\n808\\n599\\n980\\n91\\n181\\n929\", \"100\\n402\\n409\\n278\\n29\\n268\\n874\\n527\\n617\\n727\\n485\\n616\\n724\\n660\\n190\\n286\\n562\\n270\\n21\\n75\\n625\\n1\\n122\\n579\\n89\\n764\\n679\\n145\\n847\\n405\\n419\\n728\\n29\\n126\\n494\\n216\\n760\\n662\\n660\\n651\\n902\\n7\\n202\\n192\\n194\\n908\\n876\\n214\\n915\\n711\\n445\\n422\\n989\\n651\\n406\\n492\\n712\\n866\\n762\\n5\\n488\\n888\\n791\\n957\\n406\\n7\\n669\\n881\\n871\\n457\\n975\\n666\\n245\\n219\\n176\\n778\\n12\\n886\\n145\\n598\\n762\\n404\\n550\\n180\\n154\\n474\\n528\\n489\\n744\\n64\\n82\\n941\\n877\\n526\\n658\\n808\\n599\\n980\\n91\\n181\\n929\", \"5\\n7\\n14\\n76\\n67\\n40\\n\\nSAMPLE\", \"5\\n7\\n14\\n76\\n89\\n40\\n\\nSAMPLE\", \"5\\n7\\n14\\n76\\n89\\n62\\n\\nSAMPLE\", \"100\\n402\\n409\\n278\\n29\\n268\\n874\\n527\\n617\\n727\\n485\\n616\\n724\\n660\\n190\\n286\\n562\\n270\\n21\\n75\\n625\\n1\\n122\\n579\\n89\\n764\\n679\\n145\\n847\\n405\\n419\\n728\\n29\\n126\\n494\\n216\\n760\\n662\\n660\\n651\\n902\\n7\\n202\\n192\\n194\\n908\\n876\\n214\\n915\\n711\\n445\\n422\\n989\\n651\\n406\\n492\\n712\\n866\\n762\\n5\\n488\\n888\\n791\\n957\\n406\\n7\\n669\\n881\\n871\\n457\\n975\\n666\\n278\\n219\\n176\\n778\\n12\\n886\\n145\\n598\\n762\\n404\\n550\\n180\\n154\\n474\\n528\\n489\\n744\\n64\\n82\\n941\\n877\\n526\\n658\\n808\\n599\\n980\\n91\\n181\\n281\", \"5\\n2\\n14\\n76\\n67\\n40\\n\\nSAMPLE\", 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\"5\\n12\\n0\\n76\\n176\\n121\\n\\nEOLMAS\", \"5\\n12\\n0\\n62\\n80\\n79\\n\\nEPLMAS\", \"100\\n402\\n705\\n278\\n29\\n268\\n874\\n527\\n617\\n727\\n485\\n616\\n724\\n660\\n190\\n286\\n562\\n270\\n21\\n75\\n625\\n1\\n122\\n192\\n89\\n764\\n679\\n145\\n847\\n405\\n419\\n728\\n29\\n126\\n494\\n216\\n760\\n662\\n660\\n651\\n902\\n7\\n202\\n192\\n194\\n409\\n876\\n214\\n915\\n711\\n445\\n422\\n989\\n651\\n406\\n492\\n712\\n866\\n762\\n5\\n488\\n888\\n791\\n957\\n406\\n7\\n669\\n881\\n871\\n457\\n975\\n666\\n278\\n219\\n176\\n778\\n12\\n886\\n145\\n598\\n762\\n404\\n550\\n180\\n154\\n474\\n528\\n489\\n744\\n64\\n82\\n941\\n877\\n526\\n658\\n808\\n599\\n980\\n91\\n181\\n929\", \"5\\n7\\n14\\n76\\n112\\n40\\n\\nELPMAS\", \"100\\n402\\n409\\n278\\n29\\n268\\n874\\n527\\n617\\n727\\n485\\n616\\n724\\n660\\n190\\n286\\n562\\n270\\n21\\n75\\n625\\n1\\n122\\n579\\n89\\n764\\n1291\\n145\\n847\\n405\\n419\\n1070\\n29\\n126\\n494\\n216\\n760\\n662\\n660\\n651\\n902\\n7\\n202\\n192\\n194\\n908\\n578\\n214\\n915\\n711\\n445\\n422\\n989\\n651\\n406\\n492\\n712\\n866\\n762\\n5\\n488\\n888\\n791\\n957\\n406\\n7\\n669\\n881\\n871\\n457\\n975\\n666\\n245\\n219\\n176\\n778\\n12\\n886\\n145\\n598\\n762\\n404\\n550\\n180\\n154\\n474\\n528\\n489\\n744\\n64\\n82\\n941\\n877\\n526\\n658\\n808\\n599\\n980\\n91\\n181\\n929\", \"5\\n7\\n11\\n76\\n67\\n9\\n\\nSAMPLE\", \"5\\n7\\n20\\n96\\n89\\n69\\n\\nSAMPLE\", \"5\\n1\\n14\\n19\\n87\\n40\\n\\nSAMPLE\", \"5\\n7\\n2\\n29\\n162\\n62\\n\\nSAMPLE\", \"5\\n2\\n1\\n76\\n67\\n40\\n\\nSAMPLE\", \"5\\n10\\n0\\n8\\n51\\n74\\n\\nSAMPLE\", \"5\\n7\\n14\\n5\\n44\\n001\\n\\nSAMPLE\", \"5\\n7\\n2\\n76\\n81\\n9\\n\\nEPLMAS\", \"5\\n10\\n0\\n89\\n67\\n9\\n\\nSEMPLA\", \"5\\n9\\n1\\n76\\n89\\n101\\n\\nSAMPLD\", \"5\\n10\\n0\\n8\\n1\\n15\\n\\nSAMPLE\", \"5\\n17\\n2\\n109\\n89\\n121\\n\\nEPMMAS\", \"5\\n12\\n1\\n76\\n176\\n121\\n\\nEOLMAS\", \"5\\n12\\n1\\n62\\n80\\n79\\n\\nEPLMAS\", \"5\\n7\\n9\\n76\\n112\\n40\\n\\nELPMAS\", \"100\\n402\\n409\\n278\\n29\\n268\\n874\\n527\\n617\\n727\\n615\\n616\\n724\\n660\\n190\\n286\\n562\\n270\\n21\\n75\\n625\\n1\\n122\\n579\\n89\\n764\\n1291\\n145\\n847\\n405\\n419\\n1070\\n29\\n126\\n494\\n216\\n760\\n662\\n660\\n651\\n902\\n7\\n202\\n192\\n194\\n908\\n578\\n214\\n915\\n711\\n445\\n422\\n989\\n651\\n406\\n492\\n712\\n866\\n762\\n5\\n488\\n888\\n791\\n957\\n406\\n7\\n669\\n881\\n871\\n457\\n975\\n666\\n245\\n219\\n176\\n778\\n12\\n886\\n145\\n598\\n762\\n404\\n550\\n180\\n154\\n474\\n528\\n489\\n744\\n64\\n82\\n941\\n877\\n526\\n658\\n808\\n599\\n980\\n91\\n181\\n929\", \"5\\n7\\n11\\n116\\n67\\n9\\n\\nSAMPLE\", \"5\\n5\\n20\\n96\\n89\\n69\\n\\nSAMPLE\", \"5\\n4\\n14\\n110\\n89\\n62\\n\\nEAMPLS\", \"5\\n1\\n14\\n19\\n162\\n40\\n\\nSAMPLE\", \"5\\n7\\n2\\n29\\n162\\n109\\n\\nSAMPLE\", \"5\\n2\\n1\\n76\\n67\\n78\\n\\nSAMPLE\", \"5\\n7\\n14\\n5\\n44\\n000\\n\\nSAMPLE\", \"5\\n7\\n2\\n84\\n81\\n9\\n\\nEPLMAS\", \"5\\n15\\n0\\n89\\n67\\n9\\n\\nSEMPLA\", \"5\\n9\\n1\\n76\\n2\\n101\\n\\nSAMPLD\", \"5\\n1\\n20\\n76\\n67\\n0\\n\\nASMPLE\", \"5\\n12\\n0\\n8\\n1\\n15\\n\\nSAMPLE\"], \"outputs\": [\"4\\n12\\n59\\n51\\n27\\n\", \"245\\n251\\n223\\n26\\n214\\n624\\n348\\n420\\n510\\n310\\n419\\n507\\n450\\n153\\n230\\n371\\n216\\n19\\n58\\n427\\n1\\n101\\n386\\n71\\n534\\n467\\n112\\n600\\n247\\n260\\n511\\n26\\n104\\n318\\n176\\n531\\n452\\n450\\n442\\n650\\n6\\n164\\n155\\n156\\n655\\n626\\n174\\n661\\n496\\n274\\n263\\n719\\n442\\n248\\n317\\n497\\n617\\n533\\n4\\n313\\n637\\n559\\n690\\n248\\n6\\n458\\n631\\n622\\n285\\n706\\n455\\n223\\n179\\n140\\n547\\n11\\n635\\n112\\n403\\n533\\n246\\n360\\n144\\n120\\n300\\n349\\n314\\n516\\n48\\n65\\n676\\n627\\n347\\n448\\n574\\n404\\n711\\n73\\n145\\n674\\n\", 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|
One fine day, Benny decided to calculate the number of kilometers that she traveled by her bicycle. Therefore, she bought an odometer and installed it onto her bicycle. But the odometer was broken. It was not able to display the digit 3. This would precisely mean, that the odometer won't be able to display the numbers having one of their digits as 3.
For example, after the number 1299, the odometer will show 1400.
Benny was traveling a lot and now she wants to know the number of kilometers that she has traveled. You will be given only the number that Benny saw on the odometer. Your task is to determine the real distance.
Input format
The input consists of several test cases.
The first line contains one integer T denoting the number of test cases.
The next T lines contain a single integer N denoting the number that Benny saw on odometer.
Output format
For each test case, print the real distance in a single line.
Constraints
1 ≤ T ≤ 10^5
0 ≤ N < 10^9
SAMPLE INPUT
5
5
14
76
67
40
SAMPLE OUTPUT
4
12
59
51
27
Explanation
In the first sample test case, the odometer skipped the number 3 and displayed 4 after it. Hence, the numbers were displayed in the order of [1, 2, 4, 5] accounting to distance of four kilometers travelled.
In the second sample test case, the sequence in which odometer displayed numbers would be [1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14] and it skipped [3, 13]. Thus, a total of 12 kilometers were travelled.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4\\n6 7 1 4 13 16 10 9 5 11 12 14 15 2 3 8\", \"6\\n11 21 35 22 7 36 27 34 8 20 15 13 16 1 24 3 2 17 26 9 18 32 31 23 19 14 4 25 10 29 28 33 12 6 5 30\", \"3\\n1 3 7 9 5 4 8 6 2\", \"3\\n2 3 7 9 5 4 8 6 1\", \"3\\n1 3 7 9 5 8 4 6 2\", \"3\\n1 6 7 9 5 4 8 3 2\", \"3\\n2 4 7 9 5 3 8 6 1\", \"3\\n1 3 7 9 4 8 5 6 2\", \"3\\n2 3 7 9 5 4 8 6 1\"], \"outputs\": [\"3\", \"11\", \"1\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Tonight, in your favourite cinema they are giving the movie Joker and all seats are occupied. In the cinema there are N rows with N seats each, forming an N\times N square. We denote with 1, 2,\dots, N the viewers in the first row (from left to right); with N+1, \dots, 2N the viewers in the second row (from left to right); and so on until the last row, whose viewers are denoted by N^2-N+1,\dots, N^2.
At the end of the movie, the viewers go out of the cinema in a certain order: the i-th viewer leaving her seat is the one denoted by the number P_i. The viewer P_{i+1} waits until viewer P_i has left the cinema before leaving her seat. To exit from the cinema, a viewer must move from seat to seat until she exits the square of seats (any side of the square is a valid exit). A viewer can move from a seat to one of its 4 adjacent seats (same row or same column). While leaving the cinema, it might be that a certain viewer x goes through a seat currently occupied by viewer y; in that case viewer y will hate viewer x forever. Each viewer chooses the way that minimizes the number of viewers that will hate her forever.
Compute the number of pairs of viewers (x, y) such that y will hate x forever.
Constraints
* 2 \le N \le 500
* The sequence P_1, P_2, \dots, P_{N^2} is a permutation of \\{1, 2, \dots, N^2\\}.
Input
The input is given from Standard Input in the format
N
P_1 P_2 \cdots P_{N^2}
Output
If ans is the number of pairs of viewers described in the statement, you should print on Standard Output
ans
Output
If ans is the number of pairs of viewers described in the statement, you should print on Standard Output
ans
Examples
Input
3
1 3 7 9 5 4 8 6 2
Output
1
Input
4
6 7 1 4 13 16 10 9 5 11 12 14 15 2 3 8
Output
3
Input
6
11 21 35 22 7 36 27 34 8 20 15 13 16 1 24 3 2 17 26 9 18 32 31 23 19 14 4 25 10 29 28 33 12 6 5 30
Output
11
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
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|
We have a connected undirected graph with N vertices and M edges. Edge i in this graph (1 \leq i \leq M) connects Vertex U_i and Vertex V_i bidirectionally. We are additionally given N integers D_1, D_2, ..., D_N.
Determine whether the conditions below can be satisfied by assigning a color - white or black - to each vertex and an integer weight between 1 and 10^9 (inclusive) to each edge in this graph. If the answer is yes, find one such assignment of colors and integers, too.
* There is at least one vertex assigned white and at least one vertex assigned black.
* For each vertex v (1 \leq v \leq N), the following holds.
* The minimum cost to travel from Vertex v to a vertex whose color assigned is different from that of Vertex v by traversing the edges is equal to D_v.
Here, the cost of traversing the edges is the sum of the weights of the edges traversed.
Constraints
* 2 \leq N \leq 100,000
* 1 \leq M \leq 200,000
* 1 \leq D_i \leq 10^9
* 1 \leq U_i, V_i \leq N
* The given graph is connected and has no self-loops or multiple edges.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
D_1 D_2 ... D_N
U_1 V_1
U_2 V_2
\vdots
U_M V_M
Output
If there is no assignment satisfying the conditions, print a single line containing `-1`.
If such an assignment exists, print one such assignment in the following format:
S
C_1
C_2
\vdots
C_M
Here,
* the first line should contain the string S of length N. Its i-th character (1 \leq i \leq N) should be `W` if Vertex i is assigned white and `B` if it is assigned black.
* The (i + 1)-th line (1 \leq i \leq M) should contain the integer weight C_i assigned to Edge i.
Examples
Input
5 5
3 4 3 5 7
1 2
1 3
3 2
4 2
4 5
Output
BWWBB
4
3
1
5
2
Input
5 7
1 2 3 4 5
1 2
1 3
1 4
2 3
2 5
3 5
4 5
Output
-1
Input
4 6
1 1 1 1
1 2
1 3
1 4
2 3
2 4
3 4
Output
BBBW
1
1
1
2
1
1
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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14\\nC1 L1 24\\n2 1 4 6\\n100 70\\nH L1 3\\nC1 L1 12\\nB1 D 11\\nC2 M1 20\\nC1 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n68\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 31\\n2 1 8 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 6\\nC2 D 15\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n35\\nH L1 10\\nC1 D 2\\nC1 H 18\\nL1 D 24\\nC1 L1 24\\n2 1 3 6\\n100 70\\nH L1 5\\nC1 L1 12\\nB1 D 11\\nC3 L1 10\\nC2 D 0\\nL1 D 8\\n0 0 0 0\", \"1 1 2 5\\n50\\nH L1 5\\nC1 D 2\\nC1 H 12\\nL1 D 10\\nC1 L2 20\\n2 2 4 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 14\\nC2 L1 7\\nC2 D 10\\nL1 D 5\\n0 0 0 0\", \"1 1 4 5\\n68\\nH L1 5\\nC1 D 6\\nC1 H 12\\nL1 D 10\\nC1 L1 31\\n2 1 8 6\\n100 70\\nH L1 5\\nC1 L1 12\\nC1 D 11\\nC2 L1 6\\nC2 D 15\\nL1 D 8\\n0 0 0 0\"], \"outputs\": [\"1\\n-2\", \"1\\n-2\\n\", \"-13\\n-2\\n\", \"1\\n-41\\n\", \"1\\n12\\n\", \"1\\n-58\\n\", \"1\\n-22\\n\", \"-7\\n-22\\n\", \"1\\n-12\\n\", \"1\\n-6\\n\", \"-1\\n-2\\n\", \"7\\n-12\\n\", \"7\\n-4\\n\", \"7\\n4\\n\", \"1\\n-16\\n\", \"1\\n6\\n\", \"1\\n-74\\n\", \"1\\n-26\\n\", \"7\\n-84\\n\", \"7\\n-20\\n\", \"7\\n0\\n\", \"1\\n104\\n\", \"1\\n-13\\n\", \"7\\n-16\\n\", \"11\\n-74\\n\", \"-5\\n-22\\n\", \"-15\\n-84\\n\", \"1\\n14\\n\", \"11\\n-68\\n\", \"13\\n-22\\n\", \"-15\\n-96\\n\", \"11\\n-52\\n\", \"1\\n-66\\n\", \"1\\n68\\n\", \"1\\n-59\\n\", \"7\\n58\\n\", \"7\\n10\\n\", \"1\\n18\\n\", \"1\\n46\\n\", \"1\\n-30\\n\", \"7\\n-53\\n\", \"1\\n-68\\n\", \"1\\n-9\\n\", \"1\\n2\\n\", \"7\\n16\\n\", \"-15\\n-74\\n\", \"7\\n-52\\n\", \"-7\\n-2\\n\", \"1\\n-55\\n\", \"43\\n58\\n\", \"7\\n30\\n\", \"-7\\n-12\\n\", \"1\\n-28\\n\", \"7\\n38\\n\", \"1\\n-64\\n\", \"11\\n-64\\n\", \"11\\n-76\\n\", \"-32\\n-2\\n\", \"-13\\n-18\\n\", \"1\\n-125\\n\", \"-1\\n10\\n\", \"7\\n-136\\n\", \"-13\\n-16\\n\", \"1\\n22\\n\", \"5\\n-22\\n\", \"1\\n-38\\n\", \"1\\n-3\\n\", \"7\\n-28\\n\", \"1\\n4\\n\", \"11\\n-60\\n\", \"12\\n-2\\n\", \"-7\\n-26\\n\", \"-1\\n58\\n\", \"7\\n7\\n\", \"1\\n34\\n\", \"1\\n-15\\n\", \"1\\n-39\\n\", \"-7\\n10\\n\", \"-1\\n-22\\n\", \"23\\n-28\\n\", \"-32\\n-10\\n\", \"-7\\n-18\\n\", \"1\\n10\\n\", \"-13\\n12\\n\", \"-32\\n-38\\n\", \"-5\\n-46\\n\", \"-7\\n-34\\n\", \"-1\\n104\\n\", \"-20\\n7\\n\", \"-35\\n-15\\n\", \"-1\\n-48\\n\", \"23\\n-24\\n\", \"37\\n-125\\n\", \"7\\n-196\\n\", \"-1\\n-46\\n\", \"5\\n104\\n\", \"-1\\n-56\\n\", \"-32\\n104\\n\", \"5\\n-59\\n\", \"-22\\n10\\n\", \"4\\n104\\n\"]}", "source": "primeintellect"}
|
Mr. A loves sweets, but recently his wife has told him to go on a diet. One day, when Mr. A went out from his home to the city hall, his wife recommended that he go by bicycle. There, Mr. A reluctantly went out on a bicycle, but Mr. A, who likes sweets, came up with the idea of stopping by a cake shop on the way to eat cake.
If you ride a bicycle, calories are consumed according to the mileage, but if you eat cake, you will consume that much calories. The net calories burned is the calories burned on the bike minus the calories burned by eating the cake. Therefore, the net calories burned may be less than zero.
If you buy a cake at a cake shop, Mr. A will eat all the cake on the spot. Mr. A does not stop at all cake shops, but when he passes through the point where the cake shop exists, he always stops and buys and eats one cake. However, it's really tempting to pass in front of the same cake shop many times, so each cake shop should only be visited once. In addition, you may stop by the cake shop after passing the destination city hall, and then return to the city hall to finish your work, and you may visit as many times as you like except the cake shop.
Enter the map information from Mr. A's home to the city hall, a list of calories of cakes that can be eaten at the cake shop on the way, and the calories burned by traveling a unit distance, from leaving home to entering the city hall. Create a program that outputs the minimum net calories burned.
The map shows Mr. A's home and city hall, a cake shop and a landmark building. The input data representing the map contains a line consisting of a symbol representing the two points and the distance between them, when there is a road connecting Mr. A's home, city hall, cake shop and each point of the landmark. For example, if the distance between the 5th cake shop and the 3rd landmark is 10, the input data will contain a line similar to the following:
C5 L3 10
In this way, cake shops are represented by C, and landmarks are represented by L in front of the number. Also, Mr. A's home is represented by H and the city hall is represented by D. If the input data is given two points and the distance between them, advance between the two points in either direction. For example, in the example above, you can go from a cake shop to a landmark and vice versa. In addition, you must be able to reach the city hall from your home. Other input data given are the number of cake shops m, the number of landmarks n, the calories burned per unit distance k, and the cakes that can be bought at each of the first cake shop to the mth cake shop. The total number of m data representing calories and distance data d.
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by four 0 lines. Each dataset is given in the following format:
m n k d
c1 c2 ... cm
s1 t1 e1
s2 t2 e2
::
sd td ed
Number of cake shops m (1 ≤ m ≤ 6), number of landmarks n (1 ≤ n ≤ 100), calories burned per unit distance k (1 ≤ k ≤ 5), distance data on the first line The total number d (5 ≤ d ≤ 256) is given.
The second line gives the calories ci (1 ≤ ci ≤ 100) of the cake you buy at each cake shop.
The following d line is given the distance data si, ti, ei (1 ≤ ei ≤ 20) between the i-th two points.
The number of datasets does not exceed 100.
Output
Outputs the minimum total calories burned on one line for each input dataset.
Example
Input
1 1 2 5
35
H L1 5
C1 D 6
C1 H 12
L1 D 10
C1 L1 20
2 1 4 6
100 70
H L1 5
C1 L1 12
C1 D 11
C2 L1 7
C2 D 15
L1 D 8
0 0 0 0
Output
1
-2
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"15 15\\n1 2 45\\n2 3 81\\n1 4 29\\n1 5 2\\n5 6 25\\n4 7 84\\n7 8 56\\n4 9 2\\n4 10 37\\n7 11 39\\n1 12 11\\n11 13 6\\n3 14 68\\n2 15 16\\n10 13 14\\n13 14 15\\n2 14 15\\n7 12 15\\n10 14 15\\n9 10 15\\n9 14 15\\n8 13 15\\n5 6 13\\n11 13 15\\n12 13 14\\n2 3 10\\n5 13 15\\n10 11 14\\n6 8 11\", \"5 3\\n1 2 1\\n2 3 1\\n3 4 1\\n4 5 1\\n1 2 3\\n1 3 5\\n1 2 4\", \"5 4\\n1 2 3\\n2 3 4\\n2 4 2\\n4 5 3\\n1 3 4\\n1 4 5\\n1 2 3\\n2 4 5\", \"5 4\\n1 4 3\\n2 3 4\\n2 4 2\\n4 5 3\\n1 3 4\\n1 4 5\\n1 2 3\\n2 4 5\", \"5 4\\n1 4 0\\n2 3 4\\n2 4 2\\n4 5 3\\n1 3 4\\n1 4 5\\n1 2 3\\n2 4 5\", \"5 3\\n1 2 1\\n2 3 1\\n3 4 2\\n4 5 1\\n1 2 3\\n1 3 5\\n1 2 4\", \"15 15\\n1 2 45\\n2 3 81\\n1 4 29\\n1 5 2\\n1 6 25\\n4 7 84\\n7 8 56\\n4 9 2\\n4 10 37\\n7 11 39\\n1 12 11\\n11 13 6\\n3 14 68\\n2 15 16\\n10 13 14\\n13 14 15\\n2 14 15\\n7 12 15\\n10 14 15\\n9 10 15\\n9 14 15\\n8 13 15\\n5 6 13\\n11 13 15\\n12 13 14\\n2 3 10\\n5 13 15\\n10 11 14\\n6 8 11\", \"5 3\\n1 2 1\\n2 3 0\\n3 4 1\\n4 5 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\"194\\n128\\n126\\n97\\n149\\n111\\n149\\n169\\n129\\n158\\n194\\n66\\n115\\n194\\n140\\n\", \"4\\n2\\n4\\n\", \"149\\n149\\n56\\n61\\n149\\n66\\n149\\n90\\n56\\n89\\n149\\n111\\n89\\n149\\n57\\n\", \"149\\n149\\n26\\n47\\n149\\n60\\n127\\n74\\n56\\n61\\n149\\n44\\n61\\n149\\n57\\n\", \"192\\n129\\n97\\n66\\n66\\n66\\n141\\n140\\n129\\n129\\n137\\n111\\n129\\n192\\n153\\n\", \"141\\n70\\n97\\n137\\n66\\n66\\n141\\n165\\n117\\n70\\n141\\n111\\n45\\n141\\n153\\n\", \"147\\n142\\n141\\n142\\n142\\n66\\n141\\n142\\n129\\n6\\n129\\n81\\n129\\n147\\n84\\n\", \"141\\n126\\n140\\n142\\n126\\n66\\n141\\n142\\n83\\n126\\n92\\n81\\n83\\n141\\n84\\n\", \"194\\n194\\n97\\n90\\n149\\n66\\n149\\n140\\n129\\n129\\n194\\n111\\n129\\n194\\n113\\n\", \"149\\n194\\n97\\n90\\n149\\n66\\n149\\n140\\n129\\n129\\n129\\n111\\n129\\n194\\n138\\n\", \"5\\n7\\n4\\n3\\n\", \"5\\n3\\n3\\n2\\n\"]}", "source": "primeintellect"}
|
You are a teacher at Iazu High School is the Zuia Kingdom. There are $N$ cities and $N-1$ roads connecting them that allow you to move from one city to another by way of more than one road. Each of the roads allows bidirectional traffic and has a known length.
As a part of class activities, you are planning the following action assignment for your students. First, you come up with several themes commonly applicable to three different cities. Second, you assign each of the themes to a group of three students. Then, each student of a group is assigned to one of the three cities and conducts a survey on it. Finally, all students of the group get together in one of the $N$ cities and compile their results.
After a theme group has completed its survey, the three members move from the city on which they studied to the city for getting together. The longest distance they have to travel for getting together is defined as the cost of the theme. You want to select the meeting city so that the cost for each theme becomes minimum.
Given the number of cities, road information and $Q$ sets of three cities for each theme, make a program to work out the minimum cost for each theme.
Input
The input is given in the following format.
$N$ $Q$
$u_1$ $v_1$ $w_1$
$u_2$ $v_2$ $w_2$
$...$
$u_{N-1}$ $v_{N-1}$ $w_{N-1}$
$a_1$ $b_1$ $c_1$
$a_2$ $b_2$ $c_2$
$...$
$a_Q$ $b_Q$ $c_Q$
The first line provides the number of cities in the Zuia Kingdom $N$ ($3 \leq N \leq 100,000$) and the number of themes $Q$ ($1 \leq Q \leq 100,000$). Each of the subsequent $N-1$ lines provides the information regarding the $i$-th road $u_i,v_i,w_i$ ($ 1 \leq u_i < v_i \leq N, 1 \leq w_i \leq 10,000$), indicating that the road connects cities $u_i$ and $v_i$, and the road distance between the two is $w_i$. Each of the $Q$ lines that follows the above provides the three cities assigned to the $i$-th theme: $a_i,b_i,c_i$ ($1 \leq a_i < b_i < c_i \leq N$).
Output
For each theme, output the cost in one line.
Examples
Input
5 4
1 2 3
2 3 4
2 4 2
4 5 3
1 3 4
1 4 5
1 2 3
2 4 5
Output
4
5
4
3
Input
5 3
1 2 1
2 3 1
3 4 1
4 5 1
1 2 3
1 3 5
1 2 4
Output
1
2
2
Input
15 15
1 2 45
2 3 81
1 4 29
1 5 2
5 6 25
4 7 84
7 8 56
4 9 2
4 10 37
7 11 39
1 12 11
11 13 6
3 14 68
2 15 16
10 13 14
13 14 15
2 14 15
7 12 15
10 14 15
9 10 15
9 14 15
8 13 15
5 6 13
11 13 15
12 13 14
2 3 10
5 13 15
10 11 14
6 8 11
Output
194
194
97
90
149
66
149
140
129
129
194
111
129
194
140
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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4\", \"4 4\\nIN 2 1 1\\nIN 3 1 3\\nCOMPARE 1 3\\nCOMPARE 2 3\", \"10 4\\nIN 10 8 4408\\nIN 8 4 3765\\nIN 3 4 40\\nCOMPARE 4 8\", \"3 4\\nIN 1 2 1\\nIN 3 1 12\\nCOMPARE 1 3\\nCOMPARE 2 3\", \"10 4\\nIN 6 8 802\\nIN 8 4 5968\\nIN 3 11 977\\nCOMPARE 6 8\", \"8 4\\nIN 2 1 1\\nIN 1 1 0\\nCOMPARE 2 1\\nCOMPARE 2 3\", \"6 4\\nIN 2 1 1\\nIN 1 1 2\\nCOMPARE 1 3\\nCOMPARE 2 1\", \"10 4\\nIN 6 8 802\\nIN 8 4 867\\nIN 6 8 574\\nCOMPARE 4 8\", \"4 3\\nIN 1 4 25\\nIN 3 5 20\\nCOMPARE 1 4\", \"5 4\\nIN 3 1 3\\nIN 5 1 4\\nCOMPARE 2 3\\nCOMPARE 1 3\", \"10 4\\nIN 7 8 802\\nIN 8 4 2581\\nIN 6 8 574\\nCOMPARE 4 8\", \"3 4\\nIN 2 1 3\\nIN 3 1 4\\nCOMPARE 2 3\\nCOMPARE 1 3\", \"10 4\\nIN 10 8 2644\\nIN 8 4 3946\\nIN 3 8 138\\nCOMPARE 4 8\", \"4 3\\nIN 2 4 10\\nIN 2 3 20\\nCOMPARE 2 4\", \"8 4\\nIN 2 1 1\\nIN 1 1 1\\nCOMPARE 2 1\\nCOMPARE 2 3\", \"5 5\\nCOMPARE 1 2\\nIN 1 4 6\\nIN 2 2 2\\nCOMPARE 2 2\\nCOMPARE 1 3\", \"5 4\\nIN 3 1 3\\nIN 5 1 1\\nCOMPARE 2 3\\nCOMPARE 1 3\", \"20 4\\nIN 10 12 2407\\nIN 8 4 5780\\nIN 4 8 75\\nCOMPARE 4 8\", \"4 3\\nIN 1 4 18\\nIN 2 2 5\\nCOMPARE 1 4\", \"10 4\\nIN 6 2 802\\nIN 8 4 5968\\nIN 3 11 977\\nCOMPARE 6 2\", \"10 4\\nIN 6 4 1041\\nIN 8 4 7322\\nIN 4 8 977\\nCOMPARE 4 8\", \"5 4\\nIN 3 1 2\\nIN 3 1 2\\nCOMPARE 1 3\\nCOMPARE 2 3\", \"4 3\\nIN 1 3 10\\nIN 3 3 20\\nCOMPARE 1 1\", \"4 3\\nIN 1 3 10\\nIN 3 3 10\\nCOMPARE 1 1\", \"4 3\\nIN 1 3 10\\nIN 2 3 10\\nCOMPARE 1 1\", \"4 3\\nIN 1 3 1\\nIN 2 3 10\\nCOMPARE 1 1\", \"3 3\\nCOMPARE 1 2\\nIN 1 2 6\\nIN 2 3 3\\nCOMPARE 2 3\\nCOMPARE 1 3\", \"5 4\\nIN 3 1 2\\nIN 3 1 2\\nCOMPARE 2 4\\nCOMPARE 2 3\", \"4 3\\nIN 1 4 9\\nIN 2 1 20\\nCOMPARE 1 2\", \"6 3\\nIN 1 4 10\\nIN 3 3 20\\nCOMPARE 1 1\", \"4 3\\nIN 1 5 10\\nIN 3 3 20\\nCOMPARE 1 1\", \"4 3\\nIN 1 3 10\\nIN 3 3 10\\nCOMPARE 2 1\", \"4 3\\nIN 1 5 10\\nIN 2 3 10\\nCOMPARE 1 1\", \"3 4\\nIN 2 1 2\\nIN 3 1 0\\nCOMPARE 2 3\\nCOMPARE 2 3\", \"3 3\\nCOMPARE 1 2\\nIN 1 2 8\\nIN 2 3 3\\nCOMPARE 2 3\\nCOMPARE 1 3\", \"4 3\\nIN 1 3 10\\nIN 3 4 10\\nCOMPARE 2 1\", \"2 3\\nIN 1 5 10\\nIN 2 3 10\\nCOMPARE 1 1\", \"3 3\\nCOMPARE 1 2\\nIN 1 2 9\\nIN 2 3 3\\nCOMPARE 2 3\\nCOMPARE 1 3\", \"6 3\\nIN 1 3 10\\nIN 3 4 10\\nCOMPARE 2 1\", \"3 4\\nCOMPARE 1 2\\nIN 1 2 9\\nIN 2 1 3\\nCOMPARE 2 3\\nCOMPARE 1 3\", \"3 3\\nIN 1 1 0\\nIN 3 1 6\\nCOMPARE 1 3\\nCOMPARE 2 5\", \"3 4\\nCOMPARE 2 2\\nIN 1 2 9\\nIN 2 1 3\\nCOMPARE 2 3\\nCOMPARE 2 3\"], \"outputs\": [\"WARNING\", \"-3191\", \"WARNING\\n3\\n11\", \"-2\\n2\", \"15\\n10\", \"-2\\n1\\n\", \"WARNING\\n\", \"-3725\\n\", \"WARNING\\n3\\n12\\n\", \"-5\\n15\\n\", \"-1\\nWARNING\\n\", \"-2\\nWARNING\\n\", \"WARNING\\nWARNING\\n\", \"-20\\n\", \"WARNING\\n3\\n0\\n\", \"-2\\n0\\n\", \"0\\n\", \"WARNING\\n2\\n0\\n\", \"10\\n\", \"-3191\\n\", \"2\\n2\\n\", \"-3722\\n\", \"-2\\n2\\n\", \"-3\\n0\\n\", \"WARNING\\n2\\n\", \"-6\\n0\\n\", \"WARNING\\n1\\n\", \"-6\\nWARNING\\n\", \"WARNING\\n3\\n\", \"0\\n1\\n\", \"-6\\n\", \"0\\n0\\n\", \"0\\nWARNING\\n\", \"3\\n0\\n\", \"WARNING\\n0\\n5\\n\", \"-5\\n\", \"-12\\n0\\n\", \"-2788\\n\", \"5544\\n\", \"1\\n1\\n\", \"4567\\n\", \"WARNING\\n2\\n10\\n\", \"0\\n2\\n\", \"2\\n0\\n\", \"-4\\nWARNING\\n\", \"-8\\n\", \"-3431\\n\", \"WARNING\\n0\\n3\\n\", \"14\\n\", \"-6345\\n\", \"-3471\\n\", \"1376\\n\", \"-3694\\n\", \"WARNING\\n0\\n\", \"1779\\n\", \"WARNING\\n2\\nWARNING\\n\", \"WARNING\\n-3\\n\", \"-3765\\n\", \"-3627\\n\", \"14\\n10\\n\", \"0\\n-2\\n\", \"-3\\nWARNING\\n\", \"WARNING\\nWARNING\\nWARNING\\n\", \"9\\n\", \"-3\\n1\\n\", \"-3805\\n\", \"-12\\n-1\\n\", \"6770\\n\", \"1\\nWARNING\\n\", \"WARNING\\n5\\n\", \"-293\\n\", \"25\\n\", \"WARNING\\n-7\\n\", \"-2007\\n\", \"3\\n-4\\n\", \"-3808\\n\", \"-10\\n\", \"3\\nWARNING\\n\", \"WARNING\\n0\\nWARNING\\n\", \"WARNING\\n-4\\n\", \"-5780\\n\", \"18\\n\", \"802\\n\", \"-7322\\n\", \"-2\\nWARNING\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"WARNING\\n\", \"WARNING\\nWARNING\\n\", \"-20\\n\", \"0\\n\", \"0\\n\", \"WARNING\\n\", \"0\\n\", \"2\\n2\\n\", \"WARNING\\n\", \"WARNING\\n\", \"0\\n\", \"WARNING\\n\", \"WARNING\\n\", \"WARNING\\nWARNING\\n\", \"-6\\n\", \"0\\nWARNING\\n\"]}", "source": "primeintellect"}
|
Problem
In 20XX, a scientist developed a powerful android with biotechnology. This android is extremely powerful because it is made by a computer by combining the cells of combat masters.
At this rate, the earth would be dominated by androids, so the N warriors decided to fight the androids. However, today's warriors are no match for androids, so they have to practice. Also, each of the N warriors is numbered 1 to N.
At this time, the sky city AIZU had a special room for training called the SRLU room. A year in this room is the same as a day in the outside world, so you can significantly increase your fighting power in a short period of time. The maximum number of people that can enter a room at the same time is two. Also, when the two enter the room, their fighting power will increase.
The warriors asked you to write a program to handle the following queries to see how they would enter the room in the time left.
The given query is as follows.
In addition, A and B appearing in the following explanation represent the warrior numbers, respectively. A and B are never equal.
IN A B C
A and B enter the room, and their fighting power increases by C respectively. At this time, (combat power of B just before entering the room)-(combat power of A just before entering the room) = C holds. Also, at this time, the combat power of B is guaranteed to be higher than the combat power of A.
COMPARE A B
Outputs the difference in combat power between A and B (current combat power of B)-(current combat power of A). If the difference cannot be identified, output WARNING.
Constraints
The input satisfies the following conditions.
* 2 ≤ N ≤ 100000
* 1 ≤ Q ≤ 100000
* 1 ≤ A, B ≤ N
* 1 ≤ C ≤ 5000
Input
N Q
query1
..
..
..
queryQ
First, the number of warriors N and the number of queries Q are given.
Then the query is given only Q times.
Output
It processes the given queries in order as described above, and outputs when the input of COMPARE is given.
Examples
Input
3 5
COMPARE 1 2
IN 1 2 5
IN 2 3 3
COMPARE 2 3
COMPARE 1 3
Output
WARNING
3
11
Input
4 3
IN 1 4 10
IN 2 3 20
COMPARE 1 2
Output
WARNING
Input
3 4
IN 2 1 2
IN 3 1 2
COMPARE 1 3
COMPARE 2 3
Output
-2
2
Input
10 4
IN 10 8 2328
IN 8 4 3765
IN 3 8 574
COMPARE 4 8
Output
-3191
Input
3 5
IN 1 2 5
IN 1 2 5
IN 2 3 10
COMPARE 1 2
COMPARE 2 3
Output
15
10
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\n4 0 1 2 3 4\\n2 0 2 1\\n0\", \"2\\n4 0 1 2 3 4\\n2 -1 2 1\\n0\", \"2\\n4 0 1 2 3 4\\n2 1 1 1\\n0\", \"2\\n4 0 2 2 3 8\\n2 -1 2 2\\n0\", \"2\\n4 0 1 1 3 0\\n2 1 1 1\\n0\", \"2\\n4 0 1 2 0 8\\n2 0 2 1\\n0\", \"2\\n4 0 1 2 0 8\\n2 1 3 2\\n0\", \"2\\n4 0 1 2 0 5\\n2 1 3 0\\n0\", \"2\\n4 0 1 2 0 4\\n2 1 3 0\\n0\", \"2\\n4 0 0 2 0 3\\n2 2 2 0\\n0\", \"2\\n4 0 1 1 0 0\\n2 1 1 1\\n0\", \"2\\n4 0 1 2 0 13\\n2 0 2 2\\n0\", \"2\\n4 0 0 1 0 8\\n2 1 4 2\\n0\", \"2\\n4 0 0 0 0 8\\n2 1 6 3\\n0\", \"2\\n4 0 1 2 3 4\\n2 -1 2 2\\n0\", \"2\\n4 0 1 2 3 4\\n2 1 2 1\\n0\", \"2\\n4 0 1 1 3 4\\n2 -1 2 2\\n0\", \"2\\n4 0 1 2 2 4\\n2 0 2 1\\n0\", \"2\\n4 0 2 2 3 4\\n2 -1 2 2\\n0\", \"2\\n4 0 1 1 3 4\\n2 1 1 1\\n0\", \"2\\n4 0 1 2 0 4\\n2 0 2 1\\n0\", \"2\\n4 0 2 2 5 8\\n2 -1 2 2\\n0\", \"2\\n4 0 1 2 0 8\\n2 0 2 2\\n0\", \"2\\n4 0 2 1 5 8\\n2 -1 2 2\\n0\", \"2\\n4 0 1 2 0 8\\n2 0 3 2\\n0\", \"2\\n4 0 1 2 0 8\\n2 1 3 0\\n0\", \"2\\n4 0 1 2 0 4\\n2 2 3 0\\n0\", \"2\\n4 0 1 0 0 4\\n2 2 3 0\\n0\", \"2\\n4 0 1 0 0 4\\n2 2 2 0\\n0\", \"2\\n4 0 1 2 4 4\\n2 0 2 1\\n0\", \"2\\n4 0 1 2 5 4\\n2 -1 2 1\\n0\", \"2\\n4 0 2 2 3 4\\n2 1 2 1\\n0\", \"2\\n4 0 1 0 3 4\\n2 -1 2 2\\n0\", \"2\\n4 0 1 3 3 4\\n2 1 1 1\\n0\", \"2\\n4 0 1 2 2 8\\n2 0 2 1\\n0\", \"2\\n4 0 3 2 3 4\\n2 -1 2 2\\n0\", \"2\\n4 0 0 1 3 4\\n2 1 1 1\\n0\", \"2\\n4 0 1 2 1 4\\n2 0 2 1\\n0\", \"2\\n4 0 1 0 3 0\\n2 1 1 1\\n0\", \"2\\n4 0 0 2 0 8\\n2 0 2 1\\n0\", \"2\\n4 0 2 2 5 8\\n2 -1 1 2\\n0\", \"2\\n4 0 1 4 0 8\\n2 0 2 2\\n0\", \"2\\n4 0 0 2 0 8\\n2 1 3 2\\n0\", \"2\\n4 0 1 4 0 4\\n2 1 3 0\\n0\", \"2\\n4 0 1 2 0 4\\n2 2 2 0\\n0\", \"2\\n4 0 0 0 0 4\\n2 2 2 0\\n0\", \"2\\n4 0 1 2 4 4\\n2 0 2 2\\n0\", \"2\\n4 0 1 2 5 4\\n2 -1 3 1\\n0\", \"2\\n4 0 2 2 3 2\\n2 1 2 1\\n0\", \"2\\n4 0 1 0 3 4\\n2 0 2 2\\n0\", \"2\\n4 0 1 3 3 4\\n2 1 1 0\\n0\", \"2\\n4 0 1 2 3 4\\n2 -1 3 2\\n0\", \"2\\n4 0 1 0 3 0\\n2 0 1 1\\n0\", \"2\\n4 0 2 2 5 10\\n2 -1 1 2\\n0\", \"2\\n4 0 0 1 0 8\\n2 1 3 2\\n0\", \"2\\n4 0 1 4 -1 4\\n2 1 3 0\\n0\", \"2\\n4 0 0 2 0 4\\n2 2 2 0\\n0\", \"2\\n4 0 1 3 6 4\\n2 1 1 0\\n0\", \"2\\n4 1 1 2 3 4\\n2 -1 3 2\\n0\", \"2\\n4 0 0 0 0 8\\n2 1 3 2\\n0\", \"2\\n5 0 1 4 -1 4\\n2 1 3 0\\n0\", \"2\\n4 0 1 3 6 4\\n2 2 1 0\\n0\", \"2\\n4 0 0 0 0 8\\n2 1 3 3\\n0\", \"2\\n5 0 1 4 -1 4\\n2 1 3 1\\n0\", \"2\\n4 0 -1 0 0 8\\n2 1 3 3\\n0\", \"2\\n5 0 1 4 -1 4\\n2 1 4 1\\n0\", \"2\\n4 0 -1 -1 0 8\\n2 1 3 3\\n0\", \"2\\n4 0 -2 -1 0 8\\n2 1 3 3\\n0\", \"2\\n4 1 1 2 3 4\\n2 0 2 1\\n0\", \"2\\n4 0 1 2 3 8\\n2 -1 2 1\\n0\", \"2\\n4 0 1 2 3 4\\n2 1 2 2\\n0\", \"2\\n4 0 1 1 0 4\\n2 -1 2 2\\n0\", \"2\\n4 0 1 2 3 4\\n2 0 1 1\\n0\", \"2\\n4 0 2 2 3 4\\n2 -1 2 0\\n0\", \"2\\n4 0 1 2 0 3\\n2 0 2 1\\n0\", \"2\\n4 0 1 2 0 8\\n2 2 3 0\\n0\", \"2\\n4 0 1 2 0 4\\n2 1 3 1\\n0\", \"2\\n4 0 1 2 0 2\\n2 2 3 0\\n0\", \"2\\n4 0 1 0 0 4\\n2 1 3 0\\n0\", \"2\\n4 0 1 1 0 4\\n2 2 2 0\\n0\", \"2\\n4 0 1 2 4 4\\n2 -1 2 1\\n0\", \"2\\n4 0 2 2 4 4\\n2 1 2 1\\n0\", \"2\\n4 0 1 0 3 4\\n2 -1 2 1\\n0\", \"2\\n4 0 1 3 3 7\\n2 1 1 1\\n0\", \"2\\n1 0 1 2 2 8\\n2 0 2 1\\n0\", \"2\\n4 0 3 1 3 4\\n2 -1 2 2\\n0\", \"2\\n4 0 1 2 1 1\\n2 0 2 1\\n0\", \"2\\n4 0 1 0 3 0\\n2 1 0 1\\n0\", \"2\\n4 0 0 0 0 8\\n2 0 2 1\\n0\", \"2\\n4 0 2 2 5 8\\n2 -1 1 1\\n0\", \"2\\n4 0 1 4 1 8\\n2 0 2 2\\n0\", \"2\\n4 0 0 2 0 8\\n2 2 3 2\\n0\", \"2\\n4 0 1 2 0 4\\n2 2 0 0\\n0\", \"2\\n4 0 0 1 0 4\\n2 2 2 0\\n0\", \"2\\n4 0 1 2 4 4\\n2 0 2 0\\n0\", \"2\\n4 0 1 1 5 4\\n2 -1 3 1\\n0\", \"2\\n4 0 0 2 3 2\\n2 1 2 1\\n0\", \"2\\n4 1 2 2 3 4\\n2 -1 3 2\\n0\", \"2\\n4 0 0 4 0 3\\n2 2 2 0\\n0\", \"2\\n4 0 1 3 6 4\\n2 2 1 -1\\n0\", \"2\\n5 0 1 0 -1 4\\n2 1 3 1\\n0\"], \"outputs\": [\"5\", \"6\\n\", \"5\\n\", \"10\\n\", \"4\\n\", \"9\\n\", \"11\\n\", \"8\\n\", \"7\\n\", \"3\\n\", \"2\\n\", \"15\\n\", \"12\\n\", \"14\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"5\\n\", \"6\\n\", \"5\\n\", \"5\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"10\\n\", \"11\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"5\\n\", \"9\\n\", \"6\\n\", \"5\\n\", \"5\\n\", \"4\\n\", \"9\\n\", \"9\\n\", \"10\\n\", \"11\\n\", \"7\\n\", \"4\\n\", \"4\\n\", \"6\\n\", \"7\\n\", \"4\\n\", \"6\\n\", \"5\\n\", \"7\\n\", \"4\\n\", \"11\\n\", \"11\\n\", \"7\\n\", \"4\\n\", \"6\\n\", \"6\\n\", \"11\\n\", \"4\\n\", \"7\\n\", \"11\\n\", \"5\\n\", \"11\\n\", \"5\\n\", \"11\\n\", \"11\\n\", \"6\\n\", \"10\\n\", \"6\\n\", \"6\\n\", \"5\\n\", \"6\\n\", \"4\\n\", \"8\\n\", \"7\\n\", \"4\\n\", \"7\\n\", \"4\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"8\\n\", \"9\\n\", \"6\\n\", \"3\\n\", \"4\\n\", \"9\\n\", \"9\\n\", \"10\\n\", \"10\\n\", \"4\\n\", \"4\\n\", \"6\\n\", \"7\\n\", \"4\\n\", \"6\\n\", \"4\\n\", \"7\\n\", \"5\\n\"]}", "source": "primeintellect"}
|
The volume of access to a web service varies from time to time in a day. Also, the hours with the highest volume of access varies from service to service. For example, a service popular in the United States may receive more access in the daytime in the United States, while another service popular in Japan may receive more access in the daytime in Japan. When you develop a web service, you have to design the system so it can handle all requests made during the busiest hours.
You are a lead engineer in charge of a web service in the 30th century. It’s the era of Galaxy Wide Web (GWW), thanks to the invention of faster-than-light communication. The service can be accessed from all over the galaxy. Thus many intelligent creatures, not limited to human beings, can use the service. Since the volume of access to your service is increasing these days, you have decided to reinforce the server system. You want to design a new system that handles requests well even during the hours with the highest volume of access. However, this is not a trivial task. Residents in each planet have their specific length of a day, say, a cycle of life. The length of a day is not always 24 hours. Therefore, a cycle of the volume of access are different by planets of users.
You have obtained hourly data of the volume of access for all planets where you provide the service. Assuming the volume of access follows a daily cycle for each planet, you want to know the highest volume of access in one hour. It should be a quite easy task for you, a famous talented engineer in the galaxy.
Input
The input consists of multiple datasets. Each dataset has the following format:
N
d1 t1 q1,0 ... q1,d1-1
...
dN tN qN,0 ... qN,dN-1
N is the number of planets. di (1 ≤ i ≤ N) is the length of a day in the planet i. ti (0 ≤ ti ≤ di - 1) is the current time of the planet i. qi, j is the volume of access on the planet i during from the j-th hour to the (j+1)-th hour.
You may assume that N ≤ 100, di ≤ 24, qi, j ≤ 1000000 (1 ≤ i ≤ N, 0 ≤ j ≤ di - 1).
The last dataset is followed by a line containing one zero. This line is not a part of any dataset and should not be processed.
Output
For each dataset, output the maximum volume of access in one hour in a line.
Example
Input
2
4 0 1 2 3 4
2 0 2 1
0
Output
5
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
I have a lot of friends. Every friend is very small.
I often go out with my friends. Put some friends in your backpack and go out together.
Every morning I decide which friends to go out with that day. Put friends one by one in an empty backpack.
I'm not very strong. Therefore, there is a limit to the weight of friends that can be carried at the same time.
I keep friends so that I don't exceed the weight limit. The order in which you put them in depends on your mood.
I won't stop as long as I still have friends to put in. I will never stop.
…… By the way, how many patterns are there in total for the combination of friends in the backpack?
Input
N W
w1
w2
..
..
..
wn
On the first line of input, the integer N (1 ≤ N ≤ 200) and the integer W (1 ≤ W ≤ 10,000) are written in this order, separated by blanks. The integer N represents the number of friends, and the integer W represents the limit of the weight that can be carried at the same time. It cannot be carried if the total weight is greater than W.
The next N lines contain an integer that represents the weight of the friend. The integer wi (1 ≤ wi ≤ 10,000) represents the weight of the i-th friend.
Output
How many possible combinations of friends are finally in the backpack? Divide the total number by 1,000,000,007 and output the remainder. Note that 1,000,000,007 are prime numbers.
Note that "no one is in the backpack" is counted as one.
Examples
Input
4 8
1
2
7
9
Output
2
Input
4 25
20
15
20
15
Output
4
Input
6 37
5
9
13
18
26
33
Output
6
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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\"5\\n5\\n4\\n2\\n0\\n\", \"0\\n7\\n7\\n\", \"0\\n12\\n0\\n0\\n\", \"2\\n10\\n0\\n0\\n4\\n0\\n10\\n6\\n6\\n\", \"0\\n0\\n0\\n0\\n7\\n0\\n0\\n6\\n0\\n\", \"11\\n0\\n0\\n\", \"0\\n5\\n3\\n2\\n0\\n\", \"0\\n0\\n0\\n0\\n4\\n16\\n9\\n6\\n0\\n\", \"0\\n0\\n0\\n0\\n4\\n0\\n0\\n0\\n\", \"5\\n\", \"0\\n5\\n6\\n2\\n0\\n\", \"0\\n7\\n0\\n0\\n\", \"0\\n0\\n0\\n0\\n\", \"0\\n5\\n0\\n4\\n0\\n\", \"0\\n0\\n0\\n0\\n4\\n16\\n9\\n0\\n0\\n\", \"5\\n5\\n\", \"0\\n5\\n6\\n0\\n0\\n\", \"0\\n5\\n6\\n\", \"11\\n0\\n\", \"0\\n7\\n7\\n0\\n0\\n\", \"0\\n0\\n0\\n0\\n7\\n0\\n0\\n0\\n0\\n\", \"2\\n0\\n8\\n0\\n4\\n16\\n\", \"0\\n5\\n5\\n4\\n0\\n\", \"0\\n11\\n\", \"0\\n7\\n6\\n\", \"0\\n5\\n4\\n0\\n\", \"0\\n5\\n5\\n0\\n0\\n\", \"0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n\", \"0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n0\\n\", \"7\\n5\\n6\\n0\\n0\\n\", \"7\\n11\\n\", \"2\\n0\\n8\\n0\\n4\\n0\\n\", \"0\\n5\\n3\\n0\\n0\\n\", \"5\\n4\\n\", \"0\\n4\\n4\\n0\\n\", \"2\\n10\\n0\\n0\\n4\\n16\\n10\\n6\\n6\\n\", \"2\\n0\\n8\\n0\\n0\\n0\\n\", \"0\\n0\\n0\\n0\\n4\\n0\\n9\\n0\\n0\\n\", \"6\\n4\\n\", \"0\\n4\\n6\\n0\\n\", \"2\\n10\\n0\\n0\\n0\\n16\\n10\\n6\\n6\\n\", \"0\\n4\\n\", \"2\\n10\\n0\\n0\\n0\\n16\\n10\\n6\\n0\\n\", \"2\\n0\\n0\\n\", \"0\\n5\\n7\\n0\\n0\\n\", \"0\\n0\\n0\\n0\\n4\\n0\\n18\\n0\\n0\\n\"]}", "source": "primeintellect"}
|
Given the string S and m queries. The i-th query is given by the two strings xi and yi.
For each query, answer the longest substring of the string S, starting with xi and ending with yi.
For the string S, | S | represents the length of S. Also, the fact that the character string T is a substring of the character string S means that a certain integer i exists and Tj = Si + j is satisfied for 1 ≤ j ≤ | T |. Where Tj represents the jth character of T.
Constraints
* 1 ≤ | S | ≤ 2 x 105
* 1 ≤ m ≤ 105
* 1 ≤ | xi |, | yi |
* $ \ sum ^ m_ {i = 1} $ (| xi | + | yi |) ≤ 2 x 105
* S and xi, yi consist only of half-width lowercase letters.
Input
The input is given in the following format.
S
m
x1 y1
x2 y2
::
xm ym
* The character string S is given on the first line.
* The number of queries m is given in the second line.
* Of the m lines from the 3rd line, the i-th query string xi, yi is given on the i-th line, separated by spaces.
Output
Answer the maximum substring length in the following format.
len1
len2
::
lenm
Output the longest substring length leni that satisfies the condition for the i-th query on the i-th line of the m lines from the first line. If there is no such substring, output 0.
Examples
Input
abracadabra
5
ab a
a a
b c
ac ca
z z
Output
11
11
4
3
0
Input
howistheprogress
4
ist prog
s ss
how is
the progress
Output
9
12
5
11
Input
icpcsummertraining
9
mm m
icpc summer
train ing
summer mm
i c
i i
g g
train i
summer er
Output
2
10
8
0
4
16
1
6
6
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
D: Arrow / Arrow
problem
rodea is in a one-dimensional coordinate system and stands at x = 0. From this position, throw an arrow of positive integer length that always moves at speed 1 towards the target at x = N. However, rodea is powerless, so we have decided to put a total of M blowers in the section 0 \ leq x \ leq N.
Here, the case where one blower is not included in the position from the tip to the base of the arrow is defined as "loss". The loss is determined when the tip of the arrow reaches x = 1, 2, 3, $ \ ldots $, N (that is, a total of N times).
At this time, process the following query Q times.
* "Loss" Given the acceptable number of times l_i. In other words, if the total "loss" is l_i times or less in N judgments, it is possible to deliver the arrow. At this time, find the shortest arrow length required to deliver the arrow.
Input format
N M
m_1 m_2 $ \ ldots $ m_M
Q
l_1 l_2 $ \ ldots $ l_Q
The distance N and the number of blowers M are given on the first line, separated by blanks.
The second line gives the position of each of the M blowers. When m_i = j, the i-th blower is located exactly between x = j-1 and x = j.
The third line gives the number of queries Q, and the fourth line gives Q the acceptable number of "losses" l_i.
Constraint
* 1 \ leq N \ leq 10 ^ 5
* 1 \ leq M \ leq N
* 1 \ leq m_1 <m_2 <$ \ ldots $ <m_M \ leq N
* 1 \ leq Q \ leq 10 ^ 5
* 0 \ leq l_i \ leq 10 ^ 5 (1 \ leq i \ leq Q)
Output format
Output the shortest possible arrow lengths for a given Q l_i, in order, with a newline.
However, if there is no arrow with a length of a positive integer that satisfies the condition, -1 shall be output.
Input example 1
5 1
2
1
3
Output example 1
2
When the tip of the arrow reaches x = 1, the number of "losses" is 1 because the blower is not included from the tip to the base.
When the tip of the arrow reaches x = 2, the number of "losses" remains 1 because the blower is included from the tip to the base.
When the tip of the arrow reaches x = 3, the number of "losses" remains 1 because the blower is included from the tip to the base.
When the tip of the arrow reaches x = 4, the number of "losses" is 2 because the blower is not included from the tip to the base.
When the tip of the arrow reaches x = 5, the number of "losses" is 3 because the blower is not included from the tip to the base.
When throwing an arrow shorter than length 2, the number of "losses" is greater than 3, so throwing an arrow of length 2 is the shortest arrow length that meets the condition.
Input example 2
11 3
2 5 9
3
1 4 8
Output example 2
Four
3
1
Example
Input
5 1
2
1
3
Output
2
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
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|
Ivan unexpectedly saw a present from one of his previous birthdays. It is array of n numbers from 1 to 200. Array is old and some numbers are hard to read. Ivan remembers that for all elements at least one of its neighbours ls not less than it, more formally:
a_{1} ≤ a_{2},
a_{n} ≤ a_{n-1} and
a_{i} ≤ max(a_{i-1}, a_{i+1}) for all i from 2 to n-1.
Ivan does not remember the array and asks to find the number of ways to restore it. Restored elements also should be integers from 1 to 200. Since the number of ways can be big, print it modulo 998244353.
Input
First line of input contains one integer n (2 ≤ n ≤ 10^{5}) — size of the array.
Second line of input contains n integers a_{i} — elements of array. Either a_{i} = -1 or 1 ≤ a_{i} ≤ 200. a_{i} = -1 means that i-th element can't be read.
Output
Print number of ways to restore the array modulo 998244353.
Examples
Input
3
1 -1 2
Output
1
Input
2
-1 -1
Output
200
Note
In the first example, only possible value of a_{2} is 2.
In the second example, a_{1} = a_{2} so there are 200 different values because all restored elements should be integers between 1 and 200.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4 4\\n1 2 1\\n2 3 1\\n3 4 1\\n\", \"4 6\\n1 2 0\\n1 3 0\\n1 4 0\\n\", \"3 5\\n1 2 1\\n2 3 0\\n\", \"4 19\\n2 4 1\\n2 3 0\\n1 4 0\\n\", \"13 3\\n9 13 1\\n8 3 1\\n11 9 0\\n8 13 0\\n10 9 0\\n2 7 0\\n4 8 1\\n11 5 0\\n10 12 0\\n12 1 1\\n5 7 0\\n6 8 1\\n\", \"2 20\\n2 1 0\\n\", \"7 12\\n4 5 0\\n2 7 1\\n7 6 1\\n2 5 0\\n2 3 0\\n1 6 0\\n\", \"2 2\\n1 2 0\\n\", \"19 20\\n8 10 1\\n17 15 1\\n14 5 0\\n6 14 0\\n7 15 0\\n19 8 1\\n12 14 0\\n2 18 0\\n13 3 0\\n17 1 1\\n4 2 1\\n11 3 0\\n4 6 0\\n6 9 0\\n7 11 1\\n16 4 1\\n5 13 1\\n16 19 0\\n\", \"2 2\\n1 2 1\\n\", \"4 25\\n2 4 1\\n2 3 0\\n1 4 0\\n\", \"7 12\\n4 5 0\\n2 7 1\\n7 6 1\\n1 5 0\\n2 3 0\\n1 6 0\\n\", \"2 1\\n1 2 1\\n\", \"4 49\\n2 4 1\\n2 3 0\\n1 4 0\\n\", \"4 49\\n2 1 1\\n2 3 0\\n1 4 1\\n\", \"7 12\\n4 6 0\\n3 7 1\\n7 6 1\\n2 5 0\\n2 3 0\\n1 6 0\\n\", \"4 49\\n2 1 0\\n2 3 0\\n1 4 1\\n\", \"4 19\\n2 4 1\\n2 3 1\\n1 4 0\\n\", \"4 6\\n1 2 1\\n1 3 0\\n1 4 0\\n\", \"3 5\\n1 2 1\\n2 3 1\\n\", \"4 25\\n2 4 1\\n2 3 0\\n1 3 0\\n\", \"3 5\\n1 2 0\\n2 3 1\\n\", \"7 12\\n4 5 0\\n2 1 1\\n7 6 1\\n1 5 1\\n2 3 0\\n1 6 0\\n\", \"7 13\\n4 6 0\\n5 7 1\\n7 6 1\\n2 5 0\\n2 3 0\\n1 6 0\\n\", \"3 10\\n1 2 0\\n2 3 1\\n\", \"7 20\\n4 5 0\\n2 7 1\\n7 6 1\\n2 5 0\\n2 3 0\\n1 6 0\\n\", \"19 20\\n8 10 1\\n17 15 1\\n14 5 0\\n6 14 0\\n7 15 1\\n19 8 1\\n12 14 0\\n2 18 0\\n13 3 0\\n17 1 1\\n4 2 1\\n11 3 0\\n4 6 0\\n6 9 0\\n7 11 1\\n16 4 1\\n5 13 1\\n16 19 0\\n\", \"2 4\\n1 2 1\\n2 3 1\\n3 4 1\\n\", \"3 4\\n1 2 1\\n2 3 0\\n\", \"7 12\\n4 5 0\\n2 7 1\\n7 6 1\\n1 5 0\\n2 3 1\\n1 6 0\\n\", \"4 6\\n1 2 1\\n2 3 0\\n1 4 0\\n\", \"7 12\\n4 5 0\\n2 1 1\\n7 6 0\\n1 5 1\\n2 3 0\\n1 6 0\\n\", \"2 5\\n1 2 1\\n2 3 1\\n3 4 1\\n\", \"7 12\\n4 6 1\\n2 7 1\\n7 6 1\\n2 5 0\\n2 3 0\\n1 6 0\\n\", \"4 20\\n2 4 1\\n4 3 1\\n1 4 0\\n\", \"4 5\\n1 2 1\\n2 3 0\\n1 4 0\\n\", \"7 20\\n4 2 0\\n2 7 1\\n7 6 1\\n2 5 1\\n2 3 0\\n1 6 0\\n\", \"4 5\\n1 2 1\\n2 3 0\\n1 4 1\\n\", \"7 20\\n4 2 0\\n2 7 1\\n7 6 1\\n2 5 1\\n2 3 1\\n1 6 0\\n\", \"4 36\\n2 4 1\\n2 3 0\\n1 4 0\\n\", \"13 3\\n9 13 1\\n4 3 1\\n11 9 0\\n8 13 0\\n10 9 0\\n2 7 0\\n4 8 1\\n11 5 0\\n10 12 0\\n12 1 1\\n5 7 0\\n6 8 1\\n\", \"3 8\\n1 2 1\\n2 3 0\\n\", \"4 42\\n2 4 1\\n2 3 0\\n1 4 0\\n\", \"4 67\\n2 4 1\\n2 3 0\\n1 4 0\\n\", \"7 19\\n4 6 0\\n3 7 1\\n7 6 1\\n2 5 0\\n2 3 0\\n1 6 0\\n\", \"3 10\\n1 2 1\\n2 3 1\\n\", \"3 2\\n1 2 0\\n1 3 1\\n\", \"19 20\\n8 10 1\\n17 15 1\\n14 5 0\\n6 14 0\\n7 15 1\\n19 8 1\\n12 14 0\\n2 18 0\\n13 3 0\\n17 1 1\\n4 2 1\\n11 3 0\\n4 6 0\\n6 9 0\\n7 11 1\\n16 4 0\\n5 13 1\\n16 19 0\\n\", \"7 12\\n4 6 1\\n2 7 1\\n7 6 1\\n2 5 0\\n2 3 1\\n1 6 0\\n\", \"4 20\\n2 4 1\\n4 3 1\\n1 4 1\\n\", \"4 5\\n1 2 0\\n2 3 0\\n1 4 1\\n\", \"7 20\\n4 2 1\\n2 7 1\\n7 6 1\\n2 5 1\\n2 3 1\\n1 6 0\\n\", \"7 34\\n4 2 0\\n4 7 0\\n7 6 1\\n2 5 1\\n2 3 1\\n1 6 0\\n\", \"3 15\\n1 2 1\\n2 3 0\\n\", \"4 42\\n2 4 1\\n2 3 0\\n1 3 0\\n\", \"7 12\\n4 5 0\\n2 1 1\\n7 6 1\\n1 5 0\\n2 3 1\\n1 6 1\\n\", \"7 26\\n7 2 0\\n4 7 0\\n3 6 1\\n2 5 1\\n2 3 1\\n1 6 0\\n\", \"3 5\\n1 2 0\\n2 3 0\\n\", \"7 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1\\n2 5 1\\n2 3 1\\n1 6 0\\n\", \"3 10\\n1 2 0\\n2 3 0\\n\", \"4 49\\n2 1 0\\n2 3 0\\n1 4 0\\n\", \"4 25\\n3 4 1\\n2 3 0\\n1 3 0\\n\", \"7 12\\n4 5 0\\n2 1 1\\n7 6 1\\n1 5 0\\n2 3 0\\n1 6 1\\n\", \"7 12\\n4 5 0\\n2 7 1\\n7 6 1\\n1 5 0\\n2 3 1\\n1 2 0\\n\", \"7 12\\n4 6 0\\n2 7 1\\n7 6 1\\n2 5 1\\n2 3 0\\n1 6 0\\n\", \"7 20\\n4 2 0\\n2 7 1\\n7 6 1\\n3 5 0\\n2 3 0\\n1 6 0\\n\", \"2 5\\n1 2 1\\n2 0 1\\n3 1 1\\n\", \"7 12\\n4 6 1\\n2 7 1\\n7 4 1\\n2 5 1\\n2 3 0\\n1 6 0\\n\", \"7 12\\n4 6 1\\n2 7 0\\n7 6 1\\n2 5 0\\n2 3 0\\n1 6 0\\n\", \"7 20\\n4 2 0\\n4 7 1\\n7 6 1\\n2 5 1\\n2 3 1\\n1 7 0\\n\", \"7 20\\n7 2 0\\n4 7 0\\n3 6 1\\n2 5 1\\n2 3 1\\n1 6 0\\n\", \"19 20\\n8 10 1\\n17 15 1\\n14 5 0\\n6 14 0\\n7 15 1\\n19 8 1\\n12 14 0\\n2 18 0\\n13 3 0\\n17 1 1\\n4 2 1\\n11 3 0\\n4 6 0\\n6 9 0\\n7 11 1\\n16 4 0\\n5 13 1\\n9 19 0\\n\", \"7 12\\n4 6 1\\n2 7 1\\n7 6 1\\n2 5 0\\n2 3 1\\n1 2 0\\n\", \"2 5\\n1 2 1\\n2 0 1\\n3 2 1\\n\", \"7 12\\n4 3 1\\n2 7 1\\n7 6 1\\n2 5 0\\n2 3 0\\n1 6 0\\n\", \"2 5\\n1 2 1\\n1 0 1\\n3 2 1\\n\"], \"outputs\": [\" 252\\n\", \" 0\\n\", \" 210\\n\", \" 876856450\\n\", \" 1842\\n\", \" 0\\n\", \" 824505797\\n\", \" 0\\n\", \" 928042611\\n\", \" 2\\n\", \"831852467\\n\", \"824505797\\n\", \"0\\n\", \"595131499\\n\", \"544612159\\n\", \"840224227\\n\", \"257391393\\n\", \"877380736\\n\", \"3366\\n\", \"240\\n\", \"610357816\\n\", \"210\\n\", \"841274821\\n\", \"885821088\\n\", \"58024\\n\", \"226397486\\n\", \"929091185\\n\", \"14\\n\", \"64\\n\", \"824509891\\n\", \"3968\\n\", \"840747477\\n\", \"30\\n\", \"840751571\\n\", \"510571505\\n\", \"960\\n\", \"251233188\\n\", \"990\\n\", \"736968991\\n\", \"641112499\\n\", \"1842\\n\", \"6304\\n\", \"853297555\\n\", \"578961544\\n\", \"781057964\\n\", \"59046\\n\", \"4\\n\", \"808213127\\n\", \"841278915\\n\", \"511620079\\n\", \"780\\n\", \"738017565\\n\", \"262911102\\n\", \"14316138\\n\", \"366817536\\n\", \"840755665\\n\", \"459482703\\n\", \"0\\n\", \"824505797\\n\", \"595131499\\n\", 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|
You are given a tree (a connected undirected graph without cycles) of n vertices. Each of the n - 1 edges of the tree is colored in either black or red.
You are also given an integer k. Consider sequences of k vertices. Let's call a sequence [a_1, a_2, …, a_k] good if it satisfies the following criterion:
* We will walk a path (possibly visiting same edge/vertex multiple times) on the tree, starting from a_1 and ending at a_k.
* Start at a_1, then go to a_2 using the shortest path between a_1 and a_2, then go to a_3 in a similar way, and so on, until you travel the shortest path between a_{k-1} and a_k.
* If you walked over at least one black edge during this process, then the sequence is good.
<image>
Consider the tree on the picture. If k=3 then the following sequences are good: [1, 4, 7], [5, 5, 3] and [2, 3, 7]. The following sequences are not good: [1, 4, 6], [5, 5, 5], [3, 7, 3].
There are n^k sequences of vertices, count how many of them are good. Since this number can be quite large, print it modulo 10^9+7.
Input
The first line contains two integers n and k (2 ≤ n ≤ 10^5, 2 ≤ k ≤ 100), the size of the tree and the length of the vertex sequence.
Each of the next n - 1 lines contains three integers u_i, v_i and x_i (1 ≤ u_i, v_i ≤ n, x_i ∈ \{0, 1\}), where u_i and v_i denote the endpoints of the corresponding edge and x_i is the color of this edge (0 denotes red edge and 1 denotes black edge).
Output
Print the number of good sequences modulo 10^9 + 7.
Examples
Input
4 4
1 2 1
2 3 1
3 4 1
Output
252
Input
4 6
1 2 0
1 3 0
1 4 0
Output
0
Input
3 5
1 2 1
2 3 0
Output
210
Note
In the first example, all sequences (4^4) of length 4 except the following are good:
* [1, 1, 1, 1]
* [2, 2, 2, 2]
* [3, 3, 3, 3]
* [4, 4, 4, 4]
In the second example, all edges are red, hence there aren't any good sequences.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
{"tests": "{\"inputs\": [\"7\\n1 3 5 6 5 4 2\\n\", \"5\\n1 2 4 3 2\\n\", \"4\\n1 2 4 3\\n\", \"3\\n2 2 2\\n\", \"20\\n2 2 2 1 1 3 1 3 3 1 2 3 3 3 2 2 2 3 1 3\\n\", \"17\\n3 3 2 3 2 3 1 2 3 2 2 3 1 3 1 2 1\\n\", \"12\\n3 3 2 3 2 3 1 2 1 2 2 1\\n\", \"18\\n2 3 3 3 1 2 2 1 3 3 2 3 1 3 1 2 2 2\\n\", \"3\\n3 1 1\\n\", \"5\\n2 1 3 4 2\\n\", \"5\\n3 1 2 3 1\\n\", \"3\\n1 1 2\\n\", \"8\\n1 3 3 2 1 1 1 1\\n\", \"8\\n2 2 1 1 1 1 3 3\\n\", \"13\\n1 1 1 1 2 3 2 3 1 3 2 3 1\\n\", \"9\\n3 1 1 2 2 2 2 1 2\\n\", \"6\\n4 4 4 4 1 3\\n\", \"4\\n4 4 3 3\\n\", \"10\\n3 3 2 3 2 1 2 2 2 2\\n\", \"11\\n2 3 2 1 2 3 1 3 1 1 2\\n\", \"19\\n2 2 3 2 3 3 2 3 3 2 3 3 3 2 1 2 1 2 3\\n\", \"5\\n5 5 5 1 3\\n\", \"45\\n1 3 4 6 8 5 1 5 10 10 8 3 2 7 4 1 9 8 9 1 9 10 10 4 7 8 7 7 7 10 8 8 3 8 1 9 8 5 9 3 6 10 3 1 3\\n\", \"9\\n1 2 1 3 2 3 1 1 2\\n\", \"5\\n1 3 2 2 3\\n\", \"4\\n2 2 1 3\\n\", \"4\\n3 2 3 3\\n\", \"11\\n2 3 3 1 1 1 2 2 3 2 3\\n\", \"15\\n1 2 1 1 3 2 2 2 3 3 3 1 1 2 2\\n\", \"4\\n4 1 2 2\\n\", \"4\\n4 2 1 1\\n\", \"10\\n1 1 1 3 2 2 3 1 3 3\\n\", \"15\\n3 2 2 2 1 2 2 1 3 3 2 1 2 2 1\\n\", \"5\\n2 4 3 4 4\\n\", \"12\\n1 1 3 2 1 1 2 2 3 1 2 2\\n\", \"18\\n1 2 3 1 1 3 1 1 2 2 3 2 1 3 3 2 3 1\\n\", \"18\\n3 3 1 1 2 3 2 1 1 1 1 2 2 2 2 3 2 2\\n\", \"6\\n2 3 5 6 3 2\\n\", \"4\\n3 3 4 2\\n\", \"15\\n2 1 3 1 2 1 2 1 3 3 3 2 3 3 3\\n\", \"12\\n1 2 2 1 3 2 3 2 2 3 3 1\\n\", \"1\\n1\\n\", \"3\\n2 1 2\\n\", \"7\\n2 1 2 1 1 1 1\\n\", \"4\\n4 3 3 1\\n\", \"5\\n1 2 2 2 3\\n\", \"12\\n1 1 2 1 2 2 3 3 3 1 3 3\\n\", \"5\\n2 4 3 5 5\\n\", \"14\\n11 3 2 5 7 13 1 13 5 8 4 6 13 11\\n\", \"14\\n2 1 1 1 2 2 2 1 1 2 1 2 3 3\\n\", \"14\\n1 1 3 1 1 2 3 1 3 1 2 3 1 3\\n\", \"13\\n1 1 3 2 2 1 1 3 3 1 2 1 2\\n\", \"19\\n1 1 3 1 1 1 2 1 1 1 2 1 1 3 1 1 2 2 1\\n\", \"5\\n1 3 3 2 1\\n\", \"3\\n2 2 1\\n\", \"4\\n4 2 2 1\\n\", \"8\\n2 2 3 1 2 2 1 1\\n\", \"5\\n2 2 4 5 2\\n\", \"15\\n37504 79054 80071 95721 135743 164345 189260 190810 191657 196168 200000 200000 190810 190018 185437\\n\", \"17\\n1 3 2 3 3 2 1 3 1 3 3 2 2 2 3 2 1\\n\", \"13\\n2 2 1 1 1 2 3 2 2 1 3 3 1\\n\", \"18\\n1 2 3 2 1 1 2 1 2 3 2 3 2 2 3 2 1 2\\n\", \"13\\n2 1 3 1 2 3 2 1 1 3 3 1 3\\n\", \"16\\n2 1 1 1 2 3 1 1 3 2 3 1 3 3 2 2\\n\", \"4\\n3 3 2 2\\n\", \"15\\n2 2 1 3 1 3 1 3 2 2 3 3 2 3 3\\n\", \"5\\n1 2 1 2 1\\n\", \"5\\n4 3 4 4 2\\n\", \"5\\n5 1 4 4 4\\n\", \"5\\n4 4 2 5 1\\n\", \"4\\n1 3 2 2\\n\", \"18\\n1 3 2 2 2 3 2 3 3 1 1 3 1 2 1 2 2 2\\n\", \"4\\n3 4 4 4\\n\", \"14\\n1 2 3 2 3 2 2 3 3 3 2 3 1 1\\n\", \"8\\n3 2 3 1 1 2 2 1\\n\", \"5\\n4 5 5 2 1\\n\", \"12\\n7 3 5 8 10 4 10 5 4 12 7 2\\n\", \"3\\n3 2 2\\n\", \"5\\n4 3 1 1 1\\n\", \"5\\n5 5 2 4 4\\n\", \"7\\n3 1 3 1 3 1 1\\n\", \"13\\n1 1 2 1 2 3 1 1 3 1 3 1 2\\n\", \"17\\n2 2 2 2 3 2 1 1 1 3 3 2 3 1 1 1 2\\n\", \"5\\n2 5 1 1 1\\n\", \"10\\n1 2 1 5 6 1 1 2 7 1\\n\", \"5\\n5 5 3 3 1\\n\", \"15\\n3 1 1 1 1 1 1 1 2 1 1 1 1 2 1\\n\", \"5\\n4 4 2 2 2\\n\", \"20\\n1 1 2 3 1 1 3 1 2 3 2 1 2 2 1 1 2 2 3 1\\n\", \"5\\n5 2 4 4 3\\n\", \"4\\n3 4 1 1\\n\", \"5\\n3 3 1 1 2\\n\", \"6\\n2 2 3 4 2 2\\n\", \"17\\n1 2 3 1 2 2 1 2 2 1 1 1 1 3 2 2 1\\n\", \"17\\n2 1 1 2 1 2 3 1 3 1 3 2 1 2 1 1 3\\n\", \"5\\n5 1 5 1 4\\n\", \"12\\n2 1 3 1 2 2 2 1 2 2 1 2\\n\", \"16\\n1 3 2 3 2 1 1 3 1 1 2 3 2 1 2 2\\n\", \"20\\n2 2 2 3 3 3 2 1 1 1 2 3 3 3 3 2 1 2 2 3\\n\", \"4\\n4 4 2 3\\n\", \"18\\n3 1 2 1 3 1 3 2 2 2 2 1 3 3 3 3 1 2\\n\", \"15\\n2 3 1 3 2 3 2 3 1 1 2 3 3 1 1\\n\", \"93\\n6 6 10 10 8 4 7 10 2 3 4 10 7 2 8 8 4 2 4 4 7 7 3 2 3 1 5 3 7 2 4 9 10 8 10 5 1 6 2 1 10 3 5 6 6 9 3 10 1 10 1 6 2 3 8 7 1 5 4 10 4 3 5 8 8 1 3 8 2 3 10 7 2 4 5 2 6 4 10 4 4 8 5 1 6 3 1 9 5 4 9 4 3\\n\", \"17\\n2 2 3 3 2 2 1 3 1 3 1 2 1 2 2 2 1\\n\", \"6\\n5 8 7 5 6 5\\n\", \"19\\n1 1 3 3 3 1 3 1 2 2 3 1 3 2 1 3 2 3 3\\n\", \"20\\n2 2 2 3 2 3 3 1 3 2 2 1 3 1 3 2 3 1 3 3\\n\", \"4\\n4 3 1 1\\n\", \"4\\n3 3 3 4\\n\", \"17\\n2 3 1 3 2 3 2 3 3 3 1 3 2 3 2 1 2\\n\", \"4\\n1 1 1 3\\n\", \"9\\n2 5 6 5 6 9 7 5 2\\n\", \"5\\n3 4 5 2 2\\n\", \"18\\n2 2 1 2 1 3 3 1 3 2 1 1 3 2 1 1 2 2\\n\", \"4\\n3 2 3 1\\n\", \"7\\n1 4 4 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1\\n\", \"4\\n4 1 1 1\\n\", \"17\\n1 2 2 1 1 1 2 1 2 2 3 1 3 2 3 1 1\\n\", \"6\\n2 3 3 1 1 1\\n\", \"19\\n2 2 2 1 2 1 1 3 2 3 1 2 1 1 2 3 1 2 2\\n\", \"19\\n1 1 1 2 1 3 2 3 2 3 3 3 1 3 2 3 1 3 3\\n\", \"20\\n3 3 3 1 3 2 3 1 2 1 1 3 2 3 2 1 1 3 2 2\\n\", \"18\\n2 2 3 2 2 2 1 2 3 2 2 2 1 3 1 2 1 1\\n\", \"5\\n4 2 3 2 2\\n\", \"18\\n2 3 2 3 1 3 2 1 1 2 1 2 2 1 1 2 1 1\\n\", \"5\\n2 5 1 3 2\\n\", \"9\\n6 6 7 9 6 1 4 4 4\\n\", \"11\\n3 2 1 2 3 1 3 2 2 2 1\\n\", \"2\\n2 1\\n\", \"16\\n2 1 1 3 2 2 2 2 3 2 2 3 1 3 2 2\\n\", \"15\\n1 2 2 3 1 1 2 2 1 2 1 3 2 2 2\\n\", \"15\\n1 1 1 2 2 3 2 2 3 3 2 2 3 2 2\\n\", \"4\\n1 4 3 3\\n\", \"3\\n1 1 3\\n\", \"6\\n2 2 2 2 3 2\\n\", \"4\\n2 1 2 2\\n\", \"16\\n2 2 3 1 2 1 1 3 2 1 1 1 2 3 1 2\\n\", \"20\\n2 2 2 1 1 3 1 3 3 1 2 3 3 3 1 2 2 3 1 3\\n\", \"17\\n3 3 2 3 2 1 1 2 3 2 2 3 1 3 1 2 1\\n\", \"18\\n2 3 3 3 1 2 2 1 3 1 2 3 1 3 1 2 2 2\\n\", \"3\\n5 1 1\\n\", \"5\\n2 1 3 4 1\\n\", \"5\\n3 0 2 3 1\\n\", \"3\\n1 2 3\\n\", \"8\\n2 4 1 1 1 1 3 3\\n\", \"9\\n2 1 1 2 2 2 2 1 2\\n\", \"45\\n1 3 4 6 8 5 1 5 10 10 8 3 2 7 8 1 9 8 9 1 9 10 10 4 7 8 7 7 7 10 8 8 3 8 1 9 8 5 9 3 6 10 3 1 3\\n\", \"18\\n1 2 3 1 1 4 1 1 2 2 3 2 1 3 3 2 3 1\\n\", \"6\\n2 3 5 6 5 2\\n\", \"12\\n1 1 2 1 2 2 3 3 3 1 6 3\\n\", \"3\\n3 2 1\\n\", \"15\\n37504 89177 80071 95721 135743 164345 189260 190810 191657 196168 200000 200000 190810 190018 185437\\n\", \"13\\n2 4 1 1 1 2 3 2 2 1 3 3 1\\n\", \"8\\n3 2 3 1 1 4 2 1\\n\", \"5\\n4 5 5 0 1\\n\", \"12\\n3 3 2 3 2 3 1 2 0 2 2 1\\n\", \"8\\n1 3 3 2 1 0 1 1\\n\", \"13\\n1 1 1 1 2 6 2 3 1 3 2 3 1\\n\", \"6\\n4 4 6 4 1 3\\n\", \"4\\n4 0 3 3\\n\", \"10\\n3 3 2 3 2 0 2 2 2 2\\n\", \"11\\n2 3 2 1 2 3 1 3 1 0 2\\n\", \"19\\n2 2 2 2 3 3 2 3 3 2 3 3 3 2 1 2 1 2 3\\n\", \"5\\n5 5 5 0 3\\n\", \"9\\n1 2 1 3 2 3 1 2 2\\n\", \"5\\n1 6 2 2 3\\n\", \"4\\n2 3 1 3\\n\", \"4\\n2 2 3 1\\n\", \"11\\n2 3 3 1 1 1 0 2 3 2 3\\n\", \"15\\n1 2 1 1 4 2 2 2 3 3 3 1 1 2 2\\n\", \"10\\n1 1 1 3 1 2 3 1 3 3\\n\", \"15\\n3 2 2 2 1 2 2 1 3 3 0 1 2 2 1\\n\", \"5\\n4 4 3 4 4\\n\", \"12\\n2 1 3 2 1 1 2 2 3 1 2 2\\n\", \"18\\n3 3 1 1 2 3 2 1 1 2 1 2 2 2 2 3 2 2\\n\", \"15\\n2 1 3 1 2 1 2 1 3 3 3 2 3 0 3\\n\", \"12\\n1 2 2 1 3 2 4 2 2 3 3 1\\n\", \"3\\n2 1 4\\n\", \"7\\n2 1 1 1 1 1 1\\n\", \"4\\n1 3 3 1\\n\", \"5\\n1 2 2 1 3\\n\", \"14\\n11 3 2 5 7 13 1 13 5 8 1 6 13 11\\n\", \"14\\n2 1 1 1 2 2 2 0 1 2 1 2 3 3\\n\", \"14\\n1 1 3 1 1 2 3 1 3 1 4 3 1 3\\n\", \"13\\n1 1 3 2 2 1 1 3 3 1 2 2 2\\n\", \"19\\n1 1 3 1 1 1 2 1 1 1 2 1 1 3 1 0 2 2 1\\n\", \"4\\n8 2 2 1\\n\", \"8\\n2 2 3 1 2 2 2 1\\n\", \"5\\n2 2 4 5 1\\n\", \"17\\n1 3 2 3 3 2 1 3 1 3 3 2 2 0 3 2 1\\n\", \"18\\n1 3 3 2 1 1 2 1 2 3 2 3 2 2 3 2 1 2\\n\", \"13\\n2 1 3 1 2 6 2 1 1 3 3 1 3\\n\", \"16\\n2 1 1 1 2 3 1 1 3 2 6 1 3 3 2 2\\n\", \"4\\n3 1 2 2\\n\", \"15\\n2 2 1 3 1 0 1 3 2 2 3 3 2 3 3\\n\", \"5\\n1 2 1 4 1\\n\", \"5\\n4 0 4 4 2\\n\", \"5\\n5 1 1 4 4\\n\", \"5\\n4 4 4 5 1\\n\", \"4\\n1 1 2 2\\n\", \"18\\n1 3 2 2 2 3 2 3 3 1 1 3 0 2 1 2 2 2\\n\", \"14\\n1 2 3 2 2 2 2 3 3 3 2 3 1 1\\n\", \"12\\n7 3 5 8 8 4 10 5 4 12 7 2\\n\", \"5\\n4 3 1 1 2\\n\", \"5\\n5 8 2 4 4\\n\", \"7\\n4 1 3 1 3 1 1\\n\", \"13\\n1 1 2 1 2 3 1 2 3 1 3 1 2\\n\", \"17\\n2 2 2 2 3 2 1 1 1 0 3 2 3 1 1 1 2\\n\", \"5\\n2 5 1 1 2\\n\", \"10\\n1 2 1 5 6 0 1 2 7 1\\n\", \"5\\n5 5 3 6 1\\n\", \"15\\n3 1 1 1 1 1 1 1 2 2 1 1 1 2 1\\n\", \"20\\n1 1 2 3 1 1 3 0 2 3 2 1 2 2 1 1 2 2 3 1\\n\", \"5\\n5 2 4 4 2\\n\", \"4\\n3 2 1 1\\n\", \"5\\n5 3 1 1 2\\n\", \"6\\n2 2 3 4 2 4\\n\", \"17\\n3 1 1 2 1 2 3 1 3 1 3 2 1 2 1 1 3\\n\", \"5\\n5 1 7 1 4\\n\", \"12\\n2 1 3 1 0 2 2 1 2 2 1 2\\n\", \"16\\n1 3 2 3 2 1 1 3 1 1 2 3 2 2 2 2\\n\", \"20\\n2 2 2 3 3 3 0 1 1 1 2 3 3 3 3 2 1 2 2 3\\n\", \"4\\n4 4 2 5\\n\", \"18\\n3 1 2 1 3 0 3 2 2 2 2 1 3 3 3 3 1 2\\n\", \"15\\n2 3 1 3 2 3 2 3 1 1 2 3 3 0 1\\n\", \"93\\n6 6 10 10 9 4 7 10 2 3 4 10 7 2 8 8 4 2 4 4 7 7 3 2 3 1 5 3 7 2 4 9 10 8 10 5 1 6 2 1 10 3 5 6 6 9 3 10 1 10 1 6 2 3 8 7 1 5 4 10 4 3 5 8 8 1 3 8 2 3 10 7 2 4 5 2 6 4 10 4 4 8 5 1 6 3 1 9 5 4 9 4 3\\n\", \"17\\n2 1 3 3 2 2 1 3 1 3 1 2 1 2 2 2 1\\n\", \"6\\n5 4 7 5 6 5\\n\", \"19\\n1 1 3 3 3 1 3 1 1 2 3 1 3 2 1 3 2 3 3\\n\", \"20\\n2 2 4 3 2 3 3 1 3 2 2 1 3 1 3 2 3 1 3 3\\n\", \"4\\n4 3 1 2\\n\", \"4\\n4 3 3 4\\n\", \"17\\n2 3 1 3 2 3 2 3 3 3 1 3 2 3 2 2 2\\n\"], \"outputs\": [\"6\\nLRLRRR\", \"4\\nLRRR\", \"4\\nLLRR\\n\", \"1\\nR\", \"2\\nLR\", \"3\\nRRL\", \"3\\nRRL\", \"2\\nLL\", \"2\\nRL\", \"2\\nRR\", \"2\\nRR\", \"2\\nLR\", \"2\\nLL\", \"2\\nLR\", \"2\\nRR\", \"2\\nRL\", \"2\\nRL\", \"2\\nRL\", \"2\\nRL\", \"2\\nLL\", \"2\\nLR\", \"2\\nRL\", \"5\\nLLLLL\", \"2\\nLR\", \"2\\nLR\", \"2\\nLR\", \"1\\nR\", \"2\\nLR\", \"2\\nLR\", \"2\\nRL\", \"2\\nRL\", \"2\\nLR\", \"3\\nRRL\", \"2\\nLR\", \"2\\nLR\", \"3\\nLLL\", \"2\\nRL\", \"4\\nLLLL\", \"3\\nRLR\", \"2\\nLR\", \"2\\nRR\", \"1\\nR\\n\", \"1\\nR\", \"2\\nRL\", \"3\\nRRL\", \"3\\nLLR\", \"2\\nLR\", \"3\\nLLR\", \"2\\nRR\", \"2\\nLR\", \"2\\nLR\", \"2\\nLR\", \"2\\nRR\", \"3\\nRRR\", \"2\\nRR\", \"3\\nRRL\", \"2\\nRL\", \"2\\nRR\", \"13\\nLLLLLLRLRLLLL\", \"3\\nRRR\", \"3\\nRLR\", \"3\\nLLL\", \"2\\nLR\", \"1\\nR\", \"2\\nRL\", \"2\\nLR\", \"2\\nRR\", \"2\\nRR\", \"2\\nRL\", \"3\\nRLR\", \"3\\nLRL\", \"3\\nLRL\", \"2\\nLR\", \"3\\nLLL\", \"3\\nRRL\", \"4\\nRRLR\", \"3\\nRRR\", \"2\\nRL\", \"2\\nRL\", \"2\\nRL\", \"2\\nRL\", \"2\\nLR\", \"1\\nR\", \"3\\nRLL\", \"2\\nRR\", \"3\\nRRL\", \"3\\nRRL\", \"2\\nRL\", \"2\\nRR\", \"3\\nRRL\", \"3\\nRLL\", \"2\\nRL\", \"1\\nR\", \"3\\nLLL\", \"2\\nLR\", \"2\\nRL\", \"1\\nR\", \"3\\nLRL\", \"2\\nLR\", \"2\\nRL\", \"2\\nRL\", \"3\\nRLL\", \"4\\nRRLR\", \"2\\nRR\", \"2\\nRR\", \"2\\nLR\", \"2\\nLR\", \"2\\nRL\", \"2\\nLR\", \"2\\nLL\", \"2\\nLR\", \"4\\nRRRR\", \"4\\nRLLL\", \"1\\nR\", \"2\\nRR\", \"3\\nLRL\", \"2\\nLR\", \"2\\nLR\", \"2\\nRL\", \"2\\nRL\", \"1\\nR\", \"3\\nRLL\", \"2\\nRL\", \"2\\nRL\", \"3\\nLLL\", \"2\\nLL\", \"2\\nLR\", \"2\\nRR\", \"3\\nLLR\", \"2\\nLR\", \"2\\nRR\", \"3\\nLLR\", \"4\\nLLLL\", \"3\\nLLL\", \"2\\nLL\", \"2\\nRL\", \"2\\nLL\", \"2\\nLL\", \"2\\nLR\", \"3\\nLRL\", \"2\\nLL\", \"2\\nRL\", \"2\\nRR\", \"3\\nLRR\", \"2\\nRL\", \"1\\nR\", \"2\\nLR\", \"2\\nLL\", \"4\\nRRRL\", \"2\\nLL\", \"2\\nLR\", \"3\\nLRR\", \"2\\nRL\", \"3\\nRRL\", \"2\\nLL\", \"4\\nRRRL\", \"2\\nRL\", \"2\\nRR\", \"2\\nRL\", \"3\\nLRL\", \"1\\nR\", \"2\\nLR\", \"4\\nLLRR\", \"3\\nRRR\", \"2\\nRR\", \"2\\nLR\", \"2\\nRL\", \"2\\nLL\", \"1\\nR\", \"3\\nLLL\", \"2\\nLL\", \"2\\nLR\", \"2\\nRR\", \"4\\nRLLL\", \"2\\nLL\", \"3\\nLRR\", \"2\\nRR\", \"2\\nLR\", \"2\\nLR\", \"2\\nRL\", \"2\\nLL\", \"2\\nRR\", \"2\\nRL\", \"3\\nRRR\", \"3\\nLRL\", \"2\\nLL\", \"2\\nRL\", \"2\\nLR\\n\", \"2\\nLR\", \"2\\nRL\", \"3\\nLRR\", \"3\\nLLL\", \"3\\nRRL\", \"1\\nR\", \"2\\nLL\", \"2\\nRR\", \"2\\nRL\", \"3\\nRLL\", \"2\\nLL\", \"2\\nLR\", \"2\\nLL\", \"2\\nLR\", \"2\\nRL\", \"3\\nRRR\", \"4\\nLLLR\\n\", \"2\\nLL\", \"2\\nRR\", \"2\\nRL\", \"2\\nRL\", \"2\\nLL\", \"2\\nRL\", \"2\\nLR\", \"1\\nR\", \"2\\nRR\", \"2\\nRL\", \"2\\nLL\", \"3\\nRLL\", \"1\\nR\", \"2\\nLR\", \"2\\nRL\", \"2\\nRL\", \"2\\nRL\", \"3\\nRLL\", \"2\\nRR\", \"2\\nRL\", \"3\\nRRL\", \"2\\nRR\\n\", \"1\\nR\", \"2\\nLR\", \"2\\nLR\", \"3\\nLRL\", \"2\\nLR\", \"2\\nRR\", \"1\\nR\", \"1\\nR\\n\", \"2\\nLR\\n\", \"3\\nRRL\\n\", \"2\\nLL\\n\", \"2\\nRL\\n\", \"3\\nRLR\\n\", \"2\\nRR\\n\", \"3\\nLLR\\n\", \"3\\nLRL\\n\", \"1\\nR\\n\", \"5\\nLLLLL\\n\", \"3\\nLLL\\n\", \"4\\nLLLL\\n\", \"3\\nLRR\\n\", \"3\\nRRR\\n\", \"6\\nLLRRRR\\n\", \"4\\nRLRL\\n\", \"4\\nRRLR\\n\", \"3\\nRLL\\n\", \"3\\nRRL\\n\", \"2\\nLL\\n\", \"2\\nRR\\n\", \"2\\nRL\\n\", \"2\\nRL\\n\", \"2\\nRL\\n\", \"2\\nLL\\n\", \"2\\nLR\\n\", \"2\\nRL\\n\", \"2\\nLR\\n\", \"3\\nLRL\\n\", \"2\\nLR\\n\", \"3\\nRLR\\n\", \"2\\nLR\\n\", \"2\\nLR\\n\", \"2\\nLR\\n\", \"3\\nRRL\\n\", \"1\\nR\\n\", \"1\\nR\\n\", \"2\\nRL\\n\", \"2\\nLR\\n\", \"2\\nRR\\n\", \"2\\nLR\\n\", \"2\\nRL\\n\", \"2\\nRR\\n\", \"3\\nLLR\\n\", \"2\\nRR\\n\", \"2\\nLR\\n\", \"2\\nLR\\n\", \"2\\nLR\\n\", \"2\\nRR\\n\", \"3\\nRRL\\n\", \"2\\nRR\\n\", \"3\\nRLR\\n\", \"3\\nRRR\\n\", \"3\\nLRL\\n\", \"2\\nLR\\n\", \"1\\nR\\n\", \"2\\nRL\\n\", \"2\\nLR\\n\", \"2\\nRR\\n\", \"2\\nRR\\n\", \"2\\nRL\\n\", \"3\\nRLR\\n\", \"2\\nLR\\n\", \"3\\nLRL\\n\", \"3\\nLLL\\n\", \"3\\nRRR\\n\", \"2\\nRL\\n\", \"3\\nRLL\\n\", \"2\\nRL\\n\", \"2\\nLR\\n\", \"1\\nR\\n\", \"2\\nLL\\n\", \"2\\nRR\\n\", \"3\\nRLR\\n\", \"3\\nRRL\\n\", \"2\\nRR\\n\", \"3\\nRRL\\n\", \"2\\nRL\\n\", \"2\\nRL\\n\", \"2\\nLR\\n\", \"1\\nR\\n\", \"2\\nRL\\n\", \"1\\nR\\n\", \"3\\nLRL\\n\", \"2\\nLR\\n\", \"2\\nLR\\n\", \"2\\nRL\\n\", \"3\\nRLL\\n\", \"4\\nRRLR\\n\", \"2\\nRR\\n\", \"2\\nRR\\n\", \"2\\nLR\\n\", \"2\\nLR\\n\", \"2\\nRL\\n\", \"1\\nR\\n\", \"2\\nLL\\n\"]}", "source": "primeintellect"}
|
The only difference between problems C1 and C2 is that all values in input of problem C1 are distinct (this condition may be false for problem C2).
You are given a sequence a consisting of n integers.
You are making a sequence of moves. During each move you must take either the leftmost element of the sequence or the rightmost element of the sequence, write it down and remove it from the sequence. Your task is to write down a strictly increasing sequence, and among all such sequences you should take the longest (the length of the sequence is the number of elements in it).
For example, for the sequence [1, 2, 4, 3, 2] the answer is 4 (you take 1 and the sequence becomes [2, 4, 3, 2], then you take the rightmost element 2 and the sequence becomes [2, 4, 3], then you take 3 and the sequence becomes [2, 4] and then you take 4 and the sequence becomes [2], the obtained increasing sequence is [1, 2, 3, 4]).
Input
The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a.
The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 2 ⋅ 10^5), where a_i is the i-th element of a.
Output
In the first line of the output print k — the maximum number of elements in a strictly increasing sequence you can obtain.
In the second line print a string s of length k, where the j-th character of this string s_j should be 'L' if you take the leftmost element during the j-th move and 'R' otherwise. If there are multiple answers, you can print any.
Examples
Input
5
1 2 4 3 2
Output
4
LRRR
Input
7
1 3 5 6 5 4 2
Output
6
LRLRRR
Input
3
2 2 2
Output
1
R
Input
4
1 2 4 3
Output
4
LLRR
Note
The first example is described in the problem statement.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
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{"tests": "{\"inputs\": [\"6 1\\n2 1 2 3 4 3\\n\", \"6 1\\n1 1 2 2 3 3\\n\", \"6 2\\n2 1 2 3 4 3\\n\", \"10 500\\n1 2 3 4 5 6 7 8 9 10\\n\", \"40 1\\n296861916 110348711 213599874 304979682 902720247 958794999 445626005 29685036 968749742 772121742 50110079 72399009 347194050 322418543 594963355 407238845 847251668 210179965 293944170 300817194 842872332 82882809 446438478 304657690 343250734 567326942 47727237 662711343 59995716 812214268 994315801 193163726 656281454 249432773 772706196 977253852 342331261 182317828 550599535 3939813\\n\", \"8 32\\n1 2 3 4 5 6 7 8\\n\", \"2 64\\n2 3\\n\", \"1 4\\n1\\n\", \"8 64\\n1 1 1 1 1 1 1 1\\n\", \"8 63\\n1 2 3 4 5 6 7 8\\n\", \"2 1000000\\n1 1\\n\", \"9 1\\n1 2 1 2 1 2 1 2 1000000000\\n\", \"2 100000\\n2 3\\n\", \"10 100\\n1 2 3 4 5 6 7 8 9 10\\n\", \"10 100\\n1 1 2 2 2 3 3 3 3 4\\n\", \"3 288383\\n2 2 2\\n\", \"4 2\\n2 2 2 1\\n\", \"2 8\\n1 2\\n\", \"100 1000\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"7 999992\\n1 2 3 4 5 6 7\\n\", \"5 100000\\n1 2 3 4 5\\n\", \"8 64\\n1 2 3 4 5 6 7 8\\n\", \"3 10000000\\n1 2 3\\n\", \"8 33\\n1 2 3 4 5 6 7 8\\n\", \"6 100000\\n2 1 2 3 4 3\\n\", \"10 1000000\\n1 2 3 4 5 6 7 8 9 10\\n\", \"2 1000\\n1 2\\n\", \"8 31\\n1 1 2 2 3 3 4 4\\n\", \"81 800\\n2 8 5 1 10 5 9 9 3 5 6 6 2 8 2 2 6 3 8 7 2 5 3 4 3 3 2 7 9 6 8 7 2 9 10 3 8 10 6 5 4 2 3 4 4 5 2 2 4 9 8 5 3 8 8 10 4 2 10 9 7 6 1 3 9 7 1 3 5 9 7 6 1 10 1 1 7 2 4 9 10\\n\", \"2 1\\n1 3\\n\", \"64 40\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"8 65\\n1 2 3 4 5 6 7 8\\n\", \"9 100000000\\n1 2 3 4 5 6 7 8 9\\n\", \"100 800\\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\\n\", \"6 1213\\n1 1 2 2 3 3\\n\", \"8 31\\n1 1 1 1 1 1 1 1\\n\", \"100 1249\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100\\n\", \"2 10000\\n1 2\\n\", \"1 1\\n1\\n\", \"5 1234567\\n1 2 3 4 5\\n\", \"3 11\\n1 2 3\\n\", \"50 20\\n592183311 362557946 154127088 616872926 395353745 675069471 509655682 79915471 356656666 937992998 304422065 724106263 472338455 792258113 796069631 663370025 201799298 566151622 722278085 508905399 703159587 690854023 925377265 11010958 69791159 990158269 535460930 167415727 999216963 237203826 693974848 530462137 555061429 744123832 887168514 479773974 575345653 282142246 899762676 446274594 338501746 168668673 408947684 226311538 645441958 258972430 216333311 338561078 123733185 539429791\\n\", \"8 30\\n1 2 3 4 5 6 7 8\\n\", \"5 70\\n1 2 3 4 5\\n\", \"5 1000000\\n1 2 3 3 4\\n\", \"5 100000\\n1 2 3 3 4\\n\", \"10 1\\n589934963 440265648 161048053 196789927 951616256 63404428 660569162 779938975 237139603 31052281\\n\", \"100 1000\\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\\n\", \"20 8\\n1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2\\n\", \"6 48\\n2 1 2 3 4 3\\n\", \"5 100000\\n1 2 2 3 4\\n\", \"8 10000000\\n1 2 3 4 5 6 7 8\\n\", \"5 100\\n1 2 3 4 5\\n\", \"8 31\\n2 8 5 1 10 5 9 9\\n\", \"8 31\\n1 2 3 4 5 6 7 8\\n\", \"50 400\\n0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600 630 660 690 720 750 780 810 840 870 900 930 960 990 1020 1050 1080 1110 1140 1170 1200 1230 1260 1290 1320 1350 1380 1410 1440 1470\\n\", \"2 64\\n1 2\\n\", \"3 120\\n1 2 3\\n\", \"1 10000000\\n1\\n\", \"5 100000000\\n1 1 2 2 5\\n\", \"2 40000000\\n3 9\\n\", \"2 30000000\\n2 5\\n\", \"1 100000000\\n69\\n\", \"3 100000000\\n1 1 2\\n\", \"5 100000000\\n1 2 3 4 5\\n\", \"2 30000000\\n1 3\\n\", \"2 100000000\\n1 2\\n\", \"1 100000000\\n1\\n\", \"6 100000000\\n2 1 2 3 4 3\\n\", \"10 500\\n1 2 3 4 5 9 7 8 9 10\\n\", \"9 2\\n1 2 1 2 1 2 1 2 1000000000\\n\", \"50 20\\n592183311 362557946 154127088 616872926 395353745 675069471 509655682 79915471 356656666 937992998 304422065 724106263 472338455 792258113 796069631 663370025 201799298 566151622 722278085 508905399 703159587 690854023 925377265 11010958 69791159 990158269 535460930 167415727 999216963 237203826 693974848 530462137 555061429 744123832 887168514 479773974 575345653 282142246 899762676 446274594 338501746 168668673 408947684 226311538 645441958 258972430 216333311 658394075 123733185 539429791\\n\", \"10 1\\n589934963 440265648 161048053 196789927 951616256 63404428 660569162 779938975 139312880 31052281\\n\", \"6 1\\n1 1 4 2 3 3\\n\", \"9 2\\n1 2 1 2 1 0 1 2 1000000000\\n\", \"8 32\\n1 2 3 4 5 2 7 8\\n\", \"1 4\\n0\\n\", \"8 64\\n1 1 0 1 1 1 1 1\\n\", \"8 63\\n1 2 3 4 9 6 7 8\\n\", \"2 1001000\\n1 1\\n\", \"2 100000\\n2 4\\n\", \"10 100\\n2 2 3 4 5 6 7 8 9 10\\n\", \"10 100\\n1 1 2 2 2 3 3 1 3 4\\n\", \"3 288383\\n2 0 2\\n\", \"4 2\\n2 2 2 2\\n\", \"2 8\\n2 2\\n\", \"100 1000\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"7 999992\\n1 2 3 7 5 6 7\\n\", \"8 64\\n1 2 3 4 5 6 6 8\\n\", \"3 10000000\\n1 2 4\\n\", \"8 33\\n1 2 3 4 5 6 13 8\\n\", \"6 100000\\n2 1 2 4 4 3\\n\", \"10 1000000\\n1 2 3 4 5 6 6 8 9 10\\n\", \"8 31\\n1 1 2 2 3 0 4 4\\n\", \"81 800\\n2 8 5 1 10 5 9 9 3 5 6 6 2 8 2 2 6 3 8 7 2 5 3 4 3 3 2 7 9 6 8 7 2 9 10 3 8 10 6 5 4 2 3 4 4 5 2 2 4 9 8 5 3 8 8 10 4 2 10 9 7 6 1 3 9 7 1 4 5 9 7 6 1 10 1 1 7 2 4 9 10\\n\", \"2 2\\n1 3\\n\", \"64 40\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"8 65\\n1 2 0 4 5 6 7 8\\n\", \"9 100000000\\n1 2 3 4 9 6 7 8 9\\n\", \"100 800\\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 3 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\\n\", \"6 2168\\n1 1 2 2 3 3\\n\", \"8 18\\n1 1 1 1 1 1 1 1\\n\", \"100 1249\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 33 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100\\n\", \"2 10000\\n1 4\\n\", \"5 1234567\\n0 2 3 4 5\\n\", \"3 11\\n2 2 3\\n\", \"8 30\\n1 2 3 8 5 6 7 8\\n\", \"5 1010000\\n1 2 3 3 4\\n\", \"5 100000\\n1 2 3 5 4\\n\", \"100 1000\\n1 2 3 3 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\\n\", \"20 8\\n1 1 1 0 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2\\n\", \"6 48\\n2 1 2 3 8 3\\n\", \"5 100100\\n1 2 3 3 4\\n\", \"5 100\\n1 2 5 4 5\\n\", \"8 15\\n2 8 5 1 10 5 9 9\\n\", \"8 31\\n1 2 3 4 5 6 7 7\\n\", \"50 400\\n0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600 630 660 690 720 750 780 810 840 870 900 930 960 990 1020 1050 1353 1110 1140 1170 1200 1230 1260 1290 1320 1350 1380 1410 1440 1470\\n\", \"2 64\\n2 2\\n\", \"3 125\\n1 2 3\\n\", \"1 10000000\\n2\\n\", \"5 100000000\\n0 1 2 2 5\\n\", \"2 42611638\\n3 9\\n\", \"2 30000000\\n3 5\\n\", \"1 100000010\\n69\\n\", \"3 100000000\\n2 1 2\\n\", \"5 100000000\\n1 2 3 4 10\\n\", \"2 30000000\\n1 1\\n\", \"2 100000000\\n1 4\\n\", \"1 100000000\\n0\\n\", \"6 100000000\\n2 1 2 3 1 3\\n\", \"10 500\\n1 2 5 4 5 9 7 8 9 10\\n\", \"8 32\\n1 2 3 4 5 2 7 14\\n\", \"1 7\\n0\\n\", \"8 64\\n1 1 0 1 1 1 0 1\\n\", \"8 104\\n1 2 3 4 9 6 7 8\\n\", \"10 100\\n2 2 6 4 5 6 7 8 9 10\\n\", \"10 101\\n1 1 2 2 2 3 3 1 3 4\\n\", \"3 288383\\n0 0 2\\n\", \"4 2\\n2 2 2 0\\n\", \"2 10\\n2 2\\n\", \"100 1000\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1\\n\", \"7 999992\\n2 2 3 7 5 6 7\\n\", \"8 51\\n1 2 3 4 5 6 6 8\\n\"], \"outputs\": [\"2\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"39\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"5\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"42\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"9\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\\n\", \"1\\n\", \"42\\n\", \"9\\n\", \"3\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers.
If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K ⌉ bits to store each value. It then takes nk bits to store the whole file.
To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≤ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities.
Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible.
We remind you that 1 byte contains 8 bits.
k = ⌈ log_{2} K ⌉ is the smallest integer such that K ≤ 2^{k}. In particular, if K = 1, then k = 0.
Input
The first line contains two integers n and I (1 ≤ n ≤ 4 ⋅ 10^{5}, 1 ≤ I ≤ 10^{8}) — the length of the array and the size of the disk in bytes, respectively.
The next line contains n integers a_{i} (0 ≤ a_{i} ≤ 10^{9}) — the array denoting the sound file.
Output
Print a single integer — the minimal possible number of changed elements.
Examples
Input
6 1
2 1 2 3 4 3
Output
2
Input
6 2
2 1 2 3 4 3
Output
0
Input
6 1
1 1 2 2 3 3
Output
2
Note
In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed.
In the second example the disk is larger, so the initial file fits it and no changes are required.
In the third example we have to change both 1s or both 3s.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"2\\n3 2\\n1 3 5\\n4 1\\n5 2 3 5\\n\", \"1\\n3 1383\\n1 2 3\\n\", \"1\\n3 3\\n1 2 3\\n\", \"1\\n2 1383\\n1 2 3\\n\", \"2\\n3 2\\n1 3 5\\n4 1\\n5 4 3 5\\n\", \"2\\n3 2\\n1 1 5\\n4 1\\n5 4 3 5\\n\", \"2\\n3 2\\n0 1 5\\n4 1\\n5 2 3 5\\n\", \"1\\n2 1383\\n1 2 1\\n\", \"1\\n2 501\\n1 2 1\\n\", \"2\\n3 2\\n0 1 5\\n4 1\\n5 4 3 5\\n\", \"1\\n2 501\\n1 2 2\\n\", \"1\\n2 501\\n1 3 2\\n\", \"1\\n2 501\\n1 6 2\\n\", \"1\\n2 501\\n1 6 3\\n\", \"1\\n2 501\\n0 6 3\\n\", \"1\\n3 501\\n0 6 3\\n\", \"1\\n3 176\\n0 6 3\\n\", \"1\\n3 176\\n0 4 3\\n\", \"1\\n3 176\\n0 4 0\\n\", \"1\\n3 144\\n0 4 0\\n\", \"1\\n2 1383\\n1 4 3\\n\", \"1\\n3 3\\n1 2 1\\n\", \"1\\n2 1383\\n1 2 0\\n\", \"2\\n3 2\\n1 1 5\\n3 1\\n5 4 3 5\\n\", \"1\\n2 400\\n1 2 1\\n\", \"1\\n1 501\\n1 2 2\\n\", \"1\\n2 501\\n1 3 3\\n\", \"1\\n2 564\\n1 6 2\\n\", \"1\\n2 501\\n1 4 3\\n\", \"1\\n2 501\\n0 10 3\\n\", \"1\\n3 501\\n0 6 2\\n\", \"1\\n3 176\\n0 6 4\\n\", \"1\\n3 229\\n0 4 0\\n\", \"1\\n2 1383\\n1 3 3\\n\", \"1\\n3 3\\n1 2 0\\n\", \"1\\n2 2313\\n1 2 0\\n\", \"2\\n3 2\\n1 1 5\\n3 1\\n5 1 3 5\\n\", \"1\\n2 400\\n1 4 1\\n\", \"2\\n3 2\\n0 0 5\\n4 1\\n5 2 3 5\\n\", \"1\\n2 501\\n2 3 2\\n\", \"1\\n2 612\\n1 6 2\\n\", \"1\\n2 501\\n0 19 3\\n\", \"1\\n3 501\\n0 11 2\\n\", \"1\\n3 176\\n0 6 5\\n\", \"1\\n3 431\\n0 4 0\\n\", \"1\\n2 1615\\n1 3 3\\n\", \"1\\n2 3271\\n1 2 0\\n\", \"2\\n3 2\\n1 1 5\\n3 1\\n2 1 3 5\\n\", \"1\\n2 645\\n1 4 1\\n\", \"2\\n3 2\\n0 0 7\\n4 1\\n5 2 3 5\\n\", \"1\\n1 501\\n2 3 2\\n\", \"1\\n2 591\\n1 6 2\\n\", \"1\\n2 501\\n0 19 0\\n\", \"1\\n3 501\\n0 11 0\\n\", \"1\\n3 176\\n0 1 5\\n\", \"1\\n1 1615\\n1 3 3\\n\", \"2\\n3 1\\n1 1 5\\n3 1\\n2 1 3 5\\n\", \"1\\n2 645\\n1 4 0\\n\", \"2\\n3 2\\n0 0 7\\n4 1\\n5 3 3 5\\n\", \"1\\n1 501\\n2 3 1\\n\", \"1\\n2 415\\n0 19 0\\n\", \"1\\n3 501\\n0 11 1\\n\", \"1\\n3 85\\n0 1 5\\n\", \"1\\n1 1615\\n1 5 3\\n\", \"2\\n3 1\\n1 1 3\\n3 1\\n2 1 3 5\\n\", \"1\\n2 901\\n1 4 0\\n\", \"1\\n2 501\\n2 3 1\\n\", \"1\\n2 415\\n0 19 1\\n\", \"1\\n3 810\\n0 11 1\\n\", \"1\\n1 25\\n1 5 3\\n\", \"1\\n2 901\\n1 4 1\\n\", \"1\\n2 501\\n1 3 1\\n\", \"1\\n2 476\\n0 19 0\\n\", \"1\\n3 810\\n0 11 0\\n\", \"1\\n2 901\\n1 4 2\\n\", \"1\\n1 501\\n1 3 1\\n\", \"1\\n2 476\\n0 34 0\\n\", \"1\\n3 810\\n0 20 0\\n\", \"1\\n2 901\\n0 4 2\\n\", \"1\\n1 501\\n1 6 1\\n\", \"1\\n3 476\\n0 34 0\\n\", \"1\\n3 810\\n0 20 1\\n\", \"1\\n2 901\\n0 5 2\\n\", \"1\\n1 501\\n1 6 0\\n\", \"1\\n3 553\\n0 34 0\\n\", \"1\\n2 901\\n0 5 4\\n\", \"1\\n1 501\\n1 4 0\\n\", \"1\\n3 553\\n0 28 0\\n\", \"1\\n1 501\\n1 7 0\\n\", \"1\\n3 553\\n0 9 0\\n\", \"1\\n3 1102\\n0 9 0\\n\", \"1\\n3 1102\\n0 16 0\\n\", \"1\\n3 936\\n0 16 0\\n\", \"1\\n3 2395\\n1 2 3\\n\", \"1\\n3 3\\n1 1 3\\n\", \"2\\n3 2\\n1 0 5\\n4 1\\n5 2 3 5\\n\"], \"outputs\": [\"2\\n2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n3\\n\", \"1\\n3\\n\", \"1\\n2\\n\", \"1\\n\", \"1\\n\", \"1\\n3\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n3\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n2\\n\", \"1\\n\", \"1\\n2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n2\\n\", \"1\\n\", \"1\\n2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n2\\n\", \"1\\n\", \"1\\n2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n2\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n2\\n\"]}", "source": "primeintellect"}
|
Ivan plays an old action game called Heretic. He's stuck on one of the final levels of this game, so he needs some help with killing the monsters.
The main part of the level is a large corridor (so large and narrow that it can be represented as an infinite coordinate line). The corridor is divided into two parts; let's assume that the point x = 0 is where these parts meet.
The right part of the corridor is filled with n monsters — for each monster, its initial coordinate x_i is given (and since all monsters are in the right part, every x_i is positive).
The left part of the corridor is filled with crusher traps. If some monster enters the left part of the corridor or the origin (so, its current coordinate becomes less than or equal to 0), it gets instantly killed by a trap.
The main weapon Ivan uses to kill the monsters is the Phoenix Rod. It can launch a missile that explodes upon impact, obliterating every monster caught in the explosion and throwing all other monsters away from the epicenter. Formally, suppose that Ivan launches a missile so that it explodes in the point c. Then every monster is either killed by explosion or pushed away. Let some monster's current coordinate be y, then:
* if c = y, then the monster is killed;
* if y < c, then the monster is pushed r units to the left, so its current coordinate becomes y - r;
* if y > c, then the monster is pushed r units to the right, so its current coordinate becomes y + r.
Ivan is going to kill the monsters as follows: choose some integer point d and launch a missile into that point, then wait until it explodes and all the monsters which are pushed to the left part of the corridor are killed by crusher traps, then, if at least one monster is still alive, choose another integer point (probably the one that was already used) and launch a missile there, and so on.
What is the minimum number of missiles Ivan has to launch in order to kill all of the monsters? You may assume that every time Ivan fires the Phoenix Rod, he chooses the impact point optimally.
You have to answer q independent queries.
Input
The first line contains one integer q (1 ≤ q ≤ 10^5) — the number of queries.
The first line of each query contains two integers n and r (1 ≤ n, r ≤ 10^5) — the number of enemies and the distance that the enemies are thrown away from the epicenter of the explosion.
The second line of each query contains n integers x_i (1 ≤ x_i ≤ 10^5) — the initial positions of the monsters.
It is guaranteed that sum of all n over all queries does not exceed 10^5.
Output
For each query print one integer — the minimum number of shots from the Phoenix Rod required to kill all monsters.
Example
Input
2
3 2
1 3 5
4 1
5 2 3 5
Output
2
2
Note
In the first test case, Ivan acts as follows:
* choose the point 3, the first monster dies from a crusher trap at the point -1, the second monster dies from the explosion, the third monster is pushed to the point 7;
* choose the point 7, the third monster dies from the explosion.
In the second test case, Ivan acts as follows:
* choose the point 5, the first and fourth monsters die from the explosion, the second monster is pushed to the point 1, the third monster is pushed to the point 2;
* choose the point 2, the first monster dies from a crusher trap at the point 0, the second monster dies from the explosion.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"7 3 2\\n1 2 1\\n\", \"10 1 5\\n2\\n\", \"10 1 11\\n1\\n\", \"15 2 5\\n1 1\\n\", \"1000 16 2\\n20 13 16 13 22 10 18 21 18 20 20 16 19 9 11 22\\n\", \"6 3 1\\n1 2 3\\n\", \"11 1 5\\n2\\n\", \"7 1 2\\n4\\n\", \"5 2 1\\n1 1\\n\", \"10 1 4\\n10\\n\", \"10 10 1\\n1 1 1 1 1 1 1 1 1 1\\n\", \"8 4 1\\n1 1 4 1\\n\", \"3 1 1\\n2\\n\", \"1 1 1\\n1\\n\", \"5 1 2\\n2\\n\", \"50 4 7\\n4 7 10 3\\n\", \"10 9 1\\n1 1 1 1 1 1 1 1 1\\n\", \"100 1 49\\n100\\n\", \"1000 20 8\\n3 6 3 4 3 5 3 5 5 5 3 1 3 8 2 4 4 5 3 2\\n\", \"8 3 2\\n1 1 1\\n\", \"100 1 49\\n3\\n\", \"10 1 5\\n1\\n\", \"2 2 1\\n1 1\\n\", \"20 20 20\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"4 1 2\\n1\\n\", \"12 1 4\\n5\\n\", \"4 2 1\\n2 1\\n\", \"12 3 2\\n1 2 1\\n\", \"8 2 2\\n2 2\\n\", \"4 4 1\\n1 1 1 1\\n\", \"1000 11 33\\n2 1 5 1 3 1 3 1 3 2 1\\n\", \"5 4 1\\n1 1 1 1\\n\", \"1000 77 3\\n2 3 2 1 3 3 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 2 2 1 4 4 3 1 2 3 2 1 4 1 3 3 2 4 3 1 5 1 3 4 4 2 3 2 4 3 4 3 1 6 5 2 3 4 3 3 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3 1 2 6 5 4 2 6 2 3 2 3 4 3 1 2 7 5 3 6 4 1 4 4 4 5 3 2 1 2 3 4 3 2 4 2 2 3 1 2 2 5 1 1 4 1 4 3 5 3 2 3 5 3 4 4 4 4 7 2 3 1 3 3 2 3 2 5 4 1 1 4 4 5 2 4 2 3 4 2 3 1 3 2 4 1 2\\n\", \"10 1 7\\n2\\n\", \"50 4 13\\n4 13 20 3\\n\", \"1000 232 105\\n4 3 4 4 6 1 4 3 4 1 4 1 4 2 2 3 2 6 3 2 6 1 1 4 1 2 4 2 3 2 5 2 3 4 3 3 3 2 5 4 2 5 4 2 4 4 4 2 4 1 3 5 4 4 5 3 6 5 3 3 4 4 2 3 3 3 1 4 4 3 2 3 2 5 4 3 2 4 3 1 2 5 6 2 3 6 3 2 2 2 2 2 6 4 4 5 5 1 4 2 5 1 6 4 2 2 3 7 2 3 3 2 4 4 2 3 2 3 3 4 1 3 2 3 2 7 7 3 3 3 4 2 2 3 2 3 4 2 6 3 4 3 3 5 2 3 1 2 6 5 4 2 6 2 3 2 3 4 3 1 2 7 5 3 6 4 1 4 4 4 5 3 2 1 2 3 4 3 2 4 2 2 3 1 2 2 5 1 1 4 1 4 3 5 3 2 3 5 3 4 4 4 4 7 2 3 1 3 3 2 3 2 5 4 1 1 4 4 5 2 4 2 3 4 2 3 1 3 2 4 1 2\\n\", \"1000 232 105\\n4 3 4 4 6 1 4 3 4 1 4 1 4 2 2 3 2 6 3 2 6 1 1 4 1 2 4 2 3 2 5 2 3 4 3 3 3 2 5 4 2 5 4 2 4 4 4 2 4 1 3 5 4 4 5 3 6 5 3 3 4 4 2 3 3 3 1 4 4 3 2 3 2 5 4 3 2 4 3 1 2 5 6 2 3 6 3 2 2 2 2 2 6 4 4 5 5 1 4 2 5 1 6 4 2 2 3 7 2 3 3 2 4 4 2 3 2 3 3 4 1 3 2 3 2 7 7 3 3 3 4 2 2 3 2 3 4 2 8 3 4 3 3 5 2 3 1 2 6 5 4 2 6 2 3 2 3 4 3 1 2 7 5 3 6 4 1 4 4 4 5 3 2 1 2 3 4 3 2 4 2 2 3 1 2 2 5 1 1 4 1 4 3 5 3 2 3 5 3 4 4 4 4 7 2 3 1 3 3 2 3 2 5 4 1 1 4 4 5 2 4 2 3 4 2 3 1 3 2 4 1 2\\n\", \"1000 232 105\\n4 3 4 4 6 1 4 3 4 1 4 1 4 2 2 3 2 6 3 2 6 1 1 4 1 2 4 2 3 2 5 2 3 4 3 3 3 2 5 4 2 5 4 2 4 4 4 2 4 1 3 5 4 4 5 3 6 5 3 3 4 4 2 3 3 3 1 4 4 3 2 3 2 5 4 3 2 4 3 1 2 5 6 2 4 6 3 2 2 2 2 2 6 4 4 5 5 1 4 2 5 1 6 4 2 2 3 7 2 3 3 2 4 4 2 3 2 3 3 4 1 3 2 3 2 7 7 3 3 3 4 2 2 3 2 3 4 2 8 3 4 3 3 5 2 3 1 2 6 5 4 2 6 2 3 2 3 4 3 1 2 7 5 3 6 4 1 4 4 4 5 3 2 1 2 3 4 3 2 4 2 2 3 1 2 2 5 1 1 4 1 4 3 5 3 2 3 5 3 4 4 4 4 7 2 3 1 3 3 2 3 2 5 4 1 1 4 4 5 2 4 2 3 4 2 3 1 3 2 4 1 2\\n\", \"1000 232 105\\n4 3 4 4 6 1 4 3 4 1 4 1 4 2 2 3 2 6 3 2 6 1 1 4 1 2 4 2 3 2 5 2 3 4 3 3 3 2 5 4 2 5 4 2 4 4 4 2 4 1 3 5 4 4 5 3 6 5 3 3 4 4 2 3 3 3 1 4 4 3 2 3 2 5 4 3 2 4 3 1 2 5 6 2 4 6 3 2 2 2 2 2 6 4 4 5 5 1 4 2 5 1 6 4 3 2 3 7 2 3 3 2 4 4 2 3 2 3 3 4 1 3 2 3 2 7 7 3 3 3 4 2 2 3 2 3 4 2 8 3 4 3 3 5 2 3 1 2 6 5 4 2 6 2 3 2 3 4 3 1 2 7 5 3 6 4 1 4 4 4 5 3 2 1 2 3 4 3 2 4 2 2 3 1 2 2 5 1 1 4 1 4 3 5 3 2 3 5 3 4 4 4 4 7 2 3 1 3 3 2 3 2 5 4 1 1 4 4 5 2 4 2 3 4 2 3 1 3 2 4 1 2\\n\", \"1000 232 105\\n4 3 4 4 6 1 4 3 4 1 4 1 4 2 2 3 2 6 3 2 6 1 1 4 1 2 4 2 3 2 5 2 3 4 3 3 3 2 5 4 2 5 4 2 4 4 4 2 4 1 3 5 4 4 5 3 6 5 3 3 4 4 2 3 3 3 1 4 4 3 2 3 2 5 4 3 2 4 3 1 2 5 6 2 4 6 3 2 2 2 2 2 6 4 4 5 5 1 4 2 5 1 6 4 3 2 3 7 2 3 3 2 4 4 2 3 2 3 3 4 1 3 2 3 2 7 7 3 3 3 4 2 2 3 2 3 4 2 8 3 4 3 3 5 2 3 1 2 6 5 4 2 6 2 3 2 3 4 3 1 2 7 5 3 6 4 1 4 4 4 5 3 2 1 2 3 4 3 2 4 2 2 3 1 2 2 5 1 1 4 1 4 3 5 3 2 3 5 3 4 4 4 4 7 2 3 1 3 3 2 3 2 5 4 1 1 4 4 5 4 4 2 3 4 2 3 1 3 2 4 1 2\\n\", \"1000 232 105\\n4 3 4 4 6 1 4 3 4 1 4 1 4 2 2 3 2 6 3 2 6 1 1 4 1 2 4 2 3 2 5 2 3 4 3 3 3 2 5 4 2 5 4 2 4 4 4 2 4 1 3 5 4 4 5 3 6 5 3 3 4 4 2 3 3 3 1 4 4 3 2 3 2 5 4 3 2 4 3 1 2 5 6 2 4 6 3 2 2 2 2 2 6 4 4 5 5 1 4 2 5 1 6 4 3 2 3 7 2 3 3 2 4 4 2 3 2 3 3 4 1 3 2 3 2 7 7 3 3 3 4 1 2 3 2 3 4 2 8 3 4 3 3 5 2 3 1 2 6 5 4 2 6 2 3 2 3 4 3 1 2 7 5 3 6 4 1 4 4 4 5 3 2 1 2 3 4 3 2 4 2 2 3 1 2 2 5 1 1 4 1 4 3 5 3 2 3 5 3 4 4 4 4 7 2 3 1 3 3 2 3 2 5 4 1 1 4 4 5 4 4 2 3 4 2 3 1 3 2 4 1 2\\n\", \"11 1 2\\n2\\n\", \"5 2 1\\n1 0\\n\", \"8 1 2\\n2\\n\", \"1000 20 8\\n3 6 3 4 3 5 3 10 5 5 3 1 3 8 2 4 4 5 3 2\\n\", \"101 1 49\\n3\\n\", \"7 1 2\\n1\\n\", \"15 3 2\\n1 2 1\\n\", \"1000 11 33\\n2 1 3 1 3 1 3 1 3 2 1\\n\", \"1000 77 3\\n2 3 2 1 3 3 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 2 2 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 2 4 3 4 3 1 6 5 2 3 4 3 3 5 5 2 1 2 2 3 2 2 5 1 3 5 5 4 2\\n\", \"1001 6 25\\n24 19 21 18 28 16\\n\", \"4 1 1\\n1\\n\", \"12 1 1\\n6\\n\", \"9 3 2\\n0 2 1\\n\", \"15 2 5\\n1 0\\n\", \"1000 16 2\\n20 13 16 13 41 10 18 21 18 20 20 16 19 16 11 22\\n\", \"12 1 2\\n2\\n\", \"7 2 1\\n1 0\\n\", \"1000 20 8\\n2 6 3 4 3 5 3 10 5 5 3 1 3 8 2 4 4 5 3 2\\n\", \"111 1 49\\n3\\n\", \"7 1 2\\n0\\n\", \"1000 11 33\\n2 1 3 1 3 1 4 1 3 2 1\\n\", \"1000 77 3\\n2 3 2 1 3 3 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 2 2 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 2 4 3 4 3 1 6 5 2 3 4 3 3 5 5 2 1 2 2 3 2 2 9 1 3 5 5 4 2\\n\", \"1001 6 25\\n24 19 21 16 28 16\\n\", \"10 3 2\\n0 2 1\\n\", \"1000 16 2\\n20 13 16 13 41 10 18 21 18 21 20 16 19 16 11 22\\n\", \"12 1 2\\n0\\n\", \"1000 20 2\\n2 6 3 4 3 5 3 10 5 5 3 1 3 8 2 4 4 5 3 2\\n\", \"111 1 49\\n6\\n\", \"1000 11 33\\n2 1 3 1 3 1 4 1 6 2 1\\n\", \"1000 77 3\\n2 3 2 1 3 3 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 2 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 2 4 3 4 3 1 6 5 2 3 4 3 3 5 5 2 1 2 2 3 2 2 9 1 3 5 5 4 2\\n\", \"1001 6 10\\n24 19 21 16 28 16\\n\", \"1000 16 2\\n20 13 10 13 41 10 18 21 18 21 20 16 19 16 11 22\\n\", \"1000 20 2\\n2 6 3 4 3 5 3 10 5 5 3 1 6 8 2 4 4 5 3 2\\n\", \"111 1 16\\n6\\n\", \"1000 77 2\\n2 3 2 1 3 3 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 2 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 2 4 3 4 3 1 6 5 2 3 4 3 3 5 5 2 1 2 2 3 2 2 9 1 3 5 5 4 2\\n\", \"1000 16 2\\n20 13 10 13 41 10 18 21 18 21 20 25 19 16 11 22\\n\", \"1000 20 2\\n2 5 3 4 3 5 3 10 5 5 3 1 6 8 2 4 4 5 3 2\\n\", \"111 1 16\\n5\\n\", \"1000 77 2\\n2 3 2 1 3 3 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 2 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 2 4 3 4 3 1 8 5 2 3 4 3 3 5 5 2 1 2 2 3 2 2 9 1 3 5 5 4 2\\n\", \"1000 16 2\\n20 13 10 13 76 10 18 21 18 21 20 25 19 16 11 22\\n\", \"1000 20 2\\n2 5 3 4 3 5 6 10 5 5 3 1 6 8 2 4 4 5 3 2\\n\", \"111 1 16\\n4\\n\", \"1000 77 2\\n2 3 2 1 3 3 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 3 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 2 4 3 4 3 1 8 5 2 3 4 3 3 5 5 2 1 2 2 3 2 2 9 1 3 5 5 4 2\\n\", \"1000 16 2\\n32 13 10 13 76 10 18 21 18 21 20 25 19 16 11 22\\n\", \"1000 20 2\\n2 5 3 4 3 5 6 10 5 5 3 1 4 8 2 4 4 5 3 2\\n\", \"111 1 16\\n1\\n\", \"1000 77 2\\n2 3 2 1 3 3 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 3 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 3 4 3 4 3 1 8 5 2 3 4 3 3 5 5 2 1 2 2 3 2 2 9 1 3 5 5 4 2\\n\", \"1000 16 2\\n32 13 10 13 76 10 18 21 18 22 20 25 19 16 11 22\\n\", \"1000 20 2\\n2 5 3 4 3 5 6 10 5 5 3 1 4 8 2 2 4 5 3 2\\n\", \"1000 77 2\\n2 3 2 1 3 3 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 3 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 3 4 0 4 3 1 8 5 2 3 4 3 3 5 5 2 1 2 2 3 2 2 9 1 3 5 5 4 2\\n\", \"1000 16 2\\n32 13 10 3 76 10 18 21 18 22 20 25 19 16 11 22\\n\", \"1000 20 2\\n2 5 3 4 3 5 6 10 5 5 3 1 3 8 2 2 4 5 3 2\\n\", \"1000 77 2\\n2 3 2 1 3 3 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 3 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 3 4 0 4 3 1 8 5 2 3 4 3 3 5 5 2 1 2 0 3 2 2 9 1 3 5 5 4 2\\n\", \"1000 16 2\\n32 13 10 0 76 10 18 21 18 22 20 25 19 16 11 22\\n\", \"1000 20 2\\n2 5 1 4 3 5 6 10 5 5 3 1 3 8 2 2 4 5 3 2\\n\", \"1000 77 2\\n2 3 2 1 3 1 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 3 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 3 4 0 4 3 1 8 5 2 3 4 3 3 5 5 2 1 2 0 3 2 2 9 1 3 5 5 4 2\\n\", \"1000 16 2\\n32 13 10 0 76 10 18 21 18 22 16 25 19 16 11 22\\n\", \"1000 20 2\\n2 5 1 4 3 5 6 10 5 5 3 0 3 8 2 2 4 5 3 2\\n\", \"1000 77 2\\n2 3 2 1 3 1 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 3 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 3 4 0 4 3 1 1 5 2 3 4 3 3 5 5 2 1 2 0 3 2 2 9 1 3 5 5 4 2\\n\", \"1000 16 2\\n32 13 10 0 76 13 18 21 18 22 16 25 19 16 11 22\\n\", \"1000 20 2\\n2 5 0 4 3 5 6 10 5 5 3 0 3 8 2 2 4 5 3 2\\n\", \"1000 77 2\\n2 3 2 1 3 1 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 3 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 3 4 0 4 3 1 1 5 2 3 4 3 3 5 5 2 1 2 0 3 2 2 10 1 3 5 5 4 2\\n\", \"1000 16 2\\n32 13 10 0 76 13 18 25 18 22 16 25 19 16 11 22\\n\", \"1000 20 2\\n2 5 0 4 3 5 6 10 5 5 3 0 3 8 2 3 4 5 3 2\\n\", \"1000 77 2\\n2 3 2 1 3 1 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 3 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 3 4 0 4 3 1 1 5 2 3 4 3 3 5 5 2 1 2 0 3 2 2 10 1 3 10 5 4 2\\n\", \"1000 16 2\\n32 13 10 0 76 13 18 25 18 22 16 25 19 16 11 32\\n\", \"1000 20 2\\n2 5 0 4 3 5 6 10 5 5 3 0 3 8 2 3 4 5 1 2\\n\", \"1000 77 2\\n2 3 2 1 3 1 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 3 1 4 4 3 1 2 3 2 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 3 4 0 4 3 1 1 5 2 5 4 3 3 5 5 2 1 2 0 3 2 2 10 1 3 10 5 4 2\\n\", \"1000 16 2\\n32 13 10 0 46 13 18 25 18 22 16 25 19 16 11 32\\n\", \"1000 20 2\\n2 5 0 4 3 5 6 10 5 5 3 0 3 9 2 3 4 5 1 2\\n\", \"1000 77 2\\n2 3 2 1 3 1 3 3 4 5 4 3 3 1 3 5 1 4 3 2 5 3 3 3 1 4 4 3 1 2 3 4 1 1 1 3 3 2 4 3 1 5 1 3 4 4 2 3 3 4 0 4 3 1 1 5 2 5 4 3 3 5 5 2 1 2 0 3 2 2 10 1 3 10 5 4 2\\n\"], \"outputs\": [\"YES\\n0 1 0 2 2 0 3\\n\", \"YES\\n0 0 0 0 1 1 0 0 0 0\\n\", \"YES\\n0 0 0 0 0 0 0 0 0 1\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n1 2 2 3 3 3\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n1 1 1 1 1 1 1 1 1 1\\n\", \"YES\\n1 2 3 4 5 6 7 8 9 10\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n1\\n\", \"NO\\n\", \"YES\\n0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 0 0 0 0 0 0 4 4 4 0 0\\n\", \"NO\\n\", \"YES\\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n1 2\\n\", \"YES\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n1 2 3 4\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 4 4 4 4 5 5 5 5 5 5 6 7 7 7 7 8 8 8 9 9 9 9 10 11 11 11 11 12 13 13 13 13 14 14 15 15 16 16 16 17 17 18 18 18 18 18 18 19 19 19 20 20 21 21 21 21 21 21 22 23 24 24 24 24 25 26 26 27 27 27 27 28 28 29 29 29 30 30 31 31 31 31 31 32 32 33 33 33 34 34 34 34 35 35 35 36 36 36 37 37 37 38 38 39 39 39 39 39 40 40 40 40 41 41 42 42 42 42 42 43 43 43 43 44 44 45 45 46 46 46 46 47 47 47 47 48 48 49 49 49 49 50 51 51 51 52 52 52 52 52 53 53 53 53 54 54 54 54 55 55 55 55 55 56 56 56 57 57 57 57 57 57 58 58 58 58 58 59 59 59 60 60 60 61 61 61 61 62 62 62 62 63 63 64 64 64 65 65 65 66 66 66 67 68 68 68 68 69 69 69 69 70 70 70 71 71 72 72 72 73 73 74 74 74 74 74 75 75 75 75 76 76 76 77 77 78 78 78 78 79 79 79 80 81 81 82 82 82 82 82 83 83 83 83 83 83 84 84 85 85 85 86 86 86 86 86 86 87 87 87 88 88 89 89 90 90 91 91 92 92 93 93 93 93 93 93 94 94 94 94 95 95 95 95 96 96 96 96 96 97 97 97 97 97 98 99 99 99 99 100 100 101 101 101 101 101 102 103 103 103 103 103 103 104 104 104 104 105 105 106 106 107 107 107 108 108 108 108 108 108 108 109 109 110 110 110 111 111 111 112 112 113 113 113 113 114 114 114 114 115 115 116 116 116 117 117 118 118 118 119 119 119 120 120 120 120 121 122 122 122 123 123 124 124 124 125 125 126 126 126 126 126 126 126 127 127 127 127 127 127 127 128 128 128 129 129 129 130 130 130 131 131 131 131 132 132 133 133 134 134 134 135 135 136 136 136 137 137 137 137 138 138 139 139 139 140 140 140 141 141 141 141 142 142 142 143 143 143 144 144 144 144 144 145 145 146 146 146 147 148 148 149 149 149 149 149 149 150 150 150 150 150 151 151 151 151 152 152 153 153 153 153 153 153 154 154 155 155 155 156 156 157 157 157 158 158 158 158 159 159 159 160 161 161 162 162 162 162 162 162 162 163 163 163 163 163 164 164 164 165 165 165 165 165 165 166 166 166 166 167 168 168 168 168 169 169 169 169 170 170 170 170 171 171 171 171 171 172 172 172 173 173 174 175 175 176 176 176 177 177 177 177 178 178 178 179 179 180 180 180 180 181 181 182 182 183 183 183 184 185 185 186 186 187 187 187 187 187 188 189 190 190 190 190 191 192 192 192 192 193 193 193 194 194 194 194 194 195 195 195 196 196 197 197 197 198 198 198 198 198 199 199 199 200 200 200 200 201 201 201 201 202 202 202 202 203 203 203 203 204 204 204 204 204 204 204 205 205 206 206 206 207 208 208 208 209 209 209 210 210 211 211 211 212 212 213 213 213 213 213 214 214 214 214 215 216 217 217 217 217 218 218 218 218 219 219 219 219 219 220 220 221 221 221 222 222 223 223 223 224 224 224 224 225 225 226 226 226 227 228 228 228 229 229 230 230 230 230 231 232 232\\n\", \"NO\\n\", \"NO\\n\", \"YES\\n1 1 2 2 2\\n\", \"YES\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 64 64 64 64 64 65 65 65 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66 66\\n\", \"YES\\n0 0 0 0 1 0 0 0 0 2 2 0 0 0 0\\n\", \"NO\\n\", \"YES\\n1 2 2 3 3 3\\n\", \"YES\\n1 2 3 3 3 3 4 4\\n\", \"YES\\n0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 0 0 4 4 4\\n\", \"YES\\n0 0 0 0 0 1 0 0 0 0\\n\", \"YES\\n0 1 1 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\"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\", \"NO\\n\"]}", "source": "primeintellect"}
|
There is a river of width n. The left bank of the river is cell 0 and the right bank is cell n + 1 (more formally, the river can be represented as a sequence of n + 2 cells numbered from 0 to n + 1). There are also m wooden platforms on a river, the i-th platform has length c_i (so the i-th platform takes c_i consecutive cells of the river). It is guaranteed that the sum of lengths of platforms does not exceed n.
You are standing at 0 and want to reach n+1 somehow. If you are standing at the position x, you can jump to any position in the range [x + 1; x + d]. However you don't really like the water so you can jump only to such cells that belong to some wooden platform. For example, if d=1, you can jump only to the next position (if it belongs to the wooden platform). You can assume that cells 0 and n+1 belong to wooden platforms.
You want to know if it is possible to reach n+1 from 0 if you can move any platform to the left or to the right arbitrary number of times (possibly, zero) as long as they do not intersect each other (but two platforms can touch each other). It also means that you cannot change the relative order of platforms.
Note that you should move platforms until you start jumping (in other words, you first move the platforms and then start jumping).
For example, if n=7, m=3, d=2 and c = [1, 2, 1], then one of the ways to reach 8 from 0 is follow:
<image> The first example: n=7.
Input
The first line of the input contains three integers n, m and d (1 ≤ n, m, d ≤ 1000, m ≤ n) — the width of the river, the number of platforms and the maximum distance of your jump, correspondingly.
The second line of the input contains m integers c_1, c_2, ..., c_m (1 ≤ c_i ≤ n, ∑_{i=1}^{m} c_i ≤ n), where c_i is the length of the i-th platform.
Output
If it is impossible to reach n+1 from 0, print NO in the first line. Otherwise, print YES in the first line and the array a of length n in the second line — the sequence of river cells (excluding cell 0 and cell n + 1).
If the cell i does not belong to any platform, a_i should be 0. Otherwise, it should be equal to the index of the platform (1-indexed, platforms are numbered from 1 to m in order of input) to which the cell i belongs.
Note that all a_i equal to 1 should form a contiguous subsegment of the array a of length c_1, all a_i equal to 2 should form a contiguous subsegment of the array a of length c_2, ..., all a_i equal to m should form a contiguous subsegment of the array a of length c_m. The leftmost position of 2 in a should be greater than the rightmost position of 1, the leftmost position of 3 in a should be greater than the rightmost position of 2, ..., the leftmost position of m in a should be greater than the rightmost position of m-1.
See example outputs for better understanding.
Examples
Input
7 3 2
1 2 1
Output
YES
0 1 0 2 2 0 3
Input
10 1 11
1
Output
YES
0 0 0 0 0 0 0 0 0 1
Input
10 1 5
2
Output
YES
0 0 0 0 1 1 0 0 0 0
Note
Consider the first example: the answer is [0, 1, 0, 2, 2, 0, 3]. The sequence of jumps you perform is 0 → 2 → 4 → 5 → 7 → 8.
Consider the second example: it does not matter how to place the platform because you always can jump from 0 to 11.
Consider the third example: the answer is [0, 0, 0, 0, 1, 1, 0, 0, 0, 0]. The sequence of jumps you perform is 0 → 5 → 6 → 11.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
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|
Bob is about to take a hot bath.
There are two taps to fill the bath: a hot water tap and a cold water tap. The cold water's temperature is t1, and the hot water's temperature is t2. The cold water tap can transmit any integer number of water units per second from 0 to x1, inclusive. Similarly, the hot water tap can transmit from 0 to x2 water units per second.
If y1 water units per second flow through the first tap and y2 water units per second flow through the second tap, then the resulting bath water temperature will be:
<image>
Bob wants to open both taps so that the bath water temperature was not less than t0. However, the temperature should be as close as possible to this value. If there are several optimal variants, Bob chooses the one that lets fill the bath in the quickest way possible.
Determine how much each tap should be opened so that Bob was pleased with the result in the end.
Input
You are given five integers t1, t2, x1, x2 and t0 (1 ≤ t1 ≤ t0 ≤ t2 ≤ 106, 1 ≤ x1, x2 ≤ 106).
Output
Print two space-separated integers y1 and y2 (0 ≤ y1 ≤ x1, 0 ≤ y2 ≤ x2).
Examples
Input
10 70 100 100 25
Output
99 33
Input
300 500 1000 1000 300
Output
1000 0
Input
143 456 110 117 273
Output
76 54
Note
In the second sample the hot water tap shouldn't be opened, but the cold water tap should be opened at full capacity in order to fill the bath in the quickest way possible.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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34 35 36 37 38 39 40 41 76 43 44 45 46 47 48 41 50 51 52 53 54 55 97 57 58 59 60 61 62 63 64 65 66 67 68 30 70 71 72 73 74 75 76 77 78 79 80 81 88 83 84 85 86 87 88 265 90 91 92 93 94 95 96 97 98 99 100\\n\", \"50\\n0 2 3 4 5 6 7 8 9 10 2 12 13 14 17 16 11 18 18 20 1 22 23 24 26 14 27 28 29 30 31 32 33 34 35 36 0 38 39 14 41 41 43 44 45 46 47 48 49 50\\n\", \"51\\n50 52 52 7 54 55 56 57 58 59 60 61 62 63 64 65 66 67 59 69 70 71 72 75 74 75 70 100 78 84 80 81 82 83 84 85 86 87 88 16 90 91 92 93 94 307 96 97 98 99 100\\n\", \"100\\n1 2 3 4 5 6 7 15 9 10 11 5 13 14 15 16 17 18 19 20 3 22 23 24 25 26 27 28 29 29 43 32 33 34 35 36 37 38 39 40 41 76 43 44 45 46 47 48 41 50 51 52 53 54 55 97 57 58 59 60 61 62 63 64 65 66 67 68 30 70 71 72 73 74 75 76 77 78 79 80 81 88 83 84 85 86 87 88 265 90 91 92 93 94 95 96 97 98 99 100\\n\", \"50\\n0 2 3 4 5 6 7 8 9 10 2 12 13 14 17 16 11 18 18 20 1 22 23 24 26 4 27 28 29 30 31 32 33 34 35 36 0 38 39 14 41 41 43 44 45 46 47 48 49 50\\n\", \"100\\n1 2 3 4 5 6 7 15 9 10 11 5 13 14 15 16 17 18 19 20 3 22 23 24 16 26 27 28 29 29 43 32 33 34 35 36 37 38 39 40 41 76 43 44 45 46 47 48 41 50 51 52 53 54 55 97 57 58 59 60 61 62 63 64 65 66 67 68 30 70 71 72 73 74 75 76 77 78 79 80 81 88 83 84 85 86 87 88 265 90 91 92 93 94 95 96 97 98 99 100\\n\", \"50\\n0 2 3 4 5 6 7 8 9 10 2 12 13 14 17 16 11 18 18 20 1 22 23 24 26 4 27 28 29 30 31 32 33 34 35 36 0 38 39 14 41 41 43 44 45 46 47 21 49 50\\n\", \"100\\n1 2 3 4 5 6 7 15 11 10 11 5 13 14 15 16 17 18 19 20 3 22 23 24 16 26 27 28 29 29 43 32 33 34 35 36 37 38 39 40 41 76 43 44 45 46 47 48 41 50 51 52 53 54 55 97 57 58 59 60 61 62 63 64 65 66 67 68 30 70 71 72 73 74 75 76 77 78 79 80 81 88 83 84 85 86 87 88 265 90 91 92 93 94 95 96 97 98 99 100\\n\", \"51\\n50 52 52 7 54 55 56 57 58 59 60 61 62 63 64 65 66 67 59 69 70 71 72 75 74 75 70 100 78 84 80 81 82 83 84 85 11 87 88 16 90 91 92 93 94 307 77 97 98 99 101\\n\", \"100\\n1 2 3 4 5 6 7 15 11 10 11 5 20 14 15 16 17 18 19 20 3 22 23 24 16 26 27 28 29 29 43 32 33 34 35 36 37 38 39 40 41 76 43 44 45 46 47 48 41 50 51 52 53 54 55 97 57 58 59 60 61 62 63 64 65 66 67 68 30 70 71 72 73 74 75 76 77 78 79 80 81 88 83 84 85 86 87 88 265 90 91 92 93 94 95 96 97 98 99 100\\n\", \"50\\n0 2 3 4 5 1 7 8 9 10 2 12 13 14 17 16 11 18 18 20 1 22 23 24 26 4 27 28 29 30 31 32 33 34 35 36 0 38 39 18 41 41 43 44 45 46 47 21 49 50\\n\", \"3\\n1 2 4\\n\", \"2\\n2 0\\n\", \"3\\n0 1 8\\n\", \"3\\n0 2 4\\n\", \"2\\n0 0\\n\", \"3\\n0 2 5\\n\", \"51\\n50 52 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 75 74 75 70 134 78 84 80 81 82 83 84 85 86 87 88 10 90 91 92 93 94 307 96 97 98 99 100\\n\", \"50\\n0 2 3 4 5 6 7 8 9 10 2 12 13 14 17 16 17 18 18 20 1 22 23 24 26 14 27 28 29 30 31 32 33 34 35 36 0 38 39 14 41 42 43 44 45 46 47 48 49 50\\n\", \"51\\n50 52 52 7 54 55 56 57 58 59 60 61 62 63 64 65 66 67 59 69 70 71 72 75 74 75 70 100 78 84 80 81 82 83 84 85 86 87 88 16 90 91 92 93 94 307 77 97 98 99 100\\n\", \"51\\n50 52 52 7 54 55 56 57 58 59 60 61 62 63 64 65 66 67 59 69 70 71 72 75 74 75 70 100 78 84 80 81 82 83 84 85 86 87 88 16 90 91 92 93 94 307 77 97 98 99 101\\n\", \"50\\n0 2 3 4 5 1 7 8 9 10 2 12 13 14 17 16 11 18 18 20 1 22 23 24 26 4 27 28 29 30 31 32 33 34 35 36 0 38 39 14 41 41 43 44 45 46 47 21 49 50\\n\"], \"outputs\": [\"2\\n\", \"3\\n\", \"148\\n\", \"102\\n\", \"2\\n\", \"3\\n\", \"4\\n\", \"188\\n\", \"43\\n\", \"1\\n\", \"89\\n\", \"0\\n\", \"2\\n\", \"14\\n\", \"125\\n\", \"100\\n\", \"4\\n\", \"42\\n\", \"32\\n\", \"82\\n\", \"60\\n\", \"162\\n\", \"38\\n\", \"58\\n\", \"159\\n\", \"117\\n\", \"34\\n\", \"195\\n\", \"88\\n\", \"46\\n\", \"235\\n\", \"116\\n\", \"201\\n\", \"111\\n\", \"62\\n\", \"64\\n\", \"126\\n\", \"428\\n\", \"79\\n\", \"146\\n\", \"365\\n\", \"97\\n\", \"178\\n\", \"313\\n\", \"7\\n\", \"276\\n\", \"112\\n\", \"290\\n\", \"72\\n\", \"297\\n\", \"11\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"32\\n\", \"60\\n\", \"58\\n\", \"64\\n\", \"79\\n\"]}", "source": "primeintellect"}
|
Catherine received an array of integers as a gift for March 8. Eventually she grew bored with it, and she started calculated various useless characteristics for it. She succeeded to do it for each one she came up with. But when she came up with another one — xor of all pairwise sums of elements in the array, she realized that she couldn't compute it for a very large array, thus she asked for your help. Can you do it? Formally, you need to compute
$$$ (a_1 + a_2) ⊕ (a_1 + a_3) ⊕ … ⊕ (a_1 + a_n) \\\ ⊕ (a_2 + a_3) ⊕ … ⊕ (a_2 + a_n) \\\ … \\\ ⊕ (a_{n-1} + a_n) \\\ $$$
Here x ⊕ y is a bitwise XOR operation (i.e. x ^ y in many modern programming languages). You can read about it in Wikipedia: <https://en.wikipedia.org/wiki/Exclusive_or#Bitwise_operation>.
Input
The first line contains a single integer n (2 ≤ n ≤ 400 000) — the number of integers in the array.
The second line contains integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^7).
Output
Print a single integer — xor of all pairwise sums of integers in the given array.
Examples
Input
2
1 2
Output
3
Input
3
1 2 3
Output
2
Note
In the first sample case there is only one sum 1 + 2 = 3.
In the second sample case there are three sums: 1 + 2 = 3, 1 + 3 = 4, 2 + 3 = 5. In binary they are represented as 011_2 ⊕ 100_2 ⊕ 101_2 = 010_2, thus the answer is 2.
⊕ is the bitwise xor operation. To define x ⊕ y, consider binary representations of integers x and y. We put the i-th bit of the result to be 1 when exactly one of the i-th bits of x and y is 1. Otherwise, the i-th bit of the result is put to be 0. For example, 0101_2 ⊕ 0011_2 = 0110_2.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"3\\n1 2 3\\n\", \"3\\n1 1 3\\n\", \"4\\n0 0 0 2\\n\", \"7\\n0 0 2 2 5 5 6\\n\", \"1\\n1\\n\", \"10\\n1 2 3 4 4 4 7 7 7 10\\n\", \"1\\n0\\n\", \"3\\n1 1 1\\n\", \"4\\n0 0 0 3\\n\", \"4\\n0 0 0 1\\n\", \"3\\n0 2 3\\n\", \"7\\n0 0 2 2 3 5 6\\n\", \"3\\n0 1 1\\n\", \"4\\n0 0 1 3\\n\", \"4\\n0 0 1 1\\n\", \"3\\n0 2 2\\n\", \"7\\n0 0 2 2 3 5 7\\n\", \"7\\n0 0 2 4 5 5 6\\n\", \"3\\n0 1 3\\n\", \"3\\n1 1 2\\n\", \"4\\n0 0 0 4\\n\", \"7\\n0 0 0 2 3 5 7\\n\", \"3\\n1 2 2\\n\", \"3\\n0 1 2\\n\", \"3\\n0 0 1\\n\", \"4\\n0 0 0 0\\n\", \"7\\n0 0 2 2 3 3 6\\n\", \"3\\n0 0 3\\n\", \"3\\n0 0 2\\n\", \"7\\n0 0 2 3 3 3 6\\n\", \"3\\n0 0 0\\n\", \"7\\n0 0 2 3 3 4 6\\n\", \"7\\n0 0 2 2 5 5 7\\n\", \"4\\n0 1 1 2\\n\", \"4\\n0 1 1 3\\n\", \"7\\n0 0 2 2 2 3 6\\n\", \"7\\n0 0 3 3 3 3 6\\n\", \"4\\n0 1 1 4\\n\", \"7\\n0 0 2 2 2 3 4\\n\", \"7\\n0 0 2 3 5 5 6\\n\", \"4\\n0 0 2 3\\n\", \"7\\n0 0 1 2 3 5 7\\n\", \"7\\n0 0 2 3 3 5 6\\n\", \"7\\n0 0 2 3 3 4 7\\n\", \"7\\n0 0 0 2 5 5 7\\n\", \"4\\n1 1 1 3\\n\", \"7\\n0 0 2 2 2 2 6\\n\", \"4\\n0 0 1 4\\n\", \"7\\n0 0 1 2 2 5 7\\n\", \"7\\n0 0 0 4 5 5 7\\n\", \"7\\n0 0 0 2 2 2 6\\n\", \"4\\n0 0 2 4\\n\", \"7\\n0 0 1 2 2 4 7\\n\", \"7\\n0 0 0 0 2 2 6\\n\", \"4\\n0 0 2 2\\n\", \"7\\n0 0 0 0 0 2 6\\n\", \"7\\n0 0 2 3 4 5 6\\n\", \"4\\n0 1 1 1\\n\", \"7\\n0 0 2 3 5 5 7\\n\", \"4\\n1 1 1 2\\n\", \"4\\n1 1 1 4\\n\", \"4\\n0 0 3 3\\n\", \"7\\n0 0 1 2 3 5 6\\n\", \"4\\n1 1 2 3\\n\", \"4\\n0 0 1 2\\n\", \"7\\n0 1 1 2 2 4 7\\n\", \"7\\n0 0 2 4 5 5 7\\n\", \"7\\n1 1 1 2 2 4 7\\n\", \"7\\n1 1 1 2 3 4 7\\n\", \"7\\n1 1 1 1 3 4 7\\n\", \"7\\n1 1 1 1 3 5 7\\n\", \"7\\n1 1 1 2 3 5 7\\n\", \"4\\n1 1 1 1\\n\", \"7\\n0 0 0 2 3 5 6\\n\", \"7\\n0 1 2 2 3 5 7\\n\", \"7\\n0 0 2 2 3 6 6\\n\", \"7\\n0 1 1 2 3 5 6\\n\", \"7\\n0 0 0 3 5 5 7\\n\", \"7\\n0 0 0 0 2 2 7\\n\", \"4\\n0 1 3 3\\n\", \"7\\n0 0 1 4 5 5 7\\n\", \"7\\n1 1 1 2 4 5 7\\n\", \"7\\n0 0 0 1 3 5 6\\n\", \"7\\n0 1 1 2 2 5 6\\n\", \"7\\n0 1 1 2 4 5 7\\n\", \"7\\n0 1 1 1 3 5 6\\n\", \"7\\n0 0 2 2 3 4 6\\n\", \"7\\n0 1 3 3 3 3 6\\n\"], \"outputs\": [\"0 1 2\\n\", \"0 2 1\\n\", \"1 3 4 0\\n\", \"1 3 0 4 2 7 5\\n\", \"0\\n\", \"0 1 2 3 5 6 4 8 9 7\\n\", \"1\\n\", \"0 2 3 \\n\", \"1 2 4 0 \\n\", \"2 3 4 0 \\n\", \"1 0 2 \\n\", \"1 4 0 7 2 3 5 \\n\", \"2 0 3 \\n\", \"2 4 0 1 \\n\", \"2 3 0 4 \\n\", \"1 0 3 \\n\", \"1 4 0 6 2 3 5 \\n\", \"1 3 0 2 4 7 5 \\n\", \"2 0 1 \\n\", \"0 3 1 \\n\", \"1 2 3 0 \\n\", \"1 4 6 0 2 3 5 \\n\", \"0 1 3 \\n\", \"3 0 1 \\n\", \"2 3 0 \\n\", \"1 2 3 4 \\n\", \"1 4 0 5 2 7 3 \\n\", \"1 2 0 \\n\", \"1 3 0 \\n\", \"1 4 0 2 5 7 3 \\n\", \"1 2 3 \\n\", \"1 5 0 2 7 3 4 \\n\", \"1 3 0 4 2 6 5 \\n\", \"3 0 4 1 \\n\", \"2 0 4 1 \\n\", \"1 4 0 5 7 2 3 \\n\", \"1 2 0 4 5 7 3 \\n\", \"2 0 3 1 \\n\", \"1 5 0 6 7 2 3 \\n\", \"1 4 0 2 3 7 5 \\n\", \"1 4 0 2 \\n\", \"4 6 0 1 2 3 5 \\n\", \"1 4 0 2 7 3 5 \\n\", \"1 5 0 2 6 3 4 \\n\", \"1 3 4 0 2 6 5 \\n\", \"0 2 4 1 \\n\", \"1 3 0 4 5 7 2 \\n\", \"2 3 0 1 \\n\", \"3 4 0 1 6 2 5 \\n\", \"1 2 3 0 4 6 5 \\n\", \"1 3 4 0 5 7 2 \\n\", \"1 3 0 2 \\n\", \"3 5 0 1 6 2 4 \\n\", \"1 3 4 5 0 7 2 \\n\", \"1 3 0 4 \\n\", \"1 3 4 5 7 0 2 \\n\", \"1 7 0 2 3 4 5 \\n\", \"2 0 3 4 \\n\", \"1 4 0 2 3 6 5 \\n\", \"0 3 4 1 \\n\", \"0 2 3 1 \\n\", \"1 2 0 4 \\n\", \"4 7 0 1 2 3 5 \\n\", \"0 4 1 2 \\n\", \"3 4 0 1 \\n\", \"3 0 5 1 6 2 4 \\n\", \"1 3 0 2 4 6 5 \\n\", \"0 3 5 1 6 2 4 \\n\", \"0 5 6 1 2 3 4 \\n\", \"0 2 5 6 1 3 4 \\n\", \"0 2 4 6 1 3 5 \\n\", \"0 4 6 1 2 3 5 \\n\", \"0 2 3 4 \\n\", \"1 4 7 0 2 3 5 \\n\", \"4 0 1 6 2 3 5 \\n\", \"1 4 0 5 2 3 7 \\n\", \"4 0 7 1 2 3 5 \\n\", \"1 2 4 0 3 6 5 \\n\", \"1 3 4 5 0 6 2 \\n\", \"2 0 1 4 \\n\", \"2 3 0 1 4 6 5 \\n\", \"0 3 6 1 2 4 5 \\n\", \"2 4 7 0 1 3 5 \\n\", \"3 0 4 1 7 2 5 \\n\", \"3 0 6 1 2 4 5 \\n\", \"2 0 4 7 1 3 5 \\n\", \"1 5 0 7 2 3 4 \\n\", \"2 0 1 4 5 7 3 \\n\"]}", "source": "primeintellect"}
|
Given an array a of length n, find another array, b, of length n such that:
* for each i (1 ≤ i ≤ n) MEX(\\{b_1, b_2, …, b_i\})=a_i.
The MEX of a set of integers is the smallest non-negative integer that doesn't belong to this set.
If such array doesn't exist, determine this.
Input
The first line contains an integer n (1 ≤ n ≤ 10^5) — the length of the array a.
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ i) — the elements of the array a. It's guaranteed that a_i ≤ a_{i+1} for 1≤ i < n.
Output
If there's no such array, print a single line containing -1.
Otherwise, print a single line containing n integers b_1, b_2, …, b_n (0 ≤ b_i ≤ 10^6)
If there are multiple answers, print any.
Examples
Input
3
1 2 3
Output
0 1 2
Input
4
0 0 0 2
Output
1 3 4 0
Input
3
1 1 3
Output
0 2 1
Note
In the second test case, other answers like [1,1,1,0], for example, are valid.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4\\n5\\n4 1 5 1 3\\n4\\n1 0 1 6\\n1\\n0\\n2\\n5 4\\n\", \"3\\n3\\n1 2 2\\n3\\n2 2 3\\n5\\n0 0 0 2 2\\n\", \"3\\n3\\n2 2 2\\n3\\n2 2 3\\n5\\n0 0 0 2 2\\n\", \"4\\n5\\n4 1 3 1 3\\n4\\n1 0 1 6\\n1\\n0\\n2\\n5 4\\n\", \"3\\n3\\n2 2 0\\n3\\n2 2 3\\n5\\n0 0 0 2 2\\n\", \"3\\n3\\n4 2 0\\n3\\n2 2 3\\n5\\n0 0 0 2 2\\n\", \"3\\n3\\n4 2 0\\n3\\n2 2 4\\n5\\n0 0 0 2 2\\n\", \"4\\n5\\n4 1 5 1 3\\n4\\n1 0 1 6\\n1\\n1\\n2\\n5 4\\n\", \"3\\n3\\n1 2 2\\n3\\n2 2 3\\n5\\n0 1 0 2 2\\n\", \"3\\n3\\n2 2 2\\n3\\n2 2 1\\n5\\n0 0 0 2 2\\n\", \"3\\n3\\n4 4 0\\n3\\n2 2 4\\n5\\n0 0 0 2 2\\n\", \"3\\n3\\n4 2 0\\n3\\n0 2 4\\n5\\n0 0 0 1 2\\n\", \"3\\n3\\n2 2 0\\n3\\n3 2 4\\n5\\n0 1 0 2 2\\n\", \"3\\n3\\n2 2 2\\n3\\n4 2 1\\n5\\n1 0 0 2 2\\n\", \"4\\n5\\n2 1 3 1 0\\n4\\n1 0 1 6\\n1\\n0\\n2\\n5 4\\n\", \"3\\n3\\n4 2 0\\n3\\n0 2 2\\n5\\n0 0 0 1 2\\n\", \"4\\n5\\n4 1 5 1 4\\n4\\n1 0 1 12\\n1\\n1\\n2\\n5 4\\n\", \"4\\n5\\n4 1 3 1 0\\n4\\n1 0 1 6\\n1\\n0\\n2\\n5 4\\n\", \"4\\n5\\n4 1 3 1 0\\n4\\n1 0 0 6\\n1\\n0\\n2\\n5 4\\n\", \"3\\n3\\n4 2 0\\n3\\n3 2 4\\n5\\n0 0 0 2 2\\n\", \"3\\n3\\n4 2 0\\n3\\n0 2 4\\n5\\n0 0 0 2 2\\n\", \"3\\n3\\n4 0 0\\n3\\n0 2 4\\n5\\n0 0 0 2 2\\n\", \"4\\n5\\n4 1 3 1 1\\n4\\n1 0 1 6\\n1\\n0\\n2\\n5 4\\n\", \"4\\n5\\n4 1 3 1 0\\n4\\n1 0 1 2\\n1\\n0\\n2\\n5 4\\n\", \"3\\n3\\n3 2 0\\n3\\n2 2 3\\n5\\n0 0 0 2 2\\n\", \"3\\n3\\n2 2 0\\n3\\n3 2 4\\n5\\n0 0 0 2 2\\n\", \"3\\n3\\n4 0 0\\n3\\n0 2 6\\n5\\n0 0 0 2 2\\n\", \"4\\n5\\n4 1 5 1 3\\n4\\n1 0 1 12\\n1\\n1\\n2\\n5 4\\n\", \"3\\n3\\n1 2 2\\n3\\n2 2 3\\n5\\n0 1 0 1 2\\n\", \"3\\n3\\n2 2 2\\n3\\n4 2 1\\n5\\n0 0 0 2 2\\n\", \"4\\n5\\n4 1 3 1 0\\n4\\n1 1 1 2\\n1\\n0\\n2\\n5 4\\n\", \"3\\n3\\n3 2 0\\n3\\n2 2 3\\n5\\n0 0 1 2 2\\n\", \"3\\n3\\n4 0 0\\n3\\n0 2 4\\n5\\n0 0 0 1 2\\n\", \"3\\n3\\n4 0 0\\n3\\n0 2 6\\n5\\n0 0 0 2 4\\n\", \"4\\n5\\n4 1 5 1 3\\n4\\n1 0 0 12\\n1\\n1\\n2\\n5 4\\n\", \"4\\n5\\n4 1 3 1 0\\n4\\n1 1 0 2\\n1\\n0\\n2\\n5 4\\n\", \"3\\n3\\n3 1 0\\n3\\n2 2 3\\n5\\n0 0 1 2 2\\n\", \"3\\n3\\n0 2 0\\n3\\n3 2 4\\n5\\n0 1 0 2 2\\n\", \"3\\n3\\n5 0 0\\n3\\n0 2 4\\n5\\n0 0 0 1 2\\n\", \"3\\n3\\n4 1 0\\n3\\n0 2 6\\n5\\n0 0 0 2 4\\n\", \"4\\n5\\n4 1 5 1 3\\n4\\n1 0 0 12\\n1\\n0\\n2\\n5 4\\n\", \"4\\n5\\n4 1 2 1 0\\n4\\n1 1 0 2\\n1\\n0\\n2\\n5 4\\n\", \"3\\n3\\n5 0 0\\n3\\n0 2 4\\n5\\n0 0 0 1 0\\n\", \"3\\n3\\n4 1 0\\n3\\n0 2 7\\n5\\n0 0 0 2 4\\n\", \"3\\n3\\n4 1 0\\n3\\n0 2 0\\n5\\n0 0 0 2 4\\n\", \"3\\n3\\n0 1 0\\n3\\n0 2 0\\n5\\n0 0 0 2 4\\n\", \"4\\n5\\n4 1 5 1 3\\n4\\n1 0 1 6\\n1\\n0\\n2\\n5 0\\n\", \"3\\n3\\n4 2 2\\n3\\n2 2 3\\n5\\n0 0 0 2 2\\n\", \"4\\n5\\n4 1 3 1 3\\n4\\n1 0 1 6\\n1\\n0\\n2\\n5 7\\n\", \"3\\n3\\n2 2 0\\n3\\n4 2 3\\n5\\n0 0 0 2 2\\n\", \"4\\n5\\n4 1 3 1 0\\n4\\n1 0 0 6\\n1\\n0\\n2\\n0 4\\n\", \"3\\n3\\n4 2 0\\n3\\n2 1 4\\n5\\n0 0 0 2 2\\n\", \"4\\n5\\n4 1 5 1 3\\n4\\n1 0 1 6\\n1\\n1\\n2\\n7 4\\n\", \"3\\n3\\n1 2 2\\n3\\n2 2 3\\n5\\n0 1 0 3 2\\n\", \"3\\n3\\n3 2 2\\n3\\n2 2 1\\n5\\n0 0 0 2 2\\n\", \"4\\n5\\n4 1 3 1 0\\n4\\n1 0 1 2\\n1\\n0\\n2\\n3 4\\n\", \"3\\n3\\n3 4 0\\n3\\n2 2 3\\n5\\n0 0 0 2 2\\n\", \"3\\n3\\n1 4 0\\n3\\n2 2 4\\n5\\n0 0 0 2 2\\n\", \"3\\n3\\n1 2 2\\n3\\n3 2 3\\n5\\n0 1 0 1 2\\n\", \"3\\n3\\n2 2 2\\n3\\n4 3 1\\n5\\n0 0 0 2 2\\n\", \"3\\n3\\n4 0 0\\n3\\n0 2 4\\n5\\n0 0 0 1 1\\n\", \"4\\n5\\n4 1 5 1 3\\n4\\n1 0 0 12\\n1\\n1\\n2\\n5 3\\n\", \"3\\n3\\n2 2 2\\n3\\n4 3 1\\n5\\n1 0 0 2 2\\n\", \"3\\n3\\n6 1 0\\n3\\n2 2 3\\n5\\n0 0 1 2 2\\n\", \"3\\n3\\n0 2 0\\n3\\n3 2 4\\n5\\n0 1 0 2 4\\n\", \"4\\n5\\n4 1 5 1 4\\n4\\n1 0 0 12\\n1\\n0\\n2\\n5 4\\n\", \"4\\n5\\n4 1 2 1 0\\n4\\n1 1 0 2\\n1\\n0\\n2\\n7 4\\n\", \"3\\n3\\n5 0 0\\n3\\n0 2 4\\n5\\n0 0 0 2 0\\n\", \"3\\n3\\n0 1 0\\n3\\n0 2 0\\n5\\n0 1 0 2 4\\n\", \"4\\n5\\n4 1 5 1 3\\n4\\n1 0 1 6\\n1\\n0\\n2\\n5 1\\n\", \"3\\n3\\n4 2 2\\n3\\n2 2 3\\n5\\n0 0 1 2 2\\n\", \"4\\n5\\n4 1 3 1 3\\n4\\n1 0 1 6\\n1\\n1\\n2\\n5 7\\n\", \"3\\n3\\n2 2 0\\n3\\n7 2 3\\n5\\n0 0 0 2 2\\n\", \"4\\n5\\n4 1 1 1 0\\n4\\n1 0 0 6\\n1\\n0\\n2\\n0 4\\n\", \"3\\n3\\n4 4 0\\n3\\n2 1 4\\n5\\n0 0 0 2 2\\n\", \"4\\n5\\n4 1 0 1 3\\n4\\n1 0 1 6\\n1\\n1\\n2\\n7 4\\n\", \"3\\n3\\n1 2 2\\n3\\n2 2 3\\n5\\n0 1 0 3 4\\n\", \"3\\n3\\n3 8 0\\n3\\n2 2 3\\n5\\n0 0 0 2 2\\n\"], \"outputs\": [\"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nLOSE\\nDRAW\\n\", \"LOSE\\nLOSE\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"DRAW\\nLOSE\\nDRAW\\n\", \"WIN\\nLOSE\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nWIN\\nWIN\\n\", \"WIN\\nLOSE\\nWIN\\n\", \"LOSE\\nWIN\\nDRAW\\n\", \"DRAW\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nWIN\\n\", \"DRAW\\nWIN\\nWIN\\n\", \"LOSE\\nWIN\\nWIN\\n\", \"LOSE\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nDRAW\\nWIN\\n\", \"LOSE\\nWIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nLOSE\\nDRAW\\n\", \"DRAW\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nWIN\\nWIN\\n\", \"WIN\\nLOSE\\nWIN\\n\", \"LOSE\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nLOSE\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nLOSE\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nLOSE\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"DRAW\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nWIN\\nWIN\\n\", \"WIN\\nLOSE\\nDRAW\\n\", \"LOSE\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nLOSE\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\n\", \"WIN\\nLOSE\\nWIN\\n\", \"LOSE\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nWIN\\nWIN\\n\", \"LOSE\\nWIN\\nWIN\\n\", \"WIN\\nLOSE\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\n\", \"LOSE\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"WIN\\nLOSE\\nWIN\\n\", \"WIN\\nWIN\\nWIN\\nWIN\\n\", \"DRAW\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nDRAW\\nWIN\\n\", \"DRAW\\nWIN\\nDRAW\\n\", \"WIN\\nWIN\\nWIN\\nWIN\\n\", \"WIN\\nLOSE\\nWIN\\n\", \"WIN\\nLOSE\\nDRAW\\n\"]}", "source": "primeintellect"}
|
Koa the Koala and her best friend want to play a game.
The game starts with an array a of length n consisting of non-negative integers. Koa and her best friend move in turns and each have initially a score equal to 0. Koa starts.
Let's describe a move in the game:
* During his move, a player chooses any element of the array and removes it from this array, xor-ing it with the current score of the player.
More formally: if the current score of the player is x and the chosen element is y, his new score will be x ⊕ y. Here ⊕ denotes [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).
Note that after a move element y is removed from a.
* The game ends when the array is empty.
At the end of the game the winner is the player with the maximum score. If both players have the same score then it's a draw.
If both players play optimally find out whether Koa will win, lose or draw the game.
Input
Each test contains multiple test cases. The first line contains t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.
The first line of each test case contains the integer n (1 ≤ n ≤ 10^5) — the length of a.
The second line of each test case contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — elements of a.
It is guaranteed that the sum of n over all test cases does not exceed 10^5.
Output
For each test case print:
* WIN if Koa will win the game.
* LOSE if Koa will lose the game.
* DRAW if the game ends in a draw.
Examples
Input
3
3
1 2 2
3
2 2 3
5
0 0 0 2 2
Output
WIN
LOSE
DRAW
Input
4
5
4 1 5 1 3
4
1 0 1 6
1
0
2
5 4
Output
WIN
WIN
DRAW
WIN
Note
In testcase 1 of the first sample we have:
a = [1, 2, 2]. Here Koa chooses 1, other player has to choose 2, Koa chooses another 2. Score for Koa is 1 ⊕ 2 = 3 and score for other player is 2 so Koa wins.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"8\\n5 2\\nWLWLL\\n6 5\\nLLLWWL\\n7 1\\nLWLWLWL\\n15 5\\nWWWLLLWWWLLLWWW\\n40 7\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL\\n1 0\\nL\\n1 1\\nL\\n6 1\\nWLLWLW\\n\", \"8\\n5 2\\nWLWLL\\n6 5\\nLLLWWL\\n7 2\\nLWLWLWL\\n15 5\\nWWWLLLWWWLLLWWW\\n40 7\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL\\n1 0\\nL\\n1 1\\nL\\n6 1\\nWLLWLW\\n\", \"8\\n5 2\\nWLWLL\\n6 5\\nLLLWWL\\n7 2\\nLWLWLWL\\n15 5\\nWWWLLLWWWLLLWWW\\n40 11\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL\\n1 0\\nL\\n1 1\\nL\\n6 1\\nWLLWLW\\n\", \"8\\n5 2\\nWLWLL\\n6 5\\nLLLWWL\\n7 2\\nLWLWLWL\\n15 5\\nWWWLLLWWWLLLWWW\\n40 7\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL\\n1 0\\nL\\n1 1\\nL\\n6 0\\nWLLWLW\\n\", \"8\\n5 2\\nWLWLL\\n6 5\\nLLLWWL\\n7 2\\nLWLWLWL\\n15 8\\nWWWLLLWWWLLLWWW\\n40 11\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL\\n1 0\\nL\\n1 1\\nL\\n6 1\\nWLLWLW\\n\", \"8\\n5 2\\nWLWLL\\n6 5\\nLLLWWL\\n7 2\\nLWLWLWL\\n15 5\\nWWWLLLWWWLLLWWW\\n40 11\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL\\n1 0\\nL\\n1 0\\nL\\n6 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1\\nWLWLLW\\n\", \"8\\n5 2\\nWLWLL\\n6 10\\nLLLWWL\\n7 2\\nLWLWLWL\\n15 5\\nWWWLLLWWWLLLWWW\\n40 7\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL\\n1 1\\nL\\n1 1\\nL\\n6 1\\nWLLWLW\\n\", \"8\\n5 2\\nWLWLL\\n6 3\\nLLLWWL\\n7 1\\nWWLLLWL\\n15 5\\nWWWLLLWWWLLLWWW\\n40 7\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLWWLLWWWLWLL\\n1 0\\nL\\n1 0\\nL\\n6 1\\nWLWLLW\\n\", \"8\\n5 2\\nWLWLL\\n6 10\\nLLLWWL\\n7 1\\nWWLLLWL\\n15 5\\nWWWLLLWWWLLLWWW\\n40 7\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL\\n1 1\\nL\\n1 0\\nL\\n6 1\\nWLLWLW\\n\", \"8\\n5 2\\nLLWWL\\n6 5\\nLLLWWL\\n7 1\\nLWLWLWL\\n15 5\\nWWWLLLWWWLLLWWW\\n40 3\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL\\n1 0\\nL\\n1 1\\nL\\n6 1\\nWLLWLW\\n\", \"8\\n5 2\\nWLWLL\\n6 10\\nLLLWWL\\n7 1\\nLWLWLWL\\n15 5\\nWWWLLLWWWLLLWWW\\n40 1\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLWWLLWWWLWLL\\n1 0\\nL\\n1 1\\nL\\n6 1\\nWLLWLW\\n\", \"8\\n5 2\\nWLWLL\\n6 8\\nLLLWWL\\n7 2\\nLWLWLWL\\n15 5\\nWWWLLLLWWWLLWWW\\n40 7\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL\\n1 0\\nL\\n1 1\\nL\\n6 1\\nWWLLLW\\n\", \"8\\n5 2\\nWLWLL\\n6 15\\nLLLWWL\\n7 0\\nLWLWLWL\\n15 5\\nWWWLLLWWWLLLWWW\\n40 11\\nLLWLWLWWWLWLLWLWWWLWLLLLLWLLLLWLWWWWLWWL\\n1 0\\nL\\n1 0\\nL\\n6 0\\nWLWLLW\\n\", \"8\\n5 2\\nWLWLL\\n6 5\\nLLLWWL\\n7 2\\nLWLWLWL\\n15 7\\nWWWLLLWWWLLLWWW\\n40 11\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL\\n1 0\\nL\\n1 1\\nL\\n6 1\\nWLLWLW\\n\", \"8\\n5 2\\nWLWLL\\n6 5\\nLLLWWL\\n7 0\\nLWLWLWL\\n15 6\\nWWWLLLWWWLLLWWW\\n40 11\\nLWWLWWWLLWLLLLWLLWLLWLWWWLWLLWLWWWLWLWLL\\n1 0\\nL\\n1 0\\nL\\n6 0\\nWLLWLW\\n\", \"8\\n5 2\\nWLWLL\\n6 6\\nLLLWWL\\n7 0\\nLWLWLWL\\n15 8\\nWWWLLLWWWLLLWWW\\n40 11\\nLLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL\\n1 0\\nL\\n1 0\\nL\\n6 1\\nWLLWLW\\n\"], \"outputs\": [\"7\\n11\\n6\\n26\\n46\\n0\\n1\\n6\\n\", \"7\\n11\\n9\\n26\\n46\\n0\\n1\\n6\\n\", \"7\\n11\\n9\\n26\\n56\\n0\\n1\\n6\\n\", \"7\\n11\\n9\\n26\\n46\\n0\\n1\\n3\\n\", \"7\\n11\\n9\\n29\\n56\\n0\\n1\\n6\\n\", \"7\\n11\\n9\\n26\\n56\\n0\\n0\\n6\\n\", \"7\\n11\\n6\\n26\\n46\\n0\\n1\\n6\\n\", 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\"7\\n11\\n9\\n29\\n56\\n0\\n1\\n6\\n\", \"7\\n11\\n3\\n29\\n56\\n0\\n0\\n3\\n\", \"7\\n11\\n3\\n29\\n56\\n0\\n0\\n6\\n\"]}", "source": "primeintellect"}
|
You like playing chess tournaments online.
In your last tournament you played n games. For the sake of this problem, each chess game is either won or lost (no draws). When you lose a game you get 0 points. When you win you get 1 or 2 points: if you have won also the previous game you get 2 points, otherwise you get 1 point. If you win the very first game of the tournament you get 1 point (since there is not a "previous game").
The outcomes of the n games are represented by a string s of length n: the i-th character of s is W if you have won the i-th game, while it is L if you have lost the i-th game.
After the tournament, you notice a bug on the website that allows you to change the outcome of at most k of your games (meaning that at most k times you can change some symbol L to W, or W to L). Since your only goal is to improve your chess rating, you decide to cheat and use the bug.
Compute the maximum score you can get by cheating in the optimal way.
Input
Each test contains multiple test cases. The first line contains an integer t (1≤ t ≤ 20,000) — the number of test cases. The description of the test cases follows.
The first line of each testcase contains two integers n, k (1≤ n≤ 100,000, 0≤ k≤ n) – the number of games played and the number of outcomes that you can change.
The second line contains a string s of length n containing only the characters W and L. If you have won the i-th game then s_i= W, if you have lost the i-th game then s_i= L.
It is guaranteed that the sum of n over all testcases does not exceed 200,000.
Output
For each testcase, print a single integer – the maximum score you can get by cheating in the optimal way.
Example
Input
8
5 2
WLWLL
6 5
LLLWWL
7 1
LWLWLWL
15 5
WWWLLLWWWLLLWWW
40 7
LLWLWLWWWLWLLWLWWWLWLLWLLWLLLLWLLWWWLWWL
1 0
L
1 1
L
6 1
WLLWLW
Output
7
11
6
26
46
0
1
6
Note
Explanation of the first testcase. Before changing any outcome, the score is 2. Indeed, you won the first game, so you got 1 point, and you won also the third, so you got another 1 point (and not 2 because you lost the second game).
An optimal way to cheat is to change the outcomes of the second and fourth game. Doing so, you end up winning the first four games (the string of the outcomes becomes WWWWL). Hence, the new score is 7=1+2+2+2: 1 point for the first game and 2 points for the second, third and fourth game.
Explanation of the second testcase. Before changing any outcome, the score is 3. Indeed, you won the fourth game, so you got 1 point, and you won also the fifth game, so you got 2 more points (since you won also the previous game).
An optimal way to cheat is to change the outcomes of the first, second, third and sixth game. Doing so, you end up winning all games (the string of the outcomes becomes WWWWWW). Hence, the new score is 11 = 1+2+2+2+2+2: 1 point for the first game and 2 points for all the other games.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2A:13\\n\", \"11:20\\n\", \"000B:00001\\n\", \"Z:1\\n\", \"123:A\\n\", \"N:7\\n\", \"00001:00001\\n\", \"1:11\\n\", \"000G6:000GD\\n\", \"0:1N\\n\", \"Z:2\\n\", \"0:Z\\n\", \"Z:00\\n\", \"0:1A\\n\", \"000Z:000Z\\n\", \"0Z:01\\n\", \"A:10\\n\", \"00Z:01\\n\", \"0033:00202\\n\", \"000B3:00098\\n\", \"00Z:03\\n\", \"01B:4A\\n\", \"0011:124\\n\", \"0:0\\n\", \"Z:01\\n\", \"0000F:0002G\\n\", \"70:00\\n\", \"Z:0\\n\", \"00394:00321\\n\", \"N8HYJ:042JW\\n\", \"1:60\\n\", \"00Z:001\\n\", \"001:010\\n\", \"000Z:00A\\n\", \"V:V\\n\", \"003:25\\n\", \"02:130\\n\", \"0Z:00\\n\", \"00:10\\n\", \"0000N:00007\\n\", \"1001:1001\\n\", \"0:00000\\n\", \"0010:00000\\n\", \"00:0010\\n\", \"0:10\\n\", \"1:10\\n\", \"0:0Z\\n\", \"000:010\\n\", \"00:21\\n\", \"0:1\\n\", \"000Z:00001\\n\", \"00A:00A\\n\", \"Z:Z\\n\", \"100:0101\\n\", \"27:0070\\n\", \"43:210\\n\", \"000Z:0001\\n\", \"00000:00000\\n\", \"0:1Z\\n\", \"ZZZZZ:ZZZZZ\\n\", \"01:010\\n\", \"000:0010\\n\", \"00101:0101\\n\", \"00:010\\n\", \"24:0000\\n\", \"00:1A\\n\", \"10:05\\n\", \"00:1Z\\n\", \"0:10000\\n\", \"00002:00130\\n\", \"0021:00054\\n\", \"00000:00021\\n\", \"00:20\\n\", \"10101:000\\n\", \"00B:0023\\n\", \"0000P:0000E\\n\", \"1:10002\\n\", \"11:1\\n\", \"000F6:000GD\\n\", \"00:Z\\n\", \"010:100\\n\", \"02:131\\n\", \"10:00\\n\", \"1001:1101\\n\", \"01:0010\\n\", \"00:12\\n\", \"34:210\\n\", \"20:0004\\n\", \"00002:00031\\n\", \"01:20\\n\", \"02:11\\n\", \"11:2\\n\", \"0:N1\\n\", \"Z:3\\n\", \"A1:0\\n\", \"000Z00:0Z\\n\", \"1033:00202\\n\", \"000B3:00099\\n\", \"A4:B10\\n\", \"Y:0\\n\", \"00294:00321\\n\", \"M8HYJ:042JW\\n\", \"00Z:100\\n\", \"001Z:00A\\n\", \"V:W\\n\", \"52:300\\n\", \"00:Z0\\n\", \"70000:N0000\\n\", \"1:00000\\n\", \"00000:0100\\n\", \"0:00\\n\", \"01:1\\n\", \"Z0:0\\n\", \"0000:10\\n\", \"A00:A00\\n\", \"Z:Y\\n\", \"1010:001\\n\", \"10000:00000\\n\", \"1:0Z\\n\", \"ZZZZY:ZZZZZ\\n\", \"010:10\\n\", \"1010:10100\\n\", \"010:00\\n\", \"01:0A\\n\", \"1:005\\n\", \"001:000\\n\", \"10101:001\\n\", \"0B0:0023\\n\", \"0000P:0000D\\n\", \"20001:1\\n\", \"2A:12\\n\", \"000F6:000FD\\n\", \"N1:0\\n\", \"1032:00302\\n\", \"000B2:00099\\n\"], \"outputs\": [\"0\", \"3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 \", \"-1\", \"0\", \"0\", \"-1\", \"-1\", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 \", \"0\", \"24 25 26 27 28 29 30 31 32 33 34 35 36 \", \"0\", \"-1\", \"0\", \"11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 \", \"0\", \"0\", \"11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \", \"0\", \"4 5 \", \"0\", \"0\", \"12 \", \"5 6 \", \"-1\", \"0\", \"17 18 19 20 21 \", \"0\", \"0\", \"0\", \"0\", \"7 8 9 \", \"0\", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \", \"0\", \"0\", \"6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 \", \"4 5 6 \", \"0\", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \", \"-1\", \"2 \", \"-1\", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 \", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \", \"-1\", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \", \"3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 \", \"-1\", \"0\", \"-1\", \"0\", \"2 3 4 \", \"8 \", \"5 \", \"0\", \"-1\", \"0\", \"0\", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \", \"2 3 4 \", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \", \"5 6 7 8 9 \", \"11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 \", \"6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 \", \"0\", \"2 \", \"4 5 6 \", \"6 7 8 9 10 11 \", \"3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 \", \"3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 \", \"2 \", \"12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 \", \"0\", \"0\", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 \", \"0\\n\", \"-1\\n\", \"2 3 4 5 6 7 \", \"4 5 6 \", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 \", \"2 \", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \", \"3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 \", \"5 \", \"5 6 7 8 9 10 11 \", \"4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 \", \"3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 \", \"3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 \", \"3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 \", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"-1\\n\", \"2 3 4 5 6 7 \", \"-1\\n\", \"-1\\n\", \"0\\n\", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 \", \"0\\n\", \"0\\n\", \"2 \", \"2 \", \"-1\\n\", \"0\\n\", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 \", \"2 \", \"2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 \", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"2 \", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Having stayed home alone, Petya decided to watch forbidden films on the Net in secret. "What ungentlemanly behavior!" — you can say that, of course, but don't be too harsh on the kid. In his country films about the Martians and other extraterrestrial civilizations are forbidden. It was very unfair to Petya as he adored adventure stories that featured lasers and robots.
Today Petya is watching a shocking blockbuster about the Martians called "R2:D2". What can "R2:D2" possibly mean? It might be the Martian time represented in the Martian numeral system. Petya knows that time on Mars is counted just like on the Earth (that is, there are 24 hours and each hour has 60 minutes). The time is written as "a:b", where the string a stands for the number of hours (from 0 to 23 inclusive), and string b stands for the number of minutes (from 0 to 59 inclusive). The only thing Petya doesn't know is in what numeral system the Martian time is written.
Your task is to print the radixes of all numeral system which can contain the time "a:b".
Input
The first line contains a single string as "a:b" (without the quotes). There a is a non-empty string, consisting of numbers and uppercase Latin letters. String a shows the number of hours. String b is a non-empty string that consists of numbers and uppercase Latin letters. String b shows the number of minutes. The lengths of strings a and b are from 1 to 5 characters, inclusive. Please note that strings a and b can have leading zeroes that do not influence the result in any way (for example, string "008:1" in decimal notation denotes correctly written time).
We consider characters 0, 1, ..., 9 as denoting the corresponding digits of the number's representation in some numeral system, and characters A, B, ..., Z correspond to numbers 10, 11, ..., 35.
Output
Print the radixes of the numeral systems that can represent the time "a:b" in the increasing order. Separate the numbers with spaces or line breaks. If there is no numeral system that can represent time "a:b", print the single integer 0. If there are infinitely many numeral systems that can represent the time "a:b", print the single integer -1.
Note that on Mars any positional numeral systems with positive radix strictly larger than one are possible.
Examples
Input
11:20
Output
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
Input
2A:13
Output
0
Input
000B:00001
Output
-1
Note
Let's consider the first sample. String "11:20" can be perceived, for example, as time 4:6, represented in the ternary numeral system or as time 17:32 in hexadecimal system.
Let's consider the second sample test. String "2A:13" can't be perceived as correct time in any notation. For example, let's take the base-11 numeral notation. There the given string represents time 32:14 that isn't a correct time.
Let's consider the third sample. String "000B:00001" can be perceived as a correct time in the infinite number of numeral systems. If you need an example, you can take any numeral system with radix no less than 12.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.375
|
{"tests": "{\"inputs\": [\"5\\n5 2 1 3 4\\n\", \"4\\n4 3 2 1\\n\", \"3\\n1 2 3\\n\", \"4\\n2 3 1 4\\n\", \"3\\n1 3 2\\n\", \"6\\n3 2 1 6 4 5\\n\", \"67\\n45 48 40 32 11 36 18 47 56 3 22 27 37 12 25 8 57 66 50 41 49 42 30 28 14 62 43 51 9 63 13 1 2 4 5 6 7 10 15 16 17 19 20 21 23 24 26 29 31 33 34 35 38 39 44 46 52 53 54 55 58 59 60 61 64 65 67\\n\", \"132\\n13 7 33 124 118 76 94 92 16 107 130 1 46 58 28 119 42 53 102 81 99 29 57 70 125 45 100 68 10 63 34 38 19 49 56 30 103 72 106 3 121 110 78 2 31 129 128 24 77 61 87 47 15 21 88 60 5 101 82 108 84 41 86 66 79 75 54 97 55 12 69 44 83 131 9 95 11 85 52 35 115 80 111 27 109 36 39 104 105 62 32 40 98 50 64 114 120 59 20 74 51 48 14 4 127 22 18 71 65 116 6 8 17 23 25 26 37 43 67 73 89 90 91 93 96 112 113 117 122 123 126 132\\n\", \"5\\n1 2 5 3 4\\n\", \"10\\n4 2 6 9 5 3 8 1 7 10\\n\", \"10\\n8 2 7 1 5 9 3 4 10 6\\n\", \"8\\n2 6 8 3 1 4 7 5\\n\", \"2\\n1 2\\n\", \"2\\n2 1\\n\", \"9\\n6 7 1 2 3 5 4 8 9\\n\", \"7\\n2 3 4 5 6 7 1\\n\", \"10\\n10 5 9 4 1 8 3 7 2 6\\n\", \"100\\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100\\n\", \"6\\n4 5 6 1 2 3\\n\", \"100\\n2 4 82 12 47 63 52 91 87 45 53 1 17 25 64 50 9 13 22 54 21 30 43 24 38 33 68 11 41 78 99 23 28 18 58 67 79 10 71 56 49 61 26 29 59 20 90 74 5 75 3 6 7 8 14 15 16 19 27 31 32 34 35 36 37 39 40 42 44 46 48 51 55 57 60 62 65 66 69 70 72 73 76 77 80 81 83 84 85 86 88 89 92 93 94 95 96 97 98 100\\n\", \"3\\n3 1 2\\n\", \"10\\n5 8 4 9 6 1 2 3 7 10\\n\", \"1\\n1\\n\", \"10\\n6 1 2 3 4 5 7 8 9 10\\n\", \"3\\n2 1 3\\n\", \"10\\n1 2 3 4 5 6 7 8 9 10\\n\", \"4\\n1 2 3 4\\n\", \"10\\n8 2 7 1 5 2 3 4 10 6\\n\", \"7\\n2 5 4 5 6 7 1\\n\", \"10\\n10 5 9 4 1 12 3 7 2 6\\n\", \"3\\n5 1 2\\n\", \"6\\n4 5 8 1 2 3\\n\", \"8\\n2 12 8 3 1 4 7 5\\n\", \"7\\n2 8 4 5 6 7 1\\n\", \"10\\n8 2 7 1 5 2 3 4 20 6\\n\", \"7\\n2 5 8 5 6 7 1\\n\", \"10\\n10 5 9 4 1 12 3 9 2 6\\n\", \"3\\n7 1 2\\n\", \"7\\n2 2 8 5 6 7 1\\n\", \"7\\n2 2 8 5 6 9 1\\n\", \"7\\n3 2 8 5 6 9 1\\n\", \"7\\n3 2 8 8 6 9 1\\n\", \"10\\n8 2 7 1 5 9 3 4 16 6\\n\", \"10\\n10 5 12 4 1 8 3 7 2 6\\n\", \"7\\n2 5 2 5 6 7 1\\n\", \"7\\n2 8 4 5 6 13 1\\n\", \"10\\n3 2 7 1 5 2 3 4 20 6\\n\", \"7\\n2 6 8 5 6 7 1\\n\", \"10\\n10 5 9 4 1 5 3 9 2 6\\n\", \"3\\n9 1 2\\n\", \"7\\n3 3 8 5 6 9 1\\n\", \"7\\n3 2 8 7 6 9 1\\n\", \"7\\n2 5 2 6 6 7 1\\n\", \"7\\n2 9 4 5 6 13 1\\n\", \"10\\n3 2 9 1 5 2 3 4 20 6\\n\", \"7\\n3 3 8 5 6 16 1\\n\", \"7\\n3 2 8 7 12 9 1\\n\", \"7\\n2 9 4 5 6 15 1\\n\", \"7\\n3 3 8 4 6 16 1\\n\", \"7\\n2 9 4 5 12 15 1\\n\", \"7\\n2 3 4 9 6 7 1\\n\", \"10\\n10 5 3 4 1 8 3 7 2 6\\n\", \"10\\n8 4 7 1 5 2 3 4 10 6\\n\", \"7\\n2 8 6 5 6 7 1\\n\", \"10\\n8 2 7 1 5 2 3 4 30 6\\n\", \"7\\n2 5 2 5 8 7 1\\n\", \"7\\n2 2 8 5 3 7 1\\n\", \"7\\n2 2 8 5 6 6 1\\n\", \"7\\n3 2 8 5 6 12 1\\n\", \"7\\n3 4 8 8 6 9 1\\n\", \"7\\n3 3 16 5 6 9 1\\n\", \"7\\n3 2 6 7 6 9 1\\n\", \"7\\n2 5 2 6 6 5 1\\n\", \"7\\n2 5 4 5 6 13 1\\n\", \"7\\n6 3 8 5 6 16 1\\n\", \"7\\n3 2 8 5 12 9 1\\n\", \"10\\n8 3 7 1 5 2 3 4 10 6\\n\", \"7\\n2 8 6 4 6 7 1\\n\", \"7\\n3 2 8 5 3 7 1\\n\", \"7\\n3 2 8 5 5 12 1\\n\", \"7\\n3 7 8 8 6 9 1\\n\", \"7\\n3 6 16 5 6 9 1\\n\", \"7\\n3 2 6 7 6 6 1\\n\", \"7\\n2 5 4 9 6 13 1\\n\"], \"outputs\": [\"2\\n\", \"3\\n\", \"0\\n\", \"2\\n\", \"2\\n\", \"4\\n\", \"31\\n\", \"110\\n\", \"3\\n\", \"7\\n\", \"9\\n\", \"7\\n\", \"0\\n\", \"1\\n\", \"6\\n\", \"6\\n\", \"8\\n\", \"0\\n\", \"3\\n\", \"50\\n\", \"1\\n\", \"5\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"9\\n\", \"6\\n\", \"8\\n\", \"1\\n\", \"3\\n\", \"7\\n\", \"6\\n\", \"9\\n\", \"6\\n\", \"8\\n\", \"1\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"9\\n\", \"8\\n\", \"6\\n\", \"6\\n\", \"9\\n\", \"6\\n\", \"8\\n\", \"1\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"9\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"8\\n\", \"9\\n\", \"6\\n\", \"9\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"9\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\", \"6\\n\"]}", "source": "primeintellect"}
|
Emuskald is addicted to Codeforces, and keeps refreshing the main page not to miss any changes in the "recent actions" list. He likes to read thread conversations where each thread consists of multiple messages.
Recent actions shows a list of n different threads ordered by the time of the latest message in the thread. When a new message is posted in a thread that thread jumps on the top of the list. No two messages of different threads are ever posted at the same time.
Emuskald has just finished reading all his opened threads and refreshes the main page for some more messages to feed his addiction. He notices that no new threads have appeared in the list and at the i-th place in the list there is a thread that was at the ai-th place before the refresh. He doesn't want to waste any time reading old messages so he wants to open only threads with new messages.
Help Emuskald find out the number of threads that surely have new messages. A thread x surely has a new message if there is no such sequence of thread updates (posting messages) that both conditions hold:
1. thread x is not updated (it has no new messages);
2. the list order 1, 2, ..., n changes to a1, a2, ..., an.
Input
The first line of input contains an integer n, the number of threads (1 ≤ n ≤ 105). The next line contains a list of n space-separated integers a1, a2, ..., an where ai (1 ≤ ai ≤ n) is the old position of the i-th thread in the new list. It is guaranteed that all of the ai are distinct.
Output
Output a single integer — the number of threads that surely contain a new message.
Examples
Input
5
5 2 1 3 4
Output
2
Input
3
1 2 3
Output
0
Input
4
4 3 2 1
Output
3
Note
In the first test case, threads 2 and 5 are placed before the thread 1, so these threads must contain new messages. Threads 1, 3 and 4 may contain no new messages, if only threads 2 and 5 have new messages.
In the second test case, there may be no new messages at all, since the thread order hasn't changed.
In the third test case, only thread 1 can contain no new messages.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
It has been noted that if some ants are put in the junctions of the graphene integer lattice then they will act in the following fashion: every minute at each junction (x, y) containing at least four ants a group of four ants will be formed, and these four ants will scatter to the neighbouring junctions (x + 1, y), (x - 1, y), (x, y + 1), (x, y - 1) — one ant in each direction. No other ant movements will happen. Ants never interfere with each other.
Scientists have put a colony of n ants into the junction (0, 0) and now they wish to know how many ants will there be at some given junctions, when the movement of the ants stops.
Input
First input line contains integers n (0 ≤ n ≤ 30000) and t (1 ≤ t ≤ 50000), where n is the number of ants in the colony and t is the number of queries. Each of the next t lines contains coordinates of a query junction: integers xi, yi ( - 109 ≤ xi, yi ≤ 109). Queries may coincide.
It is guaranteed that there will be a certain moment of time when no possible movements can happen (in other words, the process will eventually end).
Output
Print t integers, one per line — the number of ants at the corresponding junctions when the movement of the ants stops.
Examples
Input
1 3
0 1
0 0
0 -1
Output
0
1
0
Input
6 5
0 -2
0 -1
0 0
0 1
0 2
Output
0
1
2
1
0
Note
In the first sample the colony consists of the one ant, so nothing happens at all.
In the second sample the colony consists of 6 ants. At the first minute 4 ants scatter from (0, 0) to the neighbouring junctions. After that the process stops.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 2 2\\n..\\nRL\\n\", \"3 3 4\\n...\\nR.L\\nR.U\\n\", \"2 2 2\\n..\\nUU\\n\", \"3 4 8\\n....\\nRRLL\\nUUUU\\n\", \"2 2 2\\n..\\nLR\\n\", \"3 7 14\\n.......\\nLDUDLLD\\nDLRDDLD\\n\", \"4 5 15\\n.....\\nDRRLR\\nULDLD\\nDLRRL\\n\", \"10 8 30\\n........\\n.L.LDRR.\\nD.LDLR.U\\n..RL.L..\\nUR.UL...\\n.D.....L\\nR..UDULL\\n........\\nDD.U...D\\n........\\n\", \"5 6 20\\n......\\n.UURD.\\nLUD.RR\\nU.LDDD\\nDDLDDU\\n\", \"5 7 19\\n.......\\nRDLLLRL\\nUUR..U.\\n.D.DLLL\\n..R..UU\\n\", \"8 9 28\\n.........\\n.R.LDR.D.\\n....UULU.\\nR.D..DL.L\\n.R..DLUDU\\nR........\\n.URU...UU\\n.....D.L.\\n\", \"10 10 47\\n..........\\n.R.LLL.R.L\\nR.ULUL.RUL\\nRD..RL.L..\\nRU.D....LU\\n..RRR..DL.\\n.DRUUD.ULD\\n...D...LDD\\n...UUU.U..\\nR.....D...\\n\", \"2 2 0\\n..\\n..\\n\", \"100 2 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45\\n..\\n.D\\nU.\\n..\\nU.\\n..\\n..\\n..\\nU.\\n..\\n..\\nD.\\nU.\\n..\\n..\\nD.\\nDU\\n..\\nUD\\n..\\n..\\n..\\n..\\n..\\n..\\nD.\\n.U\\n..\\n..\\nD.\\nU.\\n..\\n..\\n..\\nU.\\n..\\n..\\n.D\\n..\\n..\\n.D\\n..\\n..\\n.D\\n.U\\nD.\\n..\\n.E\\n..\\n..\\nUD\\n..\\nU.\\n..\\nU.\\n..\\nUD\\n..\\nU.\\n..\\nU.\\n..\\n..\\n..\\nU.\\n.-\\n..\\nD.\\n..\\n..\\nU.\\n..\\nU.\\n..\\nUU\\n..\\nU.\\n..\\nU.\\n..\\n..\\n..\\n..\\n..\\n..\\n..\\n..\\n..\\n.D\\n..\\n..\\nD.\\nU.\\n.D\\n..\\n..\\nU.\\n.D\\nU.\\n..\\n\", \"4 5 15\\n.....\\nDRSLR\\nDLDLU\\nMDRQL\\n\", \"100 2 45\\n..\\n.D\\nU.\\n..\\nU.\\n..\\n..\\n..\\nU.\\n..\\n..\\nD.\\nU.\\n..\\n..\\n.D\\nDU\\n..\\nUD\\n..\\n..\\n..\\n..\\n..\\n..\\nD.\\n.U\\n..\\n..\\nD.\\nU.\\n..\\n..\\n..\\nU.\\n..\\n..\\n.D\\n..\\n..\\n.D\\n..\\n..\\n.D\\n.U\\nD.\\n..\\n.E\\n..\\n..\\nUD\\n..\\nU.\\n..\\nU.\\n..\\nUD\\n..\\nU.\\n./\\nU.\\n..\\n..\\n..\\nU.\\n--\\n..\\nD.\\n..\\n..\\nU.\\n..\\nU.\\n..\\nUU\\n..\\nU.\\n..\\nU.\\n..\\n..\\n..\\n..\\n..\\n..\\n..\\n..\\n..\\n.D\\n..\\n..\\nD.\\nU.\\n.D\\n..\\n..\\nU.\\n.D\\nU.\\n..\\n\", \"4 5 15\\n.....\\nDRRLR\\nDLDLU\\nLQRDL\\n\"], \"outputs\": [\"1 1 \", \"0 2 2 \", \"0 0 \", \"1 3 3 1 \", \"0 0 \", \"0 0 0 2 2 0 0 \", \"1 2 2 1 0 \", \"6 1 4 3 0 3 2 3 \", \"0 1 0 0 1 1 \", \"1 4 2 2 1 3 3 \", \"1 2 2 3 2 4 2 2 3 \", \"1 2 6 6 7 1 0 5 5 4 \", \"0 0 \", \"23 3 \", \"0 0 0 1 0 0 0 1 1 0 0 2 0 0 0 1 1 1 0 1 0 0 0 1 1 2 0 0 1 0 0 0 1 2 1 0 0 1 0 1 0 0 0 1 1 0 0 0 2 2 0 1 0 0 0 0 0 0 2 0 0 0 1 0 0 0 0 1 0 0 2 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 1 \", \"1 2 1 0 1 \", \"0 0 0 2 2 0 0\\n\", \"1 2 2 1 0\\n\", \"6 1 4 3 0 3 2 3\\n\", \"1 2 2 3 2 4 2 2 3\\n\", \"1 2 6 5 7 1 0 5 5 4\\n\", \"22 4\\n\", \"0 2 1 0 0\\n\", \"0 0\\n\", \"0 1 0 2 2 0 0\\n\", \"0 2 2 1 1\\n\", \"6 1 3 3 0 3 2 3\\n\", \"1 2 6 4 7 1 0 4 4 3\\n\", \"0 2 2 0 1\\n\", \"2 2 5 3 7 2 0 4 4 3\\n\", \"6 2 2 4 1 3 2 1\\n\", \"0 2 2 0 2\\n\", \"5 1 2 2 1 2 1 1\\n\", \"2 1 2 1 1\\n\", \"7 1 4 2 0 3 2 3\\n\", \"1 4 2 2 1 3 3\\n\", \"2 1 3 3 2 3 1 2 2\\n\", \"1 2 6 6 7 1 0 5 5 4\\n\", \"23 3\\n\", \"0 0 2 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 2 0 0 0 1 2 0 0 1 0 0 0 1 1 2 0 1 0 0 0 0 1 2 0 0 1 2 0 0 0 0 0 0 0 1 0\\n\", \"1 1\\n\", \"2 1 1 2\\n\", \"2 2 2 1 0\\n\", \"21 5\\n\", \"1 2 1 0 1\\n\", \"0 1 0 1 1 0 0\\n\", \"5 2 2 3 0 2 2 3\\n\", \"2 3 4 2 6 2 0 3 5 3\\n\", \"1 2 2 0 1\\n\", \"22 4\\n\", \"0 0\\n\", \"6 1 3 3 0 3 2 3\\n\", \"22 4\\n\", \"0 2 2 0 1\\n\", \"2 2 5 3 7 2 0 4 4 3\\n\", \"22 4\\n\", \"0 2 2 0 1\\n\", \"6 2 2 4 1 3 2 1\\n\", \"6 2 2 4 1 3 2 1\\n\", \"6 2 2 4 1 3 2 1\\n\", \"6 1 3 3 0 3 2 3\\n\", \"22 4\\n\", \"22 4\\n\", \"0 2 2 0 1\\n\", \"22 4\\n\", \"0 2 2 1 1\\n\"]}", "source": "primeintellect"}
|
Om Nom really likes candies and doesn't like spiders as they frequently steal candies. One day Om Nom fancied a walk in a park. Unfortunately, the park has some spiders and Om Nom doesn't want to see them at all.
<image>
The park can be represented as a rectangular n × m field. The park has k spiders, each spider at time 0 is at some cell of the field. The spiders move all the time, and each spider always moves in one of the four directions (left, right, down, up). In a unit of time, a spider crawls from his cell to the side-adjacent cell in the corresponding direction. If there is no cell in the given direction, then the spider leaves the park. The spiders do not interfere with each other as they move. Specifically, one cell can have multiple spiders at the same time.
Om Nom isn't yet sure where to start his walk from but he definitely wants:
* to start walking at time 0 at an upper row cell of the field (it is guaranteed that the cells in this row do not contain any spiders);
* to walk by moving down the field towards the lowest row (the walk ends when Om Nom leaves the boundaries of the park).
We know that Om Nom moves by jumping. One jump takes one time unit and transports the little monster from his cell to either a side-adjacent cell on the lower row or outside the park boundaries.
Each time Om Nom lands in a cell he sees all the spiders that have come to that cell at this moment of time. Om Nom wants to choose the optimal cell to start the walk from. That's why he wonders: for each possible starting cell, how many spiders will he see during the walk if he starts from this cell? Help him and calculate the required value for each possible starting cell.
Input
The first line contains three integers n, m, k (2 ≤ n, m ≤ 2000; 0 ≤ k ≤ m(n - 1)).
Each of the next n lines contains m characters — the description of the park. The characters in the i-th line describe the i-th row of the park field. If the character in the line equals ".", that means that the corresponding cell of the field is empty; otherwise, the character in the line will equal one of the four characters: "L" (meaning that this cell has a spider at time 0, moving left), "R" (a spider moving right), "U" (a spider moving up), "D" (a spider moving down).
It is guaranteed that the first row doesn't contain any spiders. It is guaranteed that the description of the field contains no extra characters. It is guaranteed that at time 0 the field contains exactly k spiders.
Output
Print m integers: the j-th integer must show the number of spiders Om Nom will see if he starts his walk from the j-th cell of the first row. The cells in any row of the field are numbered from left to right.
Examples
Input
3 3 4
...
R.L
R.U
Output
0 2 2
Input
2 2 2
..
RL
Output
1 1
Input
2 2 2
..
LR
Output
0 0
Input
3 4 8
....
RRLL
UUUU
Output
1 3 3 1
Input
2 2 2
..
UU
Output
0 0
Note
Consider the first sample. The notes below show how the spider arrangement changes on the field over time:
... ... ..U ...
R.L -> .*U -> L.R -> ...
R.U .R. ..R ...
Character "*" represents a cell that contains two spiders at the same time.
* If Om Nom starts from the first cell of the first row, he won't see any spiders.
* If he starts from the second cell, he will see two spiders at time 1.
* If he starts from the third cell, he will see two spiders: one at time 1, the other one at time 2.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.25
|
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|
Valery is a PE teacher at a school in Berland. Soon the students are going to take a test in long jumps, and Valery has lost his favorite ruler!
However, there is no reason for disappointment, as Valery has found another ruler, its length is l centimeters. The ruler already has n marks, with which he can make measurements. We assume that the marks are numbered from 1 to n in the order they appear from the beginning of the ruler to its end. The first point coincides with the beginning of the ruler and represents the origin. The last mark coincides with the end of the ruler, at distance l from the origin. This ruler can be repesented by an increasing sequence a1, a2, ..., an, where ai denotes the distance of the i-th mark from the origin (a1 = 0, an = l).
Valery believes that with a ruler he can measure the distance of d centimeters, if there is a pair of integers i and j (1 ≤ i ≤ j ≤ n), such that the distance between the i-th and the j-th mark is exactly equal to d (in other words, aj - ai = d).
Under the rules, the girls should be able to jump at least x centimeters, and the boys should be able to jump at least y (x < y) centimeters. To test the children's abilities, Valery needs a ruler to measure each of the distances x and y.
Your task is to determine what is the minimum number of additional marks you need to add on the ruler so that they can be used to measure the distances x and y. Valery can add the marks at any integer non-negative distance from the origin not exceeding the length of the ruler.
Input
The first line contains four positive space-separated integers n, l, x, y (2 ≤ n ≤ 105, 2 ≤ l ≤ 109, 1 ≤ x < y ≤ l) — the number of marks, the length of the ruler and the jump norms for girls and boys, correspondingly.
The second line contains a sequence of n integers a1, a2, ..., an (0 = a1 < a2 < ... < an = l), where ai shows the distance from the i-th mark to the origin.
Output
In the first line print a single non-negative integer v — the minimum number of marks that you need to add on the ruler.
In the second line print v space-separated integers p1, p2, ..., pv (0 ≤ pi ≤ l). Number pi means that the i-th mark should be at the distance of pi centimeters from the origin. Print the marks in any order. If there are multiple solutions, print any of them.
Examples
Input
3 250 185 230
0 185 250
Output
1
230
Input
4 250 185 230
0 20 185 250
Output
0
Input
2 300 185 230
0 300
Output
2
185 230
Note
In the first sample it is impossible to initially measure the distance of 230 centimeters. For that it is enough to add a 20 centimeter mark or a 230 centimeter mark.
In the second sample you already can use the ruler to measure the distances of 185 and 230 centimeters, so you don't have to add new marks.
In the third sample the ruler only contains the initial and the final marks. We will need to add two marks to be able to test the children's skills.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
Mr. Kitayuta has just bought an undirected graph consisting of n vertices and m edges. The vertices of the graph are numbered from 1 to n. Each edge, namely edge i, has a color ci, connecting vertex ai and bi.
Mr. Kitayuta wants you to process the following q queries.
In the i-th query, he gives you two integers — ui and vi.
Find the number of the colors that satisfy the following condition: the edges of that color connect vertex ui and vertex vi directly or indirectly.
Input
The first line of the input contains space-separated two integers — n and m (2 ≤ n ≤ 100, 1 ≤ m ≤ 100), denoting the number of the vertices and the number of the edges, respectively.
The next m lines contain space-separated three integers — ai, bi (1 ≤ ai < bi ≤ n) and ci (1 ≤ ci ≤ m). Note that there can be multiple edges between two vertices. However, there are no multiple edges of the same color between two vertices, that is, if i ≠ j, (ai, bi, ci) ≠ (aj, bj, cj).
The next line contains a integer — q (1 ≤ q ≤ 100), denoting the number of the queries.
Then follows q lines, containing space-separated two integers — ui and vi (1 ≤ ui, vi ≤ n). It is guaranteed that ui ≠ vi.
Output
For each query, print the answer in a separate line.
Examples
Input
4 5
1 2 1
1 2 2
2 3 1
2 3 3
2 4 3
3
1 2
3 4
1 4
Output
2
1
0
Input
5 7
1 5 1
2 5 1
3 5 1
4 5 1
1 2 2
2 3 2
3 4 2
5
1 5
5 1
2 5
1 5
1 4
Output
1
1
1
1
2
Note
Let's consider the first sample.
<image> The figure above shows the first sample.
* Vertex 1 and vertex 2 are connected by color 1 and 2.
* Vertex 3 and vertex 4 are connected by color 3.
* Vertex 1 and vertex 4 are not connected by any single color.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
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5\\n75 1\\n0 110\\n179 20\\n100 1\\n\"], \"outputs\": [\"111\", \"100\", \"3989899086\", \"6\", \"134509124\", \"33\", \"55\", \"17\", \"3634263641\", \"12\", \"1504320408\", \"1000000\", \"200\", \"107\", \"12\", \"4489916765\\n\", \"6\\n\", \"134509124\\n\", \"26\\n\", \"3677320675\\n\", \"13\\n\", \"1504320408\\n\", \"1000000\\n\", \"20\\n\", \"105\\n\", \"100\\n\", \"1001000\\n\", \"95\\n\", \"110\\n\", \"610905515\\n\", \"97\\n\", \"585402296\\n\", \"3499356728\\n\", \"3015331948\\n\", \"8\\n\", \"246867226\\n\", \"17\\n\", \"3682173966\\n\", \"12\\n\", \"107\\n\", \"1\\n\", \"70\\n\", \"3489916765\\n\", \"70503936\\n\", \"3475808340\\n\", \"25\\n\", \"96\\n\", \"3535144131\\n\", \"543743736\\n\", \"3699704416\\n\", \"6\\n\", \"134509124\\n\", \"26\\n\", \"3677320675\\n\", \"13\\n\", \"1504320408\\n\", \"20\\n\", \"6\\n\", \"134509124\\n\", \"3677320675\\n\", \"110\\n\", \"6\\n\", \"3677320675\\n\", \"610905515\\n\", \"6\\n\", \"3677320675\\n\", \"3677320675\\n\", \"585402296\\n\", \"585402296\\n\", \"3499356728\\n\", \"585402296\\n\", \"585402296\\n\", \"585402296\\n\", \"585402296\\n\", \"585402296\\n\", \"1504320408\\n\", \"1000000\\n\", \"100\\n\", \"6\\n\", \"26\\n\", \"1504320408\\n\", \"1000000\\n\", \"20\\n\", \"105\\n\", \"20\\n\", \"6\\n\", \"134509124\\n\", \"26\\n\", \"3677320675\\n\", \"13\\n\", \"1504320408\\n\", \"1001000\\n\", \"8\\n\", \"110\\n\", \"134509124\\n\", \"97\\n\", \"110\\n\"]}", "source": "primeintellect"}
|
Kefa wants to celebrate his first big salary by going to restaurant. However, he needs company.
Kefa has n friends, each friend will agree to go to the restaurant if Kefa asks. Each friend is characterized by the amount of money he has and the friendship factor in respect to Kefa. The parrot doesn't want any friend to feel poor compared to somebody else in the company (Kefa doesn't count). A friend feels poor if in the company there is someone who has at least d units of money more than he does. Also, Kefa wants the total friendship factor of the members of the company to be maximum. Help him invite an optimal company!
Input
The first line of the input contains two space-separated integers, n and d (1 ≤ n ≤ 105, <image>) — the number of Kefa's friends and the minimum difference between the amount of money in order to feel poor, respectively.
Next n lines contain the descriptions of Kefa's friends, the (i + 1)-th line contains the description of the i-th friend of type mi, si (0 ≤ mi, si ≤ 109) — the amount of money and the friendship factor, respectively.
Output
Print the maximum total friendship factir that can be reached.
Examples
Input
4 5
75 5
0 100
150 20
75 1
Output
100
Input
5 100
0 7
11 32
99 10
46 8
87 54
Output
111
Note
In the first sample test the most profitable strategy is to form a company from only the second friend. At all other variants the total degree of friendship will be worse.
In the second sample test we can take all the friends.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"5\\n3 2 2 5 3\\n\", \"8\\n2 3 5 4 1 6 6 7\\n\", \"4\\n2 3 3 4\\n\", \"3\\n2 1 1\\n\", \"6\\n6 2 6 2 4 2\\n\", \"2\\n1 2\\n\", \"8\\n2 1 2 2 6 5 6 6\\n\", \"18\\n2 3 4 5 2 7 8 9 10 7 11 12 14 15 13 17 18 18\\n\", \"7\\n1 2 3 4 5 6 7\\n\", \"7\\n4 3 2 6 3 5 2\\n\", \"7\\n7 5 3 1 2 1 5\\n\", \"7\\n1 6 4 4 5 6 7\\n\", \"6\\n6 2 1 2 4 2\\n\", \"7\\n1 2 3 4 5 1 7\\n\", \"7\\n4 3 2 6 5 5 2\\n\", \"7\\n1 2 3 4 7 1 7\\n\", \"7\\n4 3 1 6 5 5 2\\n\", \"7\\n1 2 3 7 7 1 7\\n\", \"6\\n3 2 6 2 4 2\\n\", \"2\\n2 2\\n\", \"8\\n2 1 2 2 6 5 6 2\\n\", \"7\\n7 5 3 1 4 1 5\\n\", \"4\\n3 3 3 4\\n\", \"7\\n1 2 3 4 5 1 4\\n\", \"7\\n4 3 2 6 5 5 3\\n\", \"7\\n4 3 1 6 5 2 2\\n\", \"7\\n4 1 1 6 5 2 2\\n\", \"7\\n1 2 3 1 5 1 4\\n\", \"7\\n4 1 1 6 5 3 2\\n\", \"7\\n4 1 1 6 4 3 2\\n\", \"7\\n4 1 1 6 4 3 1\\n\", \"7\\n7 1 2 6 4 3 1\\n\", \"7\\n7 1 2 6 4 3 2\\n\", \"7\\n7 2 2 6 4 3 2\\n\", \"7\\n7 4 2 6 4 3 2\\n\", \"3\\n2 2 1\\n\", \"18\\n2 3 4 5 2 7 8 9 2 7 11 12 14 15 13 17 18 18\\n\", \"7\\n1 2 3 5 5 6 7\\n\", \"7\\n4 3 2 7 3 5 2\\n\", \"7\\n7 5 3 1 2 1 6\\n\", \"7\\n1 6 4 2 5 6 7\\n\", \"5\\n5 2 2 5 3\\n\", \"6\\n4 2 1 2 4 2\\n\", \"7\\n4 3 4 6 5 5 3\\n\", \"7\\n5 3 1 6 5 5 2\\n\", \"7\\n7 2 3 1 4 1 5\\n\", \"4\\n3 3 1 4\\n\", \"7\\n6 3 2 6 5 5 3\\n\", \"7\\n4 3 1 6 5 1 2\\n\", \"7\\n1 2 2 7 5 1 4\\n\", \"7\\n4 1 1 6 5 1 2\\n\", \"7\\n1 2 3 1 3 1 4\\n\", \"7\\n5 1 1 6 5 3 2\\n\", \"7\\n4 1 1 6 2 3 1\\n\", \"7\\n7 2 2 6 4 3 4\\n\", \"7\\n1 4 4 6 4 3 2\\n\", \"18\\n2 3 4 5 2 7 4 9 2 7 11 12 14 15 13 17 18 18\\n\", \"6\\n4 2 1 2 4 3\\n\", \"7\\n4 3 4 6 3 5 3\\n\", \"7\\n5 3 2 6 5 5 2\\n\", \"4\\n3 3 2 4\\n\", \"7\\n4 3 1 7 5 1 2\\n\", \"7\\n1 2 2 7 5 1 3\\n\", \"7\\n1 2 3 2 3 1 4\\n\", \"7\\n4 1 1 7 2 3 1\\n\", \"7\\n7 2 1 6 4 3 4\\n\", \"18\\n2 3 4 5 2 7 4 6 2 7 11 12 14 15 13 17 18 18\\n\", \"6\\n4 2 1 2 1 3\\n\", \"7\\n5 3 2 6 5 1 2\\n\", \"7\\n4 3 1 7 5 1 1\\n\", \"7\\n1 2 3 7 5 1 4\\n\", \"7\\n7 1 1 6 4 3 1\\n\", \"7\\n1 4 2 6 4 3 2\\n\", \"7\\n6 1 1 6 4 3 2\\n\", \"7\\n4 1 2 6 4 3 2\\n\", \"7\\n5 1 2 6 4 3 2\\n\", \"7\\n1 4 2 7 5 1 3\\n\"], \"outputs\": [\"0\\n3 2 2 5 3 \", \"2 \\n2 3 5 4 4 4 6 7 \\n\", \"1 \\n2 3 3 3 \\n\", \"1\\n2 2 1 \", \"0\\n6 2 6 2 4 2 \", \"1 \\n1 1 \\n\", \"2 \\n2 2 2 2 6 2 6 6 \\n\", \"5 \\n2 3 4 5 11 7 8 9 10 11 11 11 14 15 11 17 18 11 \\n\", \"6 \\n1 1 1 1 1 1 1 \\n\", \"1\\n4 3 3 6 3 5 2 \", \"1\\n7 5 3 1 3 1 5 \", \"4 \\n1 6 4 1 1 1 1 \\n\", \"0\\n6 2 1 2 4 2\\n\", \"5\\n1 1 1 1 1 1 1\\n\", \"1\\n4 5 2 6 5 5 2\\n\", \"4\\n1 1 1 1 7 1 1\\n\", \"0\\n4 3 1 6 5 5 2\\n\", \"3\\n1 1 1 7 7 1 1\\n\", \"0\\n3 2 6 2 4 2\\n\", \"0\\n2 2\\n\", \"2\\n1 1 2 2 1 5 6 2\\n\", \"1\\n3 5 3 1 4 1 5\\n\", \"1\\n3 3 3 3\\n\", \"4\\n1 1 1 1 1 1 4\\n\", \"1\\n4 5 2 6 5 5 3\\n\", \"1\\n5 3 1 6 5 2 2\\n\", \"1\\n5 1 1 6 5 2 2\\n\", \"3\\n1 1 1 1 1 1 4\\n\", \"1\\n5 1 1 6 5 3 2\\n\", \"1\\n1 1 1 6 4 3 2\\n\", \"1\\n1 1 1 6 4 3 1\\n\", \"1\\n1 1 2 6 4 3 1\\n\", \"1\\n1 1 2 6 4 3 2\\n\", \"0\\n7 2 2 6 4 3 2\\n\", \"1\\n7 2 2 6 4 3 2\\n\", \"0\\n2 2 1\\n\", \"4\\n2 11 4 5 2 7 8 9 2 7 11 11 11 15 13 17 18 11\\n\", \"5\\n1 1 1 5 1 1 1\\n\", \"1\\n4 2 2 7 3 5 2\\n\", \"2\\n3 3 3 1 2 1 6\\n\", \"3\\n1 6 4 2 1 1 1\\n\", \"0\\n5 2 2 5 3\\n\", \"0\\n4 2 1 2 4 2\\n\", \"0\\n4 3 4 6 5 5 3\\n\", \"0\\n5 3 1 6 5 5 2\\n\", \"2\\n2 2 2 1 4 1 5\\n\", \"1\\n4 3 1 4\\n\", \"1\\n6 5 2 6 5 5 3\\n\", \"1\\n5 3 1 6 5 1 2\\n\", \"3\\n1 1 2 1 1 1 4\\n\", \"1\\n5 1 1 6 5 1 2\\n\", \"2\\n1 1 1 1 3 1 4\\n\", \"0\\n5 1 1 6 5 3 2\\n\", \"1\\n1 1 1 6 2 3 1\\n\", \"0\\n7 2 2 6 4 3 4\\n\", \"1\\n1 4 4 1 4 3 2\\n\", \"4\\n2 11 4 5 2 7 4 9 2 7 11 11 11 15 13 17 18 11\\n\", \"0\\n4 2 1 2 4 3\\n\", \"1\\n4 3 4 4 3 5 3\\n\", \"1\\n5 5 2 6 5 5 2\\n\", \"1\\n3 3 4 4\\n\", \"1\\n5 3 1 7 5 1 2\\n\", \"2\\n1 1 2 7 1 1 3\\n\", \"2\\n1 1 1 2 3 1 4\\n\", \"1\\n1 1 1 7 2 3 1\\n\", \"1\\n2 2 1 6 4 3 4\\n\", \"4\\n2 11 4 5 2 7 4 6 2 7 11 11 11 15 13 17 18 11\\n\", \"0\\n4 2 1 2 1 3\\n\", \"1\\n5 5 2 6 5 1 2\\n\", \"1\\n5 3 1 7 5 1 1\\n\", \"4\\n1 1 1 1 1 1 4\\n\", \"1\\n1 1 1 6 4 3 1\\n\", \"1\\n1 1 2 6 4 3 2\\n\", \"1\\n1 1 1 6 4 3 2\\n\", \"1\\n1 1 2 6 4 3 2\\n\", \"1\\n1 1 2 6 4 3 2\\n\", \"2\\n1 1 2 7 1 1 3\\n\"]}", "source": "primeintellect"}
|
A tree is an undirected connected graph without cycles.
Let's consider a rooted undirected tree with n vertices, numbered 1 through n. There are many ways to represent such a tree. One way is to create an array with n integers p1, p2, ..., pn, where pi denotes a parent of vertex i (here, for convenience a root is considered its own parent).
<image> For this rooted tree the array p is [2, 3, 3, 2].
Given a sequence p1, p2, ..., pn, one is able to restore a tree:
1. There must be exactly one index r that pr = r. A vertex r is a root of the tree.
2. For all other n - 1 vertices i, there is an edge between vertex i and vertex pi.
A sequence p1, p2, ..., pn is called valid if the described procedure generates some (any) rooted tree. For example, for n = 3 sequences (1,2,2), (2,3,1) and (2,1,3) are not valid.
You are given a sequence a1, a2, ..., an, not necessarily valid. Your task is to change the minimum number of elements, in order to get a valid sequence. Print the minimum number of changes and an example of a valid sequence after that number of changes. If there are many valid sequences achievable in the minimum number of changes, print any of them.
Input
The first line of the input contains an integer n (2 ≤ n ≤ 200 000) — the number of vertices in the tree.
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ n).
Output
In the first line print the minimum number of elements to change, in order to get a valid sequence.
In the second line, print any valid sequence possible to get from (a1, a2, ..., an) in the minimum number of changes. If there are many such sequences, any of them will be accepted.
Examples
Input
4
2 3 3 4
Output
1
2 3 4 4
Input
5
3 2 2 5 3
Output
0
3 2 2 5 3
Input
8
2 3 5 4 1 6 6 7
Output
2
2 3 7 8 1 6 6 7
Note
In the first sample, it's enough to change one element. In the provided output, a sequence represents a tree rooted in a vertex 4 (because p4 = 4), which you can see on the left drawing below. One of other correct solutions would be a sequence 2 3 3 2, representing a tree rooted in vertex 3 (right drawing below). On both drawings, roots are painted red.
<image>
In the second sample, the given sequence is already valid.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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49\\n\", \"3 1\\n7 2\\n\", \"87 22\\n119 64\\n\", \"46 24\\n20 62\\n\", \"59 67\\n61 54\\n\", \"2 0\\n2 4\\n\", \"7 22\\n39 79\\n\", \"87 34\\n91 40\\n\", \"46 47\\n42 55\\n\", \"39 21\\n2 34\\n\", \"94 27\\n30 7\\n\", \"67 1\\n74 27\\n\", \"18 1\\n53 71\\n\", \"39 7\\n79 74\\n\", \"1 5\\n1 14\\n\", \"2 1\\n3 2\\n\", \"20 81\\n47 11\\n\", \"17 7\\n44 75\\n\", \"31 74\\n88 152\\n\", \"2 5\\n2 2\\n\", \"6 7\\n3 6\\n\", \"4 2\\n4 7\\n\", \"48 71\\n16 49\\n\", \"100 110\\n100 100\\n\", \"18 4\\n33 78\\n\", \"2 0\\n2 5\\n\", \"46 44\\n42 55\\n\", \"22 81\\n44 88\\n\", \"2 4\\n2 3\\n\", \"94 55\\n20 88\\n\", \"98 1\\n99 000\\n\", \"69 5\\n48 34\\n\", \"2 2\\n2 19\\n\", \"17 45\\n68 65\\n\", \"4 2\\n2 1\\n\", \"7 7\\n7 20\\n\", \"15 63\\n51 22\\n\", \"2 1\\n2 2\\n\", \"4 3\\n4 47\\n\", \"1 7\\n3 6\\n\", \"2 2\\n1 100\\n\", \"6 7\\n14 14\\n\", \"2 2\\n4 7\\n\", \"19 44\\n34 48\\n\", \"16 63\\n98 53\\n\", \"5 85\\n95 46\\n\", \"18 4\\n33 53\\n\", \"30 4\\n81 23\\n\", \"2 81\\n44 88\\n\", \"94 55\\n22 88\\n\", \"69 48\\n39 14\\n\", \"27 5\\n48 34\\n\", \"2 2\\n2 11\\n\", \"4 2\\n4 1\\n\", \"7 7\\n7 9\\n\", \"15 63\\n51 26\\n\", \"33 2\\n9 10\\n\", \"84 170\\n38 7\\n\", \"1 3\\n4 47\\n\", \"1 10\\n3 6\\n\", \"2 2\\n1 000\\n\", \"6 7\\n14 23\\n\", \"2 2\\n8 7\\n\", \"2 2\\n1 2\\n\"], \"outputs\": [\"82\\n\", \"-1\\n\", \"82\\n\", \"-1\\n\", \"99\\n\", \"-1\\n\", \"301\\n\", \"100\\n\", \"-1\\n\", \"20\\n\", \"4852\\n\", \"427\\n\", \"1222\\n\", \"-1\\n\", \"1\\n\", \"209\\n\", \"2\\n\", \"718\\n\", \"674\\n\", \"1748\\n\", \"1346\\n\", \"3483\\n\", \"1014\\n\", \"331\\n\", \"100\\n\", \"204\\n\", \"1156\\n\", \"5967\\n\", \"364\\n\", \"5\\n\", \"319\\n\", \"211\\n\", \"9605\\n\", \"-1\\n\", \"100\\n\", \"3414\\n\", \"-1\\n\", \"100\\n\", \"789\\n\", \"2321\\n\", \"1278\\n\", \"3\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"48\\n\", \"1255\\n\", \"5\\n\", \"9703\\n\", \"-1\\n\", \"10\\n\", \"317\\n\", \"-1\\n\", \"101\\n\", \"14\\n\", \"-1\\n\", \"-1\\n\", \"1410\\n\", \"-1\\n\", \"47\\n\", \"158\\n\", \"100\\n\", \"28\\n\", \"339\\n\", \"2102\\n\", \"2\\n\", \"9\\n\", \"1240\\n\", \"300\\n\", \"286\\n\", \"543\\n\", \"1542\\n\", \"331\\n\", \"1724\\n\", \"85\\n\", \"2122\\n\", \"9506\\n\", \"101\\n\", \"99\\n\", \"37\\n\", \"2691\\n\", \"972\\n\", \"13\\n\", \"876\\n\", \"1723\\n\", \"8\\n\", \"201\\n\", \"82\\n\", \"12\\n\", \"121\\n\", \"501\\n\", \"295\\n\", \"152\\n\", \"3\\n\", \"119\\n\", \"16\\n\", \"1849\\n\", \"162\\n\", \"2250\\n\", \"4\\n\", \"274\\n\", \"3862\\n\", \"139\\n\", \"60\\n\", \"967\\n\", \"1877\\n\", \"919\\n\", \"943\\n\", \"14\\n\", \"5\\n\", \"481\\n\", \"75\\n\", \"2616\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"99\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"47\\n\", \"9\\n\", \"100\\n\", \"-1\\n\", \"-1\\n\", \"82\\n\", \"543\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"47\\n\", \"12\\n\", \"2\\n\", \"37\\n\", \"-1\\n\", \"2\\n\"]}", "source": "primeintellect"}
|
A monster is chasing after Rick and Morty on another planet. They're so frightened that sometimes they scream. More accurately, Rick screams at times b, b + a, b + 2a, b + 3a, ... and Morty screams at times d, d + c, d + 2c, d + 3c, ....
<image>
The Monster will catch them if at any point they scream at the same time, so it wants to know when it will catch them (the first time they scream at the same time) or that they will never scream at the same time.
Input
The first line of input contains two integers a and b (1 ≤ a, b ≤ 100).
The second line contains two integers c and d (1 ≤ c, d ≤ 100).
Output
Print the first time Rick and Morty will scream at the same time, or - 1 if they will never scream at the same time.
Examples
Input
20 2
9 19
Output
82
Input
2 1
16 12
Output
-1
Note
In the first sample testcase, Rick's 5th scream and Morty's 8th time are at time 82.
In the second sample testcase, all Rick's screams will be at odd times and Morty's will be at even times, so they will never scream at the same time.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
{"tests": "{\"inputs\": [\"4 3\\n3 10\\n2 7\\n2 8\\n1 1\\n\", \"2 2\\n1 3\\n2 2\\n\", \"1 1\\n2 1\\n\", \"52 102\\n3 199\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n2 100\\n\", \"7 12\\n2 10\\n2 8\\n2 1\\n3 8\\n3 8\\n3 7\\n1 7\\n\", \"4 28\\n2 2\\n3 1\\n3 10\\n1 9\\n\", \"1 2\\n2 10\\n\", \"1 29\\n2 8\\n\", \"4 2\\n3 4\\n3 8\\n1 1\\n1 4\\n\", \"6 5\\n3 1\\n3 1\\n1 2\\n2 9\\n3 10\\n1 8\\n\", \"6 18\\n3 3\\n1 10\\n2 10\\n3 6\\n1 3\\n2 3\\n\", \"9 19\\n2 5\\n2 3\\n3 9\\n1 9\\n3 8\\n3 5\\n3 4\\n3 2\\n3 6\\n\", \"3 4\\n2 10\\n2 10\\n3 15\\n\", \"6 7\\n2 5\\n2 4\\n3 9\\n3 2\\n3 1\\n3 8\\n\", \"3 4\\n1 4\\n2 10\\n3 100\\n\", \"9 15\\n3 8\\n1 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300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n\", \"6 6\\n1 6\\n1 4\\n1 8\\n3 2\\n3 2\\n2 8\\n\", \"10 2\\n3 4\\n3 5\\n3 7\\n1 10\\n1 2\\n1 2\\n1 8\\n3 2\\n1 8\\n3 3\\n\", \"7 6\\n2 9\\n3 10\\n1 2\\n2 6\\n3 6\\n2 1\\n1 3\\n\", \"8 5\\n3 9\\n3 3\\n1 4\\n3 1\\n2 5\\n3 1\\n3 6\\n3 1\\n\", \"2 4\\n3 8\\n1 6\\n\", \"4 28\\n2 2\\n2 1\\n3 10\\n1 9\\n\", \"1 13\\n2 8\\n\", \"4 2\\n3 4\\n3 9\\n1 1\\n1 4\\n\", \"3 4\\n2 10\\n2 10\\n3 4\\n\", \"6 7\\n2 5\\n2 4\\n3 9\\n3 2\\n3 1\\n3 7\\n\", \"9 29\\n3 8\\n1 2\\n2 5\\n1 5\\n3 3\\n1 7\\n1 7\\n2 7\\n2 9\\n\", \"20 25\\n2 13\\n3 2\\n1 32\\n1 43\\n3 85\\n1 14\\n2 57\\n1 54\\n1 38\\n2 96\\n2 89\\n3 64\\n1 79\\n2 73\\n1 73\\n2 34\\n1 52\\n1 79\\n1 42\\n3 34\\n\", \"8 6\\n1 9\\n1 5\\n1 3\\n1 10\\n3 8\\n1 6\\n1 5\\n1 2\\n\", \"9 10\\n3 6\\n3 1\\n2 4\\n2 3\\n3 6\\n3 1\\n1 8\\n2 4\\n3 3\\n\", \"8 21\\n2 6\\n3 3\\n3 7\\n3 8\\n3 8\\n3 7\\n2 6\\n3 9\\n\", \"5 9\\n1 8\\n3 7\\n2 6\\n1 4\\n2 7\\n\", \"61 120\\n3 5\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 2\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n2 3\\n\", \"10 12\\n3 7\\n3 6\\n3 8\\n3 4\\n1 9\\n2 5\\n2 1\\n2 5\\n2 10\\n2 9\\n\", \"5 5\\n3 1\\n2 6\\n3 2\\n1 1\\n1 6\\n\", \"13 23\\n3 17\\n1 83\\n1 81\\n3 83\\n3 59\\n3 71\\n2 61\\n3 8\\n3 64\\n2 80\\n3 47\\n1 46\\n1 82\\n\", \"10 6\\n1 8\\n1 10\\n1 7\\n2 9\\n3 8\\n1 8\\n1 7\\n1 4\\n3 1\\n3 6\\n\", \"10 5\\n1 9\\n1 8\\n2 8\\n3 4\\n3 1\\n2 2\\n3 6\\n1 1\\n3 8\\n2 2\\n\", \"1 2\\n1 10\\n\", \"6 12\\n1 7\\n1 17\\n2 8\\n1 2\\n2 9\\n3 5\\n\", \"70 203\\n1 105\\n1 105\\n1 105\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 491\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n\", \"4 3\\n3 10\\n2 7\\n2 14\\n1 1\\n\", \"1 2\\n2 1\\n\", \"4 2\\n3 4\\n3 9\\n1 1\\n1 8\\n\", \"20 25\\n2 13\\n3 2\\n1 32\\n1 43\\n3 85\\n1 14\\n2 57\\n1 54\\n1 38\\n2 96\\n2 89\\n3 64\\n1 79\\n2 73\\n1 73\\n2 34\\n1 52\\n1 79\\n1 44\\n3 34\\n\", \"5 9\\n1 8\\n3 7\\n2 6\\n1 8\\n2 7\\n\", \"10 12\\n3 7\\n3 6\\n3 7\\n3 4\\n1 9\\n2 5\\n2 1\\n2 5\\n2 10\\n2 9\\n\", \"13 23\\n3 17\\n1 83\\n1 81\\n3 83\\n3 59\\n3 71\\n2 61\\n3 8\\n3 64\\n2 80\\n3 47\\n1 46\\n1 103\\n\", \"10 6\\n1 3\\n1 10\\n1 7\\n2 9\\n3 8\\n1 8\\n1 7\\n1 4\\n3 1\\n3 6\\n\", \"70 203\\n1 105\\n1 105\\n1 105\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 404\\n3 300\\n3 300\\n3 300\\n3 491\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n3 300\\n\", \"1 2\\n3 1\\n\", \"4 2\\n3 4\\n3 9\\n1 1\\n1 3\\n\", \"20 25\\n2 13\\n3 2\\n1 32\\n1 43\\n3 85\\n1 14\\n2 57\\n1 54\\n1 38\\n2 96\\n2 89\\n3 64\\n1 79\\n2 73\\n1 73\\n2 47\\n1 52\\n1 79\\n1 44\\n3 34\\n\", \"8 5\\n1 9\\n1 5\\n1 3\\n1 10\\n3 8\\n1 6\\n1 5\\n1 2\\n\", \"9 10\\n3 6\\n2 1\\n2 7\\n2 3\\n3 6\\n3 1\\n1 8\\n2 4\\n3 4\\n\", \"8 21\\n2 6\\n3 3\\n3 7\\n3 16\\n3 8\\n3 7\\n2 6\\n3 6\\n\", \"13 23\\n3 17\\n1 83\\n1 81\\n3 83\\n3 59\\n3 71\\n2 61\\n3 8\\n3 64\\n2 13\\n3 47\\n1 46\\n1 103\\n\", \"10 6\\n1 3\\n1 10\\n1 7\\n2 9\\n3 8\\n1 8\\n1 7\\n1 8\\n3 1\\n3 6\\n\", \"1 3\\n1 19\\n\", \"2 1\\n1 5\\n3 11\\n\", \"6 6\\n1 6\\n1 4\\n1 8\\n3 2\\n3 2\\n2 2\\n\", \"2 3\\n1 3\\n2 2\\n\", \"1 25\\n2 8\\n\", \"3 6\\n2 10\\n2 10\\n3 4\\n\", \"6 7\\n2 5\\n2 4\\n3 9\\n3 2\\n3 2\\n3 7\\n\", \"8 11\\n1 9\\n1 5\\n1 3\\n1 10\\n3 8\\n1 6\\n1 5\\n1 2\\n\", \"9 10\\n3 6\\n2 1\\n2 4\\n2 3\\n3 6\\n3 1\\n1 8\\n2 4\\n3 4\\n\", \"8 21\\n2 6\\n3 3\\n3 7\\n3 8\\n3 8\\n3 7\\n2 6\\n3 6\\n\", \"5 5\\n3 1\\n2 6\\n3 2\\n1 1\\n2 6\\n\", \"1 3\\n1 10\\n\", \"6 12\\n1 7\\n1 7\\n2 8\\n1 2\\n2 9\\n3 5\\n\", \"6 6\\n2 6\\n1 4\\n1 8\\n3 2\\n3 2\\n2 2\\n\", \"6 12\\n1 1\\n1 7\\n2 8\\n1 2\\n2 9\\n3 5\\n\", \"6 6\\n2 6\\n1 4\\n1 14\\n3 2\\n3 2\\n2 2\\n\", \"1 2\\n3 2\\n\"], \"outputs\": [\"10\\n\", \"3\\n\", \"0\\n\", \"5100\\n\", \"41\\n\", \"22\\n\", \"10\\n\", \"8\\n\", \"5\\n\", \"20\\n\", \"35\\n\", \"46\\n\", \"20\\n\", \"18\\n\", \"104\\n\", \"51\\n\", \"990\\n\", \"37\\n\", \"25\\n\", \"52\\n\", \"28\\n\", \"1605\\n\", \"46\\n\", \"180\\n\", \"46\\n\", \"13\\n\", \"711\\n\", \"44\\n\", \"28\\n\", \"10\\n\", \"5\\n\", \"16\\n\", \"28\\n\", \"41\\n\", \"20310\\n\", \"26\\n\", \"18\\n\", \"22\\n\", \"14\\n\", \"14\\n\", \"22\\n\", \"8\\n\", \"5\\n\", \"20\\n\", \"18\\n\", \"53\\n\", \"990\\n\", \"38\\n\", \"25\\n\", \"51\\n\", \"32\\n\", \"179\\n\", \"46\\n\", \"13\\n\", \"757\\n\", \"44\\n\", \"26\\n\", \"10\\n\", \"48\\n\", \"20501\\n\", \"15\\n\", \"1\\n\", \"9\\n\", \"992\\n\", \"36\\n\", \"45\\n\", \"778\\n\", \"41\\n\", \"20605\\n\", \"0\\n\", \"4\\n\", \"1005\\n\", \"35\\n\", \"28\\n\", \"56\\n\", \"711\\n\", \"43\\n\", \"19\\n\", \"5\\n\", \"20\\n\", \"5\\n\", \"8\\n\", \"20\\n\", \"18\\n\", \"48\\n\", \"25\\n\", \"48\\n\", \"13\\n\", \"10\\n\", \"38\\n\", \"20\\n\", \"32\\n\", \"26\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
After several latest reforms many tourists are planning to visit Berland, and Berland people understood that it's an opportunity to earn money and changed their jobs to attract tourists. Petya, for example, left the IT corporation he had been working for and started to sell souvenirs at the market.
This morning, as usual, Petya will come to the market. Petya has n different souvenirs to sell; ith souvenir is characterised by its weight wi and cost ci. Petya knows that he might not be able to carry all the souvenirs to the market. So Petya wants to choose a subset of souvenirs such that its total weight is not greater than m, and total cost is maximum possible.
Help Petya to determine maximum possible total cost.
Input
The first line contains two integers n and m (1 ≤ n ≤ 100000, 1 ≤ m ≤ 300000) — the number of Petya's souvenirs and total weight that he can carry to the market.
Then n lines follow. ith line contains two integers wi and ci (1 ≤ wi ≤ 3, 1 ≤ ci ≤ 109) — the weight and the cost of ith souvenir.
Output
Print one number — maximum possible total cost of souvenirs that Petya can carry to the market.
Examples
Input
1 1
2 1
Output
0
Input
2 2
1 3
2 2
Output
3
Input
4 3
3 10
2 7
2 8
1 1
Output
10
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"6\\n2 4\\n75 45\\n8 8\\n16 16\\n247 994\\n1000000000 1000000\\n\", \"1\\n1062961 1031\\n\", \"1\\n3331 11095561\\n\", \"1\\n2 3\\n\", \"3\\n1 1\\n8 27\\n1000 1331\\n\", \"1\\n90 72\\n\", \"1\\n12004 18012002\\n\", \"1\\n3 10\\n\", \"1\\n16 8\\n\", \"1\\n3 1\\n\", \"1\\n31159 970883281\\n\", \"1\\n6 12\\n\", \"1\\n9907 98148649\\n\", \"1\\n1062961 534\\n\", \"3\\n1 1\\n8 5\\n1000 1331\\n\", \"6\\n2 4\\n75 45\\n8 8\\n16 5\\n247 994\\n1000000000 1000000\\n\", \"1\\n1 1\\n\", \"3\\n1 2\\n4 5\\n1000 1247\\n\", \"1\\n1369 11095561\\n\", \"1\\n90 65\\n\", \"1\\n12004 14979606\\n\", \"1\\n1 10\\n\", \"1\\n1 8\\n\", \"1\\n5 1\\n\", \"1\\n59808 970883281\\n\", \"1\\n7 12\\n\", \"1\\n9907 193212989\\n\", \"1\\n1751864 534\\n\", \"1\\n1369 695441\\n\", \"3\\n1 1\\n8 5\\n1000 1652\\n\", \"1\\n90 50\\n\", \"1\\n12004 23485980\\n\", \"1\\n2 10\\n\", \"1\\n1 13\\n\", \"1\\n59808 1147135943\\n\", \"1\\n5 12\\n\", \"1\\n9907 77741179\\n\", \"6\\n2 4\\n75 45\\n8 8\\n16 7\\n247 994\\n1000000000 1000000\\n\", \"1\\n2682349 534\\n\", \"1\\n1369 411325\\n\", \"3\\n1 1\\n8 5\\n1000 1247\\n\", \"1\\n90 19\\n\", \"1\\n12033 23485980\\n\", \"1\\n2 19\\n\", \"1\\n1 12\\n\", \"1\\n1 2\\n\", \"1\\n1029 1147135943\\n\", \"1\\n5 21\\n\", \"1\\n365 77741179\\n\", \"1\\n2682349 821\\n\", \"1\\n113 411325\\n\", \"3\\n1 1\\n4 5\\n1000 1247\\n\", \"1\\n90 1\\n\", \"1\\n21331 23485980\\n\", \"1\\n2 12\\n\", \"1\\n1 11\\n\", \"1\\n1009 1147135943\\n\", \"1\\n1 21\\n\", \"1\\n347 77741179\\n\", \"1\\n2075461 821\\n\", \"1\\n137 411325\\n\", \"1\\n169 1\\n\", \"1\\n42429 23485980\\n\", \"1\\n1410 1147135943\\n\", \"1\\n682 77741179\\n\", \"1\\n1698406 821\\n\", \"1\\n170 411325\\n\", \"3\\n1 2\\n4 5\\n1000 1948\\n\", \"1\\n37 1\\n\", \"1\\n32885 23485980\\n\", \"1\\n1410 895339346\\n\", \"1\\n837 77741179\\n\", \"1\\n594056 821\\n\", \"1\\n252 411325\\n\", \"1\\n66 1\\n\", \"1\\n17961 23485980\\n\", \"1\\n2817 895339346\\n\", \"1\\n837 150201939\\n\", \"1\\n142712 821\\n\", \"1\\n252 144541\\n\", \"1\\n47 1\\n\", \"1\\n28408 23485980\\n\", \"1\\n2819 895339346\\n\", \"1\\n337 150201939\\n\", \"1\\n142712 413\\n\", \"1\\n252 203303\\n\", \"1\\n28408 1691073\\n\"], \"outputs\": [\"Yes\\nYes\\nYes\\nNo\\nNo\\nYes\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\nNo\\nNo\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\", \"Yes\\nNo\\nNo\", \"Yes\\nYes\\nYes\\nNo\\nNo\\nYes\", \"Yes\", \"No\\nNo\\nNo\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"Yes\\nNo\\nNo\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"Yes\\nYes\\nYes\\nNo\\nNo\\nYes\", \"No\", \"No\", \"Yes\\nNo\\nNo\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"Yes\\nNo\\nNo\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\\nNo\\nNo\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\", \"No\"]}", "source": "primeintellect"}
|
<image>
Slastyona and her loyal dog Pushok are playing a meaningless game that is indeed very interesting.
The game consists of multiple rounds. Its rules are very simple: in each round, a natural number k is chosen. Then, the one who says (or barks) it faster than the other wins the round. After that, the winner's score is multiplied by k2, and the loser's score is multiplied by k. In the beginning of the game, both Slastyona and Pushok have scores equal to one.
Unfortunately, Slastyona had lost her notepad where the history of all n games was recorded. She managed to recall the final results for each games, though, but all of her memories of them are vague. Help Slastyona verify their correctness, or, to put it another way, for each given pair of scores determine whether it was possible for a game to finish with such result or not.
Input
In the first string, the number of games n (1 ≤ n ≤ 350000) is given.
Each game is represented by a pair of scores a, b (1 ≤ a, b ≤ 109) – the results of Slastyona and Pushok, correspondingly.
Output
For each pair of scores, answer "Yes" if it's possible for a game to finish with given score, and "No" otherwise.
You can output each letter in arbitrary case (upper or lower).
Example
Input
6
2 4
75 45
8 8
16 16
247 994
1000000000 1000000
Output
Yes
Yes
Yes
No
No
Yes
Note
First game might have been consisted of one round, in which the number 2 would have been chosen and Pushok would have won.
The second game needs exactly two rounds to finish with such result: in the first one, Slastyona would have said the number 5, and in the second one, Pushok would have barked the number 3.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
{"tests": "{\"inputs\": [\"4 2 5\\n1 2 3 1\\n\", \"1 9 10\\n1\\n\", \"3 2 10\\n1 2 1\\n\", \"10 5 1000000000\\n1 1 1 2 2 1 2 2 2 2\\n\", \"5 3 3\\n1 2 2 1 1\\n\", \"2 4 1\\n1 1\\n\", \"1 1000000000 1000000000\\n100000\\n\", \"5 3 2\\n1 1 2 1 1\\n\", \"5 2 4\\n1 2 3 2 1\\n\", \"1 10 10\\n1\\n\", \"2 4 1\\n1 0\\n\", \"5 3 2\\n1 1 3 1 1\\n\", \"1 7 10\\n1\\n\", \"4 2 5\\n1 2 4 1\\n\", \"1 18 10\\n1\\n\", \"3 2 10\\n1 3 1\\n\", \"4 3 5\\n1 2 4 1\\n\", \"5 3 3\\n1 2 3 1 1\\n\", \"5 2 3\\n1 3 3 1 1\\n\", \"4 5 1\\n2 2 4 1\\n\", \"10 5 1000000000\\n1 1 1 2 2 1 2 2 3 2\\n\", \"4 2 2\\n1 2 3 1\\n\", \"5 2 5\\n1 2 3 1 1\\n\", \"4 5 2\\n4 0 4 1\\n\", \"2 3 1\\n1 0\\n\", \"5 3 2\\n1 2 3 1 1\\n\", \"3 2 14\\n1 3 1\\n\", \"4 5 5\\n1 2 4 1\\n\", \"5 2 3\\n1 2 3 1 1\\n\", \"4 5 5\\n2 2 4 1\\n\", \"4 5 1\\n2 4 4 1\\n\", \"4 5 1\\n2 0 4 1\\n\", \"4 5 1\\n4 0 4 1\\n\", \"4 5 1\\n4 0 4 2\\n\", \"5 3 3\\n1 2 2 2 1\\n\", \"2 4 1\\n1 2\\n\", \"1 1000000000 1000000000\\n110000\\n\", \"5 2 4\\n1 2 1 2 1\\n\", \"1 10 2\\n1\\n\", \"3 2 11\\n1 2 1\\n\", \"4 2 5\\n1 2 4 2\\n\", \"5 3 2\\n1 2 3 0 1\\n\", \"3 2 22\\n1 3 1\\n\", \"4 10 5\\n1 2 4 1\\n\", \"4 5 5\\n2 2 4 0\\n\", \"5 2 3\\n1 0 3 1 1\\n\", \"4 5 1\\n2 0 6 1\\n\", \"10 5 1000000000\\n1 1 1 2 0 1 2 2 3 2\\n\", \"2 4 1\\n1 4\\n\", \"1 1000000000 1000000000\\n110100\\n\", \"1 3 2\\n1\\n\", \"4 2 2\\n1 2 3 0\\n\", \"3 2 11\\n2 2 1\\n\", \"4 2 5\\n1 2 5 2\\n\", \"5 3 2\\n1 2 3 -1 1\\n\"], \"outputs\": [\"12\\n\", \"1\\n\", \"0\\n\", \"10000000000\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"7\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"7\\n\", \"3\\n\", \"12\\n\", \"10\\n\", \"0\\n\", \"20\\n\", \"9\\n\", \"1\\n\", \"4\\n\", \"10000000000\\n\", \"6\\n\", \"15\\n\", \"8\\n\", \"2\\n\", \"7\\n\", \"0\\n\", \"20\\n\", \"9\\n\", \"20\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"4\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"2\\n\", \"3\\n\", \"20\\n\", \"10\\n\", \"0\\n\", \"20\\n\", \"20\\n\", \"9\\n\", \"4\\n\", \"10000000000\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"8\\n\", \"1\\n\", \"20\\n\", \"10\\n\"]}", "source": "primeintellect"}
|
This time the Berland Team Olympiad in Informatics is held in a remote city that can only be reached by one small bus. Bus has n passenger seats, seat i can be occupied only by a participant from the city ai.
Today the bus has completed m trips, each time bringing n participants. The participants were then aligned in one line in the order they arrived, with people from the same bus standing in the order of their seats (i. e. if we write down the cities where the participants came from, we get the sequence a1, a2, ..., an repeated m times).
After that some teams were formed, each consisting of k participants form the same city standing next to each other in the line. Once formed, teams left the line. The teams were formed until there were no k neighboring participants from the same city.
Help the organizers determine how many participants have left in the line after that process ended. We can prove that answer doesn't depend on the order in which teams were selected.
Input
The first line contains three integers n, k and m (1 ≤ n ≤ 105, 2 ≤ k ≤ 109, 1 ≤ m ≤ 109).
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 105), where ai is the number of city, person from which must take seat i in the bus.
Output
Output the number of remaining participants in the line.
Examples
Input
4 2 5
1 2 3 1
Output
12
Input
1 9 10
1
Output
1
Input
3 2 10
1 2 1
Output
0
Note
In the second example, the line consists of ten participants from the same city. Nine of them will form a team. At the end, only one participant will stay in the line.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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\"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"Yes\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\", \"No\\n\"]}", "source": "primeintellect"}
|
There is a rectangular grid of n rows of m initially-white cells each.
Arkady performed a certain number (possibly zero) of operations on it. In the i-th operation, a non-empty subset of rows Ri and a non-empty subset of columns Ci are chosen. For each row r in Ri and each column c in Ci, the intersection of row r and column c is coloured black.
There's another constraint: a row or a column can only be chosen at most once among all operations. In other words, it means that no pair of (i, j) (i < j) exists such that <image> or <image>, where <image> denotes intersection of sets, and <image> denotes the empty set.
You are to determine whether a valid sequence of operations exists that produces a given final grid.
Input
The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 50) — the number of rows and columns of the grid, respectively.
Each of the following n lines contains a string of m characters, each being either '.' (denoting a white cell) or '#' (denoting a black cell), representing the desired setup.
Output
If the given grid can be achieved by any valid sequence of operations, output "Yes"; otherwise output "No" (both without quotes).
You can print each character in any case (upper or lower).
Examples
Input
5 8
.#.#..#.
.....#..
.#.#..#.
#.#....#
.....#..
Output
Yes
Input
5 5
..#..
..#..
#####
..#..
..#..
Output
No
Input
5 9
........#
#........
..##.#...
.......#.
....#.#.#
Output
No
Note
For the first example, the desired setup can be produced by 3 operations, as is shown below.
<image>
For the second example, the desired setup cannot be produced, since in order to colour the center row, the third row and all columns must be selected in one operation, but after that no column can be selected again, hence it won't be possible to colour the other cells in the center column.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
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|
Everybody knows of [spaghetti sort](https://en.wikipedia.org/wiki/Spaghetti_sort). You decided to implement an analog sorting algorithm yourself, but as you survey your pantry you realize you're out of spaghetti! The only type of pasta you have is ravioli, but you are not going to let this stop you...
You come up with the following algorithm. For each number in the array ai, build a stack of ai ravioli. The image shows the stack for ai = 4.
<image>
Arrange the stacks in one row in the order in which the corresponding numbers appear in the input array. Find the tallest one (if there are several stacks of maximal height, use the leftmost one). Remove it and add its height to the end of the output array. Shift the stacks in the row so that there is no gap between them. Repeat the procedure until all stacks have been removed.
At first you are very happy with your algorithm, but as you try it on more inputs you realize that it doesn't always produce the right sorted array. Turns out when two stacks of ravioli are next to each other (at any step of the process) and differ in height by two or more, the top ravioli of the taller stack slides down on top of the lower stack.
Given an input array, figure out whether the described algorithm will sort it correctly.
Input
The first line of input contains a single number n (1 ≤ n ≤ 10) — the size of the array.
The second line of input contains n space-separated integers ai (1 ≤ ai ≤ 100) — the elements of the array.
Output
Output "YES" if the array can be sorted using the described procedure and "NO" if it can not.
Examples
Input
3
1 2 3
Output
YES
Input
3
3 1 2
Output
NO
Note
In the second example the array will change even before the tallest stack is chosen for the first time: ravioli from stack of height 3 will slide on the stack of height 1, and the algorithm will output an array {2, 2, 2}.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
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\"260843480\\n\", \"1\\n\", \"743685088\\n\", \"3\\n\", \"1\\n\", \"32\\n\", \"378294608\\n\", \"0\\n\", \"140063906\\n\"]}", "source": "primeintellect"}
|
Kuro has recently won the "Most intelligent cat ever" contest. The three friends then decided to go to Katie's home to celebrate Kuro's winning. After a big meal, they took a small break then started playing games.
Kuro challenged Katie to create a game with only a white paper, a pencil, a pair of scissors and a lot of arrows (you can assume that the number of arrows is infinite). Immediately, Katie came up with the game called Topological Parity.
The paper is divided into n pieces enumerated from 1 to n. Shiro has painted some pieces with some color. Specifically, the i-th piece has color c_{i} where c_{i} = 0 defines black color, c_{i} = 1 defines white color and c_{i} = -1 means that the piece hasn't been colored yet.
The rules of the game is simple. Players must put some arrows between some pairs of different pieces in such a way that for each arrow, the number in the piece it starts from is less than the number of the piece it ends at. Also, two different pieces can only be connected by at most one arrow. After that the players must choose the color (0 or 1) for each of the unpainted pieces. The score of a valid way of putting the arrows and coloring pieces is defined as the number of paths of pieces of alternating colors. For example, [1 → 0 → 1 → 0], [0 → 1 → 0 → 1], [1], [0] are valid paths and will be counted. You can only travel from piece x to piece y if and only if there is an arrow from x to y.
But Kuro is not fun yet. He loves parity. Let's call his favorite parity p where p = 0 stands for "even" and p = 1 stands for "odd". He wants to put the arrows and choose colors in such a way that the score has the parity of p.
It seems like there will be so many ways which satisfy Kuro. He wants to count the number of them but this could be a very large number. Let's help him with his problem, but print it modulo 10^{9} + 7.
Input
The first line contains two integers n and p (1 ≤ n ≤ 50, 0 ≤ p ≤ 1) — the number of pieces and Kuro's wanted parity.
The second line contains n integers c_{1}, c_{2}, ..., c_{n} (-1 ≤ c_{i} ≤ 1) — the colors of the pieces.
Output
Print a single integer — the number of ways to put the arrows and choose colors so the number of valid paths of alternating colors has the parity of p.
Examples
Input
3 1
-1 0 1
Output
6
Input
2 1
1 0
Output
1
Input
1 1
-1
Output
2
Note
In the first example, there are 6 ways to color the pieces and add the arrows, as are shown in the figure below. The scores are 3, 3, 5 for the first row and 5, 3, 3 for the second row, both from left to right.
<image>
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"4\\nI want to buy Microsoft for $10000\\nthis house costs $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 6 7 8 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 6 7 8 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 6 7 0 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 0 2 3 4 5 6 7 8 9 h1lloe23\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $00001\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 6 7 0 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $00001\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 9 6 7 0 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub Microsoft for $10000\\nthis esuoh stsoc $0 1 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $00001\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 0 2 3 4 9 6 7 0 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want so buy Microsoft fpr $10000\\nthhs house costs $0 5 0 00 0 Just yub it\\nsiejfsuhn $ 1 2 3 4 10 6 7 8 9 hello123\\nshe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $00001\\nthis house stsoc $0 5 0 00 0 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$10000\\nthhs house costs $0 5 0 00 0 Just yub it\\nsiejfsuhn $ 1 2 3 4 5 6 11 8 9 hello123\\nshe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want so buy Microsoft fpr $10000\\nthhs house costs $0 5 0 00 0 Just yub it\\nsiejfsuhn $ 1 2 3 4 10 6 7 8 3 hello123\\nshe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 5 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 1 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house sttoc $0 9 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nhtis house costs $0 5 0 00 0 Just yub it\\nsiejfsuhn $ 2 2 3 4 5 6 7 8 9 hello123\\nshe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 Just bvy it\\nsiejfsuhn $ 0 2 3 2 5 6 7 8 9 h1lloe23\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 7 5 6 7 2 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLF\", \"4\\nI want to buy Microsoft for $10000\\nthhs house costs $0 5 0 00 0 Just yub it\\nsiejfsuhn $ 1 2 3 4 5 6 7 8 9 hello123\\nshe cort is zero $ 1 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $00001\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 6 13 0 9 hello123\\nthe cost is oerz $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub Microsoft for $10000\\nthis esuoh stsoc $0 5 0 1 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 4 5 6 7 2 9 hello123\\nthe cost is zern $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to yub Microsoft for $00001\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 0 2 6 4 9 6 7 0 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI wanu to bux Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 6 7 8 4 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house costs 0$ 5 0 00 1 Just buy it\\nsiejfsuhn $ 1 2 3 4 1 6 7 8 9 hello123\\nshe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house sttoc $0 9 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 0 0 0 1 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 Just bvy it\\nsiejfsuhn $ 0 3 3 2 5 6 7 8 9 h1lloe23\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthhs house costs $0 5 1 00 0 Just yub it\\nsiejfsuhn $ 1 2 3 4 5 6 7 8 9 hello123\\nshe cort is zero $ 1 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 tsuJ yub it\\nsiejfsuhn $ 1 4 3 7 5 9 7 2 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLF\", \"4\\nI want to buy Microsoft fpr $10000\\nthsh house costs $0 5 0 00 0 Just 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0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nihts esuoh stsoc $0 5 0 00 0 Just buy ti\\nsiejfsuhn $ 1 2 5 4 5 6 7 3 9 hello123\\nteh cost is zero $ 0 1 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $10000\\nthjs house stsoc $0 0 0 00 0 Just buy ti\\nsiejfsuhn $ 1 2 3 4 5 6 7 8 9 h1lloe23\\neht soct is zero $ 0 0 1 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $00100\\nthis house sttoc $0 9 0 00 0 tsuJ buy si\\nsiejfsuhn $ 1 4 3 4 5 6 7 2 9 hello123\\nthe cost is rezo $ 0 0 0 0 1 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $10000\\nhtis eusoh costs $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 2 2 3 4 5 6 7 8 9 hello123\\nshe cost is zero $ 0 1 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub Microsoft for $10000\\nthis esuoh stsoc $0 7 0 00 0 tsuJ yub it\\nsiejfsuhn $ 1 4 3 7 5 9 7 2 2 hello123\\nteh cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLF\", \"4\\nJ want to buy Microsoft for $00001\\nshis housd stsoc $0 5 0 00 0 tsuJ buy ti\\nsiejfsuhn $ 2 2 3 4 9 2 7 0 9 hello123\\nthe cott ir zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nihts esuoh stsoc $0 5 0 00 0 Just buy ti\\nsiejfsuhn $ 1 2 5 4 5 6 7 3 9 hello123\\nteh cost is zeso $ 0 2 0 0 0 0\\n\\nSAMPLE\", \"4\\nI tnaw to buy Mtcrosofi for $00001\\nthis hnuse stsoc $0 5 0 1 0 Jttu buy it\\nsiejfsuhn $ 2 2 3 4 5 6 3 0 9 hello123\\nthe tsoc is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub Microsoft for $10000\\nthis esuoh stsoc $0 7 0 00 0 tsuJ yub it\\nsiejfsuhn $ 1 4 3 7 5 9 7 2 3 hello123\\nteh cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLF\", \"4\\nI want to yub Microsoft for $10000\\nthis esuoh stsoc $0 7 0 00 0 tsuJ yub it\\nsiejfsuhn $ 1 4 3 7 5 9 7 2 3 hello123\\nteh cost is zero $ 0 0 0 1 0 0\\n\\nSAMPLF\", \"4\\nI tnaw to buy Mtcrosofi for $00001\\nthis hnuse stsoc $0 5 0 1 0 Jttu buy it\\nsiejfsuhn $ 2 2 3 4 3 6 3 0 9 hello123\\nthe tsoc is zdro $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want ot yub Microsoft for $10000\\nuhis esuoh stsoc $0 7 0 00 0 tsuJ yub iu\\nsiejfsuhn $ 1 4 3 7 5 0 7 2 3 hello123\\nteh ctso is yero $ 0 0 0 1 0 0\\n\\nSAMPLF\", \"4\\nI want ot yub Microsoft for $10000\\nuhis esuoh stsoc $0 7 0 00 0 tsuJ yub iu\\nsiejfsuhn $ 1 4 3 7 5 0 7 2 1 hello123\\nteh ctso is yero $ 0 0 0 1 0 0\\n\\nSAMPLF\", \"4\\nI want to buy Microsoft for $10000\\nthis house costs $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 6 7 8 7 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 8 6 7 0 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 5 3 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 4 5 6 7 0 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthhs house costs $0 5 0 1 0 Just yub it\\nsiejfsuhn $ 1 2 3 4 5 6 7 8 9 hello123\\nshe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub Microsoft for $10000\\nthis esuoh stsoc $0 5 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 2 5 6 7 2 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft fpr $10000\\nthhs house costs $0 5 0 00 0 Just yub it\\nsiejfsuhn $ 1 2 3 0 5 6 7 8 9 hello123\\nshe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub Microsoft for $10000\\nthis esuoh stsoc $0 1 0 0 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub Microsoft for $10000\\nthis esuoh stsoc $0 1 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 1 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want so buy Microsoft fpr $10000\\nthhs house costs $0 5 0 00 0 Just yub it\\nsiejfsuhn $ 1 2 3 4 10 6 7 8 9 hello123\\nshe cost is zero $ 0 0 0 0 0 1\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $00001\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 0 2 3 4 9 8 2 0 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub tfosorciM for $10000\\nthis esuoh stsoc $0 1 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 4 5 6 7 2 18 hello123\\nthe cost it zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house costs 0$ 5 0 0 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 6 7 8 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 8 6 7 2 9 hello123\\nthe cost is zero $ 0 1 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 4 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 2 3 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 0 1 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house costs $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 1 6 7 8 9 hello123\\nshe cost is zero $ 0 0 0 1 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house stsoc $0 5 1 00 0 Just bvy it\\nsiejfsuhn $ 0 2 3 4 5 6 7 8 9 h1lloe23\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $00001\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 1 4 5 6 7 0 9 hello123\\nthe cost is oerz $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $00001\\nthis house stsoc $0 5 1 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 9 8 7 0 9 hello123\\nthe cott is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 6 8 8 9 h1lloe23\\nthe cost is zero $ 0 0 1 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house sttoc $0 9 0 1 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub Microsoft for $10000\\nthis house stsoc $0 5 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 7 5 11 7 2 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLF\", \"4\\nJ want to buy Microsoft for $00001\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 3 3 4 5 6 13 0 9 hello123\\nthe cost is oerz $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $00001\\nthis house stsoc $0 5 0 00 0 Just buy ti\\nsiejfsuhn $ 1 2 3 4 14 6 7 0 9 hello133\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want so buy Microsoft fpr $10000\\nthhs house costs $0 5 0 00 0 Just yub it\\nsiejfsuhn $ 1 2 3 4 5 6 11 8 10 hello122\\nshe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to yub Micsosoft for $10000\\nthis esuoh stsoc $0 1 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 4 5 6 7 1 9 hello123\\nthf cost it zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis esuoh stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 5 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 2 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $10000\\nthjs house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 12 7 8 9 h1lloe23\\nthe cost is zero $ 0 0 1 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house sttoc $0 9 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 4 3 4 5 6 7 2 9 hello123\\nthe cost is zero $ 0 1 0 0 1 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nhtis house costs $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 2 2 3 4 5 6 13 8 9 hello123\\nshe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthhs house costs $0 5 1 00 0 Just yub it\\nsiejfsuhn $ 1 2 1 4 5 6 7 8 9 hello123\\nshe cort is zero $ 1 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $00001\\nthis house stsoc $0 10 0 00 0 Just buy ti\\nnhusfjeis $ 1 2 3 4 9 6 7 0 9 hello133\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI wanu to bux Microsoft ofr $10000\\nthis house stsoc $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 6 7 8 4 hello123\\nthe cost is zero $ 0 0 0 0 1 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $10000\\nthjs house stsoc $0 5 0 00 0 Just buy ti\\nsiejfsuhn $ 1 2 3 4 5 6 7 8 9 h1lloe23\\nthe cost is zero $ 0 0 1 0 1 0\\n\\nSAMPLE\", \"4\\nI tnaw so buy Microsoft fpr $10000\\nthhs house costs $0 5 0 00 0 Just yub it\\nsiejfsuhn $ 1 2 4 4 5 6 11 16 9 hello122\\nshe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want ot yub Microsoft for $00001\\nthis house stsoc $0 5 1 00 0 Just buy it\\nsiejfsuhn $ 0 2 6 4 9 6 7 0 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $00001\\nshis house stsoc $0 5 0 00 0 tsuJ buy it\\nsiejfsuhn $ 1 2 3 4 9 8 7 0 9 hello123\\nthe cott ir zero $ 1 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI wanu to bux Microsoft ofr $10000\\nthis house stsoc $0 5 0 1 1 Just buy it\\nsiejfsuhn $ 1 2 3 4 5 6 7 8 4 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft foq $10000\\nthis house costs 0$ 5 0 00 1 Just buy it\\nsiejfsuhn $ 1 2 3 4 2 6 7 8 9 hello123\\nshe cost is {ero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI want to buy Microsoft for $10000\\nthis house sttoc $0 9 0 00 0 tsuJ buy ti\\nsiejfsuhn $ 1 4 3 8 5 6 7 2 9 hello123\\nthe cost is rezo $ 0 0 0 0 1 0\\n\\nSAMPLE\", \"4\\nJ want to buy Microsoft for $10000\\nhtis esuoh costs $0 5 0 00 0 Just buy it\\nsiejfsuhn $ 2 3 3 4 5 6 7 8 9 hello123\\nshe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\", \"4\\nI tnaw to buy Mtcrosofi for $00001\\nthis hnuse stsoc $0 5 0 1 0 Jutt buy it\\nsiejfsuhn $ 1 2 3 4 10 6 7 0 9 hello123\\nthe cost is zero $ 0 0 0 0 0 0\\n\\nSAMPLE\"], \"outputs\": [\"$10000\\n$50000\\n$123456789\\n$0\\n\", \"$10000\\n$50000\\n$123456789\\n$0\\n\", \"$10000\\n$50000\\n$123456729\\n$0\\n\", \"$10000\\n$50000\\n$123456709\\n$0\\n\", \"$10000\\n$50000\\n$143456729\\n$0\\n\", \"$10000\\n$50000\\n$23456789\\n$0\\n\", \"$1\\n$50000\\n$123456709\\n$0\\n\", \"$1\\n$50000\\n$123496709\\n$0\\n\", \"$10000\\n$10000\\n$143456729\\n$0\\n\", \"$1\\n$50000\\n$23496709\\n$0\\n\", \"$10000\\n$50000\\n$1234106789\\n$0\\n\", \"$1\\n$50000\\n$23498709\\n$0\\n\", \"$1\\n$50000\\n$123498709\\n$0\\n\", \"$10000\\n$50000\\n$123456729\\n$10000\\n\", \"$10000\\n$50000\\n$123456729\\n$1000\\n\", \"$10000\\n$50000\\n$123416789\\n$0\\n\", \"$10000\\n$50000\\n$123456789\\n$1000\\n\", \"$10000\\n$50000\\n$1234561189\\n$0\\n\", \"$10000\\n$50000\\n$1234106783\\n$0\\n\", \"$10000\\n$50000\\n$125456729\\n$10000\\n\", \"$10000\\n$90000\\n$143456729\\n$0\\n\", \"$10000\\n$50000\\n$223456789\\n$0\\n\", \"$10000\\n$50000\\n$23256789\\n$0\\n\", \"$10000\\n$50000\\n$143756729\\n$0\\n\", \"$10000\\n$50000\\n$123456789\\n$100000\\n\", \"$1\\n$50000\\n$1234561309\\n$0\\n\", \"$10000\\n$5010\\n$143456729\\n$0\\n\", \"$1\\n$50000\\n$26496709\\n$0\\n\", \"$10000\\n$50000\\n$123456784\\n$0\\n\", \"$10000\\n$50001\\n$123416789\\n$0\\n\", \"$10000\\n$90000\\n$143456729\\n$10\\n\", \"$10000\\n$50000\\n$33256789\\n$0\\n\", \"$10000\\n$51000\\n$123456789\\n$100000\\n\", \"$10000\\n$50000\\n$143759729\\n$0\\n\", \"$10000\\n$50000\\n$123456789\\n$101000\\n\", \"$10000\\n$50000\\n$1244561189\\n$0\\n\", \"$10000\\n$10000\\n$143406729\\n$0\\n\", \"$10000\\n$50001\\n$123456784\\n$0\\n\", \"$1\\n$5010\\n$123456709\\n$0\\n\", \"$10000\\n$51000\\n$1234561489\\n$100000\\n\", \"$1\\n$50000\\n$46496709\\n$0\\n\", \"$10000\\n$10000\\n$143206729\\n$0\\n\", \"$1\\n$50000\\n$123492709\\n$0\\n\", \"$1\\n$5010\\n$223456709\\n$0\\n\", \"$10000\\n$50000\\n$143759722\\n$0\\n\", \"$10000\\n$10000\\n$140206729\\n$0\\n\", \"$10000\\n$50000\\n$125456739\\n$10000\\n\", \"$10000\\n$0\\n$123456789\\n$1000\\n\", \"$100\\n$90000\\n$143456729\\n$10\\n\", \"$10000\\n$50000\\n$223456789\\n$10000\\n\", \"$10000\\n$70000\\n$143759722\\n$0\\n\", \"$1\\n$50000\\n$223492709\\n$0\\n\", \"$10000\\n$50000\\n$125456739\\n$20000\\n\", \"$1\\n$5010\\n$223456309\\n$0\\n\", \"$10000\\n$70000\\n$143759723\\n$0\\n\", \"$10000\\n$70000\\n$143759723\\n$100\\n\", \"$1\\n$5010\\n$223436309\\n$0\\n\", \"$10000\\n$70000\\n$143750723\\n$100\\n\", \"$10000\\n$70000\\n$143750721\\n$100\\n\", \"$10000\\n$50000\\n$123456787\\n$0\\n\", \"$10000\\n$50000\\n$123486709\\n$0\\n\", \"$10000\\n$50000\\n$153456729\\n$0\\n\", \"$10000\\n$50000\\n$143456709\\n$0\\n\", \"$10000\\n$5010\\n$123456789\\n$0\\n\", \"$10000\\n$50000\\n$143256729\\n$0\\n\", \"$10000\\n$50000\\n$123056789\\n$0\\n\", \"$10000\\n$1000\\n$143456729\\n$0\\n\", \"$10000\\n$10000\\n$143456729\\n$10000\\n\", \"$10000\\n$50000\\n$1234106789\\n$1\\n\", \"$1\\n$50000\\n$23498209\\n$0\\n\", \"$10000\\n$10000\\n$1434567218\\n$0\\n\", \"$10000\\n$5000\\n$123456789\\n$0\\n\", \"$10000\\n$50000\\n$123486729\\n$10000\\n\", \"$10000\\n$40000\\n$123456729\\n$1000\\n\", \"$10000\\n$50000\\n$123416789\\n$100\\n\", \"$10000\\n$51000\\n$23456789\\n$0\\n\", \"$1\\n$50000\\n$121456709\\n$0\\n\", \"$1\\n$51000\\n$123498709\\n$0\\n\", \"$10000\\n$50000\\n$123456889\\n$1000\\n\", \"$10000\\n$9010\\n$143456729\\n$0\\n\", \"$10000\\n$50000\\n$1437511729\\n$0\\n\", \"$1\\n$50000\\n$1334561309\\n$0\\n\", \"$1\\n$50000\\n$1234146709\\n$0\\n\", \"$10000\\n$50000\\n$12345611810\\n$0\\n\", \"$10000\\n$10000\\n$143456719\\n$0\\n\", \"$10000\\n$50000\\n$125456729\\n$20000\\n\", \"$10000\\n$50000\\n$1234512789\\n$1000\\n\", \"$10000\\n$90000\\n$143456729\\n$10010\\n\", \"$10000\\n$50000\\n$2234561389\\n$0\\n\", \"$10000\\n$51000\\n$121456789\\n$100000\\n\", \"$1\\n$100000\\n$123496709\\n$0\\n\", \"$10000\\n$50000\\n$123456784\\n$10\\n\", \"$10000\\n$50000\\n$123456789\\n$1010\\n\", \"$10000\\n$50000\\n$12445611169\\n$0\\n\", \"$1\\n$51000\\n$26496709\\n$0\\n\", \"$1\\n$50000\\n$123498709\\n$100000\\n\", \"$10000\\n$5011\\n$123456784\\n$0\\n\", \"$10000\\n$50001\\n$123426789\\n$0\\n\", \"$10000\\n$90000\\n$143856729\\n$10\\n\", \"$10000\\n$50000\\n$233456789\\n$0\\n\", \"$1\\n$5010\\n$1234106709\\n$0\\n\"]}", "source": "primeintellect"}
|
Yesterday, Benny decided to buy something from a television shop. She created a list that consisted of small description of N orders. The description for an order number i is a string Si.
The description may consist of uppercase/lowercase Latin letters, digits and a '$' sign. But, every time after the sign '$', Benny has written one integer C. This specific integer C is the price of the items contained in the order and it might have leading zeroes.
It's guaranteed that every string contains exactly one '$' character.
As, it was rainy yesterday, there are some white spaces present within the description of each order. Therefore, the digits might be separated by some amount of spaces.
Your task is to determine the price of each order and print it without leading zeroes.
Input format
The first line contains a single integer N denoting the number of orders.
The next N lines contain a strings Si denoting the description for each i^th order.
Output format
Print the cost to each of the order in a single line .
Constraints
1 ≤ N ≤ 500
2 ≤ |Si| ≤ 1000
SAMPLE INPUT
4
I want to buy Microsoft for $10000
this house costs $0 5 0 00 0 Just buy it
siejfsuhn $ 1 2 3 4 5 6 7 8 9 hello123
the cost is zero $ 0 0 0 0 0 0
SAMPLE OUTPUT
$10000
$50000
$123456789
$0
Explanation
In the first sample test case, it is clear from the order description that the amount is 10000$
In the second test case, you have to ignore a leading zero and delete spaces between the digits. So, the answer is $50000.
The third test case is similar to the second one.
And the fourth test case has the cost equal to $0 but with many leading zeroes. Hence, to show that the order was free, it is necessary to print a single 0.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"7 6\\n4 3 7 6 7 2 2\\n\\nSAMPLE\", \"5 10\\n11 12 9 1 3\", \"8 3\\n4 4 4 4 4 4 4 4\", \"5 10\\n11 12 9 1 2\", \"7 6\\n4 3 7 6 7 4 2\\n\\nSAMPLE\", \"8 6\\n6 6 1 4 1 4 1 4\", \"7 6\\n4 3 7 9 7 4 2\\n\\nSAMPLE\", \"8 3\\n1 4 4 6 7 4 4 4\", \"8 3\\n4 1 1 3 2 1 4 4\", \"7 11\\n4 3 11 4 7 3 2\\n\\nSAMPLE\", \"8 4\\n4 5 4 2 2 5 4 6\", \"8 3\\n4 2 2 3 2 1 3 4\", \"8 3\\n4 4 1 4 4 4 4 4\", \"8 3\\n4 6 1 4 4 4 4 4\", \"8 3\\n4 6 1 4 4 4 1 4\", \"8 3\\n4 6 1 4 4 3 1 4\", \"8 3\\n4 6 2 4 4 3 1 4\", \"8 3\\n4 6 3 4 4 3 1 4\", \"5 10\\n11 18 9 1 3\", \"8 3\\n4 4 4 4 7 4 4 4\", \"7 6\\n4 3 7 6 9 2 2\\n\\nSAMPLE\", \"5 10\\n11 12 18 1 2\", \"7 6\\n4 3 7 4 7 4 2\\n\\nSAMPLE\", \"8 3\\n4 6 1 4 4 4 4 3\", \"8 3\\n6 6 1 4 4 4 1 4\", \"8 3\\n4 4 1 4 4 3 1 4\", \"8 3\\n4 6 2 8 4 3 1 4\", \"8 3\\n4 4 4 6 7 4 4 4\", \"7 6\\n4 6 7 6 9 2 2\\n\\nSAMPLE\", \"3 10\\n11 12 18 1 2\", \"7 6\\n4 3 11 4 7 4 2\\n\\nSAMPLE\", \"8 1\\n4 6 1 4 4 4 4 3\", \"8 3\\n6 6 1 4 1 4 1 4\", \"8 3\\n4 4 4 6 6 4 4 4\", \"3 10\\n12 12 18 1 2\", \"7 6\\n4 3 11 4 7 3 2\\n\\nSAMPLE\", \"8 1\\n4 6 1 4 3 4 4 3\", \"8 1\\n4 6 1 5 3 4 4 3\", \"8 6\\n6 3 1 4 1 4 1 4\", \"8 1\\n4 6 1 5 1 4 4 3\", \"8 1\\n4 6 1 3 1 4 4 3\", \"5 10\\n11 12 9 1 1\", \"8 3\\n4 4 2 4 4 4 4 4\", \"7 1\\n4 3 7 6 7 2 2\\n\\nSAMPLE\", \"5 10\\n11 22 9 1 2\", \"8 3\\n4 4 1 4 4 4 5 4\", \"8 3\\n4 6 1 7 4 4 4 4\", \"8 2\\n4 6 1 4 4 4 1 4\", \"8 3\\n4 6 3 4 4 3 1 2\", \"5 9\\n11 18 9 1 3\", \"8 3\\n4 5 4 4 7 4 4 4\", \"5 10\\n11 12 18 2 2\", \"7 6\\n4 3 7 4 7 5 2\\n\\nSAMPLE\", \"8 2\\n6 6 1 4 4 4 1 4\", \"8 3\\n5 4 1 4 4 3 1 4\", \"8 3\\n4 6 2 8 4 3 1 7\", \"7 6\\n4 6 11 6 9 2 2\\n\\nSAMPLE\", \"3 10\\n11 12 18 1 3\", \"8 2\\n4 6 1 4 4 4 4 3\", \"3 10\\n12 12 23 1 2\", \"8 1\\n4 6 1 4 3 4 3 3\", \"8 7\\n6 6 1 4 1 4 1 4\", \"8 1\\n4 6 1 5 3 1 4 3\", \"8 2\\n4 6 1 3 1 4 4 3\", \"8 3\\n4 4 2 7 4 4 4 4\", \"5 10\\n14 22 9 1 2\", \"8 3\\n4 4 1 4 5 4 5 4\", \"7 6\\n7 3 7 9 7 4 2\\n\\nSAMPLE\", \"8 2\\n4 6 1 2 4 4 1 4\", \"8 3\\n4 5 4 4 7 5 4 4\", \"5 10\\n11 12 18 2 4\", \"8 2\\n6 7 1 4 4 4 1 4\", \"5 3\\n5 4 1 4 4 3 1 4\", \"8 3\\n4 6 2 8 4 3 1 1\", \"3 10\\n11 12 18 1 5\", \"5 10\\n12 12 23 1 2\", \"8 2\\n6 6 1 4 1 4 1 4\", \"8 1\\n4 4 1 5 3 1 4 3\", \"8 3\\n4 4 2 7 4 5 4 4\", \"5 10\\n14 34 9 1 2\", \"8 3\\n4 5 4 4 2 5 4 4\", \"5 10\\n5 12 18 2 4\", \"8 2\\n6 7 1 4 4 7 1 4\", \"5 2\\n5 4 1 4 4 3 1 4\", \"8 3\\n8 6 2 8 4 3 1 1\", \"5 10\\n11 12 18 1 5\", \"5 10\\n12 12 37 1 2\", \"8 2\\n6 6 1 4 1 6 1 4\", \"8 1\\n4 4 1 5 3 1 5 3\", \"8 3\\n4 5 6 4 2 5 4 4\", \"5 10\\n5 12 21 2 4\", \"8 2\\n6 13 1 4 4 7 1 4\", \"8 3\\n7 6 2 8 4 3 1 1\", \"5 10\\n11 12 32 1 5\", \"5 10\\n12 21 37 1 2\", \"8 2\\n6 6 1 4 1 6 1 7\", \"8 3\\n4 1 6 4 2 5 4 4\", \"5 10\\n5 14 21 2 4\", \"8 2\\n10 13 1 4 4 7 1 4\", \"8 3\\n7 3 2 8 4 3 1 1\", \"5 10\\n11 12 32 2 5\", \"3 10\\n12 21 37 1 2\", \"8 4\\n6 6 1 4 1 6 1 7\"], \"outputs\": [\"3\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"8\\n\", \"2\\n\", \"1\\n\", \"5\\n\", \"7\\n\", \"4\\n\", \"6\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"8\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"8\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"1\\n\", \"1\\n\", \"0\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
Our friend Monk has an exam that has quite weird rules. Each question has a difficulty level in the form of an Integer. Now, Monk can only solve the problems that have difficulty level less than X . Now the rules are-
Score of the student is equal to the maximum number of answers he/she has attempted without skipping a question.
Student is allowed to skip just "one" question that will not be counted in the continuity of the questions.
Note- Assume the student knows the solution to the problem he/she attempts and always starts the paper from first question.
Given the number of Questions, N ,the maximum difficulty level of the problem Monk can solve , X ,and the difficulty level of each question , A_{i} can you help him determine his maximum score?
Input Format
First Line contains Integer N , the number of questions and the maximum difficulty X Monk can solve.
Next line contains N integers, A_{i} denoting the difficulty level of each question.
Output Format
Maximum score Monk can achieve in the exam.
Constraints
1 ≤ N ≤ 10^{5}
1 ≤ X ≤ 10^{9}
1 ≤ A_{i} ≤ 10^{9}
SAMPLE INPUT
7 6
4 3 7 6 7 2 2
SAMPLE OUTPUT
3
Explanation
In this example, maximum difficulty = 6, Monk solves question 0 and 1, but skips the question 2 as A[2]>6. Monk then solves the question 3 , but stops at 4 because A[4]>6 and question 2 was already skipped. As 3 questions (0,1 and 3) were solved and 2 questions (2 and 4) have been skipped, therefore we print "3".
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
{"tests": "{\"inputs\": [\"5\\n2 6 8 1 3\\n\\nSAMPLE\", \"5\\n2 10 8 1 3\\n\\nSAMPLE\", \"5\\n2 13 4 2 6\\n\\nSAMPLE\", \"5\\n-1 76 14 1 0\\n\\nELPLAR\", \"5\\n1 0 13 0 6\\n\\nSAMPLE\", \"5\\n2 10 8 2 3\\n\\nSAMPLE\", \"5\\n2 10 8 2 6\\n\\nSAMPLE\", \"5\\n2 10 13 2 6\\n\\nSAMPLE\", \"5\\n2 10 14 2 6\\n\\nSAMPLE\", \"5\\n2 13 14 2 6\\n\\nSAMPLE\", \"5\\n2 13 14 2 11\\n\\nSAMPLE\", \"5\\n2 13 14 2 11\\n\\nRAMPLE\", \"5\\n2 13 14 2 11\\n\\nELPMAR\", \"5\\n2 13 14 2 11\\n\\nELPLAR\", \"5\\n1 13 14 2 11\\n\\nELPLAR\", \"5\\n1 13 14 2 11\\n\\nRALPLE\", \"5\\n1 13 14 2 9\\n\\nRALPLE\", \"5\\n0 13 14 2 9\\n\\nRALPLE\", \"5\\n0 22 14 2 9\\n\\nRALPLE\", \"5\\n0 22 14 0 9\\n\\nRALPLE\", \"5\\n0 22 14 0 9\\n\\nELPLAR\", \"5\\n0 41 14 0 9\\n\\nELPLAR\", \"5\\n-1 41 14 0 9\\n\\nELPLAR\", \"5\\n-1 41 21 0 9\\n\\nELPLAR\", \"5\\n-1 41 21 0 6\\n\\nELPLAR\", \"5\\n-1 38 21 0 6\\n\\nELPLAR\", \"5\\n-1 38 30 0 6\\n\\nELPLAR\", \"5\\n-1 38 30 0 11\\n\\nELPLAR\", \"5\\n-1 38 30 0 11\\n\\nEAPLLR\", \"5\\n-1 38 22 0 11\\n\\nEAPLLR\", \"5\\n0 38 22 0 11\\n\\nEAPLLR\", \"5\\n-1 38 22 0 11\\n\\nEAPKLR\", \"5\\n-1 38 22 1 11\\n\\nEAPKLR\", \"5\\n-1 25 22 1 11\\n\\nEAPKLR\", \"5\\n2 4 8 1 3\\n\\nSAMPLE\", \"5\\n0 10 8 2 3\\n\\nSAMPLE\", \"5\\n0 10 13 2 6\\n\\nSAMPLE\", \"5\\n2 10 14 2 4\\n\\nSAMPLE\", \"5\\n2 13 14 2 11\\n\\nRAMPLF\", \"5\\n4 13 14 2 11\\n\\nELPMAR\", \"5\\n2 13 14 2 11\\n\\nDLPLAR\", \"5\\n1 13 18 2 11\\n\\nELPLAR\", \"5\\n1 13 14 2 11\\n\\nRPLALE\", \"5\\n1 13 14 2 9\\n\\nSALPLE\", \"5\\n0 13 14 2 4\\n\\nRALPLE\", \"5\\n0 22 14 2 3\\n\\nRALPLE\", \"5\\n0 22 14 0 9\\n\\nR@LPLE\", \"5\\n0 22 14 -1 9\\n\\nELPLAR\", \"5\\n0 49 14 0 9\\n\\nELPLAR\", \"5\\n-1 76 14 0 9\\n\\nELPLAR\", \"5\\n-1 41 21 0 5\\n\\nELPLAR\", \"5\\n-1 41 21 1 6\\n\\nELPLAR\", \"5\\n0 38 21 0 6\\n\\nELPLAR\", \"5\\n-1 38 30 0 2\\n\\nELPLAR\", \"5\\n-1 38 30 -1 11\\n\\nELPLAR\", \"5\\n-1 55 30 0 11\\n\\nEAPLLR\", \"5\\n-1 54 22 0 11\\n\\nEAPLLR\", \"5\\n0 38 22 0 16\\n\\nEAPLLR\", \"5\\n-1 64 22 0 11\\n\\nEAPKLR\", \"5\\n-1 38 22 1 4\\n\\nEAPKLR\", \"5\\n-1 25 22 1 11\\n\\nRLKPAE\", \"5\\n2 7 8 1 3\\n\\nSAMPLE\", \"5\\n-1 10 8 2 3\\n\\nSAMPLE\", \"5\\n1 10 13 2 6\\n\\nSAMPLE\", \"5\\n2 10 14 2 4\\n\\nSAEPLM\", \"5\\n4 13 4 2 6\\n\\nSAMPLE\", \"5\\n3 13 14 2 11\\n\\nRAMPLF\", \"5\\n4 13 14 2 11\\n\\nEMPMAR\", \"5\\n2 13 14 0 11\\n\\nDLPLAR\", \"5\\n1 13 10 2 11\\n\\nELPLAR\", \"5\\n2 13 14 2 11\\n\\nRPLALE\", \"5\\n1 13 3 2 9\\n\\nSALPLE\", \"5\\n0 13 14 2 4\\n\\nRALOLE\", \"5\\n0 22 14 2 4\\n\\nRALPLE\", \"5\\n0 22 18 0 9\\n\\nR@LPLE\", \"5\\n0 44 14 -1 9\\n\\nELPLAR\", \"5\\n0 49 23 0 9\\n\\nELPLAR\", \"5\\n-1 76 14 0 4\\n\\nELPLAR\", \"5\\n-1 31 21 0 5\\n\\nELPLAR\", \"5\\n-1 41 12 1 6\\n\\nELPLAR\", \"5\\n1 38 21 0 6\\n\\nELPLAR\", \"5\\n-1 38 46 0 2\\n\\nELPLAR\", \"5\\n-1 38 30 -1 4\\n\\nELPLAR\", \"5\\n-1 55 30 0 11\\n\\nEAQLLR\", \"5\\n-1 54 26 0 11\\n\\nEAPLLR\", \"5\\n0 38 13 0 16\\n\\nEAPLLR\", \"5\\n-1 64 22 1 11\\n\\nEAPKLR\", \"5\\n-1 38 22 1 4\\n\\nEAPJLR\", \"5\\n-1 14 22 1 11\\n\\nRLKPAE\", \"5\\n3 7 8 1 3\\n\\nSAMPLE\", \"5\\n-1 10 8 2 3\\n\\nSAPMLE\", \"5\\n1 7 13 2 6\\n\\nSAMPLE\", \"5\\n2 10 14 2 7\\n\\nSAEPLM\", \"5\\n4 13 4 2 9\\n\\nSAMPLE\", \"5\\n4 13 14 2 11\\n\\nEMPRAM\", \"5\\n2 13 10 2 11\\n\\nELPLAR\", \"5\\n2 13 21 2 11\\n\\nRPLALE\", \"5\\n1 16 3 2 9\\n\\nSALPLE\", \"5\\n0 13 14 2 4\\n\\nLALORE\", \"5\\n0 22 14 2 4\\n\\nRAKPLE\", \"5\\n0 22 18 0 9\\n\\nS@LPLE\"], \"outputs\": [\"1 2 3 5\", \"1 2 3 5\\n\", \"1 2 5\\n\", \"1 2 3 4 5\\n\", \"1 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 5\\n\", \"1 2 3 5\\n\", \"1 2 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 5\\n\", \"1 2 3 5\\n\", \"1 2 5\\n\", \"1 2 3 5\\n\", \"1 2 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\", \"1 2 3 5\\n\"]}", "source": "primeintellect"}
|
The Mad King arrested Shil's comrades for participating in a rebellion against the King. Instead of punishing them with death, the King decided to play the Game of survival with them. The game is played as follows:
All the N people are forced to stand in a line.
Now the king randomly chooses any two persons standing next to each other in line and kills the one having lower strength.
King keeps on performing step 2 until there are only 2 survivors.
The Last two survivors are forgiven for their crimes and are free to go.
As Shil is worried for his comrades, he wants to find out the ones who could survive - at least, one out of all the possible games.
Given N integers denoting the strengths of comrades, you must print the position of comrades who could survive at least one Game.
Input format:
The first Line of input consists of an integer N denoting the total number of comrades. The next line consists of N integers S1, S2 , ..... SN denoting the strength of comrades standing in a line. Si denotes the strength of i^th comrade standing in a line. The strengths of all the comrades will be distinct.
Output format:
Print the positions of comrades standing in line who could be one of the two possible survivors in any possible game. You must print the positions in an increasingly sorted manner.
Constraints:
3 ≤ N ≤ 10^5
1 ≤ Si ≤ 10^9
SAMPLE INPUT
5
2 6 8 1 3
SAMPLE OUTPUT
1 2 3 5
Explanation
Some of the possible games are :
[2 6] 8 1 3 -> [6 8] 1 3 -> 8 [1 3] -> 8 3
2 [6 8] 1 3 -> 2 8 [1 3] -> 2 [8 3] -> 2 8
[2 6] 8 1 3 -> 6 8 [1 3] -> 6 [8 3] -> 6 8
Here [ ] represents adjacent positions being selected in step 2 of The Game at any moment of time.
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.875
|
{"tests": "{\"inputs\": [\"5 3 100\", \"4 2 3\", \"5 3 000\", \"5 0 100\", \"4 1 3\", \"5 3 010\", \"4 0 3\", \"10 3 010\", \"8 0 3\", \"10 5 010\", \"8 1 3\", \"10 5 000\", \"10 1 3\", \"10 9 000\", \"10 2 3\", \"17 9 000\", \"10 0 3\", \"10 9 001\", \"7 0 3\", \"10 6 001\", \"7 0 6\", \"13 6 001\", \"2 0 6\", \"13 6 101\", \"2 0 1\", \"9 6 101\", \"2 0 2\", \"9 3 101\", \"1 0 2\", \"9 0 101\", \"12 0 101\", \"2 0 101\", \"4 0 101\", \"6 0 101\", \"4 3 100\", \"4 4 3\", \"6 3 000\", \"7 2 3\", \"4 0 5\", \"10 1 010\", \"10 6 000\", \"8 2 3\", \"10 0 000\", \"10 1 1\", \"10 9 100\", \"15 2 3\", \"17 12 000\", \"16 9 001\", \"7 0 0\", \"7 0 1\", \"13 6 011\", \"13 11 101\", \"3 0 1\", \"9 6 111\", \"9 3 001\", \"2 0 0\", \"11 0 101\", \"2 1 101\", \"4 1 101\", \"4 2 100\", \"6 5 000\", \"7 4 3\", \"14 1 010\", \"14 6 000\", \"8 4 3\", \"10 2 1\", \"10 6 100\", \"15 2 1\", \"16 5 001\", \"7 1 0\", \"7 0 -1\", \"13 6 111\", \"4 0 1\", \"5 3 001\", \"13 0 101\", \"2 1 001\", \"4 1 100\", \"6 5 100\", \"7 3 3\", \"4 0 0\", \"18 1 010\", \"14 0 000\", \"10 2 2\", \"10 6 110\", \"15 2 0\", \"32 5 001\", \"1 1 0\", \"10 2 000\", \"13 10 111\", \"8 0 1\", \"5 3 101\", \"13 0 111\", \"3 1 100\", \"7 5 3\", \"4 1 1\", \"18 2 010\", \"21 0 000\", \"3 2 2\", \"10 6 111\", \"5 2 0\", \"32 2 001\", \"2 1 0\"], \"outputs\": [\"50 50 50 30 70\", \"1 2 3 4\", \"0 0 0 1 1\\n\", \"101 101 101 101 101\\n\", \"3 4 4 4\\n\", \"10 10 10 11 11\\n\", \"4 4 4 4\\n\", \"10 10 10 11 11 11 11 11 11 11\\n\", \"4 4 4 4 4 4 4 4\\n\", \"10 10 10 10 10 11 11 11 11 11\\n\", \"3 4 4 4 4 4 4 4\\n\", \"0 0 0 0 0 1 1 1 1 1\\n\", \"3 4 4 4 4 4 4 4 4 4\\n\", \"0 0 0 0 0 0 0 0 0 1\\n\", \"3 3 4 4 4 4 4 4 4 4\\n\", \"0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1\\n\", \"4 4 4 4 4 4 4 4 4 4\\n\", \"1 1 1 1 1 1 1 1 1 2\\n\", \"4 4 4 4 4 4 4\\n\", \"1 1 1 1 1 1 2 2 2 2\\n\", \"7 7 7 7 7 7 7\\n\", \"1 1 1 1 1 1 2 2 2 2 2 2 2\\n\", \"7 7\\n\", \"101 101 101 101 101 101 102 102 102 102 102 102 102\\n\", \"2 2\\n\", \"101 101 101 101 101 101 102 102 102\\n\", \"3 3\\n\", \"101 101 101 102 102 102 102 102 102\\n\", \"3\\n\", \"102 102 102 102 102 102 102 102 102\\n\", \"102 102 102 102 102 102 102 102 102 102 102 102\\n\", \"102 102\\n\", \"102 102 102 102\\n\", \"102 102 102 102 102 102\\n\", \"100 100 100 101\\n\", \"3 3 3 3\\n\", \"0 0 0 1 1 1\\n\", \"3 3 4 4 4 4 4\\n\", \"6 6 6 6\\n\", \"10 11 11 11 11 11 11 11 11 11\\n\", \"0 0 0 0 0 0 1 1 1 1\\n\", \"3 3 4 4 4 4 4 4\\n\", \"1 1 1 1 1 1 1 1 1 1\\n\", \"1 2 2 2 2 2 2 2 2 2\\n\", \"100 100 100 100 100 100 100 100 100 101\\n\", \"3 3 4 4 4 4 4 4 4 4 4 4 4 4 4\\n\", \"0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1\\n\", \"1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2\\n\", \"1 1 1 1 1 1 1\\n\", \"2 2 2 2 2 2 2\\n\", \"11 11 11 11 11 11 12 12 12 12 12 12 12\\n\", \"101 101 101 101 101 101 101 101 101 101 101 102 102\\n\", \"2 2 2\\n\", \"111 111 111 111 111 111 112 112 112\\n\", \"1 1 1 2 2 2 2 2 2\\n\", \"1 1\\n\", \"102 102 102 102 102 102 102 102 102 102 102\\n\", \"101 102\\n\", \"101 102 102 102\\n\", \"100 100 101 101\\n\", \"0 0 0 0 0 1\\n\", \"3 3 3 3 4 4 4\\n\", \"10 11 11 11 11 11 11 11 11 11 11 11 11 11\\n\", \"0 0 0 0 0 0 1 1 1 1 1 1 1 1\\n\", \"3 3 3 3 4 4 4 4\\n\", \"1 1 2 2 2 2 2 2 2 2\\n\", \"100 100 100 100 100 100 101 101 101 101\\n\", \"1 1 2 2 2 2 2 2 2 2 2 2 2 2 2\\n\", \"1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2\\n\", \"0 1 1 1 1 1 1\\n\", \"0 0 0 0 0 0 0\\n\", \"111 111 111 111 111 111 112 112 112 112 112 112 112\\n\", \"2 2 2 2\\n\", \"1 1 1 2 2\\n\", \"102 102 102 102 102 102 102 102 102 102 102 102 102\\n\", \"1 2\\n\", \"100 101 101 101\\n\", \"100 100 100 100 100 101\\n\", \"3 3 3 4 4 4 4\\n\", \"1 1 1 1\\n\", \"10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11\\n\", \"1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"2 2 3 3 3 3 3 3 3 3\\n\", \"110 110 110 110 110 110 111 111 111 111\\n\", \"0 0 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\\n\", \"0\\n\", \"0 0 1 1 1 1 1 1 1 1\\n\", \"111 111 111 111 111 111 111 111 111 111 112 112 112\\n\", \"2 2 2 2 2 2 2 2\\n\", \"101 101 101 102 102\\n\", \"112 112 112 112 112 112 112 112 112 112 112 112 112\\n\", \"100 101 101\\n\", \"3 3 3 3 3 4 4\\n\", \"1 2 2 2\\n\", \"10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11\\n\", \"1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\\n\", \"2 2 3\\n\", \"111 111 111 111 111 111 112 112 112 112\\n\", \"0 0 1 1 1\\n\", \"1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\\n\", \"0 1\\n\"]}", "source": "primeintellect"}
|
Given are three integers N, K, and S.
Find a sequence A_1, A_2, ..., A_N of N integers between 1 and 10^9 (inclusive) that satisfies the condition below. We can prove that, under the conditions in Constraints, such a sequence always exists.
* There are exactly K pairs (l, r) of integers such that 1 \leq l \leq r \leq N and A_l + A_{l + 1} + \cdots + A_r = S.
Constraints
* 1 \leq N \leq 10^5
* 0 \leq K \leq N
* 1 \leq S \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N K S
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Output
Print a sequence satisfying the condition, in the following format:
A_1 A_2 ... A_N
Examples
Input
4 2 3
Output
1 2 3 4
Input
5 3 100
Output
50 50 50 30 70
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2 2\\n1 1 7 3\\n4 2 3 3\\n2 4 6\\n3 2 5\", \"7 7\\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\\n46 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\\n7 27 34\\n12 -2 22\\n4 -50 -12\\n3 -32 15\\n8 -7 23\\n3 -30 11\\n4 -2 23\", \"2 2\\n1 1 6 3\\n4 2 3 3\\n2 4 6\\n3 2 5\", \"7 7\\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\\n7 27 34\\n12 -2 22\\n4 -50 -12\\n3 -32 15\\n8 -7 23\\n3 -30 11\\n4 -2 23\", \"2 2\\n1 1 6 3\\n4 2 3 3\\n2 1 6\\n3 2 5\", \"2 2\\n1 1 6 3\\n4 2 3 3\\n2 1 6\\n1 2 5\", \"7 7\\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\\n7 27 34\\n12 -2 22\\n4 -50 -12\\n3 -32 15\\n8 -7 23\\n3 -15 11\\n4 -2 29\", \"7 7\\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\\n57 -50 -11 20 28 46 12 13 33 -11 -48 -27 35 -17\\n7 27 34\\n12 -2 22\\n4 -50 -12\\n4 -32 15\\n8 -7 23\\n3 -15 11\\n4 -2 29\", \"2 2\\n1 1 6 3\\n6 2 3 3\\n2 2 6\\n1 4 9\", \"7 7\\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\\n57 -50 -3 20 28 46 12 13 33 -11 -48 -27 35 -17\\n7 27 34\\n12 -2 22\\n4 -50 -12\\n4 -32 15\\n8 -7 23\\n3 -15 11\\n4 -2 29\", \"2 2\\n1 1 6 3\\n6 2 3 3\\n2 2 9\\n1 4 9\", \"7 7\\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\\n57 -50 -3 20 28 46 12 13 33 -11 -48 -27 35 -17\\n7 27 34\\n12 -2 22\\n4 -50 -12\\n4 -32 15\\n8 -7 23\\n3 -15 11\\n4 -2 29\", \"2 2\\n1 1 6 3\\n6 1 3 3\\n2 2 9\\n2 4 9\", \"7 7\\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\\n57 -50 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\\n7 27 49\\n12 -2 22\\n4 -50 -12\\n4 -32 15\\n8 -7 23\\n3 -15 11\\n4 -2 29\", \"7 7\\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\\n57 -50 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\\n7 27 49\\n12 -2 22\\n5 -50 -12\\n4 -32 15\\n8 -7 23\\n3 -15 11\\n4 -2 29\", \"7 7\\n22 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\\n57 -50 -3 20 28 46 12 13 33 -11 -25 -27 35 -17\\n7 27 49\\n12 -2 22\\n5 -50 -12\\n4 -32 15\\n8 -7 23\\n5 -15 11\\n4 -2 29\", \"2 2\\n1 1 6 3\\n12 -1 3 3\\n2 1 9\\n2 4 6\", \"2 2\\n1 1 6 3\\n12 -1 3 3\\n3 1 9\\n2 4 6\", \"2 2\\n2 1 6 3\\n12 -1 3 5\\n3 1 9\\n2 1 6\", \"2 2\\n2 1 6 3\\n12 -2 3 5\\n3 1 9\\n2 1 6\", \"2 2\\n2 1 6 3\\n2 -2 3 5\\n3 1 9\\n1 1 6\", \"2 2\\n1 1 6 3\\n2 -2 3 5\\n3 1 9\\n1 1 6\", \"2 2\\n1 1 6 3\\n-1 -2 3 5\\n3 0 9\\n1 0 6\", \"2 2\\n1 0 6 3\\n-1 0 3 5\\n3 0 9\\n1 0 8\", \"2 2\\n1 -1 11 5\\n-1 0 3 5\\n3 1 9\\n1 0 8\", \"2 2\\n1 -1 11 1\\n-1 0 4 5\\n3 1 2\\n1 0 8\", \"2 2\\n1 0 7 3\\n4 2 3 3\\n2 4 6\\n3 2 5\", \"7 7\\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\\n73 -50 -11 20 28 46 12 13 16 -22 -48 -27 35 -17\\n7 27 34\\n12 -2 22\\n4 -50 -12\\n3 -32 15\\n8 -7 23\\n3 -30 11\\n4 -2 23\", \"7 7\\n49 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\\n7 27 34\\n12 -2 22\\n4 -50 -12\\n3 -32 15\\n8 -7 23\\n3 -15 11\\n4 -2 23\", \"7 7\\n34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29\\n73 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17\\n7 27 34\\n12 -2 22\\n4 -50 -12\\n3 -32 15\\n8 -7 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\"291\\n296\\n240\\n271\\n279\\n275\\n310\\n\", \"360\\n361\\n309\\n335\\n345\\n341\\n376\\n\", \"16\\n17\\n\", \"12\\n15\\n\", \"301\\n302\\n250\\n276\\n286\\n282\\n323\\n\", \"334\\n335\\n283\\n310\\n320\\n348\\n362\\n\", \"293\\n294\\n242\\n269\\n279\\n293\\n335\\n\", \"322\\n323\\n271\\n298\\n308\\n325\\n339\\n\", \"322\\n323\\n263\\n234\\n233\\n262\\n276\\n\", \"322\\n326\\n269\\n243\\n253\\n276\\n290\\n\", \"341\\n342\\n288\\n259\\n258\\n281\\n313\\n\", \"11\\n12\\n\", \"11\\n21\\n\", \"14\\n13\\n\", \"13\\n11\\n\", \"6\\n5\\n\", \"305\\n310\\n254\\n285\\n293\\n289\\n324\\n\", \"340\\n341\\n289\\n315\\n325\\n321\\n356\\n\", \"300\\n301\\n249\\n275\\n285\\n281\\n264\\n\", \"324\\n325\\n273\\n254\\n264\\n260\\n301\\n\", \"319\\n320\\n268\\n295\\n312\\n326\\n340\\n\", \"20\\n23\\n\", \"293\\n294\\n242\\n223\\n233\\n247\\n283\\n\", \"19\\n19\\n\", \"313\\n314\\n262\\n289\\n299\\n316\\n330\\n\", \"10\\n13\\n\", \"341\\n354\\n300\\n271\\n270\\n293\\n325\\n\", \"13\\n20\\n20\\n\", 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|
You are given two sequences a and b, both of length 2N. The i-th elements in a and b are a_i and b_i, respectively. Using these sequences, Snuke is doing the job of calculating the beauty of pairs of balanced sequences of parentheses (defined below) of length 2N. The beauty of a pair (s,t) is calculated as follows:
* Let X=0.
* For each i between 1 and 2N (inclusive), increment X by a_i if s_i = t_i, and increment X by b_i otherwise.
* The beauty of (s,t) is the final value of X.
You will be given Q queries. Process them in order. In the i-th query, update the value of a_{p_i} to x_i, and the value of b_{p_i} to y_i. Then, find the maximum possible beauty of a pair of balanced sequences of parentheses.
In this problem, only the sequences below are defined to be balanced sequences of parentheses.
* An empty string
* The concatenation of `(`, s, `)` in this order, where s is a balanced sequence of parentheses
* The concatenation of s, t in this order, where s and t are balanced sequences of parentheses
Constraints
* 1 \leq N,Q \leq 10^{5}
* -10^{9} \leq a_i,b_i,x_i,y_i \leq 10^{9}
* 1 \leq p_i \leq 2N
* All input values are integers.
Input
Input is given from Standard Input in the following format:
N Q
a_1 a_2 ... a_{2N}
b_1 b_2 ... b_{2N}
p_1 x_1 y_1
:
p_Q x_Q y_Q
Output
Print Q lines. The i-th line should contain the response to the i-th query.
Examples
Input
2 2
1 1 7 3
4 2 3 3
2 4 6
3 2 5
Output
15
15
Input
7 7
34 -20 -27 42 44 29 9 11 20 44 27 19 -31 -29
46 -50 -11 20 28 46 12 13 33 -22 -48 -27 35 -17
7 27 34
12 -2 22
4 -50 -12
3 -32 15
8 -7 23
3 -30 11
4 -2 23
Output
311
312
260
286
296
292
327
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
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|
You are given an undirected connected weighted graph with N vertices and M edges that contains neither self-loops nor double edges.
The i-th (1≤i≤M) edge connects vertex a_i and vertex b_i with a distance of c_i.
Here, a self-loop is an edge where a_i = b_i (1≤i≤M), and double edges are two edges where (a_i,b_i)=(a_j,b_j) or (a_i,b_i)=(b_j,a_j) (1≤i<j≤M).
A connected graph is a graph where there is a path between every pair of different vertices.
Find the number of the edges that are not contained in any shortest path between any pair of different vertices.
Constraints
* 2≤N≤100
* N-1≤M≤min(N(N-1)/2,1000)
* 1≤a_i,b_i≤N
* 1≤c_i≤1000
* c_i is an integer.
* The given graph contains neither self-loops nor double edges.
* The given graph is connected.
Input
The input is given from Standard Input in the following format:
N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M
Output
Print the number of the edges in the graph that are not contained in any shortest path between any pair of different vertices.
Examples
Input
3 3
1 2 1
1 3 1
2 3 3
Output
1
Input
3 2
1 2 1
2 3 1
Output
0
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"15\\n3.14979,8.51743\\n2.39506,3.84915\\n2.68432,5.39095\\n5.61904,9.16332\\n7.85653,4.75593\\n2.84021,5.41511\\n1.79500,8.59211\\n7.55389,8.17604\\n4.70665,4.66125\\n1.63470,4.42538\\n7.34959,4.61981\\n5.09003,8.11122\\n5.24373,1.30066\\n0.13517,1.83659\\n7.57313,1.58150\\n0\", \"15\\n3.13979,8.51743\\n2.39506,3.84915\\n2.68432,5.39095\\n5.61904,9.16332\\n7.85653,4.75593\\n2.84021,5.41511\\n1.79500,8.59211\\n7.55389,8.17604\\n4.70665,4.66125\\n1.63470,4.42538\\n7.34959,4.61981\\n5.09003,8.11122\\n5.24373,1.30066\\n0.13517,1.83659\\n7.57313,1.58150\\n0\", \"15\\n3.13979,8.51743\\n2.39506,3.84915\\n58093.5,23486.2\\n5.61904,9.16332\\n7.85653,4.75593\\n2.84021,5.41511\\n1.79500,8.59211\\n7.55389,8.17604\\n4.70665,4.66125\\n1.63470,4.42538\\n7.34959,4.61981\\n5.09003,8.11122\\n5.24373,1.30066\\n0.13517,1.83659\\n7.57313,1.58150\\n0\", 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|
Stick n circular stickers with a radius of 1 on a square origami paper with a side length of 10. The stickers can be stacked. Create a program that reads the coordinates of the position where the stickers are to be attached and outputs the number of stickers at the place where the stickers overlap most on the origami paper (assuming that even one sticker "overlaps"). ..
Gives the x and y coordinates with the lower left corner of the origami as the origin. Let's put the sticker with these x and y as the center of the circle. The center of the circle never goes out of the origami. Also, multiple stickers will not be attached at the same coordinates.
Hint
It is a figure with a sticker attached as shown in the input example. The circle represents the sticker, and the number represents the number of lines in the input example. At point (2.3, 4.6), the four stickers on the second, third, sixth, and tenth lines of the input example overlap.
<image>
The distance between the centers of 6 and 9 is 2.01293, so the seals do not overlap. The distance between the centers of 1 and 12 is 1.98231, so the seals overlap.
When two circles are in contact (when the distance between the centers is 2), they are assumed to overlap.
Input
Given multiple datasets. Each dataset is given in the following format:
n
x1, y1
x2, y2
::
xn, yn
The first line gives the number of stickers n (0 ≤ 100). The next n lines give the center coordinates of each seal. xi and yi represent the x and y coordinates of the center of the i-th sticker. Each value is given as a real number, including up to 6 digits after the decimal point.
When n is 0, it is the end of the input. The number of datasets does not exceed 50.
Output
For each data set, output the number of stickers (integer) at the place where the stickers overlap most on the origami paper.
Example
Input
15
3.14979,8.51743
2.39506,3.84915
2.68432,5.39095
5.61904,9.16332
7.85653,4.75593
2.84021,5.41511
1.79500,8.59211
7.55389,8.17604
4.70665,4.66125
1.63470,4.42538
7.34959,4.61981
5.09003,8.11122
5.24373,1.30066
0.13517,1.83659
7.57313,1.58150
0
Output
4
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.75
|
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|
The Aizu Wakamatsu city office decided to lay a hot water pipeline covering the whole area of the city to heat houses. The pipeline starts from some hot springs and connects every district in the city. The pipeline can fork at a hot spring or a district, but no cycle is allowed. The city office wants to minimize the length of pipeline in order to build it at the least possible expense.
Write a program to compute the minimal length of the pipeline. The program reads an input that consists of the following three parts:
Hint
The first line correspondings to the first part: there are three hot springs and five districts. The following three lines are the second part: the distances between a hot spring and a district. For instance, the distance between the first hot spring and the third district is 25. The last four lines are the third part: the distances between two districts. For instance, the distance between the second and the third districts is 9. The second hot spring and the fourth district are not connectable The second and the fifth districts are not connectable, either.
Input
* The first part consists of two positive integers in one line, which represent the number s of hot springs and the number d of districts in the city, respectively.
* The second part consists of s lines: each line contains d non-negative integers. The i-th integer in the j-th line represents the distance between the j-th hot spring and the i-th district if it is non-zero. If zero it means they are not connectable due to an obstacle between them.
* The third part consists of d-1 lines. The i-th line has d - i non-negative integers. The i-th integer in the j-th line represents the distance between the j-th and the (i + j)-th districts if it is non-zero. The meaning of zero is the same as mentioned above.
For the sake of simplicity, you can assume the following:
* The number of hot springs and that of districts do not exceed 50.
* Each distance is no more than 100.
* Each line in the input file contains at most 256 characters.
* Each number is delimited by either whitespace or tab.
The input has several test cases. The input terminate with a line which has two 0. The number of test cases is less than 20.
Output
Output the minimum length of pipeline for each test case.
Example
Input
3 5
12 8 25 19 23
9 13 16 0 17
20 14 16 10 22
17 27 18 16
9 7 0
19 5
21
0 0
Output
38
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
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Three-valued logic is a logic system that has, in addition to "true" and "false", "unknown" as a valid value. In the following, logical values "false", "unknown" and "true" are represented by 0, 1 and 2 respectively.
Let "-" be a unary operator (i.e. a symbol representing one argument function) and let both "*" and "+" be binary operators (i.e. symbols representing two argument functions). These operators represent negation (NOT), conjunction (AND) and disjunction (OR) respectively. These operators in three-valued logic can be defined in Table C-1.
Table C-1: Truth tables of three-valued logic operators
-X| | (X*Y)| | (X+Y) | <image>| | <image>| | <image> |
---|---|---|---|---|---
Let P, Q and R be variables ranging over three-valued logic values. For a given formula, you are asked to answer the number of triples (P,Q,R) that satisfy the formula, that is, those which make the value of the given formula 2. A formula is one of the following form (X and Y represent formulas).
* Constants: 0, 1 or 2
* Variables: P, Q or R
* Negations: -X
* Conjunctions: (X*Y)
* Disjunctions: (X+Y)
Note that conjunctions and disjunctions of two formulas are always parenthesized.
For example, when formula (P*Q) is given as an input, the value of this formula is 2 when and only when (P,Q,R) is (2,2,0), (2,2,1) or (2,2,2). Therefore, you should output 3.
Input
The input consists of one or more lines. Each line contains a formula. A formula is a string which consists of 0, 1, 2, P, Q, R, -, *, +, (, ). Other characters such as spaces are not contained. The grammar of formulas is given by the following BNF.
<formula> ::= 0 | 1 | 2 | P | Q | R |
-<formula> | (<formula>*<formula>) | (<formula>+<formula>)
All the formulas obey this syntax and thus you do not have to care about grammatical errors. Input lines never exceed 80 characters.
Finally, a line which contains only a "." (period) comes, indicating the end of the input.
Output
You should answer the number (in decimal) of triples (P,Q,R) that make the value of the given formula 2. One line containing the number should be output for each of the formulas, and no other characters should be output.
Sample Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output for the Sample Input
3
11
0
27
0
7
Example
Input
(P*Q)
(--R+(P*Q))
(P*-P)
2
1
(-1+(((---P+Q)*(--Q+---R))*(-R+-P)))
.
Output
3
11
0
27
0
7
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\n10 30\\n15 20\\n2\\n10 240\\n15 160\\n3\\n2 6\\n7 2\\n8 2\\n4\\n2 4\\n7 2\\n8 2\\n18 1\\n0\", \"2\\n10 30\\n15 20\\n2\\n10 240\\n15 160\\n3\\n2 6\\n7 4\\n8 2\\n4\\n2 4\\n7 2\\n8 2\\n18 1\\n0\", \"2\\n5 30\\n15 20\\n2\\n10 240\\n15 160\\n3\\n2 6\\n7 2\\n8 2\\n4\\n2 4\\n7 2\\n8 2\\n18 1\\n0\", \"2\\n10 30\\n15 17\\n2\\n10 240\\n15 160\\n3\\n2 6\\n7 3\\n8 2\\n4\\n2 4\\n7 2\\n8 2\\n18 1\\n0\", \"2\\n10 30\\n15 17\\n2\\n10 240\\n15 160\\n3\\n2 6\\n7 3\\n8 4\\n4\\n2 4\\n1 2\\n8 2\\n18 1\\n0\", \"2\\n10 30\\n15 17\\n2\\n10 240\\n15 296\\n3\\n2 6\\n7 3\\n4 4\\n4\\n2 4\\n1 2\\n8 2\\n18 1\\n0\", \"2\\n10 30\\n15 20\\n2\\n20 240\\n15 160\\n3\\n2 6\\n7 2\\n8 2\\n4\\n2 4\\n7 2\\n8 2\\n18 1\\n0\", \"2\\n5 30\\n15 20\\n2\\n10 240\\n20 160\\n3\\n2 6\\n7 2\\n8 2\\n4\\n2 4\\n7 2\\n8 2\\n18 1\\n0\", \"2\\n10 30\\n15 17\\n2\\n10 240\\n15 160\\n3\\n2 6\\n7 4\\n8 2\\n4\\n2 4\\n7 2\\n8 2\\n10 1\\n0\", \"2\\n10 30\\n15 17\\n2\\n10 240\\n15 160\\n0\\n2 6\\n7 3\\n8 2\\n4\\n2 4\\n1 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|
Despite urging requests of the townspeople, the municipal office cannot afford to improve many of the apparently deficient city amenities under this recession. The city swimming pool is one of the typical examples. It has only two swimming lanes. The Municipal Fitness Agency, under this circumstances, settled usage rules so that the limited facilities can be utilized fully.
Two lanes are to be used for one-way swimming of different directions. Swimmers are requested to start swimming in one of the lanes, from its one end to the other, and then change the lane to swim his/her way back. When he or she reaches the original starting end, he/she should return to his/her initial lane and starts swimming again.
Each swimmer has his/her own natural constant pace. Swimmers, however, are not permitted to pass other swimmers except at the ends of the pool; as the lanes are not wide enough, that might cause accidents. If a swimmer is blocked by a slower swimmer, he/she has to follow the slower swimmer at the slower pace until the end of the lane is reached. Note that the blocking swimmer’s natural pace may be faster than the blocked swimmer; the blocking swimmer might also be blocked by another swimmer ahead, whose natural pace is slower than the blocked swimmer. Blocking would have taken place whether or not a faster swimmer was between them.
Swimmers can change their order if they reach the end of the lane simultaneously. They change their order so that ones with faster natural pace swim in front. When a group of two or more swimmers formed by a congestion reaches the end of the lane, they are considered to reach there simultaneously, and thus change their order there.
The number of swimmers, their natural paces in times to swim from one end to the other, and the numbers of laps they plan to swim are given. Note that here one "lap" means swimming from one end to the other and then swimming back to the original end. Your task is to calculate the time required for all the swimmers to finish their plans. All the swimmers start from the same end of the pool at the same time, the faster swimmers in front.
In solving this problem, you can ignore the sizes of swimmers' bodies, and also ignore the time required to change the lanes and the order in a group of swimmers at an end of the lanes.
Input
The input is a sequence of datasets. Each dataset is formatted as follows.
n
t1 c1
...
tn cn
n is an integer (1 ≤ n ≤ 50) that represents the number of swimmers. ti and ci are integers (1 ≤ ti ≤ 300, 1 ≤ ci ≤ 250) that represent the natural pace in times to swim from one end to the other and the number of planned laps for the i-th swimmer, respectively. ti and ci are separated by a space.
The end of the input is indicated by a line containing one zero.
Output
For each dataset, output the time required for all the swimmers to finish their plans in a line. No extra characters should occur in the output.
Example
Input
2
10 30
15 20
2
10 240
15 160
3
2 6
7 2
8 2
4
2 4
7 2
8 2
18 1
0
Output
600
4800
36
40
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
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10\\n.....W....\\n....W.W...\\n...WW.....\\n....W...W.\\nW...W.....\\n......W.W.\\nBBB....W..\\n..B..BBBBB\\n..B..B....\\n..B..B..W.\\n5 3\\n.B...\\nBB...\\n.....\\n1 1\\n.\\n0 0\", \"2 10\\n.....W....\\n...WW.....\\n...WW.....\\n....W...W.\\n../..W...W\\n......W.W.\\nBBB....W..\\n..B..BBBBB\\n....B..B..\\n..B..B..W.\\n5 3\\n...B.\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"2 10\\n.....W....\\n...WW.....\\n...WW.....\\n....W...W.\\n.....W...W\\n.W.W......\\nBBB....W..\\n..B..BBBBB\\n..B..B../.\\n..B..B..W.\\n5 3\\n.B...\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"2 10\\n.....W....\\n...WW.../.\\n...WW.....\\n....W...W-\\n....-W...W\\n......W.W.\\nBBB....W..\\n..B..BBBBB\\n..B..B....\\n..B..B..W.\\n5 3\\n.B...\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"4 10\\n.....W....\\n....W.W...\\n...WW.....\\n....X...W.\\nW...W.....\\n......W.W.\\nBBB....W..\\n..B.BBBB.B\\n..B..B....\\n..B..B..W.\\n5 3\\n.B...\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"6 10\\n.....W....\\n....W.W...\\n..W...W...\\n.W...W....\\nW...W.....\\n......W.W.\\nBBB....W..\\n..B..BBBBB\\n..B..B....\\n..B..B..W.\\n5 3\\n.B...\\n..BB.\\n.....\\n1 1\\n.\\n0 0\", \"2 10\\n.....W....\\n...W.....W\\n...WW.....\\n....W...W.\\n../..W...W\\n......W.W.\\nBBB....W..\\n..B..BBBBB\\n....B..B..\\n..B..B..W.\\n5 3\\n...B.\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"2 10\\n.....W....\\n...WW.../.\\n...WW.....\\n....W...W-\\n....-W...W\\n......W.W.\\nBBB....W..\\n..B..BBBBB\\n..B..B....\\n..B..BW...\\n5 3\\n.B...\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"6 10\\n.....W....\\n....W.W...\\n..W...W...\\n.W...W....\\nW...W.....\\n......W.W.\\nBBB....W..\\n..B..BBBBB\\n..B..B....\\n..B..B..W-\\n5 3\\n.B...\\n..BB.\\n.....\\n1 1\\n.\\n0 0\", \"10 10\\n.....W....\\n....W.W...\\n..W...W...\\n....W...W.\\n.....W...W\\n.W.W......\\nBBB....W..\\n..B..BBBBB\\n..B..B....\\n..B..B..W.\\n5 3\\n.B...\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"2 10\\n.....W....\\n...WW.....\\n...WW.....\\n....W...W.\\nW...W.....\\n......W.W.\\nBBB....W..\\n..B..BBBBB\\n..B..B....\\n..B..B..W.\\n5 3\\n...B.\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"6 10\\n.....W....\\n....W.W...\\n..W...W...\\n....W...W.\\n.....W...W\\n......W.W.\\n..W....BBB\\n..B..BBBBC\\n..B..B....\\n..B..B..W.\\n5 3\\n.B...\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"10 10\\n.....W....\\n....W.W...\\n..W...W...\\n....W...W.\\nW...W.....\\n......W.W.\\nBBB....W..\\n..B..BBBBB\\n..B..B....\\n...B.B..W.\\n5 3\\n...B.\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"2 10\\n.....W....\\n...WW.....\\n...WW.....\\n....W...W.\\n....-W...W\\n......W.W.\\nBBB....W..\\n..B..BBBBB\\n..B/.B....\\n..B..B..W.\\n5 3\\n.B...\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"2 10\\n.....W....\\n...WW.....\\n...WW.....\\n....W...W.\\n....-W...W\\n..-...W.W.\\nBBB....W..\\n..B..BBBBB\\n..B..B....\\n..B..B..W.\\n5 3\\n.B...\\nB..B.\\n.....\\n1 1\\n.\\n0 0\", \"6 10\\n.....W....\\n....W.W...\\n..W...W...\\n....W...W.\\n......W..W\\n......W.W.\\n..W....BBB\\n..B..BBBAB\\n....B..B..\\n..B..B..W.\\n5 3\\n.B...\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"4 10\\n.....W.../\\n....W.W...\\n...WW.....\\n....W...W.\\nW...W.....\\n......W.W.\\n..W....BBB\\n..B..BBBBB\\n..B..B....\\n..B..B..W.\\n5 3\\n.B...\\nBB...\\n.....\\n1 1\\n.\\n0 0\", \"6 10\\n.....W....\\n....W.W...\\n..W...W...\\n....W...W.\\n......W..W\\n......W.W.\\n..W....BBB\\n..B..BBBBB\\n..B..B....\\n..B..B..W.\\n5 3\\nB....\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"2 10\\n.....W....\\n...WW.....\\n...WW.....\\n....W...W.\\n.....W...W\\n......W.W.\\nBBB....W..\\n..B..BBBBB\\n....B..B..\\n..B..B..W.\\n5 3\\n.B...\\nBB...\\n.....\\n1 1\\n.\\n0 0\", \"2 10\\n.....W....\\n...WW....-\\n...WW.....\\n....W...W.\\n.....W...W\\n.W.W......\\nBBB....W..\\n..B..BBBBB\\n..B..B../.\\n..B..B..W.\\n5 3\\n...B.\\n...BB\\n.....\\n1 1\\n.\\n0 0\", \"6 10\\n.....W....\\n....W.W...\\n...W...W..\\n....W...W.\\nWW........\\n......W.W.\\nBBB....W..\\n..B..BBBBB\\n..B..B....\\n..B..B..W.\\n5 3\\n.B...\\n...BB\\n.....\\n1 1\\n.\\n0 0\"], \"outputs\": [\"6 21\\n12 0\\n0 0\", \"6 21\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"7 21\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"0 0\\n12 0\\n0 0\\n\", \"7 0\\n12 0\\n0 0\\n\", \"1 0\\n12 0\\n0 0\\n\", \"1 21\\n12 0\\n0 0\\n\", \"6 19\\n12 0\\n0 0\\n\", \"6 0\\n5 0\\n0 0\\n\", \"10 21\\n12 0\\n0 0\\n\", \"12 0\\n12 0\\n0 0\\n\", \"0 9\\n12 0\\n0 0\\n\", \"8 0\\n12 0\\n0 0\\n\", \"6 4\\n12 0\\n0 0\\n\", \"5 0\\n12 0\\n0 0\\n\", \"0 19\\n12 0\\n0 0\\n\", \"6 9\\n12 0\\n0 0\\n\", \"10 0\\n5 0\\n0 0\\n\", \"6 4\\n0 0\\n0 0\\n\", \"4 0\\n5 0\\n0 0\\n\", \"6 0\\n0 0\\n0 0\\n\", \"18 0\\n8 0\\n0 0\\n\", \"6 0\\n4 0\\n0 0\\n\", \"6 10\\n12 0\\n0 0\\n\", \"6 0\\n8 0\\n0 0\\n\", \"9 0\\n12 0\\n0 0\\n\", \"0 0\\n5 0\\n0 0\\n\", \"3 4\\n12 0\\n0 0\\n\", \"0 0\\n6 0\\n0 0\\n\", \"6 8\\n12 0\\n0 0\\n\", \"6 21\\n0 0\\n0 0\\n\", \"24 0\\n12 0\\n0 0\\n\", \"16 0\\n12 0\\n0 0\\n\", \"8 0\\n8 0\\n0 0\\n\", \"4 1\\n5 0\\n0 0\\n\", \"0 21\\n12 0\\n0 0\\n\", \"7 0\\n0 0\\n0 0\\n\", \"0 4\\n12 0\\n0 0\\n\", \"10 13\\n0 0\\n0 0\\n\", \"6 0\\n7 0\\n0 0\\n\", \"1 4\\n12 0\\n0 0\\n\", \"0 17\\n12 0\\n0 0\\n\", \"0 0\\n10 0\\n0 0\\n\", \"8 0\\n6 0\\n0 0\\n\", \"4 1\\n10 0\\n0 0\\n\", \"17 0\\n12 0\\n0 0\\n\", \"2 0\\n12 0\\n0 0\\n\", \"1 3\\n12 0\\n0 0\\n\", \"6 0\\n10 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 21\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"7 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"1 0\\n12 0\\n0 0\\n\", \"0 0\\n12 0\\n0 0\\n\", \"1 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 21\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"0 0\\n12 0\\n0 0\\n\", \"7 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"1 0\\n12 0\\n0 0\\n\", \"0 0\\n12 0\\n0 0\\n\", \"0 0\\n12 0\\n0 0\\n\", \"18 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\", \"6 0\\n12 0\\n0 0\\n\"]}", "source": "primeintellect"}
|
Surrounding Area
Land fence
English text is not available in this practice contest.
Two real estate agents were boarding a passenger ship to the southern island. Blue sky, refreshing breeze ... The two enjoyed a voyage with other passengers. However, one day a tornado suddenly sank a passenger ship. The other passengers were rescued by the rescue team, but somehow only these two were overlooked. After a few days of drifting, they landed on an uninhabited island. This uninhabited island was rectangular and was divided into grids as shown in the figure below.
Shape of uninhabited island
Figure C-1: Shape of uninhabited island
They were so greedy that they were thinking of selling the land on this uninhabited island rather than calling for help. And they did not split the land in half, but began to scramble for the land. They each began to enclose what they wanted to land on one with black stakes and the other with white stakes. All stakes were struck in the center of the grid, and no stakes were struck in one grid. After a while, both were exhausted and stopped hitting the stakes.
Your job is to write a program to find the area of land surrounded by black and white stakes. However, it is intuitive that the grid (i, j) is surrounded by black stakes. It means that. To be exact, it is defined as follows.
> Define a grid "extended adjacent" to the black stake as follows: The same applies to white stakes.
>
> * If there are no stakes in grid (i, j) and there are black stakes in any of the grids adjacent to grid (i, j), then grid (i, j) extends adjacent to the black stakes. doing.
>
> * If there are no stakes in grid (i, j) and any of the grids adjacent to grid (i, j) are extended adjacent to black stakes, then grid (i, j) is a black stake. It is adjacent to the stake. This rule is applied recursively.
>
>
>
> At this time, when the grid (i, j) is extended adjacent to the black stake and not adjacent to the white stake, and only then, the grid (i, j) is surrounded by the black stake. It is said that there is. Conversely, when the grid (i, j) is extended adjacent to the white stake and not adjacent to the black stake, and only then, the grid (i, j) is surrounded by the white stake. It is said that there is.
Input
The input consists of multiple datasets. Each data set has the following structure.
> w h
> a1,1 a2,1 a3,1 ... aw,1
> a1,2 a2,2 a3,2 ... aw, 2
> ...
> a1, h a2, h a3, h ... aw, h
w is the width of the land and h is the height of the land. These satisfy 1 ≤ w and h ≤ 50. Each ai, j is one half-width character representing the state of the grid (i, j), "` B` "is struck with a black stake, and" `W`" is struck with a white stake. "`.` "(Period) indicates that none of the stakes have been struck.
w = h = 0 represents the end of the input and is not included in the dataset.
Output
For each dataset, print the size of the land surrounded by the black stakes and the size of the land surrounded by the white stakes on one line, separated by a single space.
Sample Input
10 10
..... W ....
.... W.W ...
... W ... W ..
.... W ... W.
..... W ... W
...... W.W.
BBB .... W ..
..B..BBBBB
..B .... B ....
..B..B..W.
5 3
... B.
... BB
.....
1 1
..
0 0
Output for the Sample Input
6 21
12 0
0 0
Example
Input
10 10
.....W....
....W.W...
...W...W..
....W...W.
.....W...W
......W.W.
BBB....W..
..B..BBBBB
..B..B....
..B..B..W.
5 3
...B.
...BB
.....
1 1
.
0 0
Output
6 21
12 0
0 0
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.625
|
{"tests": "{\"inputs\": [\"3 3\\n0 0\\n8 0\\n0 8\\n2 2\\n4 2\\n2 4\\n0 0\", \"3 3\\n0 0\\n8 -1\\n0 8\\n2 2\\n4 2\\n2 4\\n0 0\", \"3 3\\n0 0\\n8 -1\\n-1 8\\n2 2\\n4 2\\n2 4\\n0 0\", \"3 3\\n0 0\\n8 0\\n0 8\\n2 2\\n4 0\\n2 4\\n0 0\", \"3 3\\n0 0\\n8 -1\\n0 2\\n2 2\\n4 2\\n2 4\\n0 0\", \"3 3\\n0 0\\n8 0\\n0 8\\n2 2\\n7 0\\n2 4\\n0 0\", \"3 3\\n0 0\\n14 0\\n0 8\\n2 2\\n7 0\\n2 4\\n0 0\", \"3 3\\n0 0\\n14 0\\n0 8\\n1 2\\n7 0\\n2 4\\n0 0\", \"3 3\\n0 0\\n8 -1\\n0 2\\n2 2\\n3 2\\n2 7\\n0 0\", \"3 3\\n0 0\\n14 0\\n0 8\\n1 0\\n7 0\\n2 4\\n0 0\", \"3 3\\n0 0\\n8 -1\\n0 2\\n2 2\\n3 0\\n2 7\\n0 0\", \"3 3\\n0 0\\n14 0\\n0 8\\n1 0\\n7 1\\n2 4\\n0 0\", \"3 3\\n0 0\\n10 -1\\n0 2\\n2 2\\n3 0\\n2 7\\n0 0\", \"3 3\\n1 0\\n10 -1\\n0 2\\n2 2\\n3 0\\n2 7\\n0 0\", \"3 3\\n1 0\\n10 -1\\n0 2\\n2 3\\n3 0\\n2 7\\n0 0\", \"3 3\\n1 0\\n10 -1\\n0 2\\n4 3\\n3 0\\n2 7\\n0 0\", \"3 3\\n1 0\\n10 -1\\n0 2\\n1 3\\n3 0\\n2 7\\n0 0\", \"3 3\\n1 0\\n10 0\\n0 2\\n1 3\\n3 0\\n2 7\\n0 0\", \"3 3\\n1 1\\n10 0\\n0 2\\n1 3\\n3 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0\\n2 7\\n0 0\", \"3 3\\n1 0\\n10 -1\\n0 2\\n1 3\\n3 1\\n2 7\\n0 0\", \"3 3\\n1 0\\n10 0\\n0 2\\n2 3\\n3 0\\n2 7\\n0 0\", \"3 3\\n1 1\\n10 0\\n0 2\\n1 8\\n6 0\\n2 7\\n0 0\", \"3 3\\n0 0\\n8 0\\n0 8\\n2 2\\n2 4\\n2 4\\n0 0\", \"3 3\\n0 0\\n8 -1\\n0 8\\n3 2\\n4 2\\n4 4\\n0 0\", \"3 3\\n0 0\\n8 0\\n0 8\\n2 2\\n4 -1\\n2 0\\n0 0\", \"3 3\\n0 0\\n8 0\\n0 8\\n2 2\\n7 1\\n2 7\\n0 0\", \"3 3\\n0 0\\n11 0\\n0 8\\n2 2\\n7 0\\n0 4\\n0 0\", \"3 3\\n0 0\\n3 -1\\n0 2\\n1 2\\n4 2\\n2 7\\n0 0\", \"3 3\\n0 0\\n30 -1\\n0 2\\n2 2\\n3 0\\n2 7\\n0 0\", \"3 3\\n0 0\\n14 1\\n0 8\\n1 0\\n7 1\\n1 4\\n0 0\", \"3 3\\n1 0\\n10 -2\\n0 2\\n0 2\\n3 0\\n2 7\\n0 0\", \"3 3\\n1 0\\n10 -1\\n0 2\\n2 3\\n1 1\\n2 7\\n0 0\", \"3 3\\n1 0\\n10 -1\\n0 4\\n1 1\\n3 0\\n2 7\\n0 0\", \"3 3\\n1 1\\n10 -1\\n0 2\\n1 5\\n3 0\\n2 7\\n0 0\", \"3 3\\n1 0\\n10 0\\n1 2\\n1 5\\n6 0\\n2 7\\n0 0\", \"3 3\\n0 0\\n8 0\\n0 1\\n2 2\\n8 1\\n2 4\\n0 0\", \"3 3\\n0 -1\\n8 -1\\n1 2\\n1 2\\n4 2\\n2 6\\n0 0\", \"3 3\\n0 0\\n16 0\\n0 2\\n2 2\\n3 0\\n2 13\\n0 0\", \"3 3\\n0 0\\n7 -1\\n0 2\\n2 2\\n3 2\\n2 7\\n0 0\", \"3 3\\n1 1\\n10 -1\\n0 4\\n1 0\\n3 0\\n2 7\\n0 0\", \"3 3\\n1 2\\n10 0\\n1 2\\n1 5\\n3 0\\n2 7\\n0 0\", \"3 3\\n1 1\\n10 0\\n1 2\\n1 5\\n7 0\\n4 7\\n0 0\", \"3 3\\n0 0\\n8 1\\n0 8\\n2 8\\n4 -1\\n2 4\\n0 0\", \"3 3\\n0 0\\n16 -1\\n0 2\\n1 2\\n2 0\\n2 13\\n0 0\"], \"outputs\": [\"9.0\\n11.5\\n11.5\", \"9.562500\\n11.878676\\n10.558824\\n\", \"10.125000\\n10.687500\\n10.687500\\n\", \"10.500000\\n9.000000\\n12.500000\\n\", \"4.875000\\n3.125000\\n0.000000\\n\", \"14.067857\\n5.432143\\n12.500000\\n\", \"14.100000\\n22.358824\\n19.541176\\n\", \"10.913690\\n23.529062\\n21.557248\\n\", \"4.218750\\n3.781250\\n0.000000\\n\", \"7.500000\\n23.402574\\n25.097426\\n\", \"2.842857\\n5.157143\\n0.000000\\n\", \"7.454257\\n24.979282\\n23.566460\\n\", \"3.111979\\n6.888021\\n0.000000\\n\", \"2.151563\\n6.348438\\n0.000000\\n\", \"1.022556\\n7.477444\\n0.000000\\n\", \"0.000000\\n8.500000\\n0.000000\\n\", \"1.108297\\n7.391703\\n0.000000\\n\", \"1.308894\\n7.691106\\n0.000000\\n\", \"0.921245\\n3.078755\\n0.000000\\n\", \"1.962798\\n2.037202\\n0.000000\\n\", \"1.300000\\n2.700000\\n0.000000\\n\", \"13.500000\\n8.000000\\n10.500000\\n\", \"14.062500\\n11.326389\\n6.611111\\n\", \"12.887500\\n6.612500\\n12.500000\\n\", \"13.500000\\n6.012500\\n12.487500\\n\", \"7.312500\\n4.687500\\n0.000000\\n\", \"14.100000\\n13.282759\\n16.617241\\n\", \"3.000000\\n0.000000\\n0.000000\\n\", \"3.626263\\n12.373737\\n0.000000\\n\", \"6.865777\\n24.323082\\n24.811141\\n\", \"2.677350\\n4.322650\\n0.000000\\n\", \"1.800000\\n6.200000\\n0.000000\\n\", \"0.664062\\n7.835938\\n0.000000\\n\", \"4.723214\\n12.776786\\n0.000000\\n\", \"0.042857\\n3.957143\\n0.000000\\n\", \"1.186364\\n3.313636\\n0.000000\\n\", \"14.222222\\n9.777778\\n8.000000\\n\", \"21.175000\\n10.825000\\n21.175000\\n\", \"3.119512\\n0.880488\\n0.000000\\n\", \"6.328125\\n5.671875\\n0.000000\\n\", \"2.712500\\n4.287500\\n0.000000\\n\", \"6.857143\\n1.142857\\n0.000000\\n\", \"4.951852\\n12.444444\\n0.103704\\n\", \"0.000000\\n4.500000\\n0.000000\\n\", \"23.250980\\n8.749020\\n23.250980\\n\", \"3.318885\\n12.681115\\n0.000000\\n\", \"0.072917\\n6.927083\\n0.000000\\n\", \"6.000000\\n0.000000\\n0.000000\\n\", \"2.907692\\n12.000000\\n0.092308\\n\", \"0.960242\\n3.539758\\n0.000000\\n\", \"4.222997\\n11.777003\\n0.000000\\n\", \"0.982456\\n9.517544\\n0.000000\\n\", \"4.285714\\n0.714286\\n0.000000\\n\", \"0.000000\\n14.600000\\n0.400000\\n\", \"0.000000\\n5.500000\\n0.000000\\n\", \"0.000000\\n10.500000\\n0.000000\\n\", \"0.000000\\n10.000000\\n0.000000\\n\", \"1.860998\\n2.639002\\n0.000000\\n\", \"0.952381\\n0.047619\\n0.000000\\n\", \"0.977273\\n0.022727\\n0.000000\\n\", \"3.814593\\n5.185407\\n0.000000\\n\", \"1.000000\\n9.000000\\n0.000000\\n\", \"1.235197\\n8.764803\\n0.000000\\n\", \"0.000000\\n9.000000\\n0.000000\\n\", \"5.062500\\n3.937500\\n0.000000\\n\", \"16.500000\\n12.000000\\n3.500000\\n\", \"9.562500\\n17.977500\\n36.460000\\n\", \"15.203125\\n10.937500\\n5.359375\\n\", \"1.454545\\n6.545455\\n0.000000\\n\", \"15.500000\\n20.591954\\n19.908046\\n\", \"8.041667\\n26.989583\\n20.968750\\n\", \"3.062500\\n22.793023\\n30.144477\\n\", \"5.523220\\n2.476780\\n0.000000\\n\", \"4.687643\\n3.812357\\n0.000000\\n\", \"1.250000\\n6.750000\\n0.000000\\n\", \"2.176515\\n6.323485\\n0.000000\\n\", \"0.871795\\n7.628205\\n0.000000\\n\", \"1.285714\\n7.714286\\n0.000000\\n\", \"0.000000\\n3.796296\\n0.203704\\n\", \"19.500000\\n12.500000\\n12.500000\\n\", \"14.328125\\n9.623264\\n8.048611\\n\", \"22.387500\\n6.112500\\n3.500000\\n\", \"19.858333\\n6.016667\\n6.125000\\n\", \"20.167680\\n13.411268\\n10.421053\\n\", \"2.916667\\n0.083333\\n0.000000\\n\", \"4.160156\\n25.839844\\n0.000000\\n\", \"7.244853\\n26.367647\\n22.387500\\n\", \"1.270677\\n6.729323\\n0.000000\\n\", \"1.897321\\n6.602679\\n0.000000\\n\", \"6.217105\\n11.282895\\n0.000000\\n\", \"0.032143\\n3.467857\\n0.000000\\n\", \"1.636364\\n7.363636\\n0.000000\\n\", \"3.353316\\n0.646684\\n0.000000\\n\", \"5.517857\\n6.482143\\n0.000000\\n\", \"3.987500\\n12.012500\\n0.000000\\n\", \"4.107143\\n2.892857\\n0.000000\\n\", \"3.511111\\n8.888889\\n0.100000\\n\", \"0.000000\\n0.000000\\n0.000000\\n\", \"1.696736\\n2.803264\\n0.000000\\n\", \"2.285714\\n8.749020\\n20.965266\\n\", \"2.227273\\n13.772727\\n0.000000\\n\"]}", "source": "primeintellect"}
|
Some of you know an old story of Voronoi Island. There were N liege lords and they are always involved in territorial disputes. The residents of the island were despaired of the disputes.
One day, a clever lord proposed to stop the disputes and divide the island fairly. His idea was to divide the island such that any piece of area belongs to the load of the nearest castle. The method is called Voronoi Division today.
Actually, there are many aspects of whether the method is fair. According to one historian, the clever lord suggested the method because he could gain broader area than other lords.
Your task is to write a program to calculate the size of the area each lord can gain. You may assume that Voronoi Island has a convex shape.
Input
The input consists of multiple datasets. Each dataset has the following format:
N M
Ix1 Iy1
Ix2 Iy2
...
IxN IyN
Cx1 Cy1
Cx2 Cy2
...
CxM CyM
N is the number of the vertices of Voronoi Island; M is the number of the liege lords; (Ixi, Iyi) denotes the coordinate of the i-th vertex; (Cxi, Cyi ) denotes the coordinate of the castle of the i-the lord.
The input meets the following constraints: 3 ≤ N ≤ 10, 2 ≤ M ≤ 10, -100 ≤ Ixi, Iyi, Cxi, Cyi ≤ 100. The vertices are given counterclockwise. All the coordinates are integers.
The last dataset is followed by a line containing two zeros. This line is not a part of any dataset and should not be processed.
Output
For each dataset, print the area gained by each liege lord with an absolute error of at most 10-4 . You may output any number of digits after the decimal point. The order of the output areas must match that of the lords in the input.
Example
Input
3 3
0 0
8 0
0 8
2 2
4 2
2 4
0 0
Output
9.0
11.5
11.5
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"1 1 1\\n2\", \"3 2 1\\n3\\n3\\n3\", \"3 1 -1\\n2\\n-3\\n2\", \"3 1 -10\\n-10\\n-10\\n-10\", \"1 0 1\\n2\", \"3 2 0\\n3\\n3\\n3\", \"3 1 -10\\n-19\\n-10\\n-10\", \"0 0 1\\n2\", \"3 2 0\\n5\\n3\\n3\", \"2 1 -10\\n-19\\n-10\\n-10\", \"3 2 1\\n5\\n3\\n3\", \"1 0 0\\n4\", \"3 2 0\\n1\\n3\\n6\", \"2 1 -10\\n-35\\n-3\\n-10\", \"2 1 -10\\n-35\\n-1\\n-10\", \"2 1 -6\\n-35\\n-1\\n-10\", \"2 1 -7\\n-34\\n-1\\n-10\", \"2 1 -5\\n-34\\n-1\\n-10\", \"1 1 -5\\n-34\\n-1\\n-10\", \"1 1 -10\\n-34\\n-2\\n-10\", \"1 1 -3\\n-64\\n-2\\n-10\", \"1 1 -1\\n-64\\n-3\\n-12\", \"2 1 0\\n-77\\n-2\\n-33\", \"2 1 1\\n-77\\n-2\\n-33\", \"2 2 1\\n-13\\n2\\n0\", \"3 3 1\\n3\\n3\\n3\", \"3 1 -19\\n-19\\n-10\\n-10\", \"2 1 -8\\n-34\\n-1\\n-10\", \"1 1 -17\\n-34\\n-2\\n-10\", \"1 1 -2\\n-64\\n-3\\n-10\", \"2 1 2\\n-77\\n-1\\n-57\", \"3 1 -10\\n-10\\n-8\\n0\", \"3 1 -19\\n-19\\n-10\\n-18\", \"2 -1 -10\\n-35\\n-5\\n-10\", \"2 2 0\\n3\\n4\\n2\", \"2 1 -13\\n-34\\n-1\\n-10\", \"1 4 2\\n-47\\n-1\\n-84\", \"2 8 1\\n-13\\n0\\n0\", \"3 6 1\\n3\\n3\\n4\", \"2 2 -10\\n-35\\n-9\\n-7\", \"3 2 1\\n0\\n10\\n4\", \"2 13 1\\n-23\\n0\\n0\", \"3 2 1\\n0\\n10\\n0\", \"2 2 -10\\n-14\\n-9\\n-7\", \"3 3 2\\n1\\n2\\n0\", \"1 1 -4\\n-47\\n-1\\n-10\", \"2 2 -10\\n-14\\n-6\\n-7\", \"3 1 -27\\n-19\\n0\\n-18\", \"2 1 -10\\n-14\\n-6\\n-7\", \"3 -1 -15\\n-55\\n-1\\n-18\", \"3 1 -27\\n-38\\n0\\n-18\", \"3 1 -1\\n2\\n-2\\n2\", \"1 1 2\\n2\", \"2 0 -10\\n-19\\n-10\\n-10\", \"1 1 0\\n2\", \"3 2 1\\n1\\n3\\n3\", \"2 1 -10\\n-35\\n-10\\n-10\", \"1 0 0\\n2\", \"3 2 1\\n1\\n3\\n6\", \"2 0 -10\\n-35\\n-10\\n-10\", \"2 0 -10\\n-35\\n-3\\n-10\", \"1 1 0\\n4\", \"0 2 0\\n1\\n3\\n6\", \"0 1 0\\n4\", \"0 2 0\\n2\\n3\\n6\", \"0 1 0\\n7\", \"0 2 0\\n2\\n3\\n2\", \"0 2 0\\n3\\n3\\n2\", \"2 1 -6\\n-57\\n-1\\n-10\", \"0 2 0\\n3\\n4\\n2\", \"2 1 -6\\n-66\\n-1\\n-10\", \"0 2 1\\n3\\n4\\n2\", \"2 1 -6\\n-100\\n-1\\n-10\", \"2 1 -6\\n-34\\n-1\\n-10\", \"1 1 -5\\n-34\\n-2\\n-10\", \"1 1 -10\\n-64\\n-2\\n-10\", \"1 1 -3\\n-64\\n-4\\n-10\", \"1 1 -3\\n-64\\n-3\\n-10\", \"1 1 -3\\n-64\\n-3\\n-6\", \"1 1 -3\\n-64\\n-3\\n-12\", \"0 1 -3\\n-64\\n-3\\n-12\", \"1 1 -1\\n-34\\n-3\\n-12\", \"1 1 -1\\n-34\\n-3\\n-20\", \"1 1 -1\\n-34\\n-3\\n-33\", \"1 1 0\\n-34\\n-3\\n-33\", \"1 1 0\\n-34\\n-2\\n-33\", \"1 1 0\\n-65\\n-2\\n-33\", \"1 1 0\\n-77\\n-2\\n-33\", \"2 1 1\\n-77\\n-4\\n-33\", \"2 1 1\\n-77\\n-4\\n-57\", \"2 1 1\\n-77\\n-1\\n-57\", \"2 1 0\\n-77\\n-1\\n-57\", \"1 1 1\\n-77\\n-1\\n-57\", \"1 1 1\\n-77\\n-1\\n-84\", \"1 1 1\\n-47\\n-1\\n-84\", \"1 1 2\\n-47\\n-1\\n-84\", \"1 0 2\\n-47\\n-1\\n-84\", \"1 0 2\\n-47\\n-1\\n-16\", \"1 0 2\\n-47\\n0\\n-16\", \"1 0 3\\n-47\\n0\\n-16\", \"1 0 3\\n-47\\n0\\n0\", \"1 0 3\\n-5\\n0\\n0\", \"2 0 3\\n-5\\n0\\n0\", \"2 0 3\\n-10\\n0\\n0\"], \"outputs\": [\"2\", \"12\", \"2\", \"-27\", \"2\\n\", \"9\\n\", \"-27\\n\", \"0\\n\", \"11\\n\", \"-19\\n\", \"12\\n\", \"4\\n\", \"10\\n\", \"-13\\n\", \"-11\\n\", \"-7\\n\", \"-8\\n\", \"-6\\n\", \"-5\\n\", \"-10\\n\", \"-3\\n\", \"-1\\n\", \"1\\n\", \"3\\n\", \"6\\n\", \"18\\n\", \"-39\\n\", \"-9\\n\", \"-17\\n\", \"-2\\n\", \"5\\n\", \"-18\\n\", \"-47\\n\", \"19\\n\", \"7\\n\", \"-14\\n\", \"8\\n\", \"24\\n\", \"36\\n\", \"-29\\n\", \"16\\n\", \"39\\n\", \"14\\n\", \"-23\\n\", \"27\\n\", \"-4\\n\", \"-20\\n\", \"-37\\n\", \"-16\\n\", \"42\\n\", \"-45\\n\", \"2\\n\", \"2\\n\", \"0\\n\", \"2\\n\", \"12\\n\", \"-19\\n\", \"2\\n\", \"12\\n\", \"0\\n\", \"0\\n\", \"4\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"-7\\n\", \"0\\n\", \"-7\\n\", \"0\\n\", \"-7\\n\", \"-7\\n\", \"-5\\n\", \"-10\\n\", \"-3\\n\", \"-3\\n\", \"-3\\n\", \"-3\\n\", \"0\\n\", \"-1\\n\", \"-1\\n\", \"-1\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"3\\n\", \"3\\n\", \"3\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"1\\n\", \"2\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\", \"0\\n\"]}", "source": "primeintellect"}
|
In the spring of 2014, a student successfully passed the university and started living alone. The problem here is what to do with the supper. He decided to plan a supper for the next N days.
He wants to maximize the total happiness he gets in N days. Of course, the more delicious or favorite you eat, the higher your happiness.
His dinner options are two, either head to a nearby dining room or cook for himself.
The happiness you get in the cafeteria depends on the menu of the day. The menu changes daily, but there is only one type every day, and all the menus for N days have already been released. So he knows all the information that if you go to the cafeteria on day i (1 ≤ i ≤ N) you will get the happiness of Ci.
The happiness obtained by self-catering is the self-catering power at the start of self-catering multiplied by a constant P. The initial value of self-catering power is Q, which is -1 if you go to the restaurant every day, +1 if you cook yourself, and fluctuates at the end of the meal of the day.
Find the maximum sum of happiness for him.
Constraints
* 1 ≤ N ≤ 500,000
* 0 ≤ P ≤ 500,000
* | Q | ≤ 500,000
* | Ci | ≤ 500,000
Input
The input is given in the following format as N + 1 line.
N P Q
C1
C2
::
CN
* The first line is given three integers N, P, and Q, which are the number of days, the constant for calculating the happiness of self-catering, and the initial value of self-catering power.
* From the 2nd line to the N + 1st line, one integer is given, and the i + 1st line gives the happiness obtained when going to the cafeteria on the i day.
Output
Output the maximum value of happiness that can be taken in one line.
Examples
Input
1 1 1
2
Output
2
Input
3 2 1
3
3
3
Output
12
Input
3 1 -1
2
-3
2
Output
2
Input
3 1 -10
-10
-10
-10
Output
-27
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0
|
{"tests": "{\"inputs\": [\"2\\n2 1\", \"2\\n1 2\", \"2\\n2 -2\", \"2\\n2 -4\", \"2\\n2 -3\", \"2\\n2 -6\", \"2\\n2 -11\", \"2\\n2 -5\", \"2\\n2 -10\", \"2\\n2 -7\", \"2\\n2 -13\", \"2\\n2 -16\", \"2\\n2 -25\", \"2\\n2 -20\", \"2\\n2 -14\", \"2\\n2 -12\", \"2\\n2 -15\", \"2\\n2 -36\", \"2\\n2 -17\", \"2\\n2 -23\", \"2\\n2 -22\", \"2\\n2 -61\", \"2\\n2 -49\", \"2\\n2 -30\", \"2\\n2 -34\", \"2\\n2 -44\", \"2\\n2 -55\", \"2\\n2 -56\", \"2\\n2 -40\", \"2\\n2 -92\", \"2\\n2 -24\", \"2\\n2 -57\", \"2\\n2 -85\", \"2\\n2 -60\", \"2\\n2 -45\", \"2\\n2 -29\", \"2\\n2 -83\", \"2\\n2 -43\", \"2\\n2 -21\", \"2\\n2 -53\", \"2\\n2 -72\", \"2\\n2 -87\", \"2\\n2 -107\", \"2\\n2 -93\", \"2\\n2 -27\", \"2\\n2 -187\", \"2\\n2 -32\", \"2\\n2 -19\", \"2\\n2 -35\", \"2\\n2 -42\", \"2\\n2 -26\", \"2\\n2 -38\", \"2\\n2 -74\", \"2\\n2 -64\", \"2\\n2 -41\", \"2\\n2 -155\", \"2\\n2 -48\", \"2\\n2 -142\", \"2\\n2 -86\", \"2\\n2 -58\", \"2\\n2 -46\", \"2\\n2 -100\", \"2\\n2 -125\", \"2\\n2 -31\", \"2\\n2 -59\", \"2\\n2 -149\", \"2\\n2 -47\", \"2\\n2 -33\", \"2\\n2 -39\", \"2\\n2 -67\", \"2\\n2 -131\", \"2\\n2 -156\", \"2\\n2 -81\", \"2\\n2 -148\", \"2\\n2 -232\", \"2\\n2 -109\", \"2\\n2 -78\", \"2\\n2 -18\", \"2\\n2 -50\", \"2\\n2 -52\", \"2\\n2 -75\", \"2\\n2 -54\", \"2\\n2 -108\", \"2\\n2 -84\", \"2\\n2 -162\", \"2\\n2 -62\", \"2\\n2 -213\", \"2\\n2 -113\", \"2\\n2 -69\", \"2\\n2 -110\", \"2\\n2 -228\", \"2\\n2 -197\", \"2\\n2 -209\", \"2\\n2 -135\", \"2\\n2 -122\", \"2\\n2 -176\", \"2\\n2 -102\", \"2\\n2 -375\", \"2\\n2 -348\", \"2\\n2 -338\", \"2\\n2 -317\"], \"outputs\": [\"(())\", \"()()\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\", \":(\\n\"]}", "source": "primeintellect"}
|
B: Parentheses Number
problem
Define the correct parenthesis string as follows:
* The empty string is the correct parenthesis string
* For the correct parenthesis string S, `(` S `)` is the correct parenthesis string
* For correct parentheses S, T ST is the correct parentheses
Here, the permutations are associated with the correct parentheses according to the following rules.
* When the i-th closing brace corresponds to the j-th opening brace, the i-th value in the sequence is j.
Given a permutation of length n, P = (p_1, p_2, $ \ ldots $, p_n), restore the corresponding parenthesis string.
However, if the parenthesis string corresponding to the permutation does not exist, output `: (`.
Input format
n
p_1 p_2 $ \ ldots $ p_n
The number of permutations n is given in the first row.
Permutations p_1, p_2, $ \ ldots $, p_i, $ \ ldots $, p_n are given in the second row, separated by blanks.
Constraint
* 1 \ leq n \ leq 10 ^ 5
* 1 \ leq p_i \ leq n
* All inputs are integers.
* P = (p_1, p_2, $ \ ldots $, p_n) is a permutation.
Output format
Output the parenthesized string corresponding to the permutation.
Print `: (` if such a parenthesis string does not exist.
Input example 1
2
twenty one
Output example 1
(())
Input example 2
Ten
1 2 3 4 5 6 7 8 9 10
Output example 2
() () () () () () () () () ()
Input example 3
3
3 1 2
Output example 3
:(
Example
Input
2
2 1
Output
(())
The input will be give
Read the inputs from stdin solve the problem and write the answer to stdout (do not directly test on the sample inputs). Enclose your code within ```python delimiters.
| 0.125
|
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