<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) {
        
        int count = 1,idx=1;
        vector<long long> ugly(n+1);
        ugly[0] = 1;
        vector<long long> m2,m3,m5;
        m2.push_back(ugly[0]*2);
        m3.push_back(ugly[0]*3);
        m5.push_back(ugly[0]*5);

        while(count < n){
            long long z = min(m2.front(),m3.front());
            ugly[idx] = min(z,m5.front());
            if(m2.front()== ugly[idx]) m2.erase(m2.begin());
            if(m3.front()== ugly[idx]) m3.erase(m3.begin());
            if(m5.front()== ugly[idx]) m5.erase(m5.begin());

            m2.push_back(ugly[idx]*2);
            m3.push_back(ugly[idx]*3);
            m5.push_back(ugly[idx]*5);

            idx++;
            count++;

        }
        
        return ugly[n-1];
        
    }
};
15871