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 sys
n,p,q,r = list(map(int,input().strip().split()))
arr = list(map(int,input().strip().split()))
def find_pref_sum(array):
    maxm = -2**63
    pref_sum = [0]*n
    for i in range(0,n):
        pref_sum[i] = max(maxm,array[i]*p)
        maxm = max(maxm,array[i]*p)
    return pref_sum
 
def find_suff_sum(array):
    maxm = -2**63
    suff_sum = [0]*n
    for j in reversed(range(n)):
        suff_sum[j] = max(maxm,array[j]*r)
        maxm = max(maxm,array[j]*r)
    return suff_sum
 
pref_sum = find_pref_sum(arr)
suff_sum = find_suff_sum(arr)
 
 
def find_max_expression(p,q,r,arr):
    max_exp = -2**63
    for i in range(0,n):
        max_exp = max(max_exp,max(p*arr[i],pref_sum[i])+arr[i]*q+max(r*arr[i],suff_sum[i]))
    return max_exp
 
max_expression_val = find_max_expression(p,q,r,arr)
print(max_expression_val)
