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.IO;
using System.Linq;
using System.Numerics;
using System.Collections.Generic;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using Debug = System.Diagnostics.Debug;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;


static class P
{
    static void Main()
    {
        var hwd = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var h = hwd[0];
        var w = hwd[1];
        var d = hwd[2];
        Tuple<int, int>[] nums = new Tuple<int, int>[h * w];
        var a = Enumerable.Repeat(0, h).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray()).ToArray();
        for (int i = 0; i < h; i++)
        {
            for (int j = 0; j < w; j++)
            {
                nums[a[i][j]] = new Tuple<int, int>(i, j);
            }
        }
        List<int>[] accumMagic = Enumerable.Repeat(0, d).Select(_ => new List<int>() { 0 }).ToArray();
        for (int i = d; i < nums.Length; i++)
        {
            accumMagic[i % d].Add(accumMagic[i % d].Last() + Abs(nums[i - d].Item1 - nums[i].Item1) + Abs(nums[i - d].Item2 - nums[i].Item2));
        }
        var q = int.Parse(Console.ReadLine());
        for (int i = 0; i < q; i++)
        {
            var lr = Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToArray();
            Console.WriteLine(accumMagic[lr[1] % d][lr[1] / d] - accumMagic[lr[0] % d][lr[0] / d]);
        }
    }
}