<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>

#define ll long long int
class Solution {
public:
    int nthUglyNumber(int n) {
        if(n==1)
            return 1;

        int rem = n-2;
        
        priority_queue<ll, vector<ll>, greater<ll>> pq;
        
        pq.push(2);
        pq.push(3);
        pq.push(5);
        
        unordered_set<ll> uset;
        
        while(rem--){
            ll temp = pq.top();
            pq.pop();
            if(uset.count(temp)){
                rem++;
                continue;                
            }
            
            uset.insert(temp);
            
            pq.push(temp*2);
            pq.push(temp*3);
            pq.push(temp*5);
            
        }
        
        while(uset.count(pq.top()))
            pq.pop();
        
        return pq.top();
        
    }
};
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