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. Example 1: Input: n = 2 Output: 1 Explanation: perm = [0,1] initially. After the 1st operation, perm = [0,1] So it takes only 1 operation. Example 2: Input: n = 4 Output: 2 Explanation: perm = [0,1,2,3] initially. After the 1st operation, perm = [0,2,1,3] After the 2nd operation, perm = [0,1,2,3] So it takes only 2 operations. Example 3: Input: n = 6 Output: 4 Constraints: 2 <= n <= 1000 n​​​​​​ is even.