



from __future__ import annotations
def 						UpperCamelCase      (  snake_case__			:       list[int]      )      ->	list[int]:  # This function is recursive
   UpperCamelCase       :    List[Any]		      =      len(snake_case__      )
   # If the array contains only one element, we return it (it's the stop condition of
   # recursion)
   if array_length <= 1:
      return array
      # Else
   UpperCamelCase       :    Tuple		      =      array[0]
   UpperCamelCase       :    str		      =      False
   UpperCamelCase       :    Tuple		      =      1
   UpperCamelCase       :    list[int]		      =      []
   while not is_found and i < array_length:
      if array[i] < pivot:
         UpperCamelCase       :    Optional[int]		      =      True
         UpperCamelCase       :    Tuple		      =      [element for element in array[i:] if element >= array[i]]
         UpperCamelCase       :    str		      =      longest_subsequence(snake_case__      )
         if len(snake_case__      ) > len(snake_case__      ):
            UpperCamelCase       :    Union[str, Any]		      =      temp_array
      else:
         i += 1

   UpperCamelCase       :    Any		      =      [element for element in array[1:] if element >= pivot]
   UpperCamelCase       :    Dict		      =      [pivot, *longest_subsequence(snake_case__      )]
   if len(snake_case__      ) > len(snake_case__      ):
      return temp_array
   else:
      return longest_subseq


if __name__ == "__main__":
    import doctest

    doctest.testmod()




"""simple docstring"""


from __future__ import annotations

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






def      __UpperCAmelCase       (      lowercase ,lowercase ,lowercase = False		):







  """simple docstring"""
  if radian_mode:
    return [magnitude * cos(lowercase		), magnitude * sin(lowercase		)]
  return [magnitude * cos(radians(lowercase		)		), magnitude * sin(radians(lowercase		)		)]






def      __UpperCAmelCase       (      lowercase ,lowercase ,lowercase = 10**-1		):







  """simple docstring"""
  _UpperCAmelCase    			=   cross(lowercase ,lowercase		)
  _UpperCAmelCase    			=   sum(lowercase		)
  return abs(lowercase		) < eps


if __name__ == "__main__":
    # Test to check if it works
    UpperCAmelCase__			=    array(
        [
            polar_force(718.4, 1_8_0 - 3_0),
            polar_force(879.54, 4_5),
            polar_force(1_0_0, -9_0),
        ]
    )

    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(3_0 * 9.81, 1_5),
            polar_force(2_1_5, 1_8_0 - 4_5),
            polar_force(2_6_4, 9_0 - 3_0),
        ]
    )

    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, -2_0_0_0], [0, -1_2_0_0], [0, 1_5_6_0_0], [0, -1_2_4_0_0]])

    UpperCAmelCase__			=    array([[0, 0], [6, 0], [1_0, 0], [1_2, 0]])

    assert in_static_equilibrium(forces, location)

    import doctest

    doctest.testmod()
