



"""simple docstring"""


from __future__ import annotations

from math import gcd







def  lowercase	(      _SCREAMING_SNAKE_CASE   :						int					,     _SCREAMING_SNAKE_CASE   :						int = 2					,     _SCREAMING_SNAKE_CASE   :						int = 1					,     _SCREAMING_SNAKE_CASE   :						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(_SCREAMING_SNAKE_CASE   :						int					,     _SCREAMING_SNAKE_CASE   :						int					,     _SCREAMING_SNAKE_CASE   :						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

					__A   :							int										=   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   :							Any										=   parser.parse_args()

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









"""simple docstring"""


from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ...utils.backbone_utils import BackboneConfigMixin, get_aligned_output_features_output_indices


__A   :							Optional[int]										=   logging.get_logger(__name__)

__A   :							Optional[Any]										=   {
    "google/bit-50": "https://huggingface.co/google/bit-50/resolve/main/config.json",
}
class 			_a (					lowerCAmelCase			,							lowerCAmelCase):
			"""simple docstring"""
			UpperCamelCase__			      =	"""bit"""
			UpperCamelCase__			      =	["""preactivation""", """bottleneck"""]
			UpperCamelCase__			      =	["""SAME""", """VALID"""]



			def __init__(		self     :    List[Any]				,   __UpperCamelCase     :    Optional[int]=3				,   __UpperCamelCase     :    Optional[int]=6_4				,   __UpperCamelCase     :    List[Any]=[2_5_6, 5_1_2, 1_0_2_4, 2_0_4_8]				,   __UpperCamelCase     :    Any=[3, 4, 6, 3]				,   __UpperCamelCase     :    str="preactivation"				,   __UpperCamelCase     :    Union[str, Any]="relu"				,   __UpperCamelCase     :    str=None				,   __UpperCamelCase     :    Dict=3_2				,   __UpperCamelCase     :    List[str]=0.0				,   __UpperCamelCase     :    Any=False				,   __UpperCamelCase     :    Union[str, Any]=3_2				,   __UpperCamelCase     :    List[str]=1				,   __UpperCamelCase     :    List[str]=None				,   __UpperCamelCase     :    Optional[Any]=None				,   **__UpperCamelCase     :    List[str]				,   )->List[Any]:
							super().__init__(**__UpperCamelCase   )
							if layer_type not in self.layer_types:
											raise ValueError(F'layer_type={layer_type} is not one of {",".join(self.layer_types   )}'   )
							if global_padding is not None:
											if global_padding.upper() in self.supported_padding:
															_UpperCAmelCase					=    global_padding.upper()
											else:
															raise ValueError(F'Padding strategy {global_padding} not supported'   )
							_UpperCAmelCase					=    num_channels
							_UpperCAmelCase					=    embedding_size
							_UpperCAmelCase					=    hidden_sizes
							_UpperCAmelCase					=    depths
							_UpperCAmelCase					=    layer_type
							_UpperCAmelCase					=    hidden_act
							_UpperCAmelCase					=    global_padding
							_UpperCAmelCase					=    num_groups
							_UpperCAmelCase					=    drop_path_rate
							_UpperCAmelCase					=    embedding_dynamic_padding
							_UpperCAmelCase					=    output_stride
							_UpperCAmelCase					=    width_factor

							_UpperCAmelCase					=    ['''stem'''] + [F'stage{idx}' for idx in range(1				,   len(__UpperCamelCase   ) + 1   )]
							_UpperCAmelCase		,						_UpperCAmelCase					=    get_aligned_output_features_output_indices(
							    out_features=__UpperCamelCase				,   out_indices=__UpperCamelCase				,   stage_names=self.stage_names   )



