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 C (GCC 5.4.1) (judge verdict: Runtime Error)

/*
 AtCoder XXX 000
 */
 
#include <stdio.h>
#include <math.h>

int main(void){
	
	int n;
	int width,height,dist;
	int a[60000];
	int q;
	int l,r;
	int i,j,k;
	int from_x,from_y;
	int goto_x,goto_y;
	int maryoku;
	
	scanf("%d",&height);
	scanf("%d",&width);
	scanf("%d",&dist);
	
	for(j=0; j<height; j++) for(i=0; i<width; i++){
		scanf("%d",&n);
		a[n] = j*width + i;
	}
	
	scanf("%d",&q);
	
	for(k=0; k<q; k++){
		maryoku=0;
		scanf("%d",&l);
		scanf("%d",&r);
		
		from_x = a[l]%width;
		from_y = (a[l] - from_x);
		
		while(l != r){
			l += dist;
			goto_x = a[l]%width;
			goto_y = (a[l] - from_x);
			maryoku += (int)fabs(from_x - goto_x);
			maryoku += (int)fabs(from_y - goto_y);
			from_x = goto_x;
			from_y = goto_y;
		}
		printf("%d\n",maryoku);
	}
	
	return 0;
}