
"""simple docstring"""





from __future__ import annotations

from math import gcd



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

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

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

						# 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``.
						__SCREAMING_SNAKE_CASE            = gcd(hare - tortoise  ,				UpperCamelCase_				)

						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.
				__SCREAMING_SNAKE_CASE            = 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

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

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








'''simple docstring'''


import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ..auto import CONFIG_MAPPING


lowerCamelCase__					=   logging.get_logger(__name__)

lowerCamelCase__					=   {
    'ut/deta': 'https://huggingface.co/ut/deta/resolve/main/config.json',
}






class 		lowerCAmelCase__	(	UpperCAmelCase__		):
			lowerCAmelCase       :		Any				      =   "deta"
			lowerCAmelCase       :		Union[str, Any]				      =   {
			    "hidden_size": "d_model",
			    "num_attention_heads": "encoder_attention_heads",
			}




			def __init__(						self     :   Optional[Any]		,     lowerCamelCase__     :   str=None		,     lowerCamelCase__     :   str=9_00		,     lowerCamelCase__     :   Any=20_48		,     lowerCamelCase__     :   Optional[int]=6		,     lowerCamelCase__     :   str=20_48		,     lowerCamelCase__     :   Dict=8		,     lowerCamelCase__     :   Any=6		,     lowerCamelCase__     :   Union[str, Any]=10_24		,     lowerCamelCase__     :   Optional[int]=8		,     lowerCamelCase__     :   List[Any]=0.0		,     lowerCamelCase__     :   Tuple=True		,     lowerCamelCase__     :   int="relu"		,     lowerCamelCase__     :   str=2_56		,     lowerCamelCase__     :   Dict=0.1		,     lowerCamelCase__     :   Dict=0.0		,     lowerCamelCase__     :   Dict=0.0		,     lowerCamelCase__     :   Optional[int]=0.0_2		,     lowerCamelCase__     :   List[Any]=1.0		,     lowerCamelCase__     :   Optional[int]=True		,     lowerCamelCase__     :   Any=False		,     lowerCamelCase__     :   Any="sine"		,     lowerCamelCase__     :   str=5		,     lowerCamelCase__     :   Optional[int]=4		,     lowerCamelCase__     :   int=4		,     lowerCamelCase__     :   Optional[Any]=True		,     lowerCamelCase__     :   Dict=3_00		,     lowerCamelCase__     :   int=True		,     lowerCamelCase__     :   Dict=True		,     lowerCamelCase__     :   Union[str, Any]=1		,     lowerCamelCase__     :   Any=5		,     lowerCamelCase__     :   List[Any]=2		,     lowerCamelCase__     :   Union[str, Any]=1		,     lowerCamelCase__     :   str=1		,     lowerCamelCase__     :   Union[str, Any]=5		,     lowerCamelCase__     :   str=2		,     lowerCamelCase__     :   Optional[Any]=0.1		,     lowerCamelCase__     :   Union[str, Any]=0.2_5		,     **lowerCamelCase__     :   Optional[Any]		,     )      ->List[str]:



					'''simple docstring'''







					if backbone_config is None:
							logger.info("`backbone_config` is `None`. Initializing the config with the default `ResNet` backbone."       )
							_UpperCAmelCase						:				int	    =					CONFIG_MAPPING["resnet"](out_features=["stage2", "stage3", "stage4"]       )
					else:
							if isinstance(lowerCamelCase__		,     lowerCamelCase__       ):
									_UpperCAmelCase						:				Any	    =					backbone_config.pop("model_type"       )
									_UpperCAmelCase						:				Optional[int]	    =					CONFIG_MAPPING[backbone_model_type]
									_UpperCAmelCase						:				List[str]	    =					config_class.from_dict(lowerCamelCase__       )

					_UpperCAmelCase						:				Optional[Any]	    =					backbone_config
					_UpperCAmelCase						:				Optional[int]	    =					num_queries
					_UpperCAmelCase						:				Union[str, Any]	    =					max_position_embeddings
					_UpperCAmelCase						:				Union[str, Any]	    =					d_model
					_UpperCAmelCase						:				str	    =					encoder_ffn_dim
					_UpperCAmelCase						:				Optional[int]	    =					encoder_layers
					_UpperCAmelCase						:				int	    =					encoder_attention_heads
					_UpperCAmelCase						:				Union[str, Any]	    =					decoder_ffn_dim
					_UpperCAmelCase						:				Tuple	    =					decoder_layers
					_UpperCAmelCase						:				Union[str, Any]	    =					decoder_attention_heads
					_UpperCAmelCase						:				Any	    =					dropout
					_UpperCAmelCase						:				List[str]	    =					attention_dropout
					_UpperCAmelCase						:				Union[str, Any]	    =					activation_dropout
					_UpperCAmelCase						:				Optional[int]	    =					activation_function
					_UpperCAmelCase						:				str	    =					init_std
					_UpperCAmelCase						:				Tuple	    =					init_xavier_std
					_UpperCAmelCase						:				Optional[Any]	    =					encoder_layerdrop
					_UpperCAmelCase						:				int	    =					auxiliary_loss
					_UpperCAmelCase						:				Union[str, Any]	    =					position_embedding_type
					# deformable attributes
					_UpperCAmelCase						:				List[Any]	    =					num_feature_levels
					_UpperCAmelCase						:				List[Any]	    =					encoder_n_points
					_UpperCAmelCase						:				Tuple	    =					decoder_n_points
					_UpperCAmelCase						:				Optional[int]	    =					two_stage
					_UpperCAmelCase						:				Dict	    =					two_stage_num_proposals
					_UpperCAmelCase						:				int	    =					with_box_refine
					_UpperCAmelCase						:				str	    =					assign_first_stage
					if two_stage is True and with_box_refine is False:
							raise ValueError("If two_stage is True, with_box_refine must be True."       )
					# Hungarian matcher
					_UpperCAmelCase						:				Optional[int]	    =					class_cost
					_UpperCAmelCase						:				Dict	    =					bbox_cost
					_UpperCAmelCase						:				int	    =					giou_cost
					# Loss coefficients
					_UpperCAmelCase						:				int	    =					mask_loss_coefficient
					_UpperCAmelCase						:				List[Any]	    =					dice_loss_coefficient
					_UpperCAmelCase						:				Dict	    =					bbox_loss_coefficient
					_UpperCAmelCase						:				int	    =					giou_loss_coefficient
					_UpperCAmelCase						:				Optional[Any]	    =					eos_coefficient
					_UpperCAmelCase						:				int	    =					focal_alpha
					super().__init__(is_encoder_decoder=lowerCamelCase__		,     **lowerCamelCase__       )




			@property
			def 							lowerCAmelCase__			(						self     :   int       )      ->int:



					'''simple docstring'''







					return self.encoder_attention_heads




			@property
			def 							lowerCAmelCase__			(						self     :   List[Any]       )      ->int:



					'''simple docstring'''







					return self.d_model






			def 							lowerCAmelCase__			(						self     :   Union[str, Any]       )      ->int:



					'''simple docstring'''







					_UpperCAmelCase						:				Optional[int]	    =					copy.deepcopy(self.__dict__       )
					_UpperCAmelCase						:				Tuple	    =					self.backbone_config.to_dict()
					_UpperCAmelCase						:				List[Any]	    =					self.__class__.model_type
					return output



