Please solve the programming task below using a self-contained code snippet in a markdown code block.

You are given an even integer n​​​​​​. You initially have a permutation perm of size n​​ where perm[i] == i​ (0-indexed)​​​​.
In one operation, you will create a new array arr, and for each i:

If i % 2 == 0, then arr[i] = perm[i / 2].
If i % 2 == 1, then arr[i] = perm[n / 2 + (i - 1) / 2].

You will then assign arr​​​​ to perm.
Return the minimum non-zero number of operations you need to perform on perm to return the permutation to its initial value.
 
Please complete the following python code precisely:
```python
class Solution:
    def reinitializePermutation(self, n: int) -> int:
```