






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 rescale, resize, to_channel_dimension_format
from ...image_utils import (
    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__)




def 					lowercase__				(					__snake_case   :							Optional[int]					,	__snake_case   :							Dict  ):


					'''simple docstring'''


					UpperCAmelCase_   :				Optional[Any]						=						b.T
					UpperCAmelCase_   :				List[str]						=						np.sum(np.square(__snake_case  )					,	axis=1  )
					UpperCAmelCase_   :				str						=						np.sum(np.square(__snake_case  )					,	axis=0  )
					UpperCAmelCase_   :				Any						=						np.matmul(__snake_case					,	__snake_case  )
					UpperCAmelCase_   :				List[Any]						=						aa[:, None] - 2 * ab + ba[None, :]
					return d




def 					lowercase__				(					__snake_case   :							Union[str, Any]					,	__snake_case   :							Optional[Any]  ):


					'''simple docstring'''


					UpperCAmelCase_   :				int						=						x.reshape(-1					,	3  )
					UpperCAmelCase_   :				int						=						squared_euclidean_distance(__snake_case					,	__snake_case  )
					return np.argmin(__snake_case					,	axis=1  )






class   lowerCamelCase				(_snake_case      ):







		'''simple docstring'''



		_snake_case   :   List[str]							=  ['''pixel_values''']



		def __init__(							self    ,		_UpperCamelCase = None    ,		_UpperCamelCase = True    ,		_UpperCamelCase = None    ,		_UpperCamelCase = PILImageResampling.BILINEAR    ,		_UpperCamelCase = True    ,		_UpperCamelCase = True    ,		**_UpperCamelCase    ,		)     ->							None:
							super().__init__(**_UpperCamelCase       )
							UpperCAmelCase_   :				int						=						size if size is not None else {'height': 2_5_6, 'width': 2_5_6}
							UpperCAmelCase_   :				str						=						get_size_dict(_UpperCamelCase       )
							UpperCAmelCase_   :				List[Any]						=						np.array(_UpperCamelCase       ) if clusters is not None else None
							UpperCAmelCase_   :				str						=						do_resize
							UpperCAmelCase_   :				Tuple						=						size
							UpperCAmelCase_   :				Tuple						=						resample
							UpperCAmelCase_   :				Union[str, Any]						=						do_normalize
							UpperCAmelCase_   :				Tuple						=						do_color_quantize



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase    ,		_UpperCamelCase = PILImageResampling.BILINEAR    ,		_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"Size dictionary must contain both height and width keys. Got {size.keys()}"       )
							return resize(
							    _UpperCamelCase    ,		size=(size['height'], size['width'])    ,		resample=_UpperCamelCase    ,		data_format=_UpperCamelCase    ,		**_UpperCamelCase       )



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase = None    ,		)     ->							np.ndarray:
							UpperCAmelCase_   :				Any						=						rescale(image=_UpperCamelCase    ,		scale=1 / 1_27.5    ,		data_format=_UpperCamelCase       )
							UpperCAmelCase_   :				str						=						image - 1
							return image



		def  __UpperCAmelCase      (							self    ,		_UpperCamelCase    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = None    ,		_UpperCamelCase = ChannelDimension.FIRST    ,		**_UpperCamelCase    ,		)     ->							PIL.Image.Image:
							UpperCAmelCase_   :				Any						=						do_resize if do_resize is not None else self.do_resize
							UpperCAmelCase_   :				Dict						=						size if size is not None else self.size
							UpperCAmelCase_   :				Any						=						get_size_dict(_UpperCamelCase       )
							UpperCAmelCase_   :				Tuple						=						resample if resample is not None else self.resample
							UpperCAmelCase_   :				Any						=						do_normalize if do_normalize is not None else self.do_normalize
							UpperCAmelCase_   :				List[Any]						=						do_color_quantize if do_color_quantize is not None else self.do_color_quantize
							UpperCAmelCase_   :				str						=						clusters if clusters is not None else self.clusters
							UpperCAmelCase_   :				str						=						np.array(_UpperCamelCase       )

							UpperCAmelCase_   :				List[Any]						=						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_color_quantize and clusters is None:
												raise ValueError('Clusters must be specified if do_color_quantize is True.'       )

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

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

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

							if do_color_quantize:
												UpperCAmelCase_   :				Dict						=						[to_channel_dimension_format(_UpperCamelCase    ,		ChannelDimension.LAST       ) for image in images]
												# color quantize from (batch_size, height, width, 3) to (batch_size, height, width)
												UpperCAmelCase_   :				Any						=						np.array(_UpperCamelCase       )
												UpperCAmelCase_   :				List[str]						=						color_quantize(_UpperCamelCase    ,		_UpperCamelCase       ).reshape(images.shape[:-1]       )

												# flatten to (batch_size, height*width)
												UpperCAmelCase_   :				Optional[Any]						=						images.shape[0]
												UpperCAmelCase_   :				Dict						=						images.reshape(_UpperCamelCase    ,		-1       )

												# We need to convert back to a list of images to keep consistent behaviour across processors.
												UpperCAmelCase_   :				Tuple						=						list(_UpperCamelCase       )
							else:
												UpperCAmelCase_   :				List[str]						=						[to_channel_dimension_format(_UpperCamelCase    ,		_UpperCamelCase       ) for image in images]

							UpperCAmelCase_   :				Optional[Any]						=						{'input_ids': 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() = }')






