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

#define LINE_BUF_SIZE 256

int main(){

    long int i,j,k;
    int H,W;
    long int D;
    char line[LINE_BUF_SIZE];
    
    fgets(line,sizeof(line),stdin);
    sscanf(line,"%d %d %ld", &H,&W,&D);

    long int **A = malloc(sizeof(long int *)*(H+1));
    long int *X = malloc(sizeof(long int)* ((H*W+1)));   
    long int *Y = malloc(sizeof(long int)* ((H*W+1)));   

    for(i=0;i<H;i++){
        A[i] = malloc(sizeof(long int)*(W+1));
        for(j=0;j<W;j++){
            
            scanf("%ld ",&A[i][j]);
                
            X[ (A[i][j]) ] = i;
            Y[ (A[i][j]) ] = j;            
    
        }
    }

    long int Q;

    fgets(line,sizeof(line),stdin);
    sscanf(line,"%ld", &Q);

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

    for(i=0;i<Q;i++){
        fgets(line,sizeof(line),stdin);
        sscanf(line,"%ld %ld",&L[i],&R[i]);
    }

    /*ここまで初期値の入力*/

    long int ans=0;

    for(k=0;k<Q;k++){

    i = 0;
    long int p;

    p = L[k];

        while(p+D <= R[k]){
            ans += fabs(X[p]-X[p+D])+fabs(Y[p]-Y[p+D]);
            p += D;
        }

        printf("%ld\n",ans);
        ans = 0;

    }

    return 0;

}