
"""simple docstring"""






def __A						(   a_ :							int = 50     )->							Tuple:




		'''simple docstring'''






		SCREAMING_SNAKE_CASE       :     Union[str, 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() = }''')







"""simple docstring"""






from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray





def __A						(   a_ :							float		,		a_ :							float		,		a_ :							bool = False     )->							list[float]:




		'''simple docstring'''






		if radian_mode:
				return [magnitude * cos(a_     ), magnitude * sin(a_     )]
		return [magnitude * cos(radians(a_     )     ), magnitude * sin(radians(a_     )     )]





def __A						(   a_ :							NDArray[floataa]		,		a_ :							NDArray[floataa]		,		a_ :							float = 10**-1     )->							bool:




		'''simple docstring'''






		SCREAMING_SNAKE_CASE       :     NDArray[floataa]				= cross(a_		,		a_     )
		SCREAMING_SNAKE_CASE       :     float				= sum(a_     )
		return abs(a_     ) < eps


if __name__ == "__main__":
					# Test to check if it works
					lowerCamelCase__ :       Optional[Any]						     =			array(
					    [
					        polar_force(7_1_8.4, 180 - 30),
					        polar_force(8_7_9.5_4, 45),
					        polar_force(100, -90),
					    ]
					)

					lowerCamelCase__ :       NDArray[floataa]						     =			array([[0, 0], [0, 0], [0, 0]])

					assert in_static_equilibrium(forces, location)

					# Problem 1 in image_data/2D_problems.jpg
					lowerCamelCase__ :       Union[str, Any]						     =			array(
					    [
					        polar_force(30 * 9.8_1, 15),
					        polar_force(215, 180 - 45),
					        polar_force(264, 90 - 30),
					    ]
					)

					lowerCamelCase__ :       Any						     =			array([[0, 0], [0, 0], [0, 0]])

					assert in_static_equilibrium(forces, location)

					# Problem in image_data/2D_problems_1.jpg
					lowerCamelCase__ :       Union[str, Any]						     =			array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])

					lowerCamelCase__ :       Optional[int]						     =			array([[0, 0], [6, 0], [10, 0], [12, 0]])

					assert in_static_equilibrium(forces, location)

					import doctest

					doctest.testmod()





