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