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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define rep2(i, m, n) for(int i = (int)(m); i < (int)(n); i++)
#define rep_inv(i, n, m) for(int i = (int)(n); i > (int)(m); i--)
using namespace std;
using ll = long long;
using vl = vector<ll>;
using vc = vector<char>;
using vvl = vector<vl>;
using vvc = vector<vc>;
using pll = pair<ll, ll>;
using vpll = vector<pll>;

int main(){
  ll H, W, D;
  cin >> H >> W >> D;
  ll A;
  vpll pos(H*W + 1);
  rep(i, H){
    rep(j, W){
      cin >> A;
      pos[A] = {i + 1, j + 1};
    }
  }
  ll Q;
  cin >> Q;
  vl L(Q), R(Q);
  rep(i, Q) cin >> L[i] >> R[i];

  vl cost(H*W + 1);

  rep2(i, 1, D + 1){
    cost[i] = 0;
    ll move = i + D;
    
    while(move <= H*W){
      cost[move] = cost[move - D] + abs(pos[move].first - pos[move - D].first) + abs(pos[move].second - pos[move - D].second);
      move += D;
    }
  }

  rep(i, Q) cout << cost[R[i]] - cost[L[i]] << endl;
  
  return 0;
}