<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:
    ugly = sorted(2**a * 3**b *5**c for a in range(32) for b in range(20) for c in range(14))
    def nthUglyNumber(self, n: int) -> int:
        # minHeap = [1]
        # factors = [2,3,5]
        # visit = set()
        # for i in range(n):
        #     num = heapq.heappop(minHeap)
        #     if i == n-1:
        #         return num
        #     else:
        #         for f in factors:
        #             if num * f not in visit:
        #                 visit.add(num * f)
        #                 heapq.heappush(minHeap,num * f)
        return self.ugly[n-1]

        
17000