using System; using System.Linq; using System.Collections.Generic; using Debug = System.Diagnostics.Debug; using StringBuilder = System.Text.StringBuilder; using System.Numerics; using Point = System.Numerics.Complex; using Number = System.Int64; using C = System.Int32; namespace Program { public class Solver { public void Solve() { var n = sc.Integer(); var a = Enumerate(3, x => new List>()); var ans = 1L; for (int i = 0; i < n; i++) { var p = sc.Integer(); var u = sc.Long(); var v = sc.Long(); var gcd = MathEx.GCD(u, v); u /= gcd; v /= gcd; a[p].Add(new KeyValuePair(u, u + v)); ans++; } for (int i = 0; i < 3; i++) a[i].Sort((l, r) => (l.Key * r.Value).CompareTo(l.Value * r.Key)); for (int i = 1; i < 3; i++) { foreach (var p in a[i]) { var u = p.Key; var d = p.Value; u = d - u; ans += a[0].Count - a[0].UpperBound(new KeyValuePair(u, d), (l, r) => (l.Key * r.Value).CompareTo(l.Value * r.Key)); } } Debug.WriteLine(ans); foreach (var p in a[1]) foreach (var q in a[2]) { var u = p.Key; var d = p.Value; var x = q.Key; var y = q.Value; u = d - u; x = y - x; var nu = u * y + x * d; var nd = d * y; var gcd = MathEx.GCD(nu, nd); nu /= gcd; nd /= gcd; if (nu > nd) continue; if (nu < nd) ans++; ans += a[0].Count - a[0].UpperBound(new KeyValuePair(nu, nd), (l, r) => (l.Key * r.Value).CompareTo(l.Value * r.Key)); ans += a[0].LowerBound(new KeyValuePair(nu, nd), (l, r) => (l.Key * r.Value).CompareTo(l.Value * r.Key)); if (u * y > x * d) ans -= a[0].LowerBound(new KeyValuePair(u, d), (l, r) => (l.Key * r.Value).CompareTo(l.Value * r.Key)); else ans -= a[0].LowerBound(new KeyValuePair(x, y), (l, r) => (l.Key * r.Value).CompareTo(l.Value * r.Key)); } IO.Printer.Out.WriteLine(ans); } public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput()); static T[] Enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; } static public void Swap(ref T a, ref T b) { var tmp = a; a = b; b = tmp; } } } #region main static class Ex { static public string AsString(this IEnumerable ie) { return new string(System.Linq.Enumerable.ToArray(ie)); } static public string AsJoinedString(this IEnumerable ie, string st = " ") { return string.Join(st, ie); } static public void Main() { var solver = new Program.Solver(); solver.Solve(); Program.IO.Printer.Out.Flush(); } } #endregion #region Ex namespace Program.IO { using System.IO; using System.Text; using System.Globalization; public class Printer: StreamWriter { static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; } public static Printer Out { get; set; } public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } } public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { } public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { } public void Write(string format, T[] source) { base.Write(format, source.OfType().ToArray()); } public void WriteLine(string format, T[] source) { base.WriteLine(format, source.OfType().ToArray()); } } public class StreamScanner { public StreamScanner(Stream stream) { str = stream; } public readonly Stream str; private readonly byte[] buf = new byte[1024]; private int len, ptr; public bool isEof = false; public bool IsEndOfStream { get { return isEof; } } private byte read() { if (isEof) return 0; if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } } return buf[ptr++]; } public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; } public string Scan() { var sb = new StringBuilder(); for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b); return sb.ToString(); } public string ScanLine() { var sb = new StringBuilder(); for (var b = Char(); b != '\n'; b = (char)read()) if (b == 0) break; else if (b != '\r') sb.Append(b); return sb.ToString(); } public long Long() { if (isEof) return long.MinValue; long ret = 0; byte b = 0; var ng = false; do b = read(); while (b != 0 && b != '-' && (b < '0' || '9' < b)); if (b == 0) return long.MinValue; if (b == '-') { ng = true; b = read(); } for (; true; b = read()) { if (b < '0' || '9' < b) return ng ? -ret : ret; else ret = ret * 10 + b - '0'; } } public int Integer() { return (isEof) ? int.MinValue : (int)Long(); } public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; } private T[] enumerate(int n, Func f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(); return a; } public char[] Char(int n) { return enumerate(n, Char); } public string[] Scan(int n) { return enumerate(n, Scan); } public double[] Double(int n) { return enumerate(n, Double); } public int[] Integer(int n) { return enumerate(n, Integer); } public long[] Long(int n) { return enumerate(n, Long); } } } #endregion #region gcd,lcm static public partial class MathEx { static public Number GCD(Number n, Number m) { bool f = true; for (; n != 0 && m != 0; f ^= true) { if (f) m %= n; else n %= m; } return n == 0 ? m : n; } static public Number LCM(Number n, Number m) { return (n / GCD(n, m)) * m; } static public Number GCD(params Number[] a) { var gcd = a[0]; foreach (var x in a) gcd = GCD(gcd, x); return gcd; } } #endregion #region BinarySearch for List static public partial class Algorithm { static private int binarySearch(this IList a, int idx, int len, T v, Comparison cmp, bool islb) { int l = idx; int h = idx + len - 1; while (l <= h) { int i = l + ((h - l) >> 1); int ord; if (a[i] == null || v == null) return -1; else ord = cmp(a[i], v); if (ord < 0) l = i + 1; else if (ord == 0) { if (!islb) l = i + 1; else h = i - 1; } else h = i - 1; } return l; } static public int UpperBound(this IList a, int idx, int len, T v, Comparison cmp) { return binarySearch(a, idx, len, v, cmp, false); } static public int UpperBound(this IList a, int idx, int len, T v) where T : IComparable { return UpperBound(a, idx, len, v, Comparer.Default.Compare); } static public int UpperBound(this IList a, T v) where T : IComparable { return UpperBound(a, 0, a.Count, v, Comparer.Default.Compare); } static public int UpperBound(this IList a, T v, IComparer cmp) { return UpperBound(a, 0, a.Count, v, cmp.Compare); } static public int UpperBound(this IList a, T v, Comparison cmp) { return UpperBound(a, 0, a.Count, v, cmp); } static public int LowerBound(this IList a, int idx, int len, T value, Comparison cmp) { return binarySearch(a, idx, len, value, cmp, true); } static public int LowerBound(this IList a, int idx, int len, T value) where T : IComparable { return LowerBound(a, idx, len, value, Comparer.Default.Compare); } static public int LowerBound(this IList a, T val) where T : IComparable { return LowerBound(a, 0, a.Count, val, Comparer.Default.Compare); } static public int LowerBound(this IList a, T val, IComparer cmp) { return LowerBound(a, 0, a.Count, val, cmp.Compare); } static public int LowerBound(this IList a, T v, Comparison cmp) { return LowerBound(a, 0, a.Count, v, cmp); } } #endregion