import std.conv, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.container, std.math, std.numeric, std.range, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } void chmin(T)(ref T t, in T f) { if (t > f) t = f; } void chmax(T)(ref T t, in T f) { if (t < f) t = f; } int binarySearch(T)(in T[] as, in bool delegate(T) test) { int low = -1, upp = cast(int)(as.length); for (; low + 1 < upp; ) { int mid = (low + upp) >> 1; (test(as[mid]) ? low : upp) = mid; } return upp; } int lowerBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a < val)); } int upperBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a <= val)); } /* dp[i] = min{ dp[j] - A (i - j - 1) + B (i - j - 1) (i - j) / 2 + D[i] | 0 <= j < i } = min{ (dp[j] + A j + B j (j + 1) / 2) - (B j) i | 0 <= j < i } - A (i - 1) + B i (i - 1) / 2 + D[i] */ int N; long A, B, W; long[] D; void main() { try { for (; ; ) { N = readInt(); A = readLong(); B = readLong(); W = readLong(); D = new long[N + 2]; foreach (i; 1 .. N + 1) { D[i] = readLong(); } debug { auto dp = new long[N + 2]; dp[0] = W; foreach (i; 1 .. N + 2) { dp[i] = iota(0, i).map!(j => (dp[j] + A * j + B * j * (j + 1) / 2) - (B * j) * i).minElement - A * (i - 1) + B * i * (i - 1) / 2 + D[i]; } writeln(dp); } long ans; auto q = new Tuple!(long, long)[N + 2]; int qHead, qTail; foreach (i; 0 .. N + 2) { long x; if (i == 0) { x = W; } else { for (; qTail - qHead >= 2 && q[qHead][0] - q[qHead][1] * i >= q[qHead + 1][0] - q[qHead + 1][1] * i; ++qHead) {} x = q[qHead][0] - q[qHead][1] * i - A * (i - 1) + B * i * (i - 1) / 2 + D[i]; } debug { writeln(i, " ", x); } if (i == N + 1) { ans = x; } else { const p = Tuple!(long, long)(x + A * i + B * i * (i + 1) / 2, B * i); // ([-1][0] - [-2][0]) / ([-1][1] - [-2][1]) >= (p[0] - [-2][0]) / (p[1] - [-2][1]) for (; qTail - qHead >= 2 && (q[qTail - 1][0] - q[qTail - 2][0]) * (p[1] - q[qTail - 2][1]) >= (p[0] - q[qTail - 2][0]) * (q[qTail - 1][1] - q[qTail - 2][1]); --qTail) {} q[qTail++] = p; } } writeln(ans); } } catch (EOFException e) { } }