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Minimum Number of Operations to Reinitialize a Permutation

You are given an even integer n​​​​​​.

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:

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.

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