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 AtCoder_ABC089_A
{
    class Program
    {
        static KeyValuePair<int,int>[] _a;

        static int h;
        static int w;

        static void Find(int number, out int row, out int column)
        {
            var kvp = _a[number-1];
            row = kvp.Key;
            column = kvp.Value;
        }


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

            _a = new KeyValuePair<int, int>[h * w];
            //a = new int[h, w];
            for (int i = 0; i < h; ++i)
            {
                string[] tmp = Console.ReadLine().Split(' ');
                for (int j = 0; j < w; ++j)
                {
                    _a[int.Parse(tmp[j])-1] = new KeyValuePair<int, int>(i, j);
                }
            }

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

            int[] l = new int[q];
            int[] r = new int[q];

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


            for (int q_ = 0; q_ < q; ++q_)
            {
                int magic = 0;
                int number = l[q_];
                int row = 0;
                int column = 0;

                Find(number, out row, out column);

                while (number != r[q_])
                {
                    number += d;

                    int row2, column2;
                    Find(number, out row2, out column2);

                    magic += Math.Abs(row - row2) + Math.Abs(column - column2);

                    row = row2;
                    column = column2;
                }

                Console.WriteLine(magic);
            }
        }
    }
}