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: Time Limit Exceeded)

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

public class Main {

	public static void main(String[] args) {
		int h;			// 列
		int w;			// 行
		int d;			// 移動量
		int testNum;	// 実技試験を行う回数
		int magicPower;	// 消費する魔力
		int[] xy_Ary;	// マスのxy座標
		// 整数と対応するマスを保管するマップ
		HashMap<Integer, int[]> cellMap = new HashMap<>();

		// H・W・Dの値を標準入力から取得
		Scanner sc = new Scanner(System.in);
		h = sc.nextInt();
		w = sc.nextInt();
		d = sc.nextInt();

		// 標準入力で受け取った整数をキーにして、対応する座標の配列を保管
		for (int x = 1; x <= h; x++) {
			for (int y = 1; y <= w; y++) {
				xy_Ary = new int[2];
				xy_Ary[0] = x;
				xy_Ary[1] = y;
				cellMap.put(sc.nextInt(), xy_Ary);
			}
		}

		// 実技試験の回数分、LとRのペア配列をリストに追加
		testNum = sc.nextInt();
		for (int i = 0; i < testNum; i++) {
			int l = sc.nextInt();	// 初期値L
			int r = sc.nextInt();	// 目的地R
			int addL = l;			// j回移動したL
			magicPower = 0;

			// （目的地R - 初期値L） / 移動量D = 瞬間移動する回数
			for (int j = 0; j < (r - l) / d; j++, addL += d) { // D>0なので0割り算は発生しない
				if (l == r)
					break; // 同じ整数の場合は差を計算する必要が無いのでスキップ
				int[] start;
				int[] gall;
				start = cellMap.get(addL);
				gall = cellMap.get(addL + d);
				int x = gall[0] - start[0];
				int y = gall[1] - start[1];
				// 移動距離は絶対値なので、負の数の場合は符号を変える
				if (x < 0) {
					x *= -1;
				}
				if (y < 0) {
					y *= -1;
				}
				magicPower += (x + y);
			}
			// コンソールに答えを表示
			System.out.println(magicPower);

		}

		sc.close();

	}
}