



"""simple docstring"""
def 			lowercase	(_snake_case			)       ->    str:




  '''simple docstring'''







  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"			)
  if len(_snake_case			) == 1:
    return True
  __UpperCamelCase  						=							series[1] - series[0]
  for index in range(len(_snake_case			) - 1			):
    if series[index + 1] - series[index] != common_diff:
      return False
  return True



def 			lowercase	(_snake_case			)       ->    str:




  '''simple docstring'''







  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  						=							0
  for val in series:
    answer += val
  return answer / len(_snake_case			)


if __name__ == "__main__":
 import doctest

 doctest.testmod()




'''simple docstring'''





def 							lowerCamelCase	(					_snake_case	:    int = 50_000_000							):





    '''simple docstring'''


    lowercase__									=    set()
    lowercase__									=    int((limit - 24) ** (1 / 2)							)

    lowercase__									=    set(range(3  ,prime_square_limit + 1  ,2							)							)
    primes.add(2							)
    for p in range(3  ,prime_square_limit + 1  ,2							):
        if p not in primes:
            continue
        primes.difference_update(set(range(p * p  ,prime_square_limit + 1  ,_snake_case							)							)							)

    for primea in primes:
        lowercase__									=    primea * primea
        for primea in primes:
            lowercase__									=    primea * primea * primea
            if square + cube >= limit - 16:
                break
            for primea in primes:
                lowercase__									=    primea * primea * primea * primea
                lowercase__									=    square + cube + tetr
                if total >= limit:
                    break
                ret.add(_snake_case							)

    return len(_snake_case							)


if __name__ == "__main__":
 print(f'''{solution() = }''')




