<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:
    Solution()
    {
        std::priority_queue<std::pair<std::uint64_t,std::uint8_t>,std::vector<std::pair<std::uint64_t,std::uint8_t>>,std::greater<>> heap;
        heap.emplace(1,2);
        int back=-1;
        
        for(int found_numbers=0;found_numbers<1690;++found_numbers)
        {
            std::uint64_t product=heap.top().first;
            std::uint8_t prev_prime=heap.top().second;
            heap.pop();
            ugly_numbers[++back]=product;

            if(2==prev_prime)
            {
                heap.emplace(2*product,2);
                heap.emplace(3*product,3);
                heap.emplace(5*product,5);
            }
            
            else if(3==prev_prime)
            {
                heap.emplace(3*product,3);
                heap.emplace(5*product,5);
            }

            else
            {
                heap.emplace(5*product,5);
            }
        }
    }

    int nthUglyNumber(int n)
    {
        return ugly_numbers[n-1];
    }

private:
    static int ugly_numbers[1690];
};

int Solution::ugly_numbers[1690]={};
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