using System; using System.Collections; using System.Collections.Generic; using System.Diagnostics; using System.Globalization; using System.IO; using System.Text; using System.Linq; using E = System.Linq.Enumerable; internal partial class Solver { public void Run() { var n = ni(); var x = new int[n]; var y = new int[n]; for (int i = 0; i < n; i++) { x[i] = ni(); y[i] = ni(); } long ans = CountTriangleNumContainsOrigin(n, x, y); cout.WriteLine(ans); } public struct Angle : IComparable { public long X { get; private set; } public long Y { get; private set; } private readonly long _a; private readonly long _b; public int Quadrant { get; private set; } public static long Gcd(long s, long t) { return t != 0 ? Gcd(t, s % t) : s; } public Angle(long x, long y) { if (x == 0 && y == 0) throw new ArgumentException(); var g = Gcd(Math.Abs(x), Math.Abs(y)); _a = X = x / g; _b = Y = y / g; Quadrant = 0; while (!(_a > 0 && _b >= 0)) { var t = _a; _a = _b; _b = -t; Quadrant++; } } public int CompareTo(Angle other) { var cmp = Quadrant.CompareTo(other.Quadrant); if (cmp != 0) return cmp; return (_b * other._a).CompareTo(other._b * _a); } } private long CountTriangleNumContainsOrigin(int n, int[] x, int[] y, bool strict = true) { var angles = new List(); for (int j = 0; j < n; j++) { var dx = x[j]; var dy = y[j]; angles.Add(new Angle(dx, dy)); } angles.Sort(); angles.AddRange(angles); int atMostFlat = 0; int lessThenFlat = 0; int zeroIndex = 0; long ans = 1L * n * (n - 1) * (n - 2) / 6; for (int i = 0; i < n; i++) { var angle1 = angles[i]; while (zeroIndex + 1 < i + n && (angle1.CompareTo(angles[zeroIndex + 1]) == 0)) { zeroIndex++; } if (lessThenFlat < zeroIndex) lessThenFlat = zeroIndex; while (lessThenFlat + 1 < i + n && angle1.X * angles[lessThenFlat + 1].Y - angle1.Y * angles[lessThenFlat + 1].X > 0) { lessThenFlat++; } if (atMostFlat < lessThenFlat) atMostFlat = lessThenFlat; while (atMostFlat + 1 < i + n && angle1.X * angles[atMostFlat + 1].Y - angle1.Y * angles[atMostFlat + 1].X >= 0) { atMostFlat++; } long half = atMostFlat - lessThenFlat; long middle = lessThenFlat - zeroIndex; long zero = zeroIndex - i + 1; ans -= zero * (zero - 1) * (zero - 2) / 6; ans -= middle * (middle - 1) / 2 * zero; ans -= middle * zero * (zero - 1) / 2; // LINE if (strict) { ans -= half * zero * (zero - 1) / 2; ans -= half * middle * zero; } i = zeroIndex; } return ans; } public static Tuple Normalize(long x, long y) { var g = Gcd(Math.Abs(x), Math.Abs(y)); x /= g; y /= g; return Tuple.Create(x, y); } public static long Gcd(long s, long t) { return t != 0 ? Gcd(t, s % t) : s; } } // PREWRITEN CODE BEGINS FROM HERE internal partial class Solver : Scanner { public static void Main(string[] args) { #if LOCAL byte[] inputBuffer = new byte[1000000]; var inputStream = Console.OpenStandardInput(inputBuffer.Length); using (var reader = new StreamReader(inputStream, Console.InputEncoding, false, inputBuffer.Length)) { Console.SetIn(reader); new Solver(Console.In, Console.Out).Run(); } #else Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false }); new Solver(Console.In, Console.Out).Run(); Console.Out.Flush(); #endif } #pragma warning disable IDE0052 private readonly TextReader cin; private readonly TextWriter cout; #pragma warning restore IDE0052 public Solver(TextReader reader, TextWriter writer) : base(reader) { cin = reader; cout = writer; } public Solver(string input, TextWriter writer) : this(new StringReader(input), writer) { } #pragma warning disable IDE1006 #pragma warning disable IDE0051 private int ni() { return NextInt(); } private int[] ni(int n) { return NextIntArray(n); } private long nl() { return NextLong(); } private long[] nl(int n) { return NextLongArray(n); } private double nd() { return NextDouble(); } private double[] nd(int n) { return NextDoubleArray(n); } private string ns() { return Next(); } private string[] ns(int n) { return NextArray(n); } #pragma warning restore IDE1006 #pragma warning restore IDE0051 } internal static class LinqPadExtension { [Conditional("DEBUG")] public static void Dump(this T obj) { #if DEBUG LINQPad.Extensions.Dump(obj); #endif } } public class Scanner { private readonly TextReader Reader; private readonly Queue TokenQueue = new Queue(); private readonly CultureInfo ci = CultureInfo.InvariantCulture; public Scanner() : this(Console.In) { } public Scanner(TextReader reader) { Reader = reader; } public int NextInt() { return int.Parse(Next(), ci); } public long NextLong() { return long.Parse(Next(), ci); } public double NextDouble() { return double.Parse(Next(), ci); } public string[] NextArray(int size) { string[] array = new string[size]; for (int i = 0; i < size; i++) { array[i] = Next(); } return array; } public int[] NextIntArray(int size) { int[] array = new int[size]; for (int i = 0; i < size; i++) { array[i] = NextInt(); } return array; } public long[] NextLongArray(int size) { long[] array = new long[size]; for (int i = 0; i < size; i++) { array[i] = NextLong(); } return array; } public double[] NextDoubleArray(int size) { double[] array = new double[size]; for (int i = 0; i < size; i++) { array[i] = NextDouble(); } return array; } public string Next() { if (TokenQueue.Count == 0) { if (!StockTokens()) { throw new InvalidOperationException(); } } return TokenQueue.Dequeue(); } public bool HasNext() { if (TokenQueue.Count > 0) { return true; } return StockTokens(); } private static readonly char[] _separator = new[] { ' ', '\t' }; private bool StockTokens() { while (true) { string line = Reader.ReadLine(); if (line == null) { return false; } string[] tokens = line.Split(_separator, StringSplitOptions.RemoveEmptyEntries); if (tokens.Length == 0) { continue; } foreach (string token in tokens) { TokenQueue.Enqueue(token); } return true; } } }