
'''simple docstring'''






from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt





def    UpperCAmelCase							(  UpperCAmelCase__							:							int):
				lowerCamelCase					:			int									= int(number**0.5)
				return number == sq * sq





def    UpperCAmelCase							(  UpperCAmelCase__							:							int       ,							UpperCAmelCase__							:							int       ,							UpperCAmelCase__							:							int       ,							UpperCAmelCase__							:							int       ,							UpperCAmelCase__							:							int       ,							UpperCAmelCase__							:							int):
				lowerCamelCase					:			int									= x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
				lowerCamelCase					:			int									= x_den * y_den * z_den
				lowerCamelCase					:			int									= gcd(UpperCAmelCase__       ,							UpperCAmelCase__)
				top //= hcf
				bottom //= hcf
				return top, bottom





def    UpperCAmelCase							(  UpperCAmelCase__							:							int = 35):
				lowerCamelCase					:			set									= set()
				lowerCamelCase					:			int
				lowerCamelCase					:			Fraction									= Fraction(0)
				lowerCamelCase					:			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
																				lowerCamelCase					:			str									= x_num * y_den + x_den * y_num
																				lowerCamelCase					:			Tuple									= x_den * y_den
																				lowerCamelCase					:			Optional[Any]									= gcd(UpperCAmelCase__       ,							UpperCAmelCase__)
																				z_num //= hcf
																				z_den //= hcf
																				if 0 < z_num < z_den <= order:
																								lowerCamelCase					:			List[Any]									= add_three(
																								    UpperCAmelCase__       ,							UpperCAmelCase__       ,							UpperCAmelCase__       ,							UpperCAmelCase__       ,							UpperCAmelCase__       ,							UpperCAmelCase__)
																								unique_s.add(UpperCAmelCase__)

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

                    # n=-1
																				lowerCamelCase					:			Optional[Any]									= x_num * y_num
																				lowerCamelCase					:			Optional[Any]									= x_den * y_num + x_num * y_den
																				lowerCamelCase					:			Optional[int]									= gcd(UpperCAmelCase__       ,							UpperCAmelCase__)
																				z_num //= hcf
																				z_den //= hcf
																				if 0 < z_num < z_den <= order:
																								lowerCamelCase					:			List[Any]									= add_three(
																								    UpperCAmelCase__       ,							UpperCAmelCase__       ,							UpperCAmelCase__       ,							UpperCAmelCase__       ,							UpperCAmelCase__       ,							UpperCAmelCase__)
																								unique_s.add(UpperCAmelCase__)

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

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

				return total.denominator + total.numerator


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 PreTrainedTokenizer
from ...utils import logging


A			      =      logging.get_logger(__name__)


A			      =      '▁'

A			      =      {'vocab_file': 'spiece.model'}

A			      =      {
    'vocab_file': {
        'google/reformer-crime-and-punishment': (
            'https://huggingface.co/google/reformer-crime-and-punishment/resolve/main/spiece.model'
        )
    }
}

A			      =      {
    'google/reformer-crime-and-punishment': 52_4288,
}




class     __snake_case		(   a__):
					_lowerCAmelCase			     =	VOCAB_FILES_NAMES
					_lowerCAmelCase			     =	PRETRAINED_VOCAB_FILES_MAP
					_lowerCAmelCase			     =	PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
					_lowerCAmelCase			     =	['''input_ids''', '''attention_mask''']
					def __init__(     self,    A,    A="</s>",    A="<unk>",    A=[],    A = None,    **A,    ):

									"""simple docstring"""


									lowerCamelCase					:			str									= {} if sp_model_kwargs is None else sp_model_kwargs

									super().__init__(
									    eos_token=A,    unk_token=A,    additional_special_tokens=A,    sp_model_kwargs=self.sp_model_kwargs,    **A,    )

									lowerCamelCase					:			Any									= vocab_file
									lowerCamelCase					:			List[Any]									= spm.SentencePieceProcessor(**self.sp_model_kwargs      )
									self.sp_model.Load(A      )
					@property
					def     UpperCAmelCase_							(     self      ):

									"""simple docstring"""


									return self.sp_model.get_piece_size()
					def     UpperCAmelCase_							(     self      ):

									"""simple docstring"""


									lowerCamelCase					:			int									= {self.convert_ids_to_tokens(A      ): i for i in range(self.vocab_size      )}
									vocab.update(self.added_tokens_encoder      )
									return vocab
					def __getstate__(     self      ):

									"""simple docstring"""


									lowerCamelCase					:			Union[str, Any]									= self.__dict__.copy()
									lowerCamelCase					:			List[Any]									= None
									return state
					def __setstate__(     self,    A      ):

									"""simple docstring"""


									lowerCamelCase					:			int									= d

									# for backward compatibility
									if not hasattr(self,    'sp_model_kwargs'      ):
													lowerCamelCase					:			List[str]									= {}

									lowerCamelCase					:			Optional[int]									= spm.SentencePieceProcessor(**self.sp_model_kwargs      )
									self.sp_model.Load(self.vocab_file      )
					def     UpperCAmelCase_							(     self,    A      ):

									"""simple docstring"""


									return self.sp_model.encode(A,    out_type=A      )
					def     UpperCAmelCase_							(     self,    A      ):

									"""simple docstring"""


									return self.sp_model.piece_to_id(A      )
					def     UpperCAmelCase_							(     self,    A      ):

									"""simple docstring"""


									if index < self.sp_model.get_piece_size():
													lowerCamelCase					:			Union[str, Any]									= self.sp_model.IdToPiece(A      )
									return token
					def     UpperCAmelCase_							(     self,    A      ):

									"""simple docstring"""


									lowerCamelCase					:			Union[str, Any]									= []
									lowerCamelCase					:			Optional[int]									= ''
									for token in tokens:
													# make sure that special tokens are not decoded using sentencepiece model
													if token in self.all_special_tokens:
																	out_string += self.sp_model.decode(A      ) + token
																	lowerCamelCase					:			Any									= []
													else:
																	current_sub_tokens.append(A      )
									out_string += self.sp_model.decode(A      )
									return out_string.strip()




					def     UpperCAmelCase_							(     self,    A,    A = None      ):

									"""simple docstring"""


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

									if os.path.abspath(self.vocab_file      ) != os.path.abspath(A      ) and os.path.isfile(self.vocab_file      ):
													copyfile(self.vocab_file,    A      )
									elif not os.path.isfile(self.vocab_file      ):
													with open(A,    'wb'      ) as fi:
																	lowerCamelCase					:			Optional[Any]									= self.sp_model.serialized_model_proto()
																	fi.write(A      )

									return (out_vocab_file,)
