import std.conv, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.container, std.math, std.numeric, std.range, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(T)(in T[] as, in bool delegate(T) test) { int low = -1, upp = cast(int)(as.length); for (; low + 1 < upp; ) { int mid = (low + upp) >> 1; (test(as[mid]) ? low : upp) = mid; } return upp; } int lowerBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a < val)); } int upperBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a <= val)); } alias Rat = Tuple!(long, long); bool compare(in Rat a, in Rat b) { return (a[0] * b[1] < b[0] * a[1]); } Rat add(in Rat a, in Rat b) { return Rat(a[0] * b[1] + b[0] * a[1], a[1] * b[1]); } Rat sub(in Rat a, in Rat b) { return Rat(a[0] * b[1] - b[0] * a[1], a[1] * b[1]); } /* a + b >= 1, a + c >= 1, b + c >= 1 a + b + c != 2 */ int N; int[] P; long[] A, B; void main() { try { for (; ; ) { N = readInt(); P = new int[N]; A = new long[N]; B = new long[N]; foreach (i; 0 .. N) { P[i] = readInt(); A[i] = readLong(); B[i] = readLong(); } auto rs = new Rat[][3]; foreach (p; 0 .. 3) { rs[p] ~= Rat(1, 1); } foreach (i; 0 .. N) { rs[P[i]] ~= tuple(A[i], A[i] + B[i]); } rs.sort!"a.length < b.length"; foreach (p; 0 .. 3) { rs[p].sort!compare; } debug { foreach (p; 0 .. 3) { writefln("rs[%s] = %s", p, rs[p]); } } long ans; foreach (a; rs[0]) foreach (b; rs[1]) { if (!compare(add(a, b), Rat(1, 1))) { Rat lb = Rat(0, 1), tmp; tmp = sub(Rat(1, 1), a); if (compare(lb, tmp)) lb = tmp; tmp = sub(Rat(1, 1), b); if (compare(lb, tmp)) lb = tmp; ans += rs[2].length - rs[2].binarySearch((Rat x) => compare(x, lb)); const c = sub(Rat(2, 1), add(a, b)); ans -= rs[2].binarySearch((Rat x) => !compare(c, x)) - rs[2].binarySearch((Rat x) => compare(x, c)); debug { writeln(a, " ", b, ": ", rs[2].binarySearch((Rat x) => compare(x, lb)), " ", rs[2].binarySearch((Rat x) => compare(x, c)), " ", rs[2].binarySearch((Rat x) => !compare(c, x))); } } } writeln(ans); } } catch (EOFException e) { } }