<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>

// O(n logn) time using hb-BST
class Solution {
public:
    int nthUglyNumber(int n) {
        vector<int> primes = {2, 3, 5};
        priority_queue<vector<int>, vector<vector<int>>, greater<vector<int>>> seenNumbers;
        seenNumbers.push({1, 0});
        while(n > 1) {
            int num = seenNumbers.top()[0];
            int i = seenNumbers.top()[1];
            seenNumbers.pop();

            for(int j = i; j < primes.size(); j++) {
                if(num <= INT_MAX / primes[j]) {
                    seenNumbers.push({primes[j] * num, j});
                }
            }
            n--;
        }
        return seenNumbers.top()[0];
    }
};
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