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  _lowerCAmelCase     (  __lowerCamelCase	):

      def __init__(   self      ,				__UpperCAmelCase      ,				__UpperCAmelCase=None      ,				__UpperCAmelCase=None      ,				__UpperCAmelCase=0		):
        lowerCAmelCase__				:  Optional[Any]		       =     1.0 if scale is None else scale
        lowerCAmelCase__				:  List[Any]		       =     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 	__magic_name__(   self		):
        return self.base_dist.mean * self.scale + self.loc

      @property
      def 	__magic_name__(   self		):
        return self.base_dist.variance * self.scale**2







      @property
      def 	__magic_name__(   self		):
        return self.variance.sqrt()






class  _lowerCAmelCase     (  nn.Module	):

      def __init__(   self      ,				__UpperCAmelCase      ,				__UpperCAmelCase      ,				__UpperCAmelCase      ,				**__UpperCAmelCase		):
        super().__init__(**SCREAMING_SNAKE_CASE_		)
        lowerCAmelCase__				:  int		       =     args_dim
        lowerCAmelCase__				:  str		       =     nn.ModuleList([nn.Linear(SCREAMING_SNAKE_CASE_      ,				SCREAMING_SNAKE_CASE_		) for dim in args_dim.values()]		)
        lowerCAmelCase__				:  Dict		       =     domain_map







      def 	__magic_name__(   self      ,				__UpperCAmelCase		):
        lowerCAmelCase__				:  Dict		       =     [proj(SCREAMING_SNAKE_CASE_		) for proj in self.proj]

        return self.domain_map(*SCREAMING_SNAKE_CASE_		)






class  _lowerCAmelCase     (  nn.Module	):

      def __init__(   self      ,				__UpperCAmelCase		):
        super().__init__()
        lowerCAmelCase__				:  Optional[int]		       =     function







      def 	__magic_name__(   self      ,				__UpperCAmelCase      ,				*__UpperCAmelCase		):
        return self.function(SCREAMING_SNAKE_CASE_      ,				*SCREAMING_SNAKE_CASE_		)






class  _lowerCAmelCase     :
      A__		     =		42
      A__		     =		42
      A__		     =		42

      def __init__(   self      ,				__UpperCAmelCase = 1		):
        lowerCAmelCase__				:  Any		       =     dim
        lowerCAmelCase__				:  Optional[Any]		       =     {k: dim * self.args_dim[k] for k in self.args_dim}

      def 	__magic_name__(   self      ,				__UpperCAmelCase		):
        if self.dim == 1:
          return self.distribution_class(*SCREAMING_SNAKE_CASE_		)
        else:
          return Independent(self.distribution_class(*SCREAMING_SNAKE_CASE_		)      ,				1		)

      def 	__magic_name__(   self      ,				__UpperCAmelCase      ,				__UpperCAmelCase = None      ,				__UpperCAmelCase = None      ,				):
        lowerCAmelCase__				:  Union[str, Any]		       =     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 	__magic_name__(   self		):
        return () if self.dim == 1 else (self.dim,)

      @property
      def 	__magic_name__(   self		):
        return len(self.event_shape		)

      @property
      def 	__magic_name__(   self		):
        return 0.0

      def 	__magic_name__(   self      ,				__UpperCAmelCase		):
        return ParameterProjection(
            in_features=SCREAMING_SNAKE_CASE_      ,				args_dim=self.args_dim      ,				domain_map=LambdaLayer(self.domain_map		)      ,				)

      def 	__magic_name__(   self      ,				*__UpperCAmelCase		):
        raise NotImplementedError()







      @staticmethod
      def 	__magic_name__(   __UpperCAmelCase		):
        return (x + torch.sqrt(torch.square(SCREAMING_SNAKE_CASE_		) + 4.0		)) / 2.0






class  _lowerCAmelCase     (  __lowerCamelCase	):
      A__		     =		{'df': 1, 'loc': 1, 'scale': 1}
      A__		     =		StudentT

      @classmethod
      def 	__magic_name__(   cls      ,				__UpperCAmelCase      ,				__UpperCAmelCase      ,				__UpperCAmelCase		):
        lowerCAmelCase__				:  List[Any]		       =     cls.squareplus(SCREAMING_SNAKE_CASE_		).clamp_min(torch.finfo(scale.dtype		).eps		)
        lowerCAmelCase__				:  Union[str, Any]		       =     2.0 + cls.squareplus(SCREAMING_SNAKE_CASE_		)
        return df.squeeze(-1		), loc.squeeze(-1		), scale.squeeze(-1		)






class  _lowerCAmelCase     (  __lowerCamelCase	):
      A__		     =		{'loc': 1, 'scale': 1}
      A__		     =		Normal

      @classmethod
      def 	__magic_name__(   cls      ,				__UpperCAmelCase      ,				__UpperCAmelCase		):
        lowerCAmelCase__				:  List[str]		       =     cls.squareplus(SCREAMING_SNAKE_CASE_		).clamp_min(torch.finfo(scale.dtype		).eps		)
        return loc.squeeze(-1		), scale.squeeze(-1		)






class  _lowerCAmelCase     (  __lowerCamelCase	):
      A__		     =		{'total_count': 1, 'logits': 1}
      A__		     =		NegativeBinomial

      @classmethod
      def 	__magic_name__(   cls      ,				__UpperCAmelCase      ,				__UpperCAmelCase		):
        lowerCAmelCase__				:  Dict		       =     cls.squareplus(SCREAMING_SNAKE_CASE_		)
        return total_count.squeeze(-1		), logits.squeeze(-1		)

      def 	__magic_name__(   self      ,				__UpperCAmelCase		):
        lowerCAmelCase__       ,			lowerCAmelCase__				:  Optional[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 	__magic_name__(   self      ,				__UpperCAmelCase      ,				__UpperCAmelCase = None      ,				__UpperCAmelCase = None		):
        lowerCAmelCase__       ,			lowerCAmelCase__				:  Any		       =     distr_args

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

        return self._base_distribution((total_count, logits)		)







from collections.abc import Callable






class  _lowerCAmelCase     :

      def __init__(   self      ,				__UpperCAmelCase = None		):
        # Stores actual heap items.
        lowerCAmelCase__				:  list		       =     []
        # Stores indexes of each item for supporting updates and deletion.
        lowerCAmelCase__				:  dict		       =     {}
        # Stores current size of heap.
        lowerCAmelCase__				:  Any		       =     0
        # Stores function used to evaluate the score of an item on which basis ordering
        # will be done.
        lowerCAmelCase__				:  Union[str, Any]		       =     key or (lambda __UpperCAmelCase		: x)

      def 	__magic_name__(   self      ,				__UpperCAmelCase		):
        return int((i - 1) / 2		) if i > 0 else None

      def 	__magic_name__(   self      ,				__UpperCAmelCase		):
        lowerCAmelCase__				:  Optional[Any]		       =     int(2 * i + 1		)
        return left if 0 < left < self.size else None

      def 	__magic_name__(   self      ,				__UpperCAmelCase		):
        lowerCAmelCase__				:  List[str]		       =     int(2 * i + 2		)
        return right if 0 < right < self.size else None

      def 	__magic_name__(   self      ,				__UpperCAmelCase      ,				__UpperCAmelCase		):
        lowerCAmelCase__       ,			lowerCAmelCase__				:  List[str]		       =     (
            self.pos_map[self.arr[j][0]],
            self.pos_map[self.arr[i][0]],
        )
        # Then swap the items in the list.
        lowerCAmelCase__       ,			lowerCAmelCase__				:  Any		       =     self.arr[j], self.arr[i]

      def 	__magic_name__(   self      ,				__UpperCAmelCase      ,				__UpperCAmelCase		):
        return self.arr[i][1] < self.arr[j][1]

      def 	__magic_name__(   self      ,				__UpperCAmelCase		):
        lowerCAmelCase__				:  Optional[int]		       =     self._left(__UpperCAmelCase		)
        lowerCAmelCase__				:  Any		       =     self._right(__UpperCAmelCase		)
        lowerCAmelCase__				:  str		       =     i

        if left is not None and not self._cmp(__UpperCAmelCase      ,				__UpperCAmelCase		):
          lowerCAmelCase__				:  Dict		       =     left
        if right is not None and not self._cmp(__UpperCAmelCase      ,				__UpperCAmelCase		):
          lowerCAmelCase__				:  List[str]		       =     right

        return valid_parent

      def 	__magic_name__(   self      ,				__UpperCAmelCase		):
        lowerCAmelCase__				:  Tuple		       =     self._parent(__UpperCAmelCase		)
        while parent is not None and not self._cmp(__UpperCAmelCase      ,				__UpperCAmelCase		):
          self._swap(__UpperCAmelCase      ,				__UpperCAmelCase		)
          lowerCAmelCase__       ,			lowerCAmelCase__				:  Dict		       =     parent, self._parent(__UpperCAmelCase		)

      def 	__magic_name__(   self      ,				__UpperCAmelCase		):
        lowerCAmelCase__				:  str		       =     self._get_valid_parent(__UpperCAmelCase		)
        while valid_parent != index:
          self._swap(__UpperCAmelCase      ,				__UpperCAmelCase		)
          lowerCAmelCase__       ,			lowerCAmelCase__				:  List[Any]		       =     valid_parent, self._get_valid_parent(__UpperCAmelCase		)

      def 	__magic_name__(   self      ,				__UpperCAmelCase      ,				__UpperCAmelCase		):
        if item not in self.pos_map:
          return
        lowerCAmelCase__				:  Tuple		       =     self.pos_map[item]
        lowerCAmelCase__				:  Any		       =     [item, self.key(__UpperCAmelCase		)]
        # Make sure heap is right in both up and down direction.
        # Ideally only one of them will make any change.
        self._heapify_up(__UpperCAmelCase		)
        self._heapify_down(__UpperCAmelCase		)

      def 	__magic_name__(   self      ,				__UpperCAmelCase		):
        if item not in self.pos_map:
          return
        lowerCAmelCase__				:  Tuple		       =     self.pos_map[item]
        del self.pos_map[item]
        lowerCAmelCase__				:  Tuple		       =     self.arr[self.size - 1]
        lowerCAmelCase__				:  int		       =     index
        self.size -= 1
        # Make sure heap is right in both up and down direction. Ideally only one
        # of them will make any change- so no performance loss in calling both.
        if self.size > index:
          self._heapify_up(__UpperCAmelCase		)
          self._heapify_down(__UpperCAmelCase		)

      def 	__magic_name__(   self      ,				__UpperCAmelCase      ,				__UpperCAmelCase		):
        lowerCAmelCase__				:  Optional[int]		       =     len(self.arr		)
        if arr_len == self.size:
          self.arr.append([item, self.key(__UpperCAmelCase		)]		)
        else:
          lowerCAmelCase__				:  str		       =     [item, self.key(__UpperCAmelCase		)]
        lowerCAmelCase__				:  Optional[Any]		       =     self.size
        self.size += 1
        self._heapify_up(self.size - 1		)

      def 	__magic_name__(   self		):
        return self.arr[0] if self.size else None







      def 	__magic_name__(   self		):
        lowerCAmelCase__				:  int		       =     self.get_top()
        if top_item_tuple:
          self.delete_item(top_item_tuple[0]		)
        return top_item_tuple



def      __lowerCAmelCase			(					)     ->	None:
  pass


if __name__ == "__main__":
     import doctest

     doctest.testmod()

