<p>An <strong>ugly number</strong> is a positive integer that is divisible by <code>a</code>, <code>b</code>, or <code>c</code>.</p>

<p>Given four integers <code>n</code>, <code>a</code>, <code>b</code>, and <code>c</code>, return the <code>n<sup>th</sup></code> <strong>ugly number</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 3, a = 2, b = 3, c = 5
<strong>Output:</strong> 4
<strong>Explanation:</strong> The ugly numbers are 2, 3, 4, 5, 6, 8, 9, 10... The 3<sup>rd</sup> is 4.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 4, a = 2, b = 3, c = 4
<strong>Output:</strong> 6
<strong>Explanation:</strong> The ugly numbers are 2, 3, 4, 6, 8, 9, 10, 12... The 4<sup>th</sup> is 6.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 5, a = 2, b = 11, c = 13
<strong>Output:</strong> 10
<strong>Explanation:</strong> The ugly numbers are 2, 4, 6, 8, 10, 11, 12, 13... The 5<sup>th</sup> is 10.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n, a, b, c &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= a * b * c &lt;= 10<sup>18</sup></code></li>
	<li>It is guaranteed that the result will be in range <code>[1, 2 * 10<sup>9</sup>]</code>.</li>
</ul>

class Solution:
    def nthUglyNumber(self, n: int, a: int, b: int, c: int) -> int:
        
        ab = a*b//gcd(a, b)
        bc = b*c//gcd(b, c)
        ca = c*a//gcd(c, a)
        abc = ab*c//gcd(ab, c)
        
        lo, hi = 1, n*min(a, b, c)
        while lo < hi: 
            mid = lo + hi >> 1
            if mid//a + mid//b + mid//c - mid//ab - mid//bc - mid//ca + mid//abc < n: lo = mid + 1
            else: hi = mid 
        return lo 
36