






from __future__ import annotations

import typing
from collections.abc import Iterable

import numpy as np

A__      :     Union[str, Any]       =					typing.Union[Iterable[float], Iterable[int], np.ndarray]  # noqa: UP007
A__      :     int       =					typing.Union[np.floataa, int, float]  # noqa: UP007






def     a     (		lowerCamelCase_						,  lowerCamelCase_							):






				'''simple docstring'''
				return np.sqrt(np.sum((np.asarray(lowerCamelCase_							) - np.asarray(lowerCamelCase_							)) ** 2							)							)






def     a     (		lowerCamelCase_						,  lowerCamelCase_							):






				'''simple docstring'''
				return sum((va - va) ** 2 for va, va in zip(lowerCamelCase_						,  lowerCamelCase_							)							) ** (1 / 2)


if __name__ == "__main__":






							def     a     (		):






											'''simple docstring'''
											from timeit import timeit

											print('''Without Numpy'''							)
											print(
											    timeit(
											        '''euclidean_distance_no_np([1, 2, 3], [4, 5, 6])'''						,  number=1_0000						,  globals=globals()						,  )							)
											print('''With Numpy'''							)
											print(
											    timeit(
											        '''euclidean_distance([1, 2, 3], [4, 5, 6])'''						,  number=1_0000						,  globals=globals()						,  )							)




							benchmark()












import sys
import turtle






def     a     (		lowerCamelCase_						,  lowerCamelCase_							):






				'''simple docstring'''
				return (pa[0] + pa[0]) / 2, (pa[1] + pa[1]) / 2






def     a     (		lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_						,  lowerCamelCase_						,  ):






				'''simple docstring'''
				my_pen.up()
				my_pen.goto(vertexa[0]						,  vertexa[1]							)
				my_pen.down()
				my_pen.goto(vertexa[0]						,  vertexa[1]							)
				my_pen.goto(vertexa[0]						,  vertexa[1]							)
				my_pen.goto(vertexa[0]						,  vertexa[1]							)

				if depth == 0:
								return

				triangle(lowerCamelCase_						,  get_mid(lowerCamelCase_						,  lowerCamelCase_							)						,  get_mid(lowerCamelCase_						,  lowerCamelCase_							)						,  depth - 1							)
				triangle(lowerCamelCase_						,  get_mid(lowerCamelCase_						,  lowerCamelCase_							)						,  get_mid(lowerCamelCase_						,  lowerCamelCase_							)						,  depth - 1							)
				triangle(lowerCamelCase_						,  get_mid(lowerCamelCase_						,  lowerCamelCase_							)						,  get_mid(lowerCamelCase_						,  lowerCamelCase_							)						,  depth - 1							)


if __name__ == "__main__":
							if len(sys.argv) != 2:
														raise ValueError(
														    'Correct format for using this script: '
														    'python fractals.py <int:depth_for_fractal>'
														)
							A__      :     Dict       =					turtle.Turtle()
							my_pen.ht()
							my_pen.speed(5)
							my_pen.pencolor('red')

							A__      :     Union[str, Any]       =					[(-1_75, -1_25), (0, 1_75), (1_75, -1_25)]  # vertices of triangle
							triangle(vertices[0], vertices[1], vertices[2], int(sys.argv[1]))




