#include using namespace std; #define _p(...) (void)printf(__VA_ARGS__) #define forr(x,arr) for(auto&& x:arr) #define _overload3(_1,_2,_3,name,...) name #define _rep2(i,n) _rep3(i,0,n) #define _rep3(i,a,b) for(int i=int(a);i=int(a);i--) #define rrep(...) _overload3(__VA_ARGS__,_rrep3,_rrep2,)(__VA_ARGS__) #define all(x) (x).begin(), (x).end() #define bit(n) (1LL<<(n)) #define sz(x) ((int)(x).size()) #define fst first #define snd second using ll=long long;using pii=pair; using vb=vector;using vs=vector; using vi=vector;using vvi=vector;using vvvi=vector; using vl=vector;using vvl=vector;using vvvl=vector; using vd=vector;using vvd=vector;using vvvd=vector; using vpii=vector;using vvpii=vector;using vvvpii=vector; templateT read(){T t;cin>>t;return t;} templateostream&operator<<(ostream&o,const pair&p){o<<'('< 0 ? gcd(b % a, a) : b; } struct rational { Integer p, q; void normalize() { // keep q positive if (q < 0) p *= -1, q *= -1; Integer d = gcd(p < 0 ? -p : p, q); if (d == 0) p = 0, q = 1; else p /= d, q /= d; } rational(Integer p, Integer q = 1) : p(p), q(q) { normalize(); } rational &operator += (const rational &a) { p = a.q * p + a.p * q; q = a.q * q; normalize(); return *this; } rational &operator -= (const rational &a) { p = a.q * p - a.p * q; q = a.q * q; normalize(); return *this; } rational &operator *= (const rational &a) { p *= a.p; q *= a.q; normalize(); return *this; } rational &operator /= (const rational &a) { p *= a.q; q *= a.p; normalize(); return *this; } rational &operator - () { p *= -1; return *this; } }; rational operator + (const rational &a, const rational &b) { return rational(a) += b; } rational operator * (const rational &a, const rational &b) { return rational(a) *= b; } rational operator - (const rational &a, const rational &b) { return rational(a) -= b; } rational operator / (const rational &a, const rational &b) { return rational(a) /= b; } bool operator < (const rational &a, const rational &b) { // avoid overflow return (long double) a.p * b.q < (long double) a.q * b.p; } bool operator <= (const rational &a, const rational &b) { return !(b < a); } bool operator > (const rational &a, const rational &b) { return b < a; } bool operator >= (const rational &a, const rational &b) { return !(a < b); } bool operator == (const rational &a, const rational &b) { return !(a < b) && !(b < a); } bool operator != (const rational &a, const rational &b) { return (a < b) || (b < a); } struct Hash { typedef std::size_t result_type; std::size_t operator()(const rational& key) const; }; inline std::size_t Hash::operator()(const rational& key) const { return (key.p << 32) + key.q; } inline int cmp(int a, int b, int c, int d) { ll ad = a * d; ll cb = c * b; ll ret = ad - cb; if (ret > 0) return 1; if (ret < 0) return -1; return 0; } inline bool cmp_b(const pii &lhs, decltype(lhs) rhs) { return cmp(lhs.A, lhs.B, rhs.A, rhs.B) <= 0; } // a/(a+b) と足したら1を越えるのが何本あるか // O(log |S|) int bs(const rational &ab, const vector &S) { int ok = sz(S); int ng = -1; while (abs(ok - ng) > 1) { int mid = (ok + ng) / 2; bool c = ab + S[mid] > 1; // cout << "ok: " << ok << ", ng: " << ng << ", "; // cout << "check(" << mid << ") -> " << c << endl; if (c) ok = mid; else ng = mid; } return sz(S) - ok; } void Main() { int n = read(); vector R[3]; rep(i, n) { int t = read(); int a = read(); int b = read(); R[t].emplace_back(a, a + b); } rep(i, 3) sort(all(R[i])); //rep(ii,3) { cout << "R["< X; unordered_map Y; { forr(ab, R[0]) { forr(cd, R[1]) { if (ab + cd >= 1) { if (ab < cd) { X.emplace_back(ab); } else { X.emplace_back(cd); } { auto e = (1-cd) + (1-ab); auto f = cd - (1-ab); if (f > 0) { //Y.emplace_back(e / (e+f)); Y[e / (e+f)]++; } } } } } } // O(N^2 log N^2) TLE? sort(all(X)); //sort(all(Y)); //cout << "X:"; rep(ii,sz(X)) cout << ' ' << X[ii]; cout << endl; // 3本 // O(n * log(N^2)) forr(ab, R[2]) { // b/(a+b) 以上の X を数える rational bab(1 - ab); ans += X.end() - lower_bound(all(X), bab); // 交点に重なる場合を除く //ans -= upper_bound(all(Y), ab) - lower_bound(all(Y), ab); ans -= Y[ab]; } cout << ans << endl; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); Main(); return 0; }