<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<vector<string>> dp(n+1, vector<string>());
        dp[0] = {""};
        for(int i = 1; i < dp.size(); i++){
            for(int j = 0; j < i; j++){
                for(string inc: dp[j]){
                    for(string out: dp[i-j-1]){
                        dp[i].push_back(out+'('+inc+')');
                    }
                }
            }
        }
        return dp[n];
    }
};
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