<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) {
        
        if(n <= 0)
        {
            return 0;
        }
        else if(n == 1)
        {
            return 1;
        }

        int l1 = 0, l2 = 0, l3 = 0;
        int dp[2000] = {0};
        dp[0] = 1;

        for(int i = 1; i < n; i++)
        {
            dp[i] = min(dp[l1]*2, min(dp[l2]*3, dp[l3]*5));

            if(dp[i] == dp[l1]*2)
            {
                l1++;
            }
            
            if(dp[i] == dp[l2]*3)
            {
                l2++;
            }
            
            if(dp[i] == dp[l3]*5)
            {
                l3++;
            }
        }

        return dp[n - 1];
    }
};
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