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())
A = [[]]
for i in range(H):
  A.append([0]+list(map(int,input().split())))
la = [[] for o in range(H*W+1)]
for i in range(1,H+1):
  for j in range(1,W+1):
    la[A[i][j]].append(i)
    la[A[i][j]].append(j)
Q = int(input())
q = []
for i in range(Q):
  q.append(list(map(int,input().split())))

l = [[0]+[0 for i in range((H*W-j)//D)] for j in range(D)]
#あまり0は特別扱い
i = 0
v = l[i]
for j in range(1,len(l[0])-1):
  mae = i + D*j
  ato = i + D*(j+1)
  v[j+1] = v[j] + abs(la[mae][0]-la[ato][0]) + abs(la[mae][1]-la[ato][1])
#あまり1~D-1まで
for i in range(1,D):
  v = l[i]
  for j in range(len(v)-1):
    mae = i + D*j
    ato = i + D*(j+1)
    v[j+1] = v[j] + abs(la[mae][0]-la[ato][0]) + abs(la[mae][1]-la[ato][1])

for i in range(Q):
  L,R = q[i][0],q[i][1]
  amari = L%D
  haji = (L-amari)//D
  owari = (R-amari)//D  
  print(l[amari][owari]-l[amari][haji])