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)

H, W, D = map(int,input().split())
dist = [0]*(H*W+1)#dist[i]はiからi+Dまでの距離
pos = [[0,0] for i in range(H*W+1)]
for i in range(H):
  A = list(map(int,input().split()))
  for j in range(W):
    pos[A[j]] = [i+1, j+1]
    
for i in range(H*W+1-D):
  dist[i] = abs(pos[i][0]-pos[i+D][0])+abs(pos[i][1]-pos[i+D][1])

distances = [[] for i in range(D)]#あまりがiの距離
for i in range(1,H*W+1-D):
  distances[i%D]+=[dist[i]]
distances2 = [[0] for i in range(D)]#累積和に直す
for i in range(D):
  for j in range(len(distances[i])):
    distances2[i]+=[distances2[i][-1]+distances[i][j]]

Q = int(input())
for i in range(Q):
  L, R = map(int, input().split())
  l, r = (L-1)//D, (R-1)//D
  print(distances2[L%D][r]-distances2[L%D][l])