<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> arr(n + 1);
        
        arr[0] = 1;
        
        int t2 = 0, t3 = 0, t5 = 0;
        
        for (int i = 1; i <= n; i++) {
            arr[i] = min(arr[t2] * 2, min(arr[t5] * 5, arr[t3] * 3));
            if (arr[i] == arr[t2] * 2) t2++;
            if (arr[i] == arr[t3] * 3) t3++;
            if (arr[i] == arr[t5] * 5) t5++;;
        }
        
        return (int)arr[n - 1];
    }
};
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