





def 	lowerCamelCase_		(							_UpperCamelCase					)						->		int:






				"""simple docstring"""


				snake_case_		:       str           =    [1]

				snake_case_     ,				snake_case_     ,				snake_case_		:       Tuple           =    0, 0, 0
				snake_case_		:       Optional[int]           =    ugly_nums[ia] * 2
				snake_case_		:       List[str]           =    ugly_nums[ia] * 3
				snake_case_		:       Union[str, Any]           =    ugly_nums[ia] * 5

				for _ in range(1					,							_UpperCamelCase					):
								snake_case_		:       Dict           =    min(_UpperCamelCase					,							_UpperCamelCase					,							_UpperCamelCase					)
								ugly_nums.append(_UpperCamelCase					)
								if next_num == next_a:
												ia += 1
												snake_case_		:       Optional[Any]           =    ugly_nums[ia] * 2
								if next_num == next_a:
												ia += 1
												snake_case_		:       List[str]           =    ugly_nums[ia] * 3
								if next_num == next_a:
												ia += 1
												snake_case_		:       Optional[Any]           =    ugly_nums[ia] * 5
				return ugly_nums[-1]


if __name__ == "__main__":
	from doctest import testmod

	testmod(verbose=True)
	print(F'''{ugly_numbers(2_0_0) = }''')








"""simple docstring"""
from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt

def 							snake_case (  A__		):
			UpperCAmelCase_	:					int     	=   int(number**0.5		)
			return number == sq * sq

def 							snake_case (  A__      ,A__      ,A__      ,A__      ,A__      ,A__		):
			UpperCAmelCase_	:					int     	=   x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
			UpperCAmelCase_	:					int     	=   x_den * y_den * z_den
			UpperCAmelCase_	:					int     	=   gcd(A__      ,A__		)
			top //= hcf
			bottom //= hcf
			return top, bottom

def 							snake_case (  A__ = 35		):
			UpperCAmelCase_	:					set     	=   set()
			UpperCAmelCase_	:					int
			UpperCAmelCase_	:					Fraction     	=   Fraction(0		)
			UpperCAmelCase_	:					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
															UpperCAmelCase_	:					Optional[int]     	=   x_num * y_den + x_den * y_num
															UpperCAmelCase_	:					List[Any]     	=   x_den * y_den
															UpperCAmelCase_	:					Tuple     	=   gcd(A__      ,A__		)
															z_num //= hcf
															z_den //= hcf
															if 0 < z_num < z_den <= order:
																		UpperCAmelCase_	:					int     	=   add_three(
																		    A__      ,A__      ,A__      ,A__      ,A__      ,A__		)
																		unique_s.add(A__		)

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

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

															# n=2
															UpperCAmelCase_	:					Optional[Any]     	=   x_num * x_num * y_num * y_num
															UpperCAmelCase_	:					Dict     	=   (
															    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
															)
															if is_sq(A__		) and is_sq(A__		):
																		UpperCAmelCase_	:					str     	=   int(sqrt(A__		)		)
																		UpperCAmelCase_	:					int     	=   int(sqrt(A__		)		)
																		UpperCAmelCase_	:					Optional[Any]     	=   gcd(A__      ,A__		)
																		z_num //= hcf
																		z_den //= hcf
																		if 0 < z_num < z_den <= order:
																					UpperCAmelCase_	:					Optional[int]     	=   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() = }')



