<p>Given <code>n</code> pairs of parentheses, write a function to <em>generate all combinations of well-formed parentheses</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> n = 3
<strong>Output:</strong> ["((()))","(()())","(())()","()(())","()()()"]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> n = 1
<strong>Output:</strong> ["()"]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 8</code></li>
</ul>

class Solution:
    def generateParenthesis(self, n: int) -> List[str]:
        #generate all possible combinations 
        #check valid parenthesis 

        res = []
        #we have n pairs of parenthesis 
        def helper(open, closing, currCombo, res):
            if closing > open:
                return 

            if closing == open and closing == n: #valid complete combo 
                res.append("".join(currCombo))
                return

            if open < n: 
                currCombo.append('(')
                helper(open + 1, closing, currCombo, res)
                currCombo.pop()
    
            if closing < open: #add a closing parenthesis or open parenthesis 
                currCombo.append(')')
                helper(open, closing + 1, currCombo, res)
                currCombo.pop()
            
        helper(0,0,[],res)
        return res
         
        

16800