





'''simple docstring'''






from __future__ import annotations





def    lowercase_   (		lowercase__    ) ->List[str]:
						_snake_case: Optional[int]	       =		[0] * max_one

						for i in range(0					,	snake_case__    ):
												_snake_case: List[str]	       =		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    lowercase_   (		lowercase__					,	lowercase__    ) ->int:
						return sorted(str(snake_case__    )    ) == sorted(str(snake_case__    )    )





def    lowercase_   (		lowercase__ = 1000_0000    ) ->int:
						_snake_case: Optional[int]	       =		1  # i
						_snake_case: Union[str, Any]	       =		0  # φ(i)
						_snake_case: int	       =		get_totients(max_n + 1    )

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

												if i * min_denominator < min_numerator * t and has_same_digits(snake_case__					,	snake_case__    ):
																		_snake_case: int	       =		i
																		_snake_case: Dict	       =		t

						return min_numerator


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











'''simple docstring'''






def      __lowerCAmelCase   (       snake_case__		):

			for insert_index, insert_value in enumerate(collection[1:]		):
						__UpperCamelCase :     Union[str, Any]										=  insert_index
						while insert_index >= 0 and insert_value < collection[insert_index]:
									__UpperCamelCase :     int										=  collection[insert_index]
									insert_index -= 1
						if insert_index != temp_index:
									__UpperCamelCase :     Tuple										=  insert_value
			return collection


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

				testmod()

				_lowerCAmelCase       =   input('''Enter numbers separated by a comma:\n''').strip()
				_lowerCAmelCase       =   [int(item) for item in user_input.split(''',''')]
				print(f'{insertion_sort(unsorted) = }')



