<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> vals(1, 1);
        set<int> singleset;
        singleset.insert(1);
        
        int last2 = 0;
        int last3 = 0;
        int last5 = 0;
        
        while(true){
            
            int a = 2 * vals[last2];
            int b = 3 * vals[last3];
            int c = 5 * vals[last5];
            
            if (a <= b && a <= c){
                if (singleset.find(a) == singleset.end()){   
                    singleset.insert(a);
                    vals.push_back(a);
                }
                last2 += 1;
            }
            else if (b <= a && b <= c){
                if (singleset.find(b) == singleset.end()){
                    singleset.insert(b);
                    vals.push_back(b);
                }
                last3 += 1;
            }
            else{
                if (singleset.find(c) == singleset.end()){
                    singleset.insert(c);
                    vals.push_back(c);
                }
                last5 += 1;                
            }
            
            if (vals.size() >= n){
                return vals[n - 1];
            }            
        }        
    }
};
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