


"""simple docstring"""
from collections import OrderedDict
from typing import Mapping

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import logging


UpperCAmelCase				=						logging.get_logger(__name__)

UpperCAmelCase				=						{
    """google/bigbird-roberta-base""": """https://huggingface.co/google/bigbird-roberta-base/resolve/main/config.json""",
    """google/bigbird-roberta-large""": """https://huggingface.co/google/bigbird-roberta-large/resolve/main/config.json""",
    """google/bigbird-base-trivia-itc""": """https://huggingface.co/google/bigbird-base-trivia-itc/resolve/main/config.json""",
    # See all BigBird models at https://huggingface.co/models?filter=big_bird
}




class 	lowercase__				(					A_				):
   __UpperCAmelCase							       =					'''big_bird'''





   def __init__(							self      ,   SCREAMING_SNAKE_CASE=5_0358      ,   SCREAMING_SNAKE_CASE=768      ,   SCREAMING_SNAKE_CASE=12      ,   SCREAMING_SNAKE_CASE=12      ,   SCREAMING_SNAKE_CASE=3072      ,   SCREAMING_SNAKE_CASE="gelu_new"      ,   SCREAMING_SNAKE_CASE=0.1      ,   SCREAMING_SNAKE_CASE=0.1      ,   SCREAMING_SNAKE_CASE=4096      ,   SCREAMING_SNAKE_CASE=2      ,   SCREAMING_SNAKE_CASE=0.02      ,   SCREAMING_SNAKE_CASE=1e-1_2      ,   SCREAMING_SNAKE_CASE=True      ,   SCREAMING_SNAKE_CASE=0      ,   SCREAMING_SNAKE_CASE=1      ,   SCREAMING_SNAKE_CASE=2      ,   SCREAMING_SNAKE_CASE=66      ,   SCREAMING_SNAKE_CASE="block_sparse"      ,   SCREAMING_SNAKE_CASE=True      ,   SCREAMING_SNAKE_CASE=False      ,   SCREAMING_SNAKE_CASE=64      ,   SCREAMING_SNAKE_CASE=3      ,   SCREAMING_SNAKE_CASE=None      ,   **SCREAMING_SNAKE_CASE      ,   )  ->  Union[str, Any]:
      super().__init__(
          pad_token_id=SCREAMING_SNAKE_CASE      ,   bos_token_id=SCREAMING_SNAKE_CASE      ,   eos_token_id=SCREAMING_SNAKE_CASE      ,   sep_token_id=SCREAMING_SNAKE_CASE      ,   **SCREAMING_SNAKE_CASE      ,   )

      _lowerCamelCase	:					Optional[Any]   =		vocab_size
      _lowerCamelCase	:					Dict   =		max_position_embeddings
      _lowerCamelCase	:					int   =		hidden_size
      _lowerCamelCase	:					Any   =		num_hidden_layers
      _lowerCamelCase	:					Optional[int]   =		num_attention_heads
      _lowerCamelCase	:					int   =		intermediate_size
      _lowerCamelCase	:					int   =		hidden_act
      _lowerCamelCase	:					Union[str, Any]   =		hidden_dropout_prob
      _lowerCamelCase	:					Optional[Any]   =		attention_probs_dropout_prob
      _lowerCamelCase	:					str   =		initializer_range
      _lowerCamelCase	:					Optional[int]   =		type_vocab_size
      _lowerCamelCase	:					Optional[int]   =		layer_norm_eps
      _lowerCamelCase	:					Optional[Any]   =		use_cache

      _lowerCamelCase	:					Any   =		rescale_embeddings
      _lowerCamelCase	:					Optional[int]   =		attention_type
      _lowerCamelCase	:					Optional[int]   =		use_bias
      _lowerCamelCase	:					List[Any]   =		block_size
      _lowerCamelCase	:					str   =		num_random_blocks
      _lowerCamelCase	:					Any   =		classifier_dropout







class 	lowercase__				(					A_				):





   @property
   def 		UpperCamelCase_  (							self)  ->  Mapping[str, Mapping[int, str]]:
      if self.task == "multiple-choice":
         _lowerCamelCase	:					str   =		{0: """batch""", 1: """choice""", 2: """sequence"""}
      else:
         _lowerCamelCase	:					Optional[Any]   =		{0: """batch""", 1: """sequence"""}
      return OrderedDict(
          [
              ("""input_ids""", dynamic_axis),
              ("""attention_mask""", dynamic_axis),
          ])






'''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}""")




