





'''simple docstring'''


import math


def 	__a(SCREAMING_SNAKE_CASE_  :					int    ):



    '''simple docstring'''





    _lowerCAmelCase				=      math.loga(math.sqrt(4 * positive_integer + 1    ) / 2 + 1 / 2    )

    return exponent == int(SCREAMING_SNAKE_CASE_    )


def 	__a(SCREAMING_SNAKE_CASE_  :					float = 1 / 12345    ):



    '''simple docstring'''





    _lowerCAmelCase				=      0
    _lowerCAmelCase				=      0

    _lowerCAmelCase				=      3
    while True:
        _lowerCAmelCase				=      (integer**2 - 1) / 4
        # if candidate is an integer, then there is a partition for k
        if partition_candidate == int(SCREAMING_SNAKE_CASE_    ):
            _lowerCAmelCase				=      int(SCREAMING_SNAKE_CASE_    )
            total_partitions += 1
            if check_partition_perfect(SCREAMING_SNAKE_CASE_    ):
                perfect_partitions += 1
        if perfect_partitions > 0:
            if perfect_partitions / total_partitions < max_proportion:
                return int(SCREAMING_SNAKE_CASE_    )
        integer += 1


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











'''simple docstring'''


def 	__a(SCREAMING_SNAKE_CASE_  :					int    ):



    '''simple docstring'''





    if not isinstance(SCREAMING_SNAKE_CASE_		,       SCREAMING_SNAKE_CASE_    ):
        raise TypeError("Input value must be an 'int' type"    )

    _lowerCAmelCase				=      0
    while number:
        position += 1
        number >>= 1

    return position


if __name__ == "__main__":
       import doctest

       doctest.testmod()


