





"""simple docstring"""





import torch
from torch import autograd





class 			snake_case		(   autograd.Function   ):

      @staticmethod
      def 						SCREAMING_SNAKE_CASE_			(			_lowerCamelCase   :List[Any]						,							_lowerCamelCase   :torch.tensor						,							_lowerCamelCase   :float						,							_lowerCamelCase   :bool						):
       __SCREAMING_SNAKE_CASE :			int												=       inputs.numel()
       __SCREAMING_SNAKE_CASE :			str												=       int(0.0_0_5 * nb_elems						) + 1
       if sigmoid:
        __SCREAMING_SNAKE_CASE :			Optional[int]												=       (torch.sigmoid(_lowerCamelCase						) > threshold).type(inputs.type()						)
       else:
        __SCREAMING_SNAKE_CASE :			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
        __SCREAMING_SNAKE_CASE :			List[Any]												=       inputs.flatten().kthvalue(max(nb_elems - nb_min						,							1						)						).values
        __SCREAMING_SNAKE_CASE :			int												=       (inputs > k_threshold).type(inputs.type()						)
       return mask



      @staticmethod
      def 						SCREAMING_SNAKE_CASE_			(			_lowerCamelCase   :List[str]						,							_lowerCamelCase   :List[str]						):
       return gradOutput, None, None







class 			snake_case		(   autograd.Function   ):

      @staticmethod
      def 						SCREAMING_SNAKE_CASE_			(			_lowerCamelCase   :Tuple						,							_lowerCamelCase   :torch.tensor						,							_lowerCamelCase   :float						):
       __SCREAMING_SNAKE_CASE :			Optional[Any]												=       inputs.clone()
       __SCREAMING_SNAKE_CASE							,      __SCREAMING_SNAKE_CASE :			List[str]												=       inputs.flatten().sort(descending=_lowerCamelCase						)
       __SCREAMING_SNAKE_CASE :			Tuple												=       int(threshold * inputs.numel()						)

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



      @staticmethod
      def 						SCREAMING_SNAKE_CASE_			(			_lowerCamelCase   :Dict						,							_lowerCamelCase   :Optional[int]						):
       return gradOutput, None







class 			snake_case		(   __UpperCAmelCase   ):

      @staticmethod
      def 						SCREAMING_SNAKE_CASE_			(			_lowerCamelCase   :torch.tensor						,							_lowerCamelCase   :float						):
       __SCREAMING_SNAKE_CASE :			Optional[Any]												=       inputs.clone()
       __SCREAMING_SNAKE_CASE							,      __SCREAMING_SNAKE_CASE :			Optional[Any]												=       inputs.abs().flatten().sort(descending=_lowerCamelCase						)
       __SCREAMING_SNAKE_CASE :			int												=       int(threshold * inputs.numel()						)

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









"""simple docstring"""







import math
from decimal import Decimal, getcontext





def 						lowercase__(A = 4_000_000						)				->int:




						"""simple docstring"""



						try:
												lowercase__				:      int=       int(A						)
						except (TypeError, ValueError):
												raise TypeError("Parameter n must be int or castable to int."						)
						if n <= 0:
												raise ValueError("Parameter n must be greater than or equal to one."						)
						lowercase__				:      Dict=       100
						lowercase__				:      Optional[Any]=       (Decimal(5						) ** Decimal(0.5						) + 1) / Decimal(2						)

						lowercase__				:      str=       (math.floor(math.log(n * (phi + 2)					,		A						) - 1						) // 3) * 3 + 2
						lowercase__				:      Optional[Any]=       Decimal(round(phi ** Decimal(index + 1						)						)						) / (phi + 2)
						lowercase__				:      Tuple=       num // 2
						return int(A						)


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






