


def        lowerCAmelCase_  (      __lowerCamelCase = 1_0_0_0			):
		__snake_case				,    __snake_case	:    Optional[Any]											=     1, 1
		__snake_case	:    Any											=     []
		for i in range(1							,			n + 1			):
				__snake_case	:    Optional[int]											=     prev_numerator + 2 * prev_denominator
				__snake_case	:    int											=     prev_numerator + prev_denominator
				if len(str(UpperCAmelCase__			)			) > len(str(UpperCAmelCase__			)			):
						result.append(UpperCAmelCase__			)
				__snake_case	:    Union[str, Any]											=     numerator
				__snake_case	:    List[str]											=     denominator

		return len(UpperCAmelCase__			)


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





import math







def        lowerCAmelCase_  (      __lowerCamelCase							,			__lowerCamelCase			):

							if initial_intensity < 0:
														raise ValueError("The value of intensity cannot be negative"			)
														# handling of negative values of initial intensity
							if angle < 0 or angle > 3_6_0:
														raise ValueError("In Malus Law, the angle is in the range 0-360 degrees"			)
														# handling of values out of allowed range
							return initial_intensity * (math.cos(math.radians(__lowerCamelCase			)			) ** 2)


if __name__ == "__main__":
			import doctest

			doctest.testmod(name="malus_law")

