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 <iostream>
#include <vector>
#include <algorithm>
#include <map>

using namespace std;

int main() {
    int h, w, d, q;
    cin >> h >> w >> d;
    map<int, pair<int, int>> grid; //数字と位置の対応
    map<int, int> cost; //そこに至るまでのコスト
    vector<int> nums;
    for(int i = 1; i <= h; i++)
    {
        for(int j = 1; j <= w; j++)
        {
            int a;
            cin >> a;
            nums.push_back(a);
            grid[a] = {i, j};
        }
    }
    cin >> q;
    vector<pair<int, int>> exams(q);
    for(int i = 0; i < q; i++)
    {
        int l, r;
        cin >> l >> r;
        exams[i] = {l, r};
    }
    //書いてある番号をソート
    sort(nums.begin(), nums.end());
    //コストの計算
    for(int i = 0; i < nums.size(); i++)
    {
        if(!cost.count(nums[i]))
        {
            int back = nums[i] - d;
            if(cost.count(back))
            {
                int dist = abs(grid[nums[i]].first - grid[back].first) + abs(grid[nums[i]].second - grid[back].second);
                cost[nums[i]] = cost[back] + dist;
            }else{
                cost[nums[i]] = 0;
            }
        }
    }
    for(auto exam : exams)
    {
        cout << cost[exam.second] - cost[exam.first] << endl;
    }
    return 0;
}