

'''simple docstring'''







import math
def       UpperCAmelCase__    (      UpperCAmelCase__				)			->			bool:
       A_						=      math.loga(math.sqrt(4 * positive_integer + 1				) / 2 + 1 / 2				)

       return exponent == int(UpperCAmelCase__				)
def       UpperCAmelCase__    (      UpperCAmelCase__ = 1 / 1_23_45				)			->			int:
       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(UpperCAmelCase__				):
                     A_						=      int(UpperCAmelCase__				)
                     total_partitions += 1
                     if check_partition_perfect(UpperCAmelCase__				):
                            perfect_partitions += 1
              if perfect_partitions > 0:
                     if perfect_partitions / total_partitions < max_proportion:
                            return int(UpperCAmelCase__				)
              integer += 1


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



'''simple docstring'''







def       UpperCAmelCase__    (      UpperCAmelCase__				)			->			int:
       assert (
           isinstance(UpperCAmelCase__,       UpperCAmelCase__				) and number_of_steps > 0
       ), F'''number_of_steps needs to be positive integer, your input {number_of_steps}'''
       if number_of_steps == 1:
              return 1
       A_					,			A_						=      1, 1
       for _ in range(number_of_steps - 1				):
              A_					,			A_						=      current + previous, current
       return current


if __name__ == "__main__":
      import doctest

      doctest.testmod()
