'''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


__lowercase          =  logging.get_logger(__name__)

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

__lowercase          =  {
    '''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'''
        ),
    },
}
__lowercase          =  {
    '''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'''
        ),
    },
}
__lowercase          =  {
    '''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'''
        ),
    },
}

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


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






class 				a__(					lowerCAmelCase__	):


			'''simple docstring'''






			UpperCAmelCase_			:     Tuple      =       VOCAB_FILES_NAMES
			UpperCAmelCase_			:     Tuple      =       CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
			UpperCAmelCase_			:     int      =       CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
			UpperCAmelCase_			:     Tuple      =       CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION







class 				a__(					lowerCAmelCase__	):


			'''simple docstring'''






			UpperCAmelCase_			:     Tuple      =       VOCAB_FILES_NAMES
			UpperCAmelCase_			:     Optional[Any]      =       QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
			UpperCAmelCase_			:     Dict      =       QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
			UpperCAmelCase_			:     List[str]      =       QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION







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

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


__lowercase          =  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(lowerCAmelCase__	)
class 				a__:


			'''simple docstring'''






			def __call__(   self       ,    __lowerCAmelCase       ,    __lowerCAmelCase = None       ,    __lowerCAmelCase = None       ,    __lowerCAmelCase = False       ,    __lowerCAmelCase = False       ,    __lowerCAmelCase = None       ,    __lowerCAmelCase = None       ,    __lowerCAmelCase = None       ,    **__lowerCAmelCase       ,    ):




					"""simple docstring"""


					if titles is None and texts is None:
							return super().__call__(
							    __lowerCAmelCase       ,    padding=__lowerCAmelCase       ,    truncation=__lowerCAmelCase       ,    max_length=__lowerCAmelCase       ,    return_tensors=__lowerCAmelCase       ,    return_attention_mask=__lowerCAmelCase       ,    **__lowerCAmelCase       ,    )
					elif titles is None or texts is None:
							lowerCAmelCase   					=  titles if texts is None else texts
							return super().__call__(
							    __lowerCAmelCase       ,    __lowerCAmelCase       ,    padding=__lowerCAmelCase       ,    truncation=__lowerCAmelCase       ,    max_length=__lowerCAmelCase       ,    return_tensors=__lowerCAmelCase       ,    return_attention_mask=__lowerCAmelCase       ,    **__lowerCAmelCase       ,    )
					lowerCAmelCase   					=  titles if not isinstance(__lowerCAmelCase       ,    __lowerCAmelCase) else [titles]
					lowerCAmelCase   					=  texts if not isinstance(__lowerCAmelCase       ,    __lowerCAmelCase) else [texts]
					lowerCAmelCase   					=  len(__lowerCAmelCase)
					lowerCAmelCase   					=  questions if not isinstance(__lowerCAmelCase       ,    __lowerCAmelCase) else [questions] * n_passages
					if len(__lowerCAmelCase) != len(__lowerCAmelCase):
							raise ValueError(
							    f"There should be as many titles than texts but got {len(__lowerCAmelCase)} titles and {len(__lowerCAmelCase)} texts.")
					lowerCAmelCase   					=  super().__call__(__lowerCAmelCase       ,    __lowerCAmelCase       ,    padding=__lowerCAmelCase       ,    truncation=__lowerCAmelCase)["""input_ids"""]
					lowerCAmelCase   					=  super().__call__(__lowerCAmelCase       ,    add_special_tokens=__lowerCAmelCase       ,    padding=__lowerCAmelCase       ,    truncation=__lowerCAmelCase)["""input_ids"""]
					lowerCAmelCase   					=  {
					    """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(__lowerCAmelCase       ,    __lowerCAmelCase)
					    ]
					}
					if return_attention_mask is not False:
							lowerCAmelCase   					=  []
							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   					=  attention_mask
					return self.pad(__lowerCAmelCase       ,    padding=__lowerCAmelCase       ,    max_length=__lowerCAmelCase       ,    return_tensors=__lowerCAmelCase)



			def 							a_       (   self       ,    __lowerCAmelCase       ,    __lowerCAmelCase       ,    __lowerCAmelCase = 16       ,    __lowerCAmelCase = 64       ,    __lowerCAmelCase = 4       ,    ):




					"""simple docstring"""


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

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







			def 							a_       (   self       ,    __lowerCAmelCase       ,    __lowerCAmelCase       ,    __lowerCAmelCase       ,    __lowerCAmelCase       ,    ):




					"""simple docstring"""


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







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


			'''simple docstring'''






			UpperCAmelCase_			:     Any      =       VOCAB_FILES_NAMES
			UpperCAmelCase_			:     List[str]      =       READER_PRETRAINED_VOCAB_FILES_MAP
			UpperCAmelCase_			:     str      =       READER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
			UpperCAmelCase_			:     List[str]      =       READER_PRETRAINED_INIT_CONFIGURATION
			UpperCAmelCase_			:     Union[str, Any]      =       ['''input_ids''', '''attention_mask''']





'''simple docstring'''




from math import sqrt






def 				snake_case__							(			_A:					int = 1000000 )    ->	int:

		'''simple docstring'''


		lowerCAmelCase   					=  0
		lowerCAmelCase   					=  0
		lowerCAmelCase   					=  42

		while num_cuboids <= limit:
				max_cuboid_size += 1
				for sum_shortest_sides in range(2      ,   2 * max_cuboid_size + 1 ):
						if sqrt(sum_shortest_sides**2 + max_cuboid_size**2 ).is_integer():
								num_cuboids += (
								    min(_A      ,   sum_shortest_sides // 2 )
								    - max(1      ,   sum_shortest_sides - max_cuboid_size )
								    + 1
								)

		return max_cuboid_size


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




