
from __future__ import annotations

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

# initial triangle of Koch snowflake
__lowerCAmelCase			:     Union[str, Any]           =   numpy.array([0, 0])
__lowerCAmelCase			:     Dict           =   numpy.array([0.5, 0.866_0254])
__lowerCAmelCase			:     Tuple           =   numpy.array([1, 0])
__lowerCAmelCase			:     str           =   [VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]

def a__    (       A_,     A_					):






  '''simple docstring'''





  __magic_name__				     =       initial_vectors
  for _ in range(A_					):
    __magic_name__				     =       iteration_step(A_					)
  return vectors

def a__    (       A_					):






  '''simple docstring'''





  __magic_name__				     =       []
  for i, start_vector in enumerate(vectors[:-1]					):
    __magic_name__				     =       vectors[i + 1]
    new_vectors.append(A_					)
    __magic_name__				     =       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 a__    (       A_,     A_					):






  '''simple docstring'''





  __magic_name__				     =       numpy.radians(A_					)
  __magic_name__     ,    __magic_name__				     =       numpy.cos(A_					), numpy.sin(A_					)
  __magic_name__				     =       numpy.array(((c, -s), (s, c))					)
  return numpy.dot(A_,     A_					)

def a__    (       A_					):






  '''simple docstring'''





  __magic_name__				     =       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()
  __magic_name__     ,    __magic_name__				     =       zip(*A_					)
  plt.plot(A_,     A_					)
  plt.show()


if __name__ == "__main__":
    import doctest

    doctest.testmod()

    __lowerCAmelCase			:     int           =   iterate(INITIAL_VECTORS, 5)
    plot(processed_vectors)





'''simple docstring'''




from __future__ import annotations

from bisect import bisect_left
from functools import total_ordering
from heapq import merge

@total_ordering
class 		UpperCAmelCase_      (  __lowercase		):





     def __lt__( self       :      Optional[int]    ,      UpperCAmelCase__       :      List[str]    )				->  List[Any]:
        return self[-1] < other[-1]





     def __eq__( self       :      str    ,      UpperCAmelCase__       :      List[str]    )				->  Tuple:
        return self[-1] == other[-1]





def 	a_					( lowerCamelCase	:     list				):
   lowerCAmelCase     =			[]
   # sort into stacks
   for element in collection:
      lowerCAmelCase     =			Stack([element]				)
      lowerCAmelCase     =			bisect_left(lowerCamelCase	, lowerCamelCase				)
      if i != len(lowerCamelCase				):
         stacks[i].append(lowerCamelCase				)
      else:
         stacks.append(lowerCamelCase				)

    # use a heap-based merge to merge stack efficiently
   lowerCAmelCase     =			merge(*(reversed(lowerCamelCase				) for stack in stacks)				)
   return collection


if __name__ == "__main__":
       __snake_case    						=input("""Enter numbers separated by a comma:\n""").strip()
       __snake_case    						=[int(item) for item in user_input.split(""",""")]
       print(patience_sort(unsorted))





