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;
using System.Text;
using System.Collections;
using System.Linq.Expressions;
using Pair = System.Tuple<long, long>;
using Graph = System.Collections.Generic.List<System.Collections.Generic.List<long>>;
using static _20200215.Cin;
using static _20200215.Util;

namespace _20200215
{
    public class Program
    {
        public static void Main(string[] args)
        {
            DontAutoFlush();

            // ABC036_C(); 13m
            // AGC038_A(); 140m
            // Tenka1_2017_C(); 60m
            // ARC067_D(); 20m
            Diverta2019_2_B(); //180m

            Flush();
        }

        /// <summary>
        /// B - Picking Up
        /// </summary>
        public static void Diverta2019_2_B()
        {
            long N = rl;
            long[] a, b;
            ReadCols(out a, out b, N);

            var hm = new HashMap<long, HashMap<long, long>>();

            for (int i = 0; i < N-1; i++)
            {
                for (int j = i + 1; j < N; j++)
                {
                    var dx = a[j] - a[i];
                    var dy = b[j] - b[i];
                    hm[dx][dy]++;
                    hm[-dx][-dy]++;
                }
            }

            long cnt = 0;
            foreach(var dx in hm.Keys)
            {
                foreach(var dy in hm[dx].Keys)
                {
                    ChMax(ref cnt, hm[dx][dy]);
                }
            }

            long ans = N - cnt;
            Console.WriteLine(ans);
        }

        /// <summary>
        /// D - Walk and Teleport
        /// </summary>
        public static void ARC067_D()
        {
            long N = rl;
            long A = rl;
            long B = rl;
            long[] X = rla;

            long ans = 0;
            for (int i = 1; i < N; i++)
            {
                long diff = X[i] - X[i-1];
                ans += Math.Min(diff * A, B);
            }

            Console.WriteLine(ans);
        }

        /// <summary>
        /// C - 4/N
        /// </summary>
        public static void Tenka1_2017_C()
        {
            long N = rl;

            for (int h = 1; h <= 3500; h++)
            {
                for (int n = 1; n <= 3500; n++)
                {
                    long hnN = h * n * N;
                    long bunbo = 4 * h * n - n * N - h * N;
                    if (bunbo <= 0)
                        continue;
                    if(hnN % bunbo == 0)
                    {
                        Console.WriteLine("{0} {1} {2}", h, n, hnN/bunbo);
                        return;
                    }
                }
            }
        }

        /// <summary>
        /// A - 01 Matrix
        /// </summary>
        public static void AGC038_A()
        {
            long H = rl;
            long W = rl;
            long A = rl;
            long B = rl;

            string s1 = new string('1', (int)A) + new string('0', (int)(W - A));
            string s2 = new string('0', (int)A) + new string('1', (int)(W - A));

            for (int i = 0; i < B; i++)
            {
                Console.WriteLine(s1);
            }
            for (int i = 0; i < H-B; i++)
            {
                Console.WriteLine(s2);
            }
        }

        /// <summary>
        /// C - 座圧
        /// </summary>
        public static void ABC036_C()
        {
            long N = rl;
            long[] A = new long[N];
            for (int i = 0; i < N; i++)
            {
                A[i] = rl;
            }

            var sorted = A.OrderBy(a => a).Distinct().ToArray();
            Dictionary<long, long> dic = new Dictionary<long, long>();
            for (int i = 0; i < sorted.Length; i++)
            {
                dic[sorted[i]] = i;
            }

            foreach(var a in A)
            {
                Console.WriteLine(dic[a]);
            }
        }

    }

    public class HashMap<K,V>:Dictionary<K,V>{V i;static Func<V>j=Expression.Lambda<Func<V>>(Expression.New(typeof(V))).Compile();public HashMap(){}public HashMap(V a){i=a;}new public V this[K a]{get{V b;if(TryGetValue(a,out b))return b;else return base[a]=i!=null?i:j();}set{base[a]=value;}}}public static class Util{public static readonly long INF=(long)1e17;public readonly static long MOD=(long)1e9+7;public static void DontAutoFlush(){var a=new StreamWriter(Console.OpenStandardOutput()){AutoFlush=false};Console.SetOut(a);}public static void Flush(){Console.Out.Flush();}public static T[]Sort<T>(T[]a){Array.Sort<T>(a);return a;}public static T[]SortDecend<T>(T[]a){Array.Sort<T>(a);Array.Reverse(a);return a;}public static void Swap<T>(ref T a,ref T b){T c=a;a=b;b=c;}public static int GCD(int a,int b){return(b==0)?a:GCD(b,a%b);}public static void ChMax(ref long a,long b){if(a<b)a=b;}public static void ChMin(ref long a,long b){if(a>b)a=b;}public static long ModAdd(long a,long b){long c=a+b;if(c>=MOD)return c%MOD;return c;}public static long ModMul(long a,long b){long c=a*b;if(c>=MOD)return c%MOD;return c;}public static void ChModAdd(ref long a,long b){a+=b;if(a>=MOD)a%=MOD;}public static void ChModMul(ref long a,long b){a*=b;if(a>=MOD)a%=MOD;}public static void FillArray<T>(T[]a,T b){int c=a.Length;for(int d=0;d<c;d++)a[d]=b;}public static void FillArray<T>(T[,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);for(int e=0;e<c;e++)for(int f=0;f<d;f++){a[e,f]=b;}}public static void FillArray<T>(T[,,]a,T b){int c=a.GetLength(0);int d=a.GetLength(1);int e=a.GetLength(2);for(int f=0;f<c;f++)for(int g=0;g<d;g++){for(int h=0;h<e;h++){a[f,g,h]=b;}}}public static long[]Accumulate(long[]a){long[]b=new long[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}public static double[]Accumulate(double[]a){double[]b=new double[a.Length+1];for(int c=0;c<a.Length;c++)b[c+1]=b[c]+a[c];return b;}}public static class Cin{public static long rl{get{return ReadLong();}}public static long[]rla{get{return ReadLongArray();}}public static double rd{get{return ReadDouble();}}public static double[]rda{get{return ReadDoubleArray();}}public static string rs{get{return ReadString();}}public static int ReadInt(){return int.Parse(k());}public static long ReadLong(){return long.Parse(k());}public static double ReadDouble(){return double.Parse(k());}public static string ReadString(){return k();}public static int[]ReadIntArray(){i=null;return Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);}public static long[]ReadLongArray(){i=null;return Array.ConvertAll(Console.ReadLine().Split(' '),long.Parse);}public static double[]ReadDoubleArray(){i=null;return Array.ConvertAll(Console.ReadLine().Split(' '),double.Parse);}public static void ReadCols(out long[]a,out long[]b,long c){a=new long[c];b=new long[c];for(int d=0;d<c;d++){a[d]=ReadLong();b[d]=ReadLong();}}public static void ReadCols(out long[]a,out long[]b,out long[]c,long d){a=new long[d];b=new long[d];c=new long[d];for(int e=0;e<d;e++){a[e]=ReadLong();b[e]=ReadLong();c[e]=ReadLong();}}public static int[][]ReadIntTable(int a){i=null;int[][]b=new int[a][];for(int c=0;c<a;c++)b[c]=ReadIntArray();return b;}public static long[][]ReadLongTable(long a){i=null;long[][]b=new long[a][];for(long c=0;c<a;c++)b[c]=ReadLongArray();return b;}static string[]i{get;set;}static int j{get;set;}static string k(){if(i==null||i.Length<=j){i=Console.ReadLine().Split(' ');j=0;}return i[j++];}}
}