# 1806. Minimum Number of Operations to Reinitialize a Permutation

https://leetcode.com/problems/minimum-number-of-operations-to-reinitialize-a-permutation

## Description

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.

## ac

```java
```
