






"""simple docstring"""



from math import ceil, sqrt



def 						lowercase    (				__snake_case				: int = 1_0_0_0_0_0_0	):
		lowercase_ : str							       =   0

		for outer_width in range(3		,					(limit // 4) + 2	):
				if outer_width**2 > limit:
						lowercase_ : Union[str, Any]							       =   max(ceil(sqrt(outer_width**2 - limit	)	)		,					1	)
				else:
						lowercase_ : Any							       =   1
				if (outer_width - hole_width_lower_bound) % 2:
						hole_width_lower_bound += 1

				answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

		return answer


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











"""simple docstring"""



import json
import pathlib
import unittest

import numpy as np

from transformers.testing_utils import require_torch, require_vision, slow
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
						import torch

if is_vision_available():
						from PIL import Image

						from transformers import YolosImageProcessor





class 					_UpperCAmelCase       ( unittest.TestCase							):




					def __init__(				self     :						List[Any]    ,						A     :						Any    ,						A     :						Tuple=7    ,						A     :						Tuple=3    ,						A     :						Optional[Any]=30    ,						A     :						List[Any]=4_00    ,						A     :						Tuple=True    ,						A     :						Dict=None    ,						A     :						List[str]=True    ,						A     :						Optional[int]=[0.5, 0.5, 0.5]    ,						A     :						Tuple=[0.5, 0.5, 0.5]    ,						A     :						List[str]=True    ,						A     :						List[Any]=1 / 2_55    ,						A     :						Union[str, Any]=True    ,						)  ->  Tuple:
							# by setting size["longest_edge"] > max_resolution we're effectively not testing this :p
							lowercase_ : Optional[int]							       =   size if size is not None else {'''shortest_edge''': 18, '''longest_edge''': 13_33}
							lowercase_ : Optional[int]							       =   parent
							lowercase_ : str							       =   batch_size
							lowercase_ : Tuple							       =   num_channels
							lowercase_ : str							       =   min_resolution
							lowercase_ : Any							       =   max_resolution
							lowercase_ : str							       =   do_resize
							lowercase_ : Any							       =   size
							lowercase_ : Optional[int]							       =   do_normalize
							lowercase_ : List[str]							       =   image_mean
							lowercase_ : Optional[Any]							       =   image_std
							lowercase_ : int							       =   do_rescale
							lowercase_ : List[str]							       =   rescale_factor
							lowercase_ : int							       =   do_pad




					def   A  (				self     :						Any   )  ->  str:
							return {
							    "do_resize": self.do_resize,
							    "size": self.size,
							    "do_normalize": self.do_normalize,
							    "image_mean": self.image_mean,
							    "image_std": self.image_std,
							    "do_rescale": self.do_rescale,
							    "rescale_factor": self.rescale_factor,
							    "do_pad": self.do_pad,
							}






					def   A  (				self     :						Optional[Any]    ,						A     :						int    ,						A     :						int=False   )  ->  Tuple:
							if not batched:
									lowercase_ : Optional[int]							       =   image_inputs[0]
									if isinstance(A    ,						Image.Image   ):
											lowercase_       ,					lowercase_ : int							       =   image.size
									else:
											lowercase_       ,					lowercase_ : Tuple							       =   image.shape[1], image.shape[2]
									if w < h:
											lowercase_ : int							       =   int(self.size['''shortest_edge'''] * h / w   )
											lowercase_ : Optional[Any]							       =   self.size['''shortest_edge''']
									elif w > h:
											lowercase_ : Optional[Any]							       =   self.size['''shortest_edge''']
											lowercase_ : Optional[int]							       =   int(self.size['''shortest_edge'''] * w / h   )
									else:
											lowercase_ : Any							       =   self.size['''shortest_edge''']
											lowercase_ : Any							       =   self.size['''shortest_edge''']

							else:
									lowercase_ : Tuple							       =   []
									for image in image_inputs:
											lowercase_       ,					lowercase_ : Optional[Any]							       =   self.get_expected_values([image]   )
											expected_values.append((expected_height, expected_width)   )
									lowercase_ : Union[str, Any]							       =   max(A    ,						key=lambda A   : item[0]   )[0]
									lowercase_ : Optional[Any]							       =   max(A    ,						key=lambda A   : item[1]   )[1]

							return expected_height, expected_width





@require_torch
@require_vision
class 					_UpperCAmelCase       ( _A   ,						unittest.TestCase							):
					SCREAMING_SNAKE_CASE_		:				Optional[Any]							    =   YolosImageProcessor if is_vision_available() else None




					def   A  (				self     :						Optional[int]   )  ->  Optional[int]:
							lowercase_ : Optional[Any]							       =   YolosImageProcessingTester(self   )




					@property
					def   A  (				self     :						str   )  ->  Any:
							return self.image_processor_tester.prepare_image_processor_dict()




					def   A  (				self     :						Optional[int]   )  ->  List[str]:
							lowercase_ : Tuple							       =   self.image_processing_class(**self.image_processor_dict   )
							self.assertTrue(hasattr(A    ,						'''image_mean'''   )   )
							self.assertTrue(hasattr(A    ,						'''image_std'''   )   )
							self.assertTrue(hasattr(A    ,						'''do_normalize'''   )   )
							self.assertTrue(hasattr(A    ,						'''do_resize'''   )   )
							self.assertTrue(hasattr(A    ,						'''size'''   )   )




					def   A  (				self     :						Dict   )  ->  Tuple:
							lowercase_ : Dict							       =   self.image_processing_class.from_dict(self.image_processor_dict   )
							self.assertEqual(image_processor.size    ,						{'''shortest_edge''': 18, '''longest_edge''': 13_33}   )
							self.assertEqual(image_processor.do_pad    ,						A   )

							lowercase_ : Tuple							       =   self.image_processing_class.from_dict(
							    self.image_processor_dict    ,						size=42    ,						max_size=84    ,						pad_and_return_pixel_mask=A   )
							self.assertEqual(image_processor.size    ,						{'''shortest_edge''': 42, '''longest_edge''': 84}   )
							self.assertEqual(image_processor.do_pad    ,						A   )




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




					def   A  (				self     :						Tuple   )  ->  int:
							# Initialize image_processing
							lowercase_ : Dict							       =   self.image_processing_class(**self.image_processor_dict   )
							# create random PIL images
							lowercase_ : str							       =   prepare_image_inputs(self.image_processor_tester    ,						equal_resolution=A   )
							for image in image_inputs:
									self.assertIsInstance(A    ,						Image.Image   )

							# Test not batched input
							lowercase_ : Optional[int]							       =   image_processing(image_inputs[0]    ,						return_tensors='''pt'''   ).pixel_values

							lowercase_       ,					lowercase_ : Union[str, Any]							       =   self.image_processor_tester.get_expected_values(A   )

							self.assertEqual(
							    encoded_images.shape    ,						(1, self.image_processor_tester.num_channels, expected_height, expected_width)    ,						)

							# Test batched
							lowercase_       ,					lowercase_ : Dict							       =   self.image_processor_tester.get_expected_values(A    ,						batched=A   )

							lowercase_ : str							       =   image_processing(A    ,						return_tensors='''pt'''   ).pixel_values
							self.assertEqual(
							    encoded_images.shape    ,						(
							        self.image_processor_tester.batch_size,
							        self.image_processor_tester.num_channels,
							        expected_height,
							        expected_width,
							    )    ,						)




					def   A  (				self     :						str   )  ->  Any:
							# Initialize image_processing
							lowercase_ : Any							       =   self.image_processing_class(**self.image_processor_dict   )
							# create random numpy tensors
							lowercase_ : List[Any]							       =   prepare_image_inputs(self.image_processor_tester    ,						equal_resolution=A    ,						numpify=A   )
							for image in image_inputs:
									self.assertIsInstance(A    ,						np.ndarray   )

							# Test not batched input
							lowercase_ : List[Any]							       =   image_processing(image_inputs[0]    ,						return_tensors='''pt'''   ).pixel_values

							lowercase_       ,					lowercase_ : int							       =   self.image_processor_tester.get_expected_values(A   )

							self.assertEqual(
							    encoded_images.shape    ,						(1, self.image_processor_tester.num_channels, expected_height, expected_width)    ,						)

							# Test batched
							lowercase_ : Optional[int]							       =   image_processing(A    ,						return_tensors='''pt'''   ).pixel_values

							lowercase_       ,					lowercase_ : List[Any]							       =   self.image_processor_tester.get_expected_values(A    ,						batched=A   )

							self.assertEqual(
							    encoded_images.shape    ,						(
							        self.image_processor_tester.batch_size,
							        self.image_processor_tester.num_channels,
							        expected_height,
							        expected_width,
							    )    ,						)




					def   A  (				self     :						Tuple   )  ->  Optional[int]:
							# Initialize image_processing
							lowercase_ : Dict							       =   self.image_processing_class(**self.image_processor_dict   )
							# create random PyTorch tensors
							lowercase_ : Optional[int]							       =   prepare_image_inputs(self.image_processor_tester    ,						equal_resolution=A    ,						torchify=A   )
							for image in image_inputs:
									self.assertIsInstance(A    ,						torch.Tensor   )

							# Test not batched input
							lowercase_ : List[str]							       =   image_processing(image_inputs[0]    ,						return_tensors='''pt'''   ).pixel_values

							lowercase_       ,					lowercase_ : Union[str, Any]							       =   self.image_processor_tester.get_expected_values(A   )

							self.assertEqual(
							    encoded_images.shape    ,						(1, self.image_processor_tester.num_channels, expected_height, expected_width)    ,						)

							# Test batched
							lowercase_ : Any							       =   image_processing(A    ,						return_tensors='''pt'''   ).pixel_values

							lowercase_       ,					lowercase_ : List[str]							       =   self.image_processor_tester.get_expected_values(A    ,						batched=A   )

							self.assertEqual(
							    encoded_images.shape    ,						(
							        self.image_processor_tester.batch_size,
							        self.image_processor_tester.num_channels,
							        expected_height,
							        expected_width,
							    )    ,						)




					def   A  (				self     :						Tuple   )  ->  Optional[Any]:
							# Initialize image_processings
							lowercase_ : Optional[Any]							       =   self.image_processing_class(**self.image_processor_dict   )
							lowercase_ : Tuple							       =   self.image_processing_class(do_resize=A    ,						do_normalize=A    ,						do_rescale=A   )
							# create random PyTorch tensors
							lowercase_ : Union[str, Any]							       =   prepare_image_inputs(self.image_processor_tester    ,						equal_resolution=A    ,						torchify=A   )
							for image in image_inputs:
									self.assertIsInstance(A    ,						torch.Tensor   )

							# Test whether the method "pad" and calling the image processor return the same tensors
							lowercase_ : Union[str, Any]							       =   image_processing_a.pad(A    ,						return_tensors='''pt'''   )
							lowercase_ : List[Any]							       =   image_processing_a(A    ,						return_tensors='''pt'''   )

							self.assertTrue(
							    torch.allclose(encoded_images_with_method['''pixel_values''']    ,						encoded_images['''pixel_values''']    ,						atol=1e-4   )   )




					@slow
					def   A  (				self     :						str   )  ->  List[Any]:
							# prepare image and target
							lowercase_ : Dict							       =   Image.open('''./tests/fixtures/tests_samples/COCO/000000039769.png'''   )
							with open('''./tests/fixtures/tests_samples/COCO/coco_annotations.txt'''    ,						'''r'''   ) as f:
									lowercase_ : List[Any]							       =   json.loads(f.read()   )

							lowercase_ : Tuple							       =   {'''image_id''': 3_97_69, '''annotations''': target}

							# encode them
							lowercase_ : Union[str, Any]							       =   YolosImageProcessor.from_pretrained('''hustvl/yolos-small'''   )
							lowercase_ : List[Any]							       =   image_processing(images=A    ,						annotations=A    ,						return_tensors='''pt'''   )

							# verify pixel values
							lowercase_ : Union[str, Any]							       =   torch.Size([1, 3, 8_00, 10_66]   )
							self.assertEqual(encoding['''pixel_values'''].shape    ,						A   )

							lowercase_ : Union[str, Any]							       =   torch.tensor([0.2796, 0.3138, 0.3481]   )
							self.assertTrue(torch.allclose(encoding['''pixel_values'''][0, 0, 0, :3]    ,						A    ,						atol=1e-4   )   )

							# verify area
							lowercase_ : Tuple							       =   torch.tensor([5887.9600, 11250.2061, 489353.8438, 837122.7500, 147967.5156, 165732.3438]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''area''']    ,						A   )   )
							# verify boxes
							lowercase_ : List[str]							       =   torch.Size([6, 4]   )
							self.assertEqual(encoding['''labels'''][0]['''boxes'''].shape    ,						A   )
							lowercase_ : Any							       =   torch.tensor([0.5503, 0.2765, 0.0604, 0.2215]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''boxes'''][0]    ,						A    ,						atol=1e-3   )   )
							# verify image_id
							lowercase_ : List[Any]							       =   torch.tensor([3_97_69]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''image_id''']    ,						A   )   )
							# verify is_crowd
							lowercase_ : Any							       =   torch.tensor([0, 0, 0, 0, 0, 0]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''iscrowd''']    ,						A   )   )
							# verify class_labels
							lowercase_ : Optional[Any]							       =   torch.tensor([75, 75, 63, 65, 17, 17]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''class_labels''']    ,						A   )   )
							# verify orig_size
							lowercase_ : List[str]							       =   torch.tensor([4_80, 6_40]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''orig_size''']    ,						A   )   )
							# verify size
							lowercase_ : Optional[Any]							       =   torch.tensor([8_00, 10_66]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''size''']    ,						A   )   )






					@slow
					def   A  (				self     :						List[Any]   )  ->  Dict:
							# prepare image, target and masks_path
							lowercase_ : Tuple							       =   Image.open('''./tests/fixtures/tests_samples/COCO/000000039769.png'''   )
							with open('''./tests/fixtures/tests_samples/COCO/coco_panoptic_annotations.txt'''    ,						'''r'''   ) as f:
									lowercase_ : str							       =   json.loads(f.read()   )

							lowercase_ : int							       =   {'''file_name''': '''000000039769.png''', '''image_id''': 3_97_69, '''segments_info''': target}

							lowercase_ : List[Any]							       =   pathlib.Path('''./tests/fixtures/tests_samples/COCO/coco_panoptic'''   )

							# encode them
							lowercase_ : int							       =   YolosImageProcessor(format='''coco_panoptic'''   )
							lowercase_ : Any							       =   image_processing(images=A    ,						annotations=A    ,						masks_path=A    ,						return_tensors='''pt'''   )

							# verify pixel values
							lowercase_ : Optional[Any]							       =   torch.Size([1, 3, 8_00, 10_66]   )
							self.assertEqual(encoding['''pixel_values'''].shape    ,						A   )

							lowercase_ : Tuple							       =   torch.tensor([0.2796, 0.3138, 0.3481]   )
							self.assertTrue(torch.allclose(encoding['''pixel_values'''][0, 0, 0, :3]    ,						A    ,						atol=1e-4   )   )

							# verify area
							lowercase_ : List[Any]							       =   torch.tensor([147979.6875, 165527.0469, 484638.5938, 11292.9375, 5879.6562, 7634.1147]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''area''']    ,						A   )   )
							# verify boxes
							lowercase_ : str							       =   torch.Size([6, 4]   )
							self.assertEqual(encoding['''labels'''][0]['''boxes'''].shape    ,						A   )
							lowercase_ : List[str]							       =   torch.tensor([0.2625, 0.5437, 0.4688, 0.8625]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''boxes'''][0]    ,						A    ,						atol=1e-3   )   )
							# verify image_id
							lowercase_ : List[str]							       =   torch.tensor([3_97_69]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''image_id''']    ,						A   )   )
							# verify is_crowd
							lowercase_ : List[str]							       =   torch.tensor([0, 0, 0, 0, 0, 0]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''iscrowd''']    ,						A   )   )
							# verify class_labels
							lowercase_ : Any							       =   torch.tensor([17, 17, 63, 75, 75, 93]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''class_labels''']    ,						A   )   )
							# verify masks
							lowercase_ : Dict							       =   82_28_73
							self.assertEqual(encoding['''labels'''][0]['''masks'''].sum().item()    ,						A   )
							# verify orig_size
							lowercase_ : Tuple							       =   torch.tensor([4_80, 6_40]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''orig_size''']    ,						A   )   )
							# verify size
							lowercase_ : List[str]							       =   torch.tensor([8_00, 10_66]   )
							self.assertTrue(torch.allclose(encoding['''labels'''][0]['''size''']    ,						A   )   )



