


'''simple docstring'''



from __future__ import annotations

from math import gcd






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int = 2						,      _SCREAMING_SNAKE_CASE      :   int = 1						,      _SCREAMING_SNAKE_CASE      :   int = 3						,      ):
					# 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(_SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int   ) -> int:
										return (pow(_SCREAMING_SNAKE_CASE						,      2   ) + step) % modulus

					for _ in range(_SCREAMING_SNAKE_CASE   ):
										# These track the position within the cycle detection logic.
										__a			:       int					    =  seed
										__a			:       Tuple					    =  seed

										while True:
															# At each iteration, the tortoise moves one step and the hare moves two.
															__a			:       List[str]					    =  rand_fn(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
															__a			:       Optional[int]					    =  rand_fn(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
															__a			:       Optional[Any]					    =  rand_fn(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )

															# 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			:       List[str]					    =  gcd(hare - tortoise						,      _SCREAMING_SNAKE_CASE   )

															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			:       List[str]					    =  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

	__lowercase	:						Any       =	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',
	)
	__lowercase	:						List[str]       =	parser.parse_args()

	__lowercase	:						List[str]       =	pollard_rho(args.num, attempts=args.attempts)
	if divisor is None:
		print(f'''{args.num} is probably prime''')
	else:
		__lowercase	:						List[str]       =	args.num // divisor
		print(f'''{args.num} = {divisor} * {quotient}''')







"""simple docstring"""







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


__lowercase    					=      logging.get_logger(__name__)

__lowercase    					=      {
    """facebook/dpr-ctx_encoder-single-nq-base""": (
        """https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/config.json"""
    ),
    """facebook/dpr-question_encoder-single-nq-base""": (
        """https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/config.json"""
    ),
    """facebook/dpr-reader-single-nq-base""": (
        """https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/config.json"""
    ),
    """facebook/dpr-ctx_encoder-multiset-base""": (
        """https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/config.json"""
    ),
    """facebook/dpr-question_encoder-multiset-base""": (
        """https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/config.json"""
    ),
    """facebook/dpr-reader-multiset-base""": (
        """https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/config.json"""
    ),
}






class 						_A  (  _a  ):







    """simple docstring"""




    UpperCAmelCase       :							int	=       """dpr"""






    def __init__(					self				:    List[Any]				, __UpperCAmelCase				:    int=30522				, __UpperCAmelCase				:    Union[str, Any]=768				, __UpperCAmelCase				:    Dict=12				, __UpperCAmelCase				:    List[str]=12				, __UpperCAmelCase				:    Any=3072				, __UpperCAmelCase				:    Optional[int]="gelu"				, __UpperCAmelCase				:    Any=0.1				, __UpperCAmelCase				:    Union[str, Any]=0.1				, __UpperCAmelCase				:    str=512				, __UpperCAmelCase				:    List[str]=2				, __UpperCAmelCase				:    Tuple=0.02				, __UpperCAmelCase				:    List[str]=1e-12				, __UpperCAmelCase				:    List[str]=0				, __UpperCAmelCase				:    str="absolute"				, __UpperCAmelCase				:    int = 0				, **__UpperCAmelCase				:    Tuple				, ):
      super().__init__(pad_token_id=__UpperCAmelCase				, **__UpperCAmelCase)

      a						:		List[Any]      							=			vocab_size
      a						:		Optional[Any]      							=			hidden_size
      a						:		Union[str, Any]      							=			num_hidden_layers
      a						:		Dict      							=			num_attention_heads
      a						:		int      							=			hidden_act
      a						:		Any      							=			intermediate_size
      a						:		Any      							=			hidden_dropout_prob
      a						:		Dict      							=			attention_probs_dropout_prob
      a						:		Any      							=			max_position_embeddings
      a						:		Union[str, Any]      							=			type_vocab_size
      a						:		Optional[Any]      							=			initializer_range
      a						:		Dict      							=			layer_norm_eps
      a						:		int      							=			projection_dim
      a						:		str      							=			position_embedding_type






