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.Scanner;
public class Harry {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int[] a=new int[n];
        long[] m={sc.nextInt(),sc.nextInt(),sc.nextInt()
        };
        long[][] dp =new long[3][n];
        for(int i=0;i<n;i++)
            a[i]=sc.nextInt();
       dp[0][0]=m[0]*a[0];
       dp[1][0]=dp[0][0]+m[1]*a[0];
       dp[2][0]=dp[1][0]+m[2]*a[0];
       for(int i=1;i<n;i++){
           dp[0][i]=Math.max(dp[0][i-1],a[i]*m[0]);
       }
       for(int i=1;i<3;i++){
           for(int j=1;j<n;j++){
               dp[i][j]=Math.max(dp[i][j-1],dp[i-1][j]+a[j]*m[i]);
           }
       }
        System.out.println(dp[2][n-1]);
    }
}
