<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:
    vector<long> ugly;
    Solution(){
        ugly.resize(1691);
        long id2=0, id3=0, id5=0;
        
        ugly[0] = 1;
        for(int i=1; i<1691; i++){
            long t2 = ugly[id2]*2, t3 = ugly[id3]*3, t5 = ugly[id5]*5;
            
            if (t2 < t3){
                if (t2 <= t5) {
                    ugly[i] = t2;
                }
                else {
                    ugly[i] = t5;
                }
            }else{
                if (t3 <= t5){
                    ugly[i] = t3;
                }
                else {
                    ugly[i] = t5;
                }
            }
            
            if (ugly[i] == t2) ++id2;
            if (ugly[i] == t3) ++id3;
            if (ugly[i] == t5) ++id5;
            
        }
    }
    
    int nthUglyNumber(int n) {
        for(int i=0; i<10; i++) cout << ugly[i] << " ";
        return ugly[n-1];
    }
};
17296