"""simple docstring"""




from math import cos, sin




def 				_snake_case     (       lowerCAmelCase							:       int     ):
		"""simple docstring"""







		SCREAMING_SNAKE_CASE_  :		Any    				=   float(A_     )
		return [[scaling_factor * int(x == y     ) for x in range(2     )] for y in range(2     )]




def 				_snake_case     (       lowerCAmelCase							:       Tuple     ):
		"""simple docstring"""







		SCREAMING_SNAKE_CASE_				,   SCREAMING_SNAKE_CASE_  :		Tuple    				=   cos(A_     ), sin(A_     )
		return [[c, -s], [s, c]]




def 				_snake_case     (       lowerCAmelCase							:       List[Any]     ):
		"""simple docstring"""







		SCREAMING_SNAKE_CASE_				,   SCREAMING_SNAKE_CASE_  :		List[str]    				=   cos(A_     ), sin(A_     )
		SCREAMING_SNAKE_CASE_  :		str    				=   c * s
		return [[c * c, cs], [cs, s * s]]




def 				_snake_case     (       lowerCAmelCase							:       Optional[int]     ):
		"""simple docstring"""







		SCREAMING_SNAKE_CASE_				,   SCREAMING_SNAKE_CASE_  :		Any    				=   cos(A_     ), sin(A_     )
		SCREAMING_SNAKE_CASE_  :		List[Any]    				=   c * s
		return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(f'''    {scaling(5) = }''')
print(f'''  {rotation(45) = }''')
print(f'''{projection(45) = }''')







print(f'''{reflection(45) = }''')

from __future__ import annotations






class 		a__						:

					def __init__(   self				:	Union[str, Any],_A				:	int   ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		List[Any]    				=   value
							SCREAMING_SNAKE_CASE_  :		Node | None    				=   None
							SCREAMING_SNAKE_CASE_  :		Node | None    				=   None







class 		a__						:
					A     	=							42

					def __init__(   self				:	Optional[Any]   ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		List[str]    				=   0

					def     __UpperCamelCase       (   self				:	List[Any],_A				:	Node | None,_A				:	int   ):







							"""simple docstring"""






							if node is None:
									return

							if path_sum == self.target:
									self.paths += 1

							if node.left:
									self.depth_first_search(node.left,path_sum + node.left.value   )
							if node.right:
									self.depth_first_search(node.right,path_sum + node.right.value   )






					def     __UpperCamelCase       (   self				:	List[str],_A				:	Node | None,_A				:	int | None = None   ):







							"""simple docstring"""






							if node is None:
									return 0
							if target is not None:
									SCREAMING_SNAKE_CASE_  :		Union[str, Any]    				=   target

							self.depth_first_search(_A,node.value   )
							self.path_sum(node.left   )
							self.path_sum(node.right   )

							return self.paths


if __name__ == "__main__":
		import doctest

		doctest.testmod()
