#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define REP(i,s,n) for(int i=(int)(s);i<(int)(n);i++) using namespace std; typedef long long int ll; typedef vector VI; typedef vector VL; typedef pair PI; typedef pair PL; const ll mod = 1e9 + 7; ll gcd(ll x, ll y) { return y == 0 ? x : gcd(y, x % y); } PL add(PL x, PL y) { PI w = PI(x.first * y.second + x.second * y.first, x.second * y.second); ll g = gcd(w.first, w.second); w.first /= g; w.second /= g; return w; } PL neg(PL x) { return PL(- x.first, x.second); } bool fr_le(PL x, PL y) { return x.first * y.second <= y.first * x.second; } bool fr_lt(PL x, PL y) { return x.first * y.second < y.first * x.second; } int main(void){ int n; cin >> n; vector pool[3]; REP(i, 0, 3) { pool[i].push_back(PL(0, 1)); } REP(i, 0, n) { int p, a, b; cin >> p >> a >> b; int g = __gcd(a, b); a /= g; b /= g; pool[p].push_back(PL(b, a + b)); } ll tot = 0; sort(pool[2].begin(), pool[2].end(), fr_lt); REP(i, 0, pool[0].size()) { REP(j, 0, pool[1].size()) { PL u = pool[0][i]; PL v = pool[1][j]; if (not fr_le(add(u, v), PL(1, 1))) { continue; } PL ma = u; if (fr_le(u, v)) { ma = v; } // find #{x | x + u <= 1 && x + v <= 1 && x + u + v != 1} PL x_ma = add(PL(1, 1), neg(ma)); int idx = upper_bound(pool[2].begin(), pool[2].end(), x_ma, fr_lt) - pool[2].begin(); tot += idx; PL excl = add(PL(1, 1), neg(add(u, v))); { int idx1 = upper_bound(pool[2].begin(), pool[2].end(), excl, fr_lt) - pool[2].begin(); int idx2 = lower_bound(pool[2].begin(), pool[2].end(), excl, fr_lt) - pool[2].begin(); assert (idx1 - idx2 <= 1); assert (idx1 >= idx2); tot -= idx1 - idx2; } } } cout << tot << endl; }