<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>primes = {2,3,5};
        priority_queue<vector<int>,vector<vector<int>>,greater<vector<int>>>pq;
        pq.push({1,0});
        while(n>1)
        {
            n--;
            int uglynum = pq.top()[0];
            int i = pq.top()[1];
            pq.pop();

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