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: Runtime Error)

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

namespace Atcoder1_A
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] str = Console.ReadLine().Split(' ');

            int H = int.Parse(str[0]);
            int W = int.Parse(str[1]);
            int D = int.Parse(str[2]);

            var A = new int[H, W];
            
            for(int i = 0; i < H; i++)
            {
                string[] num = Console.ReadLine().Split(' ');
                for(int k = 0; k < W; k++)
                {
                    A[i, k] = int.Parse(num[k]);
                }
            }

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

            int[] L = new int[Q];
            int[] R = new int[Q];
            for(int i = 0; i < Q; i++)
            {
                string[] lr = Console.ReadLine().Split(' ');
                L[i] = int.Parse(lr[0]);
                R[i] = int.Parse(lr[1]);
            }

            int[] ans = new int[Q];

            int[] count = new int[Q];
            for (int i = 0; i < Q; i++)
            {
                count[i] = (R[i] - L[i]) / D;
            }
            int[][] lX = new int[Q][];
            int[][] lY = new int[Q][];

            for(int i = 0; i < Q; i++)
            {
                lX[i] = new int[count[i] + 1];
                lY[i] = new int[count[i] + 1];
            }

            for (int j = 0; j < H; j++)
            {
                for (int k = 0; k < W; k++)
                {
                    for (int i = 0; i < Q; i++)
                    {
                        if (A[j, k] >= L[i] && A[j, k] <= R[i] && (A[j, k] - L[i]) % D == 0)
                        {
                            lX[i][(A[j, k] - L[i]) / D] = j;
                            lY[i][(A[j, k] - L[i]) / D] = k;
                        }
                    }
                }
            }

            for(int i = 0; i <= Q; i++)
            {
                for(int j = 1; j <= count[i]; j++)
                {
                    ans[i] += Math.Abs(lX[i][j - 1] - lX[i][j]);
                    ans[i] += Math.Abs(lY[i][j - 1] - lY[i][j]);
                }
            }

            foreach(var item in ans)
            {
                Console.WriteLine(item);
            }
        }
    }
}