






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		(_UpperCAmelCase   ):







			def __init__(     self:  Union[str, Any]				,     UpperCAmelCase_:  Distribution				,     UpperCAmelCase_:  int=None				,     UpperCAmelCase_:  Tuple=None				,     UpperCAmelCase_:  int=0					):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE     				=  1.0 if scale is None else scale
									_SCREAMING_SNAKE_CASE     				=  0.0 if loc is None else loc

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







			@property
			def 							UpperCamelCase				(     self:  Optional[Any]					):







									'''simple docstring'''




									return self.base_dist.mean * self.scale + self.loc







			@property
			def 							UpperCamelCase				(     self:  Union[str, Any]					):







									'''simple docstring'''




									return self.base_dist.variance * self.scale**2







			@property
			def 							UpperCamelCase				(     self:  Dict					):







									'''simple docstring'''




									return self.variance.sqrt()



class 				__UpperCAmelCase		(nn.Module   ):







			def __init__(     self:  List[Any]				,     UpperCAmelCase_:  int				,     UpperCAmelCase_:  Dict[str, int]				,     UpperCAmelCase_:  Callable[..., Tuple[torch.Tensor]]				,     **UpperCAmelCase_:  Union[str, Any]					):







									'''simple docstring'''




									super().__init__(**UpperCAmelCase_					)
									_SCREAMING_SNAKE_CASE     				=  args_dim
									_SCREAMING_SNAKE_CASE     				=  nn.ModuleList([nn.Linear(UpperCAmelCase_				,     UpperCAmelCase_					) for dim in args_dim.values()]					)
									_SCREAMING_SNAKE_CASE     				=  domain_map







			def 							UpperCamelCase				(     self:  Dict				,     UpperCAmelCase_:  torch.Tensor					):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE     				=  [proj(UpperCAmelCase_					) for proj in self.proj]

									return self.domain_map(*UpperCAmelCase_					)



class 				__UpperCAmelCase		(nn.Module   ):







			def __init__(     self:  Dict				,     UpperCAmelCase_:  List[str]					):







									'''simple docstring'''




									super().__init__()
									_SCREAMING_SNAKE_CASE     				=  function







			def 							UpperCamelCase				(     self:  Union[str, Any]				,     UpperCAmelCase_:  int				,     *UpperCAmelCase_:  str					):







									'''simple docstring'''




									return self.function(UpperCAmelCase_				,     *UpperCAmelCase_					)



class 				__UpperCAmelCase		:
			__snake_case    :				type
			__snake_case    :				int
			__snake_case    :				Dict[str, int]







			def __init__(     self:  int				,     UpperCAmelCase_:  int = 1					):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE     				=  dim
									_SCREAMING_SNAKE_CASE     				=  {k: dim * self.args_dim[k] for k in self.args_dim}







			def 							UpperCamelCase				(     self:  Optional[int]				,     UpperCAmelCase_:  Optional[Any]					):







									'''simple docstring'''




									if self.dim == 1:
															return self.distribution_class(*UpperCAmelCase_					)
									else:
															return Independent(self.distribution_class(*UpperCAmelCase_					)				,     1					)







			def 							UpperCamelCase				(     self:  Dict				,     UpperCAmelCase_:  Any				,     UpperCAmelCase_:  Optional[torch.Tensor] = None				,     UpperCAmelCase_:  Optional[torch.Tensor] = None				,     ):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE     				=  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 							UpperCamelCase				(     self:  List[Any]					):







									'''simple docstring'''




									return () if self.dim == 1 else (self.dim,)







			@property
			def 							UpperCamelCase				(     self:  Any					):







									'''simple docstring'''




									return len(self.event_shape					)







			@property
			def 							UpperCamelCase				(     self:  Optional[int]					):







									'''simple docstring'''




									return 0.0







			def 							UpperCamelCase				(     self:  int				,     UpperCAmelCase_:  int					):







									'''simple docstring'''




									return ParameterProjection(
									    in_features=UpperCAmelCase_				,     args_dim=self.args_dim				,     domain_map=LambdaLayer(self.domain_map					)				,     )







			def 							UpperCamelCase				(     self:  List[str]				,     *UpperCAmelCase_:  torch.Tensor					):







									'''simple docstring'''




									raise NotImplementedError()







			@staticmethod
			def 							UpperCamelCase				(     UpperCAmelCase_:  torch.Tensor					):







									'''simple docstring'''




									return (x + torch.sqrt(torch.square(UpperCAmelCase_					) + 4.0					)) / 2.0



class 				__UpperCAmelCase		(_UpperCAmelCase   ):
			__snake_case    :				Dict[str, int]									={"df": 1, "loc": 1, "scale": 1}
			__snake_case    :				type									=StudentT







			@classmethod
			def 							UpperCamelCase				(     cls:  List[Any]				,     UpperCAmelCase_:  torch.Tensor				,     UpperCAmelCase_:  torch.Tensor				,     UpperCAmelCase_:  torch.Tensor					):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE     				=  cls.squareplus(UpperCAmelCase_					).clamp_min(torch.finfo(scale.dtype					).eps					)
									_SCREAMING_SNAKE_CASE     				=  2.0 + cls.squareplus(UpperCAmelCase_					)
									return df.squeeze(-1					), loc.squeeze(-1					), scale.squeeze(-1					)



class 				__UpperCAmelCase		(_UpperCAmelCase   ):
			__snake_case    :				Dict[str, int]									={"loc": 1, "scale": 1}
			__snake_case    :				type									=Normal







			@classmethod
			def 							UpperCamelCase				(     cls:  str				,     UpperCAmelCase_:  torch.Tensor				,     UpperCAmelCase_:  torch.Tensor					):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE     				=  cls.squareplus(UpperCAmelCase_					).clamp_min(torch.finfo(scale.dtype					).eps					)
									return loc.squeeze(-1					), scale.squeeze(-1					)



class 				__UpperCAmelCase		(_UpperCAmelCase   ):
			__snake_case    :				Dict[str, int]									={"total_count": 1, "logits": 1}
			__snake_case    :				type									=NegativeBinomial







			@classmethod
			def 							UpperCamelCase				(     cls:  List[Any]				,     UpperCAmelCase_:  torch.Tensor				,     UpperCAmelCase_:  torch.Tensor					):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE     				=  cls.squareplus(UpperCAmelCase_					)
									return total_count.squeeze(-1					), logits.squeeze(-1					)







			def 							UpperCamelCase				(     self:  Union[str, Any]				,     UpperCAmelCase_:  int					):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE				,					_SCREAMING_SNAKE_CASE     				=  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 							UpperCamelCase				(     self:  Union[str, Any]				,     UpperCAmelCase_:  Any				,     UpperCAmelCase_:  Optional[torch.Tensor] = None				,     UpperCAmelCase_:  Optional[torch.Tensor] = None					):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE				,					_SCREAMING_SNAKE_CASE     				=  distr_args

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

									return self._base_distribution((total_count, logits)					)









UpperCamelCase			    =     {0: [2, 3], 1: [0], 2: [1], 3: [4], 4: []}

UpperCamelCase			    =     {0: [1, 2, 3], 1: [2], 2: [0], 3: [4], 4: [5], 5: [3]}

def 	__lowerCamelCase      (		snake_case__	,snake_case__	,snake_case__		)							->  list[int]:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE     				=  True
						_SCREAMING_SNAKE_CASE     				=  []

						for neighbour in graph[vert]:
												if not visited[neighbour]:
																		order += topology_sort(snake_case__	,snake_case__	,snake_case__		)

						order.append(snake_case__		)

						return order

def 	__lowerCamelCase      (		snake_case__	,snake_case__	,snake_case__		)							->  list[int]:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE     				=  True
						_SCREAMING_SNAKE_CASE     				=  [vert]

						for neighbour in reversed_graph[vert]:
												if not visited[neighbour]:
																		component += find_components(snake_case__	,snake_case__	,snake_case__		)

						return component




def 	__lowerCamelCase      (		snake_case__		)							->  list[list[int]]:






						"""simple docstring"""





						_SCREAMING_SNAKE_CASE     				=  len(snake_case__		) * [False]
						_SCREAMING_SNAKE_CASE     				=  {vert: [] for vert in range(len(snake_case__		)		)}

						for vert, neighbours in graph.items():
												for neighbour in neighbours:
																		reversed_graph[neighbour].append(snake_case__		)

						_SCREAMING_SNAKE_CASE     				=  []
						for i, was_visited in enumerate(snake_case__		):
												if not was_visited:
																		order += topology_sort(snake_case__	,snake_case__	,snake_case__		)

						_SCREAMING_SNAKE_CASE     				=  []
						_SCREAMING_SNAKE_CASE     				=  len(snake_case__		) * [False]

						for i in range(len(snake_case__		)		):
												_SCREAMING_SNAKE_CASE     				=  order[len(snake_case__		) - i - 1]
												if not visited[vert]:
																		_SCREAMING_SNAKE_CASE     				=  find_components(snake_case__	,snake_case__	,snake_case__		)
																		components_list.append(snake_case__		)

						return components_list

