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.io.*;
import java.util.*;
import java.util.Stack;
import java.util.regex.Pattern;


public class Main {

	
	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;
		//it reads the data about the specified point and divide the data about it ,it is quite fast
		//than using direct 

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception r) {
					r.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());//converts string to integer
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception r) {
				r.printStackTrace();
			}
			return str;
		}
	}
	
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	static long mod = (long)(1e9+7);
	public static void main(String[] args) {
		 FastReader sc = new FastReader();
		 int t = sc.nextInt();
		 Pair[] p = new Pair[t];
		 for(int i=0;i<t;++i) p[i] = new Pair(sc.nextInt(),sc.nextInt());
		 
		 Arrays.sort(p,new Comparator<Pair>() {

			@Override
			public int compare(Pair o1, Pair o2) {
				if(o1.x == o2.x) return o1.y - o2.y;
				return o1.x-o2.x;
			}
			 
		 });
		 Map<Integer,Integer> mapx = new HashMap<>();
		 Map<Integer,Integer> mapy = new HashMap<>();
		 for(int i=0;i+1<t;++i) {
			 add(mapx,p[i+1].x-p[i].x);
			 add(mapy,p[i+1].y-p[i].y);
		 }
		 
		 int maxx = 0,maxy=0;
		 for(int key : mapx.keySet()) maxx = Math.max(maxx,mapx.get(key));
		 for(int key : mapy.keySet()) maxy = Math.max(maxy,mapy.get(key));
		 out.println(t-Math.min(maxx, maxy));
		 out.close();
		 
	}
	private static void add(Map<Integer, Integer> map, int i) {
		// TODO Auto-generated method stub
		if(map.containsKey(i)) map.put(i, map.get(i)+1);
		else map.put(i, 1);
		
	}
	static class Pair{
		int x;
		int y;
		Pair(int x,int y){
			this.x = x;
			this.y = y;
		}
	}
}