





"""simple docstring"""
def 					A__				(			UpperCamelCase       ):
							if num < 0:
														return False

							A		=  num
							A		=  0
							while num > 0:
														A		=  rev_num * 10 + (num % 10)
														num //= 10

							return num_copy == rev_num


if __name__ == "__main__":
		import doctest

		doctest.testmod()









"""simple docstring"""
from typing import Callable, Dict, Optional, Tuple

import torch
from torch import nn
from torch.distributions import (
    AffineTransform,
    Distribution,
    Independent,
    NegativeBinomial,
    Normal,
    StudentT,
    TransformedDistribution,
)






class 					_UpperCAmelCase   (	lowercase_ ):


					def __init__(					self			:int     ,       __UpperCamelCase			:Distribution     ,       __UpperCamelCase			:Dict=None     ,       __UpperCamelCase			:Optional[int]=None     ,       __UpperCamelCase			:List[str]=0		):
												A		=  1.0 if scale is None else scale
												A		=  0.0 if loc is None else loc

												super().__init__(__UpperCamelCase     ,       [AffineTransform(loc=self.loc     ,       scale=self.scale     ,       event_dim=__UpperCamelCase		)]		)


					@property
					def 	lowerCamelCase       (					self			:Any		):
												return self.base_dist.mean * self.scale + self.loc


					@property
					def 	lowerCamelCase       (					self			:Optional[int]		):
												return self.base_dist.variance * self.scale**2


					@property
					def 	lowerCamelCase       (					self			:Dict		):
												return self.variance.sqrt()







class 					_UpperCAmelCase   (	nn.Module ):


					def __init__(					self			:Dict     ,       __UpperCamelCase			:int     ,       __UpperCamelCase			:Dict[str, int]     ,       __UpperCamelCase			:Callable[..., Tuple[torch.Tensor]]     ,       **__UpperCamelCase			:str		):
												super().__init__(**__UpperCamelCase		)
												A		=  args_dim
												A		=  nn.ModuleList([nn.Linear(__UpperCamelCase     ,       __UpperCamelCase		) for dim in args_dim.values()]		)
												A		=  domain_map


					def 	lowerCamelCase       (					self			:int     ,       __UpperCamelCase			:torch.Tensor		):
												A		=  [proj(__UpperCamelCase		) for proj in self.proj]

												return self.domain_map(*__UpperCamelCase		)







class 					_UpperCAmelCase   (	nn.Module ):


					def __init__(					self			:Dict     ,       __UpperCamelCase			:int		):
												super().__init__()
												A		=  function


					def 	lowerCamelCase       (					self			:List[str]     ,       __UpperCamelCase			:Any     ,       *__UpperCamelCase			:Any		):
												return self.function(__UpperCamelCase     ,       *__UpperCamelCase		)







class 					_UpperCAmelCase   :
					UpperCamelCase      =							42
					UpperCamelCase      =							42
					UpperCamelCase      =							42


					def __init__(					self			:Any     ,       __UpperCamelCase			:int = 1		):
												A		=  dim
												A		=  {k: dim * self.args_dim[k] for k in self.args_dim}


					def 	lowerCamelCase       (					self			:List[Any]     ,       __UpperCamelCase			:Dict		):
												if self.dim == 1:
																			return self.distribution_class(*__UpperCamelCase		)
												else:
																			return Independent(self.distribution_class(*__UpperCamelCase		)     ,       1		)


					def 	lowerCamelCase       (					self			:int     ,       __UpperCamelCase			:List[str]     ,       __UpperCamelCase			:Optional[torch.Tensor] = None     ,       __UpperCamelCase			:Optional[torch.Tensor] = None     ,       ):
												A		=  self._base_distribution(__UpperCamelCase		)
												if loc is None and scale is None:
																			return distr
												else:
																			return AffineTransformed(__UpperCamelCase     ,       loc=__UpperCamelCase     ,       scale=__UpperCamelCase     ,       event_dim=self.event_dim		)


					@property
					def 	lowerCamelCase       (					self			:List[Any]		):
												return () if self.dim == 1 else (self.dim,)


					@property
					def 	lowerCamelCase       (					self			:Tuple		):
												return len(self.event_shape		)


					@property
					def 	lowerCamelCase       (					self			:int		):
												return 0.0


					def 	lowerCamelCase       (					self			:str     ,       __UpperCamelCase			:int		):
												return ParameterProjection(
												    in_features=__UpperCamelCase     ,       args_dim=self.args_dim     ,       domain_map=LambdaLayer(self.domain_map		)     ,       )


					def 	lowerCamelCase       (					self			:List[Any]     ,       *__UpperCamelCase			:torch.Tensor		):
												raise NotImplementedError()


					@staticmethod
					def 	lowerCamelCase       (					__UpperCamelCase			:torch.Tensor		):
												return (x + torch.sqrt(torch.square(__UpperCamelCase		) + 4.0		)) / 2.0







class 					_UpperCAmelCase   (	lowercase_ ):
					UpperCamelCase      =							{"df": 1, "loc": 1, "scale": 1}
					UpperCamelCase      =							StudentT


					@classmethod
					def 	lowerCamelCase       (					cls			:List[str]     ,       __UpperCamelCase			:torch.Tensor     ,       __UpperCamelCase			:torch.Tensor     ,       __UpperCamelCase			:torch.Tensor		):
												A		=  cls.squareplus(__UpperCamelCase		).clamp_min(torch.finfo(scale.dtype		).eps		)
												A		=  2.0 + cls.squareplus(__UpperCamelCase		)
												return df.squeeze(-1		), loc.squeeze(-1		), scale.squeeze(-1		)







class 					_UpperCAmelCase   (	lowercase_ ):
					UpperCamelCase      =							{"loc": 1, "scale": 1}
					UpperCamelCase      =							Normal


					@classmethod
					def 	lowerCamelCase       (					cls			:List[Any]     ,       __UpperCamelCase			:torch.Tensor     ,       __UpperCamelCase			:torch.Tensor		):
												A		=  cls.squareplus(__UpperCamelCase		).clamp_min(torch.finfo(scale.dtype		).eps		)
												return loc.squeeze(-1		), scale.squeeze(-1		)







class 					_UpperCAmelCase   (	lowercase_ ):
					UpperCamelCase      =							{"total_count": 1, "logits": 1}
					UpperCamelCase      =							NegativeBinomial


					@classmethod
					def 	lowerCamelCase       (					cls			:str     ,       __UpperCamelCase			:torch.Tensor     ,       __UpperCamelCase			:torch.Tensor		):
												A		=  cls.squareplus(__UpperCamelCase		)
												return total_count.squeeze(-1		), logits.squeeze(-1		)


					def 	lowerCamelCase       (					self			:Tuple     ,       __UpperCamelCase			:List[str]		):
												A,	A		=  distr_args
												if self.dim == 1:
																			return self.distribution_class(total_count=__UpperCamelCase     ,       logits=__UpperCamelCase		)
												else:
																			return Independent(self.distribution_class(total_count=__UpperCamelCase     ,       logits=__UpperCamelCase		)     ,       1		)


					def 	lowerCamelCase       (					self			:List[str]     ,       __UpperCamelCase			:str     ,       __UpperCamelCase			:Optional[torch.Tensor] = None     ,       __UpperCamelCase			:Optional[torch.Tensor] = None		):
												A,	A		=  distr_args

												if scale is not None:
																			# See scaling property of Gamma.
																			logits += scale.log()

												return self._base_distribution((total_count, logits)		)


