'''simple docstring'''

def __UpperCamelCase(   _A					:				str  ,			_A					:				str    ):
   '''simple docstring'''
   UpperCAmelCase__							:				str   				=  len(_A    ) + 1
   UpperCAmelCase__							:				Dict   				=  len(_A    ) + 1

   # dp is a 2d matrix where dp[i][j] denotes whether prefix string of
   # length i of input_string matches with prefix string of length j of
   # given pattern.
   # "dp" stands for dynamic programming.
   UpperCAmelCase__							:				int   				=  [[0 for i in range(_A    )] for j in range(_A    )]

   # since string of zero length match pattern of zero length
   UpperCAmelCase__							:				Dict   				=  1

   # since pattern of zero length will never match with string of non-zero length
   for i in range(1  ,			_A    ):
      UpperCAmelCase__							:				List[Any]   				=  0

   # since string of zero length will match with pattern where there
   # is at least one * alternatively
   for j in range(1  ,			_A    ):
      UpperCAmelCase__							:				Optional[int]   				=  dp[0][j - 2] if pattern[j - 1] == '''*''' else 0

   # now using bottom-up approach to find for all remaining lengths
   for i in range(1  ,			_A    ):
      for j in range(1  ,			_A    ):
         if input_string[i - 1] == pattern[j - 1] or pattern[j - 1] == ".":
            UpperCAmelCase__							:				Optional[int]   				=  dp[i - 1][j - 1]

         elif pattern[j - 1] == "*":
            if dp[i][j - 2] == 1:
               UpperCAmelCase__							:				Optional[Any]   				=  1
            elif pattern[j - 2] in (input_string[i - 1], "."):
               UpperCAmelCase__							:				Optional[int]   				=  dp[i - 1][j]
            else:
               UpperCAmelCase__							:				Tuple   				=  0
         else:
            UpperCAmelCase__							:				int   				=  0

   return bool(dp[-1][-1]    )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  # inputing the strings
  # input_string = input("input a string :")
  # pattern = input("input a pattern :")

  UpperCamelCase__     :	Union[str, Any]				=			'aab'
  UpperCamelCase__     :	Union[str, Any]				=			'c*a*b'

  # using function to check whether given string matches the given pattern
  if match_pattern(input_string, pattern):
    print(f"""{input_string} matches the given pattern {pattern}""")
  else:
    print(f"""{input_string} does not match with the given pattern {pattern}""")





'''simple docstring'''

import torch

from transformers import AutoModel


class 				_lowercase	(      torch.nn.Module   ):
      '''simple docstring'''


      def __init__(				self					,lowerCamelCase_="sayef/fsner-bert-base-uncased"							)			->			Dict:



         '''simple docstring'''



         super(lowerCamelCase_					,self							).__init__()

         UpperCAmelCase__							:				Union[str, Any]   				=  AutoModel.from_pretrained(lowerCamelCase_					,return_dict=lowerCamelCase_							)
         UpperCAmelCase__							:				str   				=  torch.nn.CosineSimilarity(3					,1e-08							)
         UpperCAmelCase__							:				int   				=  torch.nn.Softmax(dim=1							)




      def 		lowerCAmelCase__					(				self					,**lowerCamelCase_							)			->			Optional[Any]:



         '''simple docstring'''



         return self.bert(**lowerCamelCase_							).last_hidden_state




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_							)			->			str:



         '''simple docstring'''



         return token_embeddings.sum(2					,keepdim=lowerCamelCase_							)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_					,lowerCamelCase_=1							)			->			int:



         '''simple docstring'''



         return self.softmax(T * self.cos(lowerCamelCase_					,lowerCamelCase_							)							)




      def 		lowerCAmelCase__					(				self					,lowerCamelCase_					,lowerCamelCase_							)			->			Tuple:



         '''simple docstring'''



         UpperCAmelCase__							:				List[Any]   				=  W_supports['''sizes'''].tolist()
         UpperCAmelCase__							:				Union[str, Any]   				=  W_supports['''start_token_id'''].item()
         UpperCAmelCase__							:				int   				=  W_supports['''end_token_id'''].item()

         del W_supports["sizes"]
         del W_supports["start_token_id"]
         del W_supports["end_token_id"]

         UpperCAmelCase__							:				Any   				=  self.BERT(**lowerCamelCase_							)
         UpperCAmelCase__							:				Any   				=  self.BERT(**lowerCamelCase_							)

         UpperCAmelCase__							:				Any   				=  None
         UpperCAmelCase__							:				Tuple   				=  None

         UpperCAmelCase__							:				Dict   				=  W_supports['''input_ids'''] == start_token_id
         UpperCAmelCase__							:				Any   				=  W_supports['''input_ids'''] == end_token_id

         for i, size in enumerate(lowerCamelCase_							):
            if i == 0:
               UpperCAmelCase__							:				int   				=  0
            else:
               UpperCAmelCase__							:				str   				=  support_sizes[i - 1]

            UpperCAmelCase__							:				Dict   				=  S[s : s + size][start_token_masks[s : s + size]]
            UpperCAmelCase__							:				Union[str, Any]   				=  S[s : s + size][end_token_masks[s : s + size]]

            UpperCAmelCase__							:				int   				=  torch.matmul(q[i]					,s_start.T							).sum(1							).softmax(0							)
            UpperCAmelCase__							:				int   				=  torch.matmul(q[i]					,s_end.T							).sum(1							).softmax(0							)

            if p_starts is not None:
               UpperCAmelCase__							:				str   				=  torch.vstack((p_starts, p_start)							)
               UpperCAmelCase__							:				Optional[int]   				=  torch.vstack((p_ends, p_end)							)
            else:
               UpperCAmelCase__							:				Union[str, Any]   				=  p_start
               UpperCAmelCase__							:				int   				=  p_end

         return p_starts, p_ends




