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 System.Text.RegularExpressions;

class Program
{
    static void Main(string[] args)
    {
        var N = sc.ReadInt();
        var XY = sc.ReadTupLongArray(N);
        var map = new HashMap<Tuple<long, long>, bool>();
        var PQ = new List<Tuple<long, long>>();
        for (int i = 0; i < N; i++)
        {
            map[XY[i]] = true;
            for (int j = i + 1; j < N; j++)
            {
                PQ.Add(Tuple.Create(XY[i].Item1 - XY[j].Item1, XY[i].Item2 - XY[j].Item2));
            }
        }

        var ans = N;
        foreach (var pq in PQ)
        {
            var res = N;
            for (int i = 0; i < N; i++)
            {
                var next = Tuple.Create(
                    XY[i].Item1 + pq.Item1,
                    XY[i].Item2 + pq.Item2
                );
                if (map[next])
                {
                    res--;
                }
            }
            ans = Math.Min(res, ans);
        }
        Console.WriteLine(ans);
    }
    static Scanner sc = new Scanner();
}

class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }
    public string ReadStr()
    {
        return this.Next();
    }
    public char ReadChar()
    {
        return this.Next()[0];
    }
    public int ReadInt()
    {
        return int.Parse(this.Next());
    }
    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }
    public long ReadLong()
    {
        return long.Parse(this.Next());
    }
    public double ReadDouble()
    {
        return double.Parse(this.Next());
    }
    public Tuple<int, int> ReadTup()
    {
        return Tuple.Create(this.ReadInt(), this.ReadInt());
    }
    public Tuple<int, int, int> ReadTup3()
    {
        return Tuple.Create(this.ReadInt(), this.ReadInt(), this.ReadInt());
    }
    public Tuple<int, int, int, int> ReadTup4()
    {
        return Tuple.Create(this.ReadInt(), this.ReadInt(), this.ReadInt(), this.ReadInt());
    }
    public Tuple<long, long> ReadTupLong()
    {
        return Tuple.Create(this.ReadLong(), this.ReadLong());
    }
    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }
    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }
    public double[] ReadDoubleArray(int n)
    {
        var array = new double[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadDouble();
        }
        return array;
    }
    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }
    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
    public Tuple<int, int>[] ReadTupArray(int n)
    {
        var array = new Tuple<int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup();
        }
        return array;
    }
    public Tuple<int, int, int>[] ReadTup3Array(int n)
    {
        var array = new Tuple<int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup3();
        }
        return array;
    }
    public Tuple<int, int, int, int>[] ReadTup4Array(int n)
    {
        var array = new Tuple<int, int, int, int>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTup4();
        }
        return array;
    }
    public Tuple<long, long>[] ReadTupLongArray(int n)
    {
        var array = new Tuple<long, long>[n];
        for (int i = 0; i < n; i++)
        {
            array[i] = this.ReadTupLong();
        }
        return array;
    }
}

class HashMap<K, V> : Dictionary<K, V> where V : new()
{
    private V DefaltValue = new V();
    public HashMap() { }
    public HashMap(V defaultValue)
    {
        this.DefaltValue = new V();
    }
    new public V this[K i]
    {
        get
        {
            V v;
            return TryGetValue(i, out v) ? v : base[i] = this.DefaltValue;
        }
        set { base[i] = value; }
    }
}