





from __future__ import annotations

from fractions import Fraction







def    A				(							UpperCAmelCase  ,  UpperCAmelCase				):
					return (
					    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
					)







def    A				(							UpperCAmelCase				):
					_snake_case       :					Any				       =   []
					_snake_case       :					List[Any]				       =   11
					_snake_case       :					List[str]				       =   int("1" + "0" * digit_len				)
					for num in range(UpperCAmelCase  ,  UpperCAmelCase				):
										while den <= 99:
															if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
																				if is_digit_cancelling(UpperCAmelCase  ,  UpperCAmelCase				):
																									solutions.append(F"""{num}/{den}"""				)
															den += 1
										num += 1
										_snake_case       :					Union[str, Any]				       =   10
					return solutions







def    A				(							UpperCAmelCase = 2				):
					_snake_case       :					Any				       =   1.0
					for fraction in fraction_list(UpperCAmelCase				):
										_snake_case       :					Any				       =   Fraction(UpperCAmelCase				)
										result *= frac.denominator / frac.numerator
					return int(UpperCAmelCase				)


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






import sys
import turtle







def    A				(							UpperCAmelCase  ,  UpperCAmelCase				):
					return (pa[0] + pa[0]) / 2, (pa[1] + pa[1]) / 2







def    A				(							UpperCAmelCase  ,  UpperCAmelCase  ,  UpperCAmelCase  ,  UpperCAmelCase  ,  ):
					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(UpperCAmelCase  ,  get_mid(UpperCAmelCase  ,  UpperCAmelCase				)  ,  get_mid(UpperCAmelCase  ,  UpperCAmelCase				)  ,  depth - 1				)
					triangle(UpperCAmelCase  ,  get_mid(UpperCAmelCase  ,  UpperCAmelCase				)  ,  get_mid(UpperCAmelCase  ,  UpperCAmelCase				)  ,  depth - 1				)
					triangle(UpperCAmelCase  ,  get_mid(UpperCAmelCase  ,  UpperCAmelCase				)  ,  get_mid(UpperCAmelCase  ,  UpperCAmelCase				)  ,  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>'
														)
							__lowerCAmelCase :Any     =    turtle.Turtle()
							my_pen.ht()
							my_pen.speed(5)
							my_pen.pencolor('red')

							__lowerCAmelCase :Optional[int]     =    [(-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]))