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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;


public class Pair
{
	public int I { get; private set; }
	public int J { get; private set; }

	public Pair(int i, int j)
	{
		I = i;
		J = j;
	}
}


public class D
{
	public static void Main()
	{
		string[] args;
		
		args = Console.ReadLine().Split(' ');
		int H = Int32.Parse(args[0]);
		int W = Int32.Parse(args[1]);
		int D = Int32.Parse(args[2]);

		Pair[] pairs = new Pair[H * W + 1];
		for(int i = 1; i <= H; i++)
		{
			args = Console.ReadLine().Split(' ');
			for(int j = 1; j <= W; j++)
				pairs[Int32.Parse(args[j-1])] = new Pair(i,j);
		}

		int Q = Int32.Parse(Console.ReadLine());
		int[] L = new int[Q];
		int[] R = new int[Q];
		for(int i = 0; i < Q; i++)
		{
			args = Console.ReadLine().Split(' ');
			L[i] = Int32.Parse(args[0]);
			R[i] = Int32.Parse(args[1]);
		}

		int[] csum = new int[H * W + 1];  // csum[1] = ... = csum[D] = 0
		for(int i = D + 1; i <= H * W; i++)
		{
			Pair current = pairs[i];
			Pair prev = pairs[i - D];
			int mp = Math.Abs(current.I - prev.I) + Math.Abs(current.J - prev.J);
			csum[i] = csum[i - D] + mp;
		}

		for(int i = 0; i < Q; i++)
			Console.WriteLine(csum[R[i]] - csum[L[i]]);
	}	
}