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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*; import java.io.*; import java.math.*;
public class Main{
	//Don't have to see. start------------------------------------------
	static class InputIterator{
		ArrayList<String> inputLine = new ArrayList<String>(1024);
		int index = 0; int max; String read;
		InputIterator(){
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			try{
				while((read = br.readLine()) != null){
					inputLine.add(read);
				}
			}catch(IOException e){}
			max = inputLine.size();
		}
		boolean hasNext(){return (index < max);}
		String next(){
			if(hasNext()){
				return inputLine.get(index++);
			}else{
				throw new IndexOutOfBoundsException("There is no more input");
			}
		}
	}
	static HashMap<Integer, String> CONVSTR = new HashMap<Integer, String>();
	static InputIterator ii = new InputIterator();//This class cannot be used in reactive problem.
	static PrintWriter out = new PrintWriter(System.out);
	static void flush(){out.flush();}
	static void myout(Object t){out.println(t);}
	static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
	static String next(){return ii.next();}
	static boolean hasNext(){return ii.hasNext();}
	static int nextInt(){return Integer.parseInt(next());}
	static long nextLong(){return Long.parseLong(next());}
	static double nextDouble(){return Double.parseDouble(next());}
	static ArrayList<String> nextStrArray(){return myconv(next(), 8);}
	static ArrayList<String> nextCharArray(){return myconv(next(), 0);}
	static ArrayList<Integer> nextIntArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Integer> ret = new ArrayList<Integer>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Integer.parseInt(input.get(i)));
		}
		return ret;
	}
	static ArrayList<Long> nextLongArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Long> ret = new ArrayList<Long>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Long.parseLong(input.get(i)));
		}
		return ret;
	}
	static String myconv(Object list, int no){//only join
		String joinString = CONVSTR.get(no);
		if(list instanceof String[]){
			return String.join(joinString, (String[])list);
		}else if(list instanceof ArrayList){
			return String.join(joinString, (ArrayList)list);
		}else{
			throw new ClassCastException("Don't join");
		}
	}
	static ArrayList<String> myconv(String str, int no){//only split
		String splitString = CONVSTR.get(no);
		return new ArrayList<String>(Arrays.asList(str.split(splitString)));
	}
	public static void main(String[] args){
		CONVSTR.put(8, " "); CONVSTR.put(9, "\n"); CONVSTR.put(0, "");
		solve();flush();
	}
	//Don't have to see. end------------------------------------------
	static void solve(){//Here is the main function
		int N = nextInt();
		if(N == 1){
			myout(1);
			return;
		}
		Node[] list = new Node[N];
		for(int i = 0; i < N; i++){
			ArrayList<Integer> tmp = nextIntArray();
			list[i] = new Node(tmp.get(0), tmp.get(1));
		}
		int output = 99;
		for(int i = 0; i < N - 1; i++){
			for(int j = i + 1; j < N; j++){
				int diffX = list[i].x - list[j].x;
				int diffY = list[i].y - list[j].y;
				UnionFind uf = new UnionFind(N);
				for(int k = 0; k < N; k++){
					for(int l = 0; l < N; l++){
						if(k != l){
							if(list[k].x - list[l].x == diffX && list[k].y - list[l].y == diffY){
								uf.doUnion(k, l);
							}
						}
					}
				}
				int count = 0;
				for(int k = 0; k < N; k++){
					if(uf.list[k] < 0){
						count++;
					}
				}
				output = Math.min(output, count);
			}
		}
		myout(output);
	}
	//Method addition frame start

static class Node{
	int x;
	int y;
	Node(int x, int y){
		this.x = x;
		this.y = y;
	}
}

static class UnionFind{
  int[] list;
  UnionFind(int size){
    list = new int[size];
    for(int i = 0; i < size; i++){
      list[i] = -1;
    }
  }
  boolean isSame(int mae, int ato){
    return getRootIndex(mae) == getRootIndex(ato);
  }
  int getRootIndex(int index){
    if(list[index] < 0){
      return index;
    }else{
      list[index] = getRootIndex(list[index]);
      return list[index];
    }
  }
  void doUnion(int mae, int ato){
    int maeRoot = getRootIndex(mae);
    int atoRoot = getRootIndex(ato);
    if(!isSame(maeRoot, atoRoot)){
      if(maeRoot >= atoRoot){
        list[maeRoot] += list[atoRoot];
        list[atoRoot] = maeRoot;
      }else{
        list[atoRoot] += list[maeRoot];
        list[maeRoot] = atoRoot;
      }
    }
  }
  int getSize(int index){
    return -list[getRootIndex(index)];
  }
}

	//Method addition frame end
}