<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;
        queue<pair<unsigned, unsigned>> q2, q3;
        queue<unsigned> q5;
        unsigned x = 6;
        int k = 6;
        q2.push({8, 4}); q2.push({10, 5});
        q3.push({9, 3});
        q5.push(10);
        while (k < n) {
            int newx;
            if (q2.front().first <= q3.front().first && q2.front().first <= q5.front()) {
                newx = q2.front().first;
                q3.push({3 * q2.front().second, q2.front().second});
                q2.pop();
            } else if (q3.front().first < q2.front().first && q3.front().first <= q5.front()) {
                newx = q3.front().first;
                q5.push(5 * q3.front().second);
                q3.pop();
            } else {
                newx = q5.front();
                q5.pop();
            }
            if (newx > x) {
                x = newx;
                q2.push({2*x, x});
                k++;
            }
        }
        return x;
    }
};
16228