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Contest: Task: Related: TaskF TaskH

Score : $600$ points

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

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

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