





from __future__ import annotations

from math import gcd





def       _UpperCamelCase       (a__				:int				,     a__				:int = 2				,     a__				:int = 1				,     a__				:int = 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(a__				:int				,     a__				:int				,     a__				:int    ) -> int:
														return (pow(a__				,     2    ) + step) % modulus

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

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

																					# 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``.
																					UpperCamelCase__			       =     gcd(hare - tortoise				,     a__    )

																					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.
														UpperCamelCase__			       =     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

					UpperCamelCase__     =	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",
					)
					UpperCamelCase__     =	parser.parse_args()

					UpperCamelCase__     =	pollard_rho(args.num, attempts=args.attempts)
					if divisor is None:
										print(f"""{args.num} is probably prime""")
					else:
										UpperCamelCase__     =	args.num // divisor
										print(f"""{args.num} = {divisor} * {quotient}""")











import logging

from transformers.configuration_utils import PretrainedConfig


UpperCamelCase__     =	logging.getLogger(__name__)

class     __SCREAMING_SNAKE_CASE   (       _a    ):
							snake_case       : Optional[Any]         =    """masked_bert"""






							def __init__(  self					,	__lowerCAmelCase=30522					,	__lowerCAmelCase=768					,	__lowerCAmelCase=12					,	__lowerCAmelCase=12					,	__lowerCAmelCase=3072					,	__lowerCAmelCase="gelu"					,	__lowerCAmelCase=0.1					,	__lowerCAmelCase=0.1					,	__lowerCAmelCase=512					,	__lowerCAmelCase=2					,	__lowerCAmelCase=0.02					,	__lowerCAmelCase=1E-12					,	__lowerCAmelCase=0					,	__lowerCAmelCase="topK"					,	__lowerCAmelCase="constant"					,	__lowerCAmelCase=0.0					,	**__lowerCAmelCase					,	):
														super().__init__(pad_token_id=__lowerCAmelCase					,	**__lowerCAmelCase					)

														UpperCamelCase__			       =     vocab_size
														UpperCamelCase__			       =     hidden_size
														UpperCamelCase__			       =     num_hidden_layers
														UpperCamelCase__			       =     num_attention_heads
														UpperCamelCase__			       =     hidden_act
														UpperCamelCase__			       =     intermediate_size
														UpperCamelCase__			       =     hidden_dropout_prob
														UpperCamelCase__			       =     attention_probs_dropout_prob
														UpperCamelCase__			       =     max_position_embeddings
														UpperCamelCase__			       =     type_vocab_size
														UpperCamelCase__			       =     initializer_range
														UpperCamelCase__			       =     layer_norm_eps
														UpperCamelCase__			       =     pruning_method
														UpperCamelCase__			       =     mask_init
														UpperCamelCase__			       =     mask_scale




