



"""simple docstring"""

from __future__ import annotations
def    __snake_case       (  __A			:	int    )    ->					int:






				'''simple docstring'''
				SCREAMING_SNAKE_CASE	:       int 							=    [0] * max_one

				for i in range(0       ,		lowercase__    ):
								SCREAMING_SNAKE_CASE	:       Union[str, Any] 							=    i

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

				return totients
def    __snake_case       (  __A			:	int       ,		__A			:	int    )    ->					Tuple:






				'''simple docstring'''
				return sorted(str(lowercase__    )    ) == sorted(str(lowercase__    )    )
def    __snake_case       (  __A			:	int = 10000000    )    ->					Union[str, Any]:






				'''simple docstring'''
				SCREAMING_SNAKE_CASE	:       Optional[int] 							=    1  # i
				SCREAMING_SNAKE_CASE	:       Optional[Any] 							=    0  # φ(i)
				SCREAMING_SNAKE_CASE	:       Union[str, Any] 							=    get_totients(max_n + 1    )

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

								if i * min_denominator < min_numerator * t and has_same_digits(lowercase__       ,		lowercase__    ):
												SCREAMING_SNAKE_CASE	:       Optional[Any] 							=    i
												SCREAMING_SNAKE_CASE	:       int 							=    t

				return min_numerator


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






"""simple docstring"""

def    __snake_case       (  __A			:	int    )    ->					int:






				'''simple docstring'''
				if not isinstance(__A       ,		__A    ):
								raise ValueError('double_factorial() only accepts integral values'    )
				if num < 0:
								raise ValueError('double_factorial() not defined for negative values'    )
				SCREAMING_SNAKE_CASE	:       List[str] 							=    1
				for i in range(__A       ,		0       ,		-2    ):
								value *= i
				return value


if __name__ == "__main__":
							import doctest

							doctest.testmod()





