<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) {
        return recurse(n, 0, "", 0);
    }

    vector<string> recurse(int n, int open, string curr, int depth) {
        if (depth == 2 * n) {
            if (open == 0) return {curr};
            return {};
        }
        vector<string> res = recurse(n, open + 1, curr + '(', depth + 1);
        if (open > 0) {
            vector<string> seco = recurse(n, open - 1, curr + ')', depth + 1);
            res.insert(res.begin(), seco.begin(), seco.end());
        }
        return res;
    }
};
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