





"""simple docstring"""




def        a_				(							_lowercase = 10**6   ):

						if n <= 0:
												raise ValueError('''Please enter an integer greater than 0'''   )

						_UpperCamelCase			:					Any     =    list(range(n + 1   )   )
						for number in range(2       ,						n + 1   ):
												if phi[number] == number:
																		phi[number] -= 1
																		for multiple in range(number * 2       ,						n + 1       ,						_lowercase   ):
																								_UpperCamelCase			:					List[str]     =    (phi[multiple] // number) * (number - 1)

						_UpperCamelCase			:					Union[str, Any]     =    1
						for number in range(1       ,						n + 1   ):
												if (answer / phi[answer]) < (number / phi[number]):
																		_UpperCamelCase			:					List[str]     =    number

						return answer


if __name__ == "__main__":
						print(solution())










"""simple docstring"""




import torch
from torch import autograd




class  _a						(      autograd.Function				):






				@staticmethod
				def 				snake_case	( lowerCAmelCase__		:    str, lowerCAmelCase__		:    torch.tensor, lowerCAmelCase__		:    float, lowerCAmelCase__		:    bool							)	->      List[Any]:




										'''simple docstring'''



										_UpperCamelCase			:					Optional[Any]     =    inputs.numel()
										_UpperCamelCase			:					int     =    int(0.005 * nb_elems							) + 1
										if sigmoid:
																_UpperCamelCase			:					Dict     =    (torch.sigmoid(lowerCAmelCase__							) > threshold).type(inputs.type()							)
										else:
																_UpperCamelCase			:					Optional[int]     =    (inputs > threshold).type(inputs.type()							)
										if mask.sum() < nb_min:
																# We limit the pruning so that at least 0.5% (half a percent) of the weights are remaining
																_UpperCamelCase			:					int     =    inputs.flatten().kthvalue(max(nb_elems - nb_min, 1							)							).values
																_UpperCamelCase			:					List[str]     =    (inputs > k_threshold).type(inputs.type()							)
										return mask






				@staticmethod
				def 				snake_case	( lowerCAmelCase__		:    str, lowerCAmelCase__		:    Optional[int]							)	->      Union[str, Any]:




										'''simple docstring'''



										return gradOutput, None, None




class  _a						(      autograd.Function				):






				@staticmethod
				def 				snake_case	( lowerCAmelCase__		:    Any, lowerCAmelCase__		:    torch.tensor, lowerCAmelCase__		:    float							)	->      Dict:




										'''simple docstring'''



										_UpperCamelCase			:					str     =    inputs.clone()
										_UpperCamelCase   ,							_UpperCamelCase			:					Union[str, Any]     =    inputs.flatten().sort(descending=lowerCAmelCase__							)
										_UpperCamelCase			:					Optional[Any]     =    int(threshold * inputs.numel()							)

										# flat_out and mask access the same memory.
										_UpperCamelCase			:					Tuple     =    mask.flatten()
										_UpperCamelCase			:					int     =    0
										_UpperCamelCase			:					Tuple     =    1
										return mask






				@staticmethod
				def 				snake_case	( lowerCAmelCase__		:    Any, lowerCAmelCase__		:    Union[str, Any]							)	->      int:




										'''simple docstring'''



										return gradOutput, None




class  _a						(      _lowerCAmelCase				):






				@staticmethod
				def 				snake_case	( lowerCAmelCase__		:    torch.tensor, lowerCAmelCase__		:    float							)	->      Dict:




										'''simple docstring'''



										_UpperCamelCase			:					List[Any]     =    inputs.clone()
										_UpperCamelCase   ,							_UpperCamelCase			:					Optional[int]     =    inputs.abs().flatten().sort(descending=lowerCAmelCase__							)
										_UpperCamelCase			:					List[Any]     =    int(threshold * inputs.numel()							)

										# flat_out and mask access the same memory.
										_UpperCamelCase			:					List[str]     =    mask.flatten()
										_UpperCamelCase			:					List[Any]     =    0
										_UpperCamelCase			:					str     =    1
										return mask



