1806 - Minimum Number of Operations to Reinitialize a Permutation\.

Medium

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 1^st 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 1^st operation, perm = 0,2,1,3

After the 2^nd 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.