#include using namespace std; template struct ConvexHullTrick { struct Line { // f: y=ax+b Numeric a; Numeric b; Line(Numeric _a, Numeric _b) : a(_a), b(_b) {} bool operator< (Line &l) { if (a != l.a) return a < l.a; else return b < l.b; } }; private: vector lines; bool isMinimumQuery; bool isMonotonicQuery; bool compare(Numeric a, Numeric b) { if (isMinimumQuery) return b <= a; else return a <= b; } public: // constructor ConvexHullTrick(bool monotonic, bool minimum = true) : isMinimumQuery(minimum), isMonotonicQuery(monotonic) {} // check the necessity of line2 bool check(Line l1, Line l2, Line l3) { if (l1 < l3) swap(l3, l1); return compare((l3.b-l2.b)*(l2.a-l1.a), (l2.b-l1.b)*(l3.a-l2.a)); } // add the line: y=ax+b void add(Numeric a, Numeric b) { Line line(a, b); int size = (int) lines.size(); while (size >= 2 && check(lines[size-2], lines[size-1], line)){ lines.pop_back(); --size; } lines.emplace_back(line); } // get the value of line(x) Numeric f(Line line, Numeric x) { return line.a * x + line.b; } // solve Numeric solve(Numeric x) { if (isMonotonicQuery) { static int head = 0; while (lines.size() - head >= 2 && compare(f(lines[head], x), f(lines[head+1], x))) ++head; return f(lines[head], x); } else { int low = -1; int high = lines.size()-1; while (high - low > 1) { int mid = (high+low)/2; if (compare(f(lines[mid], x), f(lines[mid+1], x))) low = mid; else high = mid; } return f(lines[high], x); } } }; int main(){ long long n, a, b, w; cin >> n >> a >> b >> w; vector d(n); for (long long i = 0; i < n; i++) { cin >> d[i]; } vector dp(n+1, 0); ConvexHullTrick convexhulltrick(true); for (long long i = 0; i < n; i++) { convexhulltrick.add(-i*b, dp[i]+i*a+(i+1)*i*b/2); dp[i+1] = convexhulltrick.solve(i+1) - a*i + (i+1)*i*b/2 + d[i]; } long long ans = 1e18; for (long long i = 0; i <= n; i++) { ans = min(ans, w+dp[i]-(n-i)*a+(n-i)*(n-i+1)*b/2); } cout << ans << endl; return 0; }