<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<pair<int, int>> index_of_multipliers = {{0, 2}, {0, 3}, {0, 5}};
        vector<long long> candidates = {2, 3, 5};
        vector<int> ugly_numbers = {1};
        ugly_numbers.reserve(n);

        for (int i = 1; i < n; ++i) {
            long long next_ugly_number = *ranges::min_element(candidates);
            ugly_numbers.push_back(next_ugly_number);

            for (int j = 0; j < 3; ++j) {
                if (candidates[j] == next_ugly_number) {
                    auto& [index, multiplier] = index_of_multipliers[j];
                    candidates[j] = ugly_numbers[++index] * multiplier;
                }
            }
        }

        return ugly_numbers.back();
    }
};
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