<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>

//#define int double
class Solution {
public:
    int nthUglyNumber(int n) {
        long long a,b,c;
        vector<int>v;
        for(int i=0;i<32;i++){
            a=pow(5,i);
            if(a>INT_MAX){
                break;
            }
            for(int j=0;j<32;j++){
                b=pow(3,j);
                if(b>INT_MAX){
                    break;
                }
                if(a*b>INT_MAX){
                    break;
                }
                for(int k=0;k<32;k++){
                    c=pow(2,k);
                    if(c>INT_MAX){
                        break;
                    }
                    if(a*b*c>INT_MAX){
                        break;
                    }
                    v.push_back(a*b*c);
                }
            }
        }
        sort(v.begin(),v.end());
        return v[n-1];
        
        
    
        

        
    }  
};
22996