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.
vals = list(map(int, input().strip().split()))
arr = list(map(int, input().strip().split()))
dp = [[0 for i in range(vals[0])] for i in range(3)]
n = vals[0]

dp[-1][-1] = vals[3]*arr[-1]
for i in range(n-2, -1, -1):
    dp[-1][i] = max(dp[-1][i+1], arr[i]*vals[3])

for i in range(1, -1, -1):
    dp[i][-1] = arr[-1]*vals[i+1]+dp[i+1][-1]
    for j in range(n-2, -1, -1):
        dp[i][j] = max(dp[i][j+1], arr[j]*vals[i+1]+dp[i+1][j])


print(dp[0][0])
# for i in dp:
#     print(i)