

'''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


__snake_case :	Union[str, Any]      						=			logging.get_logger(__name__)

__snake_case :	Union[str, Any]      						=			{'vocab_file': 'vocab.txt', 'tokenizer_file': 'tokenizer.json'}

__snake_case :	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'
        ),
    },
}
__snake_case :	int      						=			{
    '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'
        ),
    },
}
__snake_case :	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'
        ),
    },
}

__snake_case :	str      						=			{
    'facebook/dpr-ctx_encoder-single-nq-base': 512,
    'facebook/dpr-ctx_encoder-multiset-base': 512,
}
__snake_case :	Dict      						=			{
    'facebook/dpr-question_encoder-single-nq-base': 512,
    'facebook/dpr-question_encoder-multiset-base': 512,
}
__snake_case :	Optional[int]      						=			{
    'facebook/dpr-reader-single-nq-base': 512,
    'facebook/dpr-reader-multiset-base': 512,
}


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



class lowerCamelCase (  lowerCAmelCase__						):



			'''simple docstring'''






			__snake_case    	=       VOCAB_FILES_NAMES
			__snake_case    	=       CONTEXT_ENCODER_PRETRAINED_VOCAB_FILES_MAP
			__snake_case    	=       CONTEXT_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
			__snake_case    	=       CONTEXT_ENCODER_PRETRAINED_INIT_CONFIGURATION



class lowerCamelCase (  lowerCAmelCase__						):



			'''simple docstring'''






			__snake_case    	=       VOCAB_FILES_NAMES
			__snake_case    	=       QUESTION_ENCODER_PRETRAINED_VOCAB_FILES_MAP
			__snake_case    	=       QUESTION_ENCODER_PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
			__snake_case    	=       QUESTION_ENCODER_PRETRAINED_INIT_CONFIGURATION


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

__snake_case :	Tuple      						=			collections.namedtuple('DPRReaderOutput', ['start_logits', 'end_logits', 'relevance_logits'])


__snake_case :	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    ```\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(lowerCAmelCase__						)
class lowerCamelCase :



			'''simple docstring'''






			def __call__(      self       :						List[str]		,			lowerCAmelCase_       :						Tuple		,			lowerCAmelCase_       :						Tuple = None		,			lowerCAmelCase_       :						Optional[int] = None		,			lowerCAmelCase_       :						Optional[Any] = False		,			lowerCAmelCase_       :						str = False		,			lowerCAmelCase_       :						Any = None		,			lowerCAmelCase_       :						Dict = None		,			lowerCAmelCase_       :						List[str] = None		,			**lowerCAmelCase_       :						Union[str, Any]		,			)			->		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:
															A__     :   Optional[Any]      =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__		,			)
									A__     :   Union[str, Any]      =titles if not isinstance(UpperCamelCase__		,			UpperCamelCase__ ) else [titles]
									A__     :   int      =texts if not isinstance(UpperCamelCase__		,			UpperCamelCase__ ) else [texts]
									A__     :   List[Any]      =len(UpperCamelCase__ )
									A__     :   int      =questions if not isinstance(UpperCamelCase__		,			UpperCamelCase__ ) else [questions] * n_passages
									if len(UpperCamelCase__ ) != len(UpperCamelCase__ ):
															raise ValueError(
															    f"There should be as many titles than texts but got {len(UpperCamelCase__ )} titles and {len(UpperCamelCase__ )} texts." )
									A__     :   Any      =super().__call__(UpperCamelCase__		,			UpperCamelCase__		,			padding=UpperCamelCase__		,			truncation=UpperCamelCase__ )["input_ids"]
									A__     :   Any      =super().__call__(UpperCamelCase__		,			add_special_tokens=UpperCamelCase__		,			padding=UpperCamelCase__		,			truncation=UpperCamelCase__ )["input_ids"]
									A__     :   int      ={
									    "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:
															A__     :   List[Any]      =[]
															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__     :   List[str]      =attention_mask
									return self.pad(UpperCamelCase__		,			padding=UpperCamelCase__		,			max_length=UpperCamelCase__		,			return_tensors=UpperCamelCase__ )


			def lowercase__						(      self       :						Optional[int]		,			lowerCAmelCase_       :						List[Any]		,			lowerCAmelCase_       :						Any		,			lowerCAmelCase_       :						List[str] = 16		,			lowerCAmelCase_       :						Union[str, Any] = 64		,			lowerCAmelCase_       :						Dict = 4		,			)			->		List[DPRSpanPrediction]:





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

															A__     :   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=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 lowercase__						(      self       :						Dict		,			lowerCAmelCase_       :						Optional[int]		,			lowerCAmelCase_       :						Dict		,			lowerCAmelCase_       :						List[Any]		,			lowerCAmelCase_       :						List[str]		,			)			->		List[DPRSpanPrediction]:





									'''simple docstring'''
									A__     :   Any      =[]
									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) )
									A__     :   List[Any]      =sorted(UpperCamelCase__		,			key=lambda lowerCAmelCase_ : x[1]		,			reverse=UpperCamelCase__ )
									A__     :   Optional[Any]      =[]
									for (start_index, end_index), score in scores:
															if start_index > end_index:
																					raise ValueError(f"Wrong span indices: [{start_index}:{end_index}]" )
															A__     :   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(UpperCamelCase__ ) == top_spans:
																					break
									return chosen_span_intervals



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



			'''simple docstring'''






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







def      A      (      _SCREAMING_SNAKE_CASE = 100_0000    )	-> int:
       lowerCamelCase   :      Tuple			 =					1
       lowerCamelCase   :      int			 =					1
       lowerCamelCase   :      Optional[Any]			 =					{1: 1}

       for inputa in range(2 ,_SCREAMING_SNAKE_CASE    ):
              lowerCamelCase   :      Union[str, Any]			 =					0
              lowerCamelCase   :      List[str]			 =					inputa

              while True:
                     if number in counters:
                            counter += counters[number]
                            break
                     if number % 2 == 0:
                            number //= 2
                            counter += 1
                     else:
                            lowerCamelCase   :      str			 =					(3 * number) + 1
                            counter += 1

              if inputa not in counters:
                     lowerCamelCase   :      str			 =					counter

              if counter > pre_counter:
                     lowerCamelCase   :      str			 =					inputa
                     lowerCamelCase   :      Any			 =					counter
       return largest_number


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






