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;

#define _ ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define forn(i, n) for (int i = 0; i < n; i++)
#define fin(ds) for (auto &v : ds) cin >> v;
#define all(a) (a).begin(), (a).end()
#define pii pair<int, int>
#define pll pair<ll, ll>
#define nl '\n'

typedef long long ll;

map<int, pii> grid;

signed main() { _
    int H, W; cin >> H >> W;
    int D; cin >> D;
    forn(x, H) {
        forn(y, W) {
            int axy; cin >> axy;
            grid[axy] = {x, y};
        }
    }
    
    int end = H * W;
    int memo[end + 7];
    memset(memo, 0, sizeof(memo));
    forn(i, end + 1) {
        if (i - D > 0) {
            pii s = grid[i - D];
            pii e = grid[i];
            memo[i] = abs(e.first - s.first) + abs(e.second - s.second) + memo[i - D];
        }
    }

    int Q; cin >> Q;
    forn(i, Q) {
        int L, R; cin >> L >> R;
        ll cost = 0;
        int st = memo[L];
        int en = memo[R];
        cost += (en - st);
        cout << cost << endl;
    }
}