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.AbstractMap.SimpleEntry;
import java.util.HashMap;
import java.util.Map;
import java.util.Map.Entry;
import java.util.Scanner;

public class Main {
	static Map<Integer, Entry<Integer, Integer>> map = new HashMap<>();
	static int[][] lrGrid;
	static int d;
	static Map<Integer, Integer> memoMap = new HashMap<>();
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int h = sc.nextInt();
		int w = sc.nextInt();
		d = sc.nextInt();
		int[][] aGrid = new int[h][w];
		for(int i = 0; i < h;i++){
			for(int  j = 0; j < w; j++){
				map.put(sc.nextInt(), new SimpleEntry<>(i, j));
			}
		}
		int q = sc.nextInt();
		lrGrid = new int[q][2];
		for(int i = 0; i < q; i++){
			lrGrid[i][0] = sc.nextInt();
			lrGrid[i][1] = sc.nextInt();
		}
		int mp = 0;
		for(int i = 0; i< q;i++){
			System.out.println(move(lrGrid[i][1], lrGrid[i][0]));
		}
	}

	public static int move(int end, int now){
		if(now == end){
			return 0;
		}
		if(memoMap.containsKey(now)){
			return memoMap.get(now);
		}

		int mp = 0;
		Entry<Integer, Integer> e1 = map.get(now);
		Entry<Integer, Integer> e2 = map.get(now+d);
		mp += Math.abs(e1.getKey() -e2.getKey()) + Math.abs(e1.getValue() - e2.getValue());
		memoMap.put(now, mp);
		mp += move(end, now+d);
		return mp;
	}
}