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;
using System.IO;
using System.Linq;

namespace Sandbox
{
    internal class Program
    {
        private static void Main(string[] args)
        {
            var scanner = new Scanner();
            var n = scanner.GetNextAsInt();

            var balls = new int[n,2];

            for (var i = 0; i < n; i++)
            {
                balls[i, 0] = scanner.GetNextAsInt();
                balls[i, 1] = scanner.GetNextAsInt();
            }

            var dic = new Dictionary<int, Dictionary<int, int>>();

            if (n == 1)
            {
                Console.WriteLine("1");
                return;
            }

            for (var i = 0; i < n; i++)
            {
                for (var j = i + 1; j < n; j++)
                {
                    if (i == j)
                    {
                        continue;
                    }

                    var ballix = balls[i, 0];
                    var balliy = balls[i, 1];
                    var balljx = balls[j, 0];
                    var balljy = balls[j, 1];

                    var diffx = ballix - balljx;
                    var diffy = balliy - balljy;

                    if (diffx < 0)
                    {
                        diffx = -diffx;
                        diffy = -diffy;
                    }
                    else if (diffx == 0 && diffy < 0)
                    {
                        diffy = -diffy;
                    }

                    Dictionary<int, int> xdic;
                    if (dic.ContainsKey(diffx))
                    {
                        xdic = dic[diffx];
                    }
                    else
                    {
                        xdic = new Dictionary<int, int>();
                        dic[diffx] = xdic;
                    }

                    var count = 0;
                    if (xdic.ContainsKey(diffy))
                    {
                        count = xdic[diffy];
                    }

                    count++;
                    xdic[diffy] = count;
                }
            }

            var maxCount = dic.Values
                .SelectMany(_ => _.Values)
                .OrderByDescending(_ => _)
                .First();

            Console.WriteLine(n - maxCount);
        }

        #region String Scanner

        public class Scanner
        {
            private const char Separator = ' ';
            private readonly StreamReader _Stream = new StreamReader(Console.OpenStandardInput());
            private int _Pos;
            private string[] _Line = new string[0];

            #region get a element

            public string GetNext()
            {
                // ReSharper disable once InvertIf
                if (this._Pos >= this._Line.Length)
                {
                    // ReSharper disable once PossibleNullReferenceException
                    this._Line = this._Stream.ReadLine().Split(Separator);
                    this._Pos = 0;
                }

                return this._Line[this._Pos++];
            }

            public int GetNextAsInt()
            {
                return int.Parse(this.GetNext());
            }

            public long GetNextAsLong()
            {
                return long.Parse(this.GetNext());
            }

            public double GetNextAsDouble()
            {
                return double.Parse(this.GetNext());
            }

            #endregion

            #region get array

            public string[] ToArrayFromNextLine()
            {
                if (this._Pos >= this._Line.Length)
                {
                    // ReSharper disable once PossibleNullReferenceException
                    this._Line = this._Stream.ReadLine().Split(Separator);
                }

                this._Pos = this._Line.Length;
                return this._Line;
            }

            public int[] ToIntArrayFromNextLine()
            {
                return ToIntArray(this.ToArrayFromNextLine());
            }

            public long[] ToLongArrayFromNextLine()
            {
                return ToLongArray(this.ToArrayFromNextLine());
            }

            public double[] ToDoubleArrayFromNextLine()
            {
                return ToDoubleArray(this.ToArrayFromNextLine());
            }

            #endregion

            #region convert array

            private static int[] ToIntArray(string[] array)
            {
                var result = new int[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = int.Parse(array[i]);
                }

                return result;
            }

            private static long[] ToLongArray(string[] array)
            {
                var result = new long[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = long.Parse(array[i]);
                }

                return result;
            }

            private static double[] ToDoubleArray(string[] array)
            {
                var result = new double[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = double.Parse(array[i]);
                }

                return result;
            }

            #endregion
        }

        #endregion
    }
}