Score : $600$ points

问题描述

我们有一个 $N \times N$ 的网格。在这个网格中，从上到下第 $i$ 行、从左到右第 $j$ 列的方格被称为 $(i,j)$。

每个网格方格最多有一个棋子。

网格的状态由 $N$ 个字符串 $S_i$ 给出：

• 如果 $S_i$ 的第 $j$ 个字符是 O，表示 $(i,j)$ 上有一个棋子；
• 如果 $S_i$ 的第 $j$ 个字符是 X，表示 $(i,j)$ 上没有棋子。

给定一个整数 $M$，我们定义放置在 $(s,t)$ 的棋子 $P$ 覆盖了方格 $(u,v)$，当且仅当以下所有条件都满足：

• $s \le u \le N$
• $t \le v \le N$
• $(u - s) + \frac{(v - t)}{2} < M$

对于 $Q$ 个不同的方格 $(X_i,Y_i)$，找出覆盖这些方格的棋子数量。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

We have an $N \times N$ grid. The square at the $i$-th row from the top and $j$-th column from the left in this grid is called $(i,j)$.
Each square of the grid has at most one piece.
The state of the grid is given by $N$ strings $S_i$:

• if the $j$-th character of $S_i$ is O, then $(i,j)$ has a piece on it;
• if the $j$-th character of $S_i$ is X, then $(i,j)$ has no piece on it.

You are given an integer $M$. Using this $M$, we define that a piece $P$ placed at $(s,t)$ covers a square $(u,v)$ if all of the following conditions are satisfied:

• $s \le u \le N$
• $t \le v \le N$
• $(u - s) + \frac{(v - t)}{2} < M$

For each of $Q$ squares $(X_i,Y_i)$, find how many pieces cover the square.

Constraints

• $N$, $M$, $X_i$, $Y_i$, and $Q$ are integers.
• $1 \le N \le 2000$
• $1 \le M \le 2 \times N$
• $S_i$ consists of O and X.
• $1 \le Q \le 2 \times 10^5$
• $1 \le X_i,Y_i \le N$

Input

Input is given from Standard Input in the following format:

$N$ $M$

$S_1$

$S_2$

$\vdots$

$S_N$

$Q$

$X_1$ $Y_1$

$X_2$ $Y_2$

$\vdots$

$X_Q$ $Y_Q$

Output

Print $Q$ lines.
The $i$-th line ( $1 \le i \le Q$ ) should contain the number of pieces that covers $(X_i,Y_i)$ as an integer.

Sample Input 1

4 2
OXXX
XXXX
XXXX
XXXX
6
1 1
1 4
2 2
2 3
3 1
4 4

Sample Output 1

1
1
1
0
0
0

Only Square $(1,1)$ contains a piece, which covers the following # squares:

####
##..
....
....

Sample Input 2

5 10
OOOOO
OOOOO
OOOOO
OOOOO
OOOOO
5
1 1
2 3
3 4
4 2
5 5

Sample Output 2

1
6
12
8
25

Sample Input 3

8 5
OXXOXXOX
XOXXOXOX
XOOXOOXO
OXOOXOXO
OXXOXXOX
XOXXOXOX
XOOXOOXO
OXOOXOXO
6
7 2
8 1
4 5
8 8
3 4
1 7

Sample Output 3

5
3
9
14
5
3

update @ 2024/3/10 11:02:33