<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<int> store;
    store.push_back(1);

    unordered_map<int, int> mp;
    mp[2] = 1;
    mp[3] = 1;
    mp[5] = 1;

    while (store.size() != n) {
        int mini = INT_MAX;

        
        for (const auto &i : mp) {
            mini = min(mini, i.first * store[i.second - 1]);
        }

        // Increment the pointers for the factors that produced the minimum
        for (auto &i : mp) {
            if (mini == i.first * store[i.second - 1]) {
                i.second++;
            }
        }

        store.push_back(mini);
    }

    return store[n - 1];
}
};
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