
from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt


def    a      ( a	)     ->bool:




			'''simple docstring'''


			SCREAMING_SNAKE_CASE     						= int(number**0.5	)
			return number == sq * sq


def    a      ( a		,						a		,						a		,						a		,						a		,						a	)     ->tuple[int, int]:




			'''simple docstring'''


			SCREAMING_SNAKE_CASE     						= x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
			SCREAMING_SNAKE_CASE     						= x_den * y_den * z_den
			SCREAMING_SNAKE_CASE     						= gcd(a		,						a	)
			top //= hcf
			bottom //= hcf
			return top, bottom


def    a      ( a = 35	)     ->int:




			'''simple docstring'''


			SCREAMING_SNAKE_CASE     						= set()
			SCREAMING_SNAKE_CASE     						= 42
			SCREAMING_SNAKE_CASE     						= Fraction(0	)
			SCREAMING_SNAKE_CASE     						= 42

			for x_num in range(1		,						order + 1	):
						for x_den in range(x_num + 1		,						order + 1	):
									for y_num in range(1		,						order + 1	):
												for y_den in range(y_num + 1		,						order + 1	):
															# n=1
															SCREAMING_SNAKE_CASE     						= x_num * y_den + x_den * y_num
															SCREAMING_SNAKE_CASE     						= x_den * y_den
															SCREAMING_SNAKE_CASE     						= gcd(a		,						a	)
															z_num //= hcf
															z_den //= hcf
															if 0 < z_num < z_den <= order:
																		SCREAMING_SNAKE_CASE     						= add_three(
																		    a		,						a		,						a		,						a		,						a		,						a	)
																		unique_s.add(a	)

															# n=2
															SCREAMING_SNAKE_CASE     						= (
															    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
															)
															SCREAMING_SNAKE_CASE     						= x_den * x_den * y_den * y_den
															if is_sq(a	) and is_sq(a	):
																		SCREAMING_SNAKE_CASE     						= int(sqrt(a	)	)
																		SCREAMING_SNAKE_CASE     						= int(sqrt(a	)	)
																		SCREAMING_SNAKE_CASE     						= gcd(a		,						a	)
																		z_num //= hcf
																		z_den //= hcf
																		if 0 < z_num < z_den <= order:
																					SCREAMING_SNAKE_CASE     						= add_three(
																					    a		,						a		,						a		,						a		,						a		,						a	)
																					unique_s.add(a	)

                    # n=-1
															SCREAMING_SNAKE_CASE     						= x_num * y_num
															SCREAMING_SNAKE_CASE     						= x_den * y_num + x_num * y_den
															SCREAMING_SNAKE_CASE     						= gcd(a		,						a	)
															z_num //= hcf
															z_den //= hcf
															if 0 < z_num < z_den <= order:
																		SCREAMING_SNAKE_CASE     						= add_three(
																		    a		,						a		,						a		,						a		,						a		,						a	)
																		unique_s.add(a	)

															# n=2
															SCREAMING_SNAKE_CASE     						= x_num * x_num * y_num * y_num
															SCREAMING_SNAKE_CASE     						= (
															    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
															)
															if is_sq(a	) and is_sq(a	):
																		SCREAMING_SNAKE_CASE     						= int(sqrt(a	)	)
																		SCREAMING_SNAKE_CASE     						= int(sqrt(a	)	)
																		SCREAMING_SNAKE_CASE     						= gcd(a		,						a	)
																		z_num //= hcf
																		z_den //= hcf
																		if 0 < z_num < z_den <= order:
																					SCREAMING_SNAKE_CASE     						= add_three(
																					    a		,						a		,						a		,						a		,						a		,						a	)
																					unique_s.add(a	)

			for num, den in unique_s:
						total += Fraction(a		,						a	)

			return total.denominator + total.numerator


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

from PIL import Image


def    a      ( a	)     ->Image:




			'''simple docstring'''


			SCREAMING_SNAKE_CASE						,							SCREAMING_SNAKE_CASE     						= image.size
			SCREAMING_SNAKE_CASE     						= 0
			SCREAMING_SNAKE_CASE     						= image.load()
			for i in range(a	):
						for j in range(a	):
									SCREAMING_SNAKE_CASE     						= pixels[j, i]
									mean += pixel
			mean //= width * height

			for j in range(a	):
						for i in range(a	):
									SCREAMING_SNAKE_CASE     						= 255 if pixels[i, j] > mean else 0
			return image


if __name__ == "__main__":
							__lowerCAmelCase					   =       mean_threshold(Image.open('path_to_image').convert('L'))
							image.save('output_image_path')