<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) {
        priority_queue<pair<long long ,int>, vector<pair<long long,int>>, greater<pair<long long,int>>> pq;
        pq.push({1,1});
        while(n-1) {
            pair x = pq.top();
            pq.pop();
            if(x.second == 1) {
                pq.push({x.first*2, 1});
                pq.push({x.first*3, 2});
                pq.push({x.first*5, 3});
            } else if (x.second == 2) {
                pq.push({x.first*3, 2});
                pq.push({x.first*5, 3});
            } else {
                pq.push({x.first*5, 3});
            }
            n-=1;
        }

        return pq.top().first;
    }
};
14446