<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 {
    vector<int> primes = {2, 3, 5};
    int size = primes.size();
public:
    int nthUglyNumber(int n) {
        vector<int> ugs(n + 1, 0);    
        vector<int> primes_idx(size, 1);

        ugs[1] = 1;
        for (int i = 2; i <= n; i++) {
            vector<int> temp(size, 0);
            int _min = INT_MAX;
            for (int j = 0; j < size; j++) {
                temp[j] = ugs[primes_idx[j]] * primes[j];
                _min = min(_min, temp[j]);
            }
            for (int j = 0; j < size; j++) {
                if (temp[j] == _min)
                    primes_idx[j]++;
            }
            ugs[i] = _min;
        }
        return ugs[n];
    }
};
19790