'''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 ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__    ,							lowercase__=None    ,							lowercase__=None    ,							lowercase__=0 )							-> Any:
         SCREAMING_SNAKE_CASE					:			Any    	=       1.0 if scale is None else scale
         SCREAMING_SNAKE_CASE					:			int    	=       0.0 if loc is None else loc

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






    @property
    def       _UpperCamelCase    (       self )							-> Union[str, Any]:
         return self.base_dist.mean * self.scale + self.loc






    @property
    def       _UpperCamelCase    (       self )							-> List[str]:
         return self.base_dist.variance * self.scale**2






    @property
    def       _UpperCamelCase    (       self )							-> int:
         return self.variance.sqrt()






class 				UpperCAmelCase (       nn.Module ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__    ,							lowercase__    ,							lowercase__    ,							**lowercase__ )							-> None:
         super().__init__(**__a )
         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       args_dim
         SCREAMING_SNAKE_CASE					:			List[str]    	=       nn.ModuleList([nn.Linear(__a    ,							__a ) for dim in args_dim.values()] )
         SCREAMING_SNAKE_CASE					:			str    	=       domain_map






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> Tuple[torch.Tensor]:
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       [proj(__a ) for proj in self.proj]

         return self.domain_map(*__a )






class 				UpperCAmelCase (       nn.Module ):




    '''simple docstring'''







    def __init__(       self    ,							lowercase__ )							-> Tuple:
         super().__init__()
         SCREAMING_SNAKE_CASE					:			Any    	=       function






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							*lowercase__ )							-> Any:
         return self.function(__a    ,							*__a )






class 				UpperCAmelCase :




    '''simple docstring'''







    snake_case__							:   type
    snake_case__							:   int
    snake_case__							:   Dict[str, int]






    def __init__(       self    ,							lowercase__ = 1 )							-> None:
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       dim
         SCREAMING_SNAKE_CASE					:			List[Any]    	=       {k: dim * self.args_dim[k] for k in self.args_dim}






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> List[Any]:
         if self.dim == 1:
              return self.distribution_class(*__a )
         else:
              return Independent(self.distribution_class(*__a )    ,							1 )






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__ = None    ,							lowercase__ = None    ,							)							-> Distribution:
         SCREAMING_SNAKE_CASE					:			Union[str, Any]    	=       self._base_distribution(__a )
         if loc is None and scale is None:
              return distr
         else:
              return AffineTransformed(__a    ,							loc=__a    ,							scale=__a    ,							event_dim=self.event_dim )






    @property
    def       _UpperCamelCase    (       self )							-> Tuple:
         return () if self.dim == 1 else (self.dim,)






    @property
    def       _UpperCamelCase    (       self )							-> int:
         return len(self.event_shape )






    @property
    def       _UpperCamelCase    (       self )							-> float:
         return 0.0






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> nn.Module:
         return ParameterProjection(
             in_features=__a    ,							args_dim=self.args_dim    ,							domain_map=LambdaLayer(self.domain_map )    ,							)






    def       _UpperCamelCase    (       self    ,							*lowercase__ )							-> str:
         raise NotImplementedError()






    @staticmethod
    def       _UpperCamelCase    (       lowercase__ )							-> torch.Tensor:
         return (x + torch.sqrt(torch.square(__a ) + 4.0 )) / 2.0






class 				UpperCAmelCase (       __lowercase ):




    '''simple docstring'''







    snake_case__							:   Dict[str, int]							=						{"df": 1, "loc": 1, "scale": 1}
    snake_case__							:   type							=						StudentT






    @classmethod
    def       _UpperCamelCase    (       cls    ,							lowercase__    ,							lowercase__    ,							lowercase__ )							-> Tuple:
         SCREAMING_SNAKE_CASE					:			Optional[Any]    	=       cls.squareplus(__a ).clamp_min(torch.finfo(scale.dtype ).eps )
         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       2.0 + cls.squareplus(__a )
         return df.squeeze(-1 ), loc.squeeze(-1 ), scale.squeeze(-1 )






class 				UpperCAmelCase (       __lowercase ):




    '''simple docstring'''







    snake_case__							:   Dict[str, int]							=						{"loc": 1, "scale": 1}
    snake_case__							:   type							=						Normal






    @classmethod
    def       _UpperCamelCase    (       cls    ,							lowercase__    ,							lowercase__ )							-> str:
         SCREAMING_SNAKE_CASE					:			int    	=       cls.squareplus(__a ).clamp_min(torch.finfo(scale.dtype ).eps )
         return loc.squeeze(-1 ), scale.squeeze(-1 )






class 				UpperCAmelCase (       __lowercase ):




    '''simple docstring'''







    snake_case__							:   Dict[str, int]							=						{"total_count": 1, "logits": 1}
    snake_case__							:   type							=						NegativeBinomial






    @classmethod
    def       _UpperCamelCase    (       cls    ,							lowercase__    ,							lowercase__ )							-> Union[str, Any]:
         SCREAMING_SNAKE_CASE					:			int    	=       cls.squareplus(__a )
         return total_count.squeeze(-1 ), logits.squeeze(-1 )






    def       _UpperCamelCase    (       self    ,							lowercase__ )							-> Distribution:
         SCREAMING_SNAKE_CASE					:			Optional[int]    	=       distr_args
         if self.dim == 1:
              return self.distribution_class(total_count=__a    ,							logits=__a )
         else:
              return Independent(self.distribution_class(total_count=__a    ,							logits=__a )    ,							1 )






    def       _UpperCamelCase    (       self    ,							lowercase__    ,							lowercase__ = None    ,							lowercase__ = None )							-> Distribution:
         SCREAMING_SNAKE_CASE					:			List[str]    	=       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


def     __lowerCAmelCase						(       a_       ,      a_ = None		)      ->	list[list[str]]:





     '''simple docstring'''





     SCREAMING_SNAKE_CASE					:			Optional[int]    	=       word_bank or []
     # create a table
     SCREAMING_SNAKE_CASE					:			int    	=       len(a_		) + 1

     SCREAMING_SNAKE_CASE					:			list[list[list[str]]]    	=       []
     for _ in range(a_		):
          table.append([]		)
     # seed value
     SCREAMING_SNAKE_CASE					:			List[Any]    	=       [[]]  # because empty string has empty combination

     # iterate through the indices
     for i in range(a_		):
          # condition
          if table[i] != []:
               for word in word_bank:
                    # slice condition
                    if target[i : i + len(a_		)] == word:
                         SCREAMING_SNAKE_CASE					:			list[list[str]]    	=       [
                             [word, *way] for way in table[i]
                         ]
                         # adds the word to every combination the current position holds
                         # now,push that combination to the table[i+len(word)]
                         table[i + len(a_		)] += new_combinations

    # combinations are in reverse order so reverse for better output
     for combination in table[len(a_		)]:
          combination.reverse()

     return table[len(a_		)]


if __name__ == "__main__":
 print(all_construct("""jwajalapa""", ["""jwa""", """j""", """w""", """a""", """la""", """lapa"""]))
 print(all_construct("""rajamati""", ["""s""", """raj""", """amat""", """raja""", """ma""", """i""", """t"""]))
 print(
     all_construct(
         """hexagonosaurus""",
         ["""h""", """ex""", """hex""", """ag""", """ago""", """ru""", """auru""", """rus""", """go""", """no""", """o""", """s"""],
     )
 )



