#include using namespace std; #define rep(i,a,b) for(int i=a;i struct CHT { // by satanic typedef pair pa; vector lines; bool mono; function comp; // クエリが単調ならf = true CHT(bool f = false, function co = [](T l, T r) {return l >= r; }) :mono(f), comp(co) { }; bool check(pa l1, pa l2, pa l3) { if (l1 < l3) std::swap(l1, l3); return (l3.second - l2.second) * (l2.first - l1.first) >= (l2.second - l1.second) * (l3.first - l2.first); } void add(T a, T b) { // y=ax+b pa line(a, b); while (lines.size() >= 2 && check(*(lines.end() - 2), lines.back(), line)) lines.pop_back(); lines.emplace_back(line); } T f(int i, T x) { return lines[i].first * x + lines[i].second; } T f(pa line, T x) { return line.first * x + line.second; } T get(T x) { if (mono) { static int head = 0; while (lines.size() - head >= 2 && comp(f(head, x), f(head + 1, x))) ++head; return f(head, x); } else { int low = -1, high = lines.size() - 1; while (high - low > 1) { int mid = (high + low) / 2; (comp(f(mid, x), f(mid + 1, x)) ? low : high) = mid; } return f(high, x); } } }; //----------------------------------------------------------------------------------- typedef long long ll; #define INF 1LL<<60 int N, A, B, W; int D[301010]; //----------------------------------------------------------------------------------- ll dp[301010]; int main() { cin >> N >> A >> B >> W; rep(i, 0, N) scanf("%d", &D[i]); /* Naive dp[0] = W; rep(i, 1, N + 1) { dp[i] = INF; rep(j, 0, i) { ll w = dp[j]; w -= 1LL * A * (i - j - 1); w += 1LL * (i - j - 1) * (i - j) / 2 * B; dp[i] = min(dp[i], w); } dp[i] += D[i - 1]; } */ // Optimized CHT cht(true); dp[0] = W; cht.add(0, W); rep(i, 1, N + 1) { dp[i] = cht.get(i) - 1LL * (i - 1) * A + (1LL * (i - 1) * i) / 2 * B + D[i - 1]; cht.add(-1LL * B * i, dp[i] + 1LL * A * i + (1LL * i * i + i) / 2 * B); } ll ans = INF; rep(i, 0, N + 1) { ll w = dp[i]; int n = N - i; w -= 1LL * A * n; w += 1LL * n * (n + 1) / 2 * B; ans = min(ans, w); } cout << ans << endl; }