


'''simple docstring'''



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       int       ):
					__a      :	int    =  int(number**0.5       )
					return number == sq * sq






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       int						,				_SCREAMING_SNAKE_CASE				:       int       ):
					__a      :	int    =  x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
					__a      :	int    =  x_den * y_den * z_den
					__a      :	int    =  gcd(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
					top //= hcf
					bottom //= hcf
					return top, bottom






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE				:       int = 35       ):
					__a      :	set    =  set()
					__a      :	int
					__a      :	Fraction    =  Fraction(0       )
					__a      :	tuple[int, int]

					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
																									__a      :	str    =  x_num * y_den + x_den * y_num
																									__a      :	List[str]    =  x_den * y_den
																									__a      :	Tuple    =  gcd(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														__a      :	List[Any]    =  add_three(
																														    _SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
																														unique_s.add(_SCREAMING_SNAKE_CASE       )

																									# n=2
																									__a      :	Optional[int]    =  (
																									    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
																									)
																									__a      :	Optional[int]    =  x_den * x_den * y_den * y_den
																									if is_sq(_SCREAMING_SNAKE_CASE       ) and is_sq(_SCREAMING_SNAKE_CASE       ):
																														__a      :	int    =  int(sqrt(_SCREAMING_SNAKE_CASE       )       )
																														__a      :	Any    =  int(sqrt(_SCREAMING_SNAKE_CASE       )       )
																														__a      :	List[str]    =  gcd(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			__a      :	Union[str, Any]    =  add_three(
																																			    _SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
																																			unique_s.add(_SCREAMING_SNAKE_CASE       )

                    # n=-1
																									__a      :	Optional[int]    =  x_num * y_num
																									__a      :	int    =  x_den * y_num + x_num * y_den
																									__a      :	Optional[int]    =  gcd(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														__a      :	List[str]    =  add_three(
																														    _SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
																														unique_s.add(_SCREAMING_SNAKE_CASE       )

																									# n=2
																									__a      :	int    =  x_num * x_num * y_num * y_num
																									__a      :	Any    =  (
																									    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																									)
																									if is_sq(_SCREAMING_SNAKE_CASE       ) and is_sq(_SCREAMING_SNAKE_CASE       ):
																														__a      :	List[Any]    =  int(sqrt(_SCREAMING_SNAKE_CASE       )       )
																														__a      :	Any    =  int(sqrt(_SCREAMING_SNAKE_CASE       )       )
																														__a      :	int    =  gcd(_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			__a      :	Union[str, Any]    =  add_three(
																																			    _SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE						,				_SCREAMING_SNAKE_CASE       )
																																			unique_s.add(_SCREAMING_SNAKE_CASE       )

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

					return total.denominator + total.numerator


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








'''simple docstring'''



import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
	# Create universe of discourse in Python using linspace ()
	__lowercase     :						int	=     np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False)

	# Create two fuzzy sets by defining any membership function
	# (trapmf(), gbellmf(), gaussmf(), etc).
	__lowercase     :						Any	=     [0, 25, 50]
	__lowercase     :						int	=     [25, 50, 75]
	__lowercase     :						List[str]	=     fuzz.membership.trimf(X, abca)
	__lowercase     :						Any	=     fuzz.membership.trimf(X, abca)

	# Compute the different operations using inbuilt functions.
	__lowercase     :						List[Any]	=     np.ones(75)
	__lowercase     :						Any	=     np.zeros((75,))
	# 1. Union = max(µA(x), µB(x))
	__lowercase     :						int	=     fuzz.fuzzy_or(X, young, X, middle_aged)[1]
	# 2. Intersection = min(µA(x), µB(x))
	__lowercase     :						int	=     fuzz.fuzzy_and(X, young, X, middle_aged)[1]
	# 3. Complement (A) = (1- min(µA(x))
	__lowercase     :						str	=     fuzz.fuzzy_not(young)
	# 4. Difference (A/B) = min(µA(x),(1- µB(x)))
	__lowercase     :						List[Any]	=     fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1]
	# 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))]
	__lowercase     :						Optional[Any]	=     young + middle_aged - (young * middle_aged)
	# 6. Algebraic Product = (µA(x) * µB(x))
	__lowercase     :						str	=     young * middle_aged
	# 7. Bounded Sum = min[1,(µA(x), µB(x))]
	__lowercase     :						Optional[Any]	=     fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
	# 8. Bounded difference = min[0,(µA(x), µB(x))]
	__lowercase     :						Union[str, Any]	=     fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1]

	# max-min composition
	# max-product composition

	# Plot each set A, set B and each operation result using plot() and subplot().
	from matplotlib import pyplot as plt

	plt.figure()

	plt.subplot(4, 3, 1)
	plt.plot(X, young)
	plt.title('Young')
	plt.grid(True)

	plt.subplot(4, 3, 2)
	plt.plot(X, middle_aged)
	plt.title('Middle aged')
	plt.grid(True)

	plt.subplot(4, 3, 3)
	plt.plot(X, union)
	plt.title('union')
	plt.grid(True)

	plt.subplot(4, 3, 4)
	plt.plot(X, intersection)
	plt.title('intersection')
	plt.grid(True)

	plt.subplot(4, 3, 5)
	plt.plot(X, complement_a)
	plt.title('complement_a')
	plt.grid(True)

	plt.subplot(4, 3, 6)
	plt.plot(X, difference)
	plt.title('difference a/b')
	plt.grid(True)

	plt.subplot(4, 3, 7)
	plt.plot(X, alg_sum)
	plt.title('alg_sum')
	plt.grid(True)

	plt.subplot(4, 3, 8)
	plt.plot(X, alg_product)
	plt.title('alg_product')
	plt.grid(True)

	plt.subplot(4, 3, 9)
	plt.plot(X, bdd_sum)
	plt.title('bdd_sum')
	plt.grid(True)

	plt.subplot(4, 3, 10)
	plt.plot(X, bdd_difference)
	plt.title('bdd_difference')
	plt.grid(True)

	plt.subplots_adjust(hspace=0.5)
	plt.show()



