<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> res;
        for(int i=0;i<=32;i++){
            if(i > (log2(INT_MAX)/log2(2))) continue;
            int a = pow(2,i);            
            for(int j=0;j<=20;j++){
                if(j > (log2(INT_MAX)/log2(3))) continue;
                int b = pow(3,j);
                if(a > (INT_MAX/b)) continue;
                for(int k=0;k<=14;k++){
                    if(k > (log2(INT_MAX)/log2(5))) continue;
                    int c = pow(5,k);
                    if(a*b > (INT_MAX/c)) continue;
                    int subres =  a * b * c;                    
                    res.push_back(subres);
                }
            }
        }
        sort(res.begin(),res.end());
        
        return res[n-1];
    }
};
22996