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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC089_D
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] strs = Console.ReadLine().Split(' ');
            int h = int.Parse(strs[0]);
            int w = int.Parse(strs[1]);
            int d = int.Parse(strs[2]);

            int hw = h * w;

            int[,] offset = new int[d, hw / d + 1];

            int[] row = new int[hw + 1];
            int[] column = new int[hw + 1];

            string[] strsTmp = new string[h];

            for (int i = 0; i < h; ++i)
            {
                string[] strs_ = Console.ReadLine().Split(' ');

                for (int j = 0; j < w; ++j)
                {
                    int tmp_ = int.Parse(strs_[j]);
                    column[tmp_] = j + 1;
                    row[tmp_] = i + 1;

                    int next = tmp_ + d;
                    if (next <= hw)
                    {
                        if (column[next] != 0)
                        {
                            offset[tmp_ % d, tmp_ / d] = Math.Abs((i+1) - row[next]) + Math.Abs((j+1) - column[next]);
                        }
                    }

                    int prev = tmp_ - d;
                    if (prev >= 1 && offset[prev % d, prev / d] == 0)
                    {
                        if (column[prev] != 0)
                        {
                            offset[prev % d, prev / d] = Math.Abs((i + 1) - row[prev]) + Math.Abs((j + 1) - column[prev]);
                        }
                    }
                }
            }

            int q = int.Parse(Console.ReadLine());

            int[] ans = new int[q];

            for (int i = 0; i < q; ++i)
            {
                string[] strs3 = Console.ReadLine().Split(' ');
                int l = int.Parse(strs3[0]);
                int r = int.Parse(strs3[1]);

                //ans[i] = CalcMP(l, r, d);
                {
                    int mp = 0;

                    int mod = l % d;
                    int div = l / d;

                    if (l < r)
                    {
                        int loopCount = (r - l) / d;

                        for (int j = 0; j < loopCount; ++j)
                        {
                            mp += offset[mod, div + j];
                        }
                    }
                    else
                    {
                        int loopCount = -(r - l) / d;

                        for (int j = loopCount - 1; j >= 0; --j)
                        {
                            mp += offset[mod, div + j];
                        }
                    }

                    //ans[i] = mp;
                    Console.WriteLine("{0}", mp);
                }
            }

#if false
            for (int i = 0; i < q; ++i)
            {
                Console.WriteLine("{0}", ans[i]);
            }
#endif
        }
    }
}