


'''simple docstring'''





class 						a__					:





			'''simple docstring'''

			def __init__(  self							:			Optional[Any]			,    lowerCAmelCase_							:			list	)      ->		None:
						__A=	set_counts
						__A=	max(lowerCAmelCase_	)
						__A=	len(lowerCAmelCase_	)
						__A=	[1] * num_sets
						__A=	list(range(lowerCAmelCase_	)	)
			def 					lowerCAmelCase     (  self							:			Optional[Any]			,    lowerCAmelCase_							:			int			,    lowerCAmelCase_							:			int	)      ->		bool:
						__A=	self.get_parent(lowerCAmelCase_	)
						__A=	self.get_parent(lowerCAmelCase_	)

						if src_parent == dst_parent:
									return False

						if self.ranks[dst_parent] >= self.ranks[src_parent]:
									self.set_counts[dst_parent] += self.set_counts[src_parent]
									__A=	0
									__A=	dst_parent
									if self.ranks[dst_parent] == self.ranks[src_parent]:
												self.ranks[dst_parent] += 1
									__A=	self.set_counts[dst_parent]
						else:
									self.set_counts[src_parent] += self.set_counts[dst_parent]
									__A=	0
									__A=	src_parent
									__A=	self.set_counts[src_parent]

						__A=	max(self.max_set			,    lowerCAmelCase_	)
						return True

			def 					lowerCAmelCase     (  self							:			Union[str, Any]			,    lowerCAmelCase_							:			int	)      ->		int:
						if self.parents[disj_set] == disj_set:
									return disj_set
						__A=	self.get_parent(self.parents[disj_set]	)
						return self.parents[disj_set]







'''simple docstring'''





from __future__ import annotations

import math

UpperCAmelCase__  			=				'''2020.9.26'''
UpperCAmelCase__  			=				'''xcodz-dot, cclaus, dhruvmanila'''






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float ):






			"""simple docstring"""




			if not all(isinstance(_SCREAMING_SNAKE_CASE,(float, int) ) for val in locals().values() ):
						__A=	f"""Input values must either be float or int: {list(locals().values() )}"""
						raise TypeError(_SCREAMING_SNAKE_CASE )
			__A=	((x * distance) / (z + distance)) * scale
			__A=	((y * distance) / (z + distance)) * scale
			return projected_x, projected_y






def 						UpperCAmelCase__(				_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: float,_SCREAMING_SNAKE_CASE					: str,_SCREAMING_SNAKE_CASE					: float ):






			"""simple docstring"""




			if not isinstance(_SCREAMING_SNAKE_CASE,_SCREAMING_SNAKE_CASE ):
						raise TypeError('Axis must be a str' )
			__A=	locals()
			del input_variables["axis"]
			if not all(isinstance(_SCREAMING_SNAKE_CASE,(float, int) ) for val in input_variables.values() ):
						__A=	(
						    'Input values except axis must either be float or int: '
						    f"""{list(input_variables.values() )}"""
						)
						raise TypeError(_SCREAMING_SNAKE_CASE )
			__A=	(angle % 360) / 450 * 180 / math.pi
			if axis == "z":
						__A=	x * math.cos(_SCREAMING_SNAKE_CASE ) - y * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	y * math.cos(_SCREAMING_SNAKE_CASE ) + x * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	z
			elif axis == "x":
						__A=	y * math.cos(_SCREAMING_SNAKE_CASE ) - z * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	z * math.cos(_SCREAMING_SNAKE_CASE ) + y * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	x
			elif axis == "y":
						__A=	x * math.cos(_SCREAMING_SNAKE_CASE ) - z * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	z * math.cos(_SCREAMING_SNAKE_CASE ) + x * math.sin(_SCREAMING_SNAKE_CASE )
						__A=	y
			else:
						raise ValueError('not a valid axis, choose one of \'x\', \'y\', \'z\'' )

			return new_x, new_y, new_z


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					print(F"""{convert_to_ad(1.0, 2.0, 3.0, 10.0, 10.0) = }""")
					print(F"""{rotate(1.0, 2.0, 3.0, 'y', 90.0) = }""")



