






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, 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


__UpperCAmelCase     							=						logging.get_logger(__name__)



class   lowerCamelCase				(_snake_case      ):







		'''simple docstring'''



		_snake_case   :   int							=  ['''pixel_values''']



		def __init__(							self    ,		_UpperCamelCase = True    ,		_UpperCamelCase = None    ,		_UpperCamelCase = PIL.Image.BICUBIC    ,		_UpperCamelCase = True    ,		_UpperCamelCase = None    ,		_UpperCamelCase = 1 / 2_5_5    ,		_UpperCamelCase = True    ,		_UpperCamelCase = True    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		**_UpperCamelCase    ,		)     ->							None:
							super().__init__(**_UpperCamelCase       )
							UpperCAmelCase_   :				Optional[Any]						=						size if size is not None else {'height': 2_5_6, 'width': 2_5_6}
							UpperCAmelCase_   :				str						=						get_size_dict(_UpperCamelCase       )
							UpperCAmelCase_   :				Any						=						crop_size if crop_size is not None else {'height': 2_2_4, 'width': 2_2_4}
							UpperCAmelCase_   :				Optional[int]						=						get_size_dict(_UpperCamelCase    ,		param_name='crop_size'       )

							UpperCAmelCase_   :				Dict						=						do_resize
							UpperCAmelCase_   :				str						=						size
							UpperCAmelCase_   :				str						=						resample
							UpperCAmelCase_   :				Tuple						=						do_center_crop
							UpperCAmelCase_   :				Union[str, Any]						=						crop_size
							UpperCAmelCase_   :				Dict						=						do_rescale
							UpperCAmelCase_   :				Dict						=						rescale_factor
							UpperCAmelCase_   :				str						=						do_normalize
							UpperCAmelCase_   :				Optional[int]						=						image_mean if image_mean is not None else IMAGENET_STANDARD_MEAN
							UpperCAmelCase_   :				Dict						=						image_std if image_std is not None else IMAGENET_STANDARD_STD



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase = PIL.Image.BICUBIC    ,		_UpperCamelCase = None    ,		**_UpperCamelCase    ,		)     ->							np.ndarray:
							UpperCAmelCase_   :				List[str]						=						get_size_dict(_UpperCamelCase       )
							if "height" not in size or "width" not in size:
												raise ValueError(f"The size dictionary must have keys 'height' and 'width'. Got {size.keys()}"       )
							return resize(
							    _UpperCamelCase    ,		size=(size['height'], size['width'])    ,		resample=_UpperCamelCase    ,		data_format=_UpperCamelCase    ,		**_UpperCamelCase       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase = None    ,		**_UpperCamelCase    ,		)     ->							np.ndarray:
							UpperCAmelCase_   :				Union[str, Any]						=						get_size_dict(_UpperCamelCase       )
							if "height" not in size or "width" not in size:
												raise ValueError(f"The size dictionary must have keys 'height' and 'width'. Got {size.keys()}"       )
							return center_crop(_UpperCamelCase    ,		size=(size['height'], size['width'])    ,		data_format=_UpperCamelCase    ,		**_UpperCamelCase       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase = None    ,		**_UpperCamelCase    ,		)     ->							Union[str, Any]:
							return rescale(_UpperCamelCase    ,		scale=_UpperCamelCase    ,		data_format=_UpperCamelCase    ,		**_UpperCamelCase       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase = None    ,		**_UpperCamelCase    ,		)     ->							np.ndarray:
							return normalize(_UpperCamelCase    ,		mean=_UpperCamelCase    ,		std=_UpperCamelCase    ,		data_format=_UpperCamelCase    ,		**_UpperCamelCase       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase=None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = ChannelDimension.FIRST    ,		**_UpperCamelCase    ,		)     ->							PIL.Image.Image:
							UpperCAmelCase_   :				int						=						do_resize if do_resize is not None else self.do_resize
							UpperCAmelCase_   :				List[str]						=						resample if resample is not None else self.resample
							UpperCAmelCase_   :				Tuple						=						do_center_crop if do_center_crop is not None else self.do_center_crop
							UpperCAmelCase_   :				Any						=						do_rescale if do_rescale is not None else self.do_rescale
							UpperCAmelCase_   :				Optional[int]						=						rescale_factor if rescale_factor is not None else self.rescale_factor
							UpperCAmelCase_   :				Any						=						do_normalize if do_normalize is not None else self.do_normalize
							UpperCAmelCase_   :				List[str]						=						image_mean if image_mean is not None else self.image_mean
							UpperCAmelCase_   :				Dict						=						image_std if image_std is not None else self.image_std

							UpperCAmelCase_   :				Any						=						size if size is not None else self.size
							UpperCAmelCase_   :				int						=						get_size_dict(_UpperCamelCase       )
							UpperCAmelCase_   :				Any						=						crop_size if crop_size is not None else self.crop_size
							UpperCAmelCase_   :				List[str]						=						get_size_dict(_UpperCamelCase    ,		param_name='crop_size'       )

							UpperCAmelCase_   :				Tuple						=						make_list_of_images(_UpperCamelCase       )

							if not valid_images(_UpperCamelCase       ):
												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_center_crop and crop_size is None:
												raise ValueError('Crop size must be specified if do_center_crop is True.'       )

							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_   :				Any						=						[to_numpy_array(_UpperCamelCase       ) for image in images]

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

							if do_center_crop:
												UpperCAmelCase_   :				Tuple						=						[self.center_crop(image=_UpperCamelCase    ,		size=_UpperCamelCase       ) for image in images]

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

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

							UpperCAmelCase_   :				Tuple						=						[to_channel_dimension_format(_UpperCamelCase    ,		_UpperCamelCase       ) for image in images]

							UpperCAmelCase_   :				Any						=						{'pixel_values': images}
							return BatchFeature(data=_UpperCamelCase    ,		tensor_type=_UpperCamelCase       )














from collections import defaultdict
from math import ceil, sqrt




def 					lowercase__				(					__snake_case   :							int = 1_000_000					,	__snake_case   :							int = 10  ):


					'''simple docstring'''


					UpperCAmelCase_   :				defaultdict						=						defaultdict(__snake_case  )

					for outer_width in range(3					,	(t_limit // 4) + 2  ):
										if outer_width * outer_width > t_limit:
															UpperCAmelCase_   :				Union[str, Any]						=						max(
															    ceil(sqrt(outer_width * outer_width - t_limit  )  )					,	1  )
										else:
															UpperCAmelCase_   :				int						=						1

										hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

										for hole_width in range(__snake_case					,	outer_width - 1					,	2  ):
															count[outer_width * outer_width - hole_width * hole_width] += 1

					return sum(1 for n in count.values() if 1 <= n <= 10  )


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






