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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
using P = pair<ll,ll>;
constexpr ll mod = 1e9+7;
#define ALL(x) (x).begin(),(x).end()
#define REP(i,n) for(ll (i)=0;(i)<(n);(i)++)
#define REPS(i,n) for(ll (i)=1;(i)<=(n);(i)++)
#define RREP(i,n) for(ll (i)=(n-1);(i)>=0;(i)--)
#define RREPS(i,n) for(ll (i)=(n);(i)>0;(i)--)
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define F first
#define S second
#define UNIQUE(v) v.erase(unique(ALL(v)),v.end());

template<class T> inline void chmin(T& a, T b){
    if (a > b){
        a = b;
    }
}

template<class T> inline void chmax(T& a, T b){
    if (a < b){
        a = b;
    }
}

signed main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout<<fixed<<setprecision(12);
    ll H,W,D;
    cin >> H >> W >> D;
    vector<P> A(H*W);
    REP(i,H){
        REP(l,W){
            ll tmp;
            cin >> tmp;
            tmp--;
            A[tmp] = mp(i,l);
        }
    }
    vector<ll> rui(H*W);
    REP(i,D){
        ll fa = i;
        rui[fa] = 0;
        fa += D;
        while(fa < H*W){
            rui[fa] = rui[fa - D] + abs(A[fa].F-A[fa-D].F) + abs(A[fa].S-A[fa-D].S);
            fa += D;
        }
    }
    ll Q;
    cin >> Q;
    REP(i,Q){
        ll L,R;
        cin >> L >> R;
        L--;
        R--;
        cout << rui[R] - rui[L] << "\n";
    }
}