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;

namespace Competitive
{
    internal class Solution
    {
        public void Run()
        {
            int H, W, D;
            {
                int[] tmp = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
                H = tmp[0];
                W = tmp[1];
                D = tmp[2];
            }

            int[] X = Enumerable.Range(0, H * W + 1).Select(i => 0).ToArray();
            int[] Y = Enumerable.Range(0, H * W + 1).Select(i => 0).ToArray();
            for (int y = 0; y < H; y++)
            {
                int[] line = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
                for (int x = 0; x < W; x++)
                {
                    int a = line[x];
                    X[a] = x;
                    Y[a] = y;
                }
            }

            int Q = int.Parse(Console.ReadLine());
            int[] DD = Enumerable.Range(0, H * W + 1).Select(i => 0).ToArray();

            for (int m = 1; m <= D; m++)
            {
                int d = 0;
                int i = m;
                DD[i] = d;

                while (true)
                {
                    i += D;
                    if (i > H * W) break;
                    d += Math.Abs(X[i] - X[i - D]) + Math.Abs(Y[i] - Y[i - D]);
                    DD[i] = d;
                }
            }
            
            for (int q = 0; q < Q; q++)
            {
                int[] line = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
                int start = line[0];
                int end = line[1];
                Console.WriteLine(DD[end] - DD[start]);
            }
        }

    }
    
    internal class Program
    {
        public static void Main(string[] args)
        {
            var s = new Solution();
            s.Run();
        }
    }
}