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.HashMap;
import java.util.Map;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int h = scanner.nextInt();
			int w = scanner.nextInt();
			int d = scanner.nextInt();
			Map<Integer, Point> map = new HashMap<>();
			IntStream.range(0, h)
					.forEach(i -> IntStream.range(0, w).forEach(j -> map.put(scanner.nextInt(), new Point(i, j))));
			// すべての結果を計算
			int[] result = new int[h * w + 1];
			IntStream.rangeClosed(0, d).forEach(i -> result[i] = 0);
			IntStream.rangeClosed(d + 1, h * w).forEach(i -> {
				Point now = map.get(i);
				Point prev = map.get(i - d);
				result[i] = result[i - d] + Math.abs(now.x - prev.x) + Math.abs(now.y - prev.y);
			});
			int q = scanner.nextInt();
			IntStream.range(0, q).forEach(i -> {
				int l = scanner.nextInt();
				int r = scanner.nextInt();
				System.out.println(result[r] - result[l]);
			});
		}
	}

	/**
	 * 座標データを格納するクラス
	 */
	static class Point {
		/** X座標 */
		final int x;
		/** Y座標 */
		final int y;

		Point(int x, int y) {
			this.x = x;
			this.y = y;
		}
	}
}