<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 {
    void solve(string output, vector<string> &ans, int n, int o=1, int c=0) {
        if(o==n && c==n) {
            ans.push_back(output);
            return;
        }
        if(o<=n) {
            solve(output+"(", ans, n, o+1, c);
        }
        if(c<o) {
            solve(output+")", ans, n, o, c+1);
        }
    }
public:
    vector<string> generateParenthesis(int n) {
        vector<string> ans;
        solve("(", ans, n);
        return ans;
    }
};
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