<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:
    bool valid(string s){
        stack<char> st;
        for(auto c:s){
            if(c=='(') st.push(c);
            else{
                if(st.empty() || st.top()!='(') return false;
                st.pop(); 
            }
        }
        return st.empty();
    }
    vector<string> generateParenthesis(int n) {
        string s;
        for(int i=0;i<n;i++) s+='('; 
        for(int i=0;i<n;i++) s+=')';
        int k=4*n*n;
        
        set<string> ans;
        ans.insert(s);
        while(next_permutation(s.begin(),s.end())){
            if(valid(s)){
            ans.insert(s);
            }  
        }
        vector<string> res(ans.begin(),ans.end());
        return res;

    }
};
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