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)

#pragma GCC optimize ("O3")
#pragma GCC target ("tune=native")
#pragma GCC target ("avx")
#define FOR(i,j,n) for (int i=(j);i<(n);i++)
#define REP(i,n) for (int i=0;i<(n);i++)
#define REPN(i,n) for (int i=(n);i>=0;i--)
#define I(n) scanf("%d", &(n))
#define pb(n) push_back((n))
#define mp(i,j) make_pair((i),(j))
#include <bits/stdc++.h>
using namespace std;

//------------------------------typedef集
typedef vector<int> vi;
typedef pair<int,int> pi;
typedef vector<pi> vpi;
typedef vector<vi> vvi;
typedef vector<vpi> vvpi;
typedef vector<vvi> vvvi;
typedef long long ll;

int h,w,d,a[310][310],saki[90010],qn,l,r;
vpi place;
map<pi,int> query;

int magi(int i, int j){
    if (i==j) return 0;
    pi q = mp(i,j);
    if (query[q]) return query[q];

    pi ipos = place[i];
    pi ippos = place[i+d];
    int part = abs(ipos.first - ippos.first) + abs(ippos.second - ipos.second);
    query[mp(i,i+d)] = part;
    query[q] = part + magi( i+d,j );
    return query[q];
}

int main(){
    I(h); I(w); I(d);
    place.resize(h*w+1);
    REP(i,h) { REP(j,w) {
        I(a[i][j]);
        place[a[i][j]] = mp(i,j);
    } }
    I(qn);
    REP(i,qn){
        I(l); I(r);
        printf("%d\n", magi(l,r) );
    }
    return 0;
}