All Balanced Bracket Strings

You are given an integer n. Return every balanced string made of exactly n ( characters and n ) characters, in any order.

A string is balanced if every prefix has at least as many ( characters as ) characters, and the string as a whole has the same number of each.

Examples

Example 1

Input: n = 3
Output: ["((()))","(()())","(())()","()(())","()()()"]

Example 2

Input: n = 1
Output: ["()"]