<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<int> q2;
        queue<int> q3;
        queue<int> q5;

        q2.push(1);
        q3.push(1);
        q5.push(1);

        int number = 1;
        int prev = 0;
        while (n > 1) {
            number = min(q2.front(), min(q3.front(), q5.front()));
            
            if (number == q2.front()) {
                q2.pop();
            } else if (number == q3.front()) {
                q3.pop();
            } else {
                q5.pop();
            }
            if (number <= prev) {
                continue;
            }
            if (number <= INT_MAX / 2)
                q2.push(number * 2);
            if (number <= INT_MAX / 3)
                q3.push(number * 3);
            if (number <= INT_MAX / 5)
                q5.push(number * 5);

            prev = number;
            n--;
        }

        number = min(q2.front(), min(q3.front(), q5.front()));
        while (number <= prev) {
            number = min(q2.front(), min(q3.front(), q5.front()));
            if (number == q2.front()) {
                q2.pop();
            } else if (number == q3.front()) {
                q3.pop();
            } else {
                q5.pop();
            }
            if (number <= prev) {
                continue;
            }
        }

        return number;
    }
};
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