






def    UpperCamelCase__  (   UpperCAmelCase     )     ->		list:







							"""simple docstring"""





							_a  :    Tuple			=						len(UpperCAmelCase     )
							for cycle_start in range(0    ,	array_len - 1     ):
														_a  :    Dict			=						array[cycle_start]

														_a  :    List[str]			=						cycle_start
														for i in range(cycle_start + 1    ,	UpperCAmelCase     ):
																					if array[i] < item:
																												pos += 1

														if pos == cycle_start:
																					continue

														while item == array[pos]:
																					pos += 1

														_a		,					_a  :    int			=						item, array[pos]
														while pos != cycle_start:
																					_a  :    Any			=						cycle_start
																					for i in range(cycle_start + 1    ,	UpperCAmelCase     ):
																												if array[i] < item:
																																			pos += 1

																					while item == array[pos]:
																												pos += 1

																					_a		,					_a  :    Dict			=						item, array[pos]

							return array


if __name__ == "__main__":
						assert cycle_sort([4, 5, 3, 2, 1]) == [1, 2, 3, 4, 5]
						assert cycle_sort([0, 1, -10, 15, 2, -2]) == [-10, -2, 0, 1, 2, 15]







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() = }''')