/* #region Head */ #pragma GCC optimize("Ofast") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") #include // #include using namespace std; using ll = long long; using ull = unsigned long long; using pll = pair; using vll = vector; using vvll = vector; using vd = vector; using vvd = vector; using vs = vector; using vvs = vector; // using rat = boost::rational; #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 constexpr double EPS = 1e-12; constexpr double PI = 3.14159265358979323846; // vector入力 template istream &operator>>(istream &is, vector &vec) { for (T &x : vec) is >> x; return is; } // vector出力 template ostream &operator<<(ostream &os, vector &vec) { ll len = SIZE(vec); os << "{"; for (int i = 0; i < len; i++) os << vec[i] << (i == len - 1 ? "" : ", "); os << "}"; return os; } // pair入力 template istream &operator>>(istream &is, pair &pair_var) { is >> pair_var.first >> pair_var.second; return is; } // pair出力 template ostream &operator<<(ostream &os, pair &pair_var) { os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map出力 template ostream &operator<<(ostream &os, map &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; itr++; if (itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } // set 出力 template ostream &operator<<(ostream &os, set &set_var) { os << "{"; REPI(itr, set_var) { os << *itr; itr++; if (itr != set_var.end()) os << ", "; itr--; } os << "}"; return os; } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&... tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) { DUMPOUT << ", "; } dump_func(move(tail)...); } // _max の終端. template ll _max(Head &&head) { return head; } // 最大値を求める.max({}) の代わり.これにしないと vscode が壊れる. template ll _max(Head &&head, Tail &&... tail) { return max((ll)head, _max((tail)...)); } // _min の終端. template ll _min(Head &&head) { return head; } // 最小値を求める.min({}) の代わり.これにしないと vscode が壊れる. template ll _min(Head &&head, Tail &&... tail) { return min((ll)head, _min((tail)...)); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // container 内の最初の element のインデックスを探す template ll indexof(const Container &container, const typename Container::value_type &element) { auto iter = find(container.begin(), container.end(), element); size_t index = distance(container.begin(), iter); if (index == container.size()) { index = -1; } return index; } // ローカル用 #define DEBUG_ #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" \ << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) cout << unitbuf; } } ATCODER_INITIALIZE; /* #endregion */ struct MyPoint { ll quadrant; ll x; ll y; bool operator<(const MyPoint &another) const { if (quadrant == another.quadrant) // 同じ象限内 { // 辺々に x, another.x が掛けられるので,これらの正負によって不等号の向きが変わる if (x * another.x == 0.0) // どちらかの x が 0 return y < 0 ? x < another.x : x > another.x; else if (x * another.x > 0) // x が同符号 return y * another.x < x * another.y; else return y * another.x > x * another.y; } else { return quadrant < another.quadrant; } }; bool operator>(const MyPoint &another) const { if (quadrant == another.quadrant) // 同じ象限内 { if (x * another.x == 0.0) // どちらかの x が 0 return y < 0 ? x > another.x : x < another.x; else if (x * another.x > 0) return y * another.x > x * another.y; else return y * another.x < x * another.y; } else { return quadrant > another.quadrant; } }; }; ostream &operator<<(ostream &os, MyPoint &point) { os << "(" << point.quadrant << ", " << point.y << "/" << point.x << ")"; return os; }; ll get_quadrant(ll x, ll y) { if (x == 0) return y > 0 ? 2 : 0; else if (y == 0) return x > 0 ? 1 : -1; else return x > 0 ? (y > 0 ? 1 : 0) : (y > 0 ? 2 : -1); } /** ユークリッド平面上に存在する n 個の点 P_1 ... P_n が与えられます。 n 個の点から 3 つ選ぶ組合せのうち、その 3 点から構成される三角形の内部(辺上を除く)に点 (0, 0) が含まれるものは何通りありますか? */ void solve() { ll n; cin >> n; vll px(n), py(n); REP(i, 0, n) { cin >> px[i] >> py[i]; } vector tans(n); REP(i, 0, n) { tans[i] = {get_quadrant(px[i], py[i]), px[i], py[i]}; // make_pair(rat(py[i], px[i]), py[i]); } sort(ALL(tans)); REP(i, 0, n) { if (tans[i].quadrant <= 0) tans.push_back({tans[i].quadrant + 4, tans[i].x, tans[i].y}); else break; } dump(tans); ll cnt = 0, cnttmp; REP(i, 0, n - 1) { MyPoint left = tans[i]; MyPoint left2 = {left.quadrant + 2, -left.x, -left.y}; auto iter1 = upper_bound(ALL(tans), left2); // left2 より大きい最初の要素 auto iter2 = lower_bound(ALL(tans), left2); // left2 以上の最初の要素 REP(j, i + 1, n) { MyPoint right = tans[j]; if (left.y * right.x == left.x * right.y) continue; if (right < left2) { // (left + PI, right + PI) を探せばよい MyPoint right2 = {right.quadrant + 2, -right.x, -right.y}; auto iter3 = lower_bound(ALL(tans), right2); cnttmp = distance(iter1, iter3); // if (cnttmp > 0) cnt += cnttmp; dump(left2, right2, *iter1, *iter3); } else { // (right - PI, left + PI) を探せばよい auto iter3 = upper_bound(ALL(tans), MyPoint{right.quadrant - 2, -right.x, -right.y}); cnttmp = distance(iter3, iter2); // if (cnttmp > 0) cnt += cnttmp; } dump(left, right, right < left2, cnttmp, cnt); } } cout << cnt / 3 << endl; } /** * エントリポイント. * @return 0. */ int main() { solve(); return 0; }