Problem Statement

Takahashi and Aoki played N games. You are given a string S of length N, representing the results of these games. Takahashi won the i-th game if the i-th character of S is T, and Aoki won that game if it is A.

The overall winner between Takahashi and Aoki is the one who won more games than the other. If they had the same number of wins, the overall winner is the one who reached that number of wins first. Find the overall winner: Takahashi or Aoki.

Constraints

• 1\leq N \leq 100
• N is an integer.
• S is a string of length N consisting of T and A.

Sample Input 1

5
TTAAT

Sample Output 1

T

Takahashi won three games, and Aoki won two. Thus, the overall winner is Takahashi, who won more games.

Sample Input 2

6
ATTATA

Sample Output 2

T

Both Takahashi and Aoki won three games. Takahashi reached three wins in the fifth game, and Aoki in the sixth game. Thus, the overall winner is Takahashi, who reached three wins first.

Sample Input 3

1
A

Sample Output 3

A

Problem Statement

You are given integers X and Y between 1 and 12, inclusive.

Find what month it will be Y months after month X (for example, month 1 is January).

Constraints

• X and Y are integers between 1 and 12, inclusive.

Sample Input 1

5 9

Sample Output 1

2

Nine months after May is February. Therefore, output 2.

Sample Input 2

1 1

Sample Output 2

2

Sample Input 3

12 12

Sample Output 3

12

Problem Statement

An integer sequence A=(A_1,A_2,\ldots,A_N) of length N is given.

Output the numbers contained in A in ascending order, removing duplicates.

Constraints

• 1\le N\le 100
• 1\le A_i\le 100
• All input values are integers.

Sample Input 1

4
3 1 4 1

Sample Output 1

3
1 3 4

The numbers contained in A=(3,1,4,1) are 1,3,4 in ascending order, totalling 3 distinct numbers. Therefore, output as shown above.

Sample Input 2

3
7 7 7

Sample Output 2

1
7

Sample Input 3

8
19 5 5 19 5 19 4 19

Sample Output 3

3
4 5 19

Problem Statement

You are given a string S of length N.

Find the string obtained by replacing all contiguous occurrences of na in S with nya.

Constraints

• N is an integer between 1 and 1000, inclusive.
• S is a string of length N consisting of lowercase English letters.

Sample Input 1

4
naan

Sample Output 1

nyaan

Replacing all contiguous occurrences of na in naan with nya results in the string nyaan.

Sample Input 2

4
near

Sample Output 2

near

S may not contain a contiguous na.

Sample Input 3

8
national

Sample Output 3

nyationyal

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