<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> ans;

void backtrack(int remaining, string p, int open) {

    if(remaining < 0) {
        return;
    }

    if(remaining == 0 and open == 0) {
        ans.push_back(p);
    }

    if(open > 0) {
        p += ")";
        backtrack(remaining, p, open-1);
        p.pop_back();
    }

    p += "(";
    backtrack(remaining-1, p, open+1);
    p.pop_back();

}

vector<string> generateParenthesis(int n) {
    string p="";
    backtrack(n, p, 0);
    return ans;
}
};
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