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: Accepted)

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

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var hwd = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            int[][] field = new int[hwd[0]][];
            for (int i = 0; i < hwd[0]; i++)
            {
                field[i] = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            }
            var map = new Dictionary<int, int>();
            for (int i = 0; i < hwd[0]; i++)
            {
                for (int j = 0; j < hwd[1]; j++)
                {
                    map[field[i][j]] = 1000 * i + j;
                }
            }
            map = map.OrderBy(x => x.Key).ToDictionary(x => x.Key, x => x.Value);
            int[] warp = map.Values.ToArray();
            int[] ans = new int[warp.Count()];
            int q = int.Parse(Console.ReadLine());
            for (int i = ans.Count() - 1; i >= 0; i--)
            {
                if (i >= ans.Count() - hwd[2]) ans[i] = 0;
                else
                {
                    ans[i] = ans[i + hwd[2]] + Math.Abs(warp[i] % 1000 - warp[i + hwd[2]] % 1000) + Math.Abs(warp[i] / 1000 - warp[i + hwd[2]] / 1000);
                }
            }
            for (int i = 0; i < q; i++)
            {
                var lr = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
                Console.WriteLine(ans[lr[0] - 1] - ans[lr[1] - 1]);
            }
        }
    }
}