Problem Statement

On a non-empty string, a left shift moves the first character to the end of the string, and a right shift moves the last character to the beginning of the string.

For example, a left shift on abcde results in bcdea, and two right shifts on abcde result in deabc.

You are given a non-empty S consisting of lowercase English letters. Among the strings that can be obtained by performing zero or more left shifts and zero or more right shifts on S, find the lexicographically smallest string and the lexicographically largest string.

Constraints

• S consists of lowercase English letters.
• The length of S is between 1 and 1000 (inclusive).

Sample Input 1

aaba

Sample Output 1

aaab
baaa

By performing shifts, we can obtain four strings: aaab, aaba, abaa, baaa. The lexicographically smallest and largest among them are aaab and baaa, respectively.

Sample Input 2

z

Sample Output 2

z
z

Any sequence of operations results in z.

Sample Input 3

abracadabra

Sample Output 3

aabracadabr
racadabraab

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

There is a grid with H rows and W columns.

Each cell of the grid is land or sea, which is represented by H strings S_1, S_2, \ldots, S_H of length W. Let (i, j) denote the cell at the i-th row from the top and j-th column from the left, and (i, j) is land if the j-th character of S_i is ., and (i, j) is sea if the character is #.

The constraints guarantee that all cells on the perimeter of the grid (that is, the cells (i, j) that satisfy at least one of i = 1, i = H, j = 1, j = W) are sea.

Takahashi's spaceship has crash-landed on a cell in the grid. Afterward, he moved N times on the grid following the instructions represented by a string T of length N consisting of L, R, U, and D. For i = 1, 2, \ldots, N, the i-th character of T describes the i-th move as follows:

• L indicates a move of one cell to the left. That is, if he is at (i, j) before the move, he will be at (i, j-1) after the move.
• R indicates a move of one cell to the right. That is, if he is at (i, j) before the move, he will be at (i, j+1) after the move.
• U indicates a move of one cell up. That is, if he is at (i, j) before the move, he will be at (i-1, j) after the move.
• D indicates a move of one cell down. That is, if he is at (i, j) before the move, he will be at (i+1, j) after the move.

It is known that all cells along his path (including the cell where he crash-landed and the cell he is currently on) are not sea. Print the number of cells that could be his current position.

Constraints

• H, W, and N are integers.
• 3 \leq H, W \leq 500
• 1 \leq N \leq 500
• T is a string of length N consisting of L, R, U, and D.
• S_i is a string of length W consisting of . and #.
• There is at least one cell that could be Takahashi's current position.
• All cells on the perimeter of the grid are sea.

Sample Input 1

6 7 5
LULDR
#######
#...#.#
##...##
#.#...#
#...#.#
#######

Sample Output 1

2

The following two cases are possible, so there are two cells that could be Takahashi's current position: (3, 4) and (4, 5).

• He crash-landed on cell (3, 5) and moved (3, 5) \rightarrow (3, 4) \rightarrow (2, 4) \rightarrow (2, 3) \rightarrow (3, 3) \rightarrow (3, 4).
• He crash-landed on cell (4, 6) and moved (4, 6) \rightarrow (4, 5) \rightarrow (3, 5) \rightarrow (3, 4) \rightarrow (4, 4) \rightarrow (4, 5).

Sample Input 2

13 16 9
ULURDLURD
################
##..##.#..####.#
###.#..#.....#.#
#..##..#####.###
#...#..#......##
###.##.#..#....#
##.#####....##.#
###.###.#.#.#..#
######.....##..#
#...#.#.######.#
##..###..#..#.##
#...#.#.#...#..#
################

Sample Output 2

6

Problem Statement

This problem is an easier version of Problem G.

There is a slot machine with three reels.
The arrangement of symbols on the i-th reel is represented by the string S_i. Here, S_i is a string of length M consisting of digits.

Each reel has a corresponding button. For each non-negative integer t, Takahashi can either choose and press one button or do nothing exactly t seconds after the reels start spinning.
If he presses the button corresponding to the i-th reel exactly t seconds after the reels start spinning, the i-th reel will stop and display the ((t \bmod M)+1)-th character of S_i.
Here, t \bmod M denotes the remainder when t is divided by M.

Takahashi wants to stop all the reels so that all the displayed characters are the same.
Find the minimum possible number of seconds from the start of the spin until all the reels are stopped so that his goal is achieved.
If this is impossible, report that fact.

Constraints

• 1 \leq M \leq 100
• M is an integer.
• S_i is a string of length M consisting of digits.

Sample Input 1

10
1937458062
8124690357
2385760149

Sample Output 1

6

Takahashi can stop each reel as follows so that 6 seconds after the reels start spinning, all the reels display 8.

• Press the button corresponding to the second reel 0 seconds after the reels start spinning. The second reel stops and displays 8, the ((0 \bmod 10)+1=1)-st character of S_2.
• Press the button corresponding to the third reel 2 seconds after the reels start spinning. The third reel stops and displays 8, the ((2 \bmod 10)+1=3)-rd character of S_3.
• Press the button corresponding to the first reel 6 seconds after the reels start spinning. The first reel stops and displays 8, the ((6 \bmod 10)+1=7)-th character of S_1.

There is no way to make the reels display the same character in 5 or fewer seconds, so print 6.

Sample Input 2

20
01234567890123456789
01234567890123456789
01234567890123456789

Sample Output 2

20

Note that he must stop all the reels and make them display the same character.

Sample Input 3

5
11111
22222
33333

Sample Output 3

-1

It is impossible to stop the reels so that all the displayed characters are the same.
In this case, print -1.

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.