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.math.BigDecimal;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        final Scanner scanner = new Scanner(System.in);
        solve(scanner);
    }


    static class Pos {
        int h;
        int w;

        Pos(int h, int w) {
            this.h = h;
            this.w = w;
        }

        int diff(Pos other) {
            return Math.abs(h - other.h) + Math.abs(w - other.w);
        }
    }

    static void solve(Scanner scanner) {
        int H = scanner.nextInt(), W = scanner.nextInt(), D = scanner.nextInt();
        scanner.nextLine();
        Map<Integer, Pos> m = new HashMap<>();
        for (int h = 0; h < H; h++){
            for (int w = 0; w < W; w++) {
                int n = scanner.nextInt();
                m.put(n, new Pos(h, w));
            }
        }
        scanner.nextLine();

        int[] cSum = new int[H * W + 1];
        for (int i = 1 + D; i < H * W + 1; i++) {
            cSum[i] = cSum[i - D] + m.get(i).diff(m.get(i - D));
        }

        int Q = Integer.parseInt(scanner.nextLine());
        for (int i = 0; i < Q; i++) {
            int[] q = Arrays.stream(scanner.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();
            System.out.println(cSum[q[1]] - cSum[q[0]]);
        }
    }

}