<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> arr2;
        vector<long long> arr3;
        vector<long long> arr5;
        vector<long long> result;
        if(n==1){
            return 1; 
        }
        else{
            result.push_back(1);
            arr2.push_back(2);
            arr3.push_back(3);
            arr5.push_back(5);

            int i=0;
            int j=0;
            int k=0;
            
            while (result.size() < n) {
                int mini = min({arr2[i], arr3[j], arr5[k]});
                result.push_back(mini);

                if (mini == arr2[i]) i++;
                if (mini == arr3[j]) j++;
                if (mini == arr5[k]) k++;

                arr2.push_back(result.back() * 2);
                arr3.push_back(result.back() * 3);
                arr5.push_back(result.back() * 5);
            }
            return result.back();
        }
    }
};
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