



import itertools
import json
import os
import unittest

from transformers import AddedToken, LongformerTokenizer, LongformerTokenizerFast
from transformers.models.longformer.tokenization_longformer import VOCAB_FILES_NAMES
from transformers.testing_utils import require_tokenizers, slow

from ...test_tokenization_common import TokenizerTesterMixin




@require_tokenizers
class 							lowerCAmelCase__  (	UpperCamelCase					,							unittest.TestCase						):
     __A     :    int           =						LongformerTokenizer
     __A     :    Any           =						True
     __A     :    Optional[int]           =						LongformerTokenizerFast
     __A     :    Tuple           =						True







     def  _lowercase			(       self      :     Dict):
           super().setUp()

           # Adapted from Sennrich et al. 2015 and https://github.com/rsennrich/subword-nmt
           A__	:							Optional[Any]						    = [
               "l",
               "o",
               "w",
               "e",
               "r",
               "s",
               "t",
               "i",
               "d",
               "n",
               "\u0120",
               "\u0120l",
               "\u0120n",
               "\u0120lo",
               "\u0120low",
               "er",
               "\u0120lowest",
               "\u0120newer",
               "\u0120wider",
               "<unk>",
           ]
           A__	:							Any						    = dict(zip(_A			,		range(len(_A))))
           A__	:							Tuple						    = ["#version: 0.2", "\u0120 l", "\u0120l o", "\u0120lo w", "e r", ""]
           A__	:							Optional[int]						    = {"unk_token": "<unk>"}

           A__	:							Any						    = os.path.join(self.tmpdirname			,		VOCAB_FILES_NAMES["vocab_file"])
           A__	:							Union[str, Any]						    = os.path.join(self.tmpdirname			,		VOCAB_FILES_NAMES["merges_file"])
           with open(self.vocab_file			,		"w"			,		encoding="utf-8") as fp:
                 fp.write(json.dumps(_A) + "\n")
           with open(self.merges_file			,		"w"			,		encoding="utf-8") as fp:
                 fp.write("\n".join(_A))







     def  _lowercase			(       self      :     List[str]			,		**_A      :     Optional[Any]):
           kwargs.update(self.special_tokens_map)
           return self.tokenizer_class.from_pretrained(self.tmpdirname			,		**_A)







     def  _lowercase			(       self      :     List[str]			,		**_A      :     Dict):
           kwargs.update(self.special_tokens_map)
           return self.rust_tokenizer_class.from_pretrained(self.tmpdirname			,		**_A)







     def  _lowercase			(       self      :     Optional[int]			,		_A      :     Dict):
           A__	:							Optional[Any]						    = "lower newer"
           A__	:							Union[str, Any]						    = "lower newer"
           return input_text, output_text







     def  _lowercase			(       self      :     Tuple):
           A__	:							Union[str, Any]						    = self.tokenizer_class(self.vocab_file			,		self.merges_file			,		**self.special_tokens_map)
           A__	:							Optional[int]						    = "lower newer"
           A__	:							int						    = ["l", "o", "w", "er", "\u0120", "n", "e", "w", "er"]
           A__	:							List[str]						    = tokenizer.tokenize(_A)  # , add_prefix_space=True)
           self.assertListEqual(_A			,		_A)

           A__	:							Any						    = tokens + [tokenizer.unk_token]
           A__	:							Optional[int]						    = [0, 1, 2, 15, 10, 9, 3, 2, 15, 19]
           self.assertListEqual(tokenizer.convert_tokens_to_ids(_A)			,		_A)







     def  _lowercase			(       self      :     Optional[int]):
           A__	:							Optional[Any]						    = self.get_tokenizer()

           self.assertListEqual(tokenizer.encode("Hello world!"			,		add_special_tokens=_A)			,		[0, 3_1414, 232, 328, 2])
           self.assertListEqual(
               tokenizer.encode("Hello world! cécé herlolip 418"			,		add_special_tokens=_A)			,		[0, 3_1414, 232, 328, 740, 1140, 1_2695, 69, 4_6078, 1588, 2]			,		)







     @slow
     def  _lowercase			(       self      :     str):
           A__	:							List[str]						    = self.tokenizer_class.from_pretrained("allenai/longformer-base-4096")

           A__	:							Optional[Any]						    = tokenizer.encode("sequence builders"			,		add_special_tokens=_A)
           A__	:							Optional[int]						    = tokenizer.encode("multi-sequence build"			,		add_special_tokens=_A)

           A__	:							Tuple						    = tokenizer.encode(
               "sequence builders"			,		add_special_tokens=_A			,		add_prefix_space=_A)
           A__	:							str						    = tokenizer.encode(
               "sequence builders"			,		"multi-sequence build"			,		add_special_tokens=_A			,		add_prefix_space=_A)

           A__	:							Dict						    = tokenizer.build_inputs_with_special_tokens(_A)
           A__	:							Optional[int]						    = tokenizer.build_inputs_with_special_tokens(_A			,		_A)

           assert encoded_sentence == encoded_text_from_decode
           assert encoded_pair == encoded_pair_from_decode







     def  _lowercase			(       self      :     Union[str, Any]):
           A__	:							Any						    = self.get_tokenizer()

           A__	:							List[str]						    = "Encode this sequence."
           A__	:							Dict						    = tokenizer.byte_encoder[" ".encode("utf-8")[0]]

           # Testing encoder arguments
           A__	:							List[str]						    = tokenizer.encode(_A			,		add_special_tokens=_A			,		add_prefix_space=_A)
           A__	:							Optional[int]						    = tokenizer.convert_ids_to_tokens(encoded[0])[0]
           self.assertNotEqual(_A			,		_A)

           A__	:							str						    = tokenizer.encode(_A			,		add_special_tokens=_A			,		add_prefix_space=_A)
           A__	:							Optional[Any]						    = tokenizer.convert_ids_to_tokens(encoded[0])[0]
           self.assertEqual(_A			,		_A)

           tokenizer.add_special_tokens({"bos_token": "<s>"})
           A__	:							str						    = tokenizer.encode(_A			,		add_special_tokens=_A)
           A__	:							Any						    = tokenizer.convert_ids_to_tokens(encoded[1])[0]
           self.assertNotEqual(_A			,		_A)

           # Testing spaces after special tokens
           A__	:							str						    = "<mask>"
           tokenizer.add_special_tokens(
               {"mask_token": AddedToken(_A			,		lstrip=_A			,		rstrip=_A)})  # mask token has a left space
           A__	:							Dict						    = tokenizer.convert_tokens_to_ids(_A)

           A__	:							Dict						    = "Encode <mask> sequence"
           A__	:							Tuple						    = "Encode <mask>sequence"

           A__	:							List[str]						    = tokenizer.encode(_A)
           A__	:							Tuple						    = encoded.index(_A)
           A__	:							List[Any]						    = tokenizer.convert_ids_to_tokens(encoded[mask_loc + 1])[0]
           self.assertEqual(_A			,		_A)

           A__	:							Any						    = tokenizer.encode(_A)
           A__	:							Dict						    = encoded.index(_A)
           A__	:							str						    = tokenizer.convert_ids_to_tokens(encoded[mask_loc + 1])[0]
           self.assertNotEqual(_A			,		_A)







     def  _lowercase			(       self      :     Union[str, Any]):
           pass







     def  _lowercase			(       self      :     Any):
           for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
                 with self.subTest(F'{tokenizer.__class__.__name__} ({pretrained_name})'):
                       A__	:							List[Any]						    = self.rust_tokenizer_class.from_pretrained(_A			,		**_A)
                       A__	:							Tuple						    = self.tokenizer_class.from_pretrained(_A			,		**_A)
                       A__	:							Tuple						    = "A, <mask> AllenNLP sentence."
                       A__	:							int						    = tokenizer_r.encode_plus(_A			,		add_special_tokens=_A			,		return_token_type_ids=_A)
                       A__	:							str						    = tokenizer_p.encode_plus(_A			,		add_special_tokens=_A			,		return_token_type_ids=_A)

                       # token_type_ids should put 0 everywhere
                       self.assertEqual(sum(tokens_r["token_type_ids"])			,		sum(tokens_p["token_type_ids"]))

                       # attention_mask should put 1 everywhere, so sum over length should be 1
                       self.assertEqual(
                           sum(tokens_r["attention_mask"]) / len(tokens_r["attention_mask"])			,		sum(tokens_p["attention_mask"]) / len(tokens_p["attention_mask"])			,		)

                       A__	:							str						    = tokenizer_r.convert_ids_to_tokens(tokens_r["input_ids"])
                       A__	:							Optional[int]						    = tokenizer_p.convert_ids_to_tokens(tokens_p["input_ids"])

                       # Rust correctly handles the space before the mask while python doesnt
                       self.assertSequenceEqual(tokens_p["input_ids"]			,		[0, 250, 6, 5_0264, 3823, 487, 2_1992, 3645, 4, 2])
                       self.assertSequenceEqual(tokens_r["input_ids"]			,		[0, 250, 6, 5_0264, 3823, 487, 2_1992, 3645, 4, 2])

                       self.assertSequenceEqual(
                           _A			,		["<s>", "A", ",", "<mask>", "ĠAllen", "N", "LP", "Ġsentence", ".", "</s>"])
                       self.assertSequenceEqual(
                           _A			,		["<s>", "A", ",", "<mask>", "ĠAllen", "N", "LP", "Ġsentence", ".", "</s>"])







     def  _lowercase			(       self      :     int):
           for trim_offsets, add_prefix_space in itertools.product([True, False]			,		repeat=2):
                 A__	:							Dict						    = self.rust_tokenizer_class.from_pretrained(
                     self.tmpdirname			,		use_fast=_A			,		add_prefix_space=_A			,		trim_offsets=_A)

                 A__	:							int						    = json.loads(tokenizer_r.backend_tokenizer.pre_tokenizer.__getstate__())
                 A__	:							Dict						    = json.loads(tokenizer_r.backend_tokenizer.post_processor.__getstate__())

                 self.assertEqual(pre_tokenizer_state["add_prefix_space"]			,		_A)

                 self.assertEqual(post_processor_state["add_prefix_space"]			,		_A)
                 self.assertEqual(post_processor_state["trim_offsets"]			,		_A)







     def  _lowercase			(       self      :     Optional[Any]):
           # Test which aims to verify that the offsets are well adapted to the argument `add_prefix_space` and
           # `trim_offsets`
           for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
                 with self.subTest(F'{tokenizer.__class__.__name__} ({pretrained_name})'):
                       A__	:							str						    = "hello"  # `hello` is a token in the vocabulary of `pretrained_name`
                       A__	:							List[Any]						    = F'{text_of_1_token} {text_of_1_token}'

                       A__	:							Union[str, Any]						    = self.rust_tokenizer_class.from_pretrained(
                           _A			,		use_fast=_A			,		add_prefix_space=_A			,		trim_offsets=_A)
                       A__	:							Any						    = tokenizer_r(_A			,		return_offsets_mapping=_A			,		add_special_tokens=_A)
                       self.assertEqual(encoding.offset_mapping[0]			,		(0, len(_A)))
                       self.assertEqual(
                           encoding.offset_mapping[1]			,		(len(_A) + 1, len(_A) + 1 + len(_A))			,		)

                       A__	:							Tuple						    = self.rust_tokenizer_class.from_pretrained(
                           _A			,		use_fast=_A			,		add_prefix_space=_A			,		trim_offsets=_A)
                       A__	:							int						    = tokenizer_r(_A			,		return_offsets_mapping=_A			,		add_special_tokens=_A)
                       self.assertEqual(encoding.offset_mapping[0]			,		(0, len(_A)))
                       self.assertEqual(
                           encoding.offset_mapping[1]			,		(len(_A) + 1, len(_A) + 1 + len(_A))			,		)

                       A__	:							Union[str, Any]						    = self.rust_tokenizer_class.from_pretrained(
                           _A			,		use_fast=_A			,		add_prefix_space=_A			,		trim_offsets=_A)
                       A__	:							Tuple						    = tokenizer_r(_A			,		return_offsets_mapping=_A			,		add_special_tokens=_A)
                       self.assertEqual(encoding.offset_mapping[0]			,		(0, len(_A)))
                       self.assertEqual(
                           encoding.offset_mapping[1]			,		(len(_A), len(_A) + 1 + len(_A))			,		)

                       A__	:							Optional[Any]						    = self.rust_tokenizer_class.from_pretrained(
                           _A			,		use_fast=_A			,		add_prefix_space=_A			,		trim_offsets=_A)
                       A__	:							List[Any]						    = tokenizer_r(_A			,		return_offsets_mapping=_A			,		add_special_tokens=_A)
                       self.assertEqual(encoding.offset_mapping[0]			,		(0, len(_A)))
                       self.assertEqual(
                           encoding.offset_mapping[1]			,		(len(_A), len(_A) + 1 + len(_A))			,		)

                       A__	:							List[str]						    = F' {text}'

                       # tokenizer_r = self.rust_tokenizer_class.from_pretrained(
                       #     pretrained_name, use_fast=True, add_prefix_space=True, trim_offsets=True
                       # )
                       # encoding = tokenizer_r(text, return_offsets_mapping=True, add_special_tokens=False)
                       # self.assertEqual(encoding.offset_mapping[0], (1, 1 + len(text_of_1_token)))
                       # self.assertEqual(
                       #     encoding.offset_mapping[1],
                       #     (1 + len(text_of_1_token) + 1, 1 + len(text_of_1_token) + 1 + len(text_of_1_token)),
                       # )

                       A__	:							Union[str, Any]						    = self.rust_tokenizer_class.from_pretrained(
                           _A			,		use_fast=_A			,		add_prefix_space=_A			,		trim_offsets=_A)
                       A__	:							Union[str, Any]						    = tokenizer_r(_A			,		return_offsets_mapping=_A			,		add_special_tokens=_A)
                       self.assertEqual(encoding.offset_mapping[0]			,		(1, 1 + len(_A)))
                       self.assertEqual(
                           encoding.offset_mapping[1]			,		(1 + len(_A) + 1, 1 + len(_A) + 1 + len(_A))			,		)

                       A__	:							Tuple						    = self.rust_tokenizer_class.from_pretrained(
                           _A			,		use_fast=_A			,		add_prefix_space=_A			,		trim_offsets=_A)
                       A__	:							int						    = tokenizer_r(_A			,		return_offsets_mapping=_A			,		add_special_tokens=_A)
                       self.assertEqual(encoding.offset_mapping[0]			,		(0, 1 + len(_A)))
                       self.assertEqual(
                           encoding.offset_mapping[1]			,		(1 + len(_A), 1 + len(_A) + 1 + len(_A))			,		)

                       A__	:							List[Any]						    = self.rust_tokenizer_class.from_pretrained(
                           _A			,		use_fast=_A			,		add_prefix_space=_A			,		trim_offsets=_A)
                       A__	:							Dict						    = tokenizer_r(_A			,		return_offsets_mapping=_A			,		add_special_tokens=_A)
                       self.assertEqual(encoding.offset_mapping[0]			,		(0, 1 + len(_A)))
                       self.assertEqual(
                           encoding.offset_mapping[1]			,		(1 + len(_A), 1 + len(_A) + 1 + len(_A))			,		)




from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt
def 	snake_case__       (					__lowercase       )		->		bool:







						"""simple docstring"""

						A__	:							int						    = int(number**0.5       )
						return number == sq * sq
def 	snake_case__       (					__lowercase							,     __lowercase							,     __lowercase							,     __lowercase							,     __lowercase							,     __lowercase       )		->		tuple[int, int]:







						"""simple docstring"""

						A__	:							int						    = x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
						A__	:							int						    = x_den * y_den * z_den
						A__	:							int						    = gcd(__lowercase							,     __lowercase       )
						top //= hcf
						bottom //= hcf
						return top, bottom
def 	snake_case__       (					__lowercase = 3_5       )		->		int:







						"""simple docstring"""

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

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

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

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

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

						return total.denominator + total.numerator


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