A1565.[COCI-2016_2017-contest3]#3 Kvalitetni

A quality arithmetic expression consists of brackets, number and operations of multiplication and addition.
A quality arithmetic expression is defined recursively in the following way:
● An expression consisting of only one positive real​ number smaller than or equal to Z1 is of good quality.
Such expression is of the following form:
(x)
● For example, if Z1 = 5, then (4) is a quality expression.
● If A1, A2, …, Ak are quality expressions such that 2 k K and the sum​ of these ≤ ≤
expressions is at most Zk, then the following expressions are of good quality:
(A1+A2+...+Ak)
(A1A2...*Ak)
You are given a quality expression where the numbers are replaced by question marks.
Determine the maximal​ possible value that the expression could have had.

The first line of input contains integer K (2 ≤ K ≤ 50).
The second line of input contains integers Z1, …, ZK,, separated by space (1 ≤ Z1, …, ZK ≤ 50).
The third line of input contains one quality arithmetic expression in the described format.
Arithmetic expression consists of: ‘?’, ‘*’, ‘+’, ‘(‘, ‘)’, and its length is 1 000 000 characters, at most.

You must output the maximal possible value of the expression.
A solution is considered correct if the absolute or relative deviation from the official solution is less than 10^-
3.

Clarification of the first test case:
The expression ((3)+(3)) satisfies the conditions, so it is a quality expression, and it is easy to check that
6 is the maximal value.
Clarification of the second test case:
The maximum is achieved for, for instance, the expression (((1)+(2))(2)).
Clarification of the third test case:
The maximum is achieved for, for instance, the expression ((2)(2)*(2)).