<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<int>ugly{0};
        priority_queue<int, vector<int>, greater<int>>pq;

        for(int i = 1; i <= n; i++){
            if(i < 6){
                ugly.emplace_back(i);
                pq.push(i * 2);
                pq.push(i * 3);
                pq.push(i * 5);
                continue;
            }

            long long ele = pq.top();
            pq.pop();

            if(ele <= ugly.back()){
                i--;
                continue;
            }
            else{
                ugly.emplace_back(ele);
                if(ele * 2 <= INT_MAX) pq.push(ele * 2);
                if(ele * 3 <= INT_MAX) pq.push(ele * 3);
                if(ele * 5 <= INT_MAX) pq.push(ele * 5);
            }
            
        }

        return ugly[n];
    }
};
15515