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>

using namespace std;

typedef long long ll;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef pair<ll, ll> pii;
typedef vector<pii> vpii;

ll INF = (1ll << 32);
double EPS = 1e-4;

ll f(pii a, pii b) {
  return abs(a.first - b.first) + abs(a.second - b.second);
}

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

  vvi A(H, vi(W));
  for (ll i = 0; i < H; i++) {
    for (ll j = 0; j < W; j++) {
      cin >> A[i][j];
    }
  }

  ll Q;
  cin >> Q;

  vi L(Q), R(Q);
  for (ll i = 0; i < Q; i++) {
    cin >> L[i] >> R[i];
  }

  unordered_map<ll, pii> m1;
  for (ll i = 0; i < H; i++) {
    for (ll j = 0; j < W; j++) {
      m1[A[i][j]] = make_pair(i, j);
    }
  }

  unordered_map<ll, ll> m2;
  for (ll i = 0; i < D; i++) {
    for (ll j = (i == 0 ? D : i); j <= H * W; j += D) {
      if (j <= D) {
        m2[j] = 0;
      } else {
        m2[j] = m2[j - D] + f(m1[j], m1[j - D]);
      }
    }
  }

  for (ll i = 0; i < Q; i++) {
    cout << m2[R[i]] - m2[L[i]] << endl;
  }
}