

"""simple docstring"""





import sys
import turtle

def   __SCREAMING_SNAKE_CASE  (      A_						,     A_ ):
	return (pa[0] + pa[0]) / 2, (pa[1] + pa[1]) / 2

def   __SCREAMING_SNAKE_CASE  (      A_						,     A_						,     A_						,     A_						,     ):
	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(A_						,     get_mid(A_						,     A_ )						,     get_mid(A_						,     A_ )						,     depth - 1 )
	triangle(A_						,     get_mid(A_						,     A_ )						,     get_mid(A_						,     A_ )						,     depth - 1 )
	triangle(A_						,     get_mid(A_						,     A_ )						,     get_mid(A_						,     A_ )						,     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>'''
														)
							__UpperCamelCase  :      str							      =		turtle.Turtle()
							my_pen.ht()
							my_pen.speed(5)
							my_pen.pencolor('''red''')

							__UpperCamelCase  :      Union[str, 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]))







"""simple docstring"""





from collections import defaultdict
from math import ceil, sqrt

def   __SCREAMING_SNAKE_CASE  (      A_ = 1_00_00_00						,     A_ = 10 ):
	lowerCAmelCase__	:						defaultdict  				=	defaultdict(A_ )

	for outer_width in range(3						,     (t_limit // 4) + 2 ):
		if outer_width * outer_width > t_limit:
			lowerCAmelCase__	:						int  				=	max(
			    ceil(sqrt(outer_width * outer_width - t_limit ) )						,     1 )
		else:
			lowerCAmelCase__	:						Tuple  				=	1

		hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

		for hole_width in range(A_						,     outer_width - 1						,     2 ):
			count[outer_width * outer_width - hole_width * hole_width] += 1

	return sum(1 for n in count.values() if 1 <= n <= 10 )


if __name__ == "__main__":
							print(F'''{solution() = }''')




