"""simple docstring"""
from __future__ import annotations

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





def 				lowerCAmelCase__      (     _UpperCamelCase    :			float	,     _UpperCamelCase    :			float	,     _UpperCamelCase    :			bool = False   )   ->			list[float]:





						"""simple docstring"""






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





def 				lowerCAmelCase__      (     _UpperCamelCase    :			NDArray[floataa]	,     _UpperCamelCase    :			NDArray[floataa]	,     _UpperCamelCase    :			float = 1_0**-1   )   ->			bool:





						"""simple docstring"""






						snake_case        =     cross(_UpperCamelCase	,     _UpperCamelCase   )
						snake_case        =     sum(_UpperCamelCase   )
						return abs(_UpperCamelCase   ) < eps


if __name__ == "__main__":
					# Test to check if it works
					SCREAMING_SNAKE_CASE__   =					array(
					    [
					        polar_force(718.4, 180 - 30),
					        polar_force(879.54, 45),
					        polar_force(100, -90),
					    ]
					)

					SCREAMING_SNAKE_CASE__   =					array([[0, 0], [0, 0], [0, 0]])

					assert in_static_equilibrium(forces, location)

					# Problem 1 in image_data/2D_problems.jpg
					SCREAMING_SNAKE_CASE__   =					array(
					    [
					        polar_force(30 * 9.81, 15),
					        polar_force(215, 180 - 45),
					        polar_force(264, 90 - 30),
					    ]
					)

					SCREAMING_SNAKE_CASE__   =					array([[0, 0], [0, 0], [0, 0]])

					assert in_static_equilibrium(forces, location)

					# Problem in image_data/2D_problems_1.jpg
					SCREAMING_SNAKE_CASE__   =					array([[0, -2_000], [0, -1_200], [0, 15_600], [0, -12_400]])

					SCREAMING_SNAKE_CASE__   =					array([[0, 0], [6, 0], [10, 0], [12, 0]])

					assert in_static_equilibrium(forces, location)

					import doctest

					doctest.testmod()



"""simple docstring"""
SCREAMING_SNAKE_CASE__   =					{str(digit): digit**5 for digit in range(10)}





def 				lowerCAmelCase__      (     _UpperCamelCase    :			int   )   ->			int:





						"""simple docstring"""






						return sum(DIGITS_FIFTH_POWER[digit] for digit in str(_UpperCamelCase   )   )





def 				lowerCAmelCase__      (     )   ->			int:





						"""simple docstring"""






						return sum(
						    number
						    for number in range(1_0_0_0	,     1_0_0_0_0_0_0   )
						    if number == digits_fifth_powers_sum(_UpperCamelCase   )   )


if __name__ == "__main__":
					print(solution())


