

import math






def        __lowercase   (  _A      )  ->    Tuple:
      return sum(int(_A      ) for digit in str(_A      )      )






def        __lowercase   (  _A = 30      )  ->    Dict:
      SCREAMING_SNAKE_CASE			:   List[Any]	  = []
      for digit in range(2    ,     100      ):
            for power in range(2    ,     100      ):
                  SCREAMING_SNAKE_CASE			:   str	  = int(math.pow(_A    ,     _A      )      )
                  if digit == digit_sum(_A      ):
                        digit_to_powers.append(_A      )

      digit_to_powers.sort()
      return digit_to_powers[n - 1]


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





"""simple docstring"""


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

import sentencepiece as spm

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


if TYPE_CHECKING:
 from transformers.pipelines.conversational import Conversation

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

lowerCAmelCase_:       Optional[int]			     =       {"vocab_file": "tokenizer.model"}

lowerCAmelCase_:       Optional[int]			     =       {
    "vocab_file": {
        "hf-internal-testing/llama-tokenizer": "https://huggingface.co/hf-internal-testing/llama-tokenizer/resolve/main/tokenizer.model",
    },
    "tokenizer_file": {
        "hf-internal-testing/llama-tokenizer": "https://huggingface.co/hf-internal-testing/llama-tokenizer/resolve/main/tokenizer_config.json",
    },
}
lowerCAmelCase_:       Optional[int]			     =       {
    "hf-internal-testing/llama-tokenizer": 2_0_4_8,
}
lowerCAmelCase_:       str			     =       "▁"

lowerCAmelCase_     ,				lowerCAmelCase_:       str			     =       "[INST]", "[/INST]"
lowerCAmelCase_     ,				lowerCAmelCase_:       Dict			     =       "<<SYS>>\n", "\n<</SYS>>\n\n"

# fmt: off
lowerCAmelCase_:       List[Any]			     =       "You are a helpful, respectful and honest assistant. Always answer as helpfully as possible, while being safe. Your\\nanswers should not include any harmful, unethical, racist, sexist, toxic, dangerous, or illegal content. Please ensure\\nthat your responses are socially unbiased and positive in nature.\n\nIf a question does not make any sense, or is not factually coherent, explain why instead of answering something not\\ncorrect. If you don't know the answer to a question, please don't share false information."






class  a__     ( _a						):
   snake_case_				=   VOCAB_FILES_NAMES
   snake_case_				=   PRETRAINED_VOCAB_FILES_MAP
   snake_case_				=   PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
   snake_case_				=   ["input_ids", "attention_mask"]


   def __init__(  self,					_UpperCAmelCase,					_UpperCAmelCase="<unk>",					_UpperCAmelCase="<s>",					_UpperCAmelCase="</s>",					_UpperCAmelCase=None,					_UpperCAmelCase = None,					_UpperCAmelCase=True,					_UpperCAmelCase=False,					_UpperCAmelCase=False,					_UpperCAmelCase=True,					**_UpperCAmelCase,					):
        '''simple docstring'''



        lowercase__								=				{} if sp_model_kwargs is None else sp_model_kwargs
        lowercase__								=				AddedToken(_UpperCAmelCase,					lstrip=_UpperCAmelCase,					rstrip=_UpperCAmelCase	) if isinstance(_UpperCAmelCase,					_UpperCAmelCase	) else bos_token
        lowercase__								=				AddedToken(_UpperCAmelCase,					lstrip=_UpperCAmelCase,					rstrip=_UpperCAmelCase	) if isinstance(_UpperCAmelCase,					_UpperCAmelCase	) else eos_token
        lowercase__								=				AddedToken(_UpperCAmelCase,					lstrip=_UpperCAmelCase,					rstrip=_UpperCAmelCase	) if isinstance(_UpperCAmelCase,					_UpperCAmelCase	) else unk_token
        lowercase__								=				AddedToken(_UpperCAmelCase,					lstrip=_UpperCAmelCase,					rstrip=_UpperCAmelCase	) if isinstance(_UpperCAmelCase,					_UpperCAmelCase	) else pad_token
        super().__init__(
            bos_token=_UpperCAmelCase,					eos_token=_UpperCAmelCase,					unk_token=_UpperCAmelCase,					pad_token=_UpperCAmelCase,					add_bos_token=_UpperCAmelCase,					add_eos_token=_UpperCAmelCase,					sp_model_kwargs=self.sp_model_kwargs,					clean_up_tokenization_spaces=_UpperCAmelCase,					legacy=_UpperCAmelCase,					**_UpperCAmelCase,					)
        if legacy:
             logger.warning_once(
                 F'''You are using the legacy behaviour of the {self.__class__}. This means that tokens that come after special tokens will not be properly handled. We recommend you to'''
                 " read the related pull request available at https://github.com/huggingface/transformers/pull/24565"	)
        lowercase__								=				legacy
        lowercase__								=				vocab_file
        lowercase__								=				add_bos_token
        lowercase__								=				add_eos_token
        lowercase__								=				spm.SentencePieceProcessor(**self.sp_model_kwargs	)
        self.sp_model.Load(_UpperCAmelCase	)


   def __getstate__(  self	):
        '''simple docstring'''



        lowercase__								=				self.__dict__.copy()
        lowercase__								=				None
        lowercase__								=				self.sp_model.serialized_model_proto()
        return state


   def __setstate__(  self,					_UpperCAmelCase	):
        '''simple docstring'''



        lowercase__								=				d
        lowercase__								=				spm.SentencePieceProcessor(**self.sp_model_kwargs	)
        self.sp_model.LoadFromSerializedProto(self.sp_model_proto	)


   @property
   def 						snake_case__						(  self	):
        '''simple docstring'''



        return self.sp_model.get_piece_size()


   def 						snake_case__						(  self	):
        '''simple docstring'''



        lowercase__								=				{self.convert_ids_to_tokens(_UpperCAmelCase	): i for i in range(self.vocab_size	)}
        vocab.update(self.added_tokens_encoder	)
        return vocab


   def 						snake_case__						(  self,					_UpperCAmelCase,					**_UpperCAmelCase	):
        '''simple docstring'''



        if not self.legacy:
             lowercase__								=				SPIECE_UNDERLINE + text.replace(_UpperCAmelCase,					" "	)
        return super().tokenize(_UpperCAmelCase,					**_UpperCAmelCase	)


   def 						snake_case__						(  self,					_UpperCAmelCase	):
        '''simple docstring'''



        if not self.legacy:
             lowercase__								=				text.startswith(_UpperCAmelCase	)
             if is_first:
                  lowercase__								=				text[1:]

        lowercase__								=				self.sp_model.encode(_UpperCAmelCase,					out_type=_UpperCAmelCase	)

        if not self.legacy and not is_first and not text.startswith(" "	) and tokens[0].startswith(_UpperCAmelCase	):
             lowercase__								=				([tokens[0][1:]] if len(tokens[0]	) > 1 else []) + tokens[1:]
        return tokens


   def 						snake_case__						(  self,					_UpperCAmelCase	):
        '''simple docstring'''



        return self.sp_model.piece_to_id(_UpperCAmelCase	)


   def 						snake_case__						(  self,					_UpperCAmelCase	):
        '''simple docstring'''



        lowercase__								=				self.sp_model.IdToPiece(_UpperCAmelCase	)
        return token


   def 						snake_case__						(  self,					_UpperCAmelCase	):
        '''simple docstring'''



        lowercase__								=				[]
        lowercase__								=				""
        lowercase__								=				False
        for i, token in enumerate(_UpperCAmelCase	):
             # make sure that special tokens are not decoded using sentencepiece model
             if token in self.all_special_tokens:
                  if not prev_is_special and i != 0:
                       out_string += " "
                  out_string += self.sp_model.decode(_UpperCAmelCase	) + token
                  lowercase__								=				True
                  lowercase__								=				[]
             else:
                  current_sub_tokens.append(_UpperCAmelCase	)
                  lowercase__								=				False
        out_string += self.sp_model.decode(_UpperCAmelCase	)
        return out_string


   def 						snake_case__						(  self,					_UpperCAmelCase,					_UpperCAmelCase = None	):
        '''simple docstring'''



        if not os.path.isdir(_UpperCAmelCase	):
             logger.error(F'''Vocabulary path ({save_directory}) should be a directory'''	)
             return
        lowercase__								=				os.path.join(
            _UpperCAmelCase,					(filename_prefix + "-" if filename_prefix else "") + VOCAB_FILES_NAMES["vocab_file"]	)

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

        return (out_vocab_file,)


   def 						snake_case__						(  self,					_UpperCAmelCase,					_UpperCAmelCase=None	):
        '''simple docstring'''



        lowercase__								=				[self.bos_token_id] if self.add_bos_token else []
        lowercase__								=				[self.eos_token_id] if self.add_eos_token else []

        lowercase__								=				bos_token_id + token_ids_a + eos_token_id

        if token_ids_a is not None:
             lowercase__								=				output + bos_token_id + token_ids_a + eos_token_id

        return output


   def 						snake_case__						(  self,					_UpperCAmelCase,					_UpperCAmelCase = None,					_UpperCAmelCase = False	):
        '''simple docstring'''



        if already_has_special_tokens:
             return super().get_special_tokens_mask(
                 token_ids_a=_UpperCAmelCase,					token_ids_a=_UpperCAmelCase,					already_has_special_tokens=_UpperCAmelCase	)

        lowercase__								=				[1] if self.add_bos_token else []
        lowercase__								=				[1] if self.add_eos_token else []

        if token_ids_a is None:
             return bos_token_id + ([0] * len(_UpperCAmelCase	)) + eos_token_id
        return (
            bos_token_id
            + ([0] * len(_UpperCAmelCase	))
            + eos_token_id
            + bos_token_id
            + ([0] * len(_UpperCAmelCase	))
            + eos_token_id
        )


   def 						snake_case__						(  self,					_UpperCAmelCase,					_UpperCAmelCase = None	):
        '''simple docstring'''



        lowercase__								=				[self.bos_token_id] if self.add_bos_token else []
        lowercase__								=				[self.eos_token_id] if self.add_eos_token else []

        lowercase__								=				[0] * len(bos_token_id + token_ids_a + eos_token_id	)

        if token_ids_a is not None:
             output += [1] * len(bos_token_id + token_ids_a + eos_token_id	)

        return output


   def 						snake_case__						(  self,					_UpperCAmelCase	):
        '''simple docstring'''



        lowercase__								=				list(conversation.iter_texts()	)
        if not all([is_user for is_user, msg in dialogue[::2]]	) or not all(
            [not is_user for is_user, msg in dialogue[1::2]]	):
             raise ValueError(
                 "The model only supports 'user' and 'assistant' roles, starting with user and alternating (u/a/u/a/u...)"	)

        lowercase__								=				[]
        if len(conversation.past_user_inputs	) > 0:
             if not conversation.past_user_inputs[0].startswith(_UpperCAmelCase	) or E_SYS not in conversation.past_user_inputs[0]:
                  lowercase__								=				(
                      B_SYS + DEFAULT_SYSTEM_PROMPT + E_SYS + conversation.past_user_inputs[0]
                  )
        elif not dialogue[0][1].startswith(_UpperCAmelCase	) or E_SYS not in dialogue[0][1]:
             lowercase__								=				(dialogue[0][0], B_SYS + DEFAULT_SYSTEM_PROMPT + E_SYS + dialogue[0][1])

        dialog_tokens += sum(
            [
                [self.bos_token_id]
                + self.encode(
                    F'''{B_INST} {(prompt[1]).strip()} {E_INST} {(answer[1]).strip()} ''',					add_special_tokens=_UpperCAmelCase	)
                + [self.eos_token_id]
                for prompt, answer in zip(dialogue[::2],					dialogue[1::2]	)
            ],					[],					)
        if not (dialogue[-1][0]):
             raise ValueError(F'''Last message must be from user, got {dialogue[-1]['role']}'''	)
        dialog_tokens += [self.bos_token_id] + self.encode(
            F'''{B_INST} {(dialogue[-1][1]).strip()} {E_INST}''',					add_special_tokens=_UpperCAmelCase	)
        return dialog_tokens




