<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> uglyNumbers(1,1);

        std::queue<long> twoList, threeList, fiveList;
        twoList.push(1);
        threeList.push(1);
        fiveList.push(1);

        while ( uglyNumbers.size() < n )
        {
            auto nextNum2 = twoList.front() * 2;
            auto nextNum3 = threeList.front() * 3;
            auto nextNum5 = fiveList.front() * 5;
            if ( nextNum2 < nextNum3 && nextNum2 < nextNum5 )
            {
                uglyNumbers.push_back(nextNum2);  
                twoList.pop();

                twoList.push(nextNum2);
                threeList.push(nextNum2);
                fiveList.push(nextNum2);
            }
            else if ( nextNum3 < nextNum5 )
            {
                uglyNumbers.push_back(nextNum3);
                threeList.pop();

                threeList.push(nextNum3);
                fiveList.push(nextNum3);
            }
            else
            {
                uglyNumbers.push_back(nextNum5);
                fiveList.pop();

                fiveList.push(nextNum5);
            }


        }

        return uglyNumbers[n-1];
    }
};
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