<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) {
    if (n <= 6)
      return n;

    std::unordered_set<int64_t> numbers;
    std::priority_queue<int64_t, std::vector<int64_t>, std::greater<int64_t>>
        candidates;
    candidates.push(1);
    const std::vector<int64_t> mult({2, 3, 5});

    int64_t answer = 0;
    int64_t pops = 0;

    while (numbers.size() < n) {
      int64_t c = candidates.top();
      candidates.pop();
      ++pops;
      auto iter = numbers.insert(c);
      if (!iter.second) {
        continue;
      }
      answer = c;
      for (int64_t v : mult) {
        if (v * c < std::numeric_limits<int>::max())
          candidates.push(v * c);
      }
    }

    return answer;
  }
};
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