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.

Examples

Input

2
1 1
2 2


Output

1


Input

3
1 4
4 6
7 8


Output

1


Input

4
1 1
1 2
2 1
2 2


Output

2
import java.io.*;
import java.math.*;
import java.util.*;
public class Main {
	static int ans = 100;
	static int[][] balls;
	static int N;
	static boolean[] taken;
	public static void main(String[] args) { 
		/*Fixate two coordinates in ordered pairs and extend same arithmetic difference for as 
		 * long as possible (sort coordinates first)
		 * Make connected graphs of coordinates that can be achieved with set p and q values
		 * */
		FastScanner I = new FastScanner(); //Input
		OutPut O = new OutPut(); //Output
		N = I.nextInt();
		ans=N;
		balls = new int[N][2];
		for (int i = 0; i < N; i++) {
			balls[i][0] = I.nextInt();
			balls[i][1] = I.nextInt();
		}
		Arrays.sort(balls,(a,b)->Integer.compare(a[0], b[0]));
		solve();
		for (int i = 0; i < N; i++) {
			int x = balls[i][0];
			int y = balls[i][1];
			balls[i][0]=y;
			balls[i][1]=x;
		}
		Arrays.sort(balls,(a,b)->Integer.compare(a[0], b[0]));
		solve();
		O.pln(ans);
	}
	public static void solve() {
		for (int add = 1; add<N; add++) {
			taken = new boolean[N];
			int p = balls[add][0]-balls[0][0];
			int q = balls[add][1]-balls[0][1]; //Differences
			ans=min(ans,check(p,q));
		}
	}
	public static int check(int p, int q) {
		int ret = 0;
		while (true) {
			boolean added=false;
			int start = 0;
			int x = -1;
			int y = -1; //Coordinates that we want next
			for (int i = 0; i < N; i++) {
				if (!taken[i]) {
					added=true;
					ret++;
					start=i;
					taken[i]=true;
					x=balls[i][0]+p;
					y=balls[i][1]+q;
					break;
				}
			}
			if (!added) break;
			for (int i = start+1; i < N; i++) {
				if (balls[i][0]==x&&balls[i][1]==y) {
					taken[i]=true;
					x+=p;
					y+=q;
				}
			} 
		}
		return ret;
	}
	public static double max(double a, double b) {return Math.max(a, b);}
	public static double min(double a, double b) {return Math.min(a, b);}
	public static long min(long a, long b) {return Math.min(a,b);}
	public static long max(long a, long b) {return Math.max(a,b);}
	public static int min(int a, int b) {return Math.min(a,b);}
	public static int max(int a, int b) {return Math.max(a,b);}
	public static long abs(long x) {return Math.abs(x);}
	public static long ceil(long num, long den) {long ans = num/den; if (num%den!=0) 
	ans++; return ans;}
	public static long GCD(long a, long b) {
		if (a==0||b==0) return max(a,b);
		return GCD(min(a,b),max(a,b)%min(a,b));
	}
	public static long FastExp(long base, long exp, long mod) {
		long ans=1;
		while (exp>0) {
			if (exp%2==1) ans*=base;
			exp/=2;
			base*=base;
			base%=mod;
			ans%=mod;
		}
		return ans;
	}
	public static long ModInv(long num,long mod) {return FastExp(num,mod-2,mod);}
	public static int pop(long x) { //Returns number of bits within a number
		int cnt = 0;
		while (x>0) {
			if (x%2==1) cnt++;
			x/=2;
		}
		return cnt;
	}
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong() {return Long.parseLong(next());};
		double nextDouble() {return Double.parseDouble(next());}
	}
	static class OutPut{
		PrintWriter w = new PrintWriter(System.out);
		void pln(double x) {w.println(x);w.flush();}
		void pln(boolean x) {w.println(x);w.flush();}
		void pln(int x) {w.println(x);w.flush();}
		void pln(long x) {w.println(x);w.flush();}
		void pln(String x) {w.println(x);w.flush();}
		void pln(char x) {w.println(x);w.flush();}
		void pln(StringBuilder x) {w.println(x);w.flush();}
		void pln(BigInteger x) {w.println(x);w.flush();}
		void p(int x) {w.print(x);w.flush();}
		void p(long x) {w.print(x);w.flush();}
		void p(String x) {w.print(x);w.flush();}
		void p(char x) {w.print(x);w.flush();}
		void p(StringBuilder x) {w.print(x);w.flush();}
		void p(BigInteger x) {w.print(x);w.flush();}
		void p(double x) {w.print(x);w.flush();}
		void p(boolean x) {w.print(x);w.flush();}
	}
}
