<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>

vector<long long int> func(){
    priority_queue<long long int, vector<long long int>, greater<long long int>> pq;
    pq.push(1);
    set<long long int> res;
    res.insert(1);
    while(res.size() < 2000){
        long long int top = pq.top();
        pq.pop();
        if(res.insert(top*2).second) pq.push(top*2);
        if(res.insert(top*3).second) pq.push(top*3);
        if(res.insert(top*5).second) pq.push(top*5);
    }
    vector<long long int> arr(res.begin(), res.end());
    return arr;
}

vector<long long int> arr = func();



class Solution {
public:
    int nthUglyNumber(int n) {
        return arr[n-1];      
    }
};
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