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: Time Limit Exceeded)

import java.util.*;

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();

		HashMap<Integer,Integer> maps = new HashMap<>();
		int rem[][] = new int[D][H*W/D+1];

		for(int d=0;d<D;d++){
			for(int n=0;n<H*W/D+1;n++){
				rem[d][n] = -1;
			}
		}

		for(int h=0;h<H;h++){
			for(int w=0;w<W;w++){
				int val = sc.nextInt();

				rem[val%D][val/D]= h*W + w;

			}
		}

		for(int d=0;d<D;d++){
			for(int n=rem[d].length-1;n>=0;n--){
				if(n==0) rem[d][n] = 0;
				else	rem[d][n] = res(rem[d][n]/W - rem[d][n-1]/W , rem[d][n]%W - rem[d][n-1]%W);
			}
		}


		int Q = sc.nextInt();
		int ans[] = new int[Q];

		for(int q=0;q<Q;q++){
			int L = sc.nextInt();
			int R = sc.nextInt();
			if(L==R){
				ans[q] = 0;
				continue;
			}

			int mp=0;
			int px=-1,py=-1;
			for(int n=1;n<(R-L)/D+1;n++){
				mp += rem[L%D][L/D+n];
				
			}

			ans[q] = mp;

		}

		for(int a : ans){
			System.out.println(a);
		}

	}

	private static int res(int h,int w){
		return Math.abs(h) + Math.abs(w);
	}
}