


"""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


lowerCamelCase_   :   List[Any]									=  logging.get_logger(__name__)

lowerCamelCase_   :   Dict									=  {"""vocab_file""": """vocab.txt""", """tokenizer_file""": """tokenizer.json"""}

lowerCamelCase_   :   int									=  {
    """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"""
        ),
    },
}
lowerCamelCase_   :   Optional[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"""
        ),
    },
}
lowerCamelCase_   :   Tuple									=  {
    """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"""
        ),
    },
}

lowerCamelCase_   :   Optional[Any]									=  {
    """facebook/dpr-ctx_encoder-single-nq-base""": 5_1_2,
    """facebook/dpr-ctx_encoder-multiset-base""": 5_1_2,
}
lowerCamelCase_   :   Optional[Any]									=  {
    """facebook/dpr-question_encoder-single-nq-base""": 5_1_2,
    """facebook/dpr-question_encoder-multiset-base""": 5_1_2,
}
lowerCamelCase_   :   Dict									=  {
    """facebook/dpr-reader-single-nq-base""": 5_1_2,
    """facebook/dpr-reader-multiset-base""": 5_1_2,
}


lowerCamelCase_   :   Any									=  {
    """facebook/dpr-ctx_encoder-single-nq-base""": {"""do_lower_case""": True},
    """facebook/dpr-ctx_encoder-multiset-base""": {"""do_lower_case""": True},
}
lowerCamelCase_   :   List[Any]									=  {
    """facebook/dpr-question_encoder-single-nq-base""": {"""do_lower_case""": True},
    """facebook/dpr-question_encoder-multiset-base""": {"""do_lower_case""": True},
}
lowerCamelCase_   :   int									=  {
    """facebook/dpr-reader-single-nq-base""": {"""do_lower_case""": True},
    """facebook/dpr-reader-multiset-base""": {"""do_lower_case""": True},
}






class       __A				(       _SCREAMING_SNAKE_CASE			):






 """simple docstring"""




 __lowerCAmelCase 					=  VOCAB_FILES_NAMES
 __lowerCAmelCase 					=  CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
 __lowerCAmelCase 					=  CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
 __lowerCAmelCase 					=  CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION






class       __A				(       _SCREAMING_SNAKE_CASE			):






 """simple docstring"""




 __lowerCAmelCase 					=  VOCAB_FILES_NAMES
 __lowerCAmelCase 					=  QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
 __lowerCAmelCase 					=  QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
 __lowerCAmelCase 					=  QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION

lowerCamelCase_   :   str									=  collections.namedtuple(
    """DPRSpanPrediction""", ["""span_score""", """relevance_score""", """doc_id""", """start_index""", """end_index""", """text"""]
)

lowerCamelCase_   :   Any									=  collections.namedtuple("""DPRReaderOutput""", ["""start_logits""", """end_logits""", """relevance_logits"""])


lowerCamelCase_   :   Union[str, Any]									=  R"""
    Return a dictionary with the token ids of the input strings and other information to give to `.decode_best_spans`.
    It converts the strings of a question and different passages (title and text) in a sequence of IDs (integers),
    using the tokenizer and vocabulary. The resulting `input_ids` is a matrix of size `(n_passages, sequence_length)`
    with the format:

    ```
    [CLS] <question token ids> [SEP] <titles ids> [SEP] <texts ids>
    ```

    Args:
        questions (`str` or `List[str]`):
            The questions to be encoded. You can specify one question for many passages. In this case, the question
            will be duplicated like `[questions] * n_passages`. Otherwise you have to specify as many questions as in
            `titles` or `texts`.
        titles (`str` or `List[str]`):
            The passages titles to be encoded. This can be a string or a list of strings if there are several passages.
        texts (`str` or `List[str]`):
            The passages texts to be encoded. This can be a string or a list of strings if there are several passages.
        padding (`bool`, `str` or [`~utils.PaddingStrategy`], *optional*, defaults to `False`):
            Activates and controls padding. Accepts the following values:

            - `True` or `'longest'`: Pad to the longest sequence in the batch (or no padding if only a single sequence
              if provided).
            - `'max_length'`: Pad to a maximum length specified with the argument `max_length` or to the maximum
              acceptable input length for the model if that argument is not provided.
            - `False` or `'do_not_pad'` (default): No padding (i.e., can output a batch with sequences of different
              lengths).
        truncation (`bool`, `str` or [`~tokenization_utils_base.TruncationStrategy`], *optional*, defaults to `False`):
            Activates and controls truncation. Accepts the following values:

            - `True` or `'longest_first'`: Truncate to a maximum length specified with the argument `max_length` or to
              the maximum acceptable input length for the model if that argument is not provided. This will truncate
              token by token, removing a token from the longest sequence in the pair if a pair of sequences (or a batch
              of pairs) is provided.
            - `'only_first'`: Truncate to a maximum length specified with the argument `max_length` or to the maximum
              acceptable input length for the model if that argument is not provided. This will only truncate the first
              sequence of a pair if a pair of sequences (or a batch of pairs) is provided.
            - `'only_second'`: Truncate to a maximum length specified with the argument `max_length` or to the maximum
              acceptable input length for the model if that argument is not provided. This will only truncate the
              second sequence of a pair if a pair of sequences (or a batch of pairs) is provided.
            - `False` or `'do_not_truncate'` (default): No truncation (i.e., can output batch with sequence lengths
              greater than the model maximum admissible input size).
        max_length (`int`, *optional*):
                Controls the maximum length to use by one of the truncation/padding parameters.

                If left unset or set to `None`, this will use the predefined model maximum length if a maximum length
                is required by one of the truncation/padding parameters. If the model has no specific maximum input
                length (like XLNet) truncation/padding to a maximum length will be deactivated.
        return_tensors (`str` or [`~utils.TensorType`], *optional*):
                If set, will return tensors instead of list of python integers. Acceptable values are:

                - `'tf'`: Return TensorFlow `tf.constant` objects.
                - `'pt'`: Return PyTorch `torch.Tensor` objects.
                - `'np'`: Return Numpy `np.ndarray` objects.
        return_attention_mask (`bool`, *optional*):
            Whether or not to return the attention mask. If not set, will return the attention mask according to the
            specific tokenizer's default, defined by the `return_outputs` attribute.

            [What are attention masks?](../glossary#attention-mask)

    Returns:
        `Dict[str, List[List[int]]]`: A dictionary with the following keys:

        - `input_ids`: List of token ids to be fed to a model.
        - `attention_mask`: List of indices specifying which tokens should be attended to by the model.
    """






@add_start_docstrings(_SCREAMING_SNAKE_CASE			)
class       __A				:






 """simple docstring"""




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


 def       SCREAMING_SNAKE_CASE							(		self ,    __A ,    __A ,    __A = 16 ,    __A = 64 ,    __A = 4 ,    )					->     List[DPRSpanPrediction]:
     a 		=reader_input['''input_ids''']
     a		,      a		,      a 		=reader_output[:3]
     a 		=len(__A						)
     a 		=sorted(range(__A						) ,    reverse=__A ,    key=relevance_logits.__getitem__						)
     a 		=[]
     for doc_id in sorted_docs:
         a 		=list(input_ids[doc_id]						)
         # assuming question & title information is at the beginning of the sequence
         a 		=sequence_ids.index(self.sep_token_id ,    2						) + 1  # second sep id
         if sequence_ids[-1] == self.pad_token_id:
             a 		=sequence_ids.index(self.pad_token_id						)
         else:
             a 		=len(__A						)

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





 def       SCREAMING_SNAKE_CASE							(		self ,    __A ,    __A ,    __A ,    __A ,    )					->     List[DPRSpanPrediction]:
     a 		=[]
     for start_index, start_score in enumerate(__A						):
         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)						)
     a 		=sorted(__A ,    key=lambda __A						: x[1] ,    reverse=__A						)
     a 		=[]
     for (start_index, end_index), score in scores:
         if start_index > end_index:
             raise ValueError(f'''Wrong span indices: [{start_index}:{end_index}]'''						)
         a 		=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(__A						) == top_spans:
             break
     return chosen_span_intervals






@add_end_docstrings(_SCREAMING_SNAKE_CASE			)
class       __A				(       _SCREAMING_SNAKE_CASE,    _SCREAMING_SNAKE_CASE			):






 """simple docstring"""




 __lowerCAmelCase 					=  VOCAB_FILES_NAMES
 __lowerCAmelCase 					=  READER_PRETRAINED_VOCAB_FILES_MAP
 __lowerCAmelCase 					=  READER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
 __lowerCAmelCase 					=  READER_PRETRAINED_INIT_CONFIGURATION
 __lowerCAmelCase 					=  ["input_ids", "attention_mask"]



'''simple docstring'''


from collections import defaultdict
from math import ceil, sqrt







def 			snake_case_   (  SCREAMING_SNAKE_CASE__ = 100_0000							,      SCREAMING_SNAKE_CASE__ = 10     ):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE :       defaultdict     		=      defaultdict(SCREAMING_SNAKE_CASE__     )

				for outer_width in range(3							,      (t_limit // 4) + 2     ):
								if outer_width * outer_width > t_limit:
												_SCREAMING_SNAKE_CASE :       int     		=      max(
												    ceil(sqrt(outer_width * outer_width - t_limit     )     )							,      1     )
								else:
												_SCREAMING_SNAKE_CASE :       List[str]     		=      1

								hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

								for hole_width in range(SCREAMING_SNAKE_CASE__							,      outer_width - 1							,      2     ):
												count[outer_width * outer_width - hole_width * hole_width] += 1

				return sum(1 for n in count.values() if 1 <= n <= 10     )


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




