import math

class Solution:
  def sort(self, arr):
    i = j = 0

    # find the first out order position element from [left to right] -->
    for count in range(len(arr)):
      if count - 1 >= 0 and arr[count] < arr[count - 1]:
        i = count - 1
        break

    # find the first out order position element from [right to left] <--
    end = i - 1 if i >= 0 else 0
    for count in range(len(arr) - 1, end, -1):  
      if count + 1 < len(arr) and arr[count] > arr[count + 1]:
        j = count + 1
        break

    # for example i and j are in the positions below
    # [-4, -2, 1, 3, 2, 9, 0, -3, 7, 10, 30]
    #             i            j      
    # find the min and max elements between i and j inclusive
    # min = -3, max = 9  == the range is out of order between [-3, 9] 
    min_element = float('inf')
    max_element = float('-inf')
    for count in range(i, j + 1):
      min_element = min(min_element, arr[count])
      max_element = max(max_element, arr[count])
    
    # find any element before i that is larger than the min_element. if found move i to the left
    for count in range(i - 1, -1, -1):
      if arr[count] > min_element:
        i = count
    
    # find any element after j that is smaller than the max_element. if found move j to the right 
    for count in range(j + 1, len(arr)):
      if arr[count] < max_element:
        j = count

    return 0 if i == j else j - i + 1