import java.io.IOException; import java.io.InputStream; import java.io.OutputStream; import java.io.PrintWriter; import java.util.ArrayList; import java.util.Arrays; import java.util.NoSuchElementException; /* _ooOoo_ o8888888o 88" . "88 (| -_- |) O\ = /O ____/`---'\____ .' \\| |// `. / \\||| : |||// \ / _||||| -:- |||||- \ | | \\\ - /// | | | \_| ''\---/'' | | \ .-\__ `-` ___/-. / ___`. .' /--.--\ `. . __ ."" '< `.___\_<|>_/___.' >'"". | | : `- \`.;`\ _ /`;.`/ - ` : | | \ \ `-. \_ __\ /__ _/ .-` / / ======`-.____`-.___\_____/___.-`____.-'====== `=---=' ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ pass System Test! */ public class yukicoder409 { private static class Task { class ConvexHullTrick { ArrayList ls = new ArrayList<>(); ConvexHullTrick() { } boolean check(long[] l1, long[] l2, long[] l3) { return (l2[0] - l1[0]) * (l3[1] - l2[1]) >= (l2[1] - l1[1]) * (l3[0] - l2[0]); } void add(long a, long b) { long[] l = new long[]{a, b}; while (ls.size() >= 2 && check(ls.get(ls.size() - 2), ls.get(ls.size() - 1), l)) ls.remove(ls.size() - 1); ls.add(l); } long f(int k, long x) { long[] l = ls.get(k); return l[0] * x + l[1]; } long query(long x) { int low = -1; int high = ls.size() - 1; while (high - low > 1) { int mid = (high + low) / 2; if (f(mid, x) >= f(mid + 1, x)) { low = mid; } else { high = mid; } } return f(high, x); } } final long INF = (long) 1e18; void solve(FastScanner in, PrintWriter out) { int N = in.nextInt(); int A = in.nextInt(); long B = in.nextInt(); int W = in.nextInt(); int[] D = in.nextIntArray(N); if (B == 0) { out.println(W - A * N); return; } long[] dp = new long[N + 1]; Arrays.fill(dp, INF); dp[0] = W; ConvexHullTrick deq = new ConvexHullTrick(); deq.add(0, dp[0]); for (long i = 0; i < N; i++) { dp[(int) i + 1] = D[(int) i] - i * A + (B * i * (i + 1)) / 2 + deq.query(i); long a = -(i + 1) * B; long b = dp[(int) i + 1] + (i + 1) * A + (B * (i + 1) * i) / 2; deq.add(a, b); } long res = INF; for (int i = 0; i <= N; i++) res = Math.min(res, dp[i] - A * (N - i) + B * (N - i) * (N - i + 1) / 2); out.println(res); } } /** * ここから下はテンプレートです。 */ public static void main(String[] args) { OutputStream outputStream = System.out; FastScanner in = new FastScanner(); PrintWriter out = new PrintWriter(outputStream); Task solver = new Task(); solver.solve(in, out); out.close(); } private static class FastScanner { private final InputStream in = System.in; private final byte[] buffer = new byte[1024]; private int ptr = 0; private int bufferLength = 0; private boolean hasNextByte() { if (ptr < bufferLength) { return true; } else { ptr = 0; try { bufferLength = in.read(buffer); } catch (IOException e) { e.printStackTrace(); } if (bufferLength <= 0) { return false; } } return true; } private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1; } private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126; } private void skipUnprintable() { while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; } boolean hasNext() { skipUnprintable(); return hasNextByte(); } public String next() { if (!hasNext()) throw new NoSuchElementException(); StringBuilder sb = new StringBuilder(); int b = readByte(); while (isPrintableChar(b)) { sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } long nextLong() { if (!hasNext()) throw new NoSuchElementException(); long n = 0; boolean minus = false; int b = readByte(); if (b == '-') { minus = true; b = readByte(); } if (b < '0' || '9' < b) { throw new NumberFormatException(); } while (true) { if ('0' <= b && b <= '9') { n *= 10; n += b - '0'; } else if (b == -1 || !isPrintableChar(b)) { return minus ? -n : n; } else { throw new NumberFormatException(); } b = readByte(); } } double nextDouble() { return Double.parseDouble(next()); } double[] nextDoubleArray(int n) { double[] array = new double[n]; for (int i = 0; i < n; i++) { array[i] = nextDouble(); } return array; } double[][] nextDoubleMap(int n, int m) { double[][] map = new double[n][]; for (int i = 0; i < n; i++) { map[i] = nextDoubleArray(m); } return map; } public int nextInt() { return (int) nextLong(); } public int[] nextIntArray(int n) { int[] array = new int[n]; for (int i = 0; i < n; i++) array[i] = nextInt(); return array; } public long[] nextLongArray(int n) { long[] array = new long[n]; for (int i = 0; i < n; i++) array[i] = nextLong(); return array; } public String[] nextStringArray(int n) { String[] array = new String[n]; for (int i = 0; i < n; i++) array[i] = next(); return array; } public char[][] nextCharMap(int n) { char[][] array = new char[n][]; for (int i = 0; i < n; i++) array[i] = next().toCharArray(); return array; } } }