<p>A <strong>valid cut</strong> in a circle can be:</p>

<ul>
	<li>A cut that is represented by a straight line that touches two points on the edge of the circle and passes through its center, or</li>
	<li>A cut that is represented by a straight line that touches one point on the edge of the circle and its center.</li>
</ul>

<p>Some valid and invalid cuts are shown in the figures below.</p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/10/29/alldrawio.png" style="width: 450px; height: 174px;" />
<p>Given the integer <code>n</code>, return <em>the <strong>minimum</strong> number of cuts needed to divide a circle into </em><code>n</code><em> equal slices</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/10/24/11drawio.png" style="width: 200px; height: 200px;" />
<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> 2
<strong>Explanation:</strong> 
The above figure shows how cutting the circle twice through the middle divides it into 4 equal slices.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/10/24/22drawio.png" style="width: 200px; height: 201px;" />
<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 3
<strong>Explanation:</strong>
At least 3 cuts are needed to divide the circle into 3 equal slices. 
It can be shown that less than 3 cuts cannot result in 3 slices of equal size and shape.
Also note that the first cut will not divide the circle into distinct parts.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 100</code></li>
</ul>

class Solution:
    def numberOfCuts(self, n: int) -> int:
        return n//2 if n%2==0 else n*int(n!=1)
        #if n%2==0: return n//2
    
"""
If n is odd, can you have a diameter cut?
I don't think so, because you then have 2 equally sized areas. If you want to cut independently
then you would need to make n//2 and n//2+1 pieces in each, which can't be done.
Whatever number of slices in one area, there can't be the same amount in the other. Yet the
sum of area must be the same.

Therefore, you can have only radius cuts, which means we must have n cuts unless n==1.




"""
        
29