





'''simple docstring'''


def       __snake_case		( SCREAMING_SNAKE_CASE_ :			int = 1_000_000 )							->     int:

       """simple docstring"""


       UpperCAmelCase  =						set(range(3			,	SCREAMING_SNAKE_CASE_			,	2 ) )
       primes.add(2 )
       for p in range(3			,	SCREAMING_SNAKE_CASE_			,	2 ):
              if p not in primes:
                     continue
              primes.difference_update(set(range(p * p			,	SCREAMING_SNAKE_CASE_			,	SCREAMING_SNAKE_CASE_ ) ) )

       UpperCAmelCase  =						[float(SCREAMING_SNAKE_CASE_ ) for n in range(limit + 1 )]

       for p in primes:
              for n in range(SCREAMING_SNAKE_CASE_			,	limit + 1			,	SCREAMING_SNAKE_CASE_ ):
                     phi[n] *= 1 - 1 / p

       return int(sum(phi[2:] ) )


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




from typing import Dict, List, Optional, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import (
    center_crop,
    get_resize_output_image_size,
    normalize,
    rescale,
    resize,
    to_channel_dimension_format,
)
from ...image_utils import (
    IMAGENET_STANDARD_MEAN,
    IMAGENET_STANDARD_STD,
    ChannelDimension,
    ImageInput,
    PILImageResampling,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, is_vision_available, logging


if is_vision_available():
		import PIL


lowerCamelCase__						=				logging.get_logger(__name__)







class 							lowerCAmelCase__   ( __lowercase						):
						UpperCamelCase_				:			Dict						=		["pixel_values"]

						def __init__(      self							,				a = True							,				a = None							,				a = None							,				a = PILImageResampling.BILINEAR							,				a = True							,				a = 1 / 2_55							,				a = True							,				a = None							,				a = None							,				**a							,				)       ->   None:


								'''simple docstring'''

								super().__init__(**a					)
								_UpperCamelCase         =						size if size is not None else {"""shortest_edge""": 3_84}
								_UpperCamelCase         =						get_size_dict(a							,				default_to_square=a					)

								_UpperCamelCase         =						do_resize
								_UpperCamelCase         =						size
								# Default value set here for backwards compatibility where the value in config is None
								_UpperCamelCase         =						crop_pct if crop_pct is not None else 2_24 / 2_56
								_UpperCamelCase         =						resample
								_UpperCamelCase         =						do_rescale
								_UpperCamelCase         =						rescale_factor
								_UpperCamelCase         =						do_normalize
								_UpperCamelCase         =						image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
								_UpperCamelCase         =						image_std if image_std is not None else IMAGENET_STANDARD_STD

						def 			A_					(      self							,				a							,				a							,				a							,				a = PILImageResampling.BICUBIC							,				a = None							,				**a							,				)       ->   np.ndarray:


								'''simple docstring'''

								_UpperCamelCase         =						get_size_dict(a							,				default_to_square=a					)
								if "shortest_edge" not in size:
										raise ValueError(F'Size dictionary must contain \'shortest_edge\' key. Got {size.keys()}'					)
								_UpperCamelCase         =						size["""shortest_edge"""]

								if shortest_edge < 3_84:
										# maintain same ratio, resizing shortest edge to shortest_edge/crop_pct
										_UpperCamelCase         =						int(shortest_edge / crop_pct					)
										_UpperCamelCase         =						get_resize_output_image_size(a							,				size=a							,				default_to_square=a					)
										_UpperCamelCase         =						resize(image=a							,				size=a							,				resample=a							,				data_format=a							,				**a					)
										# then crop to (shortest_edge, shortest_edge)
										return center_crop(image=a							,				size=(shortest_edge, shortest_edge)							,				data_format=a							,				**a					)
								else:
										# warping (no cropping) when evaluated at 384 or larger
										return resize(
										    a							,				size=(shortest_edge, shortest_edge)							,				resample=a							,				data_format=a							,				**a					)

						def 			A_					(      self							,				a							,				a							,				a = None							,				**a							,				)       ->   Optional[int]:


								'''simple docstring'''

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

						def 			A_					(      self							,				a							,				a							,				a							,				a = None							,				**a							,				)       ->   np.ndarray:


								'''simple docstring'''

								return normalize(a							,				mean=a							,				std=a							,				data_format=a							,				**a					)







						def 			A_					(      self							,				a							,				a = None							,				a = None							,				a = None							,				a = None							,				a = None							,				a = None							,				a = None							,				a = None							,				a = None							,				a = None							,				a = ChannelDimension.FIRST							,				**a							,				)       ->   PIL.Image.Image:


								'''simple docstring'''

								_UpperCamelCase         =						do_resize if do_resize is not None else self.do_resize
								_UpperCamelCase         =						crop_pct if crop_pct is not None else self.crop_pct
								_UpperCamelCase         =						resample if resample is not None else self.resample
								_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_normalize if do_normalize is not None else self.do_normalize
								_UpperCamelCase         =						image_mean if image_mean is not None else self.image_mean
								_UpperCamelCase         =						image_std if image_std is not None else self.image_std

								_UpperCamelCase         =						size if size is not None else self.size
								_UpperCamelCase         =						get_size_dict(a							,				default_to_square=a					)

								_UpperCamelCase         =						make_list_of_images(a					)

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

								if do_resize and size is None or resample is None:
										raise ValueError("""Size and resample must be specified if do_resize is True."""					)

								if do_resize and size["shortest_edge"] < 3_84 and crop_pct is None:
										raise ValueError("""crop_pct must be specified if size < 384."""					)

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

								if do_normalize and (image_mean is None or image_std is None):
										raise ValueError("""Image mean and std must be specified if do_normalize is True."""					)

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

								if do_resize:
										_UpperCamelCase         =						[self.resize(image=a							,				size=a							,				crop_pct=a							,				resample=a					) for image in images]

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

								if do_normalize:
										_UpperCamelCase         =						[self.normalize(image=a							,				mean=a							,				std=a					) for image in images]

								_UpperCamelCase         =						[to_channel_dimension_format(a							,				a					) for image in images]

								_UpperCamelCase         =						{"""pixel_values""": images}
								return BatchFeature(data=a							,				tensor_type=a					)



