<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>

typedef long long int ll;

class Solution {
public:
    int nthUglyNumber(int n) {
        const ll two = 2, three = 3, five = 5;
        
        vector<ll> A = {1,2,3,4,5};
        //              0 1 2 3 4
        // first case [1,5]
        if( n <= 5 ) return A[n-1];

        int x = 2, y = 2, z = 4;
        n -= 5;
        while( n > 0 ){
            n --;
            
            ll a = two * A[x];
            ll b = three * A[y];
            ll c = five * A[z];

            A.push_back( min(a, min(b,c) ) );

            if( A.back() == a ) x++;
            if( A.back() == b ) y ++;
            if( A.back() == c ) z ++;
        }

        return A.back();

    }
};
15159