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.

def get_ans(n, p, q, r, a):
    maxpre = [-100000000] * n
    minpre = [100000000] * n
    maxsuf = [-100000000] * n
    minsuf = [100000000] * n

    curmax = a[0]
    curmin = a[0]

    for i in range(n):
        if a[i] > curmax:
            curmax = a[i]
        maxpre[i] = curmax

        if a[i] < curmin:
            curmin = a[i]
        minpre[i] = curmin

    curmax = a[n - 1]
    curmin = a[n - 1]

    for i in range(n - 1, -1, -1):
        if a[i] > curmax:
            curmax = a[i]
        maxsuf[i] = curmax

        if a[i] < curmin:
            curmin = a[i]
        minsuf[i] = curmin

    ans = []
    for i in range(n):
        pmas = maxpre if p > 0 else minpre
        rmas = maxsuf if r > 0 else minsuf

        ans.append(pmas[i] * p + a[i] * q + rmas[i] * r)

    return max(ans)

n, p, q, r = tuple(map(int, input().split()))
a = list(map(int, input().split()))
print(get_ans(n, p, q, r, a))

