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: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
	int[] ans = new int[90001];
	int L;
	int R;
	int d;
	int[] x = new int[900001];
	int[] y = new int[900001];
	void run() {
		Scanner sc = new Scanner(System.in);
		int h = sc.nextInt();
		int w = sc.nextInt();
		d = sc.nextInt();

		for(int i = 0; i < h; i++) {
			for(int j = 0; j < w; j++) {
				int tmp = sc.nextInt();
				x[tmp] = i;
				y[tmp] = j;
			}
		}
		int q = sc.nextInt();

		for(int i = 0; i < q; i++) {
			L = sc.nextInt();
			R = sc.nextInt();
			System.out.println(dfs(L));
		}
		sc.close();
	}
	
	int dfs(int L) {
		if(ans[L] != 0 || L == R) {
			return ans[L];
		}else {
			return ans[L] += Math.abs(x[L]-x[L+d])+Math.abs(y[L]-y[L+d])+dfs(L+d);
		}
	}

	void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	long combination(int n, int r, int m) { //nCr mod m
		long[][] Combination = new long[n + 1][n + 1];
		for (int i = 0; i <= n; i++) {
			Combination[i][0] = 1;
			for (int j = 1; j <= i; j++) {
				Combination[i][j] = (Combination[i - 1][j - 1] + Combination[i - 1][j]) % m;
			}
		}
		return Combination[n][r];
	}

	int gcd(int a, int b) {
		if (a < b) {
			int c = a;
			a = b;
			b = c;
		}
		if (b == 0)
			return a;
		else
			return gcd(b, a % b);
	}

	public static void main(String[] args) {
		new Main().run();
	}
}