<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:
    void util(int index,int sum,int n,string s,vector<string>& ans){
        if(index==(2*n)) {
            if(sum==0)
            ans.push_back(s);
            return;
        }
        if(sum<n) {
            s+='(';
            util(index+1,sum+1,n,s,ans);
            s.pop_back();
        }
        if(sum>0) {
            s+=')';
            util(index+1,sum-1,n,s,ans);
        }
    }

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