"""simple docstring"""




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


__lowerCAmelCase    :							List[str]													=						logging.get_logger(__name__)

__lowerCAmelCase    :							List[Any]													=						{
    "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_      (     _UpperCAmelCase			):

					'''simple docstring'''





					UpperCamelCase_ :	Optional[int]			=    """dpr"""




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

							lowerCAmelCase__        =   vocab_size
							lowerCAmelCase__        =   hidden_size
							lowerCAmelCase__        =   num_hidden_layers
							lowerCAmelCase__        =   num_attention_heads
							lowerCAmelCase__        =   hidden_act
							lowerCAmelCase__        =   intermediate_size
							lowerCAmelCase__        =   hidden_dropout_prob
							lowerCAmelCase__        =   attention_probs_dropout_prob
							lowerCAmelCase__        =   max_position_embeddings
							lowerCAmelCase__        =   type_vocab_size
							lowerCAmelCase__        =   initializer_range
							lowerCAmelCase__        =   layer_norm_eps
							lowerCAmelCase__        =   projection_dim
							lowerCAmelCase__        =   position_embedding_type





"""simple docstring"""




from __future__ import annotations

from math import gcd







def 							_UpperCAmelCase		(       lowerCamelCase__			,  lowerCamelCase__ = 2			,  lowerCamelCase__ = 1			,  lowerCamelCase__ = 3			,  ):





		"""simple docstring"""




		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.
				lowerCAmelCase__        =   seed
				lowerCAmelCase__        =   seed

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

			__lowerCAmelCase    :							Union[str, 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",
			)
			__lowerCAmelCase    :							List[str]													=						parser.parse_args()

			__lowerCAmelCase    :							Dict													=						pollard_rho(args.num, attempts=args.attempts)
			if divisor is None:
						print(F"{args.num} is probably prime")
			else:
						__lowerCAmelCase    :							List[str]													=						args.num // divisor
						print(F"{args.num} = {divisor} * {quotient}")




