//#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; //============================================================================================= class LiChaoTree { using T = long long; using Line = std::pair; constexpr static T INF = std::numeric_limits< T >::max() / 2; int m_size; std::vector m_x; std::vector m_node; std::unordered_map m_xtoi; static inline int calcSize(int n) { int size = 1; while(size < n) { size <<= 1; }return size; } auto f(const Line& line, const T& x)const { return line.first * x + line.second; } auto addLine(const Line& line_, int k, int l, int r) { auto line = line_; auto m = (l + r) / 2; if(f(line, m_x[m]) < f(m_node[k], m_x[m])) { std::swap(line, m_node[k]); } if(l + 1 == r) { return; } if(line.first > m_node[k].first) { addLine(line, (k << 1) + 1, l, m); } else if(line.first < m_node[k].first) { addLine(line, (k << 1) + 2, m, r); } } public: LiChaoTree(const std::vector& x_) :m_size(calcSize(x_.size())) { auto x = x_; std::sort(x.begin(), x.end()); x.erase(std::unique(x.begin(), x.end()), x.end()); m_x = decltype(m_x)(m_size); for(size_t i = 0; i < x.size(); ++i) { m_x[i] = x[i]; m_xtoi.emplace(x[i], i); } for(size_t i = x.size(); i < m_size; ++i) { m_x[i] = m_x[i - 1] + 1; } m_node = decltype(m_node)(m_size << 1, {0,INF}); } auto addLine(const Line& line) { addLine(line, 0, 0, m_size); } auto addLine(const T& a, const T& b) { addLine({a,b}); } auto addSegment(const Line& line, const T& l_, const T& r_) { auto l = m_xtoi[l_], r = m_xtoi[r_]; auto lk = l + m_size - 1; auto rk = r + m_size - 1; auto len = 1; while(lk <= rk) { if(!(lk & 1)) { addLine(line, lk, l, l + len); l += len; ++lk; } if(rk & 1) { r -= len; addLine(line, rk, r + 1, r + len + 1); --rk; } lk = (lk - 1) >> 1; rk = (rk - 1) >> 1; len <<= 1; } } auto addSegment(const T& a, const T& b, const T& l, const T& r) { addSegment({a,b}, l, r); } auto query(const T& x) { auto k = m_xtoi[x] + m_size; auto ret = INF; while(k > 0) { ret = std::min(ret, f(m_node[k - 1], x)); k >>= 1; } return ret; } auto debug()const { std::cerr << "-- Li Chao Tree --" << std::endl; for(unsigned int i = 0; i < m_node.size(); ++i) { std::cerr << i << ": (" << m_node[i].first << " " << m_node[i].second << ")" << std::endl; } } }; signed main() { ll n; cin >> n; VL a(n); cin >> a; auto lct = LiChaoTree(a); VL dp(n, 1e18); lct.addLine(-a[0], 0); FOR(i, 1, n) { dp[i] = lct.query(a[i]); lct.addLine(-a[i], dp[i]); } cout << -(*std::min_element(ALL(dp))) << endl; }