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>
#include<math.h>
int main()
{
    int h, w;
    long d;
    long a[300][300];
    long q;
    long l, r;
    long i, j, k;
    int x[301], y[301];
    long dp[10000][10000];
    scanf("%d %d %ld", &h, &w, &d);
    for (i = 0; i < 100000; i++)
        for (j = 0; j < 100000; j++)
            dp[i][j] = 1;
    for (i = 0; i < h; i++)
        for (j = 0; j < w; j++)
        {
            scanf("%ld", &a[i][j]);
            x[a[i][j]] = i;
            y[a[i][j]] = j;
        }
    scanf("%ld", &q);
    long ans;
    int n;
    for (k = 0; k < q; k++)
    {
        scanf("%ld %ld", &l, &r);
        ans = 0;
        for (i = l; i < r; i += d)
        {
            n = 0;
            for (j = i + d; j <= r; j += d)
            {
                if (dp[i][j] != 1)
                {
                    ans += dp[i][j];
                    i = j;
                    n = 1;
                    break;
                }
            }
            if (n == 0)
                ans += (abs(x[i] - x[i + d]) + abs(y[i] - y[i + d]));
        }
            printf("%ld\n", ans);
            dp[l][r] = ans;
    }
    return 0;
}