#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 /* macro */ #define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++) #define rrep(i, a, n) for (int i = ((int)(n)-1); i >= (int)(a); i--) #define Rep(i, a, n) for (i64 i = (i64)(a); i < (i64)(n); i++) #define RRep(i, a, n) for (i64 i = ((i64)(n)-i64(1)); i >= (i64)(a); i--) #define all(v) (v).begin(), (v).end() #define rall(v) (v).rbegin(), (v).rend() /* macro end */ /* template */ namespace ebi { #ifdef LOCAL #define debug(...) \ std::cerr << "LINE: " << __LINE__ << " [" << #__VA_ARGS__ << "]:", \ debug_out(__VA_ARGS__) #else #define debug(...) #endif void debug_out() { std::cerr << std::endl; } template void debug_out(Head h, Tail... t) { std::cerr << " " << h; if (sizeof...(t) > 0) std::cerr << " :"; debug_out(t...); } template std::ostream &operator<<(std::ostream &os, const std::pair &pa) { return os << pa.first << " " << pa.second; } template std::istream &operator>>(std::istream &os, std::pair &pa) { return os >> pa.first >> pa.second; } template std::ostream &operator<<(std::ostream &os, const std::vector &vec) { for (std::size_t i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : " "); return os; } template std::istream &operator>>(std::istream &os, std::vector &vec) { for (T &e : vec) std::cin >> e; return os; } template std::ostream &operator<<(std::ostream &os, const std::optional &opt) { if (opt) { os << opt.value(); } else { os << "invalid value"; } return os; } using std::size_t; using i32 = std::int32_t; using u32 = std::uint32_t; using i64 = std::int64_t; using u64 = std::uint64_t; using i128 = __int128_t; using u128 = __uint128_t; template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } template T pow(T x, i64 n) { T res = 1; while (n > 0) { if (n & 1) res = res * x; x = x * x; n >>= 1; } return res; } template struct Edge { int to; T cost; Edge(int _to, T _cost = 1) : to(_to), cost(_cost) {} }; template struct Graph : std::vector>> { using std::vector>>::vector; void add_edge(int u, int v, T w, bool directed = false) { (*this)[u].emplace_back(v, w); if (directed) return; (*this)[v].emplace_back(u, w); } }; struct graph : std::vector> { using std::vector>::vector; void add_edge(int u, int v, bool directed = false) { (*this)[u].emplace_back(v); if (directed) return; (*this)[v].emplace_back(u); } }; constexpr i64 LNF = std::numeric_limits::max() / 4; constexpr int INF = std::numeric_limits::max() / 2; const std::vector dy = {1, 0, -1, 0, 1, 1, -1, -1}; const std::vector dx = {0, 1, 0, -1, 1, -1, 1, -1}; } // namespace ebi namespace ebi { template struct convex_hull_trick { private: bool check(std::pair a, std::pair b, std::pair c) { return (b.first - a.first) * (c.second - b.second) >= (c.first - b.first) * (b.second - a.second); } T f(std::pair a, T x) { return a.first * x + a.second; } public: convex_hull_trick() = default; void add(T a, T b) { while(lines.size() >= 2 && check(*(lines.end() - 2) , lines.back(), {a, b})) { lines.pop_back(); } lines.emplace_back(a, b); } T min(T x) { assert(!lines.empty()); while(lines.size() >= 2 && f(lines[0], x) >= f(lines[1], x)) { lines.pop_front(); } return f(lines[0], x); } private: std::deque> lines; }; } // namespace ebi namespace ebi { void main_() { int n; i64 a,b,w; std::cin >> n >> a >> b >> w; convex_hull_trick cht; cht.add(-2*a - b, 2*w + 2*a); auto f = [&](i64 r) -> i64 { return -a*r + b*r*(r+1) / 2; }; i64 ans = w + f(n); rep(i,1,n+1) { i64 d; std::cin >> d; i64 val = cht.min(i); i64 res = b * i * i + 2 * d + val; res /= 2; cht.add(-2*a - 2*b*i - b, b*i*i+b*i+2*a*(i+1)+2*res); chmin(ans, res + f(n - i)); } std::cout << ans << '\n'; } } // namespace ebi int main() { std::cout << std::fixed << std::setprecision(15); std::cin.tie(nullptr); std::ios::sync_with_stdio(false); int t = 1; // std::cin >> t; while (t--) { ebi::main_(); } return 0; }