

'''simple docstring'''

lowercase__			    =			[sum(int(c, 10) ** 2 for c in i.__str__()) for i in range(100000)]




def       UpperCamelCase(     UpperCAmelCase_	):
 UpperCAmelCase       :	int											= 0
 while number:
  # Increased Speed Slightly by checking every 5 digits together.
  sum_of_digits_squared += DIGITS_SQUARED[number % 10_00_00]
  number //= 10_00_00

 return sum_of_digits_squared


# There are 2 Chains made,
# One ends with 89 with the chain member 58 being the one which when declared first,
# there will be the least number of iterations for all the members to be checked.

# The other one ends with 1 and has only one element 1.

# So 58 and 1 are chosen to be declared at the starting.

# Changed dictionary to an array to quicken the solution
lowercase__			    =			[None] * 10000000
lowercase__			    =			True
lowercase__			    =			False




def       UpperCamelCase(     UpperCAmelCase_	):


 if CHAINS[number - 1] is not None:
  return CHAINS[number - 1]  # type: ignore

 UpperCAmelCase       :	Union[str, Any]											= chain(next_number(UpperCamelCase_	)	)
 UpperCAmelCase       :	Optional[int]											= number_chain

 while number < 10_00_00_00:
  UpperCAmelCase       :	Any											= number_chain
  number *= 10

 return number_chain




def       UpperCamelCase(     UpperCAmelCase_ = 10_00_00_00	):


 for i in range(1  ,       UpperCamelCase_	):
  if CHAINS[i] is None:
   chain(i + 1	)

 return CHAINS[:number].count(UpperCamelCase_	)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 print(f'''{solution() = }''')






from typing import List, Optional, Union

import numpy as np
import PIL.Image

from ...image_processing_utils import BaseImageProcessor, BatchFeature
from ...image_transforms import rescale, resize, to_channel_dimension_format
from ...image_utils import (
    ChannelDimension,
    PILImageResampling,
    get_image_size,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, logging


__snake_case								=  logging.get_logger(__name__)




class 						lowercase__  (						_UpperCAmelCase  ):
	A__    :   List[str]				       =["""pixel_values"""]
	def __init__(			self							:   Dict       ,   UpperCAmelCase_							:   bool = True       ,   UpperCAmelCase_							:   int = 32       ,   UpperCAmelCase_							:   int=PILImageResampling.BILINEAR       ,   UpperCAmelCase_							:   bool = True       ,   **UpperCAmelCase_							:   Any       ,   ):
						SCREAMING_SNAKE_CASE__													= do_resize
						SCREAMING_SNAKE_CASE__													= do_rescale
						SCREAMING_SNAKE_CASE__													= size_divisor
						SCREAMING_SNAKE_CASE__													= resample
						super().__init__(**UpperCAmelCase_							)
	def      A_				(			self							:   Optional[int]       ,   UpperCAmelCase_							:   np.ndarray       ,   UpperCAmelCase_							:   int       ,   UpperCAmelCase_							:   Dict       ,   UpperCAmelCase_							:   Optional[ChannelDimension] = None       ,   **UpperCAmelCase_							:   Dict							):
						SCREAMING_SNAKE_CASE__						, SCREAMING_SNAKE_CASE__													= get_image_size(UpperCAmelCase_							)
						# Rounds the height and width down to the closest multiple of size_divisor
						SCREAMING_SNAKE_CASE__													= height // size_divisor * size_divisor
						SCREAMING_SNAKE_CASE__													= width // size_divisor * size_divisor
						SCREAMING_SNAKE_CASE__													= resize(UpperCAmelCase_       ,   (new_h, new_w)       ,   resample=UpperCAmelCase_       ,   data_format=UpperCAmelCase_       ,   **UpperCAmelCase_							)
						return image
	def      A_				(			self							:   Any       ,   UpperCAmelCase_							:   np.ndarray       ,   UpperCAmelCase_							:   float       ,   UpperCAmelCase_							:   Optional[ChannelDimension] = None       ,   **UpperCAmelCase_							:   List[str]							):
						return rescale(image=UpperCAmelCase_       ,   scale=UpperCAmelCase_       ,   data_format=UpperCAmelCase_       ,   **UpperCAmelCase_							)





	def      A_				(			self							:   Dict       ,   UpperCAmelCase_							:   Union["PIL.Image.Image", TensorType, List["PIL.Image.Image"], List[TensorType]]       ,   UpperCAmelCase_							:   Optional[bool] = None       ,   UpperCAmelCase_							:   Optional[int] = None       ,   UpperCAmelCase_							:   List[str]=None       ,   UpperCAmelCase_							:   Optional[bool] = None       ,   UpperCAmelCase_							:   Optional[Union[TensorType, str]] = None       ,   UpperCAmelCase_							:   ChannelDimension = ChannelDimension.FIRST       ,   **UpperCAmelCase_							:   List[Any]       ,   ):
						SCREAMING_SNAKE_CASE__													= do_resize if do_resize is not None else self.do_resize
						SCREAMING_SNAKE_CASE__													= do_rescale if do_rescale is not None else self.do_rescale
						SCREAMING_SNAKE_CASE__													= size_divisor if size_divisor is not None else self.size_divisor
						SCREAMING_SNAKE_CASE__													= resample if resample is not None else self.resample

						if do_resize and size_divisor is None:
											raise ValueError('size_divisor is required for resizing'							)

						SCREAMING_SNAKE_CASE__													= make_list_of_images(UpperCAmelCase_							)

						if not valid_images(UpperCAmelCase_							):
											raise ValueError('Invalid image(s)'							)

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

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

						if do_rescale:
											SCREAMING_SNAKE_CASE__													= [self.rescale(UpperCAmelCase_       ,   scale=1 / 255							) for image in images]

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

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





