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.*;
public class b {
    public static int n;
    public static long p, q, r;
    public static long[][][][] memo;
    public static long[] nums;
    public static void main(String[] args){
        Scanner br = new Scanner(System.in);
        n = br.nextInt();
        p = br.nextLong();
        q = br.nextLong();
        r = br.nextLong();
        nums = new long[n];
        for(int i = 0;i<n;i++){
            nums[i] = br.nextLong();
        }
        memo = new long[2][2][2][n];
        for(int i = 0;i<2;i++){
            for(int j = 0;j<2;j++){
                for(int k = 0;k<2;k++){
                    Arrays.fill(memo[i][j][k], (long)-6e18);
                }
            }
        }
        for(int i = n-1;i>=0;i--){
            go(0, 0, 0, i);
            go(1, 0, 0, i);
            go(1, 1, 0, i);
            go(1, 1, 1, i);
        }
        System.out.println(go(0, 0, 0, 0));
    }
    public static long go(int p1, int p2, int p3, int pos) {
        if (pos == n) {
            if (p1  == 0 || p2 == 0 || p3 == 0) {
                return (long)-5e18;
            }
            return 0;
        }

        if (memo[p1][p2][p3][pos] != -6e18) {
            return memo[p1][p2][p3][pos];
        }

        long max = go(p1, p2, p3, pos+1);

        if (p1 == 0) {
            max = Math.max(max, go(1, p2, p3, pos) + p*nums[pos]);
        } else if (p2 == 0) {
            max = Math.max(max, go(1, 1, p3, pos) + q*nums[pos]);
        } else if (p3 == 0) {
            max = Math.max(max, go(1, 1, 1, pos) + r*nums[pos]);
        }

        return memo[p1][p2][p3][pos] = max;
    }
} 