


'''simple docstring'''



def     _UpperCamelCase      (		):
			UpperCAmelCase__  :					str        =     []
			UpperCAmelCase__  :					List[str]        =     1

			while len(UpperCamelCase__					) < 1e6:
						constant.append(str(UpperCamelCase__					)					)
						i += 1

			UpperCAmelCase__  :					Optional[Any]        =     """""".join(UpperCamelCase__					)

			return (
			    int(constant[0]					)
			    * int(constant[9]					)
			    * int(constant[9_9]					)
			    * int(constant[9_9_9]					)
			    * int(constant[9_9_9_9]					)
			    * int(constant[9_9_9_9_9]					)
			    * int(constant[9_9_9_9_9_9]					)
			)


if __name__ == "__main__":
		print(solution())



'''simple docstring'''



from __future__ import annotations

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

# initial triangle of Koch snowflake
__A	=numpy.array([0, 0])
__A	=numpy.array([0.5, 0.8_6_6_0_2_5_4])
__A	=numpy.array([1, 0])
__A	=[VECTOR_1, VECTOR_2, VECTOR_3, VECTOR_1]







def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__					):
			UpperCAmelCase__  :					Union[str, Any]        =     initial_vectors
			for _ in range(UpperCamelCase__					):
						UpperCAmelCase__  :					Dict        =     iteration_step(UpperCamelCase__					)
			return vectors







def     _UpperCamelCase      (		UpperCamelCase__					):
			UpperCAmelCase__  :					Optional[Any]        =     []
			for i, start_vector in enumerate(vectors[:-1]					):
						UpperCAmelCase__  :					Tuple        =     vectors[i + 1]
						new_vectors.append(UpperCamelCase__					)
						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 ,      6_0					)					)
						new_vectors.append(start_vector + difference_vector * 2 / 3					)
			new_vectors.append(vectors[-1]					)
			return new_vectors







def     _UpperCamelCase      (		UpperCamelCase__ ,      UpperCamelCase__					):
			UpperCAmelCase__  :					Any        =     numpy.radians(UpperCamelCase__					)
			UpperCAmelCase__   ,       UpperCAmelCase__  :					int        =     numpy.cos(UpperCamelCase__					), numpy.sin(UpperCamelCase__					)
			UpperCAmelCase__  :					Dict        =     numpy.array(((c, -s), (s, c))					)
			return numpy.dot(UpperCamelCase__ ,      UpperCamelCase__					)







def     _UpperCamelCase      (		UpperCamelCase__					):
			UpperCAmelCase__  :					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__  :					Tuple        =     zip(*UpperCamelCase__					)
			plt.plot(UpperCamelCase__ ,      UpperCamelCase__					)
			plt.show()


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		__A	=iterate(INITIAL_VECTORS, 5)
		plot(processed_vectors)