<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 {
public:
    vector<string> ans ;
    void validParanthesis(string& out, int n , int i , int openCount , int closeCount){
        if(i == 2*n){
            ans.push_back(out);
            return;
        }
        if(openCount < n){
            out[i] = '(';
            validParanthesis(out , n , i+1 , openCount+1 , closeCount);
        }
        if(closeCount < openCount){
            out[i] = ')';
            validParanthesis(out , n , i+1 , openCount , closeCount+1);
        }
    }

    vector<string> generateParenthesis(int n) {
        string out(2 * n, ' ');
        out[0] = '(';
        validParanthesis(out , n, 1 , 1 , 0);
        return ans;
    }
};
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