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.awt.*;
import java.util.*;

import static java.lang.System.*;

public 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();

        Point[] numPoint = new Point[H * W + 1];
        for (int i = 1; i < H + 1; i++) {
            for (int j = 1; j < W + 1; j++) {
                numPoint[sc.nextInt()] = new Point(i, j);
            }
        }

        int Q = sc.nextInt();
        int[] L = new int[Q];
        int[] R = new int[Q];
        for (int i = 0; i < Q; i++) {
            L[i] = sc.nextInt();
            R[i] = sc.nextInt();
        }

        // 整数nに移動するまでに必要な魔力
        long[] accum = new long[H * W + 1];
        for (int n = D + 1; n < H * W + 1; n++) {
            accum[n] = accum[n - D] + calcMagic(numPoint[n - D], numPoint[n]);
        }

        for (int i = 0; i < Q; i++) {
            out.println(accum[R[i]] - accum[L[i]]);
        }
    }

    static long calcMagic(Point xy1, Point xy2){
        return Math.abs(xy1.x - xy2.x) + Math.abs(xy1.y - xy2.y);
    }
}