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.Collections.Generic;
using System.Linq;

namespace ABC089
{
    public class Program
    {
        struct Point
        {
            readonly int x;
            readonly int y;

            public Point(int x, int y)
            {
                this.x = x;
                this.y = y;
            }

            public int GetManhattanDistance(Point other)
            {
                return Math.Abs(x - other.x) + Math.Abs(y - other.y);
            }
        }

        void Solve(StreamScanner ss, StreamWriter sw)
        {
            //---------------------------------
            var H = ss.Next(Int);
            var W = ss.Next(Int);
            var D = ss.Next(Int);
            var A = ss.Next(Int, W, H);
            var Q = ss.Next(Int);
            var LR = ss.Next(Int, 2, Q).Select(a => new {L = a[0], R = a[1]});

            var ps = new Point[H * W];
            for (var i = 0; i < H; i++)
            {
                for (var j = 0; j < W; j++)
                {
                    ps[A[i][j] - 1] = new Point(j, i);
                }
            }

            var dist = new int[H * W - D];
            for (var i = 0; i < D; i++)
            {
                for (var j = i + D; j < H * W; j += D)
                {
                    dist[j - D] = ps[j - D].GetManhattanDistance(ps[j]);
                }
            }


            var acs = new long[H * W];
            for (var i = 0; i < D; i++)
            {
                for (var j = i + D; j < H * W; j += D)
                {
                    acs[j] = acs[j - D] + dist[j - D];
                }
            }

            foreach (var lr in LR)
            {
                sw.WriteLine(acs[lr.R - 1] - acs[lr.L - 1]);
            }
            //---------------------------------
        }

        static void Main()
        {
            var ss = new StreamScanner(new StreamReader(Console.OpenStandardInput()));
            var sw = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
            new Program().Solve(ss, sw);
            sw.Flush();
        }

        static readonly Func<string, string> String = s => s;
        static readonly Func<string, int> Int = int.Parse;
        static readonly Func<string, long> Long = long.Parse;
        static readonly Func<string, double> Double = double.Parse;
    }

    public class StreamScanner
    {
        static readonly char[] Sep = {' '};
        readonly Queue<string> buffer = new Queue<string>();
        readonly TextReader textReader;

        public StreamScanner(TextReader textReader)
        {
            this.textReader = textReader;
        }

        public T Next<T>(Func<string, T> parser)
        {
            if (buffer.Count != 0) return parser(buffer.Dequeue());
            var nextStrings = textReader.ReadLine().Split(Sep, StringSplitOptions.RemoveEmptyEntries);
            foreach (var nextString in nextStrings) buffer.Enqueue(nextString);
            return Next(parser);
        }

        public T[] Next<T>(Func<string, T> parser, int x)
        {
            var ret = new T[x];
            for (var i = 0; i < x; ++i) ret[i] = Next(parser);
            return ret;
        }

        public T[][] Next<T>(Func<string, T> parser, int x, int y)
        {
            var ret = new T[y][];
            for (var i = 0; i < y; ++i) ret[i] = Next(parser, x);
            return ret;
        }
    }
}