#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include //#include //using Bint = boost::multiprecision::cpp_int; //#include #define ll long long #define ld long double #define rep(i, n) for(int i = 0; i < n; ++i) #define rep2(i, a, b) for(int i = a; i <= b; ++i) #define rrep(i, a, b) for(int i = a; i >= b; --i) #define pii pair #define pdd pair #define pll pair #define pld pair #define fi first #define se second #define pb push_back #define eb emplace_back #define vi vector #define vd vector #define vll vector #define vld vector #define vpii vector #define vpdd vector #define vpll vector #define vpld vector #define vvi(a,b,c,d) vector> a(b,vector(c,d)); #define vvll(a,b,c,d) vector> a(b,vector(c,d)); #define all(a) a.begin(), a.end() #define rall(a) a.rbegin(), a.rend() #define MAX(x) *max_element(all(x)) #define MIN(x) *min_element(all(x)) #define sz(a) ((ll)(a).size()) #define endl '\n' using namespace std; //using namespace atcoder; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } template //切り捨て T div_floor(T a, T b) { if (b < 0) a *= -1, b *= -1; return a >= 0 ? a / b : (a + 1) / b - 1; } template T div_ceil(T a, T b) { //切り上げ if (b < 0) a *= -1, b *= -1; return a > 0 ? (a - 1) / b + 1 : a / b; } const ll INF=1e18+1; const int inf=1e9+1; const double PI=acos(-1); int dy[8] = {0,1,0,-1,-1,1,1,-1}; int dx[8] = {1,0,-1,0,1,1,-1,-1}; bool range(int y, int x, int h, int w){ if(y < 0 || x < 0 || y >= h || x >= w) return false; else return true; } //const int MOD=1000000007; //using mint = modint1000000007; //const int MOD=998244353; //using mint = modint998244353; const int M = 500001; using Graph = vector>; // LiChaoTree // 直線追加,N個の座標x(昇順)における最小値 // verify: https://judge.yosupo.jp/submission/45842 template struct LiChaoTree { const T INF = numeric_limits< T >::max() / 2; struct Line { T a, b; Line(T a, T b) : a(a), b(b) {} T eval(T x) { return a*x + b; } }; int n; //座標の数 vector< Line > data; //直線群 vector< T > pos; //i番目の座標x_i LiChaoTree(int n) { pos.resize(n); iota(pos.begin(), pos.end(), 0); //座標圧縮 init(n); } LiChaoTree(const vector< T > &pos) : pos(pos) { init(pos.size()); } void init(int n_){ //2べきにしてる n = 1; while(n < n_) n <<= 1; while((int)pos.size() < n) pos.emplace_back(pos.back() + 1); data.assign(n << 1, Line(0, INF)); } void add_line(T a, T b){ Line x(a, b); update(1, 0, n-1, x); //[0, n-1]でupdate } inline bool over(Line &a, Line &b, T lb, T ub){ return a.eval(lb) >= b.eval(lb) && a.eval(ub) >= b.eval(ub); //[lb, ub]で直線aが直線bの上にある } void update(int k, int l, int r, Line &x){ T lb = pos[l], ub = pos[r]; if(over(x, data[k], lb, ub)) return; //加えたいのが完全に上ならなんもしない if(over(data[k], x, lb, ub)) { //加えたいのが完全に下なら変える data[k] = x; return; } int c = (l+r) >> 1; if(x.eval(pos[c]) < data[k].eval(pos[c])) swap(x, data[k]); //中点で加えたい線が下に来るならswap if(x.eval(lb) <= data[k].eval(lb)) update(k << 1|0, l, c, x); //https://smijake3.hatenablog.com/entry/2018/06/16/144548のNo.3 else update(k << 1|1, c+1, r, x); //https://smijake3.hatenablog.com/entry/2018/06/16/144548のNo.4 } T get_min(ll x) { //座標xを含む区間の最小値を計算(子から親へ) int i = lower_bound(pos.begin(), pos.end(), x) - pos.begin(); T res = INF; int k = i + n; while(k > 0){ res = min(res, data[k].eval(pos[i])); k >>= 1; } return res; } }; signed main(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(15); ll n, a, b, w; cin >> n >> a >> b >> w; vll d(n); rep(i, n) cin >> d[i]; vll dp(n+1); dp[0] = 0; vll day(n+1); rep(i, n+1) day[i] = (ll)i; LiChaoTree LCT(day); LCT.add_line(0, 0); rep2(i, 1, n){ dp[i] = LCT.get_min(i) - (ll)a*(i-1) + (ll)((ll)i*i-i)*b/2 + d[i-1]; LCT.add_line(-(ll)i*b, dp[i] + (ll)i*a + (ll)((ll)i*i+i)*b/2); } ll ans = INF; rep(i, n+1){ chmin(ans, w + dp[i] - (n-i)*a + ((ll)(n-i)*(n-i+1)/2)*(ll)b); } cout << ans << endl; return 0; }