class Solution:
  def countRotations(self, arr):
    length = len(arr) - 1
    b, e = 0, length
    m = (b + e) // 2 
    
    # edge case: if the array is fully reversed like [5, 4, 3, 2, 1]
    if arr[b] > arr[m] > arr[e]:
      return length     

    while b <= e:
      m = (b + e) // 2    

      # check and discard the first half 
      if arr[b] <= arr[m]:
        # before [b = m + 1] check if we have found the index 
        if m < length and arr[m] > arr[m + 1]:
          return m + 1
        # nothing found just discard 
        b = m + 1
      
      # check and discard the the second half  
      elif arr[m] <= arr[e]:
        # before [e = m - 1] check if we have found the index 
        if m - 1 >= 0 and arr[m - 1] > arr[m]:
          return m
        # nothing found just discard 
        e = m - 1

    return 0 # no rotaion at all