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.Text;

namespace AtTest.D_Challenge
{
    class ABC_089
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int[] hwd = ReadInts();
            var grid = new int[hwd[0]][];
            var posList = new List<int[]>();
            for(int i = 0; i < hwd[0]; i++)
            {
                grid[i] = ReadInts();
                for (int j = 0; j < hwd[1]; j++)
                {
                    posList.Add(new int[3] { grid[i][j], i, j });
                }
            }
            posList.Sort((a, b) => a[0] - b[0]);
            var costGrid = new int[hwd[0], hwd[1]];
            for(int i=0;i<posList.Count;i++)
            {
                int prevIndex = i - hwd[2];
                if (prevIndex < 0)
                {
                    costGrid[posList[i][1], posList[i][2]] = 0;
                }
                else
                {
                    int[] pos = posList[i];
                    int[] prevPos = posList[prevIndex];
                    costGrid[pos[1], pos[2]]
                        = costGrid[prevPos[1], prevPos[2]];
                    costGrid[pos[1], pos[2]]
                        += Math.Abs(pos[1] - prevPos[1])
                        + Math.Abs(pos[2] - prevPos[2]);
                }
            }

            int q = ReadInt();
            var lrs = new int[q][];
            for(int i = 0; i < q; i++)
            {
                lrs[i] = ReadInts();
            }
            for(int i = 0; i < q; i++)
            {
                int l = lrs[i][0];
                int r = lrs[i][1];
                int cost
                    = costGrid[posList[r - 1][1], posList[r - 1][2]]
                    - costGrid[posList[l - 1][1], posList[l - 1][2]];
                Console.WriteLine(cost);
            }
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}