






from __future__ import annotations

__UpperCAmelCase      =				"Alexander Joslin"





def 						A_					(						lowercase_			)				->int:







 """simple docstring"""

 if number <= 0:
  SCREAMING_SNAKE_CASE				    =		f'''n must be greater than 0. Got n = {number}'''
  raise ValueError(lowercase_			)

 SCREAMING_SNAKE_CASE				    =		[number + 1] * (number + 1)

 # starting position
 SCREAMING_SNAKE_CASE				    =		0
 for i in range(1	,  lowercase_			):
  SCREAMING_SNAKE_CASE				    =		min(table[i + 1]	,  table[i] + 1			)
  # check if out of bounds
  if i * 2 <= number:
   SCREAMING_SNAKE_CASE				    =		min(table[i * 2]	,  table[i] + 1			)
  # check if out of bounds
  if i * 3 <= number:
   SCREAMING_SNAKE_CASE				    =		min(table[i * 3]	,  table[i] + 1			)
 return table[number]


if __name__ == "__main__":
      import doctest

      doctest.testmod()





import torch
from torch import autograd







class      SCREAMING_SNAKE_CASE__					(  autograd.Function    ):

       @staticmethod
       def 			snake_case__    (							_lowerCAmelCase					:     Any			,			_lowerCAmelCase					:     torch.tensor			,			_lowerCAmelCase					:     float			,			_lowerCAmelCase					:     bool			):
           __snake_case       :				Optional[int] 			=    inputs.numel()
           __snake_case       :				str 			=    int(0.005 * nb_elems			) + 1
           if sigmoid:
               __snake_case       :				Union[str, Any] 			=    (torch.sigmoid(_lowerCAmelCase			) > threshold).type(inputs.type()			)
           else:
               __snake_case       :				Any 			=    (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
               __snake_case       :				Dict 			=    inputs.flatten().kthvalue(max(nb_elems - nb_min			,			1			)			).values
               __snake_case       :				List[str] 			=    (inputs > k_threshold).type(inputs.type()			)
           return mask





       @staticmethod
       def 			snake_case__    (							_lowerCAmelCase					:     str			,			_lowerCAmelCase					:     Tuple			):
           return gradOutput, None, None







class      SCREAMING_SNAKE_CASE__					(  autograd.Function    ):

       @staticmethod
       def 			snake_case__    (							_lowerCAmelCase					:     Optional[int]			,			_lowerCAmelCase					:     torch.tensor			,			_lowerCAmelCase					:     float			):
           __snake_case       :				str 			=    inputs.clone()
           __snake_case			, __snake_case       :				Dict 			=    inputs.flatten().sort(descending=_lowerCAmelCase			)
           __snake_case       :				Optional[Any] 			=    int(threshold * inputs.numel()			)

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





       @staticmethod
       def 			snake_case__    (							_lowerCAmelCase					:     Any			,			_lowerCAmelCase					:     Optional[Any]			):
           return gradOutput, None







class      SCREAMING_SNAKE_CASE__					(  __UpperCamelCase    ):

       @staticmethod
       def 			snake_case__    (							_lowerCAmelCase					:     torch.tensor			,			_lowerCAmelCase					:     float			):
           __snake_case       :				List[str] 			=    inputs.clone()
           __snake_case			, __snake_case       :				str 			=    inputs.abs().flatten().sort(descending=_lowerCAmelCase			)
           __snake_case       :				List[Any] 			=    int(threshold * inputs.numel()			)

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



