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.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[] posx = new int[w*h];
		int[] posy = new int[w*h];
		for(int y = 0; y < h; y++)
		{
			for(int x = 0; x < w; x++)
			{
				int cur = sc.nextInt()-1;
				posx[cur] = x;
				posy[cur] = y;
			}
		}
		
		for(int i = w*h-1; i>=0;i--)
		{
			
		}
		
//		long[][] sumdis = new long[d][((h*w)/d)+1];
		long[] sumdis = new long[h*w];
		for(int offset = 0; offset < d; offset++)
		{
			long curdis = 0;
			for(int x = offset+d; x < h*w; x += d)
			{ //distance to here from 0!!!
				int disx = posx[x] - posx[x-d];
				if(disx<0)disx*=-1;
				int disy = posy[x] - posy[x-d];
				if(disy<0)disy*=-1;
				
				curdis += disx + disy;
				sumdis[x] = curdis;
			}
		}
		
		int q = sc.nextInt();
		StringBuilder sb = new StringBuilder();
		
		for(int i = 0; i < q; i++)
		{
			int l = sc.nextInt()-1;
			int r = sc.nextInt()-1;
			long an = sumdis[r] - sumdis[l];
			sb.append(an + "\n");
		}
		System.out.print(sb);
	}

}