<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) 
    {
        int a = 1, b = 1, c = 1;

        vector<int> arr(n + 1);
        arr[1] = 1;

        for(int i = 2;i <= n;i++)
        {
            int x = arr[a] * 2; 
            int y = arr[b] * 3; 
            int z = arr[c] * 5;

            arr[i] = min(x, min(y, z));

            if(x == arr[i])
            a++; 
            if(y == arr[i])
            b++; 
            if(z == arr[i])
            c++; 
        }

        return arr[n];
    }
};
9815