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.math.BigInteger;
import java.util.Scanner;

public class Main{

	public static void main(String[] args) {
		Scanner scanner=new Scanner(System.in);
		String s[] = scanner.nextLine().split(" ");
		long  n = Integer.parseInt(s[0]);
		BigInteger  p = new BigInteger(s[1]);
		BigInteger  q = new BigInteger(s[2]);
		BigInteger  r = new BigInteger(s[3]);
		s= scanner.nextLine().split(" ");
		BigInteger  a = new BigInteger("-999999999999999999999999999999999999999999999999999999999999999");
		BigInteger  b = new BigInteger("-999999999999999999999999999999999999999999999999999999999999999");
		BigInteger  c = new BigInteger("-999999999999999999999999999999999999999999999999999999999999999");
		for(int i=0;i<n;i++) {
			a = a.max( p.multiply(new BigInteger(s[i])));
			b = b.max( a.add(q.multiply(new BigInteger(s[i]))));
			c = c.max(b.add(r.multiply(new BigInteger(s[i]))));
			//System.out.println(a+" "+b+" "+c);
		}
		System.out.println(c);
		
	}

}

 		 				 				 		  		   	  			 	