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;
class Program
{
    ulong mod = 1000000009;
    static void Main(string[] args)
    {
        int[] n = Read.ints();
        int[] x = new int[n[0]*n[1]];
        int[] y = new int[n[0]*n[1]];
        for(int i = 0; i < n[0]; i++)
        {
            int[] sd = Read.ints();
            for(int j = 0; j < n[1]; j++)
            {
                x[sd[j]-1] = i;
                y[sd[j]-1] = j;
            }
        }
        int f = Read.Int();
        int[] u = new int[x.Length-n[2]];
        for(int j = 0; j < u.Length; j++)
        {
            u[j] = Math.Abs(x[j] - x[j + n[2]]) + Math.Abs(y[j] - y[j + n[2]]);
        }
        for (int i = 0; i < f; i++)
        {
            int ans = 0;
            int[] a = Read.ints();
            for (int j = a[0]-1; j != a[1]-1; j += n[2])
            {
                ans += u[j];
            }
            Console.WriteLine(ans);
        }
        Console.ReadLine();
    } public static long gcd(long a, long b)
    {
        while (true)
        {
            if (a == 0) { return b; }
            if (b == 0) { return a; }
            if (a > b) { a -= b; }
            else { b -= a; }
        }
    }
    public static long lcm(long a, long b) { return a / gcd(a, b) * b; }
    public static bool IsPrime(int num)
    {
        if (num < 2) return false;
        else if (num == 2) return true;
        else if (num % 2 == 0) return false; // 偶数はあらかじめ除く

        double sqrtNum = Math.Sqrt(num);
        for (int i = 3; i <= sqrtNum; i += 2)
        {
            if (num % i == 0)
            {
                // 素数ではない
                return false;
            }
        }

        // 素数である
        return true;
    }
}
public static class Read
{
    public static void outl(string n = "") { Console.WriteLine(n); return; }
    public static long Long() { return long.Parse(Console.ReadLine()); }
    public static long[] longs() { return Console.ReadLine().Split().Select(long.Parse).ToArray(); }
    public static int Int() { return int.Parse(Console.ReadLine()); }
    public static int[] ints() { return Console.ReadLine().Split().Select(int.Parse).ToArray(); }
    public static string Str() { return Console.ReadLine(); }
    public static string[] Strs() { return Console.ReadLine().Split(); }
}