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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.StringTokenizer;

public class Main {
	public static void main(String[] args) throws IOException {
		Main mainObj = new Main();
		mainObj.solve();
	}

	public void solve() throws IOException {
		FastScanner fs = new FastScanner();
		
		int n = fs.nextInt();
		
		ArrayList<Point> pointArr = new ArrayList<>();
		
		for(int i = 0; i < n; i++) {
			int x = fs.nextInt();
			int y = fs.nextInt();
			
			pointArr.add(new Point(i, x ,y));
		}
		
		HashMap<Integer, HashMap<Integer, Integer>> distanceMap  = new HashMap<>();
		
		for(int i = 0; i < n ; i++) {
			for(int j = i+1; j < n; j++) {
				Point startPoint = pointArr.get(i);
				Point endPoint = pointArr.get(j);
				
				if(startPoint.x > endPoint.x) {
					Point swap = startPoint;
					startPoint = endPoint;
					endPoint = swap;
				}
				
				int xDistance = endPoint.x - startPoint.x;
				int yDistance = endPoint.y - startPoint.y;
				
				HashMap<Integer,Integer> yDistanceMap;
				
				if(distanceMap.containsKey(xDistance)) {
					yDistanceMap = distanceMap.get(xDistance);
				}else {
					yDistanceMap = new HashMap<>();
				}
				
				if(yDistanceMap.containsKey(yDistance)) {
					int time = yDistanceMap.get(yDistance);
					yDistanceMap.put(yDistance, time+1);
				}else {
					yDistanceMap.put(yDistance, 1);
				}
				
				distanceMap.put(xDistance, yDistanceMap);
			}
		}
		
		int maxPair = 0;
		
		for(Integer xkey : distanceMap.keySet()) {
			
			HashMap<Integer, Integer> yDistanceMap = distanceMap.get(xkey);
			
			for(Integer yKey : yDistanceMap.keySet()) {
				if(yKey == 0 && xkey == 0) {
					continue;
				}
				
				maxPair = Math.max(maxPair, yDistanceMap.get(yKey));
			}
		}
		
		System.out.println(n-maxPair);
		
	}
	
	class Pair {
		
		int startId;;
		int endId;
		
		Pair(int startId, int endId){
			this.startId = startId;
			this.endId = endId;
		}
	}
	
	class Point {
		int id;
		int x;
		int y;
		
		Point(int id, int x, int y){
			this.id = id;
			this.x = x;
			this.y = y;
		}
	}

	

	public class FastScanner {

		BufferedReader reader;
		private StringTokenizer st;

		public FastScanner() {
			st = null;
			reader = new BufferedReader(new InputStreamReader(System.in));
		}

		public String next() throws IOException {
			if (st == null || !st.hasMoreElements()) {
				st = new StringTokenizer(reader.readLine());
			}
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			st = null;
			String readLine = null;
			readLine = reader.readLine();
			return readLine;
		}

		public int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

		public int[] nextIntArr(int n) throws NumberFormatException, IOException {
			int[] retArr = new int[n];
			for (int i = 0; i < n; i++) {
				retArr[i] = nextInt();
			}
			return retArr;
		}

		public long[] nextLongArr(int n) throws NumberFormatException, IOException {
			long[] retArr = new long[n];
			for (int i = 0; i < n; i++) {
				retArr[i] = nextLong();
			}
			return retArr;
		}

		public void close() throws IOException {
			reader.close();
		}
	}

}