import json
from typing import Iterator, List, Union

from tokenizers import AddedToken, Regex, Tokenizer, decoders, normalizers, pre_tokenizers, trainers
from tokenizers.implementations.base_tokenizer import BaseTokenizer
from tokenizers.models import Unigram
from tokenizers.processors import TemplateProcessing



class   lowercase_       (	__A						):



							def __init__(		self ,							lowercase_ = "▁" ,							lowercase_ = True ,							lowercase_ = "<unk>" ,							lowercase_ = "</s>" ,							lowercase_ = "<pad>" ,							):
													_snake_case		:	Any							=       {
													    "pad": {"id": 0, "token": pad_token},
													    "eos": {"id": 1, "token": eos_token},
													    "unk": {"id": 2, "token": unk_token},
													}

													_snake_case		:	Optional[int]							=       [None] * len(self.special_tokens							)
													for token_dict in self.special_tokens.values():
																			_snake_case		:	Any							=       token_dict["token"]

													_snake_case		:	Any							=       Tokenizer(Unigram()							)

													_snake_case		:	Optional[Any]							=       normalizers.Sequence(
													    [
													        normalizers.Nmt(),
													        normalizers.NFKC(),
													        normalizers.Replace(Regex(" {2,}"							) ,							" "							),
													        normalizers.Lowercase(),
													    ]							)
													_snake_case		:	List[str]							=       pre_tokenizers.Sequence(
													    [
													        pre_tokenizers.Metaspace(replacement=lowerCAmelCase_ ,							add_prefix_space=lowerCAmelCase_							),
													        pre_tokenizers.Digits(individual_digits=lowerCAmelCase_							),
													        pre_tokenizers.Punctuation(),
													    ]							)
													_snake_case		:	Dict							=       decoders.Metaspace(replacement=lowerCAmelCase_ ,							add_prefix_space=lowerCAmelCase_							)

													_snake_case		:	Union[str, Any]							=       TemplateProcessing(
													    single=f"""$A {self.special_tokens['eos']['token']}""" ,							special_tokens=[(self.special_tokens["eos"]["token"], self.special_tokens["eos"]["id"])] ,							)

													_snake_case		:	int							=       {
													    "model": "SentencePieceUnigram",
													    "replacement": replacement,
													    "add_prefix_space": add_prefix_space,
													}

													super().__init__(lowerCAmelCase_ ,							lowerCAmelCase_							)



							def 			UpperCamelCase			(		self ,							lowercase_ ,							lowercase_ = 8_000 ,							lowercase_ = True ,							):
													_snake_case		:	List[Any]							=       trainers.UnigramTrainer(
													    vocab_size=lowerCAmelCase_ ,							special_tokens=self.special_tokens_list ,							show_progress=lowerCAmelCase_ ,							)

													if isinstance(lowerCAmelCase_ ,							lowerCAmelCase_							):
																			_snake_case		:	List[Any]							=       [files]
													self._tokenizer.train(lowerCAmelCase_ ,							trainer=lowerCAmelCase_							)

													self.add_unk_id()



							def 			UpperCamelCase			(		self ,							lowercase_ ,							lowercase_ = 8_000 ,							lowercase_ = True ,							):
													_snake_case		:	Any							=       trainers.UnigramTrainer(
													    vocab_size=lowerCAmelCase_ ,							special_tokens=self.special_tokens_list ,							show_progress=lowerCAmelCase_ ,							)

													self._tokenizer.train_from_iterator(lowerCAmelCase_ ,							trainer=lowerCAmelCase_							)

													self.add_unk_id()



							def 			UpperCamelCase			(		self							):
													_snake_case		:	Tuple							=       json.loads(self._tokenizer.to_str()							)

													_snake_case		:	Union[str, Any]							=       self.special_tokens["unk"]["id"]

													_snake_case		:	Tuple							=       Tokenizer.from_str(json.dumps(lowerCAmelCase_							)							)







"""simple docstring"""
from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt

def 							snake_case (  A__		):
			UpperCAmelCase_	:					int     	=   int(number**0.5		)
			return number == sq * sq

def 							snake_case (  A__      ,A__      ,A__      ,A__      ,A__      ,A__		):
			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 							snake_case (  A__ = 35		):
			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_	:					Optional[int]     	=   x_num * y_den + x_den * y_num
															UpperCAmelCase_	:					List[Any]     	=   x_den * y_den
															UpperCAmelCase_	:					Tuple     	=   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__		)

															# n=2
															UpperCAmelCase_	:					Optional[Any]     	=   (
															    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_	:					int     	=   int(sqrt(A__		)		)
																		UpperCAmelCase_	:					Any     	=   int(sqrt(A__		)		)
																		UpperCAmelCase_	:					str     	=   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_	:					Optional[int]     	=   x_num * y_num
															UpperCAmelCase_	:					Dict     	=   x_den * y_num + x_num * y_den
															UpperCAmelCase_	:					Union[str, Any]     	=   gcd(A__      ,A__		)
															z_num //= hcf
															z_den //= hcf
															if 0 < z_num < z_den <= order:
																		UpperCAmelCase_	:					List[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_	:					Dict     	=   (
															    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_	:					int     	=   int(sqrt(A__		)		)
																		UpperCAmelCase_	:					Optional[Any]     	=   gcd(A__      ,A__		)
																		z_num //= hcf
																		z_den //= hcf
																		if 0 < z_num < z_den <= order:
																					UpperCAmelCase_	:					Optional[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() = }')



