<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) {
        queue<long> q2;
        queue<long> q3;
        queue<long> q5;
        q2.push(2);
        q3.push(3);
        q5.push(5);

        long ugly = 1;
        long prev = 1;

        for (int count = 1; count < n; count++) {
            prev = ugly;
            if (q2.front() < q3.front()) {
                if (q2.front() < q5.front()) {
                    ugly = q2.front();
                    q2.pop();
                }
                else {
                    ugly = q5.front();
                    q5.pop();
                }
            }
            else {
                if (q3.front() < q5.front()) {
                    ugly = q3.front();
                    q3.pop();
                }
                else {
                    ugly = q5.front();
                    q5.pop();
                }
            }

            if (prev == ugly) {
                count--;
                continue;
            }

            q2.push(ugly * 2);
            q3.push(ugly * 3);
            q5.push(ugly * 5);
        }

        return (int)ugly;
    }
};
18009