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import java.io.*; | |
import java.math.*; | |
import java.util.*; | |
import static java.util.Arrays.*; | |
public class _409 { | |
private static final int mod = (int)1e9+7; | |
final Random random = new Random(0); | |
final IOFast io = new IOFast(); | |
/// MAIN CODE | |
public void run() throws IOException { | |
// int TEST_CASE = Integer.parseInt(new String(io.nextLine()).trim()); | |
int TEST_CASE = 1; | |
while(TEST_CASE-- != 0) { | |
final int n = io.nextInt(); | |
final long A = io.nextLong(); | |
final long B = io.nextLong(); | |
final long W = io.nextLong(); | |
final int[] D = io.nextIntArray(n); | |
final long[] dp = new long[n+1]; | |
Deque<long[]> deq = new ArrayDeque<>(); | |
deq.addLast(new long[2]); | |
for (int i = 0; i < n; i++) { | |
while(deq.size() >= 2) { | |
final long[] p1 = deq.pollLast(); | |
final long[] p2 = deq.peekLast(); | |
if(p1[0]*i+p1[1] < p2[0]*i+p2[1]) { | |
deq.addLast(p1); | |
break; | |
} | |
} | |
final long[] c = deq.peekLast(); | |
dp[i+1] = D[i] - A*i + B*(i+1)*i/2 + c[0]*i + c[1]; | |
deq.addFirst(new long[]{-(i+1)*B, dp[i+1] + B*i*(i+1)/2 + A*(i+1)}); | |
while(deq.size() >= 3) { | |
final long[] p1 = deq.pollFirst(); | |
final long[] p2 = deq.pollFirst(); | |
final long[] p3 = deq.pollFirst(); | |
final long dx13 = p1[0]-p3[0]; | |
final long dy13 = p1[1]-p3[1]; | |
final long dx23 = p2[0]-p3[0]; | |
final long dy23 = p2[1]-p3[1]; | |
if(dy13*dx23 >= dy23*dx13) { | |
} else { | |
deq.addFirst(p3); | |
deq.addFirst(p2); | |
deq.addFirst(p1); | |
break; | |
} | |
deq.addFirst(p3); | |
deq.addFirst(p1); | |
} | |
} | |
long ans = Long.MAX_VALUE; | |
for(int i = 0; i <= n; i++) { | |
ans = Math.min(ans, dp[i] + B*(n-i)*(n-i+1)/2 - A*(n-i)); | |
} | |
io.out.println(W + ans); | |
} | |
} | |
/// TEMPLATE | |
static int gcd(int n, int r) { return r == 0 ? n : gcd(r, n%r); } | |
static long gcd(long n, long r) { return r == 0 ? n : gcd(r, n%r); } | |
static <T> void swap(T[] x, int i, int j) { T t = x[i]; x[i] = x[j]; x[j] = t; } | |
static void swap(int[] x, int i, int j) { int t = x[i]; x[i] = x[j]; x[j] = t; } | |
static void dump(Object... o) { System.err.println(Arrays.deepToString(o)); } | |
void main() throws IOException { | |
// IOFast.setFileIO("rle-size.in", "rle-size.out"); | |
try { run(); } | |
catch (EndOfFileRuntimeException e) { } | |
io.out.flush(); | |
} | |
public static void main(String[] args) throws IOException { new _409().main(); } | |
static class EndOfFileRuntimeException extends RuntimeException { | |
private static final long serialVersionUID = -8565341110209207657L; } | |
static | |
public class IOFast { | |
private BufferedReader in = new BufferedReader(new InputStreamReader(System.in)); | |
private PrintWriter out = new PrintWriter(System.out); | |
void setFileIn(String ins) throws IOException { in.close(); in = new BufferedReader(new FileReader(ins)); } | |
void setFileOut(String outs) throws IOException { out.flush(); out.close(); out = new PrintWriter(new FileWriter(outs)); } | |
void setFileIO(String ins, String outs) throws IOException { setFileIn(ins); setFileOut(outs); } | |
private static int pos, readLen; | |
private static final char[] buffer = new char[1024 * 8]; | |
private static char[] str = new char[500*8*2]; | |
private static boolean[] isDigit = new boolean[256]; | |
private static boolean[] isSpace = new boolean[256]; | |
private static boolean[] isLineSep = new boolean[256]; | |
static { for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; } isDigit['-'] = true; isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true; isLineSep['\r'] = isLineSep['\n'] = true; } | |
public int read() throws IOException { if(pos >= readLen) { pos = 0; readLen = in.read(buffer); if(readLen <= 0) { throw new EndOfFileRuntimeException(); } } return buffer[pos++]; } | |
public int nextInt() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; int ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; } | |
public long nextLong() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; long ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; } | |
public char nextChar() throws IOException { while(true) { final int c = read(); if(!isSpace[c]) { return (char)c; } } } | |
int reads(int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } if(str.length == len) { char[] rep = new char[str.length * 3 / 2]; System.arraycopy(str, 0, rep, 0, str.length); str = rep; } str[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; } | |
int reads(char[] cs, int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } cs[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; } | |
public char[] nextLine() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isLineSep); try { if(str[len-1] == '\r') { len--; read(); } } catch(EndOfFileRuntimeException e) { ; } return Arrays.copyOf(str, len); } | |
public String nextString() throws IOException { return new String(next()); } | |
public char[] next() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); return Arrays.copyOf(str, len); } | |
// public int next(char[] cs) throws IOException { int len = 0; cs[len++] = nextChar(); len = reads(cs, len, isSpace); return len; } | |
public double nextDouble() throws IOException { return Double.parseDouble(nextString()); } | |
public long[] nextLongArray(final int n) throws IOException { final long[] res = new long[n]; for(int i = 0; i < n; i++) { res[i] = nextLong(); } return res; } | |
public int[] nextIntArray(final int n) throws IOException { final int[] res = new int[n]; for(int i = 0; i < n; i++) { res[i] = nextInt(); } return res; } | |
public int[][] nextIntArray2D(final int n, final int k) throws IOException { final int[][] res = new int[n][]; for(int i = 0; i < n; i++) { res[i] = nextIntArray(k); } return res; } | |
public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException { final int[][] res = new int[n][k+1]; for(int i = 0; i < n; i++) { for(int j = 0; j < k; j++) { res[i][j] = nextInt(); } res[i][k] = i; } return res; } | |
public double[] nextDoubleArray(final int n) throws IOException { final double[] res = new double[n]; for(int i = 0; i < n; i++) { res[i] = nextDouble(); } return res; } | |
} | |
} |
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