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 (2.7.6) (judge verdict: Runtime Error)

import sys
def get_read_func(fileobject):
    if fileobject == None :
        return raw_input
    else:
        return fileobject.readline

dp = {}

def dp_search(L, R, D, num_dic):
    global dp
    if (L, R) in dp:
        return dp[(L, R)]
    if L== R:
        return 0

    if L + D == R:
        now_pos = num_dic[L]
        next_pos = num_dic[R]
        dp[(L, R)] =  abs(next_pos[0] - now_pos[0]) + abs(next_pos[1] - now_pos[1])
        return dp[(L, R)]

    dp[(L, R)] = dp_search(L , R - D, D , num_dic) + dp_search(L + D , R, D , num_dic)

    return dp[(L, R)]


def main():
    if len(sys.argv) > 1:
        f = open(sys.argv[1])
    else:
        f = None
    read_func = get_read_func(f);
    input_raw = read_func().strip().split()
    [H, W, D] = [int(input_raw[0]), int(input_raw[1]), int(input_raw[2])]
    num_dic= {}
    for i in range(H):
        input_raw = read_func().strip().split()
        for j in range(W):
            num_dic[int(input_raw[j])] = (i, j)
    input_raw = read_func().strip().split()
    [Q] = [int(input_raw[0])]
    test_list = []
    for i in range(Q):
        input_raw = read_func().strip().split()
        test_list.append((int(input_raw[0]), int(input_raw[1])))

    dp = [[0 for i in range(H)] for j in range(W)]
    for test in test_list:
        L = test[0]
        R = test[1]
        print dp_search(L,R,D,num_dic)




if __name__ == '__main__':
    main()