
from __future__ import annotations






def 						lowerCAmelCase_		(      _snake_case   :						int     )       ->	list[int]:







	'''simple docstring'''


	__magic_name__	:	int			     =  [0] * max_one

	for i in range(0   ,     _snake_case     ):
		__magic_name__	:	Dict			     =  i

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

	return totients






def 						lowerCAmelCase_		(      _snake_case   :						int   ,     _snake_case   :						int     )       ->	bool:







	'''simple docstring'''


	return sorted(str(_snake_case     )     ) == sorted(str(_snake_case     )     )






def 						lowerCAmelCase_		(      _snake_case   :						int = 10000000     )       ->	int:







	'''simple docstring'''


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

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

		if i * min_denominator < min_numerator * t and has_same_digits(_snake_case   ,     _snake_case     ):
			__magic_name__	:	Tuple			     =  i
			__magic_name__	:	List[str]			     =  t

	return min_numerator


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


def 						lowerCAmelCase_		(      _snake_case   :						int     )       ->	int:







	'''simple docstring'''


	if not isinstance(_snake_case   ,     _snake_case     ) or number < 0:
		raise ValueError("Input must be a non-negative integer"     )

	__magic_name__	:	Dict			     =  number & ~(number - 1)
	__magic_name__	:	Optional[Any]			     =  0
	while intermediate:
		intermediate >>= 1
		index += 1
	return index - 1


if __name__ == "__main__":
				import doctest

				doctest.testmod(verbose=True)
