<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:
    Solution(){
        ios_base :: sync_with_stdio(false);
    }
    int nthUglyNumber(int n) {
        priority_queue<int>pq;
       for(int i = 0;i<33;i++){
        for(int j = 0;j<33;j++){
            for(int k = 0;k<33;k++){
                long long number = pow(2,i);
                if(number > INT_MAX){
                    break;
                }
                if((double)pow(3,j) > INT_MAX){
                    break;
                }
                number *= pow(3,j);
                if(number > INT_MAX){
                    break;
                }
                if((double)pow(5,k) > INT_MAX){
                    break;
                }
                number*= pow(5,k);
                if(number > INT_MAX){
                    break;
                }
                pq.push(number);
                if(pq.size() > n){
                    pq.pop();
                } 
            }
        }
       } 
       return pq.top();
    }
};
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