<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 a = 2, b = 3, c = 5;
        int l1 = 1, l2 = 1, l3 = 1;
        int tr = 1;
        set<int> si;
        si.insert(tr);
        while (n-- > 1) {
            tr = min(min(l1 * a, l2 * b), l3 * c);
            si.insert(tr);
            cout << l1 << "\t" << l2 << "\t" << l3 << "\t" << tr << "\n";
            if (tr == l1 * a)
                l1 = *si.upper_bound(l1);
            if (tr == l2 * b)
                l2 = *si.upper_bound(l2);
            if (tr == l3 * c)
                l3 = *si.upper_bound(l3);
            // cout << l1 << "\t" << l2 << "\t" << l3 << "\t" << tr << "\n\n\n";
        }
        return tr;
    }
};
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