



"""simple docstring"""







from __future__ import annotations

from math import gcd

def   lowerCAmelCase__			(     lowerCamelCase__				,      lowerCamelCase__ = 2				,      lowerCamelCase__ = 1				,      lowerCamelCase__ = 3				,      ) ->							int | None:
       # A value less than 2 can cause an infinite loop in the algorithm.
       if num < 2:
              raise ValueError('The input value cannot be less than 2'			)

       # Because of the relationship between ``f(f(x))`` and ``f(x)``, this
       # algorithm struggles to find factors that are divisible by two.
       # As a workaround, we specifically check for two and even inputs.
       #   See: https://math.stackexchange.com/a/2856214/165820
       if num > 2 and num % 2 == 0:
              return 2

       # Pollard's Rho algorithm requires a function that returns pseudorandom
       # values between 0 <= X < ``num``.  It doesn't need to be random in the
       # sense that the output value is cryptographically secure or difficult
       # to calculate, it only needs to be random in the sense that all output
       # values should be equally likely to appear.
       # For this reason, Pollard suggested using ``f(x) = (x**2 - 1) % num``
       # However, the success of Pollard's algorithm isn't guaranteed and is
       # determined in part by the initial seed and the chosen random function.
       # To make retries easier, we will instead use ``f(x) = (x**2 + C) % num``
       # where ``C`` is a value that we can modify between each attempt.
       def rand_fn(lowerCamelCase__				,      lowerCamelCase__				,      lowerCamelCase__			) -> int:
              return (pow(lowerCamelCase__				,      2			) + step) % modulus

       for _ in range(lowerCamelCase__			):
              # These track the position within the cycle detection logic.
              A         =					seed
              A         =					seed

              while True:
                     # At each iteration, the tortoise moves one step and the hare moves two.
                     A         =					rand_fn(lowerCamelCase__				,      lowerCamelCase__				,      lowerCamelCase__			)
                     A         =					rand_fn(lowerCamelCase__				,      lowerCamelCase__				,      lowerCamelCase__			)
                     A         =					rand_fn(lowerCamelCase__				,      lowerCamelCase__				,      lowerCamelCase__			)

                     # At some point both the tortoise and the hare will enter a cycle whose
                     # length ``p`` is a divisor of ``num``.  Once in that cycle, at some point
                     # the tortoise and hare will end up on the same value modulo ``p``.
                     # We can detect when this happens because the position difference between
                     # the tortoise and the hare will share a common divisor with ``num``.
                     A         =					gcd(hare - tortoise				,      lowerCamelCase__			)

                     if divisor == 1:
                            # No common divisor yet, just keep searching.
                            continue
                     else:
                            # We found a common divisor!
                            if divisor == num:
                                   # Unfortunately, the divisor is ``num`` itself and is useless.
                                   break
                            else:
                                   # The divisor is a nontrivial factor of ``num``!
                                   return divisor

        # If we made it here, then this attempt failed.
        # We need to pick a new starting seed for the tortoise and hare
        # in addition to a new step value for the random function.
        # To keep this example implementation deterministic, the
        # new values will be generated based on currently available
        # values instead of using something like ``random.randint``.

        # We can use the hare's position as the new seed.
        # This is actually what Richard Brent's the "optimized" variant does.
              A         =					hare

              # The new step value for the random function can just be incremented.
              # At first the results will be similar to what the old function would
              # have produced, but the value will quickly diverge after a bit.
              step += 1

       # We haven't found a divisor within the requested number of attempts.
       # We were unlucky or ``num`` itself is actually prime.
       return None


if __name__ == "__main__":
       import argparse

       A    =			argparse.ArgumentParser()
       parser.add_argument(
           'num',
           type=int,
           help='The value to find a divisor of',
       )
       parser.add_argument(
           '--attempts',
           type=int,
           default=3,
           help='The number of attempts before giving up',
       )
       A    =			parser.parse_args()

       A    =			pollard_rho(args.num, attempts=args.attempts)
       if divisor is None:
              print(F'{args.num} is probably prime')
       else:
              A    =			args.num // divisor
              print(F'{args.num} = {divisor} * {quotient}')








"""simple docstring"""







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


A    =			logging.get_logger(__name__)

A    =			{
    '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__		(      UpperCamelCase     ):
		lowerCAmelCase_       :	Tuple 							=     """decision_transformer"""
		lowerCAmelCase_       :	Tuple 							=     ["""past_key_values"""]
		lowerCAmelCase_       :	Dict 							=     {
		    """max_position_embeddings""": """n_positions""",
		    """num_attention_heads""": """n_head""",
		    """num_hidden_layers""": """n_layer""",
		}



		def __init__( self  :    Optional[Any]      ,							snake_case  :    int=17      ,							snake_case  :    int=4      ,							snake_case  :    Union[str, Any]=128      ,							snake_case  :    Optional[Any]=4_096      ,							snake_case  :    List[Any]=True      ,							snake_case  :    str=1      ,							snake_case  :    str=1_024      ,							snake_case  :    List[str]=3      ,							snake_case  :    str=1      ,							snake_case  :    Any=None      ,							snake_case  :    Optional[int]="relu"      ,							snake_case  :    List[Any]=0.1      ,							snake_case  :    str=0.1      ,							snake_case  :    Tuple=0.1      ,							snake_case  :    Union[str, Any]=1E-5      ,							snake_case  :    Optional[int]=0.02      ,							snake_case  :    List[Any]=True      ,							snake_case  :    Tuple=True      ,							snake_case  :    Optional[Any]=50_256      ,							snake_case  :    List[Any]=50_256      ,							snake_case  :    List[str]=False      ,							snake_case  :    Any=False      ,							**snake_case  :    List[str]      ,							)			->						List[Any]:






									'''simple docstring'''

									A         =					state_dim
									A         =					act_dim
									A         =					hidden_size
									A         =					max_ep_len
									A         =					action_tanh
									A         =					vocab_size
									A         =					n_positions
									A         =					n_layer
									A         =					n_head
									A         =					n_inner
									A         =					activation_function
									A         =					resid_pdrop
									A         =					embd_pdrop
									A         =					attn_pdrop
									A         =					layer_norm_epsilon
									A         =					initializer_range
									A         =					scale_attn_weights
									A         =					use_cache
									A         =					scale_attn_by_inverse_layer_idx
									A         =					reorder_and_upcast_attn

									A         =					bos_token_id
									A         =					eos_token_id

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



