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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.io.StringReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main  implements Runnable {

    public static void main(String[] args) {

        new Thread(null, new Main(), "", 16 * 1024 * 1024).start();

    }

    public void run() {
    	FastScanner sc = new FastScanner(System.in);
		//long n = Long.parseLong(sc.next());
    	//int[] ar = new int[3];
    	//ar[0]=Integer.parseInt(sc.next());
    	//ar[1]=Integer.parseInt(sc.next());
    	//ar[2]=Integer.parseInt(sc.next());
    	//Arrays.parallelSort(ar);
		int n = Integer.parseInt(sc.next());
		//int k = Integer.parseInt(sc.next());
		//int q = Integer.parseInt(sc.next());
		//int r = Integer.parseInt(sc.next());
		//int a = Integer.parseInt(sc.next())-1;
		//int b = Integer.parseInt(sc.next())-1;
		//int c = Integer.parseInt(sc.next())-1;
		//int d = Integer.parseInt(sc.next())-1;
		//String s = sc.next();
		//int k = Integer.parseInt(sc.next());
		//int m = Integer.parseInt(sc.next());
		//int x2000 = Integer.parseInt(sc.next());
		//int t = Integer.parseInt(sc.next());
		//int k = 0;
		//int k = Integer.parseInt(sc.next());
		///String str = sc.next();
		//char c[] = str.toCharArray();
		//char a[][] = new char[n];
		//int atmp[] = new int[h];
		//int max= 0;
		//int blackar[][] = new int[h*w][2];
		//int p=0;
		ArrayList<MyClass> lists = new ArrayList<MyClass>();
		//lists = new ArrayList;

		int[][] xy = new int[n][2];
		for(int i = 0; i < n; i++)
		{
			xy[i][0]=Integer.parseInt(sc.next());
			xy[i][1]=Integer.parseInt(sc.next());
		}

		for(int i = 0; i < n; i++)
		{
			for(int j = i+1; j < n; j++)
			{
				lists.add(new MyClass(xy[i][0]-xy[j][0],xy[i][1]-xy[j][1]));
			}
		}
		int max = 1;
		while(lists.size()!=0)
		{
			int x = lists.get(0).x;
			int y = lists.get(0).y;
			int cn = 1;
			lists.remove(0);
			for(int i = lists.size()-1; i >= 0; i--)
			{
				if(lists.get(i).x == x && lists.get(i).y == y)
				{
					cn++;
					lists.remove(i);
				}
				else if(lists.get(i).x == -x && lists.get(i).y == -y)
				{
					cn++;
					lists.remove(i);
				}
			}
			if(cn > max)
			{
				max = cn;
			}
		}

		PrintWriter out = new PrintWriter(System.out);
		if(n==1)
		{
			out.println(1);
		}
		else
		{
			out.println(n-max);
		}




		out.flush();
	}

    static class FastScanner {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;
        public FastScanner(String in) {
        	StringReader sr = new StringReader(in);
            reader = new BufferedReader(new BufferedReader(sr));
            tokenizer = null;
        }
        public FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        public String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }

            return tokenizer.nextToken("\n");
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public long nextInt() {
            return Integer.parseInt(next());
        }

    }

}


class MyClass {
	int x;
    int y;

    public MyClass(int x, int y) {
    	this.x = x;
        this.y = y;
    }

}
