<p>An <strong>ugly number</strong> is a positive integer whose prime factors are limited to <code>2</code>, <code>3</code>, and <code>5</code>.</p>

<p>Given an integer <code>n</code>, return <em>the</em> <code>n<sup>th</sup></code> <em><strong>ugly number</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 10
<strong>Output:</strong> 12
<strong>Explanation:</strong> [1, 2, 3, 4, 5, 6, 8, 9, 10, 12] is the sequence of the first 10 ugly numbers.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
<strong>Explanation:</strong> 1 has no prime factors, therefore all of its prime factors are limited to 2, 3, and 5.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 1690</code></li>
</ul>

class Solution {
public:
   
    int nthUglyNumber(int n) {
       vector<int>v={2,3,5};
       priority_queue<long,vector<long>,greater<long>>q;
       vector<long>vv;
       long cur;
       q.push(1);
       vv.push_back(1);
       
       for(int i=0;i<n;i++){
        cur = q.top();
        q.pop();
        for(int i:v){
            long nn = cur*i;
            if(find(vv.begin(),vv.end(),nn) == vv.end()){
                q.push(nn);
                vv.push_back(nn);
            }  
        }
       }
       return (int)cur;
    }
};
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