<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> ans;
    ans={1,2,3,4,5};
    if(n<=5) return (int)ans[n-1];
    queue<long>a1;
    queue<long>a3;
    queue<long>a5;
    a1.push(4);a1.push(6);a1.push(8);a1.push(10);
    a3.push(6);a3.push(9);a3.push(12);a3.push(15);
    a5.push(10);a5.push(15);a5.push(20);a5.push(25);
    while(ans.size()<n){
        while(a1.front()<=ans.back()){
            a1.pop();
        }
        while(a3.front()<=ans.back()){
            a3.pop();
        }
        while(a5.front()<=ans.back()){
            a5.pop();
        }
        int m=min((int)a1.front(),(int)a3.front());
        m=min(m,(int)a5.front());
        ans.push_back(m);
        a1.push(ans.back()*2);
        a3.push(ans.back()*3);
        a5.push(ans.back()*5);
    }
    return (int)ans.back();
    }
};
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