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.
from typing import List
import sys

class Solution:
    def maxExpr(self, nums: List[int],p: int, q: int, r: int) -> int:
        n = len(nums)

        if n < 1: return 0

        pmax = [0] * n
        smax = [0] * n

        pmax[0] = p * nums[0]
        for i in range(1,n):
            pmax[i] = max(pmax[i-1], p * nums[i])

        smax[n-1] = r * nums[n-1]
        for i in range(n-2,-1,-1):
            smax[i] = max(smax[i+1], r * nums[i])

        max_expr = -2**63 # -sys.maxsize

        for i in range(0,n):
            curr_expr = pmax[i] + (q * nums[i]) + smax[i]
            max_expr = max(max_expr , curr_expr)

        return max_expr


if __name__ == '__main__':
    sol = Solution()
    n,p,q,r = map(int,input().split(' '))
    x = input()
    l = list(map(int, x.split()))
    max_expr = sol.maxExpr(l,p,q,r)
    print(max_expr)