// #pragma GCC target("avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") #include using namespace std; using ll = long long; using ld = long double; using pll = pair; using pii = pair; using vvl = vector>; using vvi = vector>; using vvpll = vector>; #define rep(i, a, b) for (ll i=(a); i<(b); i++) #define rrep(i, a, b) for (ll i=(a); i>(b); i--) #define pb push_back #define tostr to_string #define ALL(A) A.begin(), A.end() constexpr ll INF = LONG_LONG_MAX; constexpr ll MOD = 1000000007; template vector> list2d(int N, int M, T init) { vector> res(N, vector(M, init)); return res; } template vector>> list3d(int N, int M, int L, T init) { vector>> res(N, vector>(M, vector(L, init))); return res; } void print(ld out) { cout << fixed << setprecision(15) << out << '\n'; } void print(double out) { cout << fixed << setprecision(15) << out << '\n'; } template void print(T out) { cout << out << '\n'; } template void print(pair out) { cout << out.first << ' ' << out.second << '\n'; } template void print(vector A) { rep(i, 0, A.size()) { cout << A[i]; cout << (i == A.size()-1 ? '\n' : ' '); } } template void print(set S) { vector A(S.begin(), S.end()); print(A); } void Yes() { print("Yes"); } void No() { print("No"); } void YES() { print("YES"); } void NO() { print("NO"); } ll floor(ll a, ll b) { if (a < 0) { return (a-b+1) / b; } else { return a / b; } } ll ceil(ll a, ll b) { if (a >= 0) { return (a+b-1) / b; } else { return a / b; } } pll divmod(ll a, ll b) { ll d = a / b; ll m = a % b; return {d, m}; } template bool chmax(T &x, T y) { return (y > x) ? x = y, true : false; } template bool chmin(T &x, T y) { return (y < x) ? x = y, true : false; } template T sum(vector A) { T res = 0; for (T a: A) res += a; return res; } template T max(vector A) { return *max_element(ALL(A)); } template T min(vector A) { return *min_element(ALL(A)); } ll toint(string s) { ll res = 0; for (char c : s) { res *= 10; res += (c - '0'); } return res; } int toint(char num) { return num - '0'; } char tochar(int num) { return '0' + num; } int ord(char c) { return (int)c; } char chr(int a) { return (char)a; } ll pow(int x, ll n) { ll res = 1; rep(_, 0, n) res *= x; return res; } ll pow(ll x, ll n, int mod) { ll res = 1; while (n > 0) { if (n & 1) { res = (res * x) % mod; } x = (x * x) % mod; n >>= 1; } return res; } int popcount(ll S) { return __builtin_popcountll(S); } ll gcd(ll a, ll b) { return __gcd(a, b); } template int bisect_left(vector A, T val) { return lower_bound(ALL(A), val) - A.begin(); } template int bisect_right(vector A, T val) { return upper_bound(ALL(A), val) - A.begin(); } // Li Chao Tree template struct DynamicLiChaoTree { const ll x_low; const ll x_high; const T id; struct Line { T a, b; Line(T a, T b) : a(a), b(b) {} inline T get(ll x) const { return a * x + b; } }; struct Node { Line x; Node *l, *r; Node(const Line &x) : x{x}, l{nullptr}, r{nullptr} {} }; Node *root; DynamicLiChaoTree(ll x_low, ll x_high, T id) : root{nullptr}, x_low(x_low), x_high(x_high), id(id) {} Node *add_line(Node *t, Line &x, const ll &l, const ll &r, const T &x_l, const T &x_r) { if(!t) return new Node(x); T t_l = t->x.get(l), t_r = t->x.get(r); if(t_l <= x_l && t_r <= x_r) { return t; } else if(t_l >= x_l && t_r >= x_r) { t->x = x; return t; } else { ll m = (l + r) / 2; if(m == r) --m; T t_m = t->x.get(m), x_m = x.get(m); if(t_m > x_m) { swap(t->x, x); if(x_l >= t_l) t->l = add_line(t->l, x, l, m, t_l, t_m); else t->r = add_line(t->r, x, m + 1, r, t_m + x.a, t_r); } else { if(t_l >= x_l) t->l = add_line(t->l, x, l, m, x_l, x_m); else t->r = add_line(t->r, x, m + 1, r, x_m + x.a, x_r); } return t; } } void add_line(const T &a, const T &b) { Line x(a, b); root = add_line(root, x, x_low, x_high, x.get(x_low), x.get(x_high)); } Node *add_segment(Node *t, Line &x, const ll &a, const ll &b, const ll &l, const ll &r, const T &x_l, const T &x_r) { if(r < a || b < l) return t; if(a <= l && r <= b) { Line y{x}; return add_line(t, y, l, r, x_l, x_r); } if(t) { T t_l = t->x.get(l), t_r = t->x.get(r); if(t_l <= x_l && t_r <= x_r) return t; } else { t = new Node(Line(0, id)); } ll m = (l + r) / 2; if(m == r) --m; T x_m = x.get(m); t->l = add_segment(t->l, x, a, b, l, m, x_l, x_m); t->r = add_segment(t->r, x, a, b, m + 1, r, x_m + x.a, x_r); return t; } void add_segment(const ll &l, const ll &r, const T &a, const T &b) { Line x(a, b); root = add_segment(root, x, l, r - 1, x_low, x_high, x.get(x_low), x.get(x_high)); } T query(const Node *t, const ll &l, const ll &r, const T &x) const { if(!t) return id; if(l == r) return t->x.get(x); ll m = (l + r) / 2; if(m == r) --m; if(x <= m) return min(t->x.get(x), query(t->l, l, m, x)); else return min(t->x.get(x), query(t->r, m + 1, r, x)); } T query(const T &x) const { return query(root, x_low, x_high, x); } }; int main() { cin.tie(0); ios::sync_with_stdio(false); ll N, A, B, W; cin >> N >> A >> B >> W; vector D(N); rep(i, 0, N) cin >> D[i]; D.insert(D.begin(), 0); vector dp(N+1); DynamicLiChaoTree lct(0, N+1, INF); dp[0] = W; lct.add_line(0, dp[0]); rep(i, 1, N+1) { dp[i] = min(lct.query(i)+(i*i+i)/2*B-A*i, dp[i-1]+D[i]); lct.add_line(-i*B, dp[i-1]+D[i]+(i*i-i)/2*B+A*i); } ll ans = dp[N]; print(ans); return 0; }