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 static System.Math;
using System.Text;

namespace Program
{
    public static class DIVERTA2019_2B
    {
        static public void Solve()
        {
            var N = NextInt;
            var list = new List<Tuple<int, int>>();
            for (int i = 0; i < N; ++i)
            {
                var x = NextInt;
                var y = NextInt;
                list.Add(Tuple.Create(x, y));
            }
            if (N == 1)
            {
                Console.WriteLine(1);
                return;
            }
            var diff = new Dictionary<Tuple<int, int>, int>();
            for (int i = 0; i < N; ++i)
            {
                for (int j = 0; j < N; ++j)
                {
                    if (i == j) continue;
                    var key = Tuple.Create(list[i].Item1 - list[j].Item1, list[i].Item2 - list[j].Item2);
                    if (diff.ContainsKey(key))
                    {
                        diff[key]++;
                    }
                    else
                    {
                        diff[key] = 1;
                    }
                }
            }

            Console.WriteLine(N - diff.Values.Max());
        }

        static public void Main(string[] args)
        {
            if (args.Length == 0)
            {
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }
            Solve();
            Console.Out.Flush();
        }
        static Random rand = new Random();
        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            public static string NextString()
            {
                if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item);
                return param.Dequeue();
            }
        }
        static int NextInt => int.Parse(Console_.NextString());
        static long NextLong => long.Parse(Console_.NextString());
        static double NextDouble => double.Parse(Console_.NextString());
        static string NextString => Console_.NextString();
        static List<int> NextIntList(int N) => Enumerable.Repeat(0, N).Select(_ => NextInt).ToList();
        static List<long> NextLongList(int N) => Enumerable.Repeat(0, N).Select(_ => NextLong).ToList();
        static List<double> NextDoubleList(int N) => Enumerable.Repeat(0, N).Select(_ => NextDouble).ToList();
        static List<string> NextStringList(int N) => Enumerable.Repeat(0, N).Select(_ => NextString).ToList();
        static IEnumerable<T> OrderByRand<T>(this IEnumerable<T> x) => x.OrderBy(_ => rand.Next());
        static IEnumerable<T> Repeat<T>(T v, int n) => Enumerable.Repeat<T>(v, n);
        static List<T> Sort<T>(List<T> l) where T : IComparable
        {
            var tmp = l.ToArray(); Array.Sort(tmp); return tmp.ToList();
        }
        static List<T> Sort<T>(List<T> l, Comparison<T> comp) where T : IComparable
        {
            var tmp = l.ToArray(); Array.Sort(tmp, comp); return tmp.ToList();
        }
        static List<T> RevSort<T>(List<T> l) where T : IComparable
        {
            var tmp = l.ToArray(); Array.Sort(tmp, (x, y) => y.CompareTo(x)); return tmp.ToList();
        }
        static List<T> RevSort<T>(List<T> l, Comparison<T> comp) where T : IComparable
        {
            var tmp = l.ToArray(); Array.Sort(tmp, (x, y) => comp(y, x)); return tmp.ToList();
        }
        static IEnumerable<long> Prime(long x)
        {
            if (x < 2) yield break;
            yield return 2;
            var halfx = x / 2;
            var table = new bool[halfx + 1];
            var max = (long)(Math.Sqrt(x) / 2);
            for (long i = 1; i <= max; ++i)
            {
                if (table[i]) continue;
                var add = 2 * i + 1;
                yield return add;
                for (long j = 2 * i * (i + 1); j <= halfx; j += add) table[j] = true;
            }
            for (long i = max + 1; i <= halfx; ++i) if (!table[i] && 2 * i + 1 <= x) yield return 2 * i + 1;
        }
        static IEnumerable<long> Divisor(long x)
        {
            if (x < 1) yield break;
            var max = (long)Math.Sqrt(x);
            for (long i = 1; i <= max; ++i)
            {
                if (x % i != 0) continue;
                yield return i;
                if (i != x / i) yield return x / i;
            }
        }
        static long GCD(long a, long b)
        {
            while (b > 0) { var tmp = b; b = a % b; a = tmp; }
            return a;
        }
        class PQ<T> where T : IComparable
        {
            private List<T> h;
            private Comparison<T> c;
            public PQ(int cap, Comparison<T> c, bool asc = true) { h = new List<T>(cap); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(Comparison<T> c, bool asc = true) { h = new List<T>(); this.c = asc ? c : (x, y) => c(y, x); }
            public PQ(int cap, bool asc = true) : this(cap, (x, y) => x.CompareTo(y), asc) { }
            public PQ(bool asc = true) : this((x, y) => x.CompareTo(y), asc) { }
            public void Push(T v)
            {
                var i = h.Count;
                h.Add(v);
                while (i > 0)
                {
                    var ni = (i - 1) / 2;
                    if (c(v, h[ni]) >= 0) break;
                    h[i] = h[ni]; i = ni;
                }
                h[i] = v;
            }
            public T Peek => h[0];
            public int Count => h.Count;
            public T Pop()
            {
                var r = h[0];
                var v = h[h.Count - 1];
                h.RemoveAt(h.Count - 1);
                if (h.Count == 0) return r;
                var i = 0;
                while (i * 2 + 1 < h.Count)
                {
                    var i1 = i * 2 + 1;
                    var i2 = i * 2 + 2;
                    if (i2 < h.Count && c(h[i1], h[i2]) > 0) i1 = i2;
                    if (c(v, h[i1]) <= 0) break;
                    h[i] = h[i1]; i = i1;
                }
                h[i] = v;
                return r;
            }
        }
        class PQ<TKey, TValue> where TKey : IComparable
        {
            private PQ<Tuple<TKey, TValue>> q;
            public PQ(int cap, Comparison<TKey> c, bool asc = true) { q = new PQ<Tuple<TKey, TValue>>(cap, (x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(Comparison<TKey> c, bool asc = true) { q = new PQ<Tuple<TKey, TValue>>((x, y) => c(x.Item1, y.Item1), asc); }
            public PQ(int cap, bool asc = true) : this(cap, (x, y) => x.CompareTo(y), asc) { }
            public PQ(bool asc = true) : this((x, y) => x.CompareTo(y), asc) { }
            public void Push(TKey k, TValue v) => q.Push(Tuple.Create(k, v));
            public Tuple<TKey, TValue> Peek => q.Peek;
            public int Count => q.Count;
            public Tuple<TKey, TValue> Pop() => q.Pop();
        }
        class Mod
        {
            static public long _mod = 1000000007;
            private long _val = 0;
            public Mod(long x) { _val = x % _mod; }
            static public implicit operator Mod(long x) => new Mod(x);
            static public explicit operator long(Mod x) => x._val;
            static public Mod operator +(Mod x) => x._val;
            static public Mod operator -(Mod x) => -x._val;
            static public Mod operator ++(Mod x) => x._val + 1;
            static public Mod operator --(Mod x) => x._val - 1;
            static public Mod operator +(Mod x, Mod y) => (x._val + y._val) % _mod;
            static public Mod operator -(Mod x, Mod y) => ((((x._val - y._val) % _mod) + _mod) % _mod);
            static public Mod operator *(Mod x, Mod y) => (x._val * y._val) % _mod;
            static public Mod operator /(Mod x, Mod y) => (x._val * Inverse(y._val)) % _mod;
            static public bool operator ==(Mod x, Mod y) => x._val == y._val;
            static public bool operator !=(Mod x, Mod y) => x._val != y._val;
            static public bool operator <(Mod x, Mod y) => x._val < y._val;
            static public bool operator >(Mod x, Mod y) => x._val > y._val;
            static public bool operator <=(Mod x, Mod y) => x._val <= y._val;
            static public bool operator >=(Mod x, Mod y) => x._val >= y._val;
            static public Mod Pow(Mod x, long y)
            {
                Mod a = 1;
                while (y != 0)
                {
                    if ((y & 1) == 1) a *= x;
                    x *= x;
                    y >>= 1;
                }
                return a;
            }
            static public long Inverse(long x)
            {
                long b = _mod, r = 1, u = 0, t = 0;
                while (b > 0)
                {
                    var q = x / b;
                    t = u; u = r - q * u; r = t;
                    t = b; b = x - q * b; x = t;
                }
                return r < 0 ? r + _mod : r;
            }
            override public bool Equals(object obj) => obj == null ? false : _val == ((Mod)obj)._val;
            public bool Equals(Mod obj) => obj == null ? false : _val == obj._val;
            public override int GetHashCode() => _val.GetHashCode();
            public override string ToString() => _val.ToString();
            static private List<Mod> _fact = new List<Mod>();
            static private List<Mod> _ifact = new List<Mod>();
            static private void Build(int n)
            {
                if (n >= _fact.Count)
                    for (int i = _fact.Count; i <= n; ++i)
                        if (i == 0L) { _fact.Add(1); _ifact.Add(1); }
                        else { _fact.Add(_fact[i - 1] * i); _ifact.Add(_ifact[i - 1] * Mod.Pow(i, _mod - 2)); }
            }
            static public Mod Comb(int n, int k)
            {
                Build(n);
                if (n == 0 && k == 0) return 1;
                if (n < k || n < 0) return 0;
                return _ifact[n - k] * _ifact[k] * _fact[n];
            }
        }
        class Mat<T>
        {
            private T[,] m;
            public Mat(T[,] v) { m = (T[,])v.Clone(); }
            static public implicit operator Mat<T>(T[,] v) => new Mat<T>(v);
            public T this[int r, int c] { get { return m[r, c]; } set { m[r, c] = value; } }
            static public Mat<T> operator +(Mat<T> a, T x)
            {
                var tm = (T[,])a.m.Clone();
                for (int r = 0; r < tm.GetLength(0); ++r) for (int c = 0; c < tm.GetLength(1); ++c) tm[r, c] += (dynamic)x;
                return new Mat<T>(tm);
            }
            static public Mat<T> operator +(Mat<T> a, Mat<T> b)
            {
                var tm = (T[,])a.m.Clone();
                for (int r = 0; r < tm.GetLength(0); ++r) for (int c = 0; c < tm.GetLength(1); ++c) tm[r, c] += (dynamic)b[r, c];
                return new Mat<T>(tm);
            }
            static public Mat<T> operator -(Mat<T> a, T x)
            {
                var tm = (T[,])a.m.Clone();
                for (int r = 0; r < tm.GetLength(0); ++r) for (int c = 0; c < tm.GetLength(1); ++c) tm[r, c] -= (dynamic)x;
                return new Mat<T>(tm);
            }
            static public Mat<T> operator -(Mat<T> a, Mat<T> b)
            {
                var tm = (T[,])a.m.Clone();
                for (int r = 0; r < tm.GetLength(0); ++r) for (int c = 0; c < tm.GetLength(1); ++c) tm[r, c] -= (dynamic)b[r, c];
                return new Mat<T>(tm);
            }
            static public Mat<T> operator *(Mat<T> a, T x)
            {
                var tm = (T[,])a.m.Clone();
                for (int r = 0; r < tm.GetLength(0); ++r) for (int c = 0; c < tm.GetLength(1); ++c) tm[r, c] *= (dynamic)x;
                return new Mat<T>(tm);
            }
            static public Mat<T> operator *(Mat<T> a, Mat<T> b)
            {
                var nr = a.m.GetLength(0);
                var nc = b.m.GetLength(1);
                var tm = new T[nr, nc];
                for (int i = 0; i < nr; ++i) for (int j = 0; j < nc; ++j) tm[i, j] = (dynamic)0;
                for (int r = 0; r < nr; ++r) for (int c = 0; c < nc; ++c) for (int i = 0; i < a.m.GetLength(1); ++i) tm[r, c] += a[r, i] * (dynamic)b[i, c];
                return new Mat<T>(tm);
            }
            static public Mat<T> Pow(Mat<T> x, long y)
            {
                var n = x.m.GetLength(0);
                var t = (Mat<T>)new T[n, n];
                for (int i = 0; i < n; ++i) for (int j = 0; j < n; ++j) t[i, j] = (dynamic)(i == j ? 1 : 0);
                while (y != 0)
                {
                    if ((y & 1) == 1) t *= x;
                    x *= x;
                    y >>= 1;
                }
                return t;
            }
        }
        static Mat<T> Pow<T>(Mat<T> x, long y) => Mat<T>.Pow(x, y);
        static Mod Pow(Mod x, long y) => Mod.Pow(x, y);
        static long Pow(long x, long y)
        {
            long a = 1;
            while (y != 0)
            {
                if ((y & 1) == 1) a *= x;
                x *= x;
                y >>= 1;
            }
            return a;
        }
        static List<long> _fact = new List<long>();
        static void _Build(int n)
        {
            if (n >= _fact.Count)
                for (int i = _fact.Count; i <= n; ++i)
                    if (i == 0L) _fact.Add(1);
                    else _fact.Add(_fact[i - 1] * i);
        }
        static long Comb(int n, int k)
        {
            _Build(n);
            if (n == 0 && k == 0) return 1;
            if (n < k || n < 0) return 0;
            return _fact[n] / _fact[k] / _fact[n - k];
        }
    }
}