'''simple docstring'''





import json
from typing import List, Optional, Tuple

from tokenizers import pre_tokenizers, processors

from ...tokenization_utils_base import AddedToken, BatchEncoding
from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import logging
from .tokenization_bart import BartTokenizer


SCREAMING_SNAKE_CASE_:     Any  =logging.get_logger(__name__)


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

# See all BART models at https://huggingface.co/models?filter=bart
SCREAMING_SNAKE_CASE_:     str  ={
    'vocab_file': {
        'facebook/bart-base': 'https://huggingface.co/facebook/bart-base/resolve/main/vocab.json',
        'facebook/bart-large': 'https://huggingface.co/facebook/bart-large/resolve/main/vocab.json',
        'facebook/bart-large-mnli': 'https://huggingface.co/facebook/bart-large-mnli/resolve/main/vocab.json',
        'facebook/bart-large-cnn': 'https://huggingface.co/facebook/bart-large-cnn/resolve/main/vocab.json',
        'facebook/bart-large-xsum': 'https://huggingface.co/facebook/bart-large-xsum/resolve/main/vocab.json',
        'yjernite/bart_eli5': 'https://huggingface.co/yjernite/bart_eli5/resolve/main/vocab.json',
    },
    'merges_file': {
        'facebook/bart-base': 'https://huggingface.co/facebook/bart-base/resolve/main/merges.txt',
        'facebook/bart-large': 'https://huggingface.co/facebook/bart-large/resolve/main/merges.txt',
        'facebook/bart-large-mnli': 'https://huggingface.co/facebook/bart-large-mnli/resolve/main/merges.txt',
        'facebook/bart-large-cnn': 'https://huggingface.co/facebook/bart-large-cnn/resolve/main/merges.txt',
        'facebook/bart-large-xsum': 'https://huggingface.co/facebook/bart-large-xsum/resolve/main/merges.txt',
        'yjernite/bart_eli5': 'https://huggingface.co/yjernite/bart_eli5/resolve/main/merges.txt',
    },
    'tokenizer_file': {
        'facebook/bart-base': 'https://huggingface.co/facebook/bart-base/resolve/main/tokenizer.json',
        'facebook/bart-large': 'https://huggingface.co/facebook/bart-large/resolve/main/tokenizer.json',
        'facebook/bart-large-mnli': 'https://huggingface.co/facebook/bart-large-mnli/resolve/main/tokenizer.json',
        'facebook/bart-large-cnn': 'https://huggingface.co/facebook/bart-large-cnn/resolve/main/tokenizer.json',
        'facebook/bart-large-xsum': 'https://huggingface.co/facebook/bart-large-xsum/resolve/main/tokenizer.json',
        'yjernite/bart_eli5': 'https://huggingface.co/yjernite/bart_eli5/resolve/main/tokenizer.json',
    },
}

SCREAMING_SNAKE_CASE_:     int  ={
    'facebook/bart-base': 10_24,
    'facebook/bart-large': 10_24,
    'facebook/bart-large-mnli': 10_24,
    'facebook/bart-large-cnn': 10_24,
    'facebook/bart-large-xsum': 10_24,
    'yjernite/bart_eli5': 10_24,
}




class        __A      ( UpperCamelCase__	):
    a__       :						Dict          =  VOCAB_FILES_NAMES
    a__       :						Any          =  PRETRAINED_VOCAB_FILES_MAP
    a__       :						Union[str, Any]          =  PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
    a__       :						int          =  ["""input_ids""", """attention_mask"""]
    a__       :						str          =  BartTokenizer



    def __init__(self    :    List[str]   ,			__a    :    List[Any]=None   ,			__a    :    str=None   ,			__a    :    List[str]=None   ,			__a    :    Union[str, Any]="replace"   ,			__a    :    List[str]="<s>"   ,			__a    :    List[Any]="</s>"   ,			__a    :    Dict="</s>"   ,			__a    :    Optional[int]="<s>"   ,			__a    :    Any="<unk>"   ,			__a    :    List[Any]="<pad>"   ,			__a    :    List[str]="<mask>"   ,			__a    :    Tuple=False   ,			__a    :    Optional[Any]=True   ,			**__a    :    Optional[Any]   ,			):
         super().__init__(
             __a   ,			__a   ,			tokenizer_file=__a   ,			errors=__a   ,			bos_token=__a   ,			eos_token=__a   ,			sep_token=__a   ,			cls_token=__a   ,			unk_token=__a   ,			pad_token=__a   ,			mask_token=__a   ,			add_prefix_space=__a   ,			trim_offsets=__a   ,			**__a   ,			)

         UpperCAmelCase_           =   json.loads(self.backend_tokenizer.pre_tokenizer.__getstate__() )
         if pre_tok_state.get("add_prefix_space"   ,			__a ) != add_prefix_space:
              UpperCAmelCase_           =   getattr(__a   ,			pre_tok_state.pop("type" ) )
              UpperCAmelCase_           =   add_prefix_space
              UpperCAmelCase_           =   pre_tok_class(**__a )

         UpperCAmelCase_           =   add_prefix_space

         # the pre_tokenizer is already updated in the GPT2TokenizerFast `__init__`
         UpperCAmelCase_           =   "post_processor"
         UpperCAmelCase_           =   getattr(self.backend_tokenizer   ,			__a   ,			__a )
         if tokenizer_component_instance:
              UpperCAmelCase_           =   json.loads(tokenizer_component_instance.__getstate__() )

              # The lists 'sep' and 'cls' must be cased in tuples for the object `post_processor_class`
              if "sep" in state:
                   UpperCAmelCase_           =   tuple(state["sep"] )
              if "cls" in state:
                   UpperCAmelCase_           =   tuple(state["cls"] )

              UpperCAmelCase_           =   False

              if state.get("add_prefix_space"   ,			__a ) != add_prefix_space:
                   UpperCAmelCase_           =   add_prefix_space
                   UpperCAmelCase_           =   True

              if state.get("trim_offsets"   ,			__a ) != trim_offsets:
                   UpperCAmelCase_           =   trim_offsets
                   UpperCAmelCase_           =   True

              if changes_to_apply:
                   UpperCAmelCase_           =   getattr(__a   ,			state.pop("type" ) )
                   UpperCAmelCase_           =   component_class(**__a )
                   setattr(self.backend_tokenizer   ,			__a   ,			__a )



    @property
    def 					_lowercase						(self    :    Dict ):
         if self._mask_token is None:
              if self.verbose:
                   logger.error("Using mask_token, but it is not set yet." )
              return None
         return str(self._mask_token )



    @mask_token.setter
    def 					_lowercase						(self    :    Optional[int]   ,			__a    :    List[Any] ):
         UpperCAmelCase_           =   AddedToken(__a   ,			lstrip=__a   ,			rstrip=__a ) if isinstance(__a   ,			__a ) else value
         UpperCAmelCase_           =   value



    def 					_lowercase						(self    :    Any   ,			*__a    :    List[Any]   ,			**__a    :    Any ):
         UpperCAmelCase_           =   kwargs.get("is_split_into_words"   ,			__a )

         if is_split_into_words and not self.add_prefix_space:
              raise ValueError(
                  f"""You need to instantiate {self.__class__.__name__} with add_prefix_space=True """
                  "to use it with pretokenized inputs." )

         return super()._batch_encode_plus(*__a   ,			**__a )



    def 					_lowercase						(self    :    List[str]   ,			*__a    :    Optional[Any]   ,			**__a    :    Dict ):
         UpperCAmelCase_           =   kwargs.get("is_split_into_words"   ,			__a )

         if is_split_into_words and not self.add_prefix_space:
              raise ValueError(
                  f"""You need to instantiate {self.__class__.__name__} with add_prefix_space=True """
                  "to use it with pretokenized inputs." )

         return super()._encode_plus(*__a   ,			**__a )



    def 					_lowercase						(self    :    str   ,			__a    :    str   ,			__a    :    Optional[str] = None ):
         UpperCAmelCase_           =   self._tokenizer.model.save(__a   ,			name=__a )
         return tuple(__a )



    def 					_lowercase						(self    :    Any   ,			__a    :    Optional[int]   ,			__a    :    str=None ):
         UpperCAmelCase_           =   [self.bos_token_id] + token_ids_a + [self.eos_token_id]
         if token_ids_a is None:
              return output

         return output + [self.eos_token_id] + token_ids_a + [self.eos_token_id]






    def 					_lowercase						(self    :    Union[str, Any]   ,			__a    :    List[int]   ,			__a    :    Optional[List[int]] = None ):
         UpperCAmelCase_           =   [self.sep_token_id]
         UpperCAmelCase_           =   [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]








'''simple docstring'''
from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt


def 			a      (			__a   )  ->	bool:



					'''simple docstring'''






					UpperCamelCase__   :int												= int(number**0.5   )
					return number == sq * sq


def 			a      (			__a ,					__a ,					__a ,					__a ,					__a ,					__a   )  ->	tuple[int, int]:



					'''simple docstring'''






					UpperCamelCase__   :int												= x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
					UpperCamelCase__   :int												= x_den * y_den * z_den
					UpperCamelCase__   :int												= gcd(__a ,					__a   )
					top //= hcf
					bottom //= hcf
					return top, bottom


def 			a      (			__a = 35   )  ->	int:



					'''simple docstring'''






					UpperCamelCase__   :set												= set()
					UpperCamelCase__   :int
					UpperCamelCase__   :Fraction												= Fraction(0   )
					UpperCamelCase__   :tuple[int, int]

					for x_num in range(1 ,					order + 1   ):
										for x_den in range(x_num + 1 ,					order + 1   ):
															for y_num in range(1 ,					order + 1   ):
																				for y_den in range(y_num + 1 ,					order + 1   ):
																									# n=1
																									UpperCamelCase__   :int												= x_num * y_den + x_den * y_num
																									UpperCamelCase__   :Any												= x_den * y_den
																									UpperCamelCase__   :Tuple												= gcd(__a ,					__a   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														UpperCamelCase__   :Tuple												= add_three(
																														    __a ,					__a ,					__a ,					__a ,					__a ,					__a   )
																														unique_s.add(__a   )

																									# n=2
																									UpperCamelCase__   :List[str]												= (
																									    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
																									)
																									UpperCamelCase__   :Dict												= x_den * x_den * y_den * y_den
																									if is_sq(__a   ) and is_sq(__a   ):
																														UpperCamelCase__   :Any												= int(sqrt(__a   )   )
																														UpperCamelCase__   :Optional[int]												= int(sqrt(__a   )   )
																														UpperCamelCase__   :int												= gcd(__a ,					__a   )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			UpperCamelCase__   :Tuple												= add_three(
																																			    __a ,					__a ,					__a ,					__a ,					__a ,					__a   )
																																			unique_s.add(__a   )

                    # n=-1
																									UpperCamelCase__   :Tuple												= x_num * y_num
																									UpperCamelCase__   :Union[str, Any]												= x_den * y_num + x_num * y_den
																									UpperCamelCase__   :List[str]												= gcd(__a ,					__a   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														UpperCamelCase__   :Union[str, Any]												= add_three(
																														    __a ,					__a ,					__a ,					__a ,					__a ,					__a   )
																														unique_s.add(__a   )

																									# n=2
																									UpperCamelCase__   :Optional[Any]												= x_num * x_num * y_num * y_num
																									UpperCamelCase__   :Tuple												= (
																									    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																									)
																									if is_sq(__a   ) and is_sq(__a   ):
																														UpperCamelCase__   :str												= int(sqrt(__a   )   )
																														UpperCamelCase__   :Any												= int(sqrt(__a   )   )
																														UpperCamelCase__   :Dict												= gcd(__a ,					__a   )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			UpperCamelCase__   :int												= add_three(
																																			    __a ,					__a ,					__a ,					__a ,					__a ,					__a   )
																																			unique_s.add(__a   )

					for num, den in unique_s:
										total += Fraction(__a ,					__a   )

					return total.denominator + total.numerator


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