Given a positive integer (1 \le n \le 10), print all correct bracket sequences of length in alphabetical order, assuming that the character '' comes before '' in the alphabet.
A correct bracket sequence is either an empty string, or a string of the form , where is a correct bracket sequence, or a string of the form S_1S_2, where S_1 and S_2 are correct bracket sequences.
One integer (1 \le n \le 10).
Print in alphabetical order all correct bracket sequences of length , one sequence per line, without spaces.
Example 1