

def  _snake_case		(snake_case_					:     list  )							->		bool:
  if not isinstance(snake_case_    ,       snake_case_  ):
    raise ValueError('Input series is not valid, valid series - [1, 2/3, 2]'  )
  if len(snake_case_  ) == 0:
    raise ValueError('Input list must be a non empty list'  )
  if len(snake_case_  ) == 1 and series[0] != 0:
    return True
  __UpperCAmelCase	:  Optional[Any]		=     []
  __UpperCAmelCase	:  Optional[int]		=     len(snake_case_  )
  for i in range(0    ,       snake_case_  ):
    if series[i] == 0:
      raise ValueError('Input series cannot have 0 as an element'  )
    rec_series.append(1 / series[i]  )
  __UpperCAmelCase	:  List[str]		=     rec_series[1] - rec_series[0]
  for index in range(2    ,       snake_case_  ):
    if rec_series[index] - rec_series[index - 1] != common_diff:
      return False
  return True





def  _snake_case		(snake_case_					:     list  )							->		float:
  if not isinstance(snake_case_    ,       snake_case_  ):
    raise ValueError('Input series is not valid, valid series - [2, 4, 6]'  )
  if len(snake_case_  ) == 0:
    raise ValueError('Input list must be a non empty list'  )
  __UpperCAmelCase	:  Optional[int]		=     0
  for val in series:
    answer += 1 / val
  return len(snake_case_  ) / answer


if __name__ == "__main__":
      import doctest

      doctest.testmod()













"""simple docstring"""


from __future__ import annotations




def      snake_case    (A_ :list[int | float]      ,     A_ :int      ,     A_ :int ):







  '''simple docstring'''

  if len(A_ ) == 0:
    raise ValueError('find_min() arg is an empty sequence' )
  if (
      left >= len(A_ )
      or left < -len(A_ )
      or right >= len(A_ )
      or right < -len(A_ )
  ):
    raise IndexError('list index out of range' )
  if left == right:
    return nums[left]
  a	:     Optional[Any]							=  (left + right) >> 1  # the middle
  a	:     List[str]							=  find_min(A_      ,     A_      ,     A_ )  # find min in range[left, mid]
  a	:     Union[str, Any]							=  find_min(A_      ,     mid + 1      ,     A_ )  # find min in range[mid + 1, right]

  return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
   import doctest

   doctest.testmod(verbose=True)




