<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>

import heapq

class Solution:
    def nthUglyNumber(self, n: int) -> int:
        ugly_count = 0
        ugly_heap = [1]
        heapq.heapify(ugly_heap)
        added_set = {1}

        while True:
            next_val = heapq.heappop(ugly_heap)
            ugly_count += 1
            if ugly_count == n:
                return next_val
            
            if next_val*2 not in added_set:
                heapq.heappush(ugly_heap, next_val*2)
                added_set.add(next_val*2)
            if next_val*3 not in added_set:
                heapq.heappush(ugly_heap, next_val*3)
                added_set.add(next_val*3)
            if next_val*5 not in added_set:
                heapq.heappush(ugly_heap, next_val*5)
                added_set.add(next_val*5)
        
        print("We shouldn't be here!!!")
        raise Exception
16800