





def   __lowerCamelCase   (				__a  :int = 1_0**1_2       )						->							int:






		"""simple docstring"""

		A__     =  1
		A__     =  0

		A__     =  1
		A__     =  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() = }''')










import json
import os
import shutil
import tempfile
import unittest

import numpy as np
import pytest

from transformers import CLIPTokenizer, CLIPTokenizerFast
from transformers.models.clip.tokenization_clip import VOCAB_FILES_NAMES
from transformers.testing_utils import require_vision
from transformers.utils import IMAGE_PROCESSOR_NAME, is_vision_available


if is_vision_available():
					from PIL import Image

					from transformers import CLIPImageProcessor, CLIPProcessor


@require_vision
class     A     (unittest.TestCase       ):
			'''simple docstring'''




			def   a_			(     self  :       Optional[int]  )      ->      Dict:







					"""simple docstring"""






					A__     =  tempfile.mkdtemp()

					# fmt: off
					A__     =  ["""l""", """o""", """w""", """e""", """r""", """s""", """t""", """i""", """d""", """n""", """lo""", """l</w>""", """w</w>""", """r</w>""", """t</w>""", """low</w>""", """er</w>""", """lowest</w>""", """newer</w>""", """wider""", """<unk>""", """<|startoftext|>""", """<|endoftext|>"""]
					# fmt: on
					A__     =  dict(zip(__lowerCAmelCase				,      range(len(__lowerCAmelCase  )  )  )  )
					A__     =  ["""#version: 0.2""", """l o""", """lo w</w>""", """e r</w>""", """"""]
					A__     =  {"""unk_token""": """<unk>"""}

					A__     =  os.path.join(self.tmpdirname				,      VOCAB_FILES_NAMES["""vocab_file"""]  )
					A__     =  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  )  )

					A__     =  {
					    """do_resize""": True,
					    """size""": 20,
					    """do_center_crop""": True,
					    """crop_size""": 18,
					    """do_normalize""": True,
					    """image_mean""": [0.4_8_1_4_5_4_6_6, 0.4_5_7_8_2_7_5, 0.4_0_8_2_1_0_7_3],
					    """image_std""": [0.2_6_8_6_2_9_5_4, 0.2_6_1_3_0_2_5_8, 0.2_7_5_7_7_7_1_1],
					}
					A__     =  os.path.join(self.tmpdirname				,      __lowerCAmelCase  )
					with open(self.image_processor_file				,      """w"""				,      encoding="""utf-8"""  ) as fp:
							json.dump(__lowerCAmelCase				,      __lowerCAmelCase  )






			def   a_			(     self  :       str				,      **__lowerCAmelCase  :       Optional[int]  )      ->      str:







					"""simple docstring"""






					return CLIPTokenizer.from_pretrained(self.tmpdirname				,      **__lowerCAmelCase  )






			def   a_			(     self  :       Dict				,      **__lowerCAmelCase  :       List[Any]  )      ->      Optional[int]:







					"""simple docstring"""






					return CLIPTokenizerFast.from_pretrained(self.tmpdirname				,      **__lowerCAmelCase  )






			def   a_			(     self  :       List[Any]				,      **__lowerCAmelCase  :       List[Any]  )      ->      Tuple:







					"""simple docstring"""






					return CLIPImageProcessor.from_pretrained(self.tmpdirname				,      **__lowerCAmelCase  )






			def   a_			(     self  :       Optional[Any]  )      ->      str:







					"""simple docstring"""






					shutil.rmtree(self.tmpdirname  )






			def   a_			(     self  :       int  )      ->      Tuple:







					"""simple docstring"""






					A__     =  [np.random.randint(2_55				,      size=(3, 30, 4_00)				,      dtype=np.uinta  )]

					A__     =  [Image.fromarray(np.moveaxis(__lowerCAmelCase				,      0				,      -1  )  ) for x in image_inputs]

					return image_inputs






			def   a_			(     self  :       List[str]  )      ->      Optional[int]:







					"""simple docstring"""






					A__     =  self.get_tokenizer()
					A__     =  self.get_rust_tokenizer()
					A__     =  self.get_image_processor()

					A__     =  CLIPProcessor(tokenizer=__lowerCAmelCase				,      image_processor=__lowerCAmelCase  )
					processor_slow.save_pretrained(self.tmpdirname  )
					A__     =  CLIPProcessor.from_pretrained(self.tmpdirname				,      use_fast=__lowerCAmelCase  )

					A__     =  CLIPProcessor(tokenizer=__lowerCAmelCase				,      image_processor=__lowerCAmelCase  )
					processor_fast.save_pretrained(self.tmpdirname  )
					A__     =  CLIPProcessor.from_pretrained(self.tmpdirname  )

					self.assertEqual(processor_slow.tokenizer.get_vocab()				,      tokenizer_slow.get_vocab()  )
					self.assertEqual(processor_fast.tokenizer.get_vocab()				,      tokenizer_fast.get_vocab()  )
					self.assertEqual(tokenizer_slow.get_vocab()				,      tokenizer_fast.get_vocab()  )
					self.assertIsInstance(processor_slow.tokenizer				,      __lowerCAmelCase  )
					self.assertIsInstance(processor_fast.tokenizer				,      __lowerCAmelCase  )

					self.assertEqual(processor_slow.image_processor.to_json_string()				,      image_processor.to_json_string()  )
					self.assertEqual(processor_fast.image_processor.to_json_string()				,      image_processor.to_json_string()  )
					self.assertIsInstance(processor_slow.image_processor				,      __lowerCAmelCase  )
					self.assertIsInstance(processor_fast.image_processor				,      __lowerCAmelCase  )






			def   a_			(     self  :       int  )      ->      Any:







					"""simple docstring"""






					A__     =  CLIPProcessor(tokenizer=self.get_tokenizer()				,      image_processor=self.get_image_processor()  )
					processor.save_pretrained(self.tmpdirname  )

					A__     =  self.get_tokenizer(bos_token="""(BOS)"""				,      eos_token="""(EOS)"""  )
					A__     =  self.get_image_processor(do_normalize=__lowerCAmelCase				,      padding_value=1.0  )

					A__     =  CLIPProcessor.from_pretrained(
					    self.tmpdirname				,      bos_token="""(BOS)"""				,      eos_token="""(EOS)"""				,      do_normalize=__lowerCAmelCase				,      padding_value=1.0  )

					self.assertEqual(processor.tokenizer.get_vocab()				,      tokenizer_add_kwargs.get_vocab()  )
					self.assertIsInstance(processor.tokenizer				,      __lowerCAmelCase  )

					self.assertEqual(processor.image_processor.to_json_string()				,      image_processor_add_kwargs.to_json_string()  )
					self.assertIsInstance(processor.image_processor				,      __lowerCAmelCase  )






			def   a_			(     self  :       List[Any]  )      ->      Union[str, Any]:







					"""simple docstring"""






					A__     =  self.get_image_processor()
					A__     =  self.get_tokenizer()

					A__     =  CLIPProcessor(tokenizer=__lowerCAmelCase				,      image_processor=__lowerCAmelCase  )

					A__     =  self.prepare_image_inputs()

					A__     =  image_processor(__lowerCAmelCase				,      return_tensors="""np"""  )
					A__     =  processor(images=__lowerCAmelCase				,      return_tensors="""np"""  )

					for key in input_image_proc.keys():
							self.assertAlmostEqual(input_image_proc[key].sum()				,      input_processor[key].sum()				,      delta=1e-2  )






			def   a_			(     self  :       Union[str, Any]  )      ->      Tuple:







					"""simple docstring"""






					A__     =  self.get_image_processor()
					A__     =  self.get_tokenizer()

					A__     =  CLIPProcessor(tokenizer=__lowerCAmelCase				,      image_processor=__lowerCAmelCase  )

					A__     =  """lower newer"""

					A__     =  processor(text=__lowerCAmelCase  )

					A__     =  tokenizer(__lowerCAmelCase  )

					for key in encoded_tok.keys():
							self.assertListEqual(encoded_tok[key]				,      encoded_processor[key]  )






			def   a_			(     self  :       str  )      ->      Optional[Any]:







					"""simple docstring"""






					A__     =  self.get_image_processor()
					A__     =  self.get_tokenizer()

					A__     =  CLIPProcessor(tokenizer=__lowerCAmelCase				,      image_processor=__lowerCAmelCase  )

					A__     =  """lower newer"""
					A__     =  self.prepare_image_inputs()

					A__     =  processor(text=__lowerCAmelCase				,      images=__lowerCAmelCase  )

					self.assertListEqual(list(inputs.keys()  )				,      ["""input_ids""", """attention_mask""", """pixel_values"""]  )

					# test if it raises when no input is passed
					with pytest.raises(__lowerCAmelCase  ):
							processor()






			def   a_			(     self  :       Optional[int]  )      ->      Tuple:







					"""simple docstring"""






					A__     =  self.get_image_processor()
					A__     =  self.get_tokenizer()

					A__     =  CLIPProcessor(tokenizer=__lowerCAmelCase				,      image_processor=__lowerCAmelCase  )

					A__     =  [[1, 4, 5, 8, 1, 0, 8], [3, 4, 3, 1, 1, 8, 9]]

					A__     =  processor.batch_decode(__lowerCAmelCase  )
					A__     =  tokenizer.batch_decode(__lowerCAmelCase  )

					self.assertListEqual(__lowerCAmelCase				,      __lowerCAmelCase  )







			def   a_			(     self  :       Dict  )      ->      str:







					"""simple docstring"""






					A__     =  self.get_image_processor()
					A__     =  self.get_tokenizer()

					A__     =  CLIPProcessor(tokenizer=__lowerCAmelCase				,      image_processor=__lowerCAmelCase  )

					A__     =  """lower newer"""
					A__     =  self.prepare_image_inputs()

					A__     =  processor(text=__lowerCAmelCase				,      images=__lowerCAmelCase  )

					self.assertListEqual(list(inputs.keys()  )				,      processor.model_input_names  )



