
"""simple docstring"""





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







def       __a	(						__lowerCamelCase    ):
   if not isinstance(__lowerCamelCase,						__lowerCamelCase    ):
      raise ValueError("Input series is not valid, valid series - [2, 4, 6]"    )
   if len(__lowerCamelCase    ) == 0:
      raise ValueError("Input list must be a non empty list"    )
   UpperCAmelCase_   :   Dict     	=       0
   for val in series:
      answer += 1 / val
   return len(__lowerCamelCase    ) / answer


if __name__ == "__main__":
    import doctest

    doctest.testmod()






'''simple docstring'''







import itertools







def _UpperCamelCase			(	__A = 1000000       )				->						int:


      '''simple docstring'''



      UpperCamelCase__      =							[1]

      for i in itertools.count(len(__A       )       ):
            UpperCamelCase__      =							0
            for j in itertools.count(1       ):
                  UpperCamelCase__      =							-1 if j % 2 == 0 else +1
                  UpperCamelCase__      =							(j * j * 3 - j) // 2
                  if index > i:
                        break
                  item += partitions[i - index] * sign
                  item %= number
                  index += j
                  if index > i:
                        break
                  item += partitions[i - index] * sign
                  item %= number

            if item == 0:
                  return i
            partitions.append(__A       )

      return 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  print(F"""{solution() = }""")





