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Problem Statement

You are given a string $S$ of length $N$ consisting of ( and ). Your task is to insert some number of ( and ) into $S$ to obtain a correct bracket sequence.
Here, a correct bracket sequence is defined as follows:

• () is a correct bracket sequence.
• If $X$ is a correct bracket sequence, the concatenation of (, $X$ and ) in this order is also a correct bracket sequence.
• If $X$ and $Y$ are correct bracket sequences, the concatenation of $X$ and $Y$ in this order is also a correct bracket sequence.
• Every correct bracket sequence can be derived from the rules above.

Find the shortest correct bracket sequence that can be obtained. If there is more than one such sequence, find the lexicographically smallest one.

Constraints

• The length of $S$ is $N$.
• $1 ≤ N ≤ 100$
• $S$ consists of ( and ).

Sample Input 1

3
())

Sample Output 1

(())

Sample Input 2

6
)))())

Sample Output 2

(((()))())

Sample Input 3

8
))))((((

Sample Output 3

(((())))(((())))