<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> generateParenthesis(int n) {
        int index = 0;
        int count = 0;
        vector<string> res;
        string s;
        backtrack(n, res, s, count, index);
        return res;
    }
    
    void backtrack(int n, vector<string>& res, string s, int count, int index)
    {
        if (count < 0)
        {
            return;
        }
        
        if (index == 2*n)
        {
            if (count == 0)
            {
                // We have used up all the parantheses
                res.push_back(s);
            }
          return;
            
        }
        
        s+= ')';
        backtrack(n, res, s, count - 1, index + 1);
        s.pop_back();
        
        s+='(';
        backtrack(n, res, s, count + 1, index + 1);
        s.pop_back();
    }
};
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