


from __future__ import annotations

from math import gcd

def    lowercase_	(	_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.
            lowerCamelCase__	:       Dict					=						seed
            lowerCamelCase__	:       Optional[Any]					=						seed

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

    A   :					Optional[int]	=      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}')






from collections import OrderedDict
from typing import Mapping

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


A   :					int	=      logging.get_logger(__name__)

A   :					Optional[int]	=      {
    "facebook/xmod-base": "https://huggingface.co/facebook/xmod-base/resolve/main/config.json",
    "facebook/xmod-large-prenorm": "https://huggingface.co/facebook/xmod-large-prenorm/resolve/main/config.json",
    "facebook/xmod-base-13-125k": "https://huggingface.co/facebook/xmod-base-13-125k/resolve/main/config.json",
    "facebook/xmod-base-30-125k": "https://huggingface.co/facebook/xmod-base-30-125k/resolve/main/config.json",
    "facebook/xmod-base-30-195k": "https://huggingface.co/facebook/xmod-base-30-195k/resolve/main/config.json",
    "facebook/xmod-base-60-125k": "https://huggingface.co/facebook/xmod-base-60-125k/resolve/main/config.json",
    "facebook/xmod-base-60-265k": "https://huggingface.co/facebook/xmod-base-60-265k/resolve/main/config.json",
    "facebook/xmod-base-75-125k": "https://huggingface.co/facebook/xmod-base-75-125k/resolve/main/config.json",
    "facebook/xmod-base-75-269k": "https://huggingface.co/facebook/xmod-base-75-269k/resolve/main/config.json",
}







class     _lowercase				(							lowercase__):


       """simple docstring"""




       A__      		=    "xmod"





       def __init__(     self							:    int      ,   __lowerCamelCase							:    Any=30522      ,   __lowerCamelCase							:    Any=768      ,   __lowerCamelCase							:    str=12      ,   __lowerCamelCase							:    Any=12      ,   __lowerCamelCase							:    List[str]=3072      ,   __lowerCamelCase							:    List[Any]="gelu"      ,   __lowerCamelCase							:    Union[str, Any]=0.1      ,   __lowerCamelCase							:    int=0.1      ,   __lowerCamelCase							:    Tuple=512      ,   __lowerCamelCase							:    str=2      ,   __lowerCamelCase							:    List[str]=0.0_2      ,   __lowerCamelCase							:    List[str]=1E-1_2      ,   __lowerCamelCase							:    str=1      ,   __lowerCamelCase							:    Optional[int]=0      ,   __lowerCamelCase							:    Optional[Any]=2      ,   __lowerCamelCase							:    str="absolute"      ,   __lowerCamelCase							:    List[str]=True      ,   __lowerCamelCase							:    Dict=None      ,   __lowerCamelCase							:    Optional[Any]=False      ,   __lowerCamelCase							:    Optional[Any]=2      ,   __lowerCamelCase							:    Tuple=False      ,   __lowerCamelCase							:    Tuple=True      ,   __lowerCamelCase							:    Union[str, Any]=True      ,   __lowerCamelCase							:    str=("en_XX",)      ,   __lowerCamelCase							:    Union[str, Any]=None      ,   **__lowerCamelCase							:    Optional[int]      ,   ):


             '''simple docstring'''



             super().__init__(pad_token_id=__lowerCamelCase      ,   bos_token_id=__lowerCamelCase      ,   eos_token_id=__lowerCamelCase      ,   **__lowerCamelCase )

             lowerCamelCase__	:       Union[str, Any]					=						vocab_size
             lowerCamelCase__	:       Union[str, Any]					=						hidden_size
             lowerCamelCase__	:       Optional[int]					=						num_hidden_layers
             lowerCamelCase__	:       List[Any]					=						num_attention_heads
             lowerCamelCase__	:       Union[str, Any]					=						hidden_act
             lowerCamelCase__	:       Optional[int]					=						intermediate_size
             lowerCamelCase__	:       Optional[int]					=						hidden_dropout_prob
             lowerCamelCase__	:       List[Any]					=						attention_probs_dropout_prob
             lowerCamelCase__	:       Any					=						max_position_embeddings
             lowerCamelCase__	:       List[Any]					=						type_vocab_size
             lowerCamelCase__	:       int					=						initializer_range
             lowerCamelCase__	:       Tuple					=						layer_norm_eps
             lowerCamelCase__	:       Union[str, Any]					=						position_embedding_type
             lowerCamelCase__	:       str					=						use_cache
             lowerCamelCase__	:       Union[str, Any]					=						classifier_dropout
             lowerCamelCase__	:       Any					=						pre_norm
             lowerCamelCase__	:       Tuple					=						adapter_reduction_factor
             lowerCamelCase__	:       Tuple					=						adapter_layer_norm
             lowerCamelCase__	:       List[Any]					=						adapter_reuse_layer_norm
             lowerCamelCase__	:       Dict					=						ln_before_adapter
             lowerCamelCase__	:       List[Any]					=						list(__lowerCamelCase )
             lowerCamelCase__	:       Optional[Any]					=						default_language







class     _lowercase				(							lowercase__):


       """simple docstring"""




       @property
       def 		lowerCAmelCase  (     self							:    Tuple ):


             '''simple docstring'''



             if self.task == "multiple-choice":
                   lowerCamelCase__	:       Dict					=						{0: "batch", 1: "choice", 2: "sequence"}
             else:
                   lowerCamelCase__	:       List[str]					=						{0: "batch", 1: "sequence"}
             return OrderedDict(
                 [
                     ("input_ids", dynamic_axis),
                     ("attention_mask", dynamic_axis),
                 ] )


