






from __future__ import annotations

from collections.abc import Callable

lowerCamelCase     :							Union[str, Any]    =list[list[float | int]]







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase      )			->     Matrix:
     UpperCamelCase__      :       int	    =  len(__lowerCAmelCase      )
     UpperCamelCase__      :       Matrix	    =  [[0 for _ in range(size + 1      )] for _ in range(__lowerCAmelCase      )]
     UpperCamelCase__      :       int
     UpperCamelCase__      :       int
     UpperCamelCase__      :       int
     UpperCamelCase__      :       int
     UpperCamelCase__      :       int
     UpperCamelCase__      :       float

     for row in range(__lowerCAmelCase      ):
          for col in range(__lowerCAmelCase      ):
               UpperCamelCase__      :       Optional[Any]	    =  matrix[row][col]

          UpperCamelCase__      :       Optional[int]	    =  vector[row][0]

     UpperCamelCase__      :       Optional[Any]	    =  0
     UpperCamelCase__      :       Optional[int]	    =  0
     while row < size and col < size:
          # pivoting
          UpperCamelCase__      :       List[Any]	    =  max((abs(augmented[rowa][col]      ), rowa) for rowa in range(__lowerCAmelCase ,   __lowerCAmelCase      )      )[
              1
          ]
          if augmented[pivot_row][col] == 0:
               col += 1
               continue
          else:
               UpperCamelCase__      :       Union[str, Any]	    =  augmented[pivot_row], augmented[row]

          for rowa in range(row + 1 ,   __lowerCAmelCase      ):
               UpperCamelCase__      :       Union[str, Any]	    =  augmented[rowa][col] / augmented[row][col]
               UpperCamelCase__      :       str	    =  0
               for cola in range(col + 1 ,   size + 1      ):
                    augmented[rowa][cola] -= augmented[row][cola] * ratio

          row += 1
          col += 1

     # back substitution
     for col in range(1 ,   __lowerCAmelCase      ):
          for row in range(__lowerCAmelCase      ):
               UpperCamelCase__      :       str	    =  augmented[row][col] / augmented[col][col]
               for cola in range(__lowerCAmelCase ,   size + 1      ):
                    augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
     return [
         [round(augmented[row][size] / augmented[row][row] ,   10      )] for row in range(__lowerCAmelCase      )
     ]







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase      )			->     Callable[[int], int]:
     UpperCamelCase__      :       int	    =  len(__lowerCAmelCase      )
     UpperCamelCase__      :       Matrix	    =  [[0 for _ in range(__lowerCAmelCase      )] for _ in range(__lowerCAmelCase      )]
     UpperCamelCase__      :       Matrix	    =  [[0] for _ in range(__lowerCAmelCase      )]
     UpperCamelCase__      :       Matrix
     UpperCamelCase__      :       int
     UpperCamelCase__      :       int
     UpperCamelCase__      :       int

     for x_val, y_val in enumerate(__lowerCAmelCase      ):
          for col in range(__lowerCAmelCase      ):
               UpperCamelCase__      :       Any	    =  (x_val + 1) ** (size - col - 1)
          UpperCamelCase__      :       int	    =  y_val

     UpperCamelCase__      :       Dict	    =  solve(__lowerCAmelCase ,   __lowerCAmelCase      )

     def interpolated_func(__lowerCAmelCase      ) -> int:
          return sum(
              round(coeffs[x_val][0]      ) * (var ** (size - x_val - 1))
              for x_val in range(__lowerCAmelCase      )      )

     return interpolated_func







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase      )			->     int:
     return (
         1
         - variable
         + variable**2
         - variable**3
         + variable**4
         - variable**5
         + variable**6
         - variable**7
         + variable**8
         - variable**9
         + variable**10
     )







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase = question_function ,   __lowerCAmelCase = 10      )			->     int:
     UpperCamelCase__      :       list[int]	    =  [func(__lowerCAmelCase      ) for x_val in range(1 ,   order + 1      )]

     UpperCamelCase__      :       list[Callable[[int], int]]	    =  [
         interpolate(data_points[:max_coeff]      ) for max_coeff in range(1 ,   order + 1      )
     ]

     UpperCamelCase__      :       int	    =  0
     UpperCamelCase__      :       Callable[[int], int]
     UpperCamelCase__      :       int

     for poly in polynomials:
          UpperCamelCase__      :       str	    =  1
          while func(__lowerCAmelCase      ) == poly(__lowerCAmelCase      ):
               x_val += 1

          ret += poly(__lowerCAmelCase      )

     return ret


if __name__ == "__main__":
   print(F"""{solution() = }""")







from ...configuration_utils import PretrainedConfig
from ...utils import logging


lowerCamelCase     :							Optional[int]    =logging.get_logger(__name__)

lowerCamelCase     :							Optional[Any]    ={
    '''edbeeching/decision-transformer-gym-hopper-medium''': (
        '''https://huggingface.co/edbeeching/decision-transformer-gym-hopper-medium/resolve/main/config.json'''
    ),
    # See all DecisionTransformer models at https://huggingface.co/models?filter=decision_transformer
}





class       __a  (   A__	):
 _lowerCAmelCase	:	str				=			'''decision_transformer'''
 _lowerCAmelCase	:	Optional[Any]				=			['''past_key_values''']
 _lowerCAmelCase	:	Optional[int]				=			{
     '''max_position_embeddings''': '''n_positions''',
     '''num_attention_heads''': '''n_head''',
     '''num_hidden_layers''': '''n_layer''',
 }







 def __init__(		self :       List[Any]							,       SCREAMING_SNAKE_CASE :       Optional[int]=17							,       SCREAMING_SNAKE_CASE :       Optional[int]=4							,       SCREAMING_SNAKE_CASE :       Optional[int]=1_28							,       SCREAMING_SNAKE_CASE :       Dict=40_96							,       SCREAMING_SNAKE_CASE :       Union[str, Any]=True							,       SCREAMING_SNAKE_CASE :       Tuple=1							,       SCREAMING_SNAKE_CASE :       Optional[int]=10_24							,       SCREAMING_SNAKE_CASE :       Any=3							,       SCREAMING_SNAKE_CASE :       str=1							,       SCREAMING_SNAKE_CASE :       Optional[int]=None							,       SCREAMING_SNAKE_CASE :       Dict="relu"							,       SCREAMING_SNAKE_CASE :       Optional[int]=0.1							,       SCREAMING_SNAKE_CASE :       str=0.1							,       SCREAMING_SNAKE_CASE :       str=0.1							,       SCREAMING_SNAKE_CASE :       Union[str, Any]=1e-5							,       SCREAMING_SNAKE_CASE :       Optional[int]=0.0_2							,       SCREAMING_SNAKE_CASE :       Optional[Any]=True							,       SCREAMING_SNAKE_CASE :       Tuple=True							,       SCREAMING_SNAKE_CASE :       int=5_02_56							,       SCREAMING_SNAKE_CASE :       List[Any]=5_02_56							,       SCREAMING_SNAKE_CASE :       Any=False							,       SCREAMING_SNAKE_CASE :       List[Any]=False							,       **SCREAMING_SNAKE_CASE :       Optional[int]							,       ):


      '''simple docstring'''






      UpperCamelCase__      :       List[str]	    =  state_dim
      UpperCamelCase__      :       Optional[int]	    =  act_dim
      UpperCamelCase__      :       Dict	    =  hidden_size
      UpperCamelCase__      :       Any	    =  max_ep_len
      UpperCamelCase__      :       Optional[Any]	    =  action_tanh
      UpperCamelCase__      :       str	    =  vocab_size
      UpperCamelCase__      :       List[str]	    =  n_positions
      UpperCamelCase__      :       Tuple	    =  n_layer
      UpperCamelCase__      :       Union[str, Any]	    =  n_head
      UpperCamelCase__      :       Dict	    =  n_inner
      UpperCamelCase__      :       int	    =  activation_function
      UpperCamelCase__      :       List[str]	    =  resid_pdrop
      UpperCamelCase__      :       Optional[int]	    =  embd_pdrop
      UpperCamelCase__      :       Optional[Any]	    =  attn_pdrop
      UpperCamelCase__      :       Optional[Any]	    =  layer_norm_epsilon
      UpperCamelCase__      :       int	    =  initializer_range
      UpperCamelCase__      :       Dict	    =  scale_attn_weights
      UpperCamelCase__      :       Tuple	    =  use_cache
      UpperCamelCase__      :       List[str]	    =  scale_attn_by_inverse_layer_idx
      UpperCamelCase__      :       Union[str, Any]	    =  reorder_and_upcast_attn

      UpperCamelCase__      :       Optional[Any]	    =  bos_token_id
      UpperCamelCase__      :       Optional[int]	    =  eos_token_id

      super().__init__(bos_token_id=SCREAMING_SNAKE_CASE							,       eos_token_id=SCREAMING_SNAKE_CASE							,       **SCREAMING_SNAKE_CASE						)