






from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt

def   __lowercase       (			snake_case			):







				"""simple docstring"""






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

def   __lowercase       (			snake_case,	snake_case,	snake_case,	snake_case,	snake_case,	snake_case			):







				"""simple docstring"""






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

def   __lowercase       (			snake_case = 3_5			):







				"""simple docstring"""






				__magic_name__		:set   =   set()
				__magic_name__		:int
				__magic_name__		:Fraction   =   Fraction(0			)
				__magic_name__		: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
																				__magic_name__		:Any   =   x_num * y_den + x_den * y_num
																				__magic_name__		:Dict   =   x_den * y_den
																				__magic_name__		:Any   =   gcd(snake_case,	snake_case			)
																				z_num //= hcf
																				z_den //= hcf
																				if 0 < z_num < z_den <= order:
																								__magic_name__		:List[str]   =   add_three(
																								    snake_case,	snake_case,	snake_case,	snake_case,	snake_case,	snake_case			)
																								unique_s.add(snake_case			)

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

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

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

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

				return total.denominator + total.numerator


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







"""simple docstring"""



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

import sentencepiece as spm

from ...tokenization_utils import PreTrainedTokenizer
from ...utils import logging


_UpperCamelCase								=		logging.get_logger(__name__)

_UpperCamelCase								=		{"vocab_file": "sentencepiece.model"}

_UpperCamelCase								=		{
    "vocab_file": {
        "google/rembert": "https://huggingface.co/google/rembert/resolve/main/sentencepiece.model",
    },
}

_UpperCamelCase								=		{
    "google/rembert": 2_56,
}
class 						__UpperCAmelCase    (__A     ):







			'''simple docstring'''
			_UpperCamelCase  :						Dict					     =				VOCAB_FILES_NAMES
			_UpperCamelCase  :						List[str]					     =				PRETRAINED_VOCAB_FILES_MAP
			_UpperCamelCase  :						Any					     =				PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES





			def __init__(			self   ,      snake_case_   ,      snake_case_=False   ,      snake_case_=True   ,      snake_case_=True   ,      snake_case_="[CLS]"   ,      snake_case_="[SEP]"   ,      snake_case_="[UNK]"   ,      snake_case_="[SEP]"   ,      snake_case_="[PAD]"   ,      snake_case_="[CLS]"   ,      snake_case_="[MASK]"   ,      **snake_case_   ,      ):







										'''simple docstring'''


										super().__init__(
										    do_lower_case=snake_case_   ,      remove_space=snake_case_   ,      keep_accents=snake_case_   ,      bos_token=snake_case_   ,      eos_token=snake_case_   ,      unk_token=snake_case_   ,      sep_token=snake_case_   ,      pad_token=snake_case_   ,      cls_token=snake_case_   ,      mask_token=snake_case_   ,      **snake_case_   ,      )

										A__       :     List[Any]								=			do_lower_case
										A__       :     Dict								=			remove_space
										A__       :     Optional[int]								=			keep_accents
										A__       :     Tuple								=			vocab_file

										A__       :     List[str]								=			spm.SentencePieceProcessor()
										self.sp_model.Load(snake_case_							)





			@property
			def 		lowerCamelCase					(			self							):







										'''simple docstring'''


										return len(self.sp_model							)





			def 		lowerCamelCase					(			self							):







										'''simple docstring'''


										A__       :     Optional[Any]								=			{self.convert_ids_to_tokens(snake_case_							): i for i in range(self.vocab_size							)}
										vocab.update(self.added_tokens_encoder							)
										return vocab





			def __getstate__(			self							):







										'''simple docstring'''


										A__       :     str								=			self.__dict__.copy()
										A__       :     Tuple								=			None
										return state





			def __setstate__(			self   ,      snake_case_							):







										'''simple docstring'''


										A__       :     Dict								=			d
										A__       :     int								=			spm.SentencePieceProcessor()
										self.sp_model.Load(self.vocab_file							)





			def 		lowerCamelCase					(			self   ,      snake_case_   ,      snake_case_=False							):







										'''simple docstring'''


										A__       :     Tuple								=			self.sp_model.EncodeAsPieces(snake_case_							)
										return pieces





			def 		lowerCamelCase					(			self   ,      snake_case_							):







										'''simple docstring'''


										return self.sp_model.PieceToId(snake_case_							)





			def 		lowerCamelCase					(			self   ,      snake_case_							):







										'''simple docstring'''


										return self.sp_model.IdToPiece(snake_case_							)





			def 		lowerCamelCase					(			self   ,      snake_case_							):







										'''simple docstring'''


										A__       :     str								=			self.sp_model.decode_pieces(snake_case_							)
										return out_string





			def 		lowerCamelCase					(			self   ,      snake_case_   ,      snake_case_ = None							):







										'''simple docstring'''


										A__       :     List[Any]								=			[self.sep_token_id]
										A__       :     str								=			[self.cls_token_id]
										if token_ids_a is None:
																	return cls + token_ids_a + sep
										return cls + token_ids_a + sep + token_ids_a + sep





			def 		lowerCamelCase					(			self   ,      snake_case_   ,      snake_case_ = None   ,      snake_case_ = False							):







										'''simple docstring'''


										if already_has_special_tokens:
																	if token_ids_a is not None:
																								raise ValueError(
																								    """You should not supply a second sequence if the provided sequence of """
																								    """ids is already formatted with special tokens for the model."""							)
																	return [1 if x in [self.sep_token_id, self.cls_token_id] else 0 for x in token_ids_a]

										if token_ids_a is not None:
																	return [1] + ([0] * len(snake_case_							)) + [1] + ([0] * len(snake_case_							)) + [1]
										return [1] + ([0] * len(snake_case_							)) + [1]





			def 		lowerCamelCase					(			self   ,      snake_case_   ,      snake_case_ = None							):







										'''simple docstring'''


										A__       :     int								=			[self.sep_token_id]
										A__       :     Any								=			[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							) * [0] + len(token_ids_a + sep							) * [1]





			def 		lowerCamelCase					(			self   ,      snake_case_   ,      snake_case_ = None							):







										'''simple docstring'''


										if not os.path.isdir(snake_case_							):
																	logger.error("""Vocabulary path ({}) should be a directory""".format(snake_case_							)							)
																	return
										A__       :     Any								=			os.path.join(
										    snake_case_   ,      (filename_prefix + """-""" if filename_prefix else """""") + VOCAB_FILES_NAMES["""vocab_file"""]							)

										if os.path.abspath(self.vocab_file							) != os.path.abspath(snake_case_							):
																	copyfile(self.vocab_file   ,      snake_case_							)

										return (out_vocab_file,)





