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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <cassert>
#include <cstdio>
#include <algorithm>
#include <iostream>
#include <vector>

using namespace std;

int
main()
{
    int h, w, d;
    assert(scanf("%d %d %d", &h, &w, &d) == 3);
    vector<pair<int, int> > num2pos(h * w + 1);
    for (int y = 0; y < h; y++) {
        for (int x = 0; x < w; x++) {
            int num;
            assert(scanf("%d", &num) == 1);
            num2pos[num] = make_pair(x, y);
        }
    }

    int q;
    assert(scanf("%d", &q) == 1);
    for (int i = 0; i < q; i++) {
        unsigned int power = 0;
        int start, end;
        assert(scanf("%d %d", &start, &end) == 2);
        while (start != end) {
            pair<int, int> pos1 = num2pos[start];
            start = start + d;
            pair<int, int> pos2 = num2pos[start];
            power += abs(get<0>(pos2) - get<0>(pos1)) +
                abs(get<1>(pos2) - get<1>(pos1));
        }
        printf("%u\n", power);
    }
}