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)

#include<stdio.h>

typedef struct{
    int x;
    int y;
} point;

point num2point[100000];
int point2num[400][400];
int cost[1<<14];

int h, w, d;
int q;
int l, r;

void init();
void test();
void calc();
int diff_abs(int a, int b);

int main()
{
    int i;

    init();

    for (i = 0; i < q; i++) {
        scanf("%d %d", &l, &r);
        printf("%d\n", cost[r]-cost[l]);
    }

    return 0;
}

void init()
{
    int i, j;
    scanf("%d %d %d", &h, &w, &d);

    for(i = 0; i < h; i++) for(j = 0; j < w; j++){
        scanf("%d", &point2num[i][j]);
        num2point[point2num[i][j]].x = i;
        num2point[point2num[i][j]].y = j;
    }

    scanf("%d", &q);

    calc();
}

void calc()
{
    int i;
    int x1, x2;
    int y1, y2;

    for (i = 1; i <= d; i++)
        cost[i] = 0;

    for (i = d+1; i <= h*w; i++){
        x1 = num2point[i].x;
        x2 = num2point[i-d].x;
        y1 = num2point[i].y;
        y2 = num2point[i-d].y;
        cost[i] = cost[i-d] 
            + diff_abs(x1, x2) + diff_abs(y1, y2);
    }
}

int diff_abs(int a, int b)
{
    return a > b ? a - b : b - a;
}