Problem:
Score : 400 points

Problem Statement

We have a grid with H rows and W columns. The square at the i-th row and the j-th column will be called Square (i,j).

The integers from 1 through H×W are written throughout the grid, and the integer written in Square (i,j) is A_{i,j}.

You, a magical girl, can teleport a piece placed on Square (i,j) to Square (x,y) by consuming |x-i|+|y-j| magic points.

You now have to take Q practical tests of your ability as a magical girl.

The i-th test will be conducted as follows:

Initially, a piece is placed on the square where the integer L_i is written.

Let x be the integer written in the square occupied by the piece. Repeatedly move the piece to the square where the integer x+D is written, as long as x is not R_i. The test ends when x=R_i.

Here, it is guaranteed that R_i-L_i is a multiple of D.

For each test, find the sum of magic points consumed during that test.

Constraints

1 \leq H,W \leq 300

1 \leq D \leq H×W

1 \leq A_{i,j} \leq H×W

A_{i,j} \neq A_{x,y} ((i,j) \neq (x,y))

1 \leq Q \leq 10^5

1 \leq L_i \leq R_i \leq H×W

(R_i-L_i) is a multiple of D.

Input

Input is given from Standard Input in the following format:

H W D
A_{1,1} A_{1,2} ... A_{1,W}
:
A_{H,1} A_{H,2} ... A_{H,W}
Q
L_1 R_1
:
L_Q R_Q

Output

For each test, print the sum of magic points consumed during that test.

Output should be in the order the tests are conducted.

Sample Input 1

3 3 2
1 4 3
2 5 7
8 9 6
1
4 8

Sample Output 1

5

4 is written in Square (1,2).

6 is written in Square (3,3).

8 is written in Square (3,1).

Thus, the sum of magic points consumed during the first test is (|3-1|+|3-2|)+(|3-3|+|1-3|)=5.

Sample Input 2

4 2 3
3 7
1 4
5 2
6 8
2
2 2
2 2

Sample Output 2

0
0

Note that there may be a test where the piece is not moved at all, and there may be multiple identical tests.

Sample Input 3

5 5 4
13 25 7 15 17
16 22 20 2 9
14 11 12 1 19
10 6 23 8 18
3 21 5 24 4
3
13 13
2 10
13 13

Sample Output 3

0
5
0

Solution in PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
fscanf(STDIN, "%d %d %d", $h, $w, $d);

$a = [];
for ($i = 0; $i < $h; $i++) {
	$line = explode(" ", fgets(STDIN));
	for ($j = 0; $j < $w; $j++) {
		$key = (int)$line[$j];
		$a[$key] = [$j, $i];
	}
}

fscanf(STDIN, "%d", $q);

$memo = [];
for ($k = 0; $k < $q; $k++) {
	fscanf(STDIN, "%d %d", $l, $r);

	if (isset($memo[$l][$r])) {
		echo $memo[$l][$r], "\n";
		continue;
	}
	$beforeL = $l;
	$consumed = 0;
	while ($l < $r) {
		if (isset($memo[$l][$r])) {
			$consumed += $memo[$l][$r];
			$l += $d;
			continue;
		}
		$before = $a[$l];
		$after = $a[$l + $d];
		$consume = (($before[0] > $after[0])? ($before[0]-$after[0]) : ($after[0] - $before[0]))
			+ (($before[1] > $after[1])? ($before[1]-$after[1]) : ($after[1] - $before[1]));
		$memo[$l][$l + $d] = $consume;
		$l += $d;
		$consumed += $consume;
	}
	$memo[$beforeL][$r] = $consumed;
	echo $consumed, "\n";
}
var_dump($memo);