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 convert_to_rgb, normalize, rescale, resize, to_channel_dimension_format
from ...image_utils import (
    OPENAI_CLIP_MEAN,
    OPENAI_CLIP_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


lowercase_  : List[str]								=					logging.get_logger(__name__)






class 		_lowerCamelCase		( UpperCamelCase_     ):
    __a						=   ["pixel_values"]
    def __init__(	self			,			lowerCAmelCase = True			,			lowerCAmelCase = None			,			lowerCAmelCase = PILImageResampling.BICUBIC			,			lowerCAmelCase = True			,			lowerCAmelCase = 1 / 255			,			lowerCAmelCase = True			,			lowerCAmelCase = None			,			lowerCAmelCase = None			,			lowerCAmelCase = True			,			**lowerCAmelCase			,			)							->       None:
     super().__init__(**__A )
     SCREAMING_SNAKE_CASE__: List[Any]=   size if size is not None else {'''height''': 384, '''width''': 384}
     SCREAMING_SNAKE_CASE__: Any=   get_size_dict(__A			,			default_to_square=__A )

     SCREAMING_SNAKE_CASE__: str=   do_resize
     SCREAMING_SNAKE_CASE__: Union[str, Any]=   size
     SCREAMING_SNAKE_CASE__: List[Any]=   resample
     SCREAMING_SNAKE_CASE__: str=   do_rescale
     SCREAMING_SNAKE_CASE__: Optional[Any]=   rescale_factor
     SCREAMING_SNAKE_CASE__: Dict=   do_normalize
     SCREAMING_SNAKE_CASE__: List[Any]=   image_mean if image_mean is not None else OPENAI_CLIP_MEAN
     SCREAMING_SNAKE_CASE__: Optional[int]=   image_std if image_std is not None else OPENAI_CLIP_STD
     SCREAMING_SNAKE_CASE__: List[Any]=   do_convert_rgb
    def     UpperCamelCase_					(	self			,			lowerCAmelCase			,			lowerCAmelCase			,			lowerCAmelCase = PILImageResampling.BICUBIC			,			lowerCAmelCase = None			,			**lowerCAmelCase			,			)							->       np.ndarray:
     SCREAMING_SNAKE_CASE__: Any=   get_size_dict(__A			,			default_to_square=__A )
     if "height" not in size or "width" not in size:
      raise ValueError(f'The `size` dictionary must contain the keys `height` and `width`. Got {size.keys()}' )
     SCREAMING_SNAKE_CASE__: List[str]=   (size['''height'''], size['''width'''])
     return resize(__A			,			size=__A			,			resample=__A			,			data_format=__A			,			**__A )
    def     UpperCamelCase_					(	self			,			lowerCAmelCase			,			lowerCAmelCase			,			lowerCAmelCase = None			,			**lowerCAmelCase			,			)							->       str:
     return rescale(__A			,			scale=__A			,			data_format=__A			,			**__A )
    def     UpperCamelCase_					(	self			,			lowerCAmelCase			,			lowerCAmelCase			,			lowerCAmelCase			,			lowerCAmelCase = None			,			**lowerCAmelCase			,			)							->       np.ndarray:
     return normalize(__A			,			mean=__A			,			std=__A			,			data_format=__A			,			**__A )



    def     UpperCamelCase_					(	self			,			lowerCAmelCase			,			lowerCAmelCase = None			,			lowerCAmelCase = None			,			lowerCAmelCase = None			,			lowerCAmelCase = None			,			lowerCAmelCase = None			,			lowerCAmelCase = None			,			lowerCAmelCase = None			,			lowerCAmelCase = None			,			lowerCAmelCase = None			,			lowerCAmelCase = None			,			lowerCAmelCase = ChannelDimension.FIRST			,			**lowerCAmelCase			,			)							->       PIL.Image.Image:
     SCREAMING_SNAKE_CASE__: Tuple=   do_resize if do_resize is not None else self.do_resize
     SCREAMING_SNAKE_CASE__: List[Any]=   resample if resample is not None else self.resample
     SCREAMING_SNAKE_CASE__: List[Any]=   do_rescale if do_rescale is not None else self.do_rescale
     SCREAMING_SNAKE_CASE__: Optional[int]=   rescale_factor if rescale_factor is not None else self.rescale_factor
     SCREAMING_SNAKE_CASE__: Union[str, Any]=   do_normalize if do_normalize is not None else self.do_normalize
     SCREAMING_SNAKE_CASE__: List[str]=   image_mean if image_mean is not None else self.image_mean
     SCREAMING_SNAKE_CASE__: Tuple=   image_std if image_std is not None else self.image_std
     SCREAMING_SNAKE_CASE__: Optional[int]=   do_convert_rgb if do_convert_rgb is not None else self.do_convert_rgb

     SCREAMING_SNAKE_CASE__: List[Any]=   size if size is not None else self.size
     SCREAMING_SNAKE_CASE__: Union[str, Any]=   get_size_dict(__A			,			default_to_square=__A )

     SCREAMING_SNAKE_CASE__: Union[str, Any]=   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_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.''' )

     # PIL RGBA images are converted to RGB
     if do_convert_rgb:
      SCREAMING_SNAKE_CASE__: Optional[Any]=   [convert_to_rgb(__A ) for image in images]

     # All transformations expect numpy arrays.
     SCREAMING_SNAKE_CASE__: Tuple=   [to_numpy_array(__A ) for image in images]

     if do_resize:
      SCREAMING_SNAKE_CASE__: Optional[int]=   [self.resize(image=__A			,			size=__A			,			resample=__A ) for image in images]

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

     if do_normalize:
      SCREAMING_SNAKE_CASE__: Tuple=   [self.normalize(image=__A			,			mean=__A			,			std=__A ) for image in images]

     SCREAMING_SNAKE_CASE__: Optional[Any]=   [to_channel_dimension_format(__A			,			__A ) for image in images]

     SCREAMING_SNAKE_CASE__: List[Any]=   BatchFeature(data={'''pixel_values''': images}			,			tensor_type=__A )

     return encoded_outputs



from math import ceil, sqrt
def 							SCREAMING_SNAKE_CASE_	(					UpperCAmelCase_	:     int = 1_0_0_0_0_0_0				)			->						int:
       SCREAMING_SNAKE_CASE_							:				List[Any]		=0

       for outer_width in range(3			,							(limit // 4) + 2				):
              if outer_width**2 > limit:
                     SCREAMING_SNAKE_CASE_							:				List[str]		=max(ceil(sqrt(outer_width**2 - limit				)				)			,							1				)
              else:
                     SCREAMING_SNAKE_CASE_							:				List[str]		=1
              if (outer_width - hole_width_lower_bound) % 2:
                     hole_width_lower_bound += 1

              answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

       return answer


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