



'''simple docstring'''






def  snake_case_     (					_lowerCAmelCase  :						list  )      ->   list:

							if len(_lowerCAmelCase  ) <= 1:
														return [tuple(_lowerCAmelCase  )]

							UpperCAmelCase :       List[Any] 							=		[]

							def generate(_lowerCAmelCase  :						int   ,      _lowerCAmelCase  :						list  ):
														if k == 1:
																					res.append(tuple(arr[:]  )  )
																					return

														generate(k - 1   ,      _lowerCAmelCase  )

														for i in range(k - 1  ):
																					if k % 2 == 0:  # k is even
																												UpperCAmelCase							,		UpperCAmelCase :       int 							=		arr[k - 1], arr[i]
																					else:  # k is odd
																												UpperCAmelCase							,		UpperCAmelCase :       Tuple 							=		arr[k - 1], arr[0]
																					generate(k - 1   ,      _lowerCAmelCase  )

							generate(len(_lowerCAmelCase  )   ,      _lowerCAmelCase  )
							return res


if __name__ == "__main__":
						UpperCamelCase__:   Dict								=			input("Enter numbers separated by a comma:\n").strip()
						UpperCamelCase__:   Union[str, Any]								=			[int(item) for item in user_input.split(",")]
						print(heaps(arr))










'''simple docstring'''






from __future__ import annotations

import matplotlib.pyplot as plt  # type: ignore
import numpy

# initial triangle of Koch snowflake
UpperCamelCase__:   Tuple								=			numpy.array([0, 0])
UpperCamelCase__:   Union[str, Any]								=			numpy.array([0.5, 0.8660254])
UpperCamelCase__:   Dict								=			numpy.array([1, 0])
UpperCamelCase__:   int								=			[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]


def  snake_case_     (					_lowerCAmelCase  :						list[numpy.ndarray]   ,      _lowerCAmelCase  :						int  )      ->   list[numpy.ndarray]:
							UpperCAmelCase :       Union[str, Any] 							=		initial_vectors
							for _ in range(_lowerCAmelCase  ):
														UpperCAmelCase :       Union[str, Any] 							=		iteration_step(_lowerCAmelCase  )
							return vectors


def  snake_case_     (					_lowerCAmelCase  :						list[numpy.ndarray]  )      ->   list[numpy.ndarray]:
							UpperCAmelCase :       Tuple 							=		[]
							for i, start_vector in enumerate(vectors[:-1]  ):
														UpperCAmelCase :       List[str] 							=		vectors[i + 1]
														new_vectors.append(_lowerCAmelCase  )
														UpperCAmelCase :       Optional[Any] 							=		end_vector - start_vector
														new_vectors.append(start_vector + difference_vector / 3  )
														new_vectors.append(
														    start_vector + difference_vector / 3 + rotate(difference_vector / 3   ,      60  )  )
														new_vectors.append(start_vector + difference_vector * 2 / 3  )
							new_vectors.append(vectors[-1]  )
							return new_vectors


def  snake_case_     (					_lowerCAmelCase  :						numpy.ndarray   ,      _lowerCAmelCase  :						float  )      ->   numpy.ndarray:
							UpperCAmelCase :       List[str] 							=		numpy.radians(_lowerCAmelCase  )
							UpperCAmelCase							,		UpperCAmelCase :       Tuple 							=		numpy.cos(_lowerCAmelCase  ), numpy.sin(_lowerCAmelCase  )
							UpperCAmelCase :       Union[str, Any] 							=		numpy.array(((c, -s), (s, c))  )
							return numpy.dot(_lowerCAmelCase   ,      _lowerCAmelCase  )


def  snake_case_     (					_lowerCAmelCase  :						list[numpy.ndarray]  )      ->   None:
							UpperCAmelCase :       List[Any] 							=		plt.gca()
							axes.set_aspect('''equal'''  )

							# matplotlib.pyplot.plot takes a list of all x-coordinates and a list of all
							# y-coordinates as inputs, which are constructed from the vector-list using
							# zip()
							UpperCAmelCase							,		UpperCAmelCase :       str 							=		zip(*_lowerCAmelCase  )
							plt.plot(_lowerCAmelCase   ,      _lowerCAmelCase  )
							plt.show()


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						UpperCamelCase__:   List[Any]								=			iterate(INITIAL_VECTORS, 5)
						plot(processed_vectors)





