






'''simple docstring'''

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__											=     logging.get_logger(__name__)

SCREAMING_SNAKE_CASE__											=     {'vocab_file': 'vocab.txt', 'tokenizer_file': 'tokenizer.json'}

SCREAMING_SNAKE_CASE__											=     {
    '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__											=     {
    '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__											=     {
    '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__											=     {
    'facebook/dpr-ctx_encoder-single-nq-base': 5_1_2,
    'facebook/dpr-ctx_encoder-multiset-base': 5_1_2,
}
SCREAMING_SNAKE_CASE__											=     {
    'facebook/dpr-question_encoder-single-nq-base': 5_1_2,
    'facebook/dpr-question_encoder-multiset-base': 5_1_2,
}
SCREAMING_SNAKE_CASE__											=     {
    'facebook/dpr-reader-single-nq-base': 5_1_2,
    'facebook/dpr-reader-multiset-base': 5_1_2,
}


SCREAMING_SNAKE_CASE__											=     {
    'facebook/dpr-ctx_encoder-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-ctx_encoder-multiset-base': {'do_lower_case': True},
}
SCREAMING_SNAKE_CASE__											=     {
    'facebook/dpr-question_encoder-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-question_encoder-multiset-base': {'do_lower_case': True},
}
SCREAMING_SNAKE_CASE__											=     {
    'facebook/dpr-reader-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-reader-multiset-base': {'do_lower_case': True},
}






class        a_		(    lowerCamelCase       ):
  lowercase  	=   VOCAB_FILES_NAMES
  lowercase  	=   CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
  lowercase  	=   CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
  lowercase  	=   CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION






class        a_		(    lowerCamelCase       ):
  lowercase  	=   VOCAB_FILES_NAMES
  lowercase  	=   QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
  lowercase  	=   QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
  lowercase  	=   QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION


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

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


SCREAMING_SNAKE_CASE__											=     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        a_		:

  def __call__(   self    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE = None    ,	_SCREAMING_SNAKE_CASE = None    ,	_SCREAMING_SNAKE_CASE = False    ,	_SCREAMING_SNAKE_CASE = False    ,	_SCREAMING_SNAKE_CASE = None    ,	_SCREAMING_SNAKE_CASE = None    ,	_SCREAMING_SNAKE_CASE = None    ,	**_SCREAMING_SNAKE_CASE    ,	)						->   BatchEncoding:



        """simple docstring"""






        if titles is None and texts is None:
              return super().__call__(
                  _SCREAMING_SNAKE_CASE    ,	padding=_SCREAMING_SNAKE_CASE    ,	truncation=_SCREAMING_SNAKE_CASE    ,	max_length=_SCREAMING_SNAKE_CASE    ,	return_tensors=_SCREAMING_SNAKE_CASE    ,	return_attention_mask=_SCREAMING_SNAKE_CASE    ,	**_SCREAMING_SNAKE_CASE    ,	)
        elif titles is None or texts is None:
              UpperCamelCase       						=      titles if texts is None else texts
              return super().__call__(
                  _SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	padding=_SCREAMING_SNAKE_CASE    ,	truncation=_SCREAMING_SNAKE_CASE    ,	max_length=_SCREAMING_SNAKE_CASE    ,	return_tensors=_SCREAMING_SNAKE_CASE    ,	return_attention_mask=_SCREAMING_SNAKE_CASE    ,	**_SCREAMING_SNAKE_CASE    ,	)
        UpperCamelCase       						=      titles if not isinstance(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   ) else [titles]
        UpperCamelCase       						=      texts if not isinstance(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   ) else [texts]
        UpperCamelCase       						=      len(_SCREAMING_SNAKE_CASE   )
        UpperCamelCase       						=      questions if not isinstance(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   ) else [questions] * n_passages
        if len(_SCREAMING_SNAKE_CASE   ) != len(_SCREAMING_SNAKE_CASE   ):
              raise ValueError(
                  F"There should be as many titles than texts but got {len(_SCREAMING_SNAKE_CASE   )} titles and {len(_SCREAMING_SNAKE_CASE   )} texts."   )
        UpperCamelCase       						=      super().__call__(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	padding=_SCREAMING_SNAKE_CASE    ,	truncation=_SCREAMING_SNAKE_CASE   )["""input_ids"""]
        UpperCamelCase       						=      super().__call__(_SCREAMING_SNAKE_CASE    ,	add_special_tokens=_SCREAMING_SNAKE_CASE    ,	padding=_SCREAMING_SNAKE_CASE    ,	truncation=_SCREAMING_SNAKE_CASE   )["""input_ids"""]
        UpperCamelCase       						=      {
            """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(_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE   )
            ]
        }
        if return_attention_mask is not False:
              UpperCamelCase       						=      []
              for input_ids in encoded_inputs["input_ids"]:
                    attention_mask.append([int(input_id != self.pad_token_id   ) for input_id in input_ids]   )
              UpperCamelCase       						=      attention_mask
        return self.pad(_SCREAMING_SNAKE_CASE    ,	padding=_SCREAMING_SNAKE_CASE    ,	max_length=_SCREAMING_SNAKE_CASE    ,	return_tensors=_SCREAMING_SNAKE_CASE   )

  def 						A__		(   self    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE = 16    ,	_SCREAMING_SNAKE_CASE = 64    ,	_SCREAMING_SNAKE_CASE = 4    ,	)						->   List[DPRSpanPrediction]:



        """simple docstring"""






        UpperCamelCase       						=      reader_input["""input_ids"""]
        UpperCamelCase						,UpperCamelCase						,UpperCamelCase       						=      reader_output[:3]
        UpperCamelCase       						=      len(_SCREAMING_SNAKE_CASE   )
        UpperCamelCase       						=      sorted(range(_SCREAMING_SNAKE_CASE   )    ,	reverse=_SCREAMING_SNAKE_CASE    ,	key=relevance_logits.__getitem__   )
        UpperCamelCase       						=      []
        for doc_id in sorted_docs:
              UpperCamelCase       						=      list(input_ids[doc_id]   )
              # assuming question & title information is at the beginning of the sequence
              UpperCamelCase       						=      sequence_ids.index(self.sep_token_id    ,	2   ) + 1  # second sep id
              if sequence_ids[-1] == self.pad_token_id:
                    UpperCamelCase       						=      sequence_ids.index(self.pad_token_id   )
              else:
                    UpperCamelCase       						=      len(_SCREAMING_SNAKE_CASE   )

              UpperCamelCase       						=      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=_SCREAMING_SNAKE_CASE    ,	top_spans=_SCREAMING_SNAKE_CASE    ,	)
              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=_SCREAMING_SNAKE_CASE    ,	start_index=_SCREAMING_SNAKE_CASE    ,	end_index=_SCREAMING_SNAKE_CASE    ,	text=self.decode(sequence_ids[start_index : end_index + 1]   )    ,	)   )
              if len(_SCREAMING_SNAKE_CASE   ) >= num_spans:
                    break
        return nbest_spans_predictions[:num_spans]


  def 						A__		(   self    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	_SCREAMING_SNAKE_CASE    ,	)						->   List[DPRSpanPrediction]:



        """simple docstring"""






        UpperCamelCase       						=      []
        for start_index, start_score in enumerate(_SCREAMING_SNAKE_CASE   ):
              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)   )
        UpperCamelCase       						=      sorted(_SCREAMING_SNAKE_CASE    ,	key=lambda _SCREAMING_SNAKE_CASE   : x[1]    ,	reverse=_SCREAMING_SNAKE_CASE   )
        UpperCamelCase       						=      []
        for (start_index, end_index), score in scores:
              if start_index > end_index:
                    raise ValueError(F"Wrong span indices: [{start_index}:{end_index}]"   )
              UpperCamelCase       						=      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(_SCREAMING_SNAKE_CASE   ) == top_spans:
                    break
        return chosen_span_intervals






@add_end_docstrings(lowerCamelCase       )
class        a_		(    lowerCamelCase			, lowerCamelCase       ):
  lowercase  	=   VOCAB_FILES_NAMES
  lowercase  	=   READER_PRETRAINED_VOCAB_FILES_MAP
  lowercase  	=   READER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
  lowercase  	=   READER_PRETRAINED_INIT_CONFIGURATION
  lowercase  	=   ["""input_ids""", """attention_mask"""]








'''simple docstring'''

from math import factorial







def 					lowercase__				(   __UpperCamelCase = 20					)->				int:
      UpperCamelCase       						=      2 * n  # middle entry of odd rows starting at row 3 is the solution for n = 1,
      # 2, 3,...
      UpperCamelCase       						=      n // 2

      return int(factorial(__UpperCamelCase					) / (factorial(__UpperCamelCase					) * factorial(n - k					))					)


if __name__ == "__main__":
     import sys

     if len(sys.argv) == 1:
          print(solution(2_0))
     else:
          try:
               SCREAMING_SNAKE_CASE__											=     int(sys.argv[1])
               print(solution(n))
          except ValueError:
               print('Invalid entry - please enter a number.')
