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.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		if(N == 1){
			Console.WriteLine(1);
			return;
		}
		
		int min = N;
		for(int i=0;i<N;i++){
			for(int j=i+1;j<N;j++){
				long p = X[i] - X[j];
				long q = Y[i] - Y[j];
				var UF = new UnionFind(N);
				for(int ii=0;ii<N;ii++){
					for(int jj=ii+1;jj<N;jj++){
						if(X[ii] - X[jj] == p && Y[ii] - Y[jj] == q) UF.Unite(ii,jj);
						if(X[ii] - X[jj] == -p && Y[ii] - Y[jj] == -q) UF.Unite(ii,jj);
					}
				}
				min = Math.Min(UF.Compo, min);
			}
		}
		Console.WriteLine(min);
		
		
		
		
		
		
	}
	int N;
	long[] X,Y;
	public Sol(){
		N = ri();
		X = new long[N];
		Y = new long[N];
		for(int i=0;i<N;i++){
			var d = ria();
			X[i] = d[0]; Y[i] = d[1];
		}
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}

class UnionFind{
	
	int[] parent;
	int[] mem;
	int compo;
	int N;
	public UnionFind(int n_){
		Initialize(n_);
	}
	
	public void Initialize(int n_){
		N=n_;
		parent=new int[N];
		mem=new int[N];
		for(int i=0;i<N;i++){
			parent[i]=i;
			mem[i]=1;
		}
		compo=N;
	}
	
	public int Parent(int a){
		if(parent[a]==a) return a;
		return parent[a] = Parent(parent[a]);
	}
	
	public bool IsUnited(int a,int b){
		return Parent(a) == Parent(b);
	}
	
	public void Unite(int a,int b){
		a = Parent(a); b = Parent(b);//Parent()を呼ぶことでa以上のノードは全てparentがrootになる
		if(a == b) return;
		parent[a] = b;
		mem[b] += mem[a];
		compo -= 1;
	}
	
	public bool IsRoot(int x){
		return x == parent[x];
	}
	public int MemCnt(int x){
		return mem[Parent(x)];
	}
	
	public void Dump(){
		for(int i=0;i<parent.Length;i++){
			Console.Write(i==0?"{0}":" {0}",parent[i]);
		}
		Console.WriteLine("");
	}
	
	public int Compo{
		get{
			return compo;
		}
	}
	
}