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: Wrong Answer)

#include<algorithm>
#include<cmath>
#include<iomanip>
#include<iostream>
#include<map>
#include<numeric>
#include<queue>
#include<set>
#include<sstream>
#include<unordered_map>
#include<unordered_set>
#include<vector>
using ll = long long;
enum : int { M = (int)1e9 + 7 };
enum : ll { MLL = (ll)1e18L + 9 };
using namespace std;
#ifdef LOCAL
#include"rprint2.hpp"
#include"debug_deque.hpp"
#define vector DebugDeque
#else
#define FUNC(name) template <ostream& out = cout, class... T> void name(T&&...){ }
FUNC(prints) FUNC(printe) FUNC(printw) FUNC(printew) FUNC(printb) FUNC(printd) FUNC(printde);
#endif
template <class S, class T>
istream& operator >> (istream& in, pair<S, T>& p){ in >> p.first >> p.second; return in; }
template <class T>
istream& operator >> (istream& in, vector<T>& v){ for(auto& e : v){ in >> e; } return in; }
template <char d = ' ', class T>
ostream& operator << (ostream& out, vector<T>& v){ for(auto& e : v){ out << e << d; } return out; }

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int h, w, d;
    cin >> h >> w >> d;
    vector<pair<int, int>> poss(h * w);
    for(int i = 0; i < h; i++){
        for(int j = 0; j < w; j++){
            int a; cin >> a;
            a--;
            poss[a] = {i, j};
        }
    }
    vector<vector<ll>> lens(h * w, vector<ll>(20));
    for(int i = 0; i < h * w; i++){
        if(i + d >= h * w){ continue; }
        lens[i][0] = abs(poss[i].first - poss[i + d].first) + abs(poss[i].second - poss[i + d].second);
    }
    for(int i = 0; i < h * w; i++){
        for(int j = 1; j < 20; j++){
            if(i + d * (1ll << j) >= h * w){ continue; }
            ll i2 = i + d * (1 << (j - 1));
            lens[i][j] = lens[i][j - 1] + lens[i2][j - 1];
        }
    }
    int q; cin >> q;
    for(int i = 0; i < q; i++){
        int l, r;
        cin >> l >> r;
        l--; r--;
        ll ans = 0;
        while(l != r){
            int len = (r - l) / d;
            int lsb;
            for(lsb = 0; (len & (1 << lsb)) == 0; lsb++){ }
            ans += lens[l][lsb];
            l += d * (1 << lsb);
        }
        cout << ans << '\n';
    }
}