

"""simple docstring"""




import sys
def   __SCREAMING_SNAKE_CASE		(		lowercase__     ,				lowercase__ ):
					"""simple docstring"""
					if not numbers:
										return 0
					if target == 0 and target in numbers:
										return 0
					if not isinstance(lowercase__     ,				(list, tuple) ) or not all(
					    isinstance(lowercase__     ,				lowercase__ ) for number in numbers ):
										raise ValueError("numbers must be an iterable of integers" )

					A     =   A     =   A     =   0
					A     =   sys.maxsize

					while right < len(lowercase__ ):
										curr_sum += numbers[right]
										while curr_sum >= target and left <= right:
															A     =   min(lowercase__     ,				right - left + 1 )
															curr_sum -= numbers[left]
															left += 1
										right += 1

					return 0 if min_len == sys.maxsize else min_len













from __future__ import annotations






def    UpperCamelCase__  (   UpperCAmelCase     )     ->		list[int]:







							"""simple docstring"""





							_a  :    Optional[Any]			=						[0] * max_one

							for i in range(0    ,	UpperCAmelCase     ):
														_a  :    int			=						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    UpperCamelCase__  (   UpperCAmelCase    ,	UpperCAmelCase     )     ->		bool:







							"""simple docstring"""





							return sorted(str(UpperCAmelCase     )     ) == sorted(str(UpperCAmelCase     )     )






def    UpperCamelCase__  (   UpperCAmelCase = 10000000     )     ->		int:







							"""simple docstring"""





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

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

														if i * min_denominator < min_numerator * t and has_same_digits(UpperCAmelCase    ,	UpperCAmelCase     ):
																					_a  :    Any			=						i
																					_a  :    Union[str, Any]			=						t

							return min_numerator


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