
'''simple docstring'''






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


UpperCAmelCase_       :   Any   =       logging.get_logger(__name__)

UpperCAmelCase_       :   Union[str, 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  UpperCAmelCase__						(       A ):
    lowerCAmelCase_				    =		'decision_transformer'
    lowerCAmelCase_				    =		['past_key_values']
    lowerCAmelCase_				    =		{
        'max_position_embeddings': 'n_positions',
        'num_attention_heads': 'n_head',
        'num_hidden_layers': 'n_layer',
    }



    def __init__(	self      :       str,__A      :       Any=1_7,__A      :       List[Any]=4,__A      :       int=1_2_8,__A      :       List[str]=4_0_9_6,__A      :       Tuple=True,__A      :       List[Any]=1,__A      :       Any=1_0_2_4,__A      :       Any=3,__A      :       Optional[Any]=1,__A      :       Optional[int]=None,__A      :       Tuple="relu",__A      :       Union[str, Any]=0.1,__A      :       str=0.1,__A      :       Optional[Any]=0.1,__A      :       List[str]=1e-5,__A      :       List[str]=0.02,__A      :       Tuple=True,__A      :       Dict=True,__A      :       Any=5_0_2_5_6,__A      :       List[Any]=5_0_2_5_6,__A      :       Optional[int]=False,__A      :       int=False,**__A      :       Tuple,):
          _lowerCamelCase				:   Optional[Any]								=   state_dim
          _lowerCamelCase				:   str								=   act_dim
          _lowerCamelCase				:   Optional[int]								=   hidden_size
          _lowerCamelCase				:   Any								=   max_ep_len
          _lowerCamelCase				:   Dict								=   action_tanh
          _lowerCamelCase				:   int								=   vocab_size
          _lowerCamelCase				:   List[Any]								=   n_positions
          _lowerCamelCase				:   int								=   n_layer
          _lowerCamelCase				:   Any								=   n_head
          _lowerCamelCase				:   Optional[Any]								=   n_inner
          _lowerCamelCase				:   List[Any]								=   activation_function
          _lowerCamelCase				:   str								=   resid_pdrop
          _lowerCamelCase				:   str								=   embd_pdrop
          _lowerCamelCase				:   Any								=   attn_pdrop
          _lowerCamelCase				:   int								=   layer_norm_epsilon
          _lowerCamelCase				:   Optional[Any]								=   initializer_range
          _lowerCamelCase				:   Union[str, Any]								=   scale_attn_weights
          _lowerCamelCase				:   Optional[Any]								=   use_cache
          _lowerCamelCase				:   Optional[int]								=   scale_attn_by_inverse_layer_idx
          _lowerCamelCase				:   List[Any]								=   reorder_and_upcast_attn

          _lowerCamelCase				:   Optional[int]								=   bos_token_id
          _lowerCamelCase				:   int								=   eos_token_id

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

'''simple docstring'''






import math







def 		A_       (	_lowerCAmelCase   :    int							):



      """simple docstring"""




      _lowerCamelCase				:   Optional[int]								=   math.loga(math.sqrt(4 * positive_integer + 1							) / 2 + 1 / 2							)

      return exponent == int(_lowerCAmelCase							)







def 		A_       (	_lowerCAmelCase   :    float = 1 / 12345							):



      """simple docstring"""




      _lowerCamelCase				:   Optional[int]								=   0
      _lowerCamelCase				:   int								=   0

      _lowerCamelCase				:   List[str]								=   3
      while True:
            _lowerCamelCase				:   List[Any]								=   (integer**2 - 1) / 4
            # if candidate is an integer, then there is a partition for k
            if partition_candidate == int(_lowerCAmelCase							):
                  _lowerCamelCase				:   Any								=   int(_lowerCAmelCase							)
                  total_partitions += 1
                  if check_partition_perfect(_lowerCAmelCase							):
                        perfect_partitions += 1
            if perfect_partitions > 0:
                  if perfect_partitions / total_partitions < max_proportion:
                        return int(_lowerCAmelCase							)
            integer += 1


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