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: Time Limit Exceeded)

#include<bits/stdc++.h>
#include<iostream>
#include<vector>
#include<utility>
#include<numeric>
#include<functional>
#include<algorithm>
#include<queue>
#include<map>
#include<string>


#define FOR(i, a, b) for(int i=a; i<b; i++)
#define COUT(a) cout << a << endl;

using namespace std;
using Int = long long;
using UInt = unsigned long long;
using P = pair<Int, Int>;

Int H, W, D, Q;
vector<P> locs;
map<P, UInt> memo;

UInt dist(Int x, Int r){
    if (x == r){
        return 0;
    }
    if (memo.find(P(x, r)) != memo.end()){
        return memo[P(x, r)];
    }

    P px = locs[x];
    P px_ = locs[x+D];

    Int d = abs(px.first - px_.first) + abs(px.second - px_.second);
    UInt ret = d + dist(x+D, r);
    memo[P(x, r)] = ret; 
    return ret;
}

int main(){
    Int N;

    cin >> H >> W >> D;

    
    locs = vector<P>((H+1)*(W+1));

    FOR(i, 0, H){
        FOR(j, 0, W){
            Int n;
            cin >> n;
            locs[n] = P(j+1, i+1);
        }
    }

    cin >> Q;

    FOR (i, 0, Q){
        Int L, R;
        cin >> L >> R;
        cout << dist(L, R) << endl;
    }

}