alexjercan/bugnet huggingface dataset:
Score : 100 points

Problem Statement

Takahashi is a user of a site that hosts programming contests.

When a user competes in a contest, the rating of the user (not necessarily an integer) changes according to the performance of the user, as follows:

Let the current rating of the user be a.

Suppose that the performance of the user in the contest is b.

Then, the new rating of the user will be the avarage of a and b.

For example, if a user with rating 1 competes in a contest and gives performance 1000, his/her new rating will be 500.5, the average of 1 and 1000.

Takahashi's current rating is R, and he wants his rating to be exactly G after the next contest.

Find the performance required to achieve it.

Constraints

0 \leq R, G \leq 4500

All input values are integers.

Input

Input is given from Standard Input in the following format:

R
G

Output

Print the performance required to achieve the objective.

Sample Input 1

2002
2017

Sample Output 1

2032

Takahashi's current rating is 2002.

If his performance in the contest is 2032, his rating will be the average of 2002 and 2032, which is equal to the desired rating, 2017.

Sample Input 2

4500
0

Sample Output 2

-4500

Although the current and desired ratings are between 0 and 4500, the performance of a user can be below 0.
Score : 200 points

Problem Statement

Square1001 has seen an electric bulletin board displaying the integer 1.
He can perform the following operations A and B to change this value:

Operation A: The displayed value is doubled.

Operation B: The displayed value increases by K.

Square1001 needs to perform these operations N times in total.
Find the minimum possible value displayed in the board after N operations.

Constraints

1 \leq N, K \leq 10

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
K

Output

Print the minimum possible value displayed in the board after N operations.

Sample Input 1

4
3

Sample Output 1

10

The value will be minimized when the operations are performed in the following order: A, A, B, B.

In this case, the value will change as follows: 1 → 2 → 4 → 7 → 10.

Sample Input 2

10
10

Sample Output 2

76

The value will be minimized when the operations are performed in the following order: A, A, A, A, B, B, B, B, B, B.

In this case, the value will change as follows: 1 → 2 → 4 → 8 → 16 → 26 → 36 → 46 → 56 → 66 → 76.

By the way, this contest is AtCoder Beginner Contest 076.
Score : 300 points

Problem Statement

E869120 found a chest which is likely to contain treasure.

However, the chest is locked. In order to open it, he needs to enter a string S consisting of lowercase English letters.

He also found a string S', which turns out to be the string S with some of its letters (possibly all or none) replaced with ?.

One more thing he found is a sheet of paper with the following facts written on it:

Condition 1: The string S contains a string T as a contiguous substring.

Condition 2: S is the lexicographically smallest string among the ones that satisfy Condition 1.

Print the string S.

If such a string does not exist, print UNRESTORABLE.

Constraints

1 \leq |S'|, |T| \leq 50

S' consists of lowercase English letters and ?.

T consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

S
T'

Output

Print the string S.

If such a string does not exist, print UNRESTORABLE instead.

Sample Input 1

?tc????
coder

Sample Output 1

atcoder

There are 26 strings that satisfy Condition 1: atcoder, btcoder, ctcoder,..., ztcoder.
Among them, the lexicographically smallest is atcoder, so we can say S = atcoder.

Sample Input 2

??p??d??
abc

Sample Output 2

UNRESTORABLE

There is no string that satisfies Condition 1, so the string S does not exist.
Score : 100 points

Problem Statement

Snuke built an online judge to hold a programming contest.

When a program is submitted to the judge, the judge returns a verdict, which is a two-character string that appears in the string S as a contiguous substring.
(The judge can return any two-character substring of S.)

Determine whether the judge can return the string AC as the verdict to a program.

Constraints

2 \leq |S| \leq 5

S consists of uppercase English letters.

Input

Input is given from Standard Input in the following format:

S

Output

If the judge can return the string AC as a verdict to a program, print Yes; if it cannot, print No.

Sample Input 1

BACD

Sample Output 1

Yes

The string AC appears in BACD as a contiguous substring (the second and third characters).

Sample Input 2

ABCD

Sample Output 2

No

Although the string ABCD contains both A and C (the first and third characters), the string AC does not appear in ABCD as a contiguous substring.

Sample Input 3

CABD

Sample Output 3

No

Sample Input 4

ACACA

Sample Output 4

Yes

Sample Input 5

XX

Sample Output 5

No
Score : 200 points

Problem Statement

We will say that two integer sequences of length N, x_1, x_2, ..., x_N and y_1, y_2, ..., y_N, are similar when |x_i - y_i| \leq 1 holds for all i (1 \leq i \leq N).

In particular, any integer sequence is similar to itself.

You are given an integer N and an integer sequence of length N, A_1, A_2, ..., A_N.

How many integer sequences b_1, b_2, ..., b_N are there such that b_1, b_2, ..., b_N is similar to A and the product of all elements, b_1 b_2 ... b_N, is even?

Constraints

1 \leq N \leq 10

1 \leq A_i \leq 100

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the number of integer sequences that satisfy the condition.

Sample Input 1

2
2 3

Sample Output 1

7

There are seven integer sequences that satisfy the condition:

1, 2

1, 4

2, 2

2, 3

2, 4

3, 2

3, 4

Sample Input 2

3
3 3 3

Sample Output 2

26

Sample Input 3

1
100

Sample Output 3

1

Sample Input 4

10
90 52 56 71 44 8 13 30 57 84

Sample Output 4

58921
Score : 400 points

Problem Statement

We have a string s consisting of lowercase English letters.
Snuke can perform the following operation repeatedly:

Insert a letter x to any position in s of his choice, including the beginning and end of s.

Snuke's objective is to turn s into a palindrome.
Determine whether the objective is achievable. If it is achievable, find the minimum number of operations required.

Notes

A palindrome is a string that reads the same forward and backward.
For example, a, aa, abba and abcba are palindromes, while ab, abab and abcda are not.

Constraints

1 \leq |s| \leq 10^5

s consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

s

Output

If the objective is achievable, print the number of operations required.
If it is not, print -1 instead.

Sample Input 1

xabxa

Sample Output 1

2

One solution is as follows (newly inserted x are shown in bold):

xabxa → xaxbxa → xaxbxax

Sample Input 2

ab

Sample Output 2

-1

No sequence of operations can turn s into a palindrome.

Sample Input 3

a

Sample Output 3

0

s is a palindrome already at the beginning.

Sample Input 4

oxxx

Sample Output 4

3

One solution is as follows:

oxxx → xoxxx → xxoxxx → xxxoxxx
Score : 700 points

Problem Statement

We have a string s consisting of lowercase English letters.
Snuke is partitioning s into some number of non-empty substrings.
Let the subtrings obtained be s_1, s_2, ..., s_N from left to right. (Here, s = s_1 + s_2 + ... + s_N holds.)
Snuke wants to satisfy the following condition:

For each i (1 \leq i \leq N), it is possible to permute the characters in s_i and obtain a palindrome.

Find the minimum possible value of N when the partition satisfies the condition.

Constraints

1 \leq |s| \leq 2 \times 10^5

s consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

s

Output

Print the minimum possible value of N when the partition satisfies the condition.

Sample Input 1

aabxyyzz

Sample Output 1

2

The solution is to partition s as aabxyyzz = aab + xyyzz.
Here, aab can be permuted to form a palindrome aba, and xyyzz can be permuted to form a palindrome zyxyz.

Sample Input 2

byebye

Sample Output 2

1

byebye can be permuted to form a palindrome byeeyb.

Sample Input 3

abcdefghijklmnopqrstuvwxyz

Sample Output 3

26

Sample Input 4

abcabcxabcx

Sample Output 4

3

The solution is to partition s as abcabcxabcx = a + b + cabcxabcx.
Score : 1600 points

Problem Statement

We constructed a rectangular parallelepiped of dimensions A \times B \times C built of ABC cubic blocks of side 1.
Then, we placed the parallelepiped in xyz-space as follows:

For every triple i, j, k (0 \leq i < A, 0 \leq j < B, 0 \leq k < C), there exists a block that has a diagonal connecting the points (i, j, k) and (i + 1, j + 1, k + 1). All sides of the block are parallel to a coordinate axis.

For each triple i, j, k, we will call the above block as block (i, j, k).

For two blocks (i_1, j_1, k_1) and (i_2, j_2, k_2), we will define the distance between them as max(|i_1 - i_2|, |j_1 - j_2|, |k_1 - k_2|).

We have passed a wire with a negligible thickness through a segment connecting the points (0, 0, 0) and (A, B, C).
How many blocks (x,y,z) satisfy the following condition? Find the count modulo 10^9 + 7.

There exists a block (x', y', z') such that the wire passes inside the block (x', y', z') (not just boundary) and the distance between the blocks (x, y, z) and (x', y', z') is at most D.

Constraints

1 \leq A < B < C \leq 10^{9}

Any two of the three integers A, B and C are coprime.

0 \leq D \leq 50,000

Input

Input is given from Standard Input in the following format:

A B C D

Output

Print the number of the blocks that satisfy the condition, modulo 10^9 + 7.

Sample Input 1

3 4 5 1

Sample Output 1

54

The figure below shows the parallelepiped, sliced into five layers by planes parallel to xy-plane.
Here, the layer in the region i - 1 \leq z \leq i is called layer i.

The blocks painted black are penetrated by the wire, and satisfy the condition.
The other blocks that satisfy the condition are painted yellow.

There are 54 blocks that are painted black or yellow.

Sample Input 2

1 2 3 0

Sample Output 2

4

There are four blocks that are penetrated by the wire, and only these blocks satisfy the condition.

Sample Input 3

3 5 7 100

Sample Output 3

105

All blocks satisfy the condition.

Sample Input 4

3 123456781 1000000000 100

Sample Output 4

444124403

Sample Input 5

1234 12345 1234567 5

Sample Output 5

150673016

Sample Input 6

999999997 999999999 1000000000 50000

Sample Output 6

8402143
Score : 1800 points

Problem Statement

Three men, A, B and C, are eating sushi together.
Initially, there are N pieces of sushi, numbered 1 through N.
Here, N is a multiple of 3.

Each of the three has likes and dislikes in sushi.
A's preference is represented by (a_1,\ ...,\ a_N), a permutation of integers from 1 to N.
For each i (1 \leq i \leq N), A's i-th favorite sushi is Sushi a_i.
Similarly, B's and C's preferences are represented by (b_1,\ ...,\ b_N) and (c_1,\ ...,\ c_N), permutations of integers from 1 to N.

The three repeats the following action until all pieces of sushi are consumed or a fight brakes out (described later):

Each of the three A, B and C finds his most favorite piece of sushi among the remaining pieces. Let these pieces be Sushi x, y and z, respectively. If x, y and z are all different, A, B and C eats Sushi x, y and z, respectively. Otherwise, a fight brakes out.

You are given A's and B's preferences, (a_1,\ ...,\ a_N) and (b_1,\ ...,\ b_N).
How many preferences of C, (c_1,\ ...,\ c_N), leads to all the pieces of sushi being consumed without a fight?
Find the count modulo 10^9+7.

Constraints

3 \leq N \leq 399

N is a multiple of 3.

(a_1,\ ...,\ a_N) and (b_1,\ ...,\ b_N) are permutations of integers from 1 to N.

Input

Input is given from Standard Input in the following format:

N
a_1 ... a_N
b_1 ... b_N

Output

Print the number of the preferences of C that leads to all the pieces of sushi being consumed without a fight, modulo 10^9+7.

Sample Input 1

3
1 2 3
2 3 1

Sample Output 1

2

The answer is two, (c_1,\ c_2,\ c_3) = (3,\ 1,\ 2),\ (3,\ 2,\ 1).
In both cases, A, B and C will eat Sushi 1, 2 and 3, respectively, and there will be no more sushi.

Sample Input 2

3
1 2 3
1 2 3

Sample Output 2

0

Regardless of what permutation (c_1,\ c_2,\ c_3) is, A and B will try to eat Sushi 1, resulting in a fight.

Sample Input 3

6
1 2 3 4 5 6
2 1 4 3 6 5

Sample Output 3

80

For example, if (c_1,\ c_2,\ c_3,\ c_4,\ c_5,\ c_6) = (5,\ 1,\ 2,\ 6,\ 3,\ 4), A, B and C will first eat Sushi 1, 2 and 5, respectively, then they will eat Sushi 3, 4 and 6, respectively, and there will be no more sushi.

Sample Input 4

6
1 2 3 4 5 6
6 5 4 3 2 1

Sample Output 4

160

Sample Input 5

9
4 5 6 7 8 9 1 2 3
7 8 9 1 2 3 4 5 6

Sample Output 5

33600
Score : 100 points

Problem Statement

You are given three integers, A, B and C.

Among them, two are the same, but the remaining one is different from the rest.

For example, when A=5,B=7,C=5, A and C are the same, but B is different.

Find the one that is different from the rest among the given three integers.

Constraints

-100 \leq A,B,C \leq 100

A, B and C are integers.

The input satisfies the condition in the statement.

Input

Input is given from Standard Input in the following format:

A B C

Output

Among A, B and C, print the integer that is different from the rest.

Sample Input 1

5 7 5

Sample Output 1

7

This is the same case as the one in the statement.

Sample Input 2

1 1 7

Sample Output 2

7

In this case, C is the one we seek.

Sample Input 3

-100 100 100

Sample Output 3

-100
Score : 200 points

Problem Statement

You are given an H × W grid.

The squares in the grid are described by H strings, S_1,...,S_H.

The j-th character in the string S_i corresponds to the square at the i-th row from the top and j-th column from the left (1 \leq i \leq H,1 \leq j \leq W).

. stands for an empty square, and # stands for a square containing a bomb.

Dolphin is interested in how many bomb squares are horizontally, vertically or diagonally adjacent to each empty square.

(Below, we will simply say "adjacent" for this meaning. For each square, there are at most eight adjacent squares.)

He decides to replace each . in our H strings with a digit that represents the number of bomb squares adjacent to the corresponding empty square.

Print the strings after the process.

Constraints

1 \leq H,W \leq 50

S_i is a string of length W consisting of # and ..

Input

Input is given from Standard Input in the following format:

H W
S_1
:
S_H

Output

Print the H strings after the process.

The i-th line should contain a string T_i of length W, where the j-th character in T_i corresponds to the square at the i-th row from the top and j-th row from the left in the grid (1 \leq i \leq H, 1 \leq j \leq W).

Sample Input 1

3 5
.....
.#.#.
.....

Sample Output 1

11211
1#2#1
11211

For example, let us observe the empty square at the first row from the top and first column from the left.

There is one bomb square adjacent to this empty square: the square at the second row and second column.

Thus, the . corresponding to this empty square is replaced with 1.

Sample Input 2

3 5
#####
#####
#####

Sample Output 2

#####
#####
#####

It is possible that there is no empty square.

Sample Input 3

6 6
#####.
#.#.##
####.#
.#..#.
#.##..
#.#...

Sample Output 3

#####3
#8#7##
####5#
4#65#2
#5##21
#4#310
Score : 300 points

Problem Statement

You are given an undirected connected graph with N vertices and M edges that does not contain self-loops and double edges.

The i-th edge (1 \leq i \leq M) connects Vertex a_i and Vertex b_i.

An edge whose removal disconnects the graph is called a bridge.

Find the number of the edges that are bridges among the M edges.

Notes

A self-loop is an edge i such that a_i=b_i (1 \leq i \leq M).

Double edges are a pair of edges i,j such that a_i=a_j and b_i=b_j (1 \leq i<j \leq M).

An undirected graph is said to be connected when there exists a path between every pair of vertices.

Constraints

2 \leq N \leq 50

N-1 \leq M \leq min(N(N−1)⁄2,50)

1 \leq a_i<b_i \leq N

The given graph does not contain self-loops and double edges.

The given graph is connected.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
a_2 b_2
:
a_M b_M

Output

Print the number of the edges that are bridges among the M edges.

Sample Input 1

7 7
1 3
2 7
3 4
4 5
4 6
5 6
6 7

Sample Output 1

4

The figure below shows the given graph:

The edges shown in red are bridges. There are four of them.

Sample Input 2

3 3
1 2
1 3
2 3

Sample Output 2

0

It is possible that there is no bridge.

Sample Input 3

6 5
1 2
2 3
3 4
4 5
5 6

Sample Output 3

5

It is possible that every edge is a bridge.
Score : 400 points

Problem Statement

We have N points in a two-dimensional plane.

The coordinates of the i-th point (1 \leq i \leq N) are (x_i,y_i).

Let us consider a rectangle whose sides are parallel to the coordinate axes that contains K or more of the N points in its interior.

Here, points on the sides of the rectangle are considered to be in the interior.

Find the minimum possible area of such a rectangle.

Constraints

2 \leq K \leq N \leq 50

-10^9 \leq x_i,y_i \leq 10^9 (1 \leq i \leq N)

x_i≠x_j (1 \leq i<j \leq N)

y_i≠y_j (1 \leq i<j \leq N)

All input values are integers. (Added at 21:50 JST)

Input

Input is given from Standard Input in the following format:

N K
x_1 y_1
:
x_{N} y_{N}

Output

Print the minimum possible area of a rectangle that satisfies the condition.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).

Its area is (8-1) × (4-1) = 21.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Sample Output 3

3999999996000000001

Watch out for integer overflows.
Score : 100 points

Problem Statement

Rng is going to a festival.

The name of the festival is given to you as a string S, which ends with FESTIVAL, from input. Answer the question: "Rng is going to a festival of what?" Output the answer.

Here, assume that the name of "a festival of s" is a string obtained by appending FESTIVAL to the end of s.
For example, CODEFESTIVAL is a festival of CODE.

Constraints

9 \leq |S| \leq 50

S consists of uppercase English letters.

S ends with FESTIVAL.

Input

Input is given from Standard Input in the following format:

S

Output

Print the answer to the question: "Rng is going to a festival of what?"

Sample Input 1

CODEFESTIVAL

Sample Output 1

CODE

This is the same as the example in the statement.

Sample Input 2

CODEFESTIVALFESTIVAL

Sample Output 2

CODEFESTIVAL

This string is obtained by appending FESTIVAL to the end of CODEFESTIVAL, so it is a festival of CODEFESTIVAL.

Sample Input 3

YAKINIKUFESTIVAL

Sample Output 3

YAKINIKU
Score : 200 points

Problem Statement

Rng is preparing a problem set for a qualification round of CODEFESTIVAL.

He has N candidates of problems. The difficulty of the i-th candidate is D_i.

There must be M problems in the problem set, and the difficulty of the i-th problem must be T_i. Here, one candidate of a problem cannot be used as multiple problems.

Determine whether Rng can complete the problem set without creating new candidates of problems.

Constraints

1 \leq N \leq 200,000

1 \leq D_i \leq 10^9

1 \leq M \leq 200,000

1 \leq T_i \leq 10^9

All numbers in the input are integers.

Partial Score

100 points will be awarded for passing the test set satisfying N \leq 100 and M \leq 100.

Input

Input is given from Standard Input in the following format:

N
D_1 D_2 ... D_N
M
T_1 T_2 ... T_M

Output

Print YES if Rng can complete the problem set without creating new candidates of problems; print NO if he cannot.

Sample Input 1

5
3 1 4 1 5
3
5 4 3

Sample Output 1

YES

Sample Input 2

7
100 200 500 700 1200 1600 2000
6
100 200 500 700 1600 1600

Sample Output 2

NO

Not enough 1600s.

Sample Input 3

1
800
5
100 100 100 100 100

Sample Output 3

NO

Sample Input 4

15
1 2 2 3 3 3 4 4 4 4 5 5 5 5 5
9
5 4 3 2 1 2 3 4 5

Sample Output 4

YES
Score : 500 points

Problem Statement

Rng has a connected undirected graph with N vertices.
Currently, there are M edges in the graph, and the i-th edge connects Vertices A_i and B_i.

Rng will add new edges to the graph by repeating the following operation:

Operation: Choose u and v (u \neq v) such that Vertex v can be reached by traversing exactly three edges from Vertex u, and add an edge connecting Vertices u and v. It is not allowed to add an edge if there is already an edge connecting Vertices u and v.

Find the maximum possible number of edges that can be added.

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq A_i,B_i \leq N

The graph has no self-loops or multiple edges.

The graph is connected.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
:
A_M B_M

Output

Find the maximum possible number of edges that can be added.

Sample Input 1

6 5
1 2
2 3
3 4
4 5
5 6

Sample Output 1

4

If we add edges as shown below, four edges can be added, and no more.

Sample Input 2

5 5
1 2
2 3
3 1
5 4
5 1

Sample Output 2

5

Five edges can be added, for example, as follows:

Add an edge connecting Vertex 5 and Vertex 3.

Add an edge connecting Vertex 5 and Vertex 2.

Add an edge connecting Vertex 4 and Vertex 1.

Add an edge connecting Vertex 4 and Vertex 2.

Add an edge connecting Vertex 4 and Vertex 3.
Score : 700 points

Problem Statement

N cells are arranged in a row.
Some of them may contain tokens.
You are given a string s that consists of 0s and 1s.
If the i-th character of s is 1, the i-th cell (from left) contains a token.
Otherwise, it doesn't contain a token.

Snuke wants to perform the following operation as many times as possible.
In each operation, he chooses three consecutive cells.
Let's call the cells X, Y, Z from left to right.
In order for the operation to be valid, both X and Z must contain tokens and Y must not contain a token.
Then, he removes these two tokens and puts a new token on Y.

How many operations can he perform if he performs operations in the optimal way?

Constraints

1 \leq N \leq 500,000

|s| = N

Each character in s is either 0 or 1.

Input

Input is given from Standard Input in the following format:

N
s

Output

Print the answer.

Sample Input 1

7
1010101

Sample Output 1

2

For example, he can perform two operations in the following way:

Perform an operation on the last three cells. Now the string that represents tokens becomes 1010010.

Perform an operation on the first three cells. Now the string that represents tokens becomes 0100010.

Note that the choice of operations matters.
For example, if he chooses three cells in the middle first, he can perform no more operations.

Sample Input 2

50
10101000010011011110001001111110000101010111100110

Sample Output 2

10