



def 	__UpperCamelCase	(  _lowerCAmelCase		)       ->  str:



    """simple docstring"""






    A :       Dict          =   int(_lowerCAmelCase		)
    if decimal in (0, 1):  # Exit cases for the recursion
        return str(_lowerCAmelCase		)
    A     ,							A :       Dict          =   divmod(_lowerCAmelCase      ,     2		)
    return binary_recursive(_lowerCAmelCase		) + str(_lowerCAmelCase		)




def 	__UpperCamelCase	(  _lowerCAmelCase		)       ->  str:



    """simple docstring"""






    A :       Optional[Any]          =   str(_lowerCAmelCase		).strip()
    if not number:
        raise ValueError("""No input value was provided"""		)
    A :       Optional[int]          =   """-""" if number.startswith("""-"""		) else """"""
    A :       int          =   number.lstrip("""-"""		)
    if not number.isnumeric():
        raise ValueError("""Input value is not an integer"""		)
    return f'''{negative}0b{binary_recursive(int(_lowerCAmelCase		)		)}'''


if __name__ == "__main__":
     from doctest import testmod

     testmod()







def 	__UpperCamelCase	(  _lowerCAmelCase = 100_0000		)       ->  int:



    """simple docstring"""






    A :       str          =   limit + 1
    A :       Tuple          =   [0] * limit
    for first_term in range(1      ,     _lowerCAmelCase		):
        for n in range(_lowerCAmelCase      ,     _lowerCAmelCase      ,     _lowerCAmelCase		):
            A :       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

    A :       Optional[int]          =   sum(1 for x in frequency[1:limit] if x == 10		)

    return count


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


