





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


A    :					Any =      logging.get_logger(__name__)


class   A			(SCREAMING_SNAKE_CASE    ):
			'''simple docstring'''




			__lowerCamelCase	:       Tuple							=    ['''pixel_values''']






			def __init__(			self   :    int							,	__lowerCAmelCase   :    bool = True							,	__lowerCAmelCase   :    Dict[str, int] = None							,	__lowerCAmelCase   :    float = None							,	__lowerCAmelCase   :    PILImageResampling = PILImageResampling.BILINEAR							,	__lowerCAmelCase   :    bool = True							,	__lowerCAmelCase   :    Union[int, float] = 1 / 2_55							,	__lowerCAmelCase   :    bool = True							,	__lowerCAmelCase   :    Optional[Union[float, List[float]]] = None							,	__lowerCAmelCase   :    Optional[Union[float, List[float]]] = None							,	**__lowerCAmelCase   :    Optional[int]							,	)	->	None:







					"""simple docstring"""






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

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






			def    a_       (			self   :    Tuple							,	__lowerCAmelCase   :    np.ndarray							,	__lowerCAmelCase   :    Dict[str, int]							,	__lowerCAmelCase   :    float							,	__lowerCAmelCase   :    PILImageResampling = PILImageResampling.BICUBIC							,	__lowerCAmelCase   :    Optional[Union[str, ChannelDimension]] = None							,	**__lowerCAmelCase   :    int							,	)	->	np.ndarray:







					"""simple docstring"""






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

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






			def    a_       (			self   :    str							,	__lowerCAmelCase   :    np.ndarray							,	__lowerCAmelCase   :    Union[int, float]							,	__lowerCAmelCase   :    Optional[Union[str, ChannelDimension]] = None							,	**__lowerCAmelCase   :    List[Any]							,	)	->	Union[str, Any]:







					"""simple docstring"""






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






			def    a_       (			self   :    Optional[int]							,	__lowerCAmelCase   :    np.ndarray							,	__lowerCAmelCase   :    Union[float, List[float]]							,	__lowerCAmelCase   :    Union[float, List[float]]							,	__lowerCAmelCase   :    Optional[Union[str, ChannelDimension]] = None							,	**__lowerCAmelCase   :    Tuple							,	)	->	np.ndarray:







					"""simple docstring"""






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







			def    a_       (			self   :    int							,	__lowerCAmelCase   :    ImageInput							,	__lowerCAmelCase   :    bool = None							,	__lowerCAmelCase   :    Dict[str, int] = None							,	__lowerCAmelCase   :    float = None							,	__lowerCAmelCase   :    PILImageResampling = None							,	__lowerCAmelCase   :    bool = None							,	__lowerCAmelCase   :    float = None							,	__lowerCAmelCase   :    bool = None							,	__lowerCAmelCase   :    Optional[Union[float, List[float]]] = None							,	__lowerCAmelCase   :    Optional[Union[float, List[float]]] = None							,	__lowerCAmelCase   :    Optional[Union[str, TensorType]] = None							,	__lowerCAmelCase   :    ChannelDimension = ChannelDimension.FIRST							,	**__lowerCAmelCase   :    str							,	)	->	PIL.Image.Image:







					"""simple docstring"""






					A__        =   do_resize if do_resize is not None else self.do_resize
					A__        =   crop_pct if crop_pct is not None else self.crop_pct
					A__        =   resample if resample is not None else self.resample
					A__        =   do_rescale if do_rescale is not None else self.do_rescale
					A__        =   rescale_factor if rescale_factor is not None else self.rescale_factor
					A__        =   do_normalize if do_normalize is not None else self.do_normalize
					A__        =   image_mean if image_mean is not None else self.image_mean
					A__        =   image_std if image_std is not None else self.image_std

					A__        =   size if size is not None else self.size
					A__        =   get_size_dict(__lowerCAmelCase							,	default_to_square=__lowerCAmelCase   )

					A__        =   make_list_of_images(__lowerCAmelCase   )

					if not valid_images(__lowerCAmelCase   ):
							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.
					A__        =   [to_numpy_array(__lowerCAmelCase   ) for image in images]

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

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

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

					A__        =   [to_channel_dimension_format(__lowerCAmelCase							,	__lowerCAmelCase   ) for image in images]

					A__        =   {"""pixel_values""": images}
					return BatchFeature(data=__lowerCAmelCase							,	tensor_type=__lowerCAmelCase   )










def    __lowerCamelCase					(							__a   :int = 1_0_0_0_0_0_0    )		->				int:






		"""simple docstring"""

		A__        =   limit + 1
		A__        =   [0] * limit
		for first_term in range(1    ,     __a    ):
				for n in range(__a    ,     __a    ,     __a    ):
						A__        =   first_term + n / first_term
						if common_difference % 4:  # d must be divisble by 4
								continue
						else:
								common_difference /= 4
								if (
								    first_term > common_difference
								    and first_term < 4 * common_difference
								):  # since x,y,z are positive integers
										frequency[n] += 1  # so z>0 and a>d ,also 4d<a

		A__        =   sum(1 for x in frequency[1:limit] if x == 1_0    )

		return count


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



