
'''simple docstring'''

from __future__ import annotations

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


def 		_UpperCAmelCase (     _lowerCamelCase  :				Tuple     ,					_lowerCamelCase  :				Optional[int]     ,					_lowerCamelCase  :				Optional[int] = False						)			->  list[float]:
  if radian_mode:
    return [magnitude * cos(_lowerCamelCase						), magnitude * sin(_lowerCamelCase						)]
  return [magnitude * cos(radians(_lowerCamelCase						)						), magnitude * sin(radians(_lowerCamelCase						)						)]


def 		_UpperCAmelCase (     _lowerCamelCase  :				int     ,					_lowerCamelCase  :				Dict     ,					_lowerCamelCase  :				Union[str, Any] = 10**-1						)			->  bool:
  _lowerCAmelCase				:     NDArray[floataa]       =    cross(_lowerCamelCase     ,					_lowerCamelCase						)
  _lowerCAmelCase				:     float       =    sum(_lowerCamelCase						)
  return abs(_lowerCamelCase						) < eps


if __name__ == "__main__":
     # Test to check if it works
     UpperCamelCase_   	=				array(
         [
             polar_force(7_1_8.4, 1_80 - 30),
             polar_force(8_7_9.5_4, 45),
             polar_force(1_00, -90),
         ]
     )

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

     assert in_static_equilibrium(forces, location)

     # Problem 1 in image_data/2D_problems.jpg
     UpperCamelCase_   	=				array(
         [
             polar_force(30 * 9.8_1, 15),
             polar_force(2_15, 1_80 - 45),
             polar_force(2_64, 90 - 30),
         ]
     )

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

     assert in_static_equilibrium(forces, location)

     # Problem in image_data/2D_problems_1.jpg
     UpperCamelCase_   	=				array([[0, -20_00], [0, -12_00], [0, 1_56_00], [0, -1_24_00]])

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

     assert in_static_equilibrium(forces, location)

     import doctest

     doctest.testmod()









def  _SCREAMING_SNAKE_CASE				(   a  )      ->      Tuple:
					__A    ,				__A	:						Optional[Any]       =				[], []
					while len(a  ) > 1:
										__A    ,				__A	:						Any       =				min(a  ), max(a  )
										start.append(a  )
										end.append(a  )
										collection.remove(a  )
										collection.remove(a  )
					end.reverse()
					return start + collection + end


if __name__ == "__main__":
				UpperCAmelCase						:   int			  =     input('''Enter numbers separated by a comma:\n''').strip()
				UpperCAmelCase						:   Dict			  =     [int(item) for item in user_input.split(''',''')]
				print(*merge_sort(unsorted), sep=''',''')




