


from __future__ import annotations

import re
def 							UpperCAmelCase_   (				__snake_case		)	->     list[str]:







 """simple docstring"""


 def alphanum_key(__snake_case		):
  return [int(UpperCAmelCase_		) if s.isdigit() else s.lower() for s in re.split('''([0-9]+)'''	,		UpperCAmelCase_		)]

 return sorted(UpperCAmelCase_	,		key=UpperCAmelCase_		)


if __name__ == "__main__":
  import doctest

  doctest.testmod()




from __future__ import annotations






def        lowerCamelCase_  (				UpperCAmelCase_				:  int						)    ->					list[int]:




	'''simple docstring'''




	_UpperCamelCase :		Any								=    [0] * max_one

	for i in range(0				,							UpperCAmelCase_						):
		_UpperCamelCase :		List[Any]								=    i

	for i in range(2				,							UpperCAmelCase_						):
		if totients[i] == i:
			for j in range(UpperCAmelCase_				,							UpperCAmelCase_				,							UpperCAmelCase_						):
				totients[j] -= totients[j] // i

	return totients






def        lowerCamelCase_  (				UpperCAmelCase_				:  int				,							UpperCAmelCase_				:  int						)    ->					bool:




	'''simple docstring'''




	return sorted(str(UpperCAmelCase_						)						) == sorted(str(UpperCAmelCase_						)						)






def        lowerCamelCase_  (				UpperCAmelCase_				:  int = 1_0_0_0_0_0_0_0						)    ->					int:




	'''simple docstring'''




	_UpperCamelCase :		List[Any]								=    1  # i
	_UpperCamelCase :		List[str]								=    0  # φ(i)
	_UpperCamelCase :		str								=    get_totients(max_n + 1						)

	for i in range(2				,							max_n + 1						):
		_UpperCamelCase :		List[str]								=    totients[i]

		if i * min_denominator < min_numerator * t and has_same_digits(UpperCAmelCase_				,							UpperCAmelCase_						):
			_UpperCamelCase :		Optional[int]								=    i
			_UpperCamelCase :		Tuple								=    t

	return min_numerator


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




