






import sys
import turtle






def      _snake_case     (__lowercase     ,   __lowercase):
   return (pa[0] + pa[0]) / 2, (pa[1] + pa[1]) / 2






def      _snake_case     (__lowercase     ,   __lowercase     ,   __lowercase     ,   __lowercase     ,   ):
   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(__lowercase     ,   get_mid(__lowercase     ,   __lowercase)     ,   get_mid(__lowercase     ,   __lowercase)     ,   depth - 1)
   triangle(__lowercase     ,   get_mid(__lowercase     ,   __lowercase)     ,   get_mid(__lowercase     ,   __lowercase)     ,   depth - 1)
   triangle(__lowercase     ,   get_mid(__lowercase     ,   __lowercase)     ,   get_mid(__lowercase     ,   __lowercase)     ,   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>"""
  )
 snake_case__   :						Tuple													=   turtle.Turtle()
 my_pen.ht()
 my_pen.speed(5)
 my_pen.pencolor("""red""")

 snake_case__   :						Optional[Any]													=   [(-1_7_5, -1_2_5), (0, 1_7_5), (1_7_5, -1_2_5)]  # vertices of triangle
 triangle(vertices[0], vertices[1], vertices[2], int(sys.argv[1]))













import numpy as np






def      _snake_case     (__lowercase):
   return 1 / (1 + np.exp(-vector))






def      _snake_case     (__lowercase):
   return vector * sigmoid(__lowercase)


if __name__ == "__main__":
 import doctest

 doctest.testmod()





