


'''simple docstring'''


import math




def      lowerCamelCase					(      lowerCamelCase  :      int):
      A_						:  str          =				math.loga(math.sqrt(4 * positive_integer + 1) / 2 + 1 / 2)

      return exponent == int(lowerCamelCase)




def      lowerCamelCase					(      lowerCamelCase  :      float = 1 / 1_2345):
      A_						:  int          =				0
      A_						:  Dict          =				0

      A_						:  Tuple          =				3
      while True:
            A_						:  Any          =				(integer**2 - 1) / 4
            # if candidate is an integer, then there is a partition for k
            if partition_candidate == int(lowerCamelCase):
                  A_						:  Union[str, Any]          =				int(lowerCamelCase)
                  total_partitions += 1
                  if check_partition_perfect(lowerCamelCase):
                        perfect_partitions += 1
            if perfect_partitions > 0:
                  if perfect_partitions / total_partitions < max_proportion:
                        return int(lowerCamelCase)
            integer += 1


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




'''simple docstring'''


import baseaa




def      lowerCamelCase					(      lowerCamelCase  :      str):
      return baseaa.aaaencode(string.encode("""utf-8"""))




def      lowerCamelCase					(      lowerCamelCase  :      bytes):
      return baseaa.aaadecode(lowerCamelCase).decode("""utf-8""")


if __name__ == "__main__":
     import doctest

     doctest.testmod()
