


"""simple docstring"""







class 						_A  :







    """simple docstring"""




    def __init__(					self				:    int				, __UpperCAmelCase				:    int):
      a						:		Tuple      							=			size
      a						:		Dict      							=			[0] * size
      a						:		Optional[int]      							=			[0] * size






    @staticmethod
    def 	__snake_case							(					__UpperCAmelCase				:    int):
      return index | (index + 1)






    @staticmethod
    def 	__snake_case							(					__UpperCAmelCase				:    int):
      return (index & (index + 1)) - 1






    def 	__snake_case							(					self				:    List[str]				, __UpperCAmelCase				:    int				, __UpperCAmelCase				:    int):
      a						:		Union[str, Any]      							=			value
      while index < self.size:
        a						:		Dict      							=			self.get_prev(__UpperCAmelCase) + 1
        if current_left_border == index:
          a						:		Optional[int]      							=			value
        else:
          a						:		Any      							=			max(__UpperCAmelCase				, __UpperCAmelCase				, __UpperCAmelCase)
        a						:		Optional[int]      							=			self.get_next(__UpperCAmelCase)






    def 	__snake_case							(					self				:    Union[str, Any]				, __UpperCAmelCase				:    int				, __UpperCAmelCase				:    int):
      right -= 1  # Because of right is exclusive
      a						:		List[str]      							=			0
      while left <= right:
        a						:		Dict      							=			self.get_prev(__UpperCAmelCase)
        if left <= current_left:
          a						:		Optional[int]      							=			max(__UpperCAmelCase				, self.tree[right])
          a						:		Optional[Any]      							=			current_left
        else:
          a						:		List[str]      							=			max(__UpperCAmelCase				, self.arr[right])
          right -= 1
      return result


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      lowercase			(				A_  ,   A_  ,   A_ = 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      lowercase			(				A_  ,   A_  ,   A_ = 10**-1       )->      bool:
  '''simple docstring'''







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


if __name__ == "__main__":
 # Test to check if it works
 __lowercase    					=      array(
     [
         polar_force(7_18.4, 180 - 30),
         polar_force(8_79.54, 45),
         polar_force(100, -90),
     ]
 )

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

 assert in_static_equilibrium(forces, location)

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

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

 assert in_static_equilibrium(forces, location)

 # Problem in image_data/2D_problems_1.jpg
 __lowercase    					=      array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])

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

 assert in_static_equilibrium(forces, location)

 import doctest

 doctest.testmod()






