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 collections import deque

tmp = list(map(int,input().split()))
n,p,q,r = tmp[0],tmp[1],tmp[2],tmp[3]
a = list(map(int,input().split()))

minLeft = []
minRight = deque()
maxLeft = []
maxRight = deque()

minLeft.append(a[0])
maxLeft.append(a[0])
for i in range(1,n):
    minLeft.append(min(a[i],minLeft[i-1]))
    maxLeft.append(max(a[i],maxLeft[i-1]))
    
minRight.append(a[-1])
maxRight.append(a[-1])
for i in range(n-2,-1,-1):
    minRight.appendleft(min(a[i],minRight[0]))
    maxRight.appendleft(max(a[i],maxRight[0]))
    
s = q*a[0]
if p <= 0:
    s += p * minLeft[0]
else:
    s += p * maxLeft[0]
if r <= 0:
    s += r * minRight[0]
else:
    s += r * maxRight[0]
for i in range(1,n):
    tmp = q*a[i]
    if p <= 0:
        tmp += p * minLeft[i]
    else:
        tmp += p * maxLeft[i]
    if r <= 0:
        tmp += r * minRight[i]
    else:
        tmp += r * maxRight[i]
    if(tmp > s):
        s = tmp
print(s)