output_description: Print the lexicographically smallest string among the shortest correct bracket
  sequences that can be obtained by inserting some number of `(` and `)` into S.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      N
      S
attempt: n = int(input())
  s = str(input())
  r = [i for i in range(n) if s[i] == "("]
  l = [i for i in range(n) if s[i] == ")"]
  if r == []:
      print(n * "(" + s)
  elif l == []:
      print(s + n * ")")
  elif min(r) > max(l):
      print(len(l) * "(" + s + len(r) * ")")
  else:
      cnt = 0
      for i in reversed(range(len(r))):
          if r[i] < max(l):
              cnt += 1
              l.pop(-1)
          if l == []:
              break
      print((len(l)) * "(" + s + (len(r) - cnt) * ")")
  
problem_description: 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.
samples: [{"input": "3\n    ())", "output": "(())\n    \n\n* * *"}, {"input": "6\n    )))())", "output": "(((()))())\n    \n\n* * *"}, {"input": "8\n    ))))((((", "output": "(((())))(((())))"}]