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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>

// 内部定数
#define D_POS_MAX		90000									// 最大位置数

// 内部構造体 - 位置情報
typedef struct Pos {
	int miX, miY;												// 座標
} Pos;

// 内部変数
static Pos sz1Pos[D_POS_MAX + 5];								// 位置情報
static int si1Sum[D_POS_MAX + 5];								// 総和

// 内部変数 - テスト用
#ifdef D_TEST
	static int siRes;
	static FILE *szpFpT, *szpFpA;
#endif

// 実行メイン
int
fMain(
	int piTNo					// <I> テスト番号 1～
)
{
	int i, j;
	char lc1Buf[1024], lc1Out[1024];

	// テストファイルオープン
#ifdef D_TEST
	sprintf(lc1Buf, ".\\Test\\T%d.txt", piTNo);
	szpFpT = fopen(lc1Buf, "r");
	sprintf(lc1Buf, ".\\Test\\A%d.txt", piTNo);
	szpFpA = fopen(lc1Buf, "r");
	siRes = 0;
#endif

	// 高さ・幅・移動量取得
	int liH, liW, liMv;
#ifdef D_TEST
	fgets(lc1Buf, sizeof(lc1Buf), szpFpT);
#else
	fgets(lc1Buf, sizeof(lc1Buf), stdin);
#endif
	sscanf(lc1Buf, "%d%d%d", &liH, &liW, &liMv);

	// 位置情報取得
	for (i = 1; i <= liH; i++) {
		for (j = 1; j <= liW; j++) {
			int liNo;
#ifdef D_TEST
			fscanf(szpFpT, "%d", &liNo);
#else
			fscanf(stdin, "%d", &liNo);
#endif
			sz1Pos[liNo].miX = j;
			sz1Pos[liNo].miY = i;
		}
#ifdef D_TEST
		fgets(lc1Buf, sizeof(lc1Buf), szpFpT);
#else
		fgets(lc1Buf, sizeof(lc1Buf), stdin);
#endif
	}

	// 総和セット
	for (i = 1; i <= liMv; i++) {

		// 初期位置
		si1Sum[i] = 0;

		// 順に移動
		int liFNo = i;
		int liTNo;
		while (1) {
			liTNo = liFNo + liMv;
			if (liTNo > D_POS_MAX) {
				break;
			}
			si1Sum[liTNo] = si1Sum[liFNo] + abs(sz1Pos[liTNo].miX - sz1Pos[liFNo].miX) + abs(sz1Pos[liTNo].miY - sz1Pos[liFNo].miY);
			liFNo = liTNo;
		}
	}

	// クエリ数取得
	int liQCnt;
#ifdef D_TEST
	fgets(lc1Buf, sizeof(lc1Buf), szpFpT);
#else
	fgets(lc1Buf, sizeof(lc1Buf), stdin);
#endif
	sscanf(lc1Buf, "%d", &liQCnt);

	// クエリ数でループ
	for (i = 0; i < liQCnt; i++) {

		// クエリ取得
		int liFNo, liTNo;
#ifdef D_TEST
		fgets(lc1Buf, sizeof(lc1Buf), szpFpT);
#else
		fgets(lc1Buf, sizeof(lc1Buf), stdin);
#endif
		sscanf(lc1Buf, "%d%d", &liFNo, &liTNo);

		// 合計取得
		int liSum = si1Sum[liTNo] - si1Sum[liFNo];

		// 結果表示
		sprintf(lc1Out, "%d\n", liSum);
#ifdef D_TEST
		fgets(lc1Buf, sizeof(lc1Buf), szpFpA);
		if (strcmp(lc1Buf, lc1Out)) {
			siRes = -1;
		}
#else
		printf("%s", lc1Out);
#endif
	}

	// テストファイルクローズ
#ifdef D_TEST
	fclose(szpFpT);
	fclose(szpFpA);
#endif

	// テスト結果
#ifdef D_TEST
	if (siRes == 0) {
		printf("OK %d\n", piTNo);
	}
	else {
		printf("NG %d\n", piTNo);
	}
#endif

	return 0;
}

int
main()
{

#ifdef D_TEST
	int i;
	for (i = D_TEST_SNO; i <= D_TEST_ENO; i++) {
		fMain(i);
	}
#else
	fMain(0);
#endif

	return 0;
}