Problem Statement:
Generate correct parenthesis sequences in lexicographic order.
Correct parenthesis sequences are given by the rule:
S ::= ()|(S)|SS Lexicographic order is imposed by assuming '(' less than ')'.


Input Format:
Input file contains one integer number n, (1 <= n <= 10).


Output Format:
Output all correct parenthesis sequences of length 2n, one sequence a line, without spaces.


Sample Input:
3


Sample Output:
((())) (()()) (())() ()(()) ()()()





Added by: eagle93
Added at: 2014-07-06 07:00:02 UTC
Time Limit: 1 second
Partial score: No