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;

#define int ll
#define all(v) v.begin(), v.end()
#define reps(__i, a, b) for (int __i = a; i < b; i++)
#define rep(__i, n) reps(__i, 0, n)

const ll INF = (1ll << 60);
const ll MOD = (ll)1e9 + 7;

int cost(pair<int, int> t, pair<int, int> t2)
{
    return (abs(t.first - t2.first) + abs(t.second - t2.second));
}

signed main()
{
    int h, w, d, q;
    map<int, pair<int, int>> m;
    vector<pair<int, int>> v;
    cin >> h >> w >> d;
    for (int i = 1; i <= h; i++)
    {
        for (int j = 1; j <= w; j++)
        {
            int tmp;
            cin >> tmp;
            m[tmp] = make_pair(j, i);
        }
    }
    cin >> q;
    for (int i = 0; i < q; i++)
    {
        int tl, tr;
        cin >> tl >> tr;
        v.push_back(make_pair(tl, tr));
    }

    vector<vector<int>> sum;
    for (int j = 1; j <= d; j++)
    {
        vector<int> tmp;
        tmp.push_back(0);
        pair<int, int> current = m[j];
        for (int i = j + d; i <= h * w; i += d)
        {
            tmp.push_back(tmp[tmp.size() - 1] + cost(current, m[i]));
            current = m[i];
        }
        sum.push_back(tmp);
    }

    bool f = false;
    if (f)
    {
        for (int i = 0; i < sum.size(); i++)
        {
            for (int j = 0; j < sum[i].size(); j++)
            {
                cout << sum[i][j] << " ";
            }
            cout << endl;
        }
    }
    for (int i = 0; i < q; i++)
    {
        if (f)
            cout << (v[i].second - 1) / d << "," << sum[(v[i].first - 1) % d][(v[i].second - 1) / d] << " " << (v[i].first - 1) / d << "," << sum[(v[i].first - 1) % d][(v[i].first - 1) / d] << endl;
        cout << sum[(v[i].first - 1) % d][(v[i].second - 1) / d] - sum[(v[i].first - 1) % d][(v[i].first - 1) / d] << endl;
    }
}