"""simple docstring"""
from math import isqrt





def    lowerCAmelCase__    (			_UpperCamelCase       :				int					)					->				bool:





						"""simple docstring"""






						return all(number % divisor != 0 for divisor in range(2 ,			isqrt(_UpperCamelCase					) + 1					)					)





def    lowerCAmelCase__    (			_UpperCamelCase       :				int = 1_0**6					)					->				int:





						"""simple docstring"""






						snake_case								=			0
						snake_case								=			1
						snake_case								=			7
						while prime_candidate < max_prime:
												primes_count += is_prime(_UpperCamelCase					)

												cube_index += 1
												prime_candidate += 6 * cube_index

						return primes_count


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



"""simple docstring"""
import unittest

import numpy as np

from transformers.testing_utils import is_flaky, require_torch, require_vision
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 DonutImageProcessor



class   lowerCAmelCase_    (			unittest.TestCase					):



				"""simple docstring"""

				def __init__(				self		,    lowerCAmelCase		,    lowerCAmelCase=7		,    lowerCAmelCase=3		,    lowerCAmelCase=18		,    lowerCAmelCase=30		,    lowerCAmelCase=4_00		,    lowerCAmelCase=True		,    lowerCAmelCase=None		,    lowerCAmelCase=True		,    lowerCAmelCase=False		,    lowerCAmelCase=True		,    lowerCAmelCase=True		,    lowerCAmelCase=[0.5, 0.5, 0.5]		,    lowerCAmelCase=[0.5, 0.5, 0.5]		,    ):






										"""simple docstring"""

										snake_case								=			parent
										snake_case								=			batch_size
										snake_case								=			num_channels
										snake_case								=			image_size
										snake_case								=			min_resolution
										snake_case								=			max_resolution
										snake_case								=			do_resize
										snake_case								=			size if size is not None else {'height': 18, 'width': 20}
										snake_case								=			do_thumbnail
										snake_case								=			do_align_axis
										snake_case								=			do_pad
										snake_case								=			do_normalize
										snake_case								=			image_mean
										snake_case								=			image_std

				def 		snake_case (				self    ):






										"""simple docstring"""

										return {
										    "do_resize": self.do_resize,
										    "size": self.size,
										    "do_thumbnail": self.do_thumbnail,
										    "do_align_long_axis": self.do_align_axis,
										    "do_pad": self.do_pad,
										    "do_normalize": self.do_normalize,
										    "image_mean": self.image_mean,
										    "image_std": self.image_std,
										}





@require_torch
@require_vision
class   lowerCAmelCase_    (			lowerCAmelCase     ,    unittest.TestCase					):



				"""simple docstring"""
				_lowerCAmelCase     :    str			  =						DonutImageProcessor if is_vision_available() else None

				def 		snake_case (				self    ):






										"""simple docstring"""

										snake_case								=			DonutImageProcessingTester(self    )

				@property
				def 		snake_case (				self    ):






										"""simple docstring"""

										return self.image_processor_tester.prepare_image_processor_dict()

				def 		snake_case (				self    ):






										"""simple docstring"""

										snake_case								=			self.image_processing_class(**self.image_processor_dict    )
										self.assertTrue(hasattr(lowerCAmelCase		,    'do_resize'    )    )
										self.assertTrue(hasattr(lowerCAmelCase		,    'size'    )    )
										self.assertTrue(hasattr(lowerCAmelCase		,    'do_thumbnail'    )    )
										self.assertTrue(hasattr(lowerCAmelCase		,    'do_align_long_axis'    )    )
										self.assertTrue(hasattr(lowerCAmelCase		,    'do_pad'    )    )
										self.assertTrue(hasattr(lowerCAmelCase		,    'do_normalize'    )    )
										self.assertTrue(hasattr(lowerCAmelCase		,    'image_mean'    )    )
										self.assertTrue(hasattr(lowerCAmelCase		,    'image_std'    )    )

				def 		snake_case (				self    ):






										"""simple docstring"""

										snake_case								=			self.image_processing_class.from_dict(self.image_processor_dict    )
										self.assertEqual(image_processor.size		,    {'height': 18, 'width': 20}    )

										snake_case								=			self.image_processing_class.from_dict(self.image_processor_dict		,    size=42    )
										self.assertEqual(image_processor.size		,    {'height': 42, 'width': 42}    )

										# Previous config had dimensions in (width, height) order
										snake_case								=			self.image_processing_class.from_dict(self.image_processor_dict		,    size=(42, 84)    )
										self.assertEqual(image_processor.size		,    {'height': 84, 'width': 42}    )

				def 		snake_case (				self    ):






										"""simple docstring"""

										pass

				@is_flaky()
				def 		snake_case (				self    ):






										"""simple docstring"""

										snake_case								=			self.image_processing_class(**self.image_processor_dict    )
										# create random PIL images
										snake_case								=			prepare_image_inputs(self.image_processor_tester		,    equal_resolution=lowerCAmelCase    )
										for image in image_inputs:
																self.assertIsInstance(lowerCAmelCase		,    Image.Image    )

										# Test not batched input
										snake_case								=			image_processing(image_inputs[0]		,    return_tensors='pt'    ).pixel_values
										self.assertEqual(
										    encoded_images.shape		,    (
										        1,
										        self.image_processor_tester.num_channels,
										        self.image_processor_tester.size['height'],
										        self.image_processor_tester.size['width'],
										    )		,    )

										# Test batched
										snake_case								=			image_processing(lowerCAmelCase		,    return_tensors='pt'    ).pixel_values
										self.assertEqual(
										    encoded_images.shape		,    (
										        self.image_processor_tester.batch_size,
										        self.image_processor_tester.num_channels,
										        self.image_processor_tester.size['height'],
										        self.image_processor_tester.size['width'],
										    )		,    )

				@is_flaky()
				def 		snake_case (				self    ):






										"""simple docstring"""

										snake_case								=			self.image_processing_class(**self.image_processor_dict    )
										# create random numpy tensors
										snake_case								=			prepare_image_inputs(self.image_processor_tester		,    equal_resolution=lowerCAmelCase		,    numpify=lowerCAmelCase    )
										for image in image_inputs:
																self.assertIsInstance(lowerCAmelCase		,    np.ndarray    )

										# Test not batched input
										snake_case								=			image_processing(image_inputs[0]		,    return_tensors='pt'    ).pixel_values
										self.assertEqual(
										    encoded_images.shape		,    (
										        1,
										        self.image_processor_tester.num_channels,
										        self.image_processor_tester.size['height'],
										        self.image_processor_tester.size['width'],
										    )		,    )

										# Test batched
										snake_case								=			image_processing(lowerCAmelCase		,    return_tensors='pt'    ).pixel_values
										self.assertEqual(
										    encoded_images.shape		,    (
										        self.image_processor_tester.batch_size,
										        self.image_processor_tester.num_channels,
										        self.image_processor_tester.size['height'],
										        self.image_processor_tester.size['width'],
										    )		,    )

				@is_flaky()
				def 		snake_case (				self    ):






										"""simple docstring"""

										snake_case								=			self.image_processing_class(**self.image_processor_dict    )
										# create random PyTorch tensors
										snake_case								=			prepare_image_inputs(self.image_processor_tester		,    equal_resolution=lowerCAmelCase		,    torchify=lowerCAmelCase    )
										for image in image_inputs:
																self.assertIsInstance(lowerCAmelCase		,    torch.Tensor    )

										# Test not batched input
										snake_case								=			image_processing(image_inputs[0]		,    return_tensors='pt'    ).pixel_values
										self.assertEqual(
										    encoded_images.shape		,    (
										        1,
										        self.image_processor_tester.num_channels,
										        self.image_processor_tester.size['height'],
										        self.image_processor_tester.size['width'],
										    )		,    )

										# Test batched
										snake_case								=			image_processing(lowerCAmelCase		,    return_tensors='pt'    ).pixel_values
										self.assertEqual(
										    encoded_images.shape		,    (
										        self.image_processor_tester.batch_size,
										        self.image_processor_tester.num_channels,
										        self.image_processor_tester.size['height'],
										        self.image_processor_tester.size['width'],
										    )		,    )


