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 Python (3.4.3) (judge verdict: Accepted)

def solve(string):
    h, w, d, *a = map(int, string.split())
    a, q, lr = a[:h * w], a[h * w], a[h * w + 1:]
    n = h * w
    index = [0 for _ in range(n)]
    for i, _a in enumerate(a):
        index[_a - 1] = i
    # index = [a.index(i + 1) for i in range(h * w)]
    diff = [0] * d + [
        abs(i0 // w - i1 // w) + abs(i0 % w - i1 % w) for i0, i1 in zip(index, index[d:])
    ]
    costs = []
    for i in range(n):
        if i < d:
            costs.append(diff[i])
        else:
            costs.append(diff[i] + costs[i - d])
    return "\n".join([str(costs[r - 1] - costs[l - 1]) for l, r in zip(lr[::2], lr[1::2])])


if __name__ == '__main__':
    n, m, d = map(int, input().split())
    ins = '{} {} {}\n'.format(n, m, d) + '\n'.join([input() for _ in range(n)])
    n = int(input())
    print(solve(ins + '\n{}\n'.format(n) + '\n'.join([input() for _ in range(n)])))