



'''simple docstring'''





import math




def lowerCAmelCase    (__A):



     """simple docstring"""



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

     return exponent == int(__A)




def lowerCAmelCase    (__A = 1 / 12_345):



     """simple docstring"""



     _a           =    0
     _a           =    0

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


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










def   __snake_case    (       _lowerCAmelCase			:			int = 1					,					_lowerCAmelCase			:			int = 1000						)			->    int:
   A_       :					Optional[int]        =      1
   A_       :					int        =      0

   for divide_by_number in range(_lowerCAmelCase					,					digit + 1						):
      A_       :					list[int]        =      []
      A_       :					Union[str, Any]        =      numerator
      for _ in range(1					,					digit + 1						):
         if now_divide in has_been_divided:
            if longest_list_length < len(_lowerCAmelCase						):
               A_       :					Optional[Any]        =      len(_lowerCAmelCase						)
               A_       :					Union[str, Any]        =      divide_by_number
         else:
            has_been_divided.append(_lowerCAmelCase						)
            A_       :					Dict        =      now_divide * 10 % divide_by_number

   return the_digit


# Tests
if __name__ == "__main__":
 import doctest

 doctest.testmod()
