





'''simple docstring'''







UpperCamelCase    :      List[str]  			=		range(2, 20 + 1)
UpperCamelCase    :      Union[str, Any]  			=		[10**k for k in range(ks[-1] + 1)]
UpperCamelCase    :      Dict  			=		{}
def 						A__			(				__lowerCAmelCase		:			List[Any]   ,    __lowerCAmelCase		:			Union[str, Any]   ,    __lowerCAmelCase		:			int   ,    __lowerCAmelCase		:			str						):
						lowerCamelCase__         =  sum(a_i[j] for j in range(__lowercase   ,    len(__lowercase						)						)						)
						lowerCamelCase__         =  sum(a_i[j] * base[j] for j in range(min(len(__lowercase						)   ,    __lowercase						)						)						)

						lowerCamelCase__         =  0, 0
						lowerCamelCase__         =  n - i

						lowerCamelCase__         =  memo.get(__lowercase						)

						if sub_memo is not None:
												lowerCamelCase__         =  sub_memo.get(__lowercase						)

												if jumps is not None and len(__lowercase						) > 0:
																		# find and make the largest jump without going over
																		lowerCamelCase__         =  -1
																		for _k in range(len(__lowercase						) - 1   ,    -1   ,    -1						):
																								if jumps[_k][2] <= k and jumps[_k][1] <= max_dn:
																														lowerCamelCase__         =  _k
																														break

																		if max_jump >= 0:
																								lowerCamelCase__         =  jumps[max_jump]
																								# since the difference between jumps is cached, add c
																								lowerCamelCase__         =  diff + c
																								for j in range(min(__lowercase   ,    len(__lowercase						)						)						):
																														lowerCamelCase__         =  divmod(__lowercase   ,    10						)
																								if new_c > 0:
																														add(__lowercase   ,    __lowercase   ,    __lowercase						)

												else:
																		lowerCamelCase__         =  []
						else:
												lowerCamelCase__         =  {c: []}
												lowerCamelCase__         =  sub_memo

						if dn >= max_dn or c + diff >= base[k]:
												return diff, dn

						if k > ks[0]:
												while True:
																		# keep doing smaller jumps
																		lowerCamelCase__         =  next_term(__lowercase   ,    k - 1   ,    i + dn   ,    __lowercase						)
																		diff += _diff
																		dn += terms_jumped

																		if dn >= max_dn or c + diff >= base[k]:
																								break
						else:
												# would be too small a jump, just compute sequential terms instead
												lowerCamelCase__         =  compute(__lowercase   ,    __lowercase   ,    i + dn   ,    __lowercase						)
												diff += _diff
												dn += terms_jumped

						lowerCamelCase__         =  sub_memo[c]

						# keep jumps sorted by # of terms skipped
						lowerCamelCase__         =  0
						while j < len(__lowercase						):
												if jumps[j][1] > dn:
																		break
												j += 1

						# cache the jump for this value digitsum(b) and c
						sub_memo[c].insert(__lowercase   ,    (diff, dn, k)						)
						return (diff, dn)
def 						A__			(				__lowerCAmelCase		:			int   ,    __lowerCAmelCase		:			int   ,    __lowerCAmelCase		:			List[Any]   ,    __lowerCAmelCase		:			int						):




						if i >= n:
												return 0, i
						if k > len(__lowercase						):
												a_i.extend([0 for _ in range(k - len(__lowercase						)						)]						)

						# note: a_i -> b * 10^k + c
						# ds_b -> digitsum(b)
						# ds_c -> digitsum(c)
						lowerCamelCase__         =  i
						lowerCamelCase__         =  0, 0, 0
						for j in range(len(__lowercase						)						):
												if j >= k:
																		ds_b += a_i[j]
												else:
																		ds_c += a_i[j]

						while i < n:
												i += 1
												lowerCamelCase__         =  ds_c + ds_b
												diff += addend
												lowerCamelCase__         =  0
												for j in range(__lowercase						):
																		lowerCamelCase__         =  a_i[j] + addend
																		lowerCamelCase__         =  divmod(__lowercase   ,    10						)

																		ds_c += a_i[j]

												if addend > 0:
																		break

						if addend > 0:
												add(__lowercase   ,    __lowercase   ,    __lowercase						)
						return diff, i - start_i
def 						A__			(				__lowerCAmelCase		:			Optional[Any]   ,    __lowerCAmelCase		:			int   ,    __lowerCAmelCase		:			Any						):




						for j in range(__lowercase   ,    len(__lowercase						)						):
												lowerCamelCase__         =  digits[j] + addend
												if s >= 10:
																		lowerCamelCase__         =  divmod(__lowercase   ,    10						)
																		lowerCamelCase__         =  addend // 10 + quotient
												else:
																		lowerCamelCase__         =  s
																		lowerCamelCase__         =  addend // 10

												if addend == 0:
																		break

						while addend > 0:
												lowerCamelCase__         =  divmod(__lowercase   ,    10						)
												digits.append(__lowercase						)
def 						A__			(				__lowerCAmelCase		:			int = 10**15						):
						lowerCamelCase__         =  [1]
						lowerCamelCase__         =  1
						lowerCamelCase__         =  0
						while True:
												lowerCamelCase__         =  next_term(__lowercase   ,    20   ,    i + dn   ,    __lowercase						)
												dn += terms_jumped
												if dn == n - i:
																		break

						lowerCamelCase__         =  0
						for j in range(len(__lowercase						)						):
												a_n += digits[j] * 10**j
						return a_n


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









'''simple docstring'''







import os
from shutil import copyfile
from typing import Any, Dict, List, Optional, Tuple

import sentencepiece as spm

from ...tokenization_utils import AddedToken, PreTrainedTokenizer
from ...utils import logging


UpperCamelCase    :      int  			=		logging.get_logger(__name__)

UpperCamelCase    :      Optional[int]  			=		{'vocab_file': 'sentencepiece.bpe.model'}

UpperCamelCase    :      Dict  			=		{
    'vocab_file': {
        'camembert-base': 'https://huggingface.co/camembert-base/resolve/main/sentencepiece.bpe.model',
    }
}

UpperCamelCase    :      List[Any]  			=		{
    'camembert-base': 5_12,
}

UpperCamelCase    :      List[str]  			=		'▁'




class 		UpperCamelCase__    (a			):




		'''simple docstring'''





		_UpperCamelCase				  =					VOCAB_FILES_NAMES
		_UpperCamelCase				  =					PRETRAINED_VOCAB_FILES_MAP
		_UpperCamelCase				  =					PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
		_UpperCamelCase				  =					['input_ids', 'attention_mask']






		def __init__(      self   ,_lowerCAmelCase   ,_lowerCAmelCase="<s>"   ,_lowerCAmelCase="</s>"   ,_lowerCAmelCase="</s>"   ,_lowerCAmelCase="<s>"   ,_lowerCAmelCase="<unk>"   ,_lowerCAmelCase="<pad>"   ,_lowerCAmelCase="<mask>"   ,_lowerCAmelCase=["<s>NOTUSED", "</s>NOTUSED"]   ,_lowerCAmelCase = None   ,**_lowerCAmelCase   ,):
								# Mask token behave like a normal word, i.e. include the space before it
								lowerCamelCase__         =  AddedToken(_lowerCAmelCase   ,lstrip=_lowerCAmelCase   ,rstrip=_lowerCAmelCase       ) if isinstance(_lowerCAmelCase   ,_lowerCAmelCase       ) else mask_token

								lowerCamelCase__         =  {} if sp_model_kwargs is None else sp_model_kwargs

								super().__init__(
								    bos_token=_lowerCAmelCase   ,eos_token=_lowerCAmelCase   ,unk_token=_lowerCAmelCase   ,sep_token=_lowerCAmelCase   ,cls_token=_lowerCAmelCase   ,pad_token=_lowerCAmelCase   ,mask_token=_lowerCAmelCase   ,additional_special_tokens=_lowerCAmelCase   ,sp_model_kwargs=self.sp_model_kwargs   ,**_lowerCAmelCase   ,)
								lowerCamelCase__         =  spm.SentencePieceProcessor(**self.sp_model_kwargs       )
								self.sp_model.Load(str(_lowerCAmelCase       )       )
								lowerCamelCase__         =  vocab_file
								# HACK: These tokens were added by fairseq but don't seem to be actually used when duplicated in the actual
								# sentencepiece vocabulary (this is the case for <s> and </s>
								lowerCamelCase__         =  {"""<s>NOTUSED""": 0, """<pad>""": 1, """</s>NOTUSED""": 2, """<unk>""": 3}
								lowerCamelCase__         =  len(self.fairseq_tokens_to_ids       )
								lowerCamelCase__         =  len(self.sp_model       ) + len(self.fairseq_tokens_to_ids       )
								lowerCamelCase__         =  {v: k for k, v in self.fairseq_tokens_to_ids.items()}






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase = None       ):

								if token_ids_a is None:
														return [self.cls_token_id] + token_ids_a + [self.sep_token_id]
								lowerCamelCase__         =  [self.cls_token_id]
								lowerCamelCase__         =  [self.sep_token_id]
								return cls + token_ids_a + sep + sep + token_ids_a + sep






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase = None   ,_lowerCAmelCase = False       ):
								if already_has_special_tokens:
														return super().get_special_tokens_mask(
														    token_ids_a=_lowerCAmelCase   ,token_ids_a=_lowerCAmelCase   ,already_has_special_tokens=_lowerCAmelCase       )

								if token_ids_a is None:
														return [1] + ([0] * len(_lowerCAmelCase       )) + [1]
								return [1] + ([0] * len(_lowerCAmelCase       )) + [1, 1] + ([0] * len(_lowerCAmelCase       )) + [1]






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase = None       ):
								lowerCamelCase__         =  [self.sep_token_id]
								lowerCamelCase__         =  [self.cls_token_id]

								if token_ids_a is None:
														return len(cls + token_ids_a + sep       ) * [0]
								return len(cls + token_ids_a + sep + sep + token_ids_a + sep       ) * [0]






		@property
		def 			UpperCamelCase_					(      self       ):
								return len(self.fairseq_tokens_to_ids       ) + len(self.sp_model       )






		def 			UpperCamelCase_					(      self       ):
								lowerCamelCase__         =  {self.convert_ids_to_tokens(_lowerCAmelCase       ): i for i in range(self.vocab_size       )}
								vocab.update(self.added_tokens_encoder       )
								return vocab






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase       ):
								return self.sp_model.encode(_lowerCAmelCase   ,out_type=_lowerCAmelCase       )






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase       ):
								if token in self.fairseq_tokens_to_ids:
														return self.fairseq_tokens_to_ids[token]
								elif self.sp_model.PieceToId(_lowerCAmelCase       ) == 0:
														# Convert sentence piece unk token to fairseq unk token index
														return self.unk_token_id
								return self.fairseq_offset + self.sp_model.PieceToId(_lowerCAmelCase       )






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase       ):
								if index in self.fairseq_ids_to_tokens:
														return self.fairseq_ids_to_tokens[index]
								return self.sp_model.IdToPiece(index - self.fairseq_offset       )






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase       ):
								lowerCamelCase__         =  []
								lowerCamelCase__         =  """"""
								lowerCamelCase__         =  False
								for token in tokens:
														# make sure that special tokens are not decoded using sentencepiece model
														if token in self.all_special_tokens:
																				if not prev_is_special:
																										out_string += " "
																				out_string += self.sp_model.decode(_lowerCAmelCase       ) + token
																				lowerCamelCase__         =  True
																				lowerCamelCase__         =  []
														else:
																				current_sub_tokens.append(_lowerCAmelCase       )
																				lowerCamelCase__         =  False
								out_string += self.sp_model.decode(_lowerCAmelCase       )
								return out_string.strip()






		def __getstate__(      self       ):
								lowerCamelCase__         =  self.__dict__.copy()
								lowerCamelCase__         =  None
								return state






		def __setstate__(      self   ,_lowerCAmelCase       ):
								lowerCamelCase__         =  d

								# for backward compatibility
								if not hasattr(self   ,"""sp_model_kwargs"""       ):
														lowerCamelCase__         =  {}

								lowerCamelCase__         =  spm.SentencePieceProcessor(**self.sp_model_kwargs       )
								self.sp_model.Load(self.vocab_file       )






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase = None       ):
								if not os.path.isdir(_lowerCAmelCase       ):
														logger.error(F'''Vocabulary path ({save_directory}) should be a directory'''       )
														return
								lowerCamelCase__         =  os.path.join(
								    _lowerCAmelCase   ,(filename_prefix + """-""" if filename_prefix else """""") + VOCAB_FILES_NAMES["""vocab_file"""]       )

								if os.path.abspath(self.vocab_file       ) != os.path.abspath(_lowerCAmelCase       ) and os.path.isfile(self.vocab_file       ):
														copyfile(self.vocab_file   ,_lowerCAmelCase       )
								elif not os.path.isfile(self.vocab_file       ):
														with open(_lowerCAmelCase   ,"""wb"""       ) as fi:
																				lowerCamelCase__         =  self.sp_model.serialized_model_proto()
																				fi.write(_lowerCAmelCase       )

								return (out_vocab_file,)

