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: Memory Limit Exceeded)


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

public class Main {
    public static void main(final String[] args) {
        final Scanner scanner = new Scanner(System.in);
        final int h = scanner.nextInt();
        final int w = scanner.nextInt();
        final int d = scanner.nextInt();

        final Point[] points = new Point[h * w + 1];
        for (int i = 1; i <= h; i++) {
            for (int j = 1; j <= w; j++) {
                points[scanner.nextInt()] = new Point(i, j);
            }
        }

        final int[][] movingMap = new int[d + 1][h * w + 1];
        for (int i = 1; i <= d; i++) {
            int tmp = 0;
            for (int j = i + d; j <= h * w; j += d) {
                final Point previousPoint = points[j - d];
                final Point currentPoint = points[j];
                tmp += Math.abs(previousPoint.x - currentPoint.x) + Math.abs(previousPoint.y - currentPoint.y);
                movingMap[i][j] = tmp;
            }
        }

        final int q = scanner.nextInt();
        for (int i = 0; i < q; i++) {
            final int l = scanner.nextInt();
            final int r = scanner.nextInt();
            final int begin = l % d == 0 ? d : l % d;

            System.out.println(movingMap[begin][r] - movingMap[begin][l]);
        }
    }

    static class Point {
        final int x;
        final int y;

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