• Reverse the entire permutation.
• Transfer the first element of the permutation to the last position, i.e.. change arr[0], arr[1], ..., arr[n-1] to arr[1], arr[2], ..., arr[n-1], arr[0].

Formally, given a permutation arr of size n, determine the minimum number of operations needed to sort the given permutation in increasing order. The permutation provided is guaranteed to be sorted using only these two operations.

Note: A permutation of length n is a sequence of integers from 1 to n containing each number exactly once.

Method Signature

int getMinimumOperations(int[] arr)

Return the minimum number of operations required to sort arr in increasing order.

Examples

Example 1

Call: getMinimumOperations([2, 3, 4, 5, 6, 7, 8, 9, 10, 1])

Output: 3

Explanation of Optimal Operations:

1. Reverse the permutation to get [1, 10, 9, 8, 7, 6, 5, 4, 3, 2]
2. Transfer the first element to the last position to get [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]
3. Reverse the permutation to get [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

It can be shown that the given permutation can only be sorted using a minimum of 3 operations.

Example 2

Call: getMinimumOperations([1, 2, 3, 4])

Output: 0

Explanation: The permutation is already sorted.

Example 3

Call: getMinimumOperations([2, 1])

Output: 1

Explanation: Reverse the permutation once to get [1, 2].