<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:
    bool isUgly(int n) {
        if(n==0) return false;
        
        while(n%2==0 || n%3==0 || n%5==0 ){
            if(n%2==0) 
            n/=2;
           else if(n%3==0)
           n/=3;
            else if(n%5==0)
            n/=5;

            
        }
        return n==1;
       
    }
    int nthUglyNumber(int n) {
        set<long long>s;
        vector<int>ans;
        s.insert(1);
        long long it=1;
        for(int i=0;i<n;i++){
             it = *s.begin();
            s.insert(it*2);
            s.insert(it*3);
            s.insert(it*5);
            s.erase(it);
        }
        for(auto it=s.begin();it!=s.end();it++){
            if(isUgly(*it)) {
                ans.push_back(*it);
            }
        }
        return it;
    }
};
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