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.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using Debug;
//using static System.Globalization.CultureInfo;
//using Edge = Pair<long, int>;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
        Solve();
        //WriteLine(Solve());
    }
    static void Solve()
    {
        var num = Input.num; if (num == 1) { WriteLine(1);return; }
        var xy = Input.ar2D(num);var min = int.MaxValue;
        for(var i=0;i<num;i++)
            for(var j = 0; j < num; j++)
            {
                if (i == j) continue;
                var x = xy[i][0] - xy[j][0];
                var y = xy[i][1] - xy[j][1];
                var uf = new UnionFind(num);
                for(var k=0;k<num;k++)
                    for(var h=0;h<num;h++)
                    {
                        if (k == h) continue;
                        if ((xy[k][0] - xy[h][0] == x) && xy[k][1] - xy[h][1] == y)
                            uf.Union(k, h);
                    }
                var s = new HashSet<int>();
                var res = num;
                for(var p=0;p<num;p++)
                {
                    if (s.Contains(uf.Parent(p)))
                        continue;
                    s.Add(uf.Parent(p));
                    res -= uf.Size(p) - 1;
                }
                min = Min(res, min);
            }
        WriteLine(min);
    }
}

public class Input
{
    public static string read => ReadLine().Trim();
    public static int[] ar => read.Split(' ').Select(int.Parse).ToArray();
    public static int num => ToInt32(read);
    public static long[] arL => read.Split(' ').Select(long.Parse).ToArray();
    public static long numL => ToInt64(read);
    public static char[][] gred(int h)
        => Enumerable.Repeat(0, h).Select(_ => read.ToCharArray()).ToArray();
    public static int[] ar1D(int n)
        => Enumerable.Repeat(0, n).Select(_ => num).ToArray();
    public static long[] arL1D(int n)
        => Enumerable.Repeat(0, n).Select(_ => numL).ToArray();
    public static string[] strs(int n)
        => Enumerable.Repeat(0, n).Select(_ => read).ToArray();
    public static int[][] ar2D(int n)
        => Enumerable.Repeat(0, n).Select(_ => ar).ToArray();
    public static long[][] arL2D(int n)
        => Enumerable.Repeat(0, n).Select(_ => arL).ToArray();
    public static T getValue<T>(string g)
    {
        var t = typeof(T);
        if (t == typeof(int))
            return (T)(object)int.Parse(g);
        if (t == typeof(long))
            return (T)(object)long.Parse(g);
        if (t == typeof(string))
            return (T)(object)g;
        if (t == typeof(char))
            return (T)(object)char.Parse(g);
        if (t == typeof(double))
            return (T)(object)double.Parse(g);
        if (t == typeof(bool))
            return (T)(object)bool.Parse(g);
        return default(T);
    }
    public static string[] Make<T1, T2>(out T1 v1, out T2 v2)
    {
        var r = read.Split(' ');
        v1 = getValue<T1>(r[0]);
        v2 = getValue<T2>(r[1]);
        return r;
    }
    public static string[] Make<T1, T2, T3>(out T1 v1, out T2 v2, out T3 v3)
    {
        var r = Make(out v1, out v2);
        v3 = getValue<T3>(r[2]);
        return r;
    }
    public const long Inf = (long)1e18;
    public const double eps = 1e-6;
    public const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public const int MOD = 1000000007;
}

public class UnionFind
{
    private int _num;
    private int[] _parent, _size, _rank;
    public UnionFind(int num)
    {
        _num = num;
        _parent = new int[num];_size = new int[num];_rank = new int[num];
        for(var i = 0; i < num; i++) { _parent[i] = i;_size[i] = 1;}
    }
    private int Find(int i)
        => i == _parent[i] ? i : (_parent[i] = Find(_parent[i]));
    public int Parent(int i)
        => Find(i);
    public int Size(int i)
        => _size[Find(i)];
    public bool Union(int v1,int v2)
    {
        v1 = Find(v1);v2 = Find(v2);
        if (v1==v2) return false;
        _num--;
        if (_rank[v1] > _rank[v2])
        {
            _parent[v2] = v1;
            _size[v1] += _size[v2];
        }
        else
        {
            _parent[v1] = v2;
            _size[v2] += _size[v1];
            if (_rank[v1] == _rank[v2])
                _rank[v2]++;
        }
        return true;
    }
    public bool IsSame(int v1, int v2)
        => Find(v1) == Find(v2);
}