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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;

namespace ConsoleApp2
{
	class Program
	{
		static void Main(string[] args)
		{
			int n = int.Parse(Console.ReadLine());
			var list = new List<Coordinate>(n);

			for (int i = 0; i < n; i++)
			{
				var inputs = Console.ReadLine().Split(' ');
				list.Add(new Coordinate(int.Parse(inputs[0]), int.Parse(inputs[1])));
			}
			list.Sort((a, b) => 
			{
				if (a.mX == b.mX)
				{
					return a.mY - b.mY;
				}
				else
				{
					return a.mX - b.mX;
				}
			});

			var dic = new Dictionary<Diff, int>();
			for(int i = 0; i < n - 1; i++)
			{
				for (int j = i + 1; j < n; j++)
				{
					var diff = new Diff(list[i], list[j]);
					if (dic.ContainsKey(diff))
					{
						dic[diff]++;
					}
					else
					{
						dic.Add(diff, 1);
					}
				}
			}
			int sameDiff = 0;
			foreach(var val in dic.Values)
			{
				sameDiff = Math.Max(sameDiff, val);
			}
			// コスト0で回収できる回数
			int zeroCostCount = sameDiff;

			int cost = 1 + (n - 1 - zeroCostCount);

			Console.WriteLine(cost);
		}

		public class Coordinate
		{
			public int mX;
			public int mY;

			public Coordinate(int x, int y)
			{
				mX = x;
				mY = y;
			}
		}

		public struct Diff
		{
			public int mDiffX;
			public int mDiffY;

			public Diff(Coordinate a, Coordinate b)
			{
				mDiffX = b.mX - a.mX;
				mDiffY = b.mY - a.mY;
			}

			public override bool Equals(object obj)
			{
				return ((Diff)obj).mDiffX == mDiffX && ((Diff)obj).mDiffY == mDiffY;
			}

			public override int GetHashCode()
			{
				return mDiffX + mDiffY;
			}
		}
	}
}