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.util.*;
import java.util.stream.Collectors;
import java.io.*;
import java.nio.charset.StandardCharsets;

public class Main {
	public static void main(String[] args) throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);
		Main ins = new Main(in);
		ins.calc();
		ins.showResult();
	}

	static class Tuple {
		int h, w;

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

	int H, W, D;
	int[][] A;
	int Q;
	int[] L, R;
	int[] distMat;
	Map<Integer, Tuple> map;

	Main(BufferedReader in) throws IOException {
		String[] tokens = in.readLine().split(" ");
		H = Integer.parseInt(tokens[0]);
		W = Integer.parseInt(tokens[1]);
		D = Integer.parseInt(tokens[2]);
		A = new int[H][W];
		for (int i = 0; i < H; ++i) {
			tokens = in.readLine().split(" ");
			for (int j = 0; j < W; ++j) {
				A[i][j] = Integer.parseInt(tokens[j]) - 1;
			}
		}
		Q = Integer.parseInt(in.readLine());
		L = new int[Q];
		R = new int[Q];
		for (int i = 0; i < Q; ++i) {
			tokens = in.readLine().split(" ");
			L[i] = Integer.parseInt(tokens[0]) - 1;
			R[i] = Integer.parseInt(tokens[1]) - 1;
		}
		map = new HashMap<>();
		for (int i = 0; i < H; ++i) {
			for (int j = 0; j < W; ++j) {
				Tuple tuple = new Tuple(i, j);
				map.put(A[i][j], tuple);
			}
		}

		distMat = new int[H * W];
		for (int i = 0; i < D; ++i) {
			int prev = i;
			int next = i + D;
			distMat[i] = 0;

			while (next < H * W) {
				Tuple prevTuple = map.get(prev);
				Tuple nextTuple = map.get(next);
				distMat[next] = distMat[prev] + Math.abs(nextTuple.h - prevTuple.h)
						+ Math.abs(nextTuple.w - prevTuple.w);
				prev = next;
				next += D;
			}
		}
	}

	void calc() {
		for (int i = 0; i < Q; ++i) {
			int cost = distMat[R[i]] - distMat[L[i]];
			System.out.println(cost);
		}

	}

	void showResult() {
	}
}