Problem Statement

Keyence has a culture of addressing everyone with the honorific "san," regardless of their role, age, or position. Even a new employee would call the president "Nakata-san." [Translator's note: this is a bit unusual in Japan.]

You are given a person's surname and first name as strings S and T, respectively.

Print the concatenation of the surname, a space ( ), and the honorific (san) in this order.

Constraints

• Each of S and T is a string that satisfies the following conditions.
  • The length is between 1 and 10, inclusive.
  • The first character is an uppercase English letter.
  • All characters except the first one are lowercase English letters.

Sample Input 1

Takahashi Chokudai

Sample Output 1

Takahashi san

Print the concatenation of the surname (Takahashi), a space ( ), and the honorific (san) in this order.

Sample Input 2

K Eyence

Sample Output 2

K san

Problem Statement

Takahashi turned on a computer at time 0 and clicked the mouse N times. The i-th (1 \le i \le N) click was at time T_i.

If he consecutively clicked the mouse at time x_1 and time x_2 (where x_1 < x_2), a double click is said to be fired at time x_2 if and only if x_2 - x_1 \le D.

What time was a double click fired for the first time? If no double click was fired, print -1 instead.

Constraints

• 1 \le N \le 100
• 1 \le D \le 10^9
• 1 \le T_i \le 10^9(1 \le i \le N)
• T_i < T_{i+1}(1 \le i \le N-1)
• All values in the input are integers.

Sample Input 1

4 500
300 900 1300 1700

Sample Output 1

1300

Takahashi clicked the mouse at time 900 and 1300. Since 1300 - 900 \le 500, a double click was fired at time 1300.

A double click had not been fired before time 1300, so 1300 should be printed.

Sample Input 2

5 99
100 200 300 400 500

Sample Output 2

-1

No double click was fired, so print -1.

Sample Input 3

4 500
100 600 1100 1600

Sample Output 3

600

If multiple double clicks were fired, be sure to print only the first such event.

Problem Statement

There is pasta consisting of N noodles at Takahashi's home. The length of the i-th noodle is A_i.
Takahashi has a meal plan for the next M days. On the i-th day, he is going to choose a pasta noodle of length exactly B_i and eat it. If no such noodle is available on any day, his plan fails. Additionally, he cannot eat the same noodle on multiple days.

Can Takahashi accomplish his meal plan?

Constraints

• 1 \leq M \leq N \leq 1000
• 1 \leq A_i \leq 10^9
• 1 \leq B_i \leq 10^9
• All values in input are integers.

Sample Input 1

3 2
1 1 3
3 1

Sample Output 1

Yes

He can eat the 3-rd noodle on the 1-st day and the 1-st noodle on the 2-nd day, so his meal plan is feasible.

Sample Input 2

1 1
1000000000
1

Sample Output 2

No

A noodle of length exactly 1 is needed.

Sample Input 3

5 2
1 2 3 4 5
5 5

Sample Output 3

No

Since there are only 1 noodle of length 5, he cannot have a meal on the 2-nd day.

Problem Statement

Locate a piece on a chessboard.

We have a grid with 8 rows and 8 columns of squares. Each of the squares has a 2-character name determined as follows.

• The first character of the name of a square in the 1-st column from the left is a. Similarly, the first character of the name of a square in the 2-nd, 3-rd, \ldots, 8-th column from the left is b, c, d, e, f, g, h, respectively.
• The second character of the name of a square in the 1-st row from the bottom is 1. Similarly, the second character of the name of a square in the 2-nd, 3-rd, \ldots, 8-th row from the bottom is 2, 3, 4, 5, 6, 7, 8, respectively.

For instance, the bottom-left square is named a1, the bottom-right square is named h1, and the top-right square is named h8.

You are given 8 strings S_1,\ldots,S_8, each of length 8, representing the state of the grid.
The j-th character of S_i is * if the square at the i-th row from the top and j-th column from the left has a piece on it, and . otherwise. The character * occurs exactly once among S_1,\ldots,S_8. Find the name of the square that has a piece on it.

Constraints

• S_i is a string of length 8 consisting of . and*.
• The character * occurs exactly once among S_1,\ldots,S_8.

Sample Input 1

........
........
........
........
........
........
........
*.......

Sample Output 1

a1

As explained in the problem statement, the bottom-left square is named a1.

Sample Input 2

........
........
........
........
........
.*......
........
........

Sample Output 2

b3

Problem Statement

You are given a grid of H rows and W columns.
Let (i,j) denote the cell at row i (1 \leq i \leq H) from the top and column j (1 \leq j \leq W) from the left.
The state of the grid is represented by H strings S_1, S_2, \ldots, S_H, each of length W, as follows:

• If the j-th character of S_i is #, cell (i,j) is painted black.
• If the j-th character of S_i is ., cell (i,j) is painted white.
• If the j-th character of S_i is ?, cell (i,j) is not yet painted.

Takahashi wants to paint each not-yet-painted cell white or black so that all the black cells form a rectangle.
More precisely, he wants there to exist a quadruple of integers (a,b,c,d) (1 \leq a \leq b \leq H, 1 \leq c \leq d \leq W) such that:

For each cell (i,j) (1 \leq i \leq H, 1 \leq j \leq W), if a \leq i \leq b and c \leq j \leq d, the cell is black;
otherwise, the cell is white.

Determine whether this is possible.

Constraints

• 1 \leq H, W \leq 1000
• H and W are integers.
• Each S_i is a string of length W consisting of #, ., ?.
• There is at least one cell that is already painted black.

Sample Input 1

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

Sample Output 1

Yes

The grid is in the following state. ? indicates a cell that are not yet painted.

By painting cells (1,3), (2,2), and (2,4) black and cells (3,1) and (3,5) white, the black cells can form a rectangle as follows:

Therefore, print Yes.

Sample Input 2

3 3
?##
#.#
##?

Sample Output 2

No

To form a rectangle with all black cells, you would need to paint cell (2,2) black, but it is already painted white.
Therefore, it is impossible to make all black cells form a rectangle, so print No.

Sample Input 3

1 1
#

Sample Output 3

Yes

Problem Statement

Takahashi, who governs the Kingdom of AtCoder, has decided to change the alphabetical order of English lowercase letters.

The new alphabetical order is represented by a string X, which is a permutation of a, b, \ldots, z. The i-th character of X (1 \leq i \leq 26) would be the i-th smallest English lowercase letter in the new order.

The kingdom has N citizens, whose names are S_1, S_2, \dots, S_N, where each S_i (1 \leq i \leq N) consists of lowercase English letters.
Sort these names lexicographically according to the alphabetical order decided by Takahashi.

Constraints

• X is a permutation of a, b, \ldots, z.
• 2 \leq N \leq 50000
• N is an integer.
• 1 \leq |S_i| \leq 10 \, (1 \leq i \leq N)
• S_i consists of lowercase English letters. (1 \leq i \leq N)
• S_i \neq S_j (1 \leq i \lt j \leq N)

Sample Input 1

bacdefghijklmnopqrstuvwxzy
4
abx
bzz
bzy
caa

Sample Output 1

bzz
bzy
abx
caa

In the new alphabetical order set by Takahashi, b is smaller than a and z is smaller than y. Thus, sorting the citizens' names lexicographically would result in bzz, bzy, abx, caa in ascending order.

Sample Input 2

zyxwvutsrqponmlkjihgfedcba
5
a
ab
abc
ac
b

Sample Output 2

b
a
ac
ab
abc

Problem Statement

There is a grid of H rows and W columns, each cell having a side length of 1, and we have N tiles.
The i-th tile (1\leq i\leq N) is a rectangle of size A_i\times B_i.
Determine whether it is possible to place the tiles on the grid so that all of the following conditions are satisfied:

• Every cell is covered by exactly one tile.
• It is fine to have unused tiles.
• The tiles may be rotated or flipped when placed. However, each tile must be aligned with the edges of the cells without extending outside the grid.

Constraints

• 1\leq N\leq 7
• 1 \leq H,W \leq 10
• 1\leq A_i,B_i\leq 10
• All input values are integers.

Sample Input 1

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

Sample Output 1

Yes

Placing the 2-nd, 4-th, and 5-th tiles as shown below covers every cell of the grid by exactly one tile.

Hence, print Yes.

Sample Input 2

1 1 2
2 3

Sample Output 2

No

It is impossible to place the tile without letting it extend outside the grid.
Hence, print No.

Sample Input 3

1 2 2
1 1

Sample Output 3

No

It is impossible to cover all cells with the tile.
Hence, print No.

Sample Input 4

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

Sample Output 4

No

Note that each cell must be covered by exactly one tile.

Problem Statement

For a sequence X, let f(X) = (the minimum number of elements one must modify to make X a palindrome).

Given a sequence A of length N, find the sum of f(X) over all contiguous subarrays of A.

Here, a sequence X of length m is said to be a palindrome if and only if the i-th and the (m+1-i)-th elements of X are equal for all 1 \le i \le m.

Constraints

• All values in the input are integers.
• 1 \le N \le 2 \times 10^5
• 1 \le A_i \le N

Sample Input 1

5
5 2 1 2 2

Sample Output 1

9

• f(5) = 0
• f(2) = 0
• f(1) = 0
• f(2) = 0
• f(2) = 0
• f(5,2) = 1
• f(2,1) = 1
• f(1,2) = 1
• f(2,2) = 0
• f(5,2,1) = 1
• f(2,1,2) = 0
• f(1,2,2) = 1
• f(5,2,1,2) = 2
• f(2,1,2,2) = 1
• f(5,2,1,2,2) = 1

Therefore, the sought answer is 9.

Problem Statement

2^N people, numbered 1 to 2^N, will participate in a rock-paper-scissors tournament.

The tournament proceeds as follows:

• The participants are arranged in a row in the order Person 1, Person 2, \ldots, Person 2^N from left to right.
• Let 2M be the current length of the row. For each i\ (1\leq i \leq M), the (2i-1)-th and (2i)-th persons from the left play a game against each other. Then, the M losers are removed from the row. This process is repeated N times.

Here, if Person i wins exactly j games, they receive C_{i,j} yen (Japanese currency). A person winning zero games receives nothing. Find the maximum possible total amount of money received by the 2^N people if the results of all games can be manipulated freely.

Constraints

• 1 \leq N \leq 16
• 1 \leq C_{i,j} \leq 10^9
• All values in input are integers.

Sample Input 1

2
2 5
6 5
2 1
7 9

Sample Output 1

15

The initial row of the people is (1,2,3,4).

If Person 2 wins the game against Person 1, and Person 4 wins the game against Person 3, the row becomes (2,4).

Then, if Person 4 wins the game against Person 2, the row becomes (4), and the tournament ends.

Here, Person 2 wins exactly 1 game, and Person 4 wins exactly 2 games, so they receive 0+6+0+9=15 yen in total, which is the maximum possible sum.

Sample Input 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

Sample Output 2

4