





'''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 ValueError("check_bouncy() accepts only integer arguments"    )
    _lowerCAmelCase				=      str(SCREAMING_SNAKE_CASE_    )
    _lowerCAmelCase				=      "".join(sorted(SCREAMING_SNAKE_CASE_    )    )
    return sorted_str_n != str_n and sorted_str_n[::-1] != str_n


def 	__a(SCREAMING_SNAKE_CASE_  :					float = 99    ):



    '''simple docstring'''





    if not 0 < percent < 100:
        raise ValueError("solution() only accepts values from 0 to 100"    )
    _lowerCAmelCase				=      0
    _lowerCAmelCase				=      1

    while True:
        if check_bouncy(SCREAMING_SNAKE_CASE_    ):
            bouncy_num += 1
        if (bouncy_num / num) * 100 >= percent:
            return num
        num += 1


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

       testmod()
       print(f'''{solution(99)}''')


