<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) {
        vector<long> multipliers;
        multipliers.push_back(2);
        multipliers.push_back(3);
        multipliers.push_back(5);
        priority_queue<long, vector<long>, greater<long>> pq;
        unordered_set<long> distinct;
        for (int i = 1; i <= 5; i++) {
            pq.push(i);
            distinct.insert(i);
        }
        for (int i = 0; i < n-1; i++) {
            long num  = pq.top();
            pq.pop();
            for (int multiplier : multipliers)
                if (distinct.find(multiplier * num) == distinct.end()) {
                    distinct.insert(multiplier * num);
                    pq.push(multiplier * num);
                }
        }
        return pq.top();
    }
};
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