



"""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    SCREAMING_SNAKE_CASE__						(      UpperCAmelCase__				):

   def __init__(     self   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE=None   ,  _SCREAMING_SNAKE_CASE=None   ,  _SCREAMING_SNAKE_CASE=0		)						->   Optional[Any]:





    '''simple docstring'''




    UpperCAmelCase			:      List[Any]			=			1.0 if scale is None else scale
    UpperCAmelCase			:      int			=			0.0 if loc is None else loc

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

   @property
   def 			SCREAMING_SNAKE_CASE  (     self		)						->   Any:





    '''simple docstring'''




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

   @property
   def 			SCREAMING_SNAKE_CASE  (     self		)						->   List[str]:





    '''simple docstring'''




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




   @property
   def 			SCREAMING_SNAKE_CASE  (     self		)						->   Optional[Any]:





    '''simple docstring'''




    return self.variance.sqrt()



class    SCREAMING_SNAKE_CASE__						(      nn.Module				):

   def __init__(     self   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE   ,  **_SCREAMING_SNAKE_CASE		)						->   None:





    '''simple docstring'''




    super().__init__(**_SCREAMING_SNAKE_CASE		)
    UpperCAmelCase			:      str			=			args_dim
    UpperCAmelCase			:      Union[str, Any]			=			nn.ModuleList([nn.Linear(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		) for dim in args_dim.values()]		)
    UpperCAmelCase			:      Any			=			domain_map




   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE		)						->   Tuple[torch.Tensor]:





    '''simple docstring'''




    UpperCAmelCase			:      Optional[Any]			=			[proj(_SCREAMING_SNAKE_CASE		) for proj in self.proj]

    return self.domain_map(*_SCREAMING_SNAKE_CASE		)



class    SCREAMING_SNAKE_CASE__						(      nn.Module				):

   def __init__(     self   ,  _SCREAMING_SNAKE_CASE		)						->   Tuple:





    '''simple docstring'''




    super().__init__()
    UpperCAmelCase			:      List[str]			=			function




   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE   ,  *_SCREAMING_SNAKE_CASE		)						->   List[str]:





    '''simple docstring'''




    return self.function(_SCREAMING_SNAKE_CASE   ,  *_SCREAMING_SNAKE_CASE		)



class    SCREAMING_SNAKE_CASE__						:
   __lowerCAmelCase						:     type
   __lowerCAmelCase						:     int
   __lowerCAmelCase						:     Dict[str, int]

   def __init__(     self   ,  _SCREAMING_SNAKE_CASE = 1		)						->   None:





    '''simple docstring'''




    UpperCAmelCase			:      Optional[int]			=			dim
    UpperCAmelCase			:      Dict			=			{k: dim * self.args_dim[k] for k in self.args_dim}

   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE		)						->   Union[str, Any]:





    '''simple docstring'''




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

   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE = None   ,  _SCREAMING_SNAKE_CASE = None   ,  )						->   Distribution:





    '''simple docstring'''




    UpperCAmelCase			:      Tuple			=			self._base_distribution(_SCREAMING_SNAKE_CASE		)
    if loc is None and scale is None:
     return distr
    else:
     return AffineTransformed(_SCREAMING_SNAKE_CASE   ,  loc=_SCREAMING_SNAKE_CASE   ,  scale=_SCREAMING_SNAKE_CASE   ,  event_dim=self.event_dim		)

   @property
   def 			SCREAMING_SNAKE_CASE  (     self		)						->   Tuple:





    '''simple docstring'''




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

   @property
   def 			SCREAMING_SNAKE_CASE  (     self		)						->   int:





    '''simple docstring'''




    return len(self.event_shape		)

   @property
   def 			SCREAMING_SNAKE_CASE  (     self		)						->   float:





    '''simple docstring'''




    return 0.0

   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE		)						->   nn.Module:





    '''simple docstring'''




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

   def 			SCREAMING_SNAKE_CASE  (     self   ,  *_SCREAMING_SNAKE_CASE		)						->   List[str]:





    '''simple docstring'''




    raise NotImplementedError()




   @staticmethod
   def 			SCREAMING_SNAKE_CASE  (     _SCREAMING_SNAKE_CASE		)						->   torch.Tensor:





    '''simple docstring'''




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



class    SCREAMING_SNAKE_CASE__						(      UpperCAmelCase__				):
   __lowerCAmelCase						:     Dict[str, int]		=		{"df": 1, "loc": 1, "scale": 1}
   __lowerCAmelCase						:     type		=		StudentT

   @classmethod
   def 			SCREAMING_SNAKE_CASE  (     cls   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		)						->   Union[str, Any]:





    '''simple docstring'''




    UpperCAmelCase			:      Union[str, Any]			=			cls.squareplus(_SCREAMING_SNAKE_CASE		).clamp_min(torch.finfo(scale.dtype		).eps		)
    UpperCAmelCase			:      int			=			2.0 + cls.squareplus(_SCREAMING_SNAKE_CASE		)
    return df.squeeze(-1		), loc.squeeze(-1		), scale.squeeze(-1		)



class    SCREAMING_SNAKE_CASE__						(      UpperCAmelCase__				):
   __lowerCAmelCase						:     Dict[str, int]		=		{"loc": 1, "scale": 1}
   __lowerCAmelCase						:     type		=		Normal

   @classmethod
   def 			SCREAMING_SNAKE_CASE  (     cls   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		)						->   List[Any]:





    '''simple docstring'''




    UpperCAmelCase			:      List[Any]			=			cls.squareplus(_SCREAMING_SNAKE_CASE		).clamp_min(torch.finfo(scale.dtype		).eps		)
    return loc.squeeze(-1		), scale.squeeze(-1		)



class    SCREAMING_SNAKE_CASE__						(      UpperCAmelCase__				):
   __lowerCAmelCase						:     Dict[str, int]		=		{"total_count": 1, "logits": 1}
   __lowerCAmelCase						:     type		=		NegativeBinomial

   @classmethod
   def 			SCREAMING_SNAKE_CASE  (     cls   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		)						->   Optional[int]:





    '''simple docstring'''




    UpperCAmelCase			:      List[Any]			=			cls.squareplus(_SCREAMING_SNAKE_CASE		)
    return total_count.squeeze(-1		), logits.squeeze(-1		)

   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE		)						->   Distribution:





    '''simple docstring'''




    UpperCAmelCase			:      Union[str, Any]			=			distr_args
    if self.dim == 1:
     return self.distribution_class(total_count=_SCREAMING_SNAKE_CASE   ,  logits=_SCREAMING_SNAKE_CASE		)
    else:
     return Independent(self.distribution_class(total_count=_SCREAMING_SNAKE_CASE   ,  logits=_SCREAMING_SNAKE_CASE		)   ,  1		)




   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE = None   ,  _SCREAMING_SNAKE_CASE = None		)						->   Distribution:





    '''simple docstring'''




    UpperCAmelCase			:      int			=			distr_args

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

    return self._base_distribution((total_count, logits)		)





"""simple docstring"""
from __future__ import annotations

from collections.abc import Iterable, Iterator
from dataclasses import dataclass

A:     List[Any]										=	(3, 9, -1_1, 0, 7, 5, 1, -1)
A:     Union[str, Any]										=	(4, 6, 2, 0, 8, 1_0, 3, -2)



@dataclass
class    SCREAMING_SNAKE_CASE__						:
   __lowerCAmelCase						:     int
   __lowerCAmelCase						:     Node | None



class    SCREAMING_SNAKE_CASE__						:

   def __init__(     self   ,  _SCREAMING_SNAKE_CASE		)						->   None:





    '''simple docstring'''




    UpperCAmelCase			:      Node | None			=			None
    for i in sorted(_SCREAMING_SNAKE_CASE   ,  reverse=_SCREAMING_SNAKE_CASE		):
     UpperCAmelCase			:      Union[str, Any]			=			Node(_SCREAMING_SNAKE_CASE   ,  self.head		)

   def __iter__(     self		)						->   Iterator[int]:





    '''simple docstring'''




    UpperCAmelCase			:      Optional[Any]			=			self.head
    while node:
     yield node.data
     UpperCAmelCase			:      List[str]			=			node.next_node

   def __len__(     self		)						->   int:





    '''simple docstring'''




    return sum(1 for _ in self		)




   def __str__(     self		)						->   str:





    '''simple docstring'''




    return " -> ".join([str(_SCREAMING_SNAKE_CASE		) for node in self]		)

def    _snake_case		(		UpperCamelCase		:	SortedLinkedList    ,	UpperCamelCase		:	SortedLinkedList		):
 return SortedLinkedList(list(UpperCamelCase		) + list(UpperCamelCase		)		)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      A:     Dict										=	SortedLinkedList
      print(merge_lists(SSL(test_data_odd), SSL(test_data_even)))
