<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) 
    {
        std::priority_queue<int, std::vector<int>, std::greater<int>> factors;
        factors.push(1);
        int count = 0;
        std::unordered_set<int> poppedFactors;
        while(true)
        {
            if(poppedFactors.find(factors.top()) == poppedFactors.end())
            {
                count++;
                if(count == n)
                    return factors.top();
                if(factors.top() < std::numeric_limits<int>::max()/2)
                    factors.push(factors.top() * 2);
                if(factors.top() < std::numeric_limits<int>::max()/3)
                    factors.push(factors.top() * 3);
                if(factors.top() < std::numeric_limits<int>::max()/5)
                    factors.push(factors.top() * 5);
                std::cout << factors.top() << std::endl;
                poppedFactors.insert(factors.top());
            }
            factors.pop();
        }
        return -1;
    }
};
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