//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,avx512f") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #ifdef DEBUG #include "./CompetitiveProgrammingCpp/Utils/debug.hpp" #include "./CompetitiveProgrammingCpp/Utils/Timer.hpp" #include "./CompetitiveProgrammingCpp/Utils/sample.hpp" #else #define dump(...) templateconstexpr inline auto d_val(T a, T b) { return a; } #endif /* macro */ #define FOR(i, b, e) for(ll i = (ll)(b); i < (ll)(e); ++i) #define RFOR(i, b, e) for(ll i = (ll)((e)-1); i >= (ll)(b); --i) #define REP(i, n) FOR(i, 0, (n)) #define RREP(i, n) RFOR(i, 0, (n)) #define REPC(x,c) for(const auto& x:(c)) #define REPI2(it,b,e) for(auto it = (b); it != (e); ++it) #define REPI(it,c) REPI2(it, (c).begin(), (c).end()) #define RREPI(it,c) REPI2(it, (c).rbegin(), (c).rend()) #define REPI_ERACE2(it, b, e) for(auto it = (b); it != (e);) #define REPI_ERACE(it, c) REPI_ERACE2(it, (c).begin(), (c).end()) #define ALL(x) (x).begin(),(x).end() /* macro func */ template inline auto sort(T& t) { std::sort(ALL(t)); } template inline auto rsort(T& t) { std::sort((t).rbegin(), (t).rend()); } template inline auto chmax(T& t, const S& s) { if(s > t) { t = s; return true; } return false; } template inline auto chmin(T& t, const S& s) { if(s < t) { t = s; return true; } return false; } inline auto BR() { std::cout << "\n"; } /* type define */ using ll = long long; template using V = std::vector; using VS = V; using VL = V; using VVL = V; template using P = std::pair; using PAIR = P; /* using std */ using std::cout; using std::cin; using std::cerr; constexpr char endl = '\n'; /* Initial processing */ struct Preprocessing { Preprocessing() { std::cin.tie(0); std::ios::sync_with_stdio(0); }; }_Preprocessing; /* define hash */ constexpr unsigned int static_random() { return 1u * __TIME__[0] * __TIME__[1] * __TIME__[3] * __TIME__[4] * __TIME__[6] * __TIME__[7]; } template struct Hash { auto operator()(T x) const { return std::hash()(x) ^ static_random(); } }; template<> struct Hash> { auto operator()(const std::pair& x) const { return Hash()(x.first << 31 | x.second); } }; /* input */ template std::istream& operator >> (std::istream& is, std::vector& vec) { for(T& x : vec) is >> x; return is; } /* constant value */ // constexpr ll MOD = 1000000007; constexpr ll MOD = 998244353; //============================================================================================= template class DynamicLiChaoTree { constexpr static T INF = 2e18; class Line { T a, b; public: Line(const T& a, const T& b) :a(a), b(b) {} Line() :Line(0, INF) {} Line(const Line& other) noexcept :Line(other.a, other.b) {} Line(Line&& other) noexcept :Line(other) {} Line& operator=(Line&& other) noexcept { if(this != &other) { a = other.a; b = other.b; } return *this; } auto operator<(const Line& line)const { return a < line.a; } auto operator>(const Line& line)const { return line.operator<(*this); } auto f(const T& x)const { return a * x + b; } auto debug()const { if(b == INF) { std::cerr << "(" << a << " inf)" << std::endl; } else { std::cerr << "(" << a << " " << b << ")" << std::endl; } } }; struct Node { Line line; std::unique_ptr left; std::unique_ptr right; Node(const Line& line) :line(line) {} auto f(const T& x)const { return line.f(x); } }; std::unique_ptr m_root; auto addLine(std::unique_ptr& node, Line&& line, long long l, long long r) { if(!node) { node = std::make_unique(line); return; } auto m = (l + 1 == r) ? l : (l + r) / 2; if(line.f(m) < node->f(m)) { std::swap(node->line, line); } if(l + 1 == r) { return; } if(line > node->line) { addLine(node->left, std::move(line), l, m); } else if(line < node->line) { addLine(node->right, std::move(line), m, r); } } auto addSegment(std::unique_ptr& node, const Line& line, T l, T r, T sl, T sr) { if(sr <= l || r <= sl) { return; } if(l <= sl && sr <= r) { addLine(node, Line(line), sl, sr); return; } auto m = (sl + sr) / 2; if(!node) { node = std::make_unique(Line()); } addSegment(node->left, line, l, r, sl, m); addSegment(node->right, line, l, r, m, sr); } auto query(const std::unique_ptr& node, const T& x, long long l, long long r) const { if(!node) { return Line().f(x); } auto m = (l + r) / 2; return std::min( node->f(x), (x < m) ? query(node->left, x, l, m) : query(node->right, x, m, r) ); } public: DynamicLiChaoTree() {} auto addLine(const T& a, const T& b) { addLine(m_root, Line(a, b), -X_MAX, X_MAX + 1); } auto addLine(const std::pair& line) { addLine(line.first, line.second); } [[deprecated("This method is too slow. Please use LiChaoTree and not DynamicLiChaoTree.")]] auto addSegment(const T& a, const T& b, const T& l, const T& r) { addSegment(m_root, Line(a, b), l, r + 1, -X_MAX, X_MAX + 1); } auto addSegment(const std::pair& line, const T& l, const T& r) { addSegment(line.first, line.second, l, r); } auto query(const T& x) const { return query(m_root, x, -X_MAX, X_MAX + 1); } auto debug(const std::unique_ptr& node, int size)const { if(size == 0) { std::cerr << "-- li chao tree --" << std::endl; } if(!node) { return; } for(int i = 0; i < size; ++i) { std::cerr << "- "; } node->line.debug(); if(node->left) { std::cout << "L"; debug(node->left, size + 1); } if(node->right) { std::cout << "R"; debug(node->right, size + 1); } } auto debug()const { debug(m_root, 0); } }; signed main() { ll n; cin >> n; VL a(n); cin >> a; auto lct = DynamicLiChaoTree(1e6)>(); VL dp(n, 1e18); lct.addLine(-a[0], 0); FOR(i, 1, n) { dp[i] = lct.query(a[i]); chmin(dp[i], 0); lct.addLine(-a[i], dp[i]); } cout << -(*std::min_element(ALL(dp))) << endl; }