




import collections
from typing import List, Optional, Union

from ...tokenization_utils_base import BatchEncoding
from ...utils import TensorType, add_end_docstrings, add_start_docstrings, logging
from ..bert.tokenization_bert import BertTokenizer


SCREAMING_SNAKE_CASE__       :      Union[str, Any]  =   logging.get_logger(__name__)

SCREAMING_SNAKE_CASE__       :      Union[str, Any]  =   {'vocab_file': 'vocab.txt', 'tokenizer_file': 'tokenizer.json'}

SCREAMING_SNAKE_CASE__       :      Tuple  =   {
    'vocab_file': {
        'facebook/dpr-ctx_encoder-single-nq-base': (
            'https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/vocab.txt'
        ),
        'facebook/dpr-ctx_encoder-multiset-base': (
            'https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/vocab.txt'
        ),
    },
    'tokenizer_file': {
        'facebook/dpr-ctx_encoder-single-nq-base': (
            'https://huggingface.co/facebook/dpr-ctx_encoder-single-nq-base/resolve/main/tokenizer.json'
        ),
        'facebook/dpr-ctx_encoder-multiset-base': (
            'https://huggingface.co/facebook/dpr-ctx_encoder-multiset-base/resolve/main/tokenizer.json'
        ),
    },
}
SCREAMING_SNAKE_CASE__       :      int  =   {
    'vocab_file': {
        'facebook/dpr-question_encoder-single-nq-base': (
            'https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/vocab.txt'
        ),
        'facebook/dpr-question_encoder-multiset-base': (
            'https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/vocab.txt'
        ),
    },
    'tokenizer_file': {
        'facebook/dpr-question_encoder-single-nq-base': (
            'https://huggingface.co/facebook/dpr-question_encoder-single-nq-base/resolve/main/tokenizer.json'
        ),
        'facebook/dpr-question_encoder-multiset-base': (
            'https://huggingface.co/facebook/dpr-question_encoder-multiset-base/resolve/main/tokenizer.json'
        ),
    },
}
SCREAMING_SNAKE_CASE__       :      Any  =   {
    'vocab_file': {
        'facebook/dpr-reader-single-nq-base': (
            'https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/vocab.txt'
        ),
        'facebook/dpr-reader-multiset-base': (
            'https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/vocab.txt'
        ),
    },
    'tokenizer_file': {
        'facebook/dpr-reader-single-nq-base': (
            'https://huggingface.co/facebook/dpr-reader-single-nq-base/resolve/main/tokenizer.json'
        ),
        'facebook/dpr-reader-multiset-base': (
            'https://huggingface.co/facebook/dpr-reader-multiset-base/resolve/main/tokenizer.json'
        ),
    },
}

SCREAMING_SNAKE_CASE__       :      str  =   {
    'facebook/dpr-ctx_encoder-single-nq-base': 512,
    'facebook/dpr-ctx_encoder-multiset-base': 512,
}
SCREAMING_SNAKE_CASE__       :      Dict  =   {
    'facebook/dpr-question_encoder-single-nq-base': 512,
    'facebook/dpr-question_encoder-multiset-base': 512,
}
SCREAMING_SNAKE_CASE__       :      Optional[int]  =   {
    'facebook/dpr-reader-single-nq-base': 512,
    'facebook/dpr-reader-multiset-base': 512,
}


SCREAMING_SNAKE_CASE__       :      int  =   {
    'facebook/dpr-ctx_encoder-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-ctx_encoder-multiset-base': {'do_lower_case': True},
}
SCREAMING_SNAKE_CASE__       :      List[str]  =   {
    'facebook/dpr-question_encoder-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-question_encoder-multiset-base': {'do_lower_case': True},
}
SCREAMING_SNAKE_CASE__       :      Optional[int]  =   {
    'facebook/dpr-reader-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-reader-multiset-base': {'do_lower_case': True},
}




class 		UpperCamelCase__	(lowerCAmelCase__     ):

    '''simple docstring'''



    lowerCamelCase_      :	Optional[int]	     =      VOCAB_FILES_NAMES
    lowerCamelCase_      :	Optional[int]	     =      CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
    lowerCamelCase_      :	Union[str, Any]	     =      CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
    lowerCamelCase_      :	Dict	     =      CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION




class 		UpperCamelCase__	(lowerCAmelCase__     ):

    '''simple docstring'''



    lowerCamelCase_      :	Optional[Any]	     =      VOCAB_FILES_NAMES
    lowerCamelCase_      :	Optional[Any]	     =      QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
    lowerCamelCase_      :	List[Any]	     =      QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
    lowerCamelCase_      :	Optional[Any]	     =      QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION




SCREAMING_SNAKE_CASE__       :      Optional[Any]  =   collections.namedtuple(
    'DPRSpanPrediction', ['span_score', 'relevance_score', 'doc_id', 'start_index', 'end_index', 'text']
)

SCREAMING_SNAKE_CASE__       :      Tuple  =   collections.namedtuple('DPRReaderOutput', ['start_logits', 'end_logits', 'relevance_logits'])


SCREAMING_SNAKE_CASE__       :      Tuple  =   r'\n    Return a dictionary with the token ids of the input strings and other information to give to `.decode_best_spans`.\n    It converts the strings of a question and different passages (title and text) in a sequence of IDs (integers),\n    using the tokenizer and vocabulary. The resulting `input_ids` is a matrix of size `(n_passages, sequence_length)`\n    with the format:\n\n    ```\n    [CLS] <question token ids> [SEP] <titles ids> [SEP] <texts ids>\n    ```\n\n    Args:\n        questions (`str` or `List[str]`):\n            The questions to be encoded. You can specify one question for many passages. In this case, the question\n            will be duplicated like `[questions] * n_passages`. Otherwise you have to specify as many questions as in\n            `titles` or `texts`.\n        titles (`str` or `List[str]`):\n            The passages titles to be encoded. This can be a string or a list of strings if there are several passages.\n        texts (`str` or `List[str]`):\n            The passages texts to be encoded. This can be a string or a list of strings if there are several passages.\n        padding (`bool`, `str` or [`~utils.PaddingStrategy`], *optional*, defaults to `False`):\n            Activates and controls padding. Accepts the following values:\n\n            - `True` or `\'longest\'`: Pad to the longest sequence in the batch (or no padding if only a single sequence\n              if provided).\n            - `\'max_length\'`: Pad to a maximum length specified with the argument `max_length` or to the maximum\n              acceptable input length for the model if that argument is not provided.\n            - `False` or `\'do_not_pad\'` (default): No padding (i.e., can output a batch with sequences of different\n              lengths).\n        truncation (`bool`, `str` or [`~tokenization_utils_base.TruncationStrategy`], *optional*, defaults to `False`):\n            Activates and controls truncation. Accepts the following values:\n\n            - `True` or `\'longest_first\'`: Truncate to a maximum length specified with the argument `max_length` or to\n              the maximum acceptable input length for the model if that argument is not provided. This will truncate\n              token by token, removing a token from the longest sequence in the pair if a pair of sequences (or a batch\n              of pairs) is provided.\n            - `\'only_first\'`: Truncate to a maximum length specified with the argument `max_length` or to the maximum\n              acceptable input length for the model if that argument is not provided. This will only truncate the first\n              sequence of a pair if a pair of sequences (or a batch of pairs) is provided.\n            - `\'only_second\'`: Truncate to a maximum length specified with the argument `max_length` or to the maximum\n              acceptable input length for the model if that argument is not provided. This will only truncate the\n              second sequence of a pair if a pair of sequences (or a batch of pairs) is provided.\n            - `False` or `\'do_not_truncate\'` (default): No truncation (i.e., can output batch with sequence lengths\n              greater than the model maximum admissible input size).\n        max_length (`int`, *optional*):\n                Controls the maximum length to use by one of the truncation/padding parameters.\n\n                If left unset or set to `None`, this will use the predefined model maximum length if a maximum length\n                is required by one of the truncation/padding parameters. If the model has no specific maximum input\n                length (like XLNet) truncation/padding to a maximum length will be deactivated.\n        return_tensors (`str` or [`~utils.TensorType`], *optional*):\n                If set, will return tensors instead of list of python integers. Acceptable values are:\n\n                - `\'tf\'`: Return TensorFlow `tf.constant` objects.\n                - `\'pt\'`: Return PyTorch `torch.Tensor` objects.\n                - `\'np\'`: Return Numpy `np.ndarray` objects.\n        return_attention_mask (`bool`, *optional*):\n            Whether or not to return the attention mask. If not set, will return the attention mask according to the\n            specific tokenizer\'s default, defined by the `return_outputs` attribute.\n\n            [What are attention masks?](../glossary#attention-mask)\n\n    Returns:\n        `Dict[str, List[List[int]]]`: A dictionary with the following keys:\n\n        - `input_ids`: List of token ids to be fed to a model.\n        - `attention_mask`: List of indices specifying which tokens should be attended to by the model.\n    '




@add_start_docstrings(lowerCAmelCase__     )
class 		UpperCamelCase__	:

    '''simple docstring'''



    def __call__(    self     ,  UpperCamelCase__     ,  UpperCamelCase__ = None     ,  UpperCamelCase__ = None     ,  UpperCamelCase__ = False     ,  UpperCamelCase__ = False     ,  UpperCamelCase__ = None     ,  UpperCamelCase__ = None     ,  UpperCamelCase__ = None     ,  **UpperCamelCase__     ,  )     ->      BatchEncoding:
           if titles is None and texts is None:
                  return super().__call__(
                      UpperCamelCase__     ,  padding=UpperCamelCase__     ,  truncation=UpperCamelCase__     ,  max_length=UpperCamelCase__     ,  return_tensors=UpperCamelCase__     ,  return_attention_mask=UpperCamelCase__     ,  **UpperCamelCase__     ,  )
           elif titles is None or texts is None:
                  lowerCamelCase   :      Optional[Any]			 =					titles if texts is None else texts
                  return super().__call__(
                      UpperCamelCase__     ,  UpperCamelCase__     ,  padding=UpperCamelCase__     ,  truncation=UpperCamelCase__     ,  max_length=UpperCamelCase__     ,  return_tensors=UpperCamelCase__     ,  return_attention_mask=UpperCamelCase__     ,  **UpperCamelCase__     ,  )
           lowerCamelCase   :      Union[str, Any]			 =					titles if not isinstance(UpperCamelCase__     ,  UpperCamelCase__     ) else [titles]
           lowerCamelCase   :      int			 =					texts if not isinstance(UpperCamelCase__     ,  UpperCamelCase__     ) else [texts]
           lowerCamelCase   :      List[Any]			 =					len(UpperCamelCase__     )
           lowerCamelCase   :      int			 =					questions if not isinstance(UpperCamelCase__     ,  UpperCamelCase__     ) else [questions] * n_passages
           if len(UpperCamelCase__     ) != len(UpperCamelCase__     ):
                  raise ValueError(
                      F'''There should be as many titles than texts but got {len(UpperCamelCase__     )} titles and {len(UpperCamelCase__     )} texts.'''     )
           lowerCamelCase   :      Any			 =					super().__call__(UpperCamelCase__     ,  UpperCamelCase__     ,  padding=UpperCamelCase__     ,  truncation=UpperCamelCase__     )["input_ids"]
           lowerCamelCase   :      Any			 =					super().__call__(UpperCamelCase__     ,  add_special_tokens=UpperCamelCase__     ,  padding=UpperCamelCase__     ,  truncation=UpperCamelCase__     )["input_ids"]
           lowerCamelCase   :      int			 =					{
               "input_ids": [
                   (encoded_question_and_title + encoded_text)[:max_length]
                   if max_length is not None and truncation
                   else encoded_question_and_title + encoded_text
                   for encoded_question_and_title, encoded_text in zip(UpperCamelCase__     ,  UpperCamelCase__     )
               ]
           }
           if return_attention_mask is not False:
                  lowerCamelCase   :      List[Any]			 =					[]
                  for input_ids in encoded_inputs["input_ids"]:
                         attention_mask.append([int(input_id != self.pad_token_id     ) for input_id in input_ids]     )
                  lowerCamelCase   :      List[str]			 =					attention_mask
           return self.pad(UpperCamelCase__     ,  padding=UpperCamelCase__     ,  max_length=UpperCamelCase__     ,  return_tensors=UpperCamelCase__     )







    def     _lowercase     (    self     ,  UpperCamelCase__     ,  UpperCamelCase__     ,  UpperCamelCase__ = 16     ,  UpperCamelCase__ = 64     ,  UpperCamelCase__ = 4     ,  )     ->      List[DPRSpanPrediction]:
           lowerCamelCase   :      Any			 =					reader_input["input_ids"]
           lowerCamelCase ,      lowerCamelCase ,      lowerCamelCase   :      Dict			 =					reader_output[:3]
           lowerCamelCase   :      str			 =					len(UpperCamelCase__     )
           lowerCamelCase   :      Union[str, Any]			 =					sorted(range(UpperCamelCase__     )     ,  reverse=UpperCamelCase__     ,  key=relevance_logits.__getitem__     )
           lowerCamelCase   :      List[DPRReaderOutput]			 =					[]
           for doc_id in sorted_docs:
                  lowerCamelCase   :      int			 =					list(input_ids[doc_id]     )
                  # assuming question & title information is at the beginning of the sequence
                  lowerCamelCase   :      Union[str, Any]			 =					sequence_ids.index(self.sep_token_id     ,  2     ) + 1  # second sep id
                  if sequence_ids[-1] == self.pad_token_id:
                         lowerCamelCase   :      Any			 =					sequence_ids.index(self.pad_token_id     )
                  else:
                         lowerCamelCase   :      Tuple			 =					len(UpperCamelCase__     )

                  lowerCamelCase   :      Union[str, Any]			 =					self._get_best_spans(
                      start_logits=start_logits[doc_id][passage_offset:sequence_len]     ,  end_logits=end_logits[doc_id][passage_offset:sequence_len]     ,  max_answer_length=UpperCamelCase__     ,  top_spans=UpperCamelCase__     ,  )
                  for start_index, end_index in best_spans:
                         start_index += passage_offset
                         end_index += passage_offset
                         nbest_spans_predictions.append(
                             DPRSpanPrediction(
                                 span_score=start_logits[doc_id][start_index] + end_logits[doc_id][end_index]     ,  relevance_score=relevance_logits[doc_id]     ,  doc_id=UpperCamelCase__     ,  start_index=UpperCamelCase__     ,  end_index=UpperCamelCase__     ,  text=self.decode(sequence_ids[start_index : end_index + 1]     )     ,  )     )
                  if len(UpperCamelCase__     ) >= num_spans:
                         break
           return nbest_spans_predictions[:num_spans]







    def     _lowercase     (    self     ,  UpperCamelCase__     ,  UpperCamelCase__     ,  UpperCamelCase__     ,  UpperCamelCase__     ,  )     ->      List[DPRSpanPrediction]:
           lowerCamelCase   :      Any			 =					[]
           for start_index, start_score in enumerate(UpperCamelCase__     ):
                  for answer_length, end_score in enumerate(end_logits[start_index : start_index + max_answer_length]     ):
                         scores.append(((start_index, start_index + answer_length), start_score + end_score)     )
           lowerCamelCase   :      List[Any]			 =					sorted(UpperCamelCase__     ,  key=lambda UpperCamelCase__     : x[1]     ,  reverse=UpperCamelCase__     )
           lowerCamelCase   :      Optional[Any]			 =					[]
           for (start_index, end_index), score in scores:
                  if start_index > end_index:
                         raise ValueError(F'''Wrong span indices: [{start_index}:{end_index}]'''     )
                  lowerCamelCase   :      Any			 =					end_index - start_index + 1
                  if length > max_answer_length:
                         raise ValueError(F'''Span is too long: {length} > {max_answer_length}'''     )
                  if any(
                      start_index <= prev_start_index <= prev_end_index <= end_index
                      or prev_start_index <= start_index <= end_index <= prev_end_index
                      for (prev_start_index, prev_end_index) in chosen_span_intervals     ):
                         continue
                  chosen_span_intervals.append((start_index, end_index)     )

                  if len(UpperCamelCase__     ) == top_spans:
                         break
           return chosen_span_intervals




@add_end_docstrings(lowerCAmelCase__     )
class 		UpperCamelCase__	(lowerCAmelCase__    ,				lowerCAmelCase__     ):

    '''simple docstring'''



    lowerCamelCase_      :	Tuple	     =      VOCAB_FILES_NAMES
    lowerCamelCase_      :	List[Any]	     =      READER_PRETRAINED_VOCAB_FILES_MAP
    lowerCamelCase_      :	int	     =      READER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
    lowerCamelCase_      :	Tuple	     =      READER_PRETRAINED_INIT_CONFIGURATION
    lowerCamelCase_      :	List[str]	     =      ["""input_ids""", """attention_mask"""]












def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> int:
       return x if y == 0 else greatest_common_divisor(_SCREAMING_SNAKE_CASE ,x % y    )

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> int:
       return (x * y) // greatest_common_divisor(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )

def      A      (      _SCREAMING_SNAKE_CASE = 20    )	-> int:
       lowerCamelCase   :      List[Any]			 =					1
       for i in range(1 ,n + 1    ):
              lowerCamelCase   :      List[str]			 =					lcm(_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )
       return g


if __name__ == "__main__":
       print(f'''{solution() = }''')






