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;
using ll     = long long;
using pii    = pair<int, int>;
using pll    = pair<ll, ll>;
using vi     = vector<int>;
using vl     = vector<ll>;
using vvi    = vector<vi>;
using vvl    = vector<vl>;
const ll INF = 1LL << 60;
const ll MOD = 1000000007;
template <class T>
bool chmax(T &a, const T &b) {
    return (a < b) ? (a = b, 1) : 0;
}
template <class T>
bool chmin(T &a, const T &b) {
    return (b < a) ? (a = b, 1) : 0;
}
template <class C>
void print(const C &c, std::ostream &os = std::cout) {
    std::copy(std::begin(c), std::end(c), std::ostream_iterator<typename C::value_type>(os, " "));
    os << std::endl;
}

int main() {
    int h, w, d;
    cin >> h >> w >> d;
    vector<pii> a(h * w);
    for (int i = 0; i < h; ++i) {
        for (int j = 0; j < w; ++j) {
            int aa;
            cin >> aa;
            aa--;
            a[aa].first  = i;
            a[aa].second = j;
        }
    }
    int q;
    cin >> q;
    vi l(q), r(q);
    for (int i = 0; i < q; ++i) {
        cin >> l[i] >> r[i];
    }
    vi magic(h * w, 0);
    for (int i = 0; i < h * w; ++i) {
        if (i + d >= h * w)
            continue;
        magic[i + d] = magic[i] + abs(a[i + d].first - a[i].first) + abs(a[i + d].second - a[i].second);
    }
    for (int i = 0; i < q; ++i) {
        cout << magic[r[i] - 1] - magic[l[i] - 1] << "\n";
    }
    return 0;
}