





'''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


UpperCAmelCase					:		Optional[Any]		=							logging.get_logger(__name__)

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

UpperCAmelCase					:		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'
        ),
    },
}
UpperCAmelCase					:		Dict		=							{
    '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'
        ),
    },
}
UpperCAmelCase					:		int		=							{
    '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'
        ),
    },
}

UpperCAmelCase					:		int		=							{
    'facebook/dpr-ctx_encoder-single-nq-base': 5_1_2,
    'facebook/dpr-ctx_encoder-multiset-base': 5_1_2,
}
UpperCAmelCase					:		List[Any]		=							{
    'facebook/dpr-question_encoder-single-nq-base': 5_1_2,
    'facebook/dpr-question_encoder-multiset-base': 5_1_2,
}
UpperCAmelCase					:		Any		=							{
    'facebook/dpr-reader-single-nq-base': 5_1_2,
    'facebook/dpr-reader-multiset-base': 5_1_2,
}


UpperCAmelCase					:		Optional[int]		=							{
    'facebook/dpr-ctx_encoder-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-ctx_encoder-multiset-base': {'do_lower_case': True},
}
UpperCAmelCase					:		Any		=							{
    'facebook/dpr-question_encoder-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-question_encoder-multiset-base': {'do_lower_case': True},
}
UpperCAmelCase					:		Any		=							{
    'facebook/dpr-reader-single-nq-base': {'do_lower_case': True},
    'facebook/dpr-reader-multiset-base': {'do_lower_case': True},
}





class lowerCamelCase						(a__					):
  _lowercase  :	Union[str, Any]       					=				VOCAB_FILES_NAMES
  _lowercase  :	List[str]       					=				CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
  _lowercase  :	Optional[Any]       					=				CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
  _lowercase  :	Any       					=				CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION





class lowerCamelCase						(a__					):
  _lowercase  :	Any       					=				VOCAB_FILES_NAMES
  _lowercase  :	Dict       					=				QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
  _lowercase  :	Tuple       					=				QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
  _lowercase  :	List[Any]       					=				QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION



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

UpperCAmelCase					:		Union[str, Any]		=							collections.namedtuple('DPRReaderOutput', ['start_logits', 'end_logits', 'relevance_logits'])


UpperCAmelCase					:		str		=							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(a__					)
class lowerCamelCase						:







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






        """simple docstring"""





        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:
              _snake_case		:	Optional[Any]					     =     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__     ,     )
        _snake_case		:	Optional[Any]					     =     titles if not isinstance(lowercase__     ,     lowercase__		) else [titles]
        _snake_case		:	int					     =     texts if not isinstance(lowercase__     ,     lowercase__		) else [texts]
        _snake_case		:	Optional[int]					     =     len(lowercase__		)
        _snake_case		:	Tuple					     =     questions if not isinstance(lowercase__     ,     lowercase__		) else [questions] * n_passages
        if len(lowercase__		) != len(lowercase__		):
              raise ValueError(
                  F'''There should be as many titles than texts but got {len(lowercase__		)} titles and {len(lowercase__		)} texts.'''		)
        _snake_case		:	int					     =     super().__call__(lowercase__     ,     lowercase__     ,     padding=lowercase__     ,     truncation=lowercase__		)['''input_ids''']
        _snake_case		:	List[str]					     =     super().__call__(lowercase__     ,     add_special_tokens=lowercase__     ,     padding=lowercase__     ,     truncation=lowercase__		)['''input_ids''']
        _snake_case		:	str					     =     {
            '''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:
              _snake_case		:	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]		)
              _snake_case		:	int					     =     attention_mask
        return self.pad(lowercase__     ,     padding=lowercase__     ,     max_length=lowercase__     ,     return_tensors=lowercase__		)







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






        """simple docstring"""





        _snake_case		:	Optional[int]					     =     reader_input['''input_ids''']
        _snake_case     ,							_snake_case     ,							_snake_case		:	Union[str, Any]					     =     reader_output[:3]
        _snake_case		:	List[Any]					     =     len(lowercase__		)
        _snake_case		:	Union[str, Any]					     =     sorted(range(lowercase__		)     ,     reverse=lowercase__     ,     key=relevance_logits.__getitem__		)
        _snake_case		:	List[DPRReaderOutput]					     =     []
        for doc_id in sorted_docs:
              _snake_case		:	Optional[int]					     =     list(input_ids[doc_id]		)
              # assuming question & title information is at the beginning of the sequence
              _snake_case		:	Union[str, Any]					     =     sequence_ids.index(self.sep_token_id     ,     2		) + 1  # second sep id
              if sequence_ids[-1] == self.pad_token_id:
                    _snake_case		:	Optional[Any]					     =     sequence_ids.index(self.pad_token_id		)
              else:
                    _snake_case		:	int					     =     len(lowercase__		)

              _snake_case		:	Union[str, Any]					     =     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     ,     lowercase__     ,     lowercase__     ,     lowercase__     ,     lowercase__     ,     )		->						List[DPRSpanPrediction]:






        """simple docstring"""





        _snake_case		:	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)		)
        _snake_case		:	str					     =     sorted(lowercase__     ,     key=lambda lowercase__		: x[1]     ,     reverse=lowercase__		)
        _snake_case		:	List[str]					     =     []
        for (start_index, end_index), score in scores:
              if start_index > end_index:
                    raise ValueError(F'''Wrong span indices: [{start_index}:{end_index}]'''		)
              _snake_case		:	Union[str, Any]					     =     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(lowercase__		) == top_spans:
                    break
        return chosen_span_intervals





@add_end_docstrings(a__					)
class lowerCamelCase						(a__						,      a__					):
  _lowercase  :	Dict       					=				VOCAB_FILES_NAMES
  _lowercase  :	Optional[int]       					=				READER_PRETRAINED_VOCAB_FILES_MAP
  _lowercase  :	List[Any]       					=				READER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
  _lowercase  :	List[Any]       					=				READER_PRETRAINED_INIT_CONFIGURATION
  _lowercase  :	Union[str, Any]       					=				["""input_ids""", """attention_mask"""]









'''simple docstring'''

def    _a    (							lowerCAmelCase_	):





      """simple docstring"""



      if n == 1 or not isinstance(lowerCAmelCase_			,      lowerCAmelCase_	):
            return 0
      elif n == 2:
            return 1
      else:
            _snake_case		:	Union[str, Any]					     =     [0, 1]
            for i in range(2			,      n + 1	):
                  sequence.append(sequence[i - 1] + sequence[i - 2]	)

            return sequence[n]




def    _a    (							lowerCAmelCase_	):





      """simple docstring"""



      _snake_case		:	Optional[int]					     =     0
      _snake_case		:	int					     =     2

      while digits < n:
            index += 1
            _snake_case		:	Tuple					     =     len(str(fibonacci(lowerCAmelCase_	)	)	)

      return index




def    _a    (							lowerCAmelCase_ = 1_000	):





      """simple docstring"""



      return fibonacci_digits_index(lowerCAmelCase_	)


if __name__ == "__main__":
   print(solution(int(str(input()).strip())))


