description: A bracket sequence is a string containing only characters "(" and ")". A regular bracket sequence (or, shortly, an RBS) is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example:
  
    * bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"); 
    * bracket sequences ")(", "(" and ")" are not. 
  
  
  
  Let's denote the concatenation of two strings x and y as x+y. For example, "()()" + ")(" = "()())(".
  
  You are given n bracket sequences s_1, s_2, ..., s_n. You can rearrange them in any order (you can rearrange only the strings themselves, but not the characters in them).
  
  Your task is to rearrange the strings in such a way that the string s_1 + s_2 + ... + s_n has as many non-empty prefixes that are RBS as possible.
  
  Input
  
  The first line contains a single integer n (1 ≤ n ≤ 20).
  
  Then n lines follow, the i-th of them contains s_i — a bracket sequence (a string consisting of characters "(" and/or ")". All sequences s_i are non-empty, their total length does not exceed 4 ⋅ 10^5.
  
  Output
  
  Print one integer — the maximum number of non-empty prefixes that are RBS for the string s_1 + s_2 + ... + s_n, if the strings s_1, s_2, ..., s_n can be rearranged arbitrarily.
  
  Examples
  
  Input
  
  
  2
  (
  )
  
  
  Output
  
  
  1
  
  
  Input
  
  
  4
  ()()())
  (
  (
  )
  
  
  Output
  
  
  4
  
  
  Input
  
  
  1
  (())
  
  
  Output
  
  
  1
  
  
  Input
  
  
  1
  )(()
  
  
  Output
  
  
  0
  
  Note
  
  In the first example, you can concatenate the strings as follows: "(" + ")" = "()", the resulting string will have one prefix, that is an RBS: "()".
  
  In the second example, you can concatenate the strings as follows: "(" + ")" + "()()())" + "(" = "()()()())(", the resulting string will have four prefixes that are RBS: "()", "()()", "()()()", "()()()()".
  
  The third and the fourth examples contain only one string each, so the order is fixed.
solution: import io,os
  import bisect
  #input = io.BytesIO(os.read(0, os.fstat(0).st_size)).readline
  
  
  
  def getnext(state,pre,infor,dic,dp):
  
  
      if state in dp:  return dp[state]
  
  #    print(state,pre[state])
      output = 0
      for i in range(len(infor)):
          if state & (1<<i) > 0:  continue 
          if pre[state] + infor[i][1] < 0:
             
              firstappear = dic[i][-pre[state]-1][0]
  
              temp = 0
              if -pre[state] in dic[i]:
                  temp = bisect.bisect_left( dic[i][-pre[state]], firstappear )
              output = max(output,temp)
              continue 
  
          base = 0
          if -pre[state] in dic[i]:  base = len( dic[i][-pre[state]] )
  
          temp = base + getnext(state+(1<<i), pre,infor,dic,dp)
          output = max(output,temp)
  
      dp[state] = output 
      return output 
   
  
              
              
          
  
  
  
     
  
  
      
      
  
  
  
  
      
  
  
  
  def main(t):
  
  
      n = int(input())
      grid = []
      infor = []
      dic = [{} for _ in range(n)]
  
      pre = [0 for _ in range(1<<n)]
  
  
      for k in range(n): 
          curr = 0
          minimum = 1
          s = input()
          for i in range(len(s)):
              if s[i]=='(':  curr += 1
              else:  curr -= 1
              if curr < minimum:  minimum = curr
              if curr not in dic[k]:  dic[k][curr] = []
              dic[k][curr].append(i)
          infor.append([curr, minimum, len(dic[k][minimum])]  )  
  
  
      for state in range(1<<n):
          s = bin(state)[2:][::-1]
          s += '0'*(n-len(s))
  
          for i in range(n):
              if s[i]=='1':   pre[state] += infor[i][0]
  
  
               
  
      dp = {}
      ans = getnext(0,pre,infor,dic,dp)
  #    print(dp)
  #    print(pre)
  #    print(infor)
  
  
      print(ans)
  
          
              
  
  
  
          
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  T = 1 #int(input())
  t = 1
  while t<=T:
      main(t)
      t += 1
  