


"""simple docstring"""
import math







def     _a					(   _SCREAMING_SNAKE_CASE					)     ->					bool:

							if 1 < number < 4:
														# 2 and 3 are primes
														return True
							elif number < 2 or number % 2 == 0 or number % 3 == 0:
														# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
														return False

							# All primes number are in format of 6k +/- 1
							for i in range(5					,			int(math.sqrt(__UpperCamelCase					) + 1					)					,			6					):
														if number % i == 0 or number % (i + 2) == 0:
																					return False
							return True







def     _a					(   _SCREAMING_SNAKE_CASE = 600_851_475_143					)     ->					int:

							try:
														snake_case_     							=		int(__UpperCamelCase					)
							except (TypeError, ValueError):
														raise TypeError("""Parameter n must be int or castable to int."""					)
							if n <= 0:
														raise ValueError("""Parameter n must be greater than or equal to one."""					)
							snake_case_     							=		0
							if is_prime(__UpperCamelCase					):
														return n
							while n % 2 == 0:
														n //= 2
							if is_prime(__UpperCamelCase					):
														return n
							for i in range(3					,			int(math.sqrt(__UpperCamelCase					)					) + 1					,			2					):
														if n % i == 0:
																					if is_prime(n // i					):
																												snake_case_     							=		n // i
																												break
																					elif is_prime(__UpperCamelCase					):
																												snake_case_     							=		i
							return max_number


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





"""simple docstring"""


import unittest

import numpy as np
import PIL
import torch

from diffusers.image_processor import VaeImageProcessor







class 						lowerCamelCase__   (   unittest.TestCase							):





			'''simple docstring'''



			@property
			def    _lowerCAmelCase						(				self    )					->	List[str]:
				_lowerCAmelCase								=1
				_lowerCAmelCase								=3
				_lowerCAmelCase								=8
				_lowerCAmelCase								=8

				_lowerCAmelCase								=torch.rand((batch_size, num_channels, height, width)    )

				return sample



			def    _lowerCAmelCase						(				self	,	__UpperCAmelCase    )					->	Any:
				if isinstance(image[0]	,	PIL.Image.Image    ):
					return np.stack([np.array(__UpperCAmelCase    ) for i in image]	,	axis=0    )
				elif isinstance(__UpperCAmelCase	,	torch.Tensor    ):
					return image.cpu().numpy().transpose(0	,	2	,	3	,	1    )
				return image



			def    _lowerCAmelCase						(				self    )					->	Tuple:
				_lowerCAmelCase								=VaeImageProcessor(do_resize=__UpperCAmelCase	,	do_normalize=__UpperCAmelCase    )

				_lowerCAmelCase								=self.dummy_sample
				_lowerCAmelCase								=self.to_np(__UpperCAmelCase    )

				for output_type in ["pt", "np", "pil"]:
					_lowerCAmelCase								=image_processor.postprocess(
					    image_processor.preprocess(__UpperCAmelCase    )	,	output_type=__UpperCAmelCase	,	)
					_lowerCAmelCase								=self.to_np(__UpperCAmelCase    )
					_lowerCAmelCase								=(input_np * 2_55).round() if output_type == """pil""" else input_np
					assert (
					    np.abs(in_np - out_np    ).max() < 1e-6
					), f'''decoded output does not match input for output_type {output_type}'''



			def    _lowerCAmelCase						(				self    )					->	Union[str, Any]:
				_lowerCAmelCase								=VaeImageProcessor(do_resize=__UpperCAmelCase	,	do_normalize=__UpperCAmelCase    )
				_lowerCAmelCase								=self.dummy_sample.cpu().numpy().transpose(0	,	2	,	3	,	1    )

				for output_type in ["pt", "np", "pil"]:
					_lowerCAmelCase								=image_processor.postprocess(image_processor.preprocess(__UpperCAmelCase    )	,	output_type=__UpperCAmelCase    )

					_lowerCAmelCase								=self.to_np(__UpperCAmelCase    )
					_lowerCAmelCase								=(input_np * 2_55).round() if output_type == """pil""" else input_np
					assert (
					    np.abs(in_np - out_np    ).max() < 1e-6
					), f'''decoded output does not match input for output_type {output_type}'''



			def    _lowerCAmelCase						(				self    )					->	List[str]:
				_lowerCAmelCase								=VaeImageProcessor(do_resize=__UpperCAmelCase	,	do_normalize=__UpperCAmelCase    )

				_lowerCAmelCase								=self.dummy_sample.cpu().numpy().transpose(0	,	2	,	3	,	1    )
				_lowerCAmelCase								=image_processor.numpy_to_pil(__UpperCAmelCase    )

				for output_type in ["pt", "np", "pil"]:
					_lowerCAmelCase								=image_processor.postprocess(image_processor.preprocess(__UpperCAmelCase    )	,	output_type=__UpperCAmelCase    )
					for i, o in zip(__UpperCAmelCase	,	__UpperCAmelCase    ):
						_lowerCAmelCase								=np.array(__UpperCAmelCase    )
						_lowerCAmelCase								=self.to_np(__UpperCAmelCase    ) if output_type == """pil""" else (self.to_np(__UpperCAmelCase    ) * 2_55).round()
						assert (
						    np.abs(in_np - out_np    ).max() < 1e-6
						), f'''decoded output does not match input for output_type {output_type}'''



			def    _lowerCAmelCase						(				self    )					->	Tuple:
				_lowerCAmelCase								=VaeImageProcessor(do_resize=__UpperCAmelCase	,	do_normalize=__UpperCAmelCase    )

				_lowerCAmelCase								=self.dummy_sample
				_lowerCAmelCase								=input_pt_ad.squeeze(0    )

				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)
				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)

				_lowerCAmelCase								=self.to_np(self.dummy_sample    )
				_lowerCAmelCase								=input_np_ad.squeeze(0    )

				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)
				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)

				assert np.abs(out_pt_ad - out_pt_ad    ).max() < 1e-6
				assert np.abs(out_np_ad - out_np_ad    ).max() < 1e-6



			def    _lowerCAmelCase						(				self    )					->	Optional[Any]:
				_lowerCAmelCase								=VaeImageProcessor(do_resize=__UpperCAmelCase	,	do_normalize=__UpperCAmelCase    )

				_lowerCAmelCase								=self.dummy_sample
				_lowerCAmelCase								=list(__UpperCAmelCase    )

				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)

				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)

				_lowerCAmelCase								=self.to_np(self.dummy_sample    )
				list(__UpperCAmelCase    )

				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)

				_lowerCAmelCase								=image_processor.postprocess(
				    image_processor.preprocess(__UpperCAmelCase    )	,	output_type="""np"""	,	)

				assert np.abs(out_pt_ad - out_pt_list    ).max() < 1e-6
				assert np.abs(out_np_ad - out_np_list    ).max() < 1e-6



