


"""simple docstring"""






from __future__ import annotations

from math import gcd







def        lowerCamelCase_(		_lowerCamelCase			,		_lowerCamelCase = 2			,		_lowerCamelCase = 1			,		_lowerCamelCase = 3			,		)    ->     int | None:
   '''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(_lowerCamelCase			,		_lowerCamelCase			,		_lowerCamelCase       ) -> int:
      return (pow(_lowerCamelCase			,		2       ) + step) % modulus

   for _ in range(_lowerCamelCase       ):
      # These track the position within the cycle detection logic.
      _lowerCamelCase   :				Union[str, Any]							=     seed
      _lowerCamelCase   :				Optional[Any]							=     seed

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

  _lowerCAmelCase							:    Optional[int]					   =	pollard_rho(args.num, attempts=args.attempts)
  if divisor is None:
    print(f'''{args.num} is probably prime''')
  else:
    _lowerCAmelCase							:    List[str]					   =	args.num // divisor
    print(f'''{args.num} = {divisor} * {quotient}''')







import logging

import torch
from torch import nn
from torch.nn import CrossEntropyLoss, MSELoss

from transformers.file_utils import add_start_docstrings, add_start_docstrings_to_model_forward
from transformers.models.bert.modeling_bert import (
    BERT_INPUTS_DOCSTRING,
    BERT_START_DOCSTRING,
    BertEncoder,
    BertModel,
    BertPreTrainedModel,
)


UpperCamelCase    							=      logging.getLogger(__name__)







class 		_A						( UpperCAmelCase_ ):

  def    a					(    self						:	Tuple   ,				lowerCamelCase__						:	Optional[int]   ,				lowerCamelCase__						:	Union[str, Any]   ,				lowerCamelCase__						:	str=None   ,				lowerCamelCase__						:	int=None			):
     """simple docstring"""

     __UpperCamelCase	:			Optional[Any]					=					self.layer[current_layer](lowerCamelCase__   ,				lowerCamelCase__   ,				head_mask[current_layer]			)

     __UpperCamelCase	:			Optional[Any]					=					layer_outputs[0]

     return hidden_states







@add_start_docstrings(
    '''The bare Bert Model transformer with PABEE outputting raw hidden-states without any specific head on top.'''	,				UpperCAmelCase_	,				)
class 		_A						( UpperCAmelCase_ ):

  def __init__(    self						:	Tuple   ,				lowerCamelCase__						:	Tuple			):
     """simple docstring"""

     super().__init__(lowerCamelCase__			)

     __UpperCamelCase	:			List[str]					=					BertEncoderWithPabee(lowerCamelCase__			)

     self.init_weights()
     __UpperCamelCase	:			Optional[int]					=					0
     __UpperCamelCase	:			Tuple					=					0
     __UpperCamelCase	:			Any					=					0

     __UpperCamelCase	:			Optional[Any]					=					0

  def    a					(    self						:	Union[str, Any]   ,				lowerCamelCase__						:	Any			):
     """simple docstring"""

     __UpperCamelCase	:			List[Any]					=					threshold

  def    a					(    self						:	Optional[int]   ,				lowerCamelCase__						:	Union[str, Any]			):
     """simple docstring"""

     __UpperCamelCase	:			int					=					patience

  def    a					(    self						:	Optional[int]			):
     """simple docstring"""

     __UpperCamelCase	:			int					=					0
     __UpperCamelCase	:			Tuple					=					0

  def    a					(    self						:	int			):
     """simple docstring"""

     __UpperCamelCase	:			int					=					self.inference_layers_num / self.inference_instances_num
     __UpperCamelCase	:			str					=					(
         f'*** Patience = {self.patience} Avg. Inference Layers = {avg_inf_layers:.2f} Speed Up ='
         f' {1 - avg_inf_layers / self.config.num_hidden_layers:.2f} ***'
     )
     print(lowerCamelCase__			)

  @add_start_docstrings_to_model_forward(lowerCamelCase__			)
  def    a					(    self						:	Any   ,				lowerCamelCase__						:	List[Any]=None   ,				lowerCamelCase__						:	List[str]=None   ,				lowerCamelCase__						:	List[Any]=None   ,				lowerCamelCase__						:	Optional[Any]=None   ,				lowerCamelCase__						:	List[str]=None   ,				lowerCamelCase__						:	str=None   ,				lowerCamelCase__						:	List[Any]=None   ,				lowerCamelCase__						:	Any=None   ,				lowerCamelCase__						:	List[str]=None   ,				lowerCamelCase__						:	List[str]=None   ,				lowerCamelCase__						:	str=False   ,				):
     """simple docstring"""

     if input_ids is not None and inputs_embeds is not None:
        raise ValueError("""You cannot specify both input_ids and inputs_embeds at the same time"""			)
     elif input_ids is not None:
        __UpperCamelCase	:			Optional[Any]					=					input_ids.size()
     elif inputs_embeds is not None:
        __UpperCamelCase	:			Tuple					=					inputs_embeds.size()[:-1]
     else:
        raise ValueError("""You have to specify either input_ids or inputs_embeds"""			)

     __UpperCamelCase	:			Tuple					=					input_ids.device if input_ids is not None else inputs_embeds.device

     if attention_mask is None:
        __UpperCamelCase	:			Optional[Any]					=					torch.ones(lowerCamelCase__   ,				device=lowerCamelCase__			)
     if token_type_ids is None:
        __UpperCamelCase	:			str					=					torch.zeros(lowerCamelCase__   ,				dtype=torch.long   ,				device=lowerCamelCase__			)

     # We can provide a self-attention mask of dimensions [batch_size, from_seq_length, to_seq_length]
     # ourselves in which case we just need to make it broadcastable to all heads.
     __UpperCamelCase	:			torch.Tensor					=					self.get_extended_attention_mask(lowerCamelCase__   ,				lowerCamelCase__   ,				lowerCamelCase__			)

     # If a 2D ou 3D attention mask is provided for the cross-attention
     # we need to make broadcastable to [batch_size, num_heads, seq_length, seq_length]
     if self.config.is_decoder and encoder_hidden_states is not None:
        __UpperCamelCase	,     __UpperCamelCase	,     __UpperCamelCase	:			Optional[Any]					=					encoder_hidden_states.size()
        __UpperCamelCase	:			Union[str, Any]					=					(encoder_batch_size, encoder_sequence_length)
        if encoder_attention_mask is None:
           __UpperCamelCase	:			Union[str, Any]					=					torch.ones(lowerCamelCase__   ,				device=lowerCamelCase__			)
        __UpperCamelCase	:			Optional[int]					=					self.invert_attention_mask(lowerCamelCase__			)
     else:
        __UpperCamelCase	:			str					=					None

     # Prepare head mask if needed
     # 1.0 in head_mask indicate we keep the head
     # attention_probs has shape bsz x n_heads x N x N
     # input head_mask has shape [num_heads] or [num_hidden_layers x num_heads]
     # and head_mask is converted to shape [num_hidden_layers x batch x num_heads x seq_length x seq_length]
     __UpperCamelCase	:			int					=					self.get_head_mask(lowerCamelCase__   ,				self.config.num_hidden_layers			)

     __UpperCamelCase	:			Any					=					self.embeddings(
         input_ids=lowerCamelCase__   ,				position_ids=lowerCamelCase__   ,				token_type_ids=lowerCamelCase__   ,				inputs_embeds=lowerCamelCase__			)
     __UpperCamelCase	:			Optional[int]					=					embedding_output

     if self.training:
        __UpperCamelCase	:			List[Any]					=					[]
        for i in range(self.config.num_hidden_layers			):
           __UpperCamelCase	:			List[Any]					=					self.encoder.adaptive_forward(
               lowerCamelCase__   ,				current_layer=lowerCamelCase__   ,				attention_mask=lowerCamelCase__   ,				head_mask=lowerCamelCase__			)

           __UpperCamelCase	:			Tuple					=					self.pooler(lowerCamelCase__			)
           __UpperCamelCase	:			str					=					output_layers[i](output_dropout(lowerCamelCase__			)			)
           res.append(lowerCamelCase__			)
     elif self.patience == 0:  # Use all layers for inference
        __UpperCamelCase	:			Union[str, Any]					=					self.encoder(
            lowerCamelCase__   ,				attention_mask=lowerCamelCase__   ,				head_mask=lowerCamelCase__   ,				encoder_hidden_states=lowerCamelCase__   ,				encoder_attention_mask=lowerCamelCase__   ,				)
        __UpperCamelCase	:			Optional[int]					=					self.pooler(encoder_outputs[0]			)
        __UpperCamelCase	:			Union[str, Any]					=					[output_layers[self.config.num_hidden_layers - 1](lowerCamelCase__			)]
     else:
        __UpperCamelCase	:			Union[str, Any]					=					0
        __UpperCamelCase	:			Optional[Any]					=					None
        __UpperCamelCase	:			List[Any]					=					0
        for i in range(self.config.num_hidden_layers			):
           calculated_layer_num += 1
           __UpperCamelCase	:			Union[str, Any]					=					self.encoder.adaptive_forward(
               lowerCamelCase__   ,				current_layer=lowerCamelCase__   ,				attention_mask=lowerCamelCase__   ,				head_mask=lowerCamelCase__			)

           __UpperCamelCase	:			str					=					self.pooler(lowerCamelCase__			)
           __UpperCamelCase	:			Any					=					output_layers[i](lowerCamelCase__			)
           if regression:
              __UpperCamelCase	:			Optional[int]					=					logits.detach()
              if patient_result is not None:
                 __UpperCamelCase	:			Dict					=					patient_result.detach()
              if (patient_result is not None) and torch.abs(patient_result - labels			) < self.regression_threshold:
                 patient_counter += 1
              else:
                 __UpperCamelCase	:			List[str]					=					0
           else:
              __UpperCamelCase	:			Optional[int]					=					logits.detach().argmax(dim=1			)
              if patient_result is not None:
                 __UpperCamelCase	:			Union[str, Any]					=					patient_result.detach().argmax(dim=1			)
              if (patient_result is not None) and torch.all(labels.eq(lowerCamelCase__			)			):
                 patient_counter += 1
              else:
                 __UpperCamelCase	:			str					=					0

           __UpperCamelCase	:			Union[str, Any]					=					logits
           if patient_counter == self.patience:
              break
        __UpperCamelCase	:			List[str]					=					[patient_result]
        self.inference_layers_num += calculated_layer_num
        self.inference_instances_num += 1

     return res







@add_start_docstrings(
    '''Bert Model transformer with PABEE and a sequence classification/regression head on top (a linear layer on top of
    the pooled output) e.g. for GLUE tasks. '''	,				UpperCAmelCase_	,				)
class 		_A						( UpperCAmelCase_ ):

  def __init__(    self						:	Any   ,				lowerCamelCase__						:	Union[str, Any]			):
     """simple docstring"""

     super().__init__(lowerCamelCase__			)
     __UpperCamelCase	:			Dict					=					config.num_labels

     __UpperCamelCase	:			List[Any]					=					BertModelWithPabee(lowerCamelCase__			)
     __UpperCamelCase	:			Optional[int]					=					nn.Dropout(config.hidden_dropout_prob			)
     __UpperCamelCase	:			List[Any]					=					nn.ModuleList(
         [nn.Linear(config.hidden_size   ,				self.config.num_labels			) for _ in range(config.num_hidden_layers			)]			)

     self.init_weights()

  @add_start_docstrings_to_model_forward(lowerCamelCase__			)
  def    a					(    self						:	List[Any]   ,				lowerCamelCase__						:	Union[str, Any]=None   ,				lowerCamelCase__						:	Dict=None   ,				lowerCamelCase__						:	Union[str, Any]=None   ,				lowerCamelCase__						:	List[Any]=None   ,				lowerCamelCase__						:	Optional[Any]=None   ,				lowerCamelCase__						:	Optional[int]=None   ,				lowerCamelCase__						:	Dict=None   ,				):
     """simple docstring"""

     __UpperCamelCase	:			str					=					self.bert(
         input_ids=lowerCamelCase__   ,				attention_mask=lowerCamelCase__   ,				token_type_ids=lowerCamelCase__   ,				position_ids=lowerCamelCase__   ,				head_mask=lowerCamelCase__   ,				inputs_embeds=lowerCamelCase__   ,				output_dropout=self.dropout   ,				output_layers=self.classifiers   ,				regression=self.num_labels == 1   ,				)

     __UpperCamelCase	:			List[str]					=					(logits[-1],)

     if labels is not None:
        __UpperCamelCase	:			Tuple					=					None
        __UpperCamelCase	:			Union[str, Any]					=					0
        for ix, logits_item in enumerate(lowerCamelCase__			):
           if self.num_labels == 1:
              #  We are doing regression
              __UpperCamelCase	:			Union[str, Any]					=					MSELoss()
              __UpperCamelCase	:			Optional[Any]					=					loss_fct(logits_item.view(-1			)   ,				labels.view(-1			)			)
           else:
              __UpperCamelCase	:			Dict					=					CrossEntropyLoss()
              __UpperCamelCase	:			Dict					=					loss_fct(logits_item.view(-1   ,				self.num_labels			)   ,				labels.view(-1			)			)
           if total_loss is None:
              __UpperCamelCase	:			Dict					=					loss
           else:
              total_loss += loss * (ix + 1)
           total_weights += ix + 1
        __UpperCamelCase	:			Tuple					=					(total_loss / total_weights,) + outputs

     return outputs



