<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) {

        int maxval = std::numeric_limits<int>::max();
        
        std::queue<int> arr2;
        arr2.push(1);
        std::queue<int> arr3;
        arr3.push(1);
        std::queue<int> arr5;
        arr5.push(1);

        // std::vector<int> prevs = {1};

        int cur = 1;

        for (int i = 0; i < n; i++) {
            std::vector<int> possib_vals = {arr2.front(), arr3.front(), arr5.front()};

            cur = *std::min_element(possib_vals.begin(), possib_vals.end());

            if (maxval / cur >= 2)
                arr2.push(2 * cur);
            if (maxval / cur >= 3)
                arr3.push(3 * cur);
            if (maxval / cur >= 5)
                arr5.push(5 * cur);

            if (possib_vals[0] == cur) arr2.pop();
            if (possib_vals[1] == cur) arr3.pop();
            if (possib_vals[2] == cur) arr5.pop();

            // std::cout << cur << std::endl;
        }

        return cur;
    }
};
23709