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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

//
import java.math.*;
import java.util.*;
import java.io.*;
  
public class Main { 
  
    static BufferedReader in;
    static PrintWriter out = new PrintWriter(System.out);
    static String file = "../in";
    static int test = 10; // 0 for local testing, 1 for std input
    static int inf = 1_000_000;

    int gcd(int a, int b)
    {
        if(b == 0) return a;
        return gcd(b, a % b);
    }

    void swap(int[]ary, int i, int j)
    {
        int t = ary[i];
        ary[i] = ary[j];
        ary[j] = t;
    }
    
    String[] split() throws Exception
    {
        return in.readLine().split(" ");
    }

    int readInt() throws Exception
    {
        return Integer.valueOf(in.readLine());
    }

    int[] toIntArray() throws Exception
    {
        String[] sp = split();
        int n = sp.length;
        int[] ary = new int[n];
        for(int i = 0; i < n; i++) ary[i] = Integer.valueOf(sp[i]);
        return ary;
    }

    String reverse(String str)
    {
        return new StringBuilder(str).reverse().toString();
    }

    public static void main(String[] args) throws Exception
    {
        int _k = Integer.valueOf("1");
        if(test > 0) in = new BufferedReader(new InputStreamReader(System.in));
        else in = new BufferedReader(new FileReader(file));
        if(test < 0) {String[] str = in.readLine().split(" ");}
/***********************************************************************/
/***********************************************************************/
/***********************************************************************/
/***********************************************************************/
        // System.out.println((-100 + 0) / 2);

        new Main().b();
        out.flush();
    }

    void b() throws Exception
    {
        int n = readInt();
        int[][] points = new int[n][2];
        for(int i = 0; i < n; i++)
        {
            points[i] = toIntArray();
        }
        
        int[] vis = new int[n];
        int total = 0;
        int re = 0;
        while(total < n)
        {
            for(int i = 0; i < n; i++)
            {
                if(vis[i] > 0) continue;
                // point[i] is starting point
                vis[i] = 1;
                total++;
                Map<String, Integer> map = new HashMap<>();
                String slp = "";
                int count = 0;
                for(int j = i + 1; j < n; j++)
                {
                    if(vis[j] > 0) continue;
                    String slope = getSlope(points[i], points[j]);
                    map.put(slope, map.getOrDefault(slope, 0) + 1);
                    if(count < map.get(slope)) 
                    {
                        slp = slope;
                        count = map.get(slope);
                    }
                }

                // System.out.println("...");
                // System.out.println(slp);
                // System.out.println("...");

                for(int j = i + 1; j < n; j++)
                {
                    if(vis[j] > 0) continue;
                    String slope = getSlope(points[i], points[j]);
                    if(slp.equals(slope))
                    {
                        vis[j] = 1;
                    }
                }
                // System.out.println(map);
                re++;
                total += count;
                // System.out.println(Arrays.toString(vis));
                // System.out.println(total);
            }
        }

      	out.println(re);
    }

    String getSlope(int[] a, int[] b)
    {
        int dx = b[0] - a[0], dy = b[1] - a[1];
        if(dx == 0) return "null";
        int gcd = gcd(dx, dy);
        return "" + (dy / gcd) + "/" + (dx / gcd);
    }
}