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.

Problem Statement

AtCoder in another world holds 10 types of contests called AAC, ..., AJC. There will be N contests from now on.
The types of these N contests are given to you as a string S: if the i-th character of S is x, the i-th contest will be AxC.
AtCoDeer will choose and participate in one or more contests from the N so that the following condition is satisfied.

• In the sequence of contests he will participate in, the contests of the same type are consecutive.
  • Formally, when AtCoDeer participates in x contests and the i-th of them is of type T_i, for every triple of integers (i,j,k) such that 1 \le i < j < k \le x, T_i=T_j must hold if T_i=T_k.

Find the number of ways for AtCoDeer to choose contests to participate in, modulo 998244353.
Two ways to choose contests are considered different when there is a contest c such that AtCoDeer participates in c in one way but not in the other.

Constraints

• 1 \le N \le 1000
• |S|=N
• S consists of uppercase English letters from A through J.

Sample Input 1

4
BGBH

Sample Output 1

13

For example, participating in the 1-st and 3-rd contests is valid, and so is participating in the 2-nd and 4-th contests.
On the other hand, participating in the 1-st, 2-nd, 3-rd, and 4-th contests is invalid, since the participations in ABCs are not consecutive, violating the condition for the triple (i,j,k)=(1,2,3).
Additionally, it is not allowed to participate in zero contests.
In total, there are 13 valid ways to participate in some contests.

Sample Input 2

100
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBIEIJEIJIJCGCCFGIEBIHFCGFBFAEJIEJAJJHHEBBBJJJGJJJCCCBAAADCEHIIFEHHBGF

Sample Output 2

330219020

Be sure to find the count modulo 998244353.

Problem Statement

There are N items.
Each of these is one of a pull-tab can, a regular can, or a can opener.
The i-th item is described by an integer pair (T_i, X_i) as follows:

• If T_i = 0, the i-th item is a pull-tab can; if you obtain it, you get a happiness of X_i.
• If T_i = 1, the i-th item is a regular can; if you obtain it and use a can opener against it, you get a happiness of X_i.
• If T_i = 2, the i-th item is a can opener; it can be used against at most X_i cans.

Find the maximum total happiness that you get by obtaining M items out of N.

Constraints

• 1 \leq M \leq N \leq 2 \times 10^5
• T_i is 0, 1, or 2.
• 1 \leq X_i \leq 10^9
• All input values are integers.

Sample Input 1

8 4
0 6
0 6
1 3
1 5
1 15
2 1
2 10
2 100

Sample Output 1

27

If you obtain the 1-st, 2-nd, 5-th, and 7-th items, and use the 7-th item (a can opener) against the 5-th item, you will get a happiness of 6 + 6 + 15 = 27.
There are no ways to obtain items to get a happiness of 28 or greater, but you can still get a happiness of 27 by obtaining the 6-th or 8-th items instead of the 7-th in the combination above.

Sample Input 2

5 5
1 5
1 5
1 5
1 5
1 5

Sample Output 2

0

Sample Input 3

12 6
2 2
0 1
0 9
1 3
1 5
1 3
0 4
2 1
1 8
2 1
0 1
0 4

Sample Output 3

30