def      __SCREAMING_SNAKE_CASE  ( __UpperCamelCase   :	Dict=2_81_23     )							-> str:







		"""simple docstring"""





		SCREAMING_SNAKE_CASE__      							=				[1] * (limit + 1)

		for i in range(2			,					int(limit**0.5     ) + 1     ):
				sum_divs[i * i] += i
				for k in range(i + 1			,					limit // i + 1     ):
						sum_divs[k * i] += k + i

		SCREAMING_SNAKE_CASE__      							=				set()
		SCREAMING_SNAKE_CASE__      							=				0

		for n in range(1			,					limit + 1     ):
				if sum_divs[n] > n:
						abundants.add(__UpperCamelCase     )

				if not any((n - a in abundants) for a in abundants     ):
						res += n

		return res


if __name__ == "__main__":
			print(solution())

from typing import Dict, List, Optional, Tuple, Union

import numpy as np

from ...image_processing_utils import BaseImageProcessor, BatchFeature, get_size_dict
from ...image_transforms import (
    center_crop,
    flip_channel_order,
    get_resize_output_image_size,
    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_torch_available, is_torch_tensor, is_vision_available, logging


if is_vision_available():
   import PIL

if is_torch_available():
   import torch


__lowerCamelCase      :			int							       =		logging.get_logger(__name__)







class __snake_case    (						lowerCamelCase_		):
   lowerCAmelCase_														=							["pixel_values"]




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



     """simple docstring"""






     super().__init__(**_lowercase				)
     SCREAMING_SNAKE_CASE__      							=				size if size is not None else {"""shortest_edge""": 2_24}
     SCREAMING_SNAKE_CASE__      							=				get_size_dict(_lowercase	,     default_to_square=_lowercase				)
     SCREAMING_SNAKE_CASE__      							=				crop_size if crop_size is not None else {"""height""": 2_56, """width""": 2_56}
     SCREAMING_SNAKE_CASE__      							=				get_size_dict(_lowercase	,     param_name="""crop_size"""				)

     SCREAMING_SNAKE_CASE__      							=				do_resize
     SCREAMING_SNAKE_CASE__      							=				size
     SCREAMING_SNAKE_CASE__      							=				resample
     SCREAMING_SNAKE_CASE__      							=				do_rescale
     SCREAMING_SNAKE_CASE__      							=				rescale_factor
     SCREAMING_SNAKE_CASE__      							=				do_center_crop
     SCREAMING_SNAKE_CASE__      							=				crop_size
     SCREAMING_SNAKE_CASE__      							=				do_flip_channel_order




   def      __a						(   self      :    List[Any]	,     _lowercase      :    np.ndarray	,     _lowercase      :    Dict[str, int]	,     _lowercase      :    PILImageResampling = PIL.Image.BILINEAR	,     _lowercase      :    Optional[Union[str, ChannelDimension]] = None	,     **_lowercase      :    str	,     ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__      							=				get_size_dict(_lowercase	,     default_to_square=_lowercase				)
     if "shortest_edge" not in size:
       raise ValueError(f"""The `size` dictionary must contain the key `shortest_edge`. Got {size.keys()}"""				)
     SCREAMING_SNAKE_CASE__      							=				get_resize_output_image_size(_lowercase	,     size=size["""shortest_edge"""]	,     default_to_square=_lowercase				)
     return resize(_lowercase	,     size=_lowercase	,     resample=_lowercase	,     data_format=_lowercase	,     **_lowercase				)




   def      __a						(   self      :    str	,     _lowercase      :    np.ndarray	,     _lowercase      :    Dict[str, int]	,     _lowercase      :    Optional[Union[str, ChannelDimension]] = None	,     **_lowercase      :    Any	,     ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__      							=				get_size_dict(_lowercase				)
     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()}"""				)
     return center_crop(_lowercase	,     size=(size["""height"""], size["""width"""])	,     data_format=_lowercase	,     **_lowercase				)




   def      __a						(   self      :    Optional[Any]	,     _lowercase      :    np.ndarray	,     _lowercase      :    Union[int, float]	,     _lowercase      :    Optional[Union[str, ChannelDimension]] = None	,     **_lowercase      :    Any	,     ):



     """simple docstring"""






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




   def      __a						(   self      :    Tuple	,     _lowercase      :    np.ndarray	,     _lowercase      :    Optional[Union[str, ChannelDimension]] = None				):



     """simple docstring"""






     return flip_channel_order(_lowercase	,     data_format=_lowercase				)




   def      __a						(   self      :    List[str]	,     _lowercase      :    ImageInput	,     _lowercase      :    bool = None	,     _lowercase      :    Dict[str, int] = None	,     _lowercase      :    PILImageResampling = None	,     _lowercase      :    bool = None	,     _lowercase      :    float = None	,     _lowercase      :    bool = None	,     _lowercase      :    Dict[str, int] = None	,     _lowercase      :    bool = None	,     _lowercase      :    Optional[Union[str, TensorType]] = None	,     _lowercase      :    ChannelDimension = ChannelDimension.FIRST	,     **_lowercase      :    int	,     ):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__      							=				do_resize if do_resize is not None else self.do_resize
     SCREAMING_SNAKE_CASE__      							=				resample if resample is not None else self.resample
     SCREAMING_SNAKE_CASE__      							=				do_rescale if do_rescale is not None else self.do_rescale
     SCREAMING_SNAKE_CASE__      							=				rescale_factor if rescale_factor is not None else self.rescale_factor
     SCREAMING_SNAKE_CASE__      							=				do_center_crop if do_center_crop is not None else self.do_center_crop
     SCREAMING_SNAKE_CASE__      							=				(
         do_flip_channel_order if do_flip_channel_order is not None else self.do_flip_channel_order
     )

     SCREAMING_SNAKE_CASE__      							=				size if size is not None else self.size
     SCREAMING_SNAKE_CASE__      							=				get_size_dict(_lowercase	,     default_to_square=_lowercase				)
     SCREAMING_SNAKE_CASE__      							=				crop_size if crop_size is not None else self.crop_size
     SCREAMING_SNAKE_CASE__      							=				get_size_dict(_lowercase	,     param_name="""crop_size"""				)

     SCREAMING_SNAKE_CASE__      							=				make_list_of_images(_lowercase				)

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

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

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

     if do_center_crop:
       SCREAMING_SNAKE_CASE__      							=				[self.center_crop(image=_lowercase	,     size=_lowercase				) for image in images]

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

     # the pretrained checkpoints assume images are BGR, not RGB
     if do_flip_channel_order:
       SCREAMING_SNAKE_CASE__      							=				[self.flip_channel_order(image=_lowercase				) for image in images]

     SCREAMING_SNAKE_CASE__      							=				[to_channel_dimension_format(_lowercase	,     _lowercase				) for image in images]

     SCREAMING_SNAKE_CASE__      							=				{"""pixel_values""": images}
     return BatchFeature(data=_lowercase	,     tensor_type=_lowercase				)




   def      __a						(   self      :    List[Any]	,     _lowercase      :    Dict	,     _lowercase      :    List[Tuple] = None				):



     """simple docstring"""






     SCREAMING_SNAKE_CASE__      							=				outputs.logits

     # Resize logits and compute semantic segmentation maps
     if target_sizes is not None:
       if len(_lowercase				) != len(_lowercase				):
         raise ValueError(
             """Make sure that you pass in as many target sizes as the batch dimension of the logits"""				)

       if is_torch_tensor(_lowercase				):
         SCREAMING_SNAKE_CASE__      							=				target_sizes.numpy()

       SCREAMING_SNAKE_CASE__      							=				[]

       for idx in range(len(_lowercase				)				):
         SCREAMING_SNAKE_CASE__      							=				torch.nn.functional.interpolate(
             logits[idx].unsqueeze(dim=0				)	,     size=target_sizes[idx]	,     mode="""bilinear"""	,     align_corners=_lowercase				)
         SCREAMING_SNAKE_CASE__      							=				resized_logits[0].argmax(dim=0				)
         semantic_segmentation.append(_lowercase				)
     else:
       SCREAMING_SNAKE_CASE__      							=				logits.argmax(dim=1				)
       SCREAMING_SNAKE_CASE__      							=				[semantic_segmentation[i] for i in range(semantic_segmentation.shape[0]				)]

     return semantic_segmentation
