#include #include #include #include #include #define repeat(i,n) for (int i = 0; (i) < int(n); ++(i)) #define whole(f,x,...) ([&](decltype((x)) whole) { return (f)(begin(whole), end(whole), ## __VA_ARGS__); })(x) typedef long long ll; using namespace std; struct rational { ll p, q; }; rational make_rational(ll p) { return { p, 1 }; } rational make_rational(ll p, ll q) { if (p == 0) return { 0, 1 }; ll gcd = __gcd(p, q); return { p/gcd, q/gcd }; } rational operator + (rational a, rational b) { return make_rational(a.p * b.q + b.p * a.q, a.q * b.q); } rational operator - (ll a, rational b) { return make_rational(a * b.q - b.p, b.q); } bool operator < (rational a, rational b) { return a.p * b.q < a.q * b.p; } bool operator == (rational a, rational b) { return a.p * b.q == a.q * b.p; } bool operator <= (rational a, ll b) { return a.p <= a.q * b; } int main() { int n; cin >> n; array, 3> qs = {}; repeat (i,n) { int p, a, b; cin >> p >> a >> b; qs[p].push_back(make_rational(a, a + b)); } repeat (i,3) { qs[i].emplace_back(make_rational(1)); whole(sort, qs[i]); } ll cnt = 0; repeat (i,3) { for (rational q1 : qs[(i + 1) % 3]) { for (rational q2 : qs[(i + 2) % 3]) { rational qm = max(1 - q1, 1 - q2); rational qc = (1 - q1) + (1 - q2); if (qc <= 1) { int lm = whole(lower_bound, qs[i], qm) - qs[i].begin(); int lc = whole(lower_bound, qs[i], qc) - qs[i].begin(); cnt += qs[i].size() - lm - (qs[i][lc] == qc); } } } } assert (cnt % 3 == 0); cout << cnt / 3 << endl; return 0; }