code: 
  
  
  
  
  
  
  import functools
  from contextlib import contextmanager
  
  import bert_score
  from packaging import version
  
  import datasets
  
  
  @contextmanager
  def 						_A     (       ):
      def filter_log(SCREAMING_SNAKE_CASE__						:			Union[str, Any] ):
          return False if "This IS expected if you are initializing" in record.msg else True
  
      UpperCamelCase :str										=     datasets.utils.logging.get_logger('''transformers.modeling_utils''' )
      logger.addFilter(SCREAMING_SNAKE_CASE__ )
      try:
          yield
      finally:
          logger.removeFilter(SCREAMING_SNAKE_CASE__ )
  
  
  __snake_case							      =						"""\
  @inproceedings{bert-score,
    title={BERTScore: Evaluating Text Generation with BERT},
    author={Tianyi Zhang* and Varsha Kishore* and Felix Wu* and Kilian Q. Weinberger and Yoav Artzi},
    booktitle={International Conference on Learning Representations},
    year={2020},
    url={https://openreview.net/forum?id=SkeHuCVFDr}
  }
  """
  
  __snake_case							      =						"""\
  BERTScore leverages the pre-trained contextual embeddings from BERT and matches words in candidate and reference
  sentences by cosine similarity.
  It has been shown to correlate with human judgment on sentence-level and system-level evaluation.
  Moreover, BERTScore computes precision, recall, and F1 measure, which can be useful for evaluating different language
  generation tasks.
  
  See the project's README at https://github.com/Tiiiger/bert_score#readme for more information.
  """
  
  __snake_case							      =						"""
  BERTScore Metrics with the hashcode from a source against one or more references.
  
  Args:
      predictions (list of str): Prediction/candidate sentences.
      references (list of str or list of list of str): Reference sentences.
      lang (str): Language of the sentences; required (e.g. 'en').
      model_type (str): Bert specification, default using the suggested
          model for the target language; has to specify at least one of
          `model_type` or `lang`.
      num_layers (int): The layer of representation to use,
          default using the number of layers tuned on WMT16 correlation data.
      verbose (bool): Turn on intermediate status update.
      idf (bool or dict): Use idf weighting; can also be a precomputed idf_dict.
      device (str): On which the contextual embedding model will be allocated on.
          If this argument is None, the model lives on cuda:0 if cuda is available.
      nthreads (int): Number of threads.
      batch_size (int): Bert score processing batch size,
          at least one of `model_type` or `lang`. `lang` needs to be
          specified when `rescale_with_baseline` is True.
      rescale_with_baseline (bool): Rescale bertscore with pre-computed baseline.
      baseline_path (str): Customized baseline file.
      use_fast_tokenizer (bool): `use_fast` parameter passed to HF tokenizer. New in version 0.3.10.
  
  Returns:
      precision: Precision.
      recall: Recall.
      f1: F1 score.
      hashcode: Hashcode of the library.
  
  Examples:
  
      >>> predictions = [\"hello there\", \"general kenobi\"]
      >>> references = [\"hello there\", \"general kenobi\"]
      >>> bertscore = datasets.load_metric(\"bertscore\")
      >>> results = bertscore.compute(predictions=predictions, references=references, lang=\"en\")
      >>> print([round(v, 2) for v in results[\"f1\"]])
      [1.0, 1.0]
  """
  
  
  
  
  
  
  
  @datasets.utils.file_utils.add_start_docstrings(_DESCRIPTION,			_KWARGS_DESCRIPTION				)
  class     UpperCAmelCase_		(      datasets.Metric				):
  
  
  
        """simple docstring"""
        def 					UpperCAmelCase		(       self				)       ->   Optional[Any]:
            return datasets.MetricInfo(
                description=_DESCRIPTION					,       citation=_CITATION					,       homepage='''https://github.com/Tiiiger/bert_score'''					,       inputs_description=_KWARGS_DESCRIPTION					,       features=datasets.Features(
                    {
                        '''predictions''': datasets.Value('''string'''					,       id='''sequence'''				),
                        '''references''': datasets.Sequence(datasets.Value('''string'''					,       id='''sequence'''				)					,       id='''references'''				),
                    }				)					,       codebase_urls=['''https://github.com/Tiiiger/bert_score''']					,       reference_urls=[
                    '''https://github.com/Tiiiger/bert_score''',
                    '''https://arxiv.org/abs/1904.09675''',
                ]					,       )
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_					,       SCREAMING_SNAKE_CASE_					,       SCREAMING_SNAKE_CASE_=None					,       SCREAMING_SNAKE_CASE_=None					,       SCREAMING_SNAKE_CASE_=None					,       SCREAMING_SNAKE_CASE_=False					,       SCREAMING_SNAKE_CASE_=False					,       SCREAMING_SNAKE_CASE_=None					,       SCREAMING_SNAKE_CASE_=64					,       SCREAMING_SNAKE_CASE_=4					,       SCREAMING_SNAKE_CASE_=False					,       SCREAMING_SNAKE_CASE_=False					,       SCREAMING_SNAKE_CASE_=None					,       SCREAMING_SNAKE_CASE_=False					,       )       ->   Optional[int]:
            UpperCamelCase :Dict										=     bert_score.utils.get_hash
            UpperCamelCase :Union[str, Any]										=     bert_score.BERTScorer
  
            if version.parse(bert_score.__version__				) >= version.parse('''0.3.10'''				):
                UpperCamelCase :Tuple										=     functools.partial(SCREAMING_SNAKE_CASE_					,       use_fast_tokenizer=SCREAMING_SNAKE_CASE_				)
                UpperCamelCase :Union[str, Any]										=     functools.partial(SCREAMING_SNAKE_CASE_					,       use_fast_tokenizer=SCREAMING_SNAKE_CASE_				)
            elif use_fast_tokenizer:
                raise ImportWarning(
                    '''To use a fast tokenizer, the module `bert-score>=0.3.10` is required, and the current version of `bert-score` doesn\'t match this condition.\n'''
                    '''You can install it with `pip install "bert-score>=0.3.10"`.'''				)
  
            if model_type is None:
                assert lang is not None, "either lang or model_type should be specified"
                UpperCamelCase :Union[str, Any]										=     bert_score.utils.langamodel[lang.lower()]
  
            if num_layers is None:
                UpperCamelCase :List[Any]										=     bert_score.utils.modelalayers[model_type]
  
            UpperCamelCase :str										=     get_hash(
                model=SCREAMING_SNAKE_CASE_					,       num_layers=SCREAMING_SNAKE_CASE_					,       idf=SCREAMING_SNAKE_CASE_					,       rescale_with_baseline=SCREAMING_SNAKE_CASE_					,       use_custom_baseline=baseline_path is not None					,       )
  
            with filter_logging_context():
                if not hasattr(self					,       '''cached_bertscorer'''				) or self.cached_bertscorer.hash != hashcode:
                    UpperCamelCase :Optional[int]										=     scorer(
                        model_type=SCREAMING_SNAKE_CASE_					,       num_layers=SCREAMING_SNAKE_CASE_					,       batch_size=SCREAMING_SNAKE_CASE_					,       nthreads=SCREAMING_SNAKE_CASE_					,       all_layers=SCREAMING_SNAKE_CASE_					,       idf=SCREAMING_SNAKE_CASE_					,       device=SCREAMING_SNAKE_CASE_					,       lang=SCREAMING_SNAKE_CASE_					,       rescale_with_baseline=SCREAMING_SNAKE_CASE_					,       baseline_path=SCREAMING_SNAKE_CASE_					,       )
  
            ((UpperCamelCase)							,     (UpperCamelCase)							,     (UpperCamelCase)) :int										=     self.cached_bertscorer.score(
                cands=SCREAMING_SNAKE_CASE_					,       refs=SCREAMING_SNAKE_CASE_					,       verbose=SCREAMING_SNAKE_CASE_					,       batch_size=SCREAMING_SNAKE_CASE_					,       )
            UpperCamelCase :Optional[Any]										=     {
                '''precision''': P.tolist(),
                '''recall''': R.tolist(),
                '''f1''': F.tolist(),
                '''hashcode''': hashcode,
            }
            return output_dict
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_=None					,       SCREAMING_SNAKE_CASE_=None					,       **SCREAMING_SNAKE_CASE_				)       ->   Optional[Any]:
            # References can be strings or lists of strings
            # Let's change strings to lists of strings with one element
            if references is not None:
                UpperCamelCase :Optional[Any]										=     [[ref] if isinstance(SCREAMING_SNAKE_CASE_					,       SCREAMING_SNAKE_CASE_				) else ref for ref in references]
            super().add_batch(predictions=SCREAMING_SNAKE_CASE_					,       references=SCREAMING_SNAKE_CASE_					,       **SCREAMING_SNAKE_CASE_				)
  
  
  
  
        def 					UpperCAmelCase		(       self					,       SCREAMING_SNAKE_CASE_=None					,       SCREAMING_SNAKE_CASE_=None					,       **SCREAMING_SNAKE_CASE_				)       ->   int:
            # References can be strings or lists of strings
            # Let's change strings to lists of strings with one element
            if isinstance(SCREAMING_SNAKE_CASE_					,       SCREAMING_SNAKE_CASE_				):
                UpperCamelCase :List[str]										=     [reference]
            super().add(prediction=SCREAMING_SNAKE_CASE_					,       reference=SCREAMING_SNAKE_CASE_					,       **SCREAMING_SNAKE_CASE_				)
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  from __future__ import annotations
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int ):
      UpperCamelCase :int										=     {1}
      UpperCamelCase :Optional[int]										=     [1]
      for _ in range(2  ,						depth + 1 ):
          UpperCamelCase :Union[str, Any]										=     [*previous_coefficients, 0]
          UpperCamelCase :List[str]										=     [0, *previous_coefficients]
          UpperCamelCase :List[str]										=     []
          for x, y in zip(SCREAMING_SNAKE_CASE__  ,						SCREAMING_SNAKE_CASE__ ):
              coefficients.add(x + y )
              previous_coefficients.append(x + y )
      return coefficients
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			set[int] ):
      UpperCamelCase :Union[str, Any]										=     set()
      for number in unique_coefficients:
          UpperCamelCase :Optional[int]										=     2
          UpperCamelCase :List[Any]										=     number
          while divisor**2 <= copy_number:
              UpperCamelCase :List[Any]										=     0
              while copy_number % divisor == 0:
                  copy_number //= divisor
                  multiplicity += 1
              if multiplicity >= 2:
                  non_squarefrees.add(SCREAMING_SNAKE_CASE__ )
                  break
              divisor += 1
  
      return unique_coefficients.difference(SCREAMING_SNAKE_CASE__ )
  
  
  def 						_A     (       SCREAMING_SNAKE_CASE__						:			int = 51 ):
      UpperCamelCase :Any										=     get_pascal_triangle_unique_coefficients(SCREAMING_SNAKE_CASE__ )
      UpperCamelCase :str										=     get_squarefrees(SCREAMING_SNAKE_CASE__ )
      return sum(SCREAMING_SNAKE_CASE__ )
  
  
  if __name__ == "__main__":
   print(f'''{solution() = }''')
  
  
  
  
  
  