<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 isvalid(string s){
        stack<char> st;
        for(char c:s){
            if(c=='(')st.push('(');
            else if(c==')'){
                if(st.empty())return false;
                if(st.top()!='(')return false;
                st.pop();
            }
        }
        if(!st.empty())return false;
        return true;
    }
    vector<string> generateParenthesis(int n) {
        string s;
        vector<string> poss;
        vector<string> ans;
        for(int i=0;i<n;i++){
            s.push_back('(');
            s.push_back(')');
        }
        sort(s.begin(),s.end());
        poss.push_back(s);
        while(next_permutation(s.begin(),s.end())){
            poss.push_back(s);
        }
        for(string s:poss)if(isvalid(s))ans.push_back(s);
        return ans;
    }
};
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