

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


lowerCamelCase			:				int 			=					logging.get_logger(__name__)

lowerCamelCase			:				Optional[int] 			=					{"vocab_file": "vocab.txt", "tokenizer_file": "tokenizer.json"}

lowerCamelCase			:				Union[str, Any] 			=					{
    "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			:				str 			=					{
    "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			:				Union[str, 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"
        ),
    },
}

lowerCamelCase			:				Union[str, Any] 			=					{
    "facebook/dpr-ctx_encoder-single-nq-base": 5_1_2,
    "facebook/dpr-ctx_encoder-multiset-base": 5_1_2,
}
lowerCamelCase			:				List[str] 			=					{
    "facebook/dpr-question_encoder-single-nq-base": 5_1_2,
    "facebook/dpr-question_encoder-multiset-base": 5_1_2,
}
lowerCamelCase			:				Optional[int] 			=					{
    "facebook/dpr-reader-single-nq-base": 5_1_2,
    "facebook/dpr-reader-multiset-base": 5_1_2,
}


lowerCamelCase			:				int 			=					{
    "facebook/dpr-ctx_encoder-single-nq-base": {"do_lower_case": True},
    "facebook/dpr-ctx_encoder-multiset-base": {"do_lower_case": True},
}
lowerCamelCase			:				int 			=					{
    "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__   (	__snake_case  ):
  A__					=    VOCAB_FILES_NAMES
  A__					=    CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
  A__					=    CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
  A__					=    CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION
  A__					=    DPRContextEncoderTokenizer







class 							A__   (	__snake_case  ):
  A__					=    VOCAB_FILES_NAMES
  A__					=    QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
  A__					=    QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
  A__					=    QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION
  A__					=    DPRQuestionEncoderTokenizer

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

lowerCamelCase			:				List[str] 			=					collections.namedtuple("DPRReaderOutput", ["start_logits", "end_logits", "relevance_logits"])


lowerCamelCase			:				Union[str, Any] 			=					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(__snake_case  )
class 							A__   :





  def __call__(		self				:     int							, _a				:     Optional[Any]							, _a				:     Optional[str] = None							, _a				:     Optional[str] = None							, _a				:     Union[bool, str] = False							, _a				:     Union[bool, str] = False							, _a				:     Optional[int] = None							, _a				:     Optional[Union[str, TensorType]] = None							, _a				:     Optional[bool] = None							, **_a				:     Dict							, )     ->   BatchEncoding:





       '''simple docstring'''






       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:
            _SCREAMING_SNAKE_CASE							   =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__							, )
       _SCREAMING_SNAKE_CASE							   =titles if not isinstance(UpperCamelCase__							, UpperCamelCase__			) else [titles]
       _SCREAMING_SNAKE_CASE							   =texts if not isinstance(UpperCamelCase__							, UpperCamelCase__			) else [texts]
       _SCREAMING_SNAKE_CASE							   =len(UpperCamelCase__			)
       _SCREAMING_SNAKE_CASE							   =questions if not isinstance(UpperCamelCase__							, UpperCamelCase__			) else [questions] * n_passages
       assert len(UpperCamelCase__			) == len(
           UpperCamelCase__			), f"There should be as many titles than texts but got {len(UpperCamelCase__			)} titles and {len(UpperCamelCase__			)} texts."
       _SCREAMING_SNAKE_CASE							   =super().__call__(UpperCamelCase__							, UpperCamelCase__							, padding=UpperCamelCase__							, truncation=UpperCamelCase__			)["input_ids"]
       _SCREAMING_SNAKE_CASE							   =super().__call__(UpperCamelCase__							, add_special_tokens=UpperCamelCase__							, padding=UpperCamelCase__							, truncation=UpperCamelCase__			)["input_ids"]
       _SCREAMING_SNAKE_CASE							   ={
           "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:
            _SCREAMING_SNAKE_CASE							   =[]
            for input_ids in encoded_inputs["input_ids"]:
                 attention_mask.append([int(input_id != self.pad_token_id			) for input_id in input_ids]			)
            _SCREAMING_SNAKE_CASE							   =attention_mask
       return self.pad(UpperCamelCase__							, padding=UpperCamelCase__							, max_length=UpperCamelCase__							, return_tensors=UpperCamelCase__			)





  def 						A  (		self				:     List[Any]							, _a				:     BatchEncoding							, _a				:     DPRReaderOutput							, _a				:     int = 16							, _a				:     int = 64							, _a				:     int = 4							, )     ->   List[DPRSpanPrediction]:





       '''simple docstring'''






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

            _SCREAMING_SNAKE_CASE							   =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 						A  (		self				:     int							, _a				:     List[int]							, _a				:     List[int]							, _a				:     int							, _a				:     int							, )     ->   List[DPRSpanPrediction]:





       '''simple docstring'''






       _SCREAMING_SNAKE_CASE							   =[]
       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)			)
       _SCREAMING_SNAKE_CASE							   =sorted(UpperCamelCase__							, key=lambda _a			: x[1]							, reverse=UpperCamelCase__			)
       _SCREAMING_SNAKE_CASE							   =[]
       for (start_index, end_index), score in scores:
            assert start_index <= end_index, f"Wrong span indices: [{start_index}:{end_index}]"
            _SCREAMING_SNAKE_CASE							   =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(UpperCamelCase__			) == top_spans:
                 break
       return chosen_span_intervals







@add_end_docstrings(__snake_case  )
class 							A__   (	__snake_case					,       __snake_case  ):
  A__					=    VOCAB_FILES_NAMES
  A__					=    READER_PRETRAINED_VOCAB_FILES_MAP
  A__					=    READER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
  A__					=    READER_PRETRAINED_INIT_CONFIGURATION
  A__					=    ["""input_ids""", """attention_mask"""]
  A__					=    DPRReaderTokenizer



'''simple docstring'''
import os


def 	_lowerCAmelCase (						)				->      List[str]:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							   =os.path.dirname(os.path.realpath(_UpperCamelCase    )    )
     _SCREAMING_SNAKE_CASE							   =os.path.join(_UpperCamelCase							,			'triangle.txt'    )

     with open(_UpperCamelCase    ) as f:
          _SCREAMING_SNAKE_CASE							   =f.readlines()

     _SCREAMING_SNAKE_CASE							   =[]
     for line in triangle:
          _SCREAMING_SNAKE_CASE							   =[]
          for number in line.strip().split(' '    ):
               numbers_from_line.append(int(_UpperCamelCase    )    )
          a.append(_UpperCamelCase    )

     for i in range(1							,			len(_UpperCamelCase    )    ):
          for j in range(len(a[i]    )    ):
               _SCREAMING_SNAKE_CASE							   =a[i - 1][j] if j != len(a[i - 1]    ) else 0
               _SCREAMING_SNAKE_CASE							   =a[i - 1][j - 1] if j > 0 else 0
               a[i][j] += max(_UpperCamelCase							,			_UpperCamelCase    )
     return max(a[-1]    )


if __name__ == "__main__":
     print(solution())
