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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.awt.Point;
import java.util.Scanner;
public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        
        int H = sc.nextInt();
        int W = sc.nextInt();
        int D = sc.nextInt();
        int[] gridX = new int[H*W+1];
        int[] gridY = new int[H*W+1];
        int x1, y1, x2, y2;
        //Point[] grid = new Point[H*W+1];
        //Point p1, p2;
        int[] dp = new int[H*W+1];
        int k;
        
        for(int i = 1; i <= H; i++)
            for(int j = 1; j <= W; j++){
                k = sc.nextInt();
                //grid[sc.nextInt()] =  new Point(i,j);
                gridX[k] = i;
                gridY[k] = j;
            }
        
        int Q = sc.nextInt();
        int L, R;
        for(int i = 1; i <= D; i++){
            for(int j = i+D; j < dp.length; j+=D){
                //p1 = grid[j];
                //p2 = grid[j+D];
                x1 = gridX[j];
                y1 = gridY[j];
                x2 = gridX[j-D];
                y2 = gridY[j-D];
                //dp[j] = Math.abs(p2.x-p1.x) + Math.abs(p2.y-p1.y);
                dp[j] = Math.abs(x2-x1) + Math.abs(y2-y1);
                if(j > D)
                    dp[j] += dp[j-D];
            }
        }
        
        int res;
        while(Q-- > 0){
            res = 0;
            L = sc.nextInt();
            R = sc.nextInt();
            res = dp[R] - dp[L];
            System.out.println(res);
        }
    }
}