A quality arithmetic expression consists of brackets, numbers 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 $Z_1$ is of good quality. For example, if $Z_1=5$, then $(4)$ is a quality expression.
• If $A_1,A_2,\dots ,A_k$ are quality expressions such that $2\le k\le K$ and the sum of these expressions is at most $Z_k$, then the following expressions are of good quality:

$${\displaystyle (A_1+A_2+\cdots +A_k)}$$

$${\displaystyle (A_1\times A_2\times \cdots \times A_k)}$$

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.

Input Specification

The first line of input contains integer $K$ $(2\le K\le 50)$.

The second line of input contains integers $Z_1,\dots ,Z_K$, separated by spaces $(1\le Z_1,\dots ,Z_K\le 50)$.

The third line of input contains one quality arithmetic expression in the described format.

An arithmetic expression consists of: ?, *, +, (, ), and its length is at most $1000000$ characters.

Output Specification

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 ${10}^{-3}$.

Sample Input 1

2
10 6
((?)+(?))

Sample Output 1

6.00000

Explanation for Sample Output 1

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.

Sample Input 2

3
2 5 3
(((?)+(?))*(?))

Sample Output 2

6.00000

Explanation for Sample Output 2

The maximum is achieved for, for instance, the expression (((1)+(2))*(2)).

Sample Input 3

3
2 10 6
((?)*(?)*(?))

Sample Output 3

8.000000000

Explanation for Sample Output 3

The maximum is achieved for, for instance, the expression ((2)*(2)*(2)).