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;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
public class ABC
{


    public static void Main()
    {
        var read = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long N = read[0];
        SortedDictionary<string, long> balls = new SortedDictionary<string, long>();
        bool[] collected = new bool[N];
        Tuple<long, long>[] balls_tuple = new Tuple<long, long>[N];
        for (long i = 0; i < N; i++)
        {
            string readline = Console.ReadLine();
            long[] split = readline.Split().Select(long.Parse).ToArray();
            balls[readline] = i;
            balls_tuple[i] = new Tuple<long, long>(split[0], split[1]);
            collected[i] = false;
        }
        long minimum_cost = long.MaxValue;
        if (N == 1)
        {
            Console.WriteLine(1);
            return;
        }
        else
        for (long firstball = 0; firstball < N - 1; firstball++)
        {
            for (long lastball = firstball + 1; lastball < N; lastball++)
            {
                long p = balls_tuple[firstball].Item1 - balls_tuple[lastball].Item1;
                long q = balls_tuple[firstball].Item2 - balls_tuple[lastball].Item2;
                bool[] thisTime_collected = new bool[N];
                collected.CopyTo(thisTime_collected,0);
                long n_collected = 0;
                long cost = 0;
                bool isDAME = false;
                for (long lookingyounger = 0; lookingyounger < N; lookingyounger++)
                {
                    //回収する珠のスタートを選ぶ
                    if (thisTime_collected[lookingyounger] == true) continue;
                    else
                    {
                        cost++;
                        if (cost > minimum_cost)
                        {
                            isDAME = true;
                            break;
                        }


                        long x = balls_tuple[lookingyounger].Item1;
                        long y = balls_tuple[lookingyounger].Item2;
                        thisTime_collected[lookingyounger] = true;
                        n_collected++;
                        while (balls.ContainsKey((longs2key(x - p, y - q))))
                        {
                            long key_nextball = balls[longs2key(x - p, y - q)];
                            thisTime_collected[key_nextball] = true;
                            n_collected++;
                            x -= p;
                            y -= q;

                        }

                            x = balls_tuple[lookingyounger].Item1;
                        y = balls_tuple[lookingyounger].Item2;
                        while (balls.ContainsKey((longs2key(x + p, y + q))))
                        {
                            long key_nextball = balls[longs2key(x + p, y + q)];
                            thisTime_collected[key_nextball] = true;
                            n_collected++;
                            x += p;
                            y += q;
                        }

                    }


                }
                if (isDAME == false)
                {
                    if (minimum_cost > cost)
                    {
                        minimum_cost = cost;
                    }
                }


            }

        }


        Console.WriteLine(minimum_cost);

    }

    public static string longs2key(long x, long y)
    {
        return x + " " + y;
    }

}