<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 long int> alpha = {1};
    int start = 0;
    for(int i = 2;i<=n;i++)
    {
        long long int curUgly = INT_MAX;
        for(int j = start; j<alpha.size();j++)
        {
            if(alpha[j]*2>alpha.back()) curUgly = min(curUgly,alpha[j]*2);
            if(alpha[j]*3>alpha.back()) curUgly = min(curUgly,alpha[j]*3);
            if(alpha[j]*5>alpha.back()) curUgly = min(curUgly,alpha[j]*5);
            if(alpha[j]*5<=alpha.back()) start = j+1;
        }
        alpha.push_back(curUgly);
    }
    return alpha.back();
}
};
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