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>
#define MAX 500
#define QM 100100

int h,w,d;
int bs[MAX][MAX];

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

typedef struct LIST{
    int x,y;
}list;


list idx[MAX*MAX];

void make_list(){
    int i,j;
    for(i=1;i<=h;i++){
        for(j=1;j<=w;j++){
            idx[bs[i][j]].x=i;
            idx[bs[i][j]].y=j;
        }
    }
}

void search(int key,int * x,int*  y){
    *x=idx[key].x;
    *y=idx[key].y;
}
    

int calc(int A,int B){
        int xa,xb,ya,yb;
        int res;
        search(A,&xa,&ya);
        search(B,&xb,&yb);
        res=abs(xa-xb)+abs(ya-yb);
        return res;
    }
    
    int main(void){
        //puts("H W D");
        scanf("%d%d%d",&h,&w,&d);
        //puts("Base");
        int i,j;
        for(i=1;i<=h;i++){
            for(j=1;j<=w;j++){
                scanf("%d",&bs[i][j]);
            }
        }
        int Q;
        int L[QM],R[QM];
        //puts("Q");
        scanf("%d",&Q);
        //puts("L R");
        for(i=1;i<=Q;i++)    scanf("%d%d",&L[i],&R[i]);
        make_list();
        for(i=1;i<=Q;i++){
            int sum=0;
            while(L[i]!=R[i]){
                sum+=calc(L[i],L[i]+d);
                L[i]+=d;
            }
            printf("%d\n",sum);
        }
        return 0;
    }