<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:
    long nthUglyNumber(int n) {
        vector<long> vecs(1, 1);
        vector<int> primes = {2, 3, 5};
        vector<int> indices = {0, 0, 0};
        for (int i = 0; i < n; ++i) {
            vector<long> ugly_cands = {
                vecs[indices[0]] * primes[0], 
                vecs[indices[1]] * primes[1], 
                vecs[indices[2]] * primes[2]};
            auto minval = *min_element(ugly_cands.begin(), ugly_cands.end());
            vecs.push_back(minval);
            for (int j = 0; j < 3; ++j) {
                if (minval == ugly_cands[j]) {
                    ++indices[j];
                }
            }
        }
        return vecs[n - 1];
    }
};
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