Professor Dumbledore is helping Harry destroy the Horcruxes. He went to Gaunt Shack as he suspected a Horcrux to be present there. He saw Marvolo Gaunt's Ring and identified it as a Horcrux. Although he destroyed it, he is still affected by its curse. Professor Snape is helping Dumbledore remove the curse. For this, he wants to give Dumbledore exactly x drops of the potion he made. 

Value of x is calculated as maximum of p·ai + q·aj + r·ak for given p, q, r and array a1, a2, ... an such that 1 ≤ i ≤ j ≤ k ≤ n. Help Snape find the value of x. Do note that the value of x may be negative.

Input

First line of input contains 4 integers n, p, q, r ( - 109 ≤ p, q, r ≤ 109, 1 ≤ n ≤ 105).

Next line of input contains n space separated integers a1, a2, ... an ( - 109 ≤ ai ≤ 109).

Output

Output a single integer the maximum value of p·ai + q·aj + r·ak that can be obtained provided 1 ≤ i ≤ j ≤ k ≤ n.

Examples

Input

5 1 2 3
1 2 3 4 5


Output

30


Input

5 1 2 -3
-1 -2 -3 -4 -5


Output

12

Note

In the first sample case, we can take i = j = k = 5, thus making the answer as 1·5 + 2·5 + 3·5 = 30.

In second sample case, selecting i = j = 1 and k = 5 gives the answer 12.
import java.util.Arrays;
import java.util.Scanner;

public class marvolo {
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		n=scan.nextInt();
		long[] val={scan.nextLong(),scan.nextLong(),scan.nextLong()};
		a=new long[n];
		for(int i=0;i<n;i++) a[i]=scan.nextLong();
		dp=new long[n][3];
		for(long[] d:dp) Arrays.fill(d,Long.MAX_VALUE);
		System.out.println(go(0,0,val));
	}
	static long[][] dp;
	static long[] a;
	static int n,p,q,r;
	public static long go(int at, int k, long[] val) {
		if(at==n) {
			return k==3?0L:Long.MIN_VALUE;
		}
		if(k==3) return 0L;
		if(dp[at][k]!=Long.MAX_VALUE) return dp[at][k];
		long res=Long.MIN_VALUE;
		res=Math.max(res,val[k]*a[at]+go(at,k+1,val));
		res=Math.max(res,go(at+1,k,val));
		return dp[at][k]=res;
	}
}