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: Time Limit Exceeded)

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

void set_pos(int** values, int H, int W, int* fpx, int* fpy, int target_value) {
    int fps = 0;
    for (int i = 0; i < H; i++) {
        for (int j = 0; j < W; j++) {
            if (values[i][j] == target_value) {
                *fpx = i;
                *fpy = j;
                fps = 1;
                break;
            }
        }
    if (fps) break;
    }
}

int main(void) {
    char buffer[20];
    if (fgets(buffer, 20, stdin) == NULL) {
        return 1;
    }
    int H = atoi(strtok(buffer, " "));
    int W = atoi(strtok(NULL, " "));
    int D = atoi(strtok(NULL, " "));

    char* buffer2 = malloc(sizeof(char)*W*6);
    int** a_values = malloc(sizeof(int*)*H);
    for (int i = 0; i < H; i++) {
        a_values[i] = malloc(sizeof(int)*W);
    }
    for (int i = 0; i < H; i++) {
        if (fgets(buffer2, W*6, stdin) != NULL) {
            a_values[i][0] = atoi(strtok(buffer2, " "));
            for (int j = 1; j < W; j++) {
                a_values[i][j] = atoi(strtok(NULL, " "));
            }
        }
    }

    int Q = atoi(fgets(buffer, 20 ,stdin));

    int *l_values = malloc(sizeof(int)*Q);
    int *r_values = malloc(sizeof(int)*Q);
    for (int i = 0; i < Q; i++) {
        if (fgets(buffer, 20, stdin) != NULL) {
            l_values[i] = atoi(strtok(buffer, " "));
            r_values[i] = atoi(strtok(NULL, " "));
        }
    }
    int fpx, fpy, fps;
    int old_fpx, old_fpy;
    int target_value, current_value, move_sum;
    for (int lr_num = 0; lr_num < Q; lr_num++) {
        fps = 0;
        move_sum = 0;
        current_value = l_values[lr_num];
        target_value  = r_values[lr_num];

        set_pos(a_values, H, W, &fpx, &fpy, current_value);

        while(current_value != target_value) {
            old_fpx = fpx;
            old_fpy = fpy;
            current_value += D;
            set_pos(a_values, H, W, &fpx, &fpy, current_value);
            move_sum += abs(fpx-old_fpx)+abs(fpy-old_fpy);
        }

        printf("%d\n", move_sum);
    }
    return 0;
}