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;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

public static class TemplateExtension
{
    public static X[] MakeArray<X>(this int count, Func<int, X> func)
    {
        var xs = new X[count];
        for (var i = 0; i < count; i++)
        {
            xs[i] = func(i);
        }
        return xs;
    }

    public static int[] Range(this int count, int start = 0)
    {
        return count.MakeArray(i => i + start);
    }

    public static string Intercalate<X>(this IEnumerable<X> @this, string separator)
    {
        return string.Join(separator, @this);
    }

    public sealed class ValueIndexPair<T>
        : Tuple<T, int>
    {
        public T Value { get { return Item1; } }
        public int Index { get { return Item2; } }

        public ValueIndexPair(T value, int index)
            : base(value, index)
        {
        }
    }

    public static IEnumerable<ValueIndexPair<X>> Indexed<X>(this IEnumerable<X> @this)
    {
        var i = 0;
        foreach (var x in @this)
        {
            yield return new ValueIndexPair<X>(x, i);
            i++;
        }
    }
}

public sealed class Scanner
{
    private readonly TextReader _reader;
    private readonly StringBuilder _sb = new StringBuilder();

    /// <summary>
    /// Reads next word separated by spaces.
    /// </summary>
    public string Word()
    {
        _sb.Clear();

        while (true)
        {
            var r = _reader.Read();

            if (r == ' ' || r == '\r' || r == '\n')
            {
                if (r == '\r' && _reader.Peek() == '\n')
                {
                    _reader.Read();
                }

                // Ignore leading spaces.
                if (_sb.Length == 0) continue;

                break;
            }
            else if (r == -1)
            {
                break;
            }
            else
            {
                _sb.Append((char)r);
            }
        }

        return _sb.ToString();
    }

    /// <summary>
    /// Reads next word as <see cref="int"/>.
    /// </summary>
    public int N()
    {
        return int.Parse(Word().Trim());
    }

    /// <summary>
    /// Reads next word as <see cref="long"/>.
    /// </summary>
    public long L()
    {
        return long.Parse(Word());
    }

    /// <summary>
    /// Reads next word as <see cref="double"/>.
    /// </summary>
    public double F()
    {
        return double.Parse(Word());
    }

    /// <summary>
    /// Reads next line and splits it by spaces.
    /// </summary>
    public X[] Words<X>(Func<string, X> func)
    {
        return _reader.ReadLine().Split(' ').Select(func).ToArray();
    }

    public Scanner(TextReader reader)
    {
        _reader = reader;
    }
}

public partial class Program
{
    private readonly TextReader _input;
    private readonly TextWriter _output;
    private readonly Scanner _scanner;

    private void WriteLine(int value)
    {
        _output.WriteLine(value);
    }

    private void WriteLine(long value)
    {
        _output.WriteLine(value);
    }

    private void WriteLine(double value)
    {
        _output.WriteLine(value);
    }

    private void WriteLine(char value)
    {
        _output.WriteLine(value);
    }

    private void WriteLine(string value)
    {
        _output.WriteLine(value);
    }

    public Program(TextReader input, TextWriter output)
    {
        _input = input;
        _output = output;
        _scanner = new Scanner(input);
    }

    public static void Main(string[] args)
    {
        new Program(Console.In, Console.Out).EntryPoint();
    }
}

public sealed partial class Program
{
    int H, W, D;
    int[][] A;

    int HW { get { return H * W; } }

    Tuple<int, int>[] Ps;
    long[] Costs;

    long Distance(Tuple<int, int> p, Tuple<int, int> q)
    {
        return Math.Abs(p.Item1 - q.Item1) + Math.Abs(p.Item2 - q.Item2);
    }

    void Build()
    {
        Ps = new Tuple<int, int>[HW];
        for (var y = 0; y < H; y++)
        {
            for (var x = 0; x < W; x++)
            {
                Ps[A[y][x]] = Tuple.Create(y, x);
            }
        }

        Costs = new long[HW];
        for (var i = 0; i < HW; i++)
        {
            if (i < D)
            {
                Costs[i] = 0;
            }
            else
            {
                var c = i % D;
                Costs[i] = Costs[i - D] + Distance(Ps[i], Ps[i - D]);
            }
        }
    }

    public void EntryPoint()
    {
        var I = _scanner;
        H = I.N();
        W = I.N();
        D = I.N();
        A = H.MakeArray(y => W.MakeArray(x => I.N() - 1));

        Build();

        var Q = I.N();
        for (var i = 0; i < Q; i++)
        {
            var l = I.N() - 1;
            var r = I.N() - 1;
            WriteLine(Costs[r] - Costs[l]);
        }
    }
}