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.
P_I = 0
Q_I = 1
R_I = 2
def solve(n, pqr, a):
    # key idea: i is upper-bounded by j and k is lower-bounded by j
    # if we compute the maximum values for p * a_i for each index x s.t. x <= j and do the same for r * a_k
    # then we can check at each point j and add the max's for each, and then choose the max

    # time complexity: O(N)

    max_p = [0 for _ in range(n)]
    max_r = [0 for _ in range(n)]
    max_p[0] = pqr[P_I] * a[0]
    max_r[n - 1] = pqr[R_I] * a[n - 1]


    # compute the max p * a_i up til index i
    for i in range(1, n):
        max_p[i] = max(max_p[i-1], pqr[P_I] * a[i])

    # compute the max q * a_k after index i
    for k in range(n - 2, -1, -1):
        max_r[k] = max(max_r[k+1], pqr[R_I] * a[k])

    m = -3000000000000000000000
    for j in range(n):
        prod = pqr[Q_I] * a[j]
        s = max_p[j] + prod + max_r[j]
        m = max(s, m)

    return m

line1 = input().split()
n = int(line1[0])
pqr = [int(i) for i in line1[1:]]
a = [int(i) for i in input().split()]

print(solve(n, pqr, a))
