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.Linq;
using BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var N = consoleReader.Int;
            var points = consoleReader.Repeat(N).SplitInt.Select(l => new Point(l)).ToArray();
            var dic = new Dictionary<Diff, int>();

            if (N == 1) return 1;

            for (int i = 0; i < points.Length; i++)
                for (int j = 0; j < points.Length; j++)
                {
                    if (i == j) continue;
                    var diff = points[i] - points[j];
                    var count = dic.GetOrDefault(diff);
                    dic[diff] = count + 1;
                }
            return N - dic.Values.Max();
        }

        struct Point
        {
            public int x;
            public int y;
            public static Diff operator -(Point a, Point b)
            {
                return new Diff { p = a.x - b.x, q = a.y - b.y };
            }
            public Point(int[] l)
            {
                x = l[0];
                y = l[1];
            }
        }

        struct Diff : IEquatable<Diff>
        {
            public int p;
            public int q;

            public override bool Equals(object obj)
            {
                if (obj is Diff)
                {
                    return ((Diff)obj).Equals(this);
                }
                return false;
            }
            public bool Equals(Diff other) => this.p == other.p && this.q == other.q;

            public override int GetHashCode()
            {
                var hashCode = -554926429;
                hashCode = hashCode * -1521134295 + this.p.GetHashCode();
                hashCode = hashCode * -1521134295 + this.q.GetHashCode();
                return hashCode;
            }
        }


        #region いつもの
        private readonly ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader()).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
        #endregion
    }

    public static class DicExt
    {
        public static V GetOrDefault<K, V>(this IDictionary<K, V> dic, K key, V defaultValue = default(V))
        {
            V val;
            return dic.TryGetValue(key, out val) ? val : defaultValue;
        }
        public static V GetOrInit<K, V>(this IDictionary<K, V> dic, K key) where V : new()
        {
            V val;
            if (dic.TryGetValue(key, out val))
                return val;

            val = new V();
            dic.Add(key, val);
            return val;
        }
    }
#pragma warning disable
    public class ConsoleReader { public class SplitLine { string[] splited; public SplitLine(string line) { splited = line.Split(); } public string[] String => splited.ToArray(); public int[] Int => splited.Select(int.Parse).ToArray(); public long[] Long => splited.Select(long.Parse).ToArray(); public ulong[] ULong => splited.Select(ulong.Parse).ToArray(); public double[] Double => splited.Select(double.Parse).ToArray(); } public class RepeatLine { ConsoleReader reader; int num; public RepeatLine(ConsoleReader reader, int num) { this.reader = reader; this.num = num; } public IEnumerable<string> String { get { for (int i = 0; i < num; i++) yield return reader.String; } } public IEnumerable<int> Int { get { for (int i = 0; i < num; i++) yield return reader.Int; } } public IEnumerable<long> Long { get { for (int i = 0; i < num; i++) yield return reader.Long; } } public IEnumerable<string[]> Split { get { for (int i = 0; i < num; i++) yield return reader.Split.String; } } public IEnumerable<int[]> SplitInt { get { for (int i = 0; i < num; i++) yield return reader.Split.Int; } } } public virtual string String => Console.ReadLine(); public int Int => int.Parse(String); public long Long => long.Parse(String); public ulong ULong => ulong.Parse(String); public double Double => double.Parse(String); public SplitLine Split => new SplitLine(String); public RepeatLine Repeat(int count) => new RepeatLine(this, count); }
}