<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) {
        queue<long> a, b, c;
        a.push(1);
        b.push(1);
        c.push(1);
        int ans = 1;
        for(int i =1;i<n;i++){
            ans = min(min(a.front()*2, b.front()*3),c.front()*5);
            a.push(ans);
            b.push(ans);
            c.push(ans);
            if(a.front()*2 == ans)
                a.pop();
            if(b.front()*3 == ans)
                b.pop();
            if(c.front()*5 == ans)
                c.pop();
        }
        return ans;
    }
};

18009