
def      __lowerCAmelCase						(							UpperCAmelCase__				:      int = 1_0**1_2       )  ->    int:
							lowerCamelCase_							  =					1
							lowerCamelCase_							  =					0

							lowerCamelCase_							  =					1
							lowerCamelCase_							  =					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 OwlViTImageProcessor, OwlViTProcessor





@require_vision
class       __A(				unittest.TestCase       ):

					def    lowercase__      (	self					:     Union[str, Any]   ):
												lowerCamelCase_							  =					tempfile.mkdtemp()

												# fmt: off
												lowerCamelCase_							  =					["""""", """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
												lowerCamelCase_							  =					dict(zip(__UpperCamelCase   ,					range(len(__UpperCamelCase   )   )   )   )
												lowerCamelCase_							  =					["""#version: 0.2""", """l o""", """lo w</w>""", """e r</w>""", """"""]
												lowerCamelCase_							  =					{"""unk_token""": """<unk>"""}

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

												lowerCamelCase_							  =					{
												    """do_resize""": True,
												    """size""": 2_0,
												    """do_center_crop""": True,
												    """crop_size""": 1_8,
												    """do_normalize""": True,
												    """image_mean""": [0.48145466, 0.4578275, 0.40821073],
												    """image_std""": [0.26862954, 0.26130258, 0.27577711],
												}
												lowerCamelCase_							  =					os.path.join(self.tmpdirname   ,					__UpperCamelCase   )
												with open(self.image_processor_file   ,					"""w"""   ,					encoding="""utf-8"""   ) as fp:
																			json.dump(__UpperCamelCase   ,					__UpperCamelCase   )

					def    lowercase__      (	self					:     str   ,					**__UpperCamelCase					:     Optional[Any]   ):
												return CLIPTokenizer.from_pretrained(self.tmpdirname   ,					pad_token="""!"""   ,					**__UpperCamelCase   )

					def    lowercase__      (	self					:     Any   ,					**__UpperCamelCase					:     List[Any]   ):
												return CLIPTokenizerFast.from_pretrained(self.tmpdirname   ,					pad_token="""!"""   ,					**__UpperCamelCase   )

					def    lowercase__      (	self					:     List[Any]   ,					**__UpperCamelCase					:     Optional[int]   ):
												return OwlViTImageProcessor.from_pretrained(self.tmpdirname   ,					**__UpperCamelCase   )

					def    lowercase__      (	self					:     Union[str, Any]   ):
												shutil.rmtree(self.tmpdirname   )

					def    lowercase__      (	self					:     str   ):
												lowerCamelCase_							  =					[np.random.randint(2_5_5   ,					size=(3, 3_0, 4_0_0)   ,					dtype=np.uinta   )]

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

												return image_inputs

					def    lowercase__      (	self					:     Optional[int]   ):
												lowerCamelCase_							  =					self.get_tokenizer()
												lowerCamelCase_							  =					self.get_rust_tokenizer()
												lowerCamelCase_							  =					self.get_image_processor()

												lowerCamelCase_							  =					OwlViTProcessor(tokenizer=__UpperCamelCase   ,					image_processor=__UpperCamelCase   )
												processor_slow.save_pretrained(self.tmpdirname   )
												lowerCamelCase_							  =					OwlViTProcessor.from_pretrained(self.tmpdirname   ,					use_fast=__UpperCamelCase   )

												lowerCamelCase_							  =					OwlViTProcessor(tokenizer=__UpperCamelCase   ,					image_processor=__UpperCamelCase   )
												processor_fast.save_pretrained(self.tmpdirname   )
												lowerCamelCase_							  =					OwlViTProcessor.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   ,					__UpperCamelCase   )
												self.assertIsInstance(processor_fast.tokenizer   ,					__UpperCamelCase   )

												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   ,					__UpperCamelCase   )
												self.assertIsInstance(processor_fast.image_processor   ,					__UpperCamelCase   )

					def    lowercase__      (	self					:     Optional[int]   ):
												lowerCamelCase_							  =					OwlViTProcessor(tokenizer=self.get_tokenizer()   ,					image_processor=self.get_image_processor()   )
												processor.save_pretrained(self.tmpdirname   )

												lowerCamelCase_							  =					self.get_tokenizer(bos_token="""(BOS)"""   ,					eos_token="""(EOS)"""   )
												lowerCamelCase_							  =					self.get_image_processor(do_normalize=__UpperCamelCase   )

												lowerCamelCase_							  =					OwlViTProcessor.from_pretrained(
												    self.tmpdirname   ,					bos_token="""(BOS)"""   ,					eos_token="""(EOS)"""   ,					do_normalize=__UpperCamelCase   )

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

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

					def    lowercase__      (	self					:     Any   ):
												lowerCamelCase_							  =					self.get_image_processor()
												lowerCamelCase_							  =					self.get_tokenizer()

												lowerCamelCase_							  =					OwlViTProcessor(tokenizer=__UpperCamelCase   ,					image_processor=__UpperCamelCase   )

												lowerCamelCase_							  =					self.prepare_image_inputs()

												lowerCamelCase_							  =					image_processor(__UpperCamelCase   ,					return_tensors="""np"""   )
												lowerCamelCase_							  =					processor(images=__UpperCamelCase   ,					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    lowercase__      (	self					:     Union[str, Any]   ):
												lowerCamelCase_							  =					self.get_image_processor()
												lowerCamelCase_							  =					self.get_tokenizer()

												lowerCamelCase_							  =					OwlViTProcessor(tokenizer=__UpperCamelCase   ,					image_processor=__UpperCamelCase   )

												lowerCamelCase_							  =					"""lower newer"""

												lowerCamelCase_							  =					processor(text=__UpperCamelCase   ,					return_tensors="""np"""   )

												lowerCamelCase_							  =					tokenizer(__UpperCamelCase   ,					return_tensors="""np"""   )

												for key in encoded_tok.keys():
																			self.assertListEqual(encoded_tok[key][0].tolist()   ,					encoded_processor[key][0].tolist()   )

					def    lowercase__      (	self					:     List[str]   ):
												lowerCamelCase_							  =					self.get_image_processor()
												lowerCamelCase_							  =					self.get_tokenizer()

												lowerCamelCase_							  =					OwlViTProcessor(tokenizer=__UpperCamelCase   ,					image_processor=__UpperCamelCase   )

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

												lowerCamelCase_							  =					processor(text=__UpperCamelCase   ,					images=__UpperCamelCase   )

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

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

					def    lowercase__      (	self					:     List[Any]   ):
												lowerCamelCase_							  =					"""google/owlvit-base-patch32"""
												lowerCamelCase_							  =					OwlViTProcessor.from_pretrained(__UpperCamelCase   )

												lowerCamelCase_							  =					["""cat""", """nasa badge"""]
												lowerCamelCase_							  =					processor(text=__UpperCamelCase   )

												lowerCamelCase_							  =					1_6
												self.assertListEqual(list(inputs.keys()   )   ,					["""input_ids""", """attention_mask"""]   )
												self.assertEqual(inputs["""input_ids"""].shape   ,					(2, seq_length)   )

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

					def    lowercase__      (	self					:     Optional[int]   ):
												lowerCamelCase_							  =					"""google/owlvit-base-patch32"""
												lowerCamelCase_							  =					OwlViTProcessor.from_pretrained(__UpperCamelCase   )

												lowerCamelCase_							  =					[["""cat""", """nasa badge"""], ["""person"""]]
												lowerCamelCase_							  =					processor(text=__UpperCamelCase   )

												lowerCamelCase_							  =					1_6
												lowerCamelCase_							  =					len(__UpperCamelCase   )
												lowerCamelCase_							  =					max([len(__UpperCamelCase   ) for texts in input_texts]   )

												self.assertListEqual(list(inputs.keys()   )   ,					["""input_ids""", """attention_mask"""]   )
												self.assertEqual(inputs["""input_ids"""].shape   ,					(batch_size * num_max_text_queries, seq_length)   )

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

					def    lowercase__      (	self					:     str   ):
												lowerCamelCase_							  =					"""google/owlvit-base-patch32"""
												lowerCamelCase_							  =					OwlViTProcessor.from_pretrained(__UpperCamelCase   )

												lowerCamelCase_							  =					["""cat""", """nasa badge"""]
												lowerCamelCase_							  =					processor(text=__UpperCamelCase   )

												lowerCamelCase_							  =					1_6
												lowerCamelCase_							  =					inputs["""input_ids"""]
												lowerCamelCase_							  =					[
												    [4_9_4_0_6, 2_3_6_8, 4_9_4_0_7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
												    [4_9_4_0_6, 6_8_4_1, 1_1_3_0_1, 4_9_4_0_7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
												]

												self.assertListEqual(list(inputs.keys()   )   ,					["""input_ids""", """attention_mask"""]   )
												self.assertEqual(inputs["""input_ids"""].shape   ,					(2, seq_length)   )
												self.assertListEqual(list(input_ids[0]   )   ,					predicted_ids[0]   )
												self.assertListEqual(list(input_ids[1]   )   ,					predicted_ids[1]   )

					def    lowercase__      (	self					:     int   ):
												lowerCamelCase_							  =					self.get_image_processor()
												lowerCamelCase_							  =					self.get_tokenizer()

												lowerCamelCase_							  =					OwlViTProcessor(tokenizer=__UpperCamelCase   ,					image_processor=__UpperCamelCase   )

												lowerCamelCase_							  =					self.prepare_image_inputs()
												lowerCamelCase_							  =					self.prepare_image_inputs()

												lowerCamelCase_							  =					processor(images=__UpperCamelCase   ,					query_images=__UpperCamelCase   )

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

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



					def    lowercase__      (	self					:     Dict   ):
												lowerCamelCase_							  =					self.get_image_processor()
												lowerCamelCase_							  =					self.get_tokenizer()

												lowerCamelCase_							  =					OwlViTProcessor(tokenizer=__UpperCamelCase   ,					image_processor=__UpperCamelCase   )

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

												lowerCamelCase_							  =					processor.batch_decode(__UpperCamelCase   )
												lowerCamelCase_							  =					tokenizer.batch_decode(__UpperCamelCase   )

												self.assertListEqual(__UpperCamelCase   ,					__UpperCamelCase   )





