#pragma GCC optimize ("O3") #include "bits/stdc++.h" using namespace std; using ll = long long int; #define debugos cout #define debug(v) {printf("L%d %s > ",__LINE__,#v);debugos<<(v)< ",__LINE__,#v);for(auto e:(v)){debugos< ",__LINE__,#m);for(int x=0;x<(w);x++){debugos<<(m)[x]<<" ";}debugos<\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){debugos<<(m)[y][x]<<" ";}debugos<::type();(cnt)<(l);++(cnt)) #define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt)) #define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt)) #define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt)) const ll MD = 1000000007ll; const long double PI = 3.1415926535897932384626433832795L; inline void assert_call(bool assertion, function f) { if (!assertion) { cerr << "assertion fault:" << endl; f(); abort(); } } template inline ostream& operator <<(ostream &o, const pair p) { o << '(' << p.first << ':' << p.second << ')'; return o; } template inline ostream& _ostream_vecprint(ostream& os, const Vec& a) { os << '['; for (const auto& e : a) os << ' ' << e << ' '; os << ']'; return os; } template inline ostream& operator<<(ostream& o, const vector& v) { return _ostream_vecprint(o, v); } template inline ostream& operator<<(ostream& o, const array& v) { return _ostream_vecprint(o, v); } template inline T& chmax(T& to, const T& val) { return to = max(to, val); } template inline T& chmin(T& to, const T& val) { return to = min(to, val); } void bye(string s, int code = 0) { cout << s << endl; exit(code); } mt19937_64 randdev(8901016); template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_int_distribution(l, h)(rand); } template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_real_distribution(l, h)(rand); } #if defined(_WIN32) || defined(_WIN64) #define getc_x _getc_nolock #define putc_x _putc_nolock #elif defined(__GNUC__) #define getc_x getc_unlocked #define putc_x putc_unlocked #else #define getc_x getc #define putc_x putc #endif #define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E) class MaiScanner { FILE* fp_; public: inline MaiScanner(FILE* fp):fp_(fp){} template void input_integer(T& var) noexcept { var = 0; T sign = 1; int cc = getc_x(fp_); for (; cc < '0' || '9' < cc; cc = getc_x(fp_)) if (cc == '-') sign = -1; for (; '0' <= cc && cc <= '9'; cc = getc_x(fp_)) var = (var << 3) + (var << 1) + cc - '0'; var = var * sign; } inline int c() noexcept { return getc_x(fp_); } inline MaiScanner& operator>>(int& var) noexcept { input_integer(var); return *this; } inline MaiScanner& operator>>(long long& var) noexcept { input_integer(var); return *this; } inline MaiScanner& operator>>(string& var) { int cc = getc_x(fp_); for (; !isvisiblechar(cc); cc = getc_x(fp_)); for (; isvisiblechar(cc); cc = getc_x(fp_)) var.push_back(cc); return *this; } template inline void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; } }; class MaiPrinter { FILE* fp_; public: inline MaiPrinter(FILE* fp):fp_(fp){} template void output_integer(T var) noexcept { if (var == 0) { putc_x('0', fp_); return; } if (var < 0) putc_x('-', fp_), var = -var; char stack[32]; int stack_p = 0; while (var) stack[stack_p++] = '0' + (var % 10), var /= 10; while (stack_p) putc_x(stack[--stack_p], fp_); } inline MaiPrinter& operator<<(char c) noexcept { putc_x(c, fp_); return *this; } inline MaiPrinter& operator<<(int var) noexcept { output_integer(var); return *this; } inline MaiPrinter& operator<<(long long var) noexcept { output_integer(var); return *this; } inline MaiPrinter& operator<<(char* str_p) noexcept { while (*str_p) putc_x(*(str_p++), fp_); return *this; } inline MaiPrinter& operator<<(const string& str) { const char* p = str.c_str(); const char* l = p + str.size(); while (p < l) putc_x(*p++, fp_); return *this; } template void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; } }; MaiScanner scanner(stdin); MaiPrinter printer(stdout); struct Rational{ ll num, den; inline void fix() { if (den == 0) num = (0 < num) - (0 > num); else { auto g = gcd(num, den); num /= g; den /= g; if (den < 0) { den *= -1; num *= -1; } } } inline bool operator==(const Rational& r) const noexcept { return den == 0 ? num == r.num : num*r.den == r.num*den; } inline bool operator<(const Rational& r) const noexcept { return den == 0 ? num < r.num : num*r.den < r.num*den; } inline bool operator>(const Rational& r) const noexcept { return den == 0 ? num > r.num : num*r.den > r.num*den; } inline Rational(ll n=0, ll d=1) : num(n), den(d) { fix(); } }; inline ostream& operator <<(ostream &o, Rational p) { o << p.num << '/' << p.den ; return o; } using Angle = pair; // 3,4象限ならfirst&1 = 1, second = tangent inline Angle ataan(ll y, ll x) { return pair{0 < x, Rational{y, x}}; } // 180度回転させる。 // a.first ^= 1 だけで十分だが、これだけでは // ある角度に対してAngleが唯一にならなくなる // 0度と180度は angle.first&1 == 0の時のみに存在するため inline Angle inverse(Angle a) { if (a.second.den == 0) a.second.num *= -1; else a.first ^= 1; return a; } inline void fix(Angle& a, Angle& b) { a.first &= 1; b.first &= 1; if (a.first == b.first) { // R180を超えない if (a.second > b.second) swap(a, b); } else { if (a.second < b.second) swap(a, b); if (a.first > b.first) b.first += 2; } } // int N; Angle angles[10101]; // int main() { scanner >> N; repeat(i, N) { int x, y; scanner >> x >> y; angles[i] = ataan(y, x); // 角度情報として保持 } sort(angles, angles+N); // 実装を楽にするため、二週にしておく repeat(i, N) { angles[i+N] = angles[i]; angles[i+N].first += 2; } ll ans = 0; repeat(i, N-1) { auto ai = angles[i]; iterate(j, i+1, N) { auto aj = angles[j]; // 角度が同じ <=> 直線状に並んでいる <=> 面積が0 => 省略する if (ai.second == aj.second) continue; if (ai.second.den == 0 && aj.second.den == 0) continue; // この角度の範囲の頂点を選べば、原点が内部に入る三角形になる // -> ai+180 から aj+180 まで auto abe = inverse(ai); auto aen = inverse(aj); // 間違った弧を取ってしまうことがあるので修正 fix(abe, aen); auto ibe = upper_bound(angles, angles+N*2, abe); auto ien = lower_bound(angles, angles+N*2, aen); ans += distance(ibe, ien); } } cout << ans/3 << endl; return 0; }