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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			long[] hwd = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
			long h = hwd[0];
			long w = hwd[1];
			long d = hwd[2];

			Tuple<long, long>[] a = new Tuple<long, long>[h * w];
			for (int i = 0; i < h; i++) {
				long[] aa = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
				for (int j = 0; j < w; j++) {
					a[aa[j] - 1] = new Tuple<long, long>(i + 1, j + 1);
				}

			}

			long[] p = new long[h * w];
			for (int i = 0; i < h * w; i++) {
				if (i / d == 0) {
					p[i] = 0;
				} else {
					var dst = a[i];
					var src = a[i - d];
					p[i] = Math.Abs(src.Item2 - dst.Item2) + Math.Abs(src.Item1 - dst.Item1)
						+ p[i - d];
				}
			}

			long q = long.Parse(Console.ReadLine());
			for (int i = 0; i < q; i++) {
				long[] lr = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
				Console.WriteLine(p[lr[1] - 1] - p[lr[0] - 1]); 
			}
		}
	}
}