



'''simple docstring'''

from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt






def 						_snake_case						(   _SCREAMING_SNAKE_CASE	:		int				)     ->		Any:







	"""simple docstring"""
	lowerCAmelCase       =      int(number**0.5				)
	return number == sq * sq






def 						_snake_case						(   _SCREAMING_SNAKE_CASE	:		int				,						_SCREAMING_SNAKE_CASE	:		int				,						_SCREAMING_SNAKE_CASE	:		int				,						_SCREAMING_SNAKE_CASE	:		int				,						_SCREAMING_SNAKE_CASE	:		int				,						_SCREAMING_SNAKE_CASE	:		int				)     ->		Optional[Any]:







	"""simple docstring"""
	lowerCAmelCase       =      x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
	lowerCAmelCase       =      x_den * y_den * z_den
	lowerCAmelCase       =      gcd(__a				,						__a				)
	top //= hcf
	bottom //= hcf
	return top, bottom






def 						_snake_case						(   _SCREAMING_SNAKE_CASE	:		int = 35				)     ->		Dict:







	"""simple docstring"""
	lowerCAmelCase       =      set()
	lowerCAmelCase       =      42
	lowerCAmelCase       =      Fraction(0				)
	lowerCAmelCase       =      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
					lowerCAmelCase       =      x_num * y_den + x_den * y_num
					lowerCAmelCase       =      x_den * y_den
					lowerCAmelCase       =      gcd(__a				,						__a				)
					z_num //= hcf
					z_den //= hcf
					if 0 < z_num < z_den <= order:
						lowerCAmelCase       =      add_three(
						    __a				,						__a				,						__a				,						__a				,						__a				,						__a				)
						unique_s.add(__a				)

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

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

					# n=2
					lowerCAmelCase       =      x_num * x_num * y_num * y_num
					lowerCAmelCase       =      (
					    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
					)
					if is_sq(__a				) and is_sq(__a				):
						lowerCAmelCase       =      int(sqrt(__a				)				)
						lowerCAmelCase       =      int(sqrt(__a				)				)
						lowerCAmelCase       =      gcd(__a				,						__a				)
						z_num //= hcf
						z_den //= hcf
						if 0 < z_num < z_den <= order:
							lowerCAmelCase       =      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 __future__ import annotations

_lowerCAmelCase:						str   				=       '#'




class       lowercase_					:





				def __init__(				self)  -> None:
											a__      ={}





				def 						__UpperCamelCase    (				self       ,  lowercase_)  -> None:
											a__      =self._trie
											for char in text:
																		if char not in trie:
																									a__      ={}
																		a__      =trie[char]
											a__      =True





				def 						__UpperCamelCase    (				self       ,  lowercase_)  -> tuple | list:
											a__      =self._trie
											for char in prefix:
																		if char in trie:
																									a__      =trie[char]
																		else:
																									return []
											return self._elements(lowercase_)





				def 						__UpperCamelCase    (				self       ,  lowercase_)  -> tuple:
											a__      =[]
											for c, v in d.items():
																		a__      =[' '] if c == END else [(c + s) for s in self._elements(lowercase_)]
																		result.extend(lowercase_)
											return tuple(lowercase_)







_lowerCAmelCase:						Optional[int]   				=       Trie()
_lowerCAmelCase:						List[str]   				=       ('depart', 'detergent', 'daring', 'dog', 'deer', 'deal')
for word in words:
	trie.insert_word(word)






def   _lowercase(					__a				:						str     ):
							a__      =trie.find_word(__a     )
							return tuple(string + word for word in suffixes     )






def   _lowercase(					):
							print(autocomplete_using_trie('de'     )     )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()

