






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_fast import BertTokenizerFast
from .tokenization_dpr import DPRContextEncoderTokenizer, DPRQuestionEncoderTokenizer, DPRReaderTokenizer


a						:			Dict     	=					logging.get_logger(__name__)

a						:			List[Any]     	=					{"vocab_file": "vocab.txt", "tokenizer_file": "tokenizer.json"}

a						:			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"
        ),
    },
}
a						:			Any     	=					{
    "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"
        ),
    },
}
a						:			Dict     	=					{
    "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"
        ),
    },
}

a						:			Optional[int]     	=					{
    "facebook/dpr-ctx_encoder-single-nq-base": 512,
    "facebook/dpr-ctx_encoder-multiset-base": 512,
}
a						:			int     	=					{
    "facebook/dpr-question_encoder-single-nq-base": 512,
    "facebook/dpr-question_encoder-multiset-base": 512,
}
a						:			Any     	=					{
    "facebook/dpr-reader-single-nq-base": 512,
    "facebook/dpr-reader-multiset-base": 512,
}


a						:			Optional[int]     	=					{
    "facebook/dpr-ctx_encoder-single-nq-base": {"do_lower_case": True},
    "facebook/dpr-ctx_encoder-multiset-base": {"do_lower_case": True},
}
a						:			List[str]     	=					{
    "facebook/dpr-question_encoder-single-nq-base": {"do_lower_case": True},
    "facebook/dpr-question_encoder-multiset-base": {"do_lower_case": True},
}
a						:			List[str]     	=					{
    "facebook/dpr-reader-single-nq-base": {"do_lower_case": True},
    "facebook/dpr-reader-multiset-base": {"do_lower_case": True},
}
class        a       (					lowercase__  ):



      """simple docstring"""


      a    :					Dict							=      VOCAB_FILES_NAMES
      a    :					Tuple							=      CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
      a    :					Tuple							=      CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
      a    :					Any							=      CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION
      a    :					str							=      DPRContextEncoderTokenizer


class        a       (					lowercase__  ):



      """simple docstring"""


      a    :					Union[str, Any]							=      VOCAB_FILES_NAMES
      a    :					List[Any]							=      QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
      a    :					List[str]							=      QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
      a    :					Dict							=      QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION
      a    :					List[Any]							=      DPRQuestionEncoderTokenizer


a						:			Optional[int]     	=					collections.namedtuple(
    "DPRSpanPrediction", ["span_score", "relevance_score", "doc_id", "start_index", "end_index", "text"]
)

a						:			Dict     	=					collections.namedtuple("DPRReaderOutput", ["start_logits", "end_logits", "relevance_logits"])


a						:			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    [CLS] <question token ids> [SEP] <titles ids> [SEP] <texts ids>\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    Return:\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(lowercase__  )
class        a       :



      """simple docstring"""


      def __call__( self   :     Optional[Any]						, __lowercase   :     Union[str, Any]						, __lowercase   :     Optional[str] = None						, __lowercase   :     Optional[str] = None						, __lowercase   :     Union[bool, str] = False						, __lowercase   :     Union[bool, str] = False						, __lowercase   :     Optional[int] = None						, __lowercase   :     Optional[Union[str, TensorType]] = None						, __lowercase   :     Optional[bool] = None						, **__lowercase   :     List[Any]						, )				-> BatchEncoding:
        if titles is None and texts is None:
          return super().__call__(
              __lowercase						, padding=__lowercase						, truncation=__lowercase						, max_length=__lowercase						, return_tensors=__lowercase						, return_attention_mask=__lowercase						, **__lowercase						, )
        elif titles is None or texts is None:
          __UpperCAmelCase				:      Optional[int]	 =    titles if texts is None else texts
          return super().__call__(
              __lowercase						, __lowercase						, padding=__lowercase						, truncation=__lowercase						, max_length=__lowercase						, return_tensors=__lowercase						, return_attention_mask=__lowercase						, **__lowercase						, )
        __UpperCAmelCase				:      Optional[int]	 =    titles if not isinstance(__lowercase						, __lowercase   ) else [titles]
        __UpperCAmelCase				:      Dict	 =    texts if not isinstance(__lowercase						, __lowercase   ) else [texts]
        __UpperCAmelCase				:      Union[str, Any]	 =    len(__lowercase   )
        __UpperCAmelCase				:      Dict	 =    questions if not isinstance(__lowercase						, __lowercase   ) else [questions] * n_passages
        assert len(__lowercase   ) == len(
            __lowercase   ), f"""There should be as many titles than texts but got {len(__lowercase   )} titles and {len(__lowercase   )} texts."""
        __UpperCAmelCase				:      Union[str, Any]	 =    super().__call__(__lowercase						, __lowercase						, padding=__lowercase						, truncation=__lowercase   )["""input_ids"""]
        __UpperCAmelCase				:      Any	 =    super().__call__(__lowercase						, add_special_tokens=__lowercase						, padding=__lowercase						, truncation=__lowercase   )["""input_ids"""]
        __UpperCAmelCase				:      Union[str, Any]	 =    {
            """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(__lowercase						, __lowercase   )
            ]
        }
        if return_attention_mask is not False:
          __UpperCAmelCase				:      Tuple	 =    []
          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				:      int	 =    attention_mask
        return self.pad(__lowercase						, padding=__lowercase						, max_length=__lowercase						, return_tensors=__lowercase   )
      def       UpperCAmelCase ( self   :     Union[str, Any]						, __lowercase   :     BatchEncoding						, __lowercase   :     DPRReaderOutput						, __lowercase   :     int = 16						, __lowercase   :     int = 64						, __lowercase   :     int = 4						, )				-> List[DPRSpanPrediction]:
        __UpperCAmelCase				:      List[Any]	 =    reader_input["""input_ids"""]
        __UpperCAmelCase ,					__UpperCAmelCase ,					__UpperCAmelCase				:      Dict	 =    reader_output[:3]
        __UpperCAmelCase				:      Any	 =    len(__lowercase   )
        __UpperCAmelCase				:      Union[str, Any]	 =    sorted(range(__lowercase   )						, reverse=__lowercase						, key=relevance_logits.__getitem__   )
        __UpperCAmelCase				:      List[DPRReaderOutput]	 =    []
        for doc_id in sorted_docs:
          __UpperCAmelCase				:      List[Any]	 =    list(input_ids[doc_id]   )
          # assuming question & title information is at the beginning of the sequence
          __UpperCAmelCase				:      Tuple	 =    sequence_ids.index(self.sep_token_id						, 2   ) + 1  # second sep id
          if sequence_ids[-1] == self.pad_token_id:
            __UpperCAmelCase				:      Dict	 =    sequence_ids.index(self.pad_token_id   )
          else:
            __UpperCAmelCase				:      Any	 =    len(__lowercase   )

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




      def       UpperCAmelCase ( self   :     Union[str, Any]						, __lowercase   :     List[int]						, __lowercase   :     List[int]						, __lowercase   :     int						, __lowercase   :     int						, )				-> List[DPRSpanPrediction]:
        __UpperCAmelCase				:      Union[str, Any]	 =    []
        for start_index, start_score in enumerate(__lowercase   ):
          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				:      Tuple	 =    sorted(__lowercase						, key=lambda __lowercase   : x[1]						, reverse=__lowercase   )
        __UpperCAmelCase				:      List[Any]	 =    []
        for (start_index, end_index), score in scores:
          assert start_index <= end_index, f"""Wrong span indices: [{start_index}:{end_index}]"""
          __UpperCAmelCase				:      Optional[Any]	 =    end_index - start_index + 1
          assert length <= max_answer_length, 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(__lowercase   ) == top_spans:
            break
        return chosen_span_intervals


@add_end_docstrings(lowercase__  )
class        a       (					lowercase__				,			lowercase__  ):



      """simple docstring"""


      a    :					Optional[int]							=      VOCAB_FILES_NAMES
      a    :					Optional[Any]							=      READER_PRETRAINED_VOCAB_FILES_MAP
      a    :					int							=      READER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
      a    :					List[Any]							=      READER_PRETRAINED_INIT_CONFIGURATION
      a    :					List[Any]							=      ['input_ids', 'attention_mask']
      a    :					Optional[Any]							=      DPRReaderTokenizer







"""simple docstring"""







from math import ceil, sqrt

def     UpperCAmelCase_					(				__a   :			int = 1_00_00_00						):




			'''simple docstring'''



			_lowerCamelCase					:					Tuple	       =    0

			for outer_width in range(3      ,							(limit // 4) + 2						):
						if outer_width**2 > limit:
									_lowerCamelCase					:					Optional[int]	       =    max(ceil(sqrt(outer_width**2 - limit						)						)      ,							1						)
						else:
									_lowerCamelCase					:					Any	       =    1
						if (outer_width - hole_width_lower_bound) % 2:
									hole_width_lower_bound += 1

						answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

			return answer


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





