






"""simple docstring"""
import torch
from torch import autograd



class 		a_      (	autograd.Function ):







      '''simple docstring'''

      @staticmethod
      def 			a__							(lowerCamelCase_,     lowerCamelCase_,     lowerCamelCase_,     lowerCamelCase_					):

       '''simple docstring'''



       lowerCamelCase__     :			Dict     				=						inputs.numel()
       lowerCamelCase__     :			Any     				=						int(0.005 * nb_elems					) + 1
       if sigmoid:
        lowerCamelCase__     :			Dict     				=						(torch.sigmoid(lowerCamelCase_					) > threshold).type(inputs.type()					)
       else:
        lowerCamelCase__     :			Dict     				=						(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
        lowerCamelCase__     :			Optional[int]     				=						inputs.flatten().kthvalue(max(nb_elems - nb_min,     1					)					).values
        lowerCamelCase__     :			Dict     				=						(inputs > k_threshold).type(inputs.type()					)
       return mask





      @staticmethod
      def 			a__							(lowerCamelCase_,     lowerCamelCase_					):

       '''simple docstring'''



       return gradOutput, None, None



class 		a_      (	autograd.Function ):







      '''simple docstring'''

      @staticmethod
      def 			a__							(lowerCamelCase_,     lowerCamelCase_,     lowerCamelCase_					):

       '''simple docstring'''



       lowerCamelCase__     :			Dict     				=						inputs.clone()
       lowerCamelCase__				,     lowerCamelCase__     :			List[Any]     				=						inputs.flatten().sort(descending=lowerCamelCase_					)
       lowerCamelCase__     :			Optional[int]     				=						int(threshold * inputs.numel()					)

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





      @staticmethod
      def 			a__							(lowerCamelCase_,     lowerCamelCase_					):

       '''simple docstring'''



       return gradOutput, None



class 		a_      (	snake_case_ ):







      '''simple docstring'''

      @staticmethod
      def 			a__							(lowerCamelCase_,     lowerCamelCase_					):

       '''simple docstring'''



       lowerCamelCase__     :			int     				=						inputs.clone()
       lowerCamelCase__				,     lowerCamelCase__     :			Dict     				=						inputs.abs().flatten().sort(descending=lowerCamelCase_					)
       lowerCamelCase__     :			Union[str, Any]     				=						int(threshold * inputs.numel()					)

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



"""simple docstring"""


import itertools



def     _lowerCamelCase(__UpperCamelCase       )				-> List[str]:
	return (
	    int("""""".join(combination[0:2]       )       ) * int("""""".join(combination[2:5]       )       )
	    == int("""""".join(combination[5:9]       )       )
	) or (
	    int("""""".join(combination[0]       )       ) * int("""""".join(combination[1:5]       )       )
	    == int("""""".join(combination[5:9]       )       )
	)



def     _lowerCamelCase()				-> Dict:
	return sum(
	    {
	        int("""""".join(pandigital[5:9]       )       )
	        for pandigital in itertools.permutations("""123456789"""       )
	        if is_combination_valid(__UpperCamelCase       )
	    }       )


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



