Problem:
Score : 300 points

Problem Statement

There are N balls in a two-dimensional plane. The i-th ball is at coordinates (x_i, y_i).

We will collect all of these balls, by choosing two integers p and q such that p \neq 0 or q \neq 0 and then repeating the following operation:

Choose a ball remaining in the plane and collect it. Let (a, b) be the coordinates of this ball. If we collected a ball at coordinates (a - p, b - q) in the previous operation, the cost of this operation is 0. Otherwise, including when this is the first time to do this operation, the cost of this operation is 1.

Find the minimum total cost required to collect all the balls when we optimally choose p and q.

Constraints

1 \leq N \leq 50

|x_i|, |y_i| \leq 10^9

If i \neq j, x_i \neq x_j or y_i \neq y_j.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the minimum total cost required to collect all the balls.

Sample Input 1

2
1 1
2 2

Sample Output 1

1

If we choose p = 1, q = 1, we can collect all the balls at a cost of 1 by collecting them in the order (1, 1), (2, 2).

Sample Input 2

3
1 4
4 6
7 8

Sample Output 2

1

If we choose p = -3, q = -2, we can collect all the balls at a cost of 1 by collecting them in the order (7, 8), (4, 6), (1, 4).

Sample Input 3

4
1 1
1 2
2 1
2 2

Sample Output 3

2

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Runtime.InteropServices;

namespace Contest
{
    struct S
    {
        public int X, Y;

        public S(int x, int y)
        {
            X = x;
            Y = y;
        }
    }
    class Program
    {
        private Scanner sc;

        public void Solve()
        {
            sc = new Scanner();
            int N = sc.NextInt();
            var ar = new S[N];
            Dictionary<S, bool> map = new Dictionary<S, bool>();
            for (int i = 0; i < N; i++)
            {
                ar[i] = new S(sc.NextInt(), sc.NextInt());
                map[ar[i]] = true;
            }

            long ans = N;

            for (int i = 0; i < N - 1; i++)
            {
                for (int j = i + 1; j < N; j++)
                {
                    int p = ar[i].X - ar[j].X;
                    int q = ar[i].Y - ar[j].Y;
                    int cnt = 0;
                    for (int k = 0; k < N; k++)
                    {
                        S b = new S(ar[k].X - p, ar[k].Y - q);
                        bool o;
                        if (map.TryGetValue(b, out o))
                        {
                            cnt++;
                        }
                    }

                    ans = Math.Min(ans, N - cnt);
                }
            }
            Console.WriteLine(ans);
        }



        static void Main() => new Program().Solve();
    }
}

class Scanner
{
    public Scanner()
    {
        _stream = new StreamReader(Console.OpenStandardInput());
        _pos = 0;
        _line = new string[0];
        _separator = ' ';
    }
    private readonly char _separator;
    private readonly StreamReader _stream;
    private int _pos;
    private string[] _line;
    #region get a element
    public string Next()
    {
        if (_pos >= _line.Length)
        {
            _line = _stream.ReadLine().Split(_separator);
            _pos = 0;
        }
        return _line[_pos++];
    }
    public int NextInt()
    {
        return int.Parse(Next());
    }
    public long NextLong()
    {
        return long.Parse(Next());
    }
    public double NextDouble()
    {
        return double.Parse(Next());
    }
    #endregion
    #region convert array
    private int[] ToIntArray(string[] array)
    {
        var result = new int[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = int.Parse(array[i]);
        }

        return result;
    }
    private long[] ToLongArray(string[] array)
    {
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = long.Parse(array[i]);
        }

        return result;
    }
    private double[] ToDoubleArray(string[] array)
    {
        var result = new double[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = double.Parse(array[i]);
        }

        return result;
    }
    #endregion
    #region get array
    public string[] Array()
    {
        if (_pos >= _line.Length)
            _line = _stream.ReadLine().Split(_separator);
        _pos = _line.Length;
        return _line;
    }
    public int[] IntArray()
    {
        return ToIntArray(Array());
    }
    public long[] LongArray()
    {
        return ToLongArray(Array());
    }
    public double[] DoubleArray()
    {
        return ToDoubleArray(Array());
    }
    #endregion
}