





"""simple docstring"""






from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt



def  __lowerCamelCase					(					lowerCAmelCase__				):
				A__							 =       int(number**0.5				)
				return number == sq * sq



def  __lowerCamelCase					(					lowerCAmelCase__       ,lowerCAmelCase__       ,lowerCAmelCase__       ,lowerCAmelCase__       ,lowerCAmelCase__       ,lowerCAmelCase__				):
				A__							 =       x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
				A__							 =       x_den * y_den * z_den
				A__							 =       gcd(a__       ,a__				)
				top //= hcf
				bottom //= hcf
				return top, bottom



def  __lowerCamelCase					(					lowerCAmelCase__ = 35				):
				A__							 =       set()
				A__							 =       42
				A__							 =       Fraction(0				)
				A__							 =       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
																				A__							 =       x_num * y_den + x_den * y_num
																				A__							 =       x_den * y_den
																				A__							 =       gcd(a__       ,a__				)
																				z_num //= hcf
																				z_den //= hcf
																				if 0 < z_num < z_den <= order:
																								A__							 =       add_three(
																								    a__       ,a__       ,a__       ,a__       ,a__       ,a__				)
																								unique_s.add(a__				)

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

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

																				# n=2
																				A__							 =       x_num * x_num * y_num * y_num
																				A__							 =       (
																				    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																				)
																				if is_sq(a__				) and is_sq(a__				):
																								A__							 =       int(sqrt(a__				)				)
																								A__							 =       int(sqrt(a__				)				)
																								A__							 =       gcd(a__       ,a__				)
																								z_num //= hcf
																								z_den //= hcf
																								if 0 < z_num < z_den <= order:
																												A__							 =       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() = }''')










"""simple docstring"""






import numpy as np



def  __lowerCamelCase					(					lowerCAmelCase__				):
				return 1 / (1 + np.exp(-vector				))



def  __lowerCamelCase					(					lowerCAmelCase__				):
				return vector * sigmoid(lowerCAmelCase__				)


if __name__ == "__main__":
					import doctest

					doctest.testmod()


