




from math import factorial
class 			_UpperCamelCase      :
      def __init__(			self   :Dict ,      lowerCamelCase   :List[str] ,      lowerCamelCase   :List[Any]      )     ->			Optional[Any]:
       UpperCAmelCase__							 =						real
       if isinstance(lowerCamelCase ,      lowerCamelCase      ):
        UpperCAmelCase__							 =						[1] * rank
       else:
        UpperCAmelCase__							 =						rank
      def __repr__(			self   :Dict      )     ->			Optional[int]:
       return (
           f'''{self.real}+'''
           f'''{"+".join(str(lowerCamelCase      )+"E"+str(n+1      )for n,dual in enumerate(self.duals      )      )}'''
       )
      def 	UpperCAmelCase_						(			self   :Optional[Any]      )     ->			int:
       UpperCAmelCase__							 =						self.duals.copy()
       while cur[-1] == 0:
        cur.pop(-1      )
       return Dual(self.real ,      lowerCamelCase      )
      def __add__(			self   :Tuple ,      lowerCamelCase   :List[str]      )     ->			Optional[int]:
       if not isinstance(lowerCamelCase ,      lowerCamelCase      ):
        return Dual(self.real + other ,      self.duals      )
       UpperCAmelCase__							 =						self.duals.copy()
       UpperCAmelCase__							 =						other.duals.copy()
       if len(lowerCamelCase      ) > len(lowerCamelCase      ):
        o_dual.extend([1] * (len(lowerCamelCase      ) - len(lowerCamelCase      ))      )
       elif len(lowerCamelCase      ) < len(lowerCamelCase      ):
        s_dual.extend([1] * (len(lowerCamelCase      ) - len(lowerCamelCase      ))      )
       UpperCAmelCase__							 =						[]
       for i in range(len(lowerCamelCase      )      ):
        new_duals.append(s_dual[i] + o_dual[i]      )
       return Dual(self.real + other.real ,      lowerCamelCase      )

      UpperCAmelCase_        =		__add__
      def __sub__(			self   :str ,      lowerCamelCase   :Any      )     ->			Any:
       return self + other * -1
      def __mul__(			self   :Tuple ,      lowerCamelCase   :Optional[int]      )     ->			List[str]:
       if not isinstance(lowerCamelCase ,      lowerCamelCase      ):
        UpperCAmelCase__							 =						[]
        for i in self.duals:
         new_duals.append(i * other      )
        return Dual(self.real * other ,      lowerCamelCase      )
       UpperCAmelCase__							 =						[0] * (len(self.duals      ) + len(other.duals      ) + 1)
       for i, item in enumerate(self.duals      ):
        for j, jtem in enumerate(other.duals      ):
         new_duals[i + j + 1] += item * jtem
       for k in range(len(self.duals      )      ):
        new_duals[k] += self.duals[k] * other.real
       for index in range(len(other.duals      )      ):
        new_duals[index] += other.duals[index] * self.real
       return Dual(self.real * other.real ,      lowerCamelCase      )

      UpperCAmelCase_        =		__mul__
      def __truediv__(			self   :List[str] ,      lowerCamelCase   :Union[str, Any]      )     ->			Union[str, Any]:
       if not isinstance(lowerCamelCase ,      lowerCamelCase      ):
        UpperCAmelCase__							 =						[]
        for i in self.duals:
         new_duals.append(i / other      )
        return Dual(self.real / other ,      lowerCamelCase      )
       raise ValueError
      def __floordiv__(			self   :Union[str, Any] ,      lowerCamelCase   :Union[str, Any]      )     ->			Union[str, Any]:
       if not isinstance(lowerCamelCase ,      lowerCamelCase      ):
        UpperCAmelCase__							 =						[]
        for i in self.duals:
         new_duals.append(i // other      )
        return Dual(self.real // other ,      lowerCamelCase      )
       raise ValueError







      def __pow__(			self   :List[Any] ,      lowerCamelCase   :Optional[int]      )     ->			Optional[int]:
       if n < 0 or isinstance(lowerCamelCase ,      lowerCamelCase      ):
        raise ValueError("power must be a positive integer"      )
       if n == 0:
        return 1
       if n == 1:
        return self
       UpperCAmelCase__							 =						self
       for _ in range(n - 1      ):
        x *= self
       return x



def 						lowerCAmelCase		(		_lowerCAmelCase							:   List[Any]						,							_lowerCAmelCase							:   Tuple						,							_lowerCAmelCase							:   List[Any]	):




 """simple docstring"""







 if not callable(_lowerCAmelCase	):
  raise ValueError("differentiate() requires a function as input for func"	)
 if not isinstance(_lowerCAmelCase						,							(float, int)	):
  raise ValueError("differentiate() requires a float as input for position"	)
 if not isinstance(_lowerCAmelCase						,							_lowerCAmelCase	):
  raise ValueError("differentiate() requires an int as input for order"	)
 UpperCAmelCase__							 =						Dual(_lowerCAmelCase						,							1	)
 UpperCAmelCase__							 =						func(_lowerCAmelCase	)
 if order == 0:
  return result.real
 return result.duals[order - 1] * factorial(_lowerCAmelCase	)


if __name__ == "__main__":
  import doctest

  doctest.testmod()



  def 						lowerCAmelCase		(		_lowerCAmelCase							:   List[Any]	):




   """simple docstring"""







   return y**2 * y**4


  print(differentiate(f, 9, 2))











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


_lowerCAmelCase						:   Union[str, Any]		=   logging.get_logger(__name__)

_lowerCAmelCase						:   Tuple		=   {
    "CarlCochet/trajectory-transformer-halfcheetah-medium-v2": (
        "https://huggingface.co/CarlCochet/trajectory-transformer-halfcheetah-medium-v2/resolve/main/config.json"
    ),
    # See all TrajectoryTransformer models at https://huggingface.co/models?filter=trajectory_transformer
}
class 			_UpperCamelCase      (				lowerCAmelCase		):
      UpperCAmelCase_        =		"""trajectory_transformer"""
      UpperCAmelCase_        =		["""past_key_values"""]
      UpperCAmelCase_        =		{
          """hidden_size""": """n_embd""",
          """num_attention_heads""": """n_head""",
          """num_hidden_layers""": """n_layer""",
      }
      def __init__(			self   :Union[str, Any] ,      lowerCamelCase   :Optional[int]=100 ,      lowerCamelCase   :Optional[int]=5 ,      lowerCamelCase   :Optional[Any]=1 ,      lowerCamelCase   :Any=1 ,      lowerCamelCase   :int=249 ,      lowerCamelCase   :Optional[Any]=6 ,      lowerCamelCase   :Optional[Any]=17 ,      lowerCamelCase   :Optional[int]=25 ,      lowerCamelCase   :Union[str, Any]=4 ,      lowerCamelCase   :Union[str, Any]=4 ,      lowerCamelCase   :Optional[int]=128 ,      lowerCamelCase   :List[Any]=0.1 ,      lowerCamelCase   :List[str]=0.1 ,      lowerCamelCase   :Tuple=0.1 ,      lowerCamelCase   :Dict=0.00_06 ,      lowerCamelCase   :Dict=512 ,      lowerCamelCase   :Optional[Any]=0.02 ,      lowerCamelCase   :Any=1e-12 ,      lowerCamelCase   :Optional[Any]=1 ,      lowerCamelCase   :List[Any]=True ,      lowerCamelCase   :int=1 ,      lowerCamelCase   :Dict=5_0256 ,      lowerCamelCase   :Union[str, Any]=5_0256 ,      **lowerCamelCase   :int ,      )     ->			Optional[Any]:
       UpperCAmelCase__							 =						vocab_size
       UpperCAmelCase__							 =						action_weight
       UpperCAmelCase__							 =						reward_weight
       UpperCAmelCase__							 =						value_weight
       UpperCAmelCase__							 =						max_position_embeddings
       UpperCAmelCase__							 =						block_size
       UpperCAmelCase__							 =						action_dim
       UpperCAmelCase__							 =						observation_dim
       UpperCAmelCase__							 =						transition_dim
       UpperCAmelCase__							 =						learning_rate
       UpperCAmelCase__							 =						n_layer
       UpperCAmelCase__							 =						n_head
       UpperCAmelCase__							 =						n_embd
       UpperCAmelCase__							 =						embd_pdrop
       UpperCAmelCase__							 =						attn_pdrop
       UpperCAmelCase__							 =						resid_pdrop
       UpperCAmelCase__							 =						initializer_range
       UpperCAmelCase__							 =						layer_norm_eps
       UpperCAmelCase__							 =						kaiming_initializer_range
       UpperCAmelCase__							 =						use_cache
       super().__init__(pad_token_id=lowerCamelCase ,      bos_token_id=lowerCamelCase ,      eos_token_id=lowerCamelCase ,      **lowerCamelCase      )





