/** * date : 2023-05-28 14:25:35 * author : Nyaan */ #define NDEBUG using namespace std; // intrinstic #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N,F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector mkiota(int n) { vector ret(n); iota(begin(ret), end(ret), 0); return ret; } template T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template bool nxp(vector &v) { return next_permutation(begin(v), end(v)); } template using minpq = priority_queue, greater>; } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug #ifdef NyaanDebug #define trc(...) (void(0)) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) (void(0)) #else #define trc2(...) (void(0)) #endif // macro #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // using namespace std; using namespace std; namespace internal { template using is_broadly_integral = typename conditional_t || is_same_v || is_same_v, true_type, false_type>::type; template using is_broadly_signed = typename conditional_t || is_same_v, true_type, false_type>::type; template using is_broadly_unsigned = typename conditional_t || is_same_v, true_type, false_type>::type; #define ENABLE_VALUE(x) \ template \ constexpr bool x##_v = x::value; ENABLE_VALUE(is_broadly_integral); ENABLE_VALUE(is_broadly_signed); ENABLE_VALUE(is_broadly_unsigned); #undef ENABLE_VALUE #define ENABLE_HAS_TYPE(var) \ template \ struct has_##var : std::false_type {}; \ template \ struct has_##var> : std::true_type {}; \ template \ constexpr auto has_##var##_v = has_##var::value; } // namespace internal namespace fastio { static constexpr int SZ = 1 << 17; static constexpr int offset = 64; char inbuf[SZ], outbuf[SZ]; int in_left = 0, in_right = 0, out_right = 0; struct Pre { char num[40000]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i * 4 + j] = n % 10 + '0'; n /= 10; } } } } constexpr pre; void load() { int len = in_right - in_left; memmove(inbuf, inbuf + in_left, len); in_right = len + fread(inbuf + len, 1, SZ - len, stdin); in_left = 0; } void flush() { fwrite(outbuf, 1, out_right, stdout); out_right = 0; } void skip_space() { if (in_left + offset > in_right) load(); while (inbuf[in_left] <= ' ') in_left++; } void single_read(char& c) { if (in_left + offset > in_right) load(); skip_space(); c = inbuf[in_left++]; } void single_read(string& S) { skip_space(); while (true) { if (in_left == in_right) load(); int i = in_left; for (; i != in_right; i++) { if (inbuf[i] <= ' ') break; } copy(inbuf + in_left, inbuf + i, back_inserter(S)); in_left = i; if (i != in_right) break; } } template >* = nullptr> inline void single_read(T& x) { if (in_left + offset > in_right) load(); skip_space(); char c = inbuf[in_left++]; [[maybe_unused]] bool minus = false; if constexpr (internal::is_broadly_signed_v) { if (c == '-') minus = true, c = inbuf[in_left++]; } x = 0; while (c >= '0') { x = x * 10 + (c & 15); c = inbuf[in_left++]; } if constexpr (internal::is_broadly_signed_v) { if (minus) x = -x; } } inline void rd() {} template inline void rd(Head& head, Tail&... tail) { single_read(head); rd(tail...); } inline void single_write(const char& c) { if (out_right > SZ - offset) flush(); outbuf[out_right++] = c; } inline void single_write(const bool& b) { if (out_right > SZ - offset) flush(); outbuf[out_right++] = b ? '1' : '0'; } inline void single_write(const string& S) { int i = 0; while (i != (int)S.size()) { if (out_right == SZ) flush(); int len = min((int)S.size() - i, SZ - out_right); memcpy(outbuf + out_right, S.data() + i, sizeof(char) * len); i += len, out_right += len; } } template >* = nullptr> inline void single_write(const T& _x) { if (out_right > SZ - offset) flush(); if (_x == 0) { outbuf[out_right++] = '0'; return; } T x = _x; if constexpr (internal::is_broadly_signed_v) { if (x < 0) outbuf[out_right++] = '-', x = -x; } constexpr int buffer_size = sizeof(T) * 10 / 4; char buf[buffer_size]; int i = buffer_size; while (x >= 10000) { i -= 4; memcpy(buf + i, pre.num + (x % 10000) * 4, 4); x /= 10000; } if (x < 100) { if (x < 10) { outbuf[out_right] = '0' + x; ++out_right; } else { uint32_t q = (uint32_t(x) * 205) >> 11; uint32_t r = uint32_t(x) - q * 10; outbuf[out_right] = '0' + q; outbuf[out_right + 1] = '0' + r; out_right += 2; } } else { if (x < 1000) { memcpy(outbuf + out_right, pre.num + (x << 2) + 1, 3); out_right += 3; } else { memcpy(outbuf + out_right, pre.num + (x << 2), 4); out_right += 4; } } memcpy(outbuf + out_right, buf + i, buffer_size - i); out_right += buffer_size - i; } inline void wt() {} template inline void wt(const Head& head, const Tail&... tail) { single_write(head); wt(forward(tail)...); } template inline void wtn(const Args&... x) { wt(forward(x)...); wt('\n'); } struct Dummy { Dummy() { atexit(flush); } } dummy; } // namespace fastio using fastio::rd; using fastio::skip_space; using fastio::wt; using fastio::wtn; namespace my_rand { using i64 = long long; using u64 = unsigned long long; // [0, 2^64 - 1) u64 rng() { static u64 _x = u64(chrono::duration_cast( chrono::high_resolution_clock::now().time_since_epoch()) .count()) * 10150724397891781847ULL; _x ^= _x << 7; return _x ^= _x >> 9; } // [l, r] i64 rng(i64 l, i64 r) { assert(l <= r); return l + rng() % (r - l + 1); } // [l, r) i64 randint(i64 l, i64 r) { assert(l < r); return l + rng() % (r - l); } // choose n numbers from [l, r) without overlapping vector randset(i64 l, i64 r, i64 n) { assert(l <= r && n <= r - l); unordered_set s; for (i64 i = n; i; --i) { i64 m = randint(l, r + 1 - i); if (s.find(m) != s.end()) m = r - i; s.insert(m); } vector ret; for (auto& x : s) ret.push_back(x); return ret; } // [0.0, 1.0) double rnd() { return rng() * 5.42101086242752217004e-20; } template void randshf(vector& v) { int n = v.size(); for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]); } } // namespace my_rand using my_rand::randint; using my_rand::randset; using my_rand::randshf; using my_rand::rnd; using my_rand::rng; struct Timer { chrono::high_resolution_clock::time_point st; Timer() { reset(); } void reset() { st = chrono::high_resolution_clock::now(); } chrono::milliseconds::rep elapsed() { auto ed = chrono::high_resolution_clock::now(); return chrono::duration_cast(ed - st).count(); } }; using namespace Nyaan; #pragma GCC optimize("O3,unroll-loops") #pragma GCC target("avx2") int N, X[512], Y[512], ans[3] = {}; int cross(int ax, int ay, int bx, int by) { return ax * by - ay * bx; } int calc(int i, int j, int k) { return cross(X[j] - X[i], Y[j] - Y[i], X[k] - X[i], Y[k] - Y[i]); } void check(int i, int j, int k) { int s = calc(i, j, k); if (s < 0) s = -s, swap(i, j); for (int l = 0; l < k; l++) { ans[0] = max(ans[0], s + calc(i, k, l)); ans[1] = max(ans[1], s + calc(j, i, l)); ans[2] = max(ans[2], s + calc(k, j, l)); } } void q() { Timer timer; in(N); rep(i, N) in(X[i], Y[i]); vi buf(N); vi ord = mkiota(N); auto rearrange = [&](int* p) { rep(i, N) buf[i] = p[ord[i]]; copy(buf.data(), buf.data() + N, p); }; while (timer.elapsed() < 1900) { randshf(ord); rearrange(X), rearrange(Y); rep(i, N) rep(j, i) { if (timer.elapsed() > 1900) break; rep(k, j) check(i, j, k); } } out(max({ans[0], ans[1], ans[2]})); } void Nyaan::solve() { int t = 1; // in(t); while (t--) q(); }