



"""simple docstring"""
import operator as op



def        lowerCAmelCase_(   lowercase_     :							Dict							)	->       Dict:
				_lowerCamelCase        =				[]
				_lowerCamelCase        =				lambda lowercase_						,   lowercase_							: int(x / y							)  # noqa: E731 integer division operation
				_lowerCamelCase        =				{
				    '''^''': op.pow,
				    '''*''': op.mul,
				    '''/''': div,
				    '''+''': op.add,
				    '''-''': op.sub,
				}  # operators & their respective operation

				# print table header
				print('''Symbol'''.center(8							)						,   '''Action'''.center(12							)						,   '''Stack'''						,   sep=''' | '''							)
				print('''-''' * (30 + len(lowercase_							))							)

				for x in post_fix:
								if x.isdigit():  # if x in digit
												stack.append(lowercase_							)  # append x to stack
												# output in tabular format
												print(x.rjust(8							)						,   ('''push(''' + x + ''')''').ljust(12							)						,   ''','''.join(lowercase_							)						,   sep=''' | '''							)
								else:
												_lowerCamelCase        =				stack.pop()  # pop stack
												# output in tabular format
												print(''''''.rjust(8							)						,   ('''pop(''' + b + ''')''').ljust(12							)						,   ''','''.join(lowercase_							)						,   sep=''' | '''							)

												_lowerCamelCase        =				stack.pop()  # pop stack
												# output in tabular format
												print(''''''.rjust(8							)						,   ('''pop(''' + a + ''')''').ljust(12							)						,   ''','''.join(lowercase_							)						,   sep=''' | '''							)

												stack.append(
												    str(opr[x](int(lowercase_							)						,   int(lowercase_							)							)							)							)  # evaluate the 2 values popped from stack & push result to stack
												# output in tabular format
												print(
												    x.rjust(8							)						,   ('''push(''' + a + x + b + ''')''').ljust(12							)						,   ''','''.join(lowercase_							)						,   sep=''' | '''						,   )

				return int(stack[0]							)


if __name__ == "__main__":
			__SCREAMING_SNAKE_CASE  :						Union[str, Any]    							=      input('''\n\nEnter a Postfix Equation (space separated) = ''').split(''' ''')
			print('''\n\tResult = ''', solve(Postfix))





"""simple docstring"""
from __future__ import annotations

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

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



def        lowerCAmelCase_(   lowercase_     :							list[numpy.ndarray]						,   lowercase_     :							int							)	->       list[numpy.ndarray]:
				_lowerCamelCase        =				initial_vectors
				for _ in range(lowercase_							):
								_lowerCamelCase        =				iteration_step(lowercase_							)
				return vectors



def        lowerCAmelCase_(   lowercase_     :							list[numpy.ndarray]							)	->       list[numpy.ndarray]:
				_lowerCamelCase        =				[]
				for i, start_vector in enumerate(vectors[:-1]							):
								_lowerCamelCase        =				vectors[i + 1]
								new_vectors.append(lowercase_							)
								_lowerCamelCase        =				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        lowerCAmelCase_(   lowercase_     :							numpy.ndarray						,   lowercase_     :							float							)	->       numpy.ndarray:
				_lowerCamelCase        =				numpy.radians(lowercase_							)
				_lowerCamelCase  ,     _lowerCamelCase        =				numpy.cos(lowercase_							), numpy.sin(lowercase_							)
				_lowerCamelCase        =				numpy.array(((c, -s), (s, c))							)
				return numpy.dot(lowercase_						,   lowercase_							)



def        lowerCAmelCase_(   lowercase_     :							list[numpy.ndarray]							)	->       None:
				_lowerCamelCase        =				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()
				_lowerCamelCase  ,     _lowerCamelCase        =				zip(*lowercase_							)
				plt.plot(lowercase_						,   lowercase_							)
				plt.show()


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			__SCREAMING_SNAKE_CASE  :						str    							=      iterate(INITIAL_VECTORS, 5)
			plot(processed_vectors)
