<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;

    int answer = 0;
    int count = 1;

    std::vector<int64_t> v2({2});
    std::vector<int64_t> v3({3});
    std::vector<int64_t> v5({5});
    v2.reserve(n);
    v2.reserve(n);
    v2.reserve(n);

    int i2 = 0;
    int i3 = 0;
    int i5 = 0;

    while (count < n) {
      int64_t m = std::min(std::min(v2[i2], v3[i3]), v5[i5]);
      answer = m;
      ++count;
      if (v2[i2] == m)
        ++i2;
      if (v3[i3] == m)
        ++i3;
      if (v5[i5] == m)
        ++i5;

      v2.push_back(2 * m);
      v3.push_back(3 * m);
      v5.push_back(5 * m);
    }

    return answer;
  }
};
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