<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) {
        if(n==0) return 1 ;

        set<long long int> seen ;

        priority_queue<long long int,vector<long long int>,greater<long long int>> min_heap ;

        min_heap.push(1) ;
        seen.insert(1) ;
        for(int i = 1 ; i < n ; i++){
            long long int e = min_heap.top() ;
            min_heap.pop() ;
            if(!seen.count(2*e)) min_heap.push(2*e) ;
            if(!seen.count(3*e)) min_heap.push(3*e) ;
            if(!seen.count(5*e)) min_heap.push(5*e) ;
            seen.insert(2*e) ;
            seen.insert(3*e) ;
            seen.insert(5*e) ;
        } 
        return min_heap.top() ;
    }
};
35821