
import math







def        A__					(						lowerCamelCase     ,    lowerCamelCase						)  ->	float:
				return math.pow(lowerCamelCase     ,    2						) - a







def        A__					(						lowerCamelCase						)  ->	float:
				return 2 * x







def        A__					(						lowerCamelCase						)  ->	float:
				UpperCamelCase_:							str	=						2.0

				while start <= a:
								UpperCamelCase_:							Union[str, Any]	=						math.pow(lowerCamelCase     ,    2						)

				return start







def        A__					(						lowerCamelCase     ,    lowerCamelCase = 99_99     ,    lowerCamelCase = 0.00000000000001						)  ->	float:

				if a < 0:
								raise ValueError("""math domain error"""						)

				UpperCamelCase_:							Optional[int]	=						get_initial_point(lowerCamelCase						)

				for _ in range(lowerCamelCase						):
								UpperCamelCase_:							Any	=						value
								UpperCamelCase_:							List[Any]	=						value - fx(lowerCamelCase     ,    lowerCamelCase						) / fx_derivative(lowerCamelCase						)
								if abs(prev_value - value						) < tolerance:
												return value

				return value


if __name__ == "__main__":
							from doctest import testmod

							testmod()








def        A__					(						lowerCamelCase = 50						)  ->	int:
				UpperCamelCase_:							List[Any]	=						[[0] * 3 for _ in range(length + 1						)]

				for row_length in range(length + 1						):
								for tile_length in range(2     ,    5						):
												for tile_start in range(row_length - tile_length + 1						):
																different_colour_ways_number[row_length][tile_length - 2] += (
																    different_colour_ways_number[row_length - tile_start - tile_length][
																        tile_length - 2
																    ]
																    + 1
																)

				return sum(different_colour_ways_number[length]						)


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






