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 (Clang 3.8.0) (judge verdict: Runtime Error)

#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <string>
#include <queue>
#include <stack>
using namespace std;

int main(){
  int H, W, D, Q;
  cin >> H >> W >> D;

  vector<vector<long>> v(H, vector<long>(W));
  for (int i=0; i<H; i++)
    for (int l=0; l<W; l++)
      cin >> v[i][l];

  cin >> Q;
  vector<long> L(Q);
  vector<long> R(Q);
  for (int i=0; i<Q; i++)
    cin >> L[i] >> R[i];

  vector<pair<int,int>> vr(H*W+1);
  for (int i=0; i<H; i++) {
    for (int k=0; k<W; k++) {
      vr[v[i][k]] = make_pair(i+1, k+1);
    }
  }

  vector<vector<int>> memo(H*W+1, vector<int>(H*W+1, -1));
  for (int i=0; i<Q; i++) {
    if (L[i] == R[i]) {
      cout << 0 << endl;
      continue;
    }
    if (memo[L[i]][R[i]] != -1) {
      cout << memo[L[i]][R[i]] << endl;
      continue;
    }
    long res = 0;
    for (int k=L[i]+D; k<=R[i]; k+=D) {
      res += abs(vr[k].first - vr[k-D].first) + abs(vr[k].second - vr[k-D].second);
      memo[L[i]][k] = res;
    }
    cout << res << endl;
  }
}