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: Runtime Error)

h,w,d = list(map(int,input().split(" ")))
numbers = {}
flag = 1
if h==1 and w==1:
    flag = 0

for hh in range(h):
    hh_numbers = list(map(int,input().split(" ")))
    for ww in range(w):
        numbers[hh_numbers[ww]] = [hh,ww]
ruiseki = [[0]*(h*w//d+1) for i in range(d)]  # mod=1,2....,0

for i in range(d):
    if flag == 0:
        break
    for j in range(h*w//d+1):
        bannme = d*j+i+1
        if bannme > h*w:
            break
        ruiseki[i][j] = numbers[bannme]
# print(ruiseki)

ruiseki2 = [[0]*(h*w//d) for i in range(d)]
for i in range(d):
    if flag == 0:
        break
    for j in range(len(ruiseki[i])-1):
        ruiseki2[i][j] = abs(ruiseki[i][j+1][1] - ruiseki[i][j][1]) + abs(ruiseki[i][j+1][0] - ruiseki[i][j][0])
# print(ruiseki2)
n = int(input())

ruiseki3 = [[0]*(h*w//d) for i in range(d)]
for i in range(d):
    if flag == 0:
        break
    ruiseki3[i][0] = ruiseki2[i][0]
    for j in range(1,len(ruiseki2[i])):
        ruiseki3[i][j] = ruiseki3[i][j-1] + ruiseki2[i][j]
# print(ruiseki3)

for i in range(n):
    if flag == 0:
        print(0)
        continue
    l,r = list(map(int,input().split(" ")))
    if l==r:
        print(0)
        continue
    amari = l%d
    n_l = (l-amari)//d
    n_r = (r-amari)//d
    if amari==0:
        amari=d
        n_l = n_l - 1
        n_r = n_r - 1
    # print(n_l,n_r,amari)
    if n_l == 0:
        print(ruiseki3[amari-1][n_r-1])
        continue
    print(ruiseki3[amari-1][n_r-1]-ruiseki3[amari-1][n_l-1])