




'''simple docstring'''

def 		__magic_name__    (	__UpperCAmelCase	)		->					bool:

					'''simple docstring'''

					if not isinstance(__UpperCAmelCase,      __UpperCAmelCase	):
										raise ValueError('''Input series is not valid, valid series - [2, 4, 6]'''	)
					if len(__UpperCAmelCase	) == 0:
										raise ValueError('''Input list must be a non empty list'''	)
					if len(__UpperCAmelCase	) == 1:
										return True
					snake_case_									=				series[1] - series[0]
					for index in range(len(__UpperCAmelCase	) - 1	):
										if series[index + 1] - series[index] != common_diff:
															return False
					return True


def 		__magic_name__    (	__UpperCAmelCase	)		->					float:

					'''simple docstring'''

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


if __name__ == "__main__":
							import doctest

							doctest.testmod()








def        SCREAMING_SNAKE_CASE      (       _UpperCAmelCase = 100_0000 )			->     int:
    lowerCamelCase__    :      int					 =		limit + 1
    lowerCamelCase__    :      Optional[Any]					 =		[0] * limit
    for first_term in range(1						,	_UpperCAmelCase ):
        for n in range(_UpperCAmelCase						,	_UpperCAmelCase						,	_UpperCAmelCase ):
            lowerCamelCase__    :      Optional[Any]					 =		first_term + n / first_term
            if common_difference % 4:  # d must be divisble by 4
                continue
            else:
                common_difference /= 4
                if (
                    first_term > common_difference
                    and first_term < 4 * common_difference
                ):  # since x,y,z are positive integers
                    frequency[n] += 1  # so z>0 and a>d ,also 4d<a

    lowerCamelCase__    :      List[str]					 =		sum(1 for x in frequency[1:limit] if x == 10 )

    return count


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





