



'''simple docstring'''

from __future__ import annotations

from math import gcd



def 	__lowerCamelCase	( lowerCAmelCase_		,     lowerCAmelCase_ = 2		,     lowerCAmelCase_ = 1		,     lowerCAmelCase_ = 3		,     )     -> int | None:
		# 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(lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_    ) -> int:
				return (pow(lowerCAmelCase_		,     2    ) + step) % modulus

		for _ in range(lowerCAmelCase_    ):
				# These track the position within the cycle detection logic.
				_a	: Optional[int]								=				seed
				_a	: str								=				seed

				while True:
						# At each iteration, the tortoise moves one step and the hare moves two.
						_a	: str								=				rand_fn(lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_    )
						_a	: Dict								=				rand_fn(lowerCAmelCase_		,     lowerCAmelCase_		,     lowerCAmelCase_    )
						_a	: Tuple								=				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``.
						_a	: Optional[Any]								=				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.
				_a	: Union[str, Any]								=				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		     =  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		     =  parser.parse_args()

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









'''simple docstring'''

from dataclasses import asdict, dataclass
from typing import Optional

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


__lowerCAmelCase		     =  logging.get_logger(__name__)

# TODO Update this
__lowerCAmelCase		     =  {
    '''facebook/esm-1b''': '''https://huggingface.co/facebook/esm-1b/resolve/main/config.json''',
    # See all ESM models at https://huggingface.co/models?filter=esm
}

class       __magic_name__		(       _UpperCamelCase  ):
							lowerCAmelCase			:       Any  							=   'esm'







							def __init__(				self   :			Optional[int]      ,_UpperCAmelCase   :			Optional[Any]=None      ,_UpperCAmelCase   :			Dict=None      ,_UpperCAmelCase   :			Union[str, Any]=None      ,_UpperCAmelCase   :			List[Any]=768      ,_UpperCAmelCase   :			Union[str, Any]=12      ,_UpperCAmelCase   :			List[str]=12      ,_UpperCAmelCase   :			Tuple=3072      ,_UpperCAmelCase   :			Dict=0.1      ,_UpperCAmelCase   :			Tuple=0.1      ,_UpperCAmelCase   :			List[str]=1026      ,_UpperCAmelCase   :			List[str]=0.02      ,_UpperCAmelCase   :			Optional[int]=1E-12      ,_UpperCAmelCase   :			List[str]="absolute"      ,_UpperCAmelCase   :			Tuple=True      ,_UpperCAmelCase   :			Tuple=None      ,_UpperCAmelCase   :			List[Any]=False      ,_UpperCAmelCase   :			int=False      ,_UpperCAmelCase   :			int=None      ,_UpperCAmelCase   :			Union[str, Any]=None      ,**_UpperCAmelCase   :			List[Any]      ,):
									super().__init__(pad_token_id=_UpperCAmelCase      ,mask_token_id=_UpperCAmelCase      ,**_UpperCAmelCase						)

									_a	: Optional[Any]								=				vocab_size
									_a	: Union[str, Any]								=				hidden_size
									_a	: Dict								=				num_hidden_layers
									_a	: int								=				num_attention_heads
									_a	: Dict								=				intermediate_size
									_a	: List[Any]								=				hidden_dropout_prob
									_a	: List[Any]								=				attention_probs_dropout_prob
									_a	: Optional[Any]								=				max_position_embeddings
									_a	: Optional[int]								=				initializer_range
									_a	: List[Any]								=				layer_norm_eps
									_a	: int								=				position_embedding_type
									_a	: Optional[int]								=				use_cache
									_a	: Any								=				emb_layer_norm_before
									_a	: List[str]								=				token_dropout
									_a	: List[str]								=				is_folding_model
									if is_folding_model:
											if esmfold_config is None:
													logger.info('No esmfold_config supplied for folding model, using default values.'						)
													_a	: Dict								=				EsmFoldConfig()
											elif isinstance(_UpperCAmelCase      ,_UpperCAmelCase						):
													_a	: Dict								=				EsmFoldConfig(**_UpperCAmelCase						)
											_a	: Optional[int]								=				esmfold_config
											if vocab_list is None:
													logger.warning('No vocab_list supplied for folding model, assuming the ESM-2 vocabulary!'						)
													_a	: Optional[int]								=				get_default_vocab_list()
											else:
													_a	: Optional[int]								=				vocab_list
									else:
											_a	: Optional[Any]								=				None
											_a	: Union[str, Any]								=				None
									if self.esmfold_config is not None and getattr(self.esmfold_config      ,'use_esm_attn_map'      ,_UpperCAmelCase						):
											raise ValueError('The HuggingFace port of ESMFold does not support use_esm_attn_map at this time!'						)







							def 				__lowercase     (				self   :			Any						):
									_a	: str								=				super().to_dict()
									if isinstance(self.esmfold_config      ,_UpperCAmelCase						):
											_a	: List[str]								=				self.esmfold_config.to_dict()
									return output

@dataclass
class       __magic_name__		:
							lowerCAmelCase			:       str  							=   None
							lowerCAmelCase			:       bool  							=   True
							lowerCAmelCase			:       bool  							=   False
							lowerCAmelCase			:       bool  							=   False
							lowerCAmelCase			:       bool  							=   False
							lowerCAmelCase			:       float  							=   0

							lowerCAmelCase			:       bool  							=   True
							lowerCAmelCase			:       bool  							=   False

							lowerCAmelCase			:       int  							=   1_2_8
							lowerCAmelCase			:       "TrunkConfig"  							=   None







							def 				__lowercase     (				self   :			List[str]						):
									if self.trunk is None:
											_a	: Dict								=				TrunkConfig()
									elif isinstance(self.trunk      ,_UpperCAmelCase						):
											_a	: str								=				TrunkConfig(**self.trunk						)







							def 				__lowercase     (				self   :			List[Any]						):
									_a	: List[str]								=				asdict(self						)
									_a	: List[str]								=				self.trunk.to_dict()
									return output

@dataclass
class       __magic_name__		:
							lowerCAmelCase			:       int  							=   4_8
							lowerCAmelCase			:       int  							=   1_0_2_4
							lowerCAmelCase			:       int  							=   1_2_8
							lowerCAmelCase			:       int  							=   3_2
							lowerCAmelCase			:       int  							=   3_2
							lowerCAmelCase			:       int  							=   3_2
							lowerCAmelCase			:       float  							=   0
							lowerCAmelCase			:       float  							=   0
							lowerCAmelCase			:       bool  							=   False
							lowerCAmelCase			:       int  							=   4
							lowerCAmelCase			:       Optional[int]  							=   1_2_8
							lowerCAmelCase			:       "StructureModuleConfig"  							=   None







							def 				__lowercase     (				self   :			str						):
									if self.structure_module is None:
											_a	: Tuple								=				StructureModuleConfig()
									elif isinstance(self.structure_module      ,_UpperCAmelCase						):
											_a	: List[str]								=				StructureModuleConfig(**self.structure_module						)

									if self.max_recycles <= 0:
											raise ValueError(F"""`max_recycles` should be positive, got {self.max_recycles}."""						)
									if self.sequence_state_dim % self.sequence_state_dim != 0:
											raise ValueError(
											    '`sequence_state_dim` should be a round multiple of `sequence_state_dim`, got'
											    F""" {self.sequence_state_dim} and {self.sequence_state_dim}."""						)
									if self.pairwise_state_dim % self.pairwise_state_dim != 0:
											raise ValueError(
											    '`pairwise_state_dim` should be a round multiple of `pairwise_state_dim`, got'
											    F""" {self.pairwise_state_dim} and {self.pairwise_state_dim}."""						)

									_a	: Optional[int]								=				self.sequence_state_dim // self.sequence_head_width
									_a	: int								=				self.pairwise_state_dim // self.pairwise_head_width

									if self.sequence_state_dim != sequence_num_heads * self.sequence_head_width:
											raise ValueError(
											    '`sequence_state_dim` should be equal to `sequence_num_heads * sequence_head_width, got'
											    F""" {self.sequence_state_dim} != {sequence_num_heads} * {self.sequence_head_width}."""						)
									if self.pairwise_state_dim != pairwise_num_heads * self.pairwise_head_width:
											raise ValueError(
											    '`pairwise_state_dim` should be equal to `pairwise_num_heads * pairwise_head_width, got'
											    F""" {self.pairwise_state_dim} != {pairwise_num_heads} * {self.pairwise_head_width}."""						)
									if self.pairwise_state_dim % 2 != 0:
											raise ValueError(F"""`pairwise_state_dim` should be even, got {self.pairwise_state_dim}."""						)

									if self.dropout >= 0.4:
											raise ValueError(F"""`dropout` should not be greater than 0.4, got {self.dropout}."""						)







							def 				__lowercase     (				self   :			Optional[int]						):
									_a	: Optional[Any]								=				asdict(self						)
									_a	: Optional[Any]								=				self.structure_module.to_dict()
									return output

@dataclass
class       __magic_name__		:
							lowerCAmelCase			:       int  							=   3_8_4
							lowerCAmelCase			:       int  							=   1_2_8
							lowerCAmelCase			:       int  							=   1_6
							lowerCAmelCase			:       int  							=   1_2_8
							lowerCAmelCase			:       int  							=   1_2
							lowerCAmelCase			:       int  							=   4
							lowerCAmelCase			:       int  							=   8
							lowerCAmelCase			:       float  							=   0.1
							lowerCAmelCase			:       int  							=   8
							lowerCAmelCase			:       int  							=   1
							lowerCAmelCase			:       int  							=   2
							lowerCAmelCase			:       int  							=   7
							lowerCAmelCase			:       int  							=   1_0
							lowerCAmelCase			:       float  							=   1e-8
							lowerCAmelCase			:       float  							=   1e5







							def 				__lowercase     (				self   :			str						):
									return asdict(self						)



def 	__lowerCamelCase	( )     -> Optional[int]:
		return (
		    "<cls>",
		    "<pad>",
		    "<eos>",
		    "<unk>",
		    "L",
		    "A",
		    "G",
		    "V",
		    "S",
		    "E",
		    "R",
		    "T",
		    "I",
		    "D",
		    "P",
		    "K",
		    "Q",
		    "N",
		    "F",
		    "Y",
		    "M",
		    "H",
		    "W",
		    "C",
		    "X",
		    "B",
		    "U",
		    "Z",
		    "O",
		    ".",
		    "-",
		    "<null_1>",
		    "<mask>",
		)




