





'''simple docstring'''



def 				snake_case_      (		SCREAMING_SNAKE_CASE__ = 10**12       ):







  '''simple docstring'''



  _snake_case     		=				1
  _snake_case     		=				0

  _snake_case     		=				1
  _snake_case     		=				1

  while numerator <= 2 * min_total - 1:
    prev_numerator += 2 * numerator
    numerator += 2 * prev_numerator

    prev_denominator += 2 * denominator
    denominator += 2 * prev_denominator

  return (denominator + 1) // 2


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









'''simple docstring'''



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       __SCREAMING_SNAKE_CASE	(						__UpperCamelCase					,    unittest.TestCase			):



     '''simple docstring'''






     UpperCAmelCase__       :						List[Any]      =   LongformerTokenizer
     UpperCAmelCase__       :						Dict      =   True
     UpperCAmelCase__       :						Union[str, Any]      =   LongformerTokenizerFast
     UpperCAmelCase__       :						List[str]      =   True

     def 	UpperCamelCase(					self	):
       super().setUp()

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

       _snake_case     		=				os.path.join(self.tmpdirname						,   VOCAB_FILES_NAMES["vocab_file"]	)
       _snake_case     		=				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(lowerCamelCase	) + "\n"	)
       with open(self.merges_file						,   "w"						,   encoding="utf-8"	) as fp:
         fp.write("\n".join(lowerCamelCase	)	)

     def 	UpperCamelCase(					self						,   **lowerCamelCase	):
       kwargs.update(self.special_tokens_map	)
       return self.tokenizer_class.from_pretrained(self.tmpdirname						,   **lowerCamelCase	)

     def 	UpperCamelCase(					self						,   **lowerCamelCase	):
       kwargs.update(self.special_tokens_map	)
       return self.rust_tokenizer_class.from_pretrained(self.tmpdirname						,   **lowerCamelCase	)

     def 	UpperCamelCase(					self						,   lowerCamelCase	):
       _snake_case     		=				"lower newer"
       _snake_case     		=				"lower newer"
       return input_text, output_text

     def 	UpperCamelCase(					self	):
       _snake_case     		=				self.tokenizer_class(self.vocab_file						,   self.merges_file						,   **self.special_tokens_map	)
       _snake_case     		=				"lower newer"
       _snake_case     		=				["l", "o", "w", "er", "\u0120", "n", "e", "w", "er"]
       _snake_case     		=				tokenizer.tokenize(lowerCamelCase	)  # , add_prefix_space=True)
       self.assertListEqual(lowerCamelCase						,   lowerCamelCase	)

       _snake_case     		=				tokens + [tokenizer.unk_token]
       _snake_case     		=				[0, 1, 2, 15, 10, 9, 3, 2, 15, 19]
       self.assertListEqual(tokenizer.convert_tokens_to_ids(lowerCamelCase	)						,   lowerCamelCase	)

     def 	UpperCamelCase(					self	):
       _snake_case     		=				self.get_tokenizer()

       self.assertListEqual(tokenizer.encode("Hello world!"						,   add_special_tokens=lowerCamelCase	)						,   [0, 31_414, 232, 328, 2]	)
       self.assertListEqual(
           tokenizer.encode("Hello world! cécé herlolip 418"						,   add_special_tokens=lowerCamelCase	)						,   [0, 31_414, 232, 328, 740, 1_140, 12_695, 69, 46_078, 1_588, 2]						,   )

     @slow
     def 	UpperCamelCase(					self	):
       _snake_case     		=				self.tokenizer_class.from_pretrained("allenai/longformer-base-4096"	)

       _snake_case     		=				tokenizer.encode("sequence builders"						,   add_special_tokens=lowerCamelCase	)
       _snake_case     		=				tokenizer.encode("multi-sequence build"						,   add_special_tokens=lowerCamelCase	)

       _snake_case     		=				tokenizer.encode(
           "sequence builders"						,   add_special_tokens=lowerCamelCase						,   add_prefix_space=lowerCamelCase	)
       _snake_case     		=				tokenizer.encode(
           "sequence builders"						,   "multi-sequence build"						,   add_special_tokens=lowerCamelCase						,   add_prefix_space=lowerCamelCase	)

       _snake_case     		=				tokenizer.build_inputs_with_special_tokens(lowerCamelCase	)
       _snake_case     		=				tokenizer.build_inputs_with_special_tokens(lowerCamelCase						,   lowerCamelCase	)

       assert encoded_sentence == encoded_text_from_decode
       assert encoded_pair == encoded_pair_from_decode

     def 	UpperCamelCase(					self	):
       _snake_case     		=				self.get_tokenizer()

       _snake_case     		=				"Encode this sequence."
       _snake_case     		=				tokenizer.byte_encoder[" ".encode("utf-8"	)[0]]

       # Testing encoder arguments
       _snake_case     		=				tokenizer.encode(lowerCamelCase						,   add_special_tokens=lowerCamelCase						,   add_prefix_space=lowerCamelCase	)
       _snake_case     		=				tokenizer.convert_ids_to_tokens(encoded[0]	)[0]
       self.assertNotEqual(lowerCamelCase						,   lowerCamelCase	)

       _snake_case     		=				tokenizer.encode(lowerCamelCase						,   add_special_tokens=lowerCamelCase						,   add_prefix_space=lowerCamelCase	)
       _snake_case     		=				tokenizer.convert_ids_to_tokens(encoded[0]	)[0]
       self.assertEqual(lowerCamelCase						,   lowerCamelCase	)

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

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

       _snake_case     		=				"Encode <mask> sequence"
       _snake_case     		=				"Encode <mask>sequence"

       _snake_case     		=				tokenizer.encode(lowerCamelCase	)
       _snake_case     		=				encoded.index(lowerCamelCase	)
       _snake_case     		=				tokenizer.convert_ids_to_tokens(encoded[mask_loc + 1]	)[0]
       self.assertEqual(lowerCamelCase						,   lowerCamelCase	)

       _snake_case     		=				tokenizer.encode(lowerCamelCase	)
       _snake_case     		=				encoded.index(lowerCamelCase	)
       _snake_case     		=				tokenizer.convert_ids_to_tokens(encoded[mask_loc + 1]	)[0]
       self.assertNotEqual(lowerCamelCase						,   lowerCamelCase	)

     def 	UpperCamelCase(					self	):
       pass

     def 	UpperCamelCase(					self	):
       for tokenizer, pretrained_name, kwargs in self.tokenizers_list:
         with self.subTest(F'''{tokenizer.__class__.__name__} ({pretrained_name})'''	):
           _snake_case     		=				self.rust_tokenizer_class.from_pretrained(lowerCamelCase						,   **lowerCamelCase	)
           _snake_case     		=				self.tokenizer_class.from_pretrained(lowerCamelCase						,   **lowerCamelCase	)
           _snake_case     		=				"A, <mask> AllenNLP sentence."
           _snake_case     		=				tokenizer_r.encode_plus(lowerCamelCase						,   add_special_tokens=lowerCamelCase						,   return_token_type_ids=lowerCamelCase	)
           _snake_case     		=				tokenizer_p.encode_plus(lowerCamelCase						,   add_special_tokens=lowerCamelCase						,   return_token_type_ids=lowerCamelCase	)

           # 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"]	)						,   )

           _snake_case     		=				tokenizer_r.convert_ids_to_tokens(tokens_r["input_ids"]	)
           _snake_case     		=				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, 50_264, 3_823, 487, 21_992, 3_645, 4, 2]	)
           self.assertSequenceEqual(tokens_r["input_ids"]						,   [0, 250, 6, 50_264, 3_823, 487, 21_992, 3_645, 4, 2]	)

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

     def 	UpperCamelCase(					self	):
       for trim_offsets, add_prefix_space in itertools.product([True, False]						,   repeat=2	):
         _snake_case     		=				self.rust_tokenizer_class.from_pretrained(
             self.tmpdirname						,   use_fast=lowerCamelCase						,   add_prefix_space=lowerCamelCase						,   trim_offsets=lowerCamelCase	)

         _snake_case     		=				json.loads(tokenizer_r.backend_tokenizer.pre_tokenizer.__getstate__()	)
         _snake_case     		=				json.loads(tokenizer_r.backend_tokenizer.post_processor.__getstate__()	)

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

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






     def 	UpperCamelCase(					self	):
       # 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})'''	):
           _snake_case     		=				"hello"  # `hello` is a token in the vocabulary of `pretrained_name`
           _snake_case     		=				F'''{text_of_1_token} {text_of_1_token}'''

           _snake_case     		=				self.rust_tokenizer_class.from_pretrained(
               lowerCamelCase						,   use_fast=lowerCamelCase						,   add_prefix_space=lowerCamelCase						,   trim_offsets=lowerCamelCase	)
           _snake_case     		=				tokenizer_r(lowerCamelCase						,   return_offsets_mapping=lowerCamelCase						,   add_special_tokens=lowerCamelCase	)
           self.assertEqual(encoding.offset_mapping[0]						,   (0, len(lowerCamelCase	))	)
           self.assertEqual(
               encoding.offset_mapping[1]						,   (len(lowerCamelCase	) + 1, len(lowerCamelCase	) + 1 + len(lowerCamelCase	))						,   )

           _snake_case     		=				self.rust_tokenizer_class.from_pretrained(
               lowerCamelCase						,   use_fast=lowerCamelCase						,   add_prefix_space=lowerCamelCase						,   trim_offsets=lowerCamelCase	)
           _snake_case     		=				tokenizer_r(lowerCamelCase						,   return_offsets_mapping=lowerCamelCase						,   add_special_tokens=lowerCamelCase	)
           self.assertEqual(encoding.offset_mapping[0]						,   (0, len(lowerCamelCase	))	)
           self.assertEqual(
               encoding.offset_mapping[1]						,   (len(lowerCamelCase	) + 1, len(lowerCamelCase	) + 1 + len(lowerCamelCase	))						,   )

           _snake_case     		=				self.rust_tokenizer_class.from_pretrained(
               lowerCamelCase						,   use_fast=lowerCamelCase						,   add_prefix_space=lowerCamelCase						,   trim_offsets=lowerCamelCase	)
           _snake_case     		=				tokenizer_r(lowerCamelCase						,   return_offsets_mapping=lowerCamelCase						,   add_special_tokens=lowerCamelCase	)
           self.assertEqual(encoding.offset_mapping[0]						,   (0, len(lowerCamelCase	))	)
           self.assertEqual(
               encoding.offset_mapping[1]						,   (len(lowerCamelCase	), len(lowerCamelCase	) + 1 + len(lowerCamelCase	))						,   )

           _snake_case     		=				self.rust_tokenizer_class.from_pretrained(
               lowerCamelCase						,   use_fast=lowerCamelCase						,   add_prefix_space=lowerCamelCase						,   trim_offsets=lowerCamelCase	)
           _snake_case     		=				tokenizer_r(lowerCamelCase						,   return_offsets_mapping=lowerCamelCase						,   add_special_tokens=lowerCamelCase	)
           self.assertEqual(encoding.offset_mapping[0]						,   (0, len(lowerCamelCase	))	)
           self.assertEqual(
               encoding.offset_mapping[1]						,   (len(lowerCamelCase	), len(lowerCamelCase	) + 1 + len(lowerCamelCase	))						,   )

           _snake_case     		=				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)),
           # )

           _snake_case     		=				self.rust_tokenizer_class.from_pretrained(
               lowerCamelCase						,   use_fast=lowerCamelCase						,   add_prefix_space=lowerCamelCase						,   trim_offsets=lowerCamelCase	)
           _snake_case     		=				tokenizer_r(lowerCamelCase						,   return_offsets_mapping=lowerCamelCase						,   add_special_tokens=lowerCamelCase	)
           self.assertEqual(encoding.offset_mapping[0]						,   (1, 1 + len(lowerCamelCase	))	)
           self.assertEqual(
               encoding.offset_mapping[1]						,   (1 + len(lowerCamelCase	) + 1, 1 + len(lowerCamelCase	) + 1 + len(lowerCamelCase	))						,   )

           _snake_case     		=				self.rust_tokenizer_class.from_pretrained(
               lowerCamelCase						,   use_fast=lowerCamelCase						,   add_prefix_space=lowerCamelCase						,   trim_offsets=lowerCamelCase	)
           _snake_case     		=				tokenizer_r(lowerCamelCase						,   return_offsets_mapping=lowerCamelCase						,   add_special_tokens=lowerCamelCase	)
           self.assertEqual(encoding.offset_mapping[0]						,   (0, 1 + len(lowerCamelCase	))	)
           self.assertEqual(
               encoding.offset_mapping[1]						,   (1 + len(lowerCamelCase	), 1 + len(lowerCamelCase	) + 1 + len(lowerCamelCase	))						,   )

           _snake_case     		=				self.rust_tokenizer_class.from_pretrained(
               lowerCamelCase						,   use_fast=lowerCamelCase						,   add_prefix_space=lowerCamelCase						,   trim_offsets=lowerCamelCase	)
           _snake_case     		=				tokenizer_r(lowerCamelCase						,   return_offsets_mapping=lowerCamelCase						,   add_special_tokens=lowerCamelCase	)
           self.assertEqual(encoding.offset_mapping[0]						,   (0, 1 + len(lowerCamelCase	))	)
           self.assertEqual(
               encoding.offset_mapping[1]						,   (1 + len(lowerCamelCase	), 1 + len(lowerCamelCase	) + 1 + len(lowerCamelCase	))						,   )


