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
initial_inp = []
inp = []
n = input().split()
count = int(n[0],10)
p = int(n[1],10)
q = int(n[2],10)
r = int(n[3],10)
arrString = input().split()
arr = count * [None]
 
for i in range(0,count):
    arr[i] = int(arrString[i],10)
    
def maximum(a,b):
    if a < b:
        return b
    else:
        return a
 
#find prefix max
pmax = [1] * count
pmax[0] = arr[0] * p
 
for i in range(1,count):
    pmax[i] = maximum(pmax[i-1],(p*arr[i]))
 
#find suffix max
 
smax = [1] * count
smax[count-1] = arr[count-1]*r
 
for i in range(count-2,-1,-1):
    smax[i]=maximum(smax[i+1],(r*arr[i]))
 
#to find best position for q multiplier
ans = -sys.maxsize - (sys.maxsize*sys.maxsize*10)
 
for i in range(0,count):
    ans = maximum((pmax[i]+(q*arr[i])+smax[i]),ans)
 
print(ans)