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 9.2.1) (judge verdict: Time Limit Exceeded)


// D - Practical Skill Test

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
// const int INF = 2147483647;
// const ll INF = 9223372036854775807;
// const ll MOD = 1e9 + 7;

using POS = pair<int, int>;

int A[300][300];
unordered_map<int, POS> n_to_pos;
map<POS, int> LR_to_power;

int main() {
	int H, W, D;
	cin >> H >> W >> D;

	for (int i=0; i<H; i++) {
		for (int j=0; j<W; j++) {
			cin >> A[i][j];
			n_to_pos[A[i][j]] = make_pair(i, j);
		}
	}

	int Q;
	cin >> Q;

	vector<int> ans;

	for (int i=0; i<Q; i++) {
		int L, R;
		cin >> L >> R;
		POS LR = make_pair(L, R);

		if (LR_to_power[LR] > 0) {
			ans.push_back(LR_to_power[LR]);
			continue;
		}

		int power = 0;
		int r = R;
		POS L_pos = n_to_pos[L];
		POS R_pos = n_to_pos[R];
		while(1) {
			if (r == L) {
				LR_to_power[make_pair(L, R)] = power;
				ans.push_back(power);
				break;
			}

			int l = r - D;
			POS r_pos = n_to_pos[r];
			POS l_pos = n_to_pos[l];

			power += abs(l_pos.first - r_pos.first) + abs(l_pos.second - r_pos.second);
			LR_to_power[make_pair(l, R)] = power;
			r = l;
		}
	}

	for (int a : ans) {
		cout << a << endl;
	}

	return 0;
}