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 (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int judge(int cur_L, int cur_R, int *L, int *R, int Q){
    int i = 0;

    for(i = 0; i <= Q; i ++){
        if(cur_L == L[i] && cur_R == R[i]){
            return i;
        }
    }
    return -1;
}

int main(void){
    int H, W, D;

    scanf("%d%d%d", &H, &W, &D);

    int **masu;

    masu = (int **) malloc(sizeof(int *) * H);

    int i, j;

    for(i = 0; i < H; i ++){
        masu[i] = (int *) malloc(sizeof(int) * W);

        for(j = 0; j < W; j ++){
            scanf("%d", masu[i] + j);
        }
    }
    int *masu_x = (int *) malloc(sizeof(int) * (H * W + 1));
    int *masu_y = (int *) malloc(sizeof(int) * (H * W + 1));

    for(i = 0; i < H; i ++){
        for(j = 0; j < W; j ++){
            masu_x[masu[i][j]] = j;
            masu_y[masu[i][j]] = i;
        }
    }
    int Q;

    scanf("%d", &Q);

    int *sum = (int *) malloc(sizeof(int) * Q);
    int *L = (int *) malloc(sizeof(int) * Q);
    int *R = (int *) malloc(sizeof(int) * Q);

    for(i = 0; i < Q; i ++){
        sum[i] = 0;

        scanf("%d%d", L + i, R + i);

        int index = judge(L[i], R[i], L, R, i - 1);

        if(index >= 0){
            sum[i] = sum[index];
            
            continue;
        }

        int x, y;
        int cur_L = L[i];
        x = masu_x[cur_L];
        y = masu_y[cur_L];

        while(cur_L < R[i]){
            int x2, y2;

            cur_L += D;

            x2 = masu_x[cur_L];
            y2 = masu_y[cur_L];

            sum[i] += abs(x2 - x) + abs(y2 - y);
            x = x2;
            y = y2;
        }
    }
    for(i = 0; i < Q - 1; i ++){
        printf("%d\n", sum[i]);
    }
    printf("%d", sum[Q - 1]);

    return 0;
}