




'''simple docstring'''






import math

import torch
from torch import nn
from torch.nn import init

from .binarizer import MagnitudeBinarizer, ThresholdBinarizer, TopKBinarizer



class    A						(					nn.Linear						):




				'''simple docstring'''





				def __init__(self					,    _UpperCAmelCase					,    _UpperCAmelCase					,    _UpperCAmelCase = True					,    _UpperCAmelCase = "constant"					,    _UpperCAmelCase = 0.0					,    _UpperCAmelCase = "topK"					,    )      ->			Optional[int]:
							super(_UpperCAmelCase					,    self     ).__init__(in_features=_UpperCAmelCase					,    out_features=_UpperCAmelCase					,    bias=_UpperCAmelCase     )
							assert pruning_method in ["topK", "threshold", "sigmoied_threshold", "magnitude", "l0"]
							__UpperCamelCase :     Tuple										=  pruning_method

							if self.pruning_method in ["topK", "threshold", "sigmoied_threshold", "l0"]:
										__UpperCamelCase :     Any										=  mask_scale
										__UpperCamelCase :     Tuple										=  mask_init
										__UpperCamelCase :     Tuple										=  nn.Parameter(torch.empty(self.weight.size()     )     )
										self.init_mask()
				def 			a_			(self     )      ->			Optional[Any]:
							if self.mask_init == "constant":
										init.constant_(self.mask_scores					,    val=self.mask_scale     )
							elif self.mask_init == "uniform":
										init.uniform_(self.mask_scores					,    a=-self.mask_scale					,    b=self.mask_scale     )
							elif self.mask_init == "kaiming":
										init.kaiming_uniform_(self.mask_scores					,    a=math.sqrt(5     )     )





				def 			a_			(self					,    _UpperCAmelCase					,    _UpperCAmelCase     )      ->			Optional[Any]:
							# Get the mask
							if self.pruning_method == "topK":
										__UpperCamelCase :     Tuple										=  TopKBinarizer.apply(self.mask_scores					,    _UpperCAmelCase     )
							elif self.pruning_method in ["threshold", "sigmoied_threshold"]:
										__UpperCamelCase :     Optional[Any]										=  "sigmoied" in self.pruning_method
										__UpperCamelCase :     Dict										=  ThresholdBinarizer.apply(self.mask_scores					,    _UpperCAmelCase					,    _UpperCAmelCase     )
							elif self.pruning_method == "magnitude":
										__UpperCamelCase :     List[str]										=  MagnitudeBinarizer.apply(self.weight					,    _UpperCAmelCase     )
							elif self.pruning_method == "l0":
										__UpperCamelCase						,   __UpperCamelCase						,   __UpperCamelCase :     Tuple										=  -0.1, 1.1, 2 / 3
										if self.training:
													__UpperCamelCase :     Tuple										=  torch.zeros_like(self.mask_scores     ).uniform_().clamp(0.0_001					,    0.9_999     )
													__UpperCamelCase :     Union[str, Any]										=  torch.sigmoid((u.log() - (1 - u).log() + self.mask_scores) / b     )
										else:
													__UpperCamelCase :     int										=  torch.sigmoid(self.mask_scores     )
										__UpperCamelCase :     str										=  s * (r - l) + l
										__UpperCamelCase :     Any										=  s_bar.clamp(min=0.0					,    max=1.0     )
							# Mask weights with computed mask
							__UpperCamelCase :     List[Any]										=  mask * self.weight
							# Compute output (linear layer) with masked weights
							return nn.functional.linear(_UpperCAmelCase					,    _UpperCAmelCase					,    self.bias     )









'''simple docstring'''






import itertools

def      __lowerCAmelCase   (       snake_case__		):
			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   (       ):
			return sum(
			    {
			        int("".join(pandigital[5:9]		)		)
			        for pandigital in itertools.permutations("123456789"		)
			        if is_combination_valid(snake_case__		)
			    }		)


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



