Problem Statement

There is a device with a screen that shows a single-digit number, and a button.

When the screen is showing a number k, pressing the button once changes the number on the screen to a_k.

The device currently shows 0. After pressing the button 3 times, what will be shown on the screen?

Constraints

• 0\leq a_i \leq 9
• All values in input are integers.

Sample Input 1

9 0 1 2 3 4 5 6 7 8

Sample Output 1

7

The number on the screen transitions as 0 \rightarrow 9 \rightarrow 8 \rightarrow 7.

Sample Input 2

4 8 8 8 0 8 8 8 8 8

Sample Output 2

4

The number on the screen transitions as 0 \rightarrow 4 \rightarrow 0 \rightarrow 4.

Sample Input 3

0 0 0 0 0 0 0 0 0 0

Sample Output 3

0

Problem Statement

Team Takahashi and Team Aoki are playing a baseball game, with Team Takahashi batting first.
Currently, the game has finished through the top of the ninth inning, and the bottom of the ninth is about to begin.

Team Takahashi scored A_i runs in the top of the i-th inning (1\leq i\leq 9), and Team Aoki scored B_j runs in the bottom of the j-th inning (1\leq j\leq 8).
At the end of the top of the ninth, Team Takahashi's score is not less than Team Aoki's score.
Determine the minimum number of runs Team Aoki needs to score in the bottom of the ninth to win the game.

Here, if the game is tied at the end of the bottom of the ninth, it results in a draw. Therefore, for Team Aoki to win, they must score strictly more runs than Team Takahashi by the end of the bottom of the ninth.
Team Takahashi's score at any point is the total runs scored in the tops of the innings up to that point, and Team Aoki's score is the total runs scored in the bottoms of the innings.

Constraints

• 0\leq A_i, B_j\leq 99
• A_1 + A_2 + A_3 + A_4 + A_5 + A_6 + A_7 + A_8 + A_9 \geq B_1 + B_2 + B_3 + B_4 + B_5 + B_6 + B_7 + B_8
• All input values are integers.

Sample Input 1

0 1 0 1 2 2 0 0 1
1 1 0 0 0 0 1 0

Sample Output 1

5

At the end of the top of the ninth inning, Team Takahashi has scored seven runs, and Team Aoki has scored three runs.
Therefore, if Team Aoki scores five runs in the bottom of the ninth, the scores will be 7-8, allowing them to win.
Note that scoring four runs would result in a draw and not a victory.

Sample Input 2

0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0

Sample Output 2

1

Problem Statement

Takahashi tried to type a string S consisting of lowercase English letters using a keyboard.

He was typing while looking only at the keyboard, not the screen.

Whenever he mistakenly typed a different lowercase English letter, he immediately pressed the backspace key. However, the backspace key was broken, so the mistakenly typed letter was not deleted, and the actual string typed was T.

He did not mistakenly press any keys other than those for lowercase English letters.

The characters in T that were not mistakenly typed are called correctly typed characters.

Determine the positions in T of the correctly typed characters.

Constraints

• S and T are strings of lowercase English letters with lengths between 1 and 2 \times 10^5, inclusive.
• T is a string obtained by the procedure described in the problem statement.

Sample Input 1

abc
axbxyc

Sample Output 1

1 3 6

The sequence of Takahashi's typing is as follows:

• Type a.
• Try to type b but mistakenly type x.
• Press the backspace key, but the character is not deleted.
• Type b.
• Try to type c but mistakenly type x.
• Press the backspace key, but the character is not deleted.
• Try to type c but mistakenly type y.
• Press the backspace key, but the character is not deleted.
• Type c.

The correctly typed characters are the first, third, and sixth characters.

Sample Input 2

aaaa
bbbbaaaa

Sample Output 2

5 6 7 8

Sample Input 3

atcoder
atcoder

Sample Output 3

1 2 3 4 5 6 7

Takahashi did not mistakenly type any characters.

Problem Statement

You are given integers A and B, in base K.
Print A \times B in decimal.

Notes

For base-K representation, see Wikipedia's article on Positional notation.

Constraints

• 2 \leq K \leq 10
• 1 \leq A,B \leq 10^5
• A and B are in base-K representation.

Sample Input 1

2
1011 10100

Sample Output 1

220

1011 in base 2 corresponds to 11 in base 10.
10100 in base 2 corresponds to 20 in base 10.
We have 11 \times 20 = 220, so print 220.

Sample Input 2

7
123 456

Sample Output 2

15642

123 in base 7 corresponds to 66 in base 10.
456 in base 7 corresponds to 237 in base 10.
We have 66 \times 237 = 15642, so print 15642.

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