Problem Statement

You are given a sequence of N integers: A=(A _ 1,A _ 2,\ldots,A _ N).

Print all even numbers in A without changing the order.

Constraints

• 1\leq N\leq 100
• 1\leq A _ i\leq 100\ (1\leq i\leq N)
• A contains at least one even number.
• All values in the input are integers.

Sample Input 1

5
1 2 3 5 6

Sample Output 1

2 6

We have A=(1,2,3,5,6). Among them are two even numbers, A _ 2=2 and A _ 5=6, so print 2 and 6 in this order, with a space in between.

Sample Input 2

5
2 2 2 3 3

Sample Output 2

2 2 2

A may contain equal elements.

Sample Input 3

10
22 3 17 8 30 15 12 14 11 17

Sample Output 3

22 8 30 12 14

Problem Statement

You are given a string S of length N consisting of o and x, and integers L and R.

Determine whether all characters from the L-th through the R-th character of S are o.

Constraints

• 1\leq N \leq 100
• 1\leq L \leq R \leq N
• S is a string of length N consisting of o and x.
• N, L, and R are all integers.

Sample Input 1

10 6 8
xoxxooooxo

Sample Output 1

Yes

All characters from the 6-th through the 8-th character of S are o, so the answer is Yes.

Sample Input 2

9 6 8
xoxxoxoox

Sample Output 2

No

The 6-th character is x, so the answer is No.

Problem Statement

You are given N integers A_1,A_2,\dots,A_N, one per line, over N lines. However, N is not given in the input.
Furthermore, the following is guaranteed:

• A_i \neq 0 ( 1 \le i \le N-1 )
• A_N = 0

Print A_N, A_{N-1},\dots,A_1 in this order.

Constraints

• All input values are integers.
• 1 \le N \le 100
• 1 \le A_i \le 10^9 ( 1 \le i \le N-1 )
• A_N = 0

Sample Input 1

3
2
1
0

Sample Output 1

0
1
2
3

Note again that N is not given in the input. Here, N=4 and A=(3,2,1,0).

Sample Input 2

0

Sample Output 2

0

A=(0).

Sample Input 3

123
456
789
987
654
321
0

Sample Output 3

0
321
654
987
789
456
123

Problem Statement

A string T is called a 1122 string if and only if it satisfies all of the following three conditions:

• \lvert T \rvert is even. Here, \lvert T \rvert denotes the length of T.
• For each integer i satisfying 1\leq i\leq \frac{|T|}{2}, the (2i-1)-th and 2i-th characters of T are equal.
• Each character appears in T exactly zero or two times. That is, every character contained in T appears exactly twice in T.

Given a string S consisting of lowercase English letters, print Yes if S is a 1122 string, and No otherwise.

Constraints

• S is a string of length between 1 and 100, inclusive, consisting of lowercase English letters.

Sample Input 1

aabbcc

Sample Output 1

Yes

S=aabbcc satisfies all the conditions for a 1122 string, so print Yes.

Sample Input 2

aab

Sample Output 2

No

S=aab has an odd length and does not satisfy the first condition, so print No.

Sample Input 3

zzzzzz

Sample Output 3

No

S=zzzzzz contains six zs and does not satisfy the third condition, so print No.

Problem Statement

You are given simple undirected graphs G and H, each with N vertices: vertices 1, 2, \ldots, N. Graph G has M_G edges, and its i-th edge (1\leq i\leq M_G) connects vertices u_i and v_i. Graph H has M_H edges, and its i-th edge (1\leq i\leq M_H) connects vertices a_i and b_i.

You can perform the following operation on graph H any number of times, possibly zero.

• Choose a pair of integers (i,j) satisfying 1\leq i<j\leq N. Pay A_{i,j} yen, and if there is no edge between vertices i and j in H, add one; if there is, remove it.

Find the minimum total cost required to make G and H isomorphic.

Constraints

• 1\leq N\leq8
• 0\leq M _ G\leq\dfrac{N(N-1)}2
• 0\leq M _ H\leq\dfrac{N(N-1)}2
• 1\leq u _ i\lt v _ i\leq N\ (1\leq i\leq M _ G)
• (u _ i,v _ i)\neq(u _ j,v _ j)\ (1\leq i\lt j\leq M _ G)
• 1\leq a _ i\lt b _ i\leq N\ (1\leq i\leq M _ H)
• (a _ i,b _ i)\neq(a _ j,b _ j)\ (1\leq i\lt j\leq M _ H)
• 1\leq A _ {i,j}\leq 10 ^ 6\ (1\leq i\lt j\leq N)
• All input values are integers.

Sample Input 1

5
4
1 2
2 3
3 4
4 5
4
1 2
1 3
1 4
1 5
3 1 4 1
5 9 2
6 5
3

Sample Output 1

9

The given graphs are as follows:

For example, you can perform the following four operations on H to make it isomorphic to G at a cost of 9 yen.

• Choose (i,j)=(1,3). There is an edge between vertices 1 and 3 in H, so pay 1 yen to remove it.
• Choose (i,j)=(2,5). There is no edge between vertices 2 and 5 in H, so pay 2 yen to add it.
• Choose (i,j)=(1,5). There is an edge between vertices 1 and 5 in H, so pay 1 yen to remove it.
• Choose (i,j)=(3,5). There is no edge between vertices 3 and 5 in H, so pay 5 yen to add it.

After these operations, H becomes:

You cannot make G and H isomorphic at a cost less than 9 yen, so print 9.

Sample Input 2

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

Sample Output 2

3

For example, performing the operations (i,j)=(2,3),(2,4),(3,4) on H will make it isomorphic to G.

Sample Input 3

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

Sample Output 3

5

For example, performing the operation (i,j)=(4,5) once will make G and H isomorphic.

Sample Input 4

2
0
0
371

Sample Output 4

0

Note that G and H may have no edges.

Also, it is possible that no operations are needed.

Sample Input 5

8
13
1 8
5 7
4 6
1 5
7 8
1 6
1 2
5 8
2 6
5 6
6 7
3 7
4 8
15
3 5
1 7
4 6
3 8
7 8
1 2
5 6
1 6
1 5
1 4
2 8
2 6
2 4
4 7
1 3
7483 1694 5868 3296 9723 5299 4326
5195 4088 5871 1384 2491 6562
1149 6326 2996 9845 7557
4041 7720 1554 5060
8329 8541 3530
4652 3874
3748

Sample Output 5

21214

Problem Statement

You are given a string S. Find the number of strings that can result from performing the following operation exactly once.

• Let N be the length of S. Choose a pair of integers (i,j) such that 1\leq i<j\leq N and swap the i-th and j-th characters of S.

It can be proved that you can always perform it under the constraints of this problem.

Constraints

• S is a string of length between 2 and 10^6, inclusive, consisting of lowercase English letters.

Sample Input 1

abc

Sample Output 1

3

The length of S is 3, so 1\leq i<j\leq 3 is satisfied by three pairs of integers (i,j): (1,2), (1,3), and (2,3).

• Swapping the 1-st and 2-nd characters of S results in S being bac.
• Swapping the 1-st and 3-rd characters of S results in S being cba.
• Swapping the 2-nd and 3-rd characters of S results in S being acb.

Therefore, the operation on abc results in one of the three strings: bac, cba, and acb, so print 3.

Sample Input 2

aaaaa

Sample Output 2

1

Swapping any two characters results in S remaining aaaaa. Thus, only one string can result from the operation.

Problem Statement

You are given a sequence A of N positive integers and a positive integer K.
You can perform the following operation on the sequence A any number of times.

• Choose an integer i with 1 \leq i \leq N, and add K to A_i.

Find the minimum possible value of \max(A) - \min(A).

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq K \leq 10^9
• 1 \leq A_i \leq 10^9
• All input values are integers.

Sample Input 1

3 10
3 21 9

Sample Output 1

4

First, choosing i=1 makes the sequence A=(13,21,9).
Next, choosing i=3 makes the sequence A=(13,21,19).
Next, choosing i=1 makes the sequence A=(23,21,19).
At this point, \max(A)-\min(A)=23-19=4.
It is impossible to make \max(A)-\min(A) at most 3, so the answer is 4.

Sample Input 2

5 6
4 100 5 10 450

Sample Output 2

2

Problem Statement

AtCoder Ski Area has N open spaces called Space 1, Space 2, \ldots, Space N. The altitude of Space i is H_i. There are M slopes that connect two spaces bidirectionally. The i-th slope (1 \leq i \leq M) connects Space U_i and Space V_i. It is possible to travel between any two spaces using some slopes.

Takahashi can only travel between spaces by using slopes. Each time he goes through a slope, his happiness changes. Specifically, when he goes from Space X to Space Y by using the slope that directly connects them, his happiness changes as follows.

• If the altitude of Space X is strictly higher than that of Space Y, the happiness increases by their difference: H_X-H_Y.
• If the altitude of Space X is strictly lower than that of Space Y, the happiness decreases by their difference multiplied by 2: 2(H_Y-H_X).
• If the altitude of Space X is equal to that of Space Y, the happiness does not change.

The happiness may be a negative value.

Initially, Takahashi is in Space 1, and his happiness is 0. Find his maximum possible happiness after going through any number of slopes (possibly zero), ending in any space.

Constraints

• 2 \leq N \leq 2\times 10^5
• N-1 \leq M \leq \min( 2\times 10^5,\frac{N(N-1)}{2})
• 0 \leq H_i\leq 10^8 (1 \leq i \leq N)
• 1 \leq U_i < V_i \leq N (1 \leq i \leq M)
• (U_i,V_i) \neq (U_j, V_j) if i \neq j.
• All values in input are integers.
• It is possible to travel between any two spaces using some slopes.

Sample Input 1

4 4
10 8 12 5
1 2
1 3
2 3
3 4

Sample Output 1

3

If Takahashi takes the route Space 1 \to Space 3 \to Space 4, his happiness changes as follows.

• When going from Space 1 (altitude 10) to Space 3 (altitude 12), it decreases by 2\times (12-10)=4 and becomes 0-4=-4.
• When going from Space 3 (altitude 12) to Space 4 (altitude 5), it increases by 12-5=7 and becomes -4+7=3.

If he ends the travel here, the final happiness will be 3, which is the maximum possible value.

Sample Input 2

2 1
0 10
1 2

Sample Output 2

0

His happiness is maximized by not moving at all.

Problem Statement

We have N cards. The i-th card has a string S_i written on it.

Find the lexicographically smallest string that can be obtained by choosing K of these cards and concatenating them in any order.

Constraints

• 1 \leq K \leq N \leq 50
• 1 \leq |S_i| \leq 50
• S_i consists of lowercase English letters.

Sample Input 1

4 3
ode
zaaa
r
atc

Sample Output 1

atcoder

Note that it is not possible to reverse or permute the string written on a card.
For example, ode written on the first card cannot be used as edo or deo.

Sample Input 2

5 2
z
z
zzz
z
zzzzzz

Sample Output 2

zz

There may be a pair i, j (i\neq j) such that S_i = S_j.