<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 == 1) {
            return 1;
        }

        int result;

        priority_queue<int, vector<int>, greater<int>> minHeap;
        minHeap.push(2);
        minHeap.push(3);
        minHeap.push(5);

        unordered_set<int> seen;

        for (int i = 1; i < n; i++) {
            while (seen.count(minHeap.top())) {
                minHeap.pop();
            }

            result = minHeap.top();
            minHeap.pop();

            if (result < INT_MAX / 2) {
                minHeap.push(result * 2);
            }

            if (result < INT_MAX / 3) {
                minHeap.push(result * 3);
            }

            if (result < INT_MAX / 5) {
                minHeap.push(result * 5);
            }
            seen.insert(result);
        }

        return result;
    }
};
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