<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:
    void helper(string curr, stack<char> st, int open_count, vector<string> &ans, int &n){
        if((open_count == n) && st.empty()){
            ans.push_back(curr);
            return;
        }

        if(st.empty()){
            st.push('(');
            helper(curr+"(", st, open_count+1, ans, n);
            return;
        }

        if(open_count == n){
            st.pop();
            helper(curr+")", st, open_count, ans, n);
            return;
        }

        st.push('(');
        helper(curr+"(", st, open_count+1, ans, n);
        st.pop();
        st.pop();
        helper(curr+")", st, open_count, ans, n);
    }
    vector<string> generateParenthesis(int n) {
        vector<string> ans;
        helper("", stack<char>(), 0, ans, n);
        return ans;
    }
};
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