#include using namespace std; #define int long long // #define double long double #define FOR(i, a, b) for(int i = (a); i < (b); ++i) #define FORR(i, a, b) for(int i = (a); i > (b); --i) #define REP(i, n) for(int i = 0; i < (n); ++i) #define REPR(i, n) for(int i = n; i >= 0; i--) #define FOREACH(x, a) for(auto &(x) : (a)) #define VECCIN(x) \ for(auto &youso_ : (x)) cin >> youso_ #define bitcnt(x) __builtin_popcount(x) #define lbit(x) __builtin_ffsll(x) #define rbit(x) (64 - __builtin_clzll(x)) #define fi first #define se second #define All(a) (a).begin(), (a).end() #define rAll(a) (a).rbegin(), (a).rend() #define cinfast() cin.tie(0), ios::sync_with_stdio(false) #define precise(x) cout << fixed << setprecision(x) #define PERM(c) \ sort(All(c)); \ for(bool cp = true; cp; cp = next_permutation(All(c))) #define COMB(n, k) \ for(ll bit = (1LL << k) - 1; bit < (1LL << n); bit = next_combination(bit)) #define PERM2(n, k) \ COMB(n, k) { \ vector sel; \ for(int bitindex = 0; bitindex < n; bitindex++) \ if(bit >> bitindex & 1) sel.emplace_back(bitindex); \ PERM(sel) { Printv(sel); } \ } #define MKORDER(n) \ vector od(n); \ iota(All(od), 0LL); template inline T IN() { T x; cin >> x; return (x); } inline void CIN() {} template inline void CIN(Head &&head, Tail &&... tail) { cin >> head; CIN(move(tail)...); } template inline void COUT(Head &&head) { cout << (head) << "\n"; } template inline void COUT(Head &&head, Tail &&... tail) { cout << (head) << " "; COUT(forward(tail)...); } #define CCIN(...) \ char __VA_ARGS__; \ CIN(__VA_ARGS__) #define DCIN(...) \ double __VA_ARGS__; \ CIN(__VA_ARGS__) #define LCIN(...) \ long long __VA_ARGS__; \ CIN(__VA_ARGS__) #define SCIN(...) \ string __VA_ARGS__; \ CIN(__VA_ARGS__) #define Printv(v) \ { \ REP(hoge, v.size()) \ cout << v[hoge] << (hoge == v.size() - 1 ? "" : " "); \ cout << "\n"; \ } template inline void eputs(T s) { cout << s << "\n"; exit(0); } template void Fill(A (&array)[N], const T &val) { std::fill((T *)array, (T *)(array + N), val); } long long next_combination(long long sub) { long long x = sub & -sub, y = sub + x; return (((sub & ~y) / x) >> 1) | y; } template inline bool chmax(T &a, const T &b) { if(a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, const T &b) { if(a > b) { a = b; return 1; } return 0; } // generic lambdas template #if defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard) [[nodiscard]] #elif defined(__GNUC__) && \ (__GNUC__ > 3 || __GNUC__ == 3 && __GNUC_MINOR__ >= 4) __attribute__((warn_unused_result)) #endif // defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard) static inline constexpr decltype(auto) fix(first &&f) noexcept { return [f = std::forward(f)](auto &&... args) { return f(f, std::forward(args)...); }; } template using PQG = priority_queue, greater>; template using PQ = priority_queue; typedef long long ll; typedef vector VL; typedef vector VVL; typedef pair PL; typedef vector VPL; typedef vector VB; typedef vector VD; typedef vector VS; const int INF = 1e9; const int MOD = 1e9 + 7; // const int MOD = 998244353; const ll LINF = 1e18; const ll dw[] = {1, 1, 0, -1, -1, -1, 0, 1}; const ll dh[] = {0, 1, 1, 1, 0, -1, -1, -1}; #define PI 3.141592653589793230 #define EPS 1e-7 // monotonic template struct ConvexHullTrick { using P = pair; deque

H; bool empty() const { return H.empty(); } void clear() { H.clear(); } inline int sgn(T x) { return x == 0 ? 0 : (x < 0 ? -1 : 1); } using D = long double; inline bool check(const P &a, const P &b, const P &c) { if(b.second == a.second || c.second == b.second) return sgn(b.first - a.first) * sgn(c.second - b.second) >= sgn(c.first - b.first) * sgn(b.second - a.second); // return (b.first-a.first)*(c.second-b.second) >= // (b.second-a.second)*(c.first-b.first); return D(b.first - a.first) * sgn(c.second - b.second) / D(abs(b.second - a.second)) >= D(c.first - b.first) * sgn(b.second - a.second) / D(abs(c.second - b.second)); } void addLine(T m, T b) { if(!isMin) m *= -1, b *= -1; P line(m, b); if(empty()) { H.emplace_front(line); return; } if(H.front().first <= m) { if(H.front().first == m) { if(H.front().second <= b) return; H.pop_front(); } while(H.size() >= 2 && check(line, H.front(), H[1])) H.pop_front(); H.emplace_front(line); } else { assert(m <= H.back().first); if(H.back().first == m) { if(H.back().second <= b) return; H.pop_back(); } while(H.size() >= 2 && check(H[H.size() - 2], H.back(), line)) H.pop_back(); H.emplace_back(line); } } inline T getY(const P &a, const T &x) { return a.first * x + a.second; } T query(T x) { assert(!empty()); int l = -1, r = H.size() - 1; while(l + 1 < r) { int m = (l + r) >> 1; if(getY(H[m], x) >= getY(H[m + 1], x)) l = m; else r = m; } if(isMin) return getY(H[r], x); return -getY(H[r], x); } T queryMonotoneInc(T x) { assert(!empty()); while(H.size() >= 2 && getY(H.front(), x) >= getY(H[1], x)) H.pop_front(); if(isMin) return getY(H.front(), x); return -getY(H.front(), x); } T queryMonotoneDec(T x) { assert(!empty()); while(H.size() >= 2 && getY(H.back(), x) >= getY(H[H.size() - 2], x)) H.pop_back(); if(isMin) return getY(H.back(), x); return -getY(H.back(), x); } }; ll dp[300003]; ll ans[300003]; signed main() { LCIN(N, A, B, W); VL D(N); VECCIN(D); ConvexHullTrick cht; cht.addLine(0, 2 * W); FOR(i, 1, N + 1) { dp[i] = cht.query(i - 1) + i * (i - 1) * B - 2 * A * (i - 1) + 2 * D[i - 1]; ans[i] = min(dp[i], cht.query(i) + (i + 1) * i * B - 2 * A * i); cht.addLine(-2 * i * B, (i * i - i) * B + 2 * A * i + dp[i]); } cout << ans[N] / 2 << "\n"; }