<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) {
        vector<string> result;
        queue<pair<string, pair<int, int>>> q;
        q.push({"", {0, 0}});
        
        while (!q.empty()) {
            auto current = q.front();
            q.pop();
            string s = current.first;
            int open = current.second.first;
            int close = current.second.second;
            
            if (s.size() == 2 * n) {
                result.push_back(s);
                continue;
            }
            
            if (open < n) {
                q.push({s + "(", {open + 1, close}});
            }
            if (close < open) {
                q.push({s + ")", {open, close + 1}});
            }
        }
        
        return result;
    }
};

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