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


def getX(ai, aj, ak):
    return ai * p + aj * q + ak * r


if __name__ == "__main__":

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

    minLeft = []
    maxLeft = []

    minRight = []
    maxRight = []

    for i in range(n):
        if i == 0:
            minLeft.append(arr[i])
            maxLeft.append(arr[i])
        else:
            minLeft.append(min(minLeft[len(minLeft) - 1], arr[i]))
            maxLeft.append(max(maxLeft[len(maxLeft) - 1], arr[i]))

    arr.reverse()

    for i in range(n):
        if i == 0:
            minRight.append(arr[i])
            maxRight.append(arr[i])
        else:
            minRight.append(min(minRight[len(minRight) - 1], arr[i]))
            maxRight.append(max(maxRight[len(maxRight) - 1], arr[i]))

    minRight.reverse()
    maxRight.reverse()

    result = -9223372036854775808

    arr.reverse()

    for j in range(n):

        if p < 0:
            ai = minLeft[j]
        else:
            ai = maxLeft[j]

        if r < 0:
            ak = minRight[j]
        else:
            ak = maxRight[j]

        result = max(result, getX(ai, arr[j], ak))

    print(result)
