<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> nums;
        deque<long long> test2;
        deque<long long> test3;
        deque<long long> test5;
        test2.push_back(1);
        while (nums.size()!=n){
            long long num = min({
                (!test2.empty())?test2.front():INT_MAX,
                (!test3.empty())?test3.front():INT_MAX, 
                (!test5.empty())?test5.front():INT_MAX});
            if (test2.front() == num) test2.pop_front();
            if (test3.front() == num) test3.pop_front();
            if (test5.front() == num) test5.pop_front();
            test2.push_back(num*2);
            test3.push_back(num*3);
            test5.push_back(num*5);
            nums.push_back(num);
        }
        return (int)nums[n-1];
        
    }
};
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