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.*;

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();
		Map<Integer, Integer> hs = new HashMap<>();
		Map<Integer, Integer> ws = new HashMap<>();

		for (int i = 0; i < h; i++) {
			for (int j = 0; j < w; j++) {
				int x = sc.nextInt() - 1;
				hs.put(x, i);
				ws.put(x, j);
			}
		}

		int maxSteps = (h * w / d) + 1;
		int[][] costs = new int[d][maxSteps];

		for (int i = 0; i < d; i++) {
			int ihPrev = hs.get(i);
			int iwPrev = ws.get(i);
			int steps = 1;
			while (steps < maxSteps) {
				if (i + steps * d > h * w - 1) break;
				int ih = hs.get(i + steps * d);
				int iw = ws.get(i + steps * d);
				costs[i][steps] = Math.abs(ih - ihPrev) + Math.abs(iw - iwPrev) + costs[i][steps - 1];
				ihPrev = ih;
				iwPrev = iw;
				steps++;
			}
		}

		int q = sc.nextInt();
		StringBuilder sb = new StringBuilder();
		while (q-- > 0) {
			int l = sc.nextInt() - 1;
			int r = sc.nextInt() - 1;
			sb.append(costs[r % d][r / d] - costs[l % d][l / d]);
			sb.append("\n");
		}

		System.out.print(sb.toString());
	}
}