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;

int abs(int a){
    return a > 0? a : -a;
}

int magic_power(point from, point to){
    return abs(from.x-to.x) + abs(from.y-to.y);
}

int main(){
    int H, W, D;
    int x, y;

    scanf("%d %d %d", &H, &W, &D);
    point A[H * W];
    int temp;

    for(y = 0; y < H; ++y){
        for(x = 0; x < W; ++x){
            scanf("%d", &temp);
            A[temp - 1].x = x;
            A[temp - 1].y = y;
        }
    }

    int Q, L, R;
    int ans = 0;
    unsigned long int answers[H * W][H * W];

    for(y = 0; y < H * W; ++y){
        for(x = 0; x < H * W; ++x){
            answers[y][x] = 0;
        }
    }

    scanf("%d", &Q);
    for(x = 0; x < Q; ++x){
        ans = 0;
        scanf("%d %d", &L, &R);

        int firstL = L;
        if(L == R && answers[L - 1][R - 1] != 0){
            ans = answers[L - 1][R - 1];
        }else{
            while(L < R){
                if(answers[L - 1][L + D - 1] == 0){
                    answers[L - 1][L + D - 1] = magic_power(A[L - 1], A[L + D - 1]);
                }
                int s;
                for(s = firstL; s <= L; s+=D){
                    if(answers[firstL - 1][L + D - 1] != 0 && answers[firstL - 1][s - 1]!= 0){
                        answers[s - 1][L + D - 1] = answers[firstL - 1][L + D - 1] - answers[firstL - 1][s - 1];
                    }
                }

                ans += answers[L - 1][L + D - 1];
                answers[firstL - 1][L + D - 1] = ans;
                L+=D;
            }
        }

        printf("%d\n", ans);

    }
    return 0;
}