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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;
using System.Threading.Tasks;

class Program
{
    int n;
    List<Tuple<long, long>> l;
    bool[] visit;
    void Run()
    {
        var sc = new Scanner();
        n = sc.NextInt();
        l = new List<Tuple<long, long>>();
        long[] a = new long[n];
        long[] b = new long[n];
        int init = 0;
        for (int i = 0; i < n; i++)
        {
            long x = sc.NextLong();
            long y = sc.NextLong();
            l.Add(Tuple.Create(x, y));
            a[i] = x;
            b[i] = y;
            if (i > 0 && x < l[init].Item1) init = i;
        }
        Array.Sort(a);
        Array.Sort(b);
        var ds = new Dictionary<Tuple<long, long>, int>();
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < n; j++)
            {
                if (i == j) continue;
                var d = Tuple.Create(Math.Abs(l[j].Item1 - l[i].Item1), Math.Abs(l[j].Item2 - l[i].Item2));
                if (!ds.ContainsKey(d)) ds.Add(d, 0);
                ds[d]++;
            }
        }
        var dd = ds.OrderByDescending(p => p.Value).First().Key;
        int min = 100;
        min = Math.Min(Dfs(0, 0, init, dd.Item1, dd.Item2), min);
        min = Math.Min(Dfs(0, 0, init, -dd.Item1, dd.Item2), min);
        min = Math.Min(Dfs(0, 0, init, dd.Item1, -dd.Item2), min);
        min = Math.Min(Dfs(0, 0, init, -dd.Item1, -dd.Item2), min);
        Console.WriteLine(min);
    }

    int Dfs(int d, int c, int last, long p, long q)
    {
        if (d == 0)
        {
            visit = new bool[n];
            visit[last] = true;
            return Dfs(d + 1, 1, last, p, q);
        }
        visit[last] = true;
        if (d == n) return c;
        bool find = false;
        for (int i = 0; i < n; i++)
        {
            if (visit[i]) continue;
            if (l[i].Item1 - p == l[last].Item1 && l[i].Item2 - q == l[last].Item2)
            {
                c = Dfs(d + 1, c, i, p, q);
                find = true;
            }
        }
        if (find) return c;
        for (int i = 0; i < n; i++)
        {
            if (visit[i]) continue;
            c = Dfs(d + 1, c + 1, i, p, q);
        }
        return c;
    }

    static void Main(string[] args)
    {
        new Program().Run();
    }

    static long Gcd(long a, long b)

    {
        if (a < b) return Gcd(b, a);
        if (b == 0) return a;
        return Gcd(b, a % b);
    }
}

class Scanner
{
    int index = -1;
    string[] buf;

    public Scanner()
    {
    }

    public int NextInt()
    {
        CheckNext();
        return int.Parse(buf[index++]);
    }

    public long NextLong()
    {
        CheckNext();
        return long.Parse(buf[index++]);
    }

    public double NextDouble()
    {
        CheckNext();
        return double.Parse(buf[index++]);
    }

    public string NextString()
    {
        CheckNext();
        return buf[index++];
    }

    private void CheckNext()
    {
        if (index >= 0 && index < buf.Length) return;

        buf = Console.ReadLine().Split(' ');
        index = 0;
    }
}