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.io.*;
import java.util.*;

public class Main {
  static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
  static int[][] arr, indices;
  static int[] prefix;
  
	public static void main (String[] args) throws IOException {    
    String[] first = br.readLine().split(" ");
    int H = Integer.parseInt(first[0]);
    int W = Integer.parseInt(first[1]);
    int D = Integer.parseInt(first[2]);
    
    arr = new int[H][W];
    indices = new int[H*W+1][2];
    prefix = new int[H*W+1];
    
    for(int i = 0; i < H; i++) {
      String[] line = br.readLine().split(" ");
      for(int j = 0; j < W; j++) {
        int curr = Integer.parseInt(line[j]);
        arr[i][j] = curr;
        indices[curr] = new int[]{i+1, j+1};
      }
    }
      
    for(int j = 1; j <= H*W; j++) {
      if(j + D <= H*W) {
        int[] a = indices[j];
        int[] b = indices[j+D];
        int curr = Math.abs(b[0]-a[0]) + Math.abs(b[1]-a[1]);
        if(j - D <= 0) {
          prefix[j] = curr;
        }
        else {
          prefix[j] = prefix[j-D] + curr;
        }
      }
    }
    
    int Q = Integer.parseInt(br.readLine());
    
    for(int i = 0; i < Q; i++) {
      String[] line = br.readLine().split(" ");
      int L = Integer.parseInt(line[0]);
      int R = Integer.parseInt(line[1]);
      
      int ans = 0;
      
      if(R < D) {}
      else if(L < D) {
        ans = prefix[R-D];
      }
      else {
        ans = prefix[R-D]-prefix[L-D]; 
      }
      
      bw.write(ans + "\n");
    }
    
    bw.close();
	}
}