<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:
    vector<int> m_ugly;
    Solution()
    {
        m_ugly = getUgly();
    }


    int nthUglyNumber(int n)
    {
        ios_base::sync_with_stdio(false);
        return m_ugly[n - 1];   
    }

    vector<int> getUgly()
    {
        vector<int> ugly;

        for (int i{}; i < 31; ++i)
            ugly.push_back(1 << i);

        const int nums[2] = {3, 5};

        for (int k{}; k < 2; ++k)
        {
            auto tmp = ugly;
            while (!tmp.empty())
            {
                int i{}, size = tmp.size();
                for (; i < size; ++i)
                {
                    // if (tmp[i] * nums[k] <= INT_MAX)
                    if (INT_MAX / nums[k] > tmp[i] )
                        tmp[i] *= nums[k];
                    else
                        break;
                }

                for (; i < size; ++i)
                    tmp.pop_back();

                ugly.insert(ugly.end(), tmp.begin(), tmp.end());
            }
            sort(ugly.begin(), ugly.end());
        }

        return ugly;
    }
};
26559