





from collections import OrderedDict
from typing import TYPE_CHECKING, Any, List, Mapping, Optional

from packaging import version


if TYPE_CHECKING:
  from ... import PreTrainedTokenizer, TensorType

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfigWithPast, PatchingSpec
from ...utils import is_torch_available, logging


__lowerCAmelCase							:     Dict		     =logging.get_logger(__name__)

__lowerCAmelCase							:     Union[str, Any]		     ={
    "bigscience/bloom": "https://huggingface.co/bigscience/bloom/resolve/main/config.json",
    "bigscience/bloom-560m": "https://huggingface.co/bigscience/bloom-560m/blob/main/config.json",
    "bigscience/bloom-1b1": "https://huggingface.co/bigscience/bloom-1b1/blob/main/config.json",
    "bigscience/bloom-1b7": "https://huggingface.co/bigscience/bloom-1b7/blob/main/config.json",
    "bigscience/bloom-3b": "https://huggingface.co/bigscience/bloom-3b/blob/main/config.json",
    "bigscience/bloom-7b1": "https://huggingface.co/bigscience/bloom-7b1/blob/main/config.json",
}






class        UpperCAmelCase     (	__lowercase    ):
 __lowercase       		=    """bloom"""
 __lowercase       		=    ["""past_key_values"""]
 __lowercase       		=    {
     """num_hidden_layers""": """n_layer""",
     """num_attention_heads""": """n_head""",
 }
 def __init__(    self				:List[Any]						,	lowercase_				:Tuple=25_08_80						,	lowercase_				:Optional[int]=64						,	lowercase_				:List[Any]=2						,	lowercase_				:Tuple=8						,	lowercase_				:Union[str, Any]=1E-5						,	lowercase_				:str=0.0_2						,	lowercase_				:Optional[Any]=True						,	lowercase_				:List[str]=1						,	lowercase_				:Union[str, Any]=2						,	lowercase_				:Any=False						,	lowercase_				:List[Any]=0.0						,	lowercase_				:int=0.0						,	lowercase_				:Tuple=1						,	lowercase_				:List[Any]=False						,	**lowercase_				:str						,	)->							Dict:
     A__    =      vocab_size
     # Backward compatibility with n_embed kwarg
     A__    =      kwargs.pop("n_embed"						,	_a							)
     A__    =      hidden_size if n_embed is None else n_embed
     A__    =      n_layer
     A__    =      n_head
     A__    =      layer_norm_epsilon
     A__    =      initializer_range
     A__    =      use_cache
     A__    =      pretraining_tp
     A__    =      apply_residual_connection_post_layernorm
     A__    =      hidden_dropout
     A__    =      attention_dropout

     A__    =      bos_token_id
     A__    =      eos_token_id
     A__    =      slow_but_exact

     super().__init__(bos_token_id=_a						,	eos_token_id=_a						,	**_a							)






class        UpperCAmelCase     (	__lowercase    ):
 __lowercase       		=    version.parse("""1.12"""    )
 def __init__(    self				:Any						,	lowercase_				:int						,	lowercase_				:Dict = "default"						,	lowercase_				:Dict = None						,	lowercase_				:Union[str, Any] = False						,	)->							int:
     super().__init__(_a						,	task=_a						,	patching_specs=_a						,	use_past=_a							)
     if not getattr(self._config						,	"pad_token_id"						,	_a							):
         # TODO: how to do that better?
         A__    =      0
 @property
 def 					UpperCAmelCase_							(    self				:List[str]							)->							Mapping[str, Mapping[int, str]]:
     A__    =      OrderedDict({"input_ids": {0: "batch", 1: "sequence"}}							)
     if self.use_past:
         # BLOOM stores values on dynamic axis 2. For more details see: https://github.com/huggingface/transformers/pull/18344
         self.fill_with_past_key_values_(_a						,	direction="inputs"						,	inverted_values_shape=_a							)
         A__    =      {0: "batch", 1: "past_sequence + sequence"}
     else:
         A__    =      {0: "batch", 1: "sequence"}

     return common_inputs
 @property
 def 					UpperCAmelCase_							(    self				:Union[str, Any]							)->							int:
     return self._config.n_layer
 @property
 def 					UpperCAmelCase_							(    self				:Union[str, Any]							)->							int:
     return self._config.n_head
 @property
 def 					UpperCAmelCase_							(    self				:Dict							)->							float:
     return 1E-3
 def 					UpperCAmelCase_							(    self				:Dict						,	lowercase_				:Optional[int]						,	lowercase_				:Dict = -1						,	lowercase_				:Optional[int] = -1						,	lowercase_				:Optional[Any] = False						,	lowercase_				:Optional[int] = None						,	)->							Mapping[str, Any]:
     A__    =      super(_a						,	self							).generate_dummy_inputs(
         _a						,	batch_size=_a						,	seq_length=_a						,	is_pair=_a						,	framework=_a							)

     # We need to order the input in the way they appears in the forward()
     A__    =      OrderedDict({"input_ids": common_inputs["input_ids"]}							)

     # Need to add the past_keys
     if self.use_past:
         if not is_torch_available():
             raise ValueError("Cannot generate dummy past_keys inputs without PyTorch installed."							)
         else:
             import torch

             A__,     A__    =      common_inputs["input_ids"].shape
             # Not using the same length for past_key_values
             A__    =      seqlen + 2
             A__    =      self._config.hidden_size // self.num_attention_heads
             A__    =      (
                 batch * self.num_attention_heads,
                 head_dim,
                 past_key_values_length,
             )
             A__    =      (
                 batch * self.num_attention_heads,
                 past_key_values_length,
                 head_dim,
             )
             A__    =      [
                 (torch.zeros(_a							), torch.zeros(_a							)) for _ in range(self.num_layers							)
             ]

     A__    =      common_inputs["attention_mask"]
     if self.use_past:
         A__    =      ordered_inputs["attention_mask"].dtype
         A__    =      torch.cat(
             [ordered_inputs["attention_mask"], torch.ones(_a						,	_a						,	dtype=_a							)]						,	dim=1							)

     return ordered_inputs



 @property
 def 					UpperCAmelCase_							(    self				:Any							)->							int:
     return 13










'''simple docstring'''

from __future__ import annotations

from math import gcd





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

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

        while True:
            # At each iteration, the tortoise moves one step and the hare moves two.
            A__    =      rand_fn(_lowerCamelCase						,	_lowerCamelCase						,	_lowerCamelCase	)
            A__    =      rand_fn(_lowerCamelCase						,	_lowerCamelCase						,	_lowerCamelCase	)
            A__    =      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__    =      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__    =      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							:     Optional[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",
  )
  __lowerCAmelCase							:     Optional[int]		     =parser.parse_args()

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



