Given an integer N representing the number of pairs of parentheses, the task is to generate all combinations of well-formed(balanced) parentheses.

Example 1:

Input:
N = 3
Output:
((()))
(()())
(())()
()(())
()()()

Example 2:

Input:
N = 1
Output:
()

Your Task:
You don't need to read input or print anything. Complete the function AllParenthesis() which takes N as input parameter and returns the list of balanced parenthesis.

Expected Time Complexity: O(2^N * N).
Expected Auxiliary Space: O(2*N*X), X = Number of valid Parenthesis.

Constraints:
1 ≤ N ≤ 12