//#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() #define cauto const auto& /* 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 unique(T& t) { (t).erase(unique((t).begin(), (t).end()), (t).end()); } 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; using VS = std::vector; using VL = std::vector; using VVL = std::vector; using VVVL = std::vector; using VVVVL = std::vector; using VVVVVL = std::vector; using VD = std::vector; template using V = std::vector; template using P = std::pair; using PAIR = P; /* using std */ using std::cout; constexpr char endl = '\n'; using std::cin; using std::pair; using std::string; using std::stack; using std::queue; using std::deque; using std::vector; using std::list; using std::map; using std::unordered_map; using std::multimap; using std::unordered_multimap; using std::set; using std::unordered_set; using std::unordered_multiset; using std::multiset; using std::bitset; using std::priority_queue; /* Initial processing */ struct Preprocessing { Preprocessing() { std::cin.tie(0); std::ios::sync_with_stdio(0); }; }_Preprocessing; /* Remove the source of the bug */ auto pow(signed, signed) { assert(false); } /* define hash */ namespace std { template <> class hash> { public: size_t operator()(const std::pair& x) const { return hash()(1000000000 * x.first + x.second); } }; } /* input */ template std::istream& operator >> (std::istream& is, 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 add(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) { add(line, (k << 1) + 1, l, m); } else if(line.first < m_node[k].first) { add(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 add(const Line& line) { add(line, 0, 0, m_size); } auto add(const T& a, const T& b) { add({a,b}); } 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; } }; signed main() { ll n, a, b, w; cin >> n >> a >> b >> w; VL d(n); cin >> d; VL xs(n); std::iota(ALL(xs), 1); LiChaoTree lct(xs); constexpr ll mx = 1e18; VL dp(n + 1, mx); auto update = [&](ll i, ll x) { chmin(dp[i], x); auto pa = -b * i; auto pb = a * i + i * (i + 1) / 2 * b + dp[i]; lct.add(pa, pb); }; update(0, w); FOR(i, 1, n + 1) { auto ad = d[i - 1] - a * i + a + i * (i - 1) / 2 * b; auto min = lct.query(i); update(i, ad + min); } ll ans = dp[n]; REP(i, n) { ll k = n - i; chmin(ans, dp[i] + -a * k + k * (k + 1) / 2 * b); } cout << ans << endl; }