


from typing import Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature
from ...image_transforms import get_image_size, pad, rescale, to_channel_dimension_format
from ...image_utils import ChannelDimension, ImageInput, make_list_of_images, to_numpy_array, valid_images
from ...utils import TensorType, logging


__snake_case            =   logging.get_logger(__name__)




class    UpperCAmelCase					(       __snake_case    ):
			lowercase						= ["""pixel_values"""]




			def __init__(						self							:		Optional[Any]       ,       __magic_name__							:		bool = True       ,       __magic_name__							:		Union[int, float] = 1 / 2_5_5       ,       __magic_name__							:		bool = True       ,       __magic_name__							:		int = 8       ,       **__magic_name__							:		Optional[Any]       ,       ):







						"""simple docstring"""







						super().__init__(**__magic_name__						)

						UpperCamelCase         =					do_rescale
						UpperCamelCase         =					rescale_factor
						UpperCamelCase         =					do_pad
						UpperCamelCase         =					pad_size




			def   lowerCamelCase_					(						self							:		Any       ,       __magic_name__							:		np.ndarray       ,       __magic_name__							:		float       ,       __magic_name__							:		Optional[Union[str, ChannelDimension]] = None       ,       **__magic_name__							:		str						):







						"""simple docstring"""







						return rescale(__magic_name__       ,       scale=__magic_name__       ,       data_format=__magic_name__       ,       **__magic_name__						)




			def   lowerCamelCase_					(						self							:		List[Any]       ,       __magic_name__							:		np.ndarray       ,       __magic_name__							:		int       ,       __magic_name__							:		Optional[Union[str, ChannelDimension]] = None						):







						"""simple docstring"""







						UpperCamelCase  ,  UpperCamelCase         =					get_image_size(__magic_name__						)
						UpperCamelCase         =					(old_height // size + 1) * size - old_height
						UpperCamelCase         =					(old_width // size + 1) * size - old_width

						return pad(__magic_name__       ,       ((0, pad_height), (0, pad_width))       ,       mode="""symmetric"""       ,       data_format=__magic_name__						)





			def   lowerCamelCase_					(						self							:		List[str]       ,       __magic_name__							:		ImageInput       ,       __magic_name__							:		Optional[bool] = None       ,       __magic_name__							:		Optional[float] = None       ,       __magic_name__							:		Optional[bool] = None       ,       __magic_name__							:		Optional[int] = None       ,       __magic_name__							:		Optional[Union[str, TensorType]] = None       ,       __magic_name__							:		Union[str, ChannelDimension] = ChannelDimension.FIRST       ,       **__magic_name__							:		int       ,       ):







						"""simple docstring"""







						UpperCamelCase         =					do_rescale if do_rescale is not None else self.do_rescale
						UpperCamelCase         =					rescale_factor if rescale_factor is not None else self.rescale_factor
						UpperCamelCase         =					do_pad if do_pad is not None else self.do_pad
						UpperCamelCase         =					pad_size if pad_size is not None else self.pad_size

						UpperCamelCase         =					make_list_of_images(__magic_name__						)

						if not valid_images(__magic_name__						):
									raise ValueError(
									    """Invalid image type. Must be of type PIL.Image.Image, numpy.ndarray, """
									    """torch.Tensor, tf.Tensor or jax.ndarray."""						)

						if do_rescale and rescale_factor is None:
									raise ValueError("""Rescale factor must be specified if do_rescale is True."""						)

						# All transformations expect numpy arrays.
						UpperCamelCase         =					[to_numpy_array(__magic_name__						) for image in images]

						if do_rescale:
									UpperCamelCase         =					[self.rescale(image=__magic_name__       ,       scale=__magic_name__						) for image in images]

						if do_pad:
									UpperCamelCase         =					[self.pad(__magic_name__       ,       size=__magic_name__						) for image in images]

						UpperCamelCase         =					[to_channel_dimension_format(__magic_name__       ,       __magic_name__						) for image in images]

						UpperCamelCase         =					{"""pixel_values""": images}
						return BatchFeature(data=__magic_name__       ,       tensor_type=__magic_name__						)








import math






def 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		int	):





			"""simple docstring"""




			UpperCamelCase         =					[True] * n
			UpperCamelCase         =					False
			UpperCamelCase         =					False
			UpperCamelCase         =					True

			for i in range(3       ,  int(n**0.5 + 1	)       ,  2	):
						UpperCamelCase         =					i * 2
						while index < n:
									UpperCamelCase         =					False
									UpperCamelCase         =					index + i

			UpperCamelCase         =					[2]

			for i in range(3       ,  SCREAMING_SNAKE_CASE_       ,  2	):
						if is_prime[i]:
									primes.append(SCREAMING_SNAKE_CASE_	)

			return primes






def 							_lowercase    (		SCREAMING_SNAKE_CASE_   :		int = 999_966_663_333	):





			"""simple docstring"""




			UpperCamelCase         =					math.floor(math.sqrt(SCREAMING_SNAKE_CASE_	)	) + 100
			UpperCamelCase         =					prime_sieve(SCREAMING_SNAKE_CASE_	)

			UpperCamelCase         =					0
			UpperCamelCase         =					0
			UpperCamelCase         =					primes[prime_index]

			while (last_prime**2) <= limit:
						UpperCamelCase         =					primes[prime_index + 1]

						UpperCamelCase         =					last_prime**2
						UpperCamelCase         =					next_prime**2

						# Get numbers divisible by lps(current)
						UpperCamelCase         =					lower_bound + last_prime
						while upper_bound > current <= limit:
									matches_sum += current
									current += last_prime

						# Reset the upper_bound
						while (upper_bound - next_prime) > limit:
									upper_bound -= next_prime

						# Add the numbers divisible by ups(current)
						UpperCamelCase         =					upper_bound - next_prime
						while current > lower_bound:
									matches_sum += current
									current -= next_prime

						# Remove the numbers divisible by both ups and lps
						UpperCamelCase         =					0
						while upper_bound > current <= limit:
									if current <= lower_bound:
												# Increment the current number
												current += last_prime * next_prime
												continue

									if current > limit:
												break

									# Remove twice since it was added by both ups and lps
									matches_sum -= current * 2

									# Increment the current number
									current += last_prime * next_prime

						# Setup for next pair
						UpperCamelCase         =					next_prime
						prime_index += 1

			return matches_sum


if __name__ == "__main__":
			print(solution())




