<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)
    {
        unordered_set<long> s;
        priority_queue<long, vector<long>, greater<long>> q;
        q.push(1);
        s.insert(1);

        for (int i = 1; i < n; ++i)
        {
            long curr = q.top();
            q.pop();
            s.erase(curr);
            if (s.find(curr * 2) == s.end())
            {
                s.insert(curr * 2);
                q.push(curr * 2);
            }

            if (s.find(curr * 3) == s.end())
            {
                s.insert(curr * 3);
                q.push(curr * 3);
            }

            if (s.find(curr * 5) == s.end())
            {
                s.insert(curr * 5);
                q.push(curr * 5);
            }
        }

        return q.top();
    }
};
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