Problem

You are given an integer N representing the size of the array A and an integer array A. The goal is to find the count of distinct values of K from 1 to N that allow you to transform the given array into sorted order using swap operations with the following constraints:

• The swap operation involves swapping elements at indices i and i + K.
• The swap operation can only be performed if the absolute difference between the indices is K.

Input

• input1: An integer value N, representing the size of the array A.
• input2: An integer array A.

Output

Return an integer value, representing the count of distinct values of K from 1 to N that allow you to transform the given array into sorted order using the above operations.

Constraints

• 1 <= N <= 1000
• The elements of the array A are distinct integers between 1 and N.

Test Cases

• Example 1:
  • input1: 6
  • input2: [2,3,5,4,1,6]
  • output: 2
• Example 2:
  • input1: 4
  • input2: [1,2,3,4]
  • output: 4