



from math import factorial, radians






def  lowerCamelCase_	(      lowerCAmelCase__	:	float			,	lowerCAmelCase__	:	int = 18			,	lowerCAmelCase__	:	int = 10				)       ->							float:

							'''simple docstring'''






							A      						=    angle_in_degrees - ((angle_in_degrees // 360.0) * 360.0)

							# Converting from degrees to radians
							A      						=    radians(lowerCAmelCase__				)

							A      						=    angle_in_radians
							A      						=    3
							A      						=    -1

							for _ in range(lowerCAmelCase__				):
														result += (b * (angle_in_radians**a)) / factorial(lowerCAmelCase__				)

														A      						=    -b  # One positive term and the next will be negative and so on...
														a += 2  # Increased by 2 for every term.

							return round(lowerCAmelCase__			,	lowerCAmelCase__				)


if __name__ == "__main__":
				__import__('doctest').testmod()
"""simple docstring"""






import math


def      UpperCAmelCase__			(							lowerCAmelCase__	:int						)					->       bool:
      '''simple docstring'''


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

      return exponent == int(lowerCAmelCase__						)


def      UpperCAmelCase__			(							lowerCAmelCase__	:float = 1 / 1_2_3_4_5						)					->       int:
      '''simple docstring'''


      lowercase								=      0
      lowercase								=      0

      lowercase								=      3
      while True:
            lowercase								=      (integer**2 - 1) / 4
            # if candidate is an integer, then there is a partition for k
            if partition_candidate == int(lowerCAmelCase__						):
                  lowercase								=      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() = }""")



