<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> s1{}; 
    void check(string& s, int l, int r)
    {
        sort(s.begin(),s.end());
        do
        {
            stack <char> s2;
            for(auto c : s)
            {
                if(c == '(')
                    s2.push(c);
                else if(c == ')')
                {
                    if(!s2.empty() && s2.top() == '(')
                        s2.pop();
                }
            }
            if(s2.empty())
            {
                s1.push_back(s);
            }
        }while(next_permutation(s.begin(),s.end()));
    }
    
    vector<string> generateParenthesis(int n) 
    {
        string a = "";
        for(int i = 1; i<=n ;i++)
        {
            a+="()";
        }
        check(a,0,a.length()-1);
        return s1;
    }
};
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