<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<long long> uglies(n);
    uglies[0] = 1;
    
    int i2 = 0, i3 = 0, i5 = 0;
    long long multi2 = 2;
    long long multi3 = 3;
    long long multi5 = 5;
    long long uglies1;
    
    for (int i = 1; i < n; ++i) {
        uglies1 = std::min({multi2,multi3,multi5});
        uglies[i] = uglies1;
        
        if (uglies1 == multi2) {
            ++i2;
            multi2 = uglies[i2] * 2;
        }
        if (uglies1 == multi3) {
            ++i3;
            multi3 = uglies[i3] * 3;
        }
        if (uglies1 == multi5) {
            ++i5;
            multi5 = uglies[i5] * 5;
        }
    }
    
    return uglies[n-1];
    }
};
10884