
"""simple docstring"""





_a		       =							[sum(int(c, 10) ** 2 for c in i.__str__()) for i in range(100_000)]







def 	__a     (		__lowerCamelCase  ):
   UpperCAmelCase_					:					Optional[Any]			     =    0
   while number:
      # Increased Speed Slightly by checking every 5 digits together.
      sum_of_digits_squared += DIGITS_SQUARED[number % 10_0000]
      number //= 10_0000

   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
_a		       =							[None] * 10_000_000
_a		       =							True
_a		       =							False







def 	__a     (		__lowerCamelCase  ):

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

   UpperCAmelCase_					:					List[Any]			     =    chain(next_number(__lowerCamelCase  )  )
   UpperCAmelCase_					:					List[Any]			     =    number_chain

   while number < 1000_0000:
      UpperCAmelCase_					:					Dict			     =    number_chain
      number *= 10

   return number_chain







def 	__a     (		__lowerCamelCase = 1000_0000  ):
   for i in range(1,		__lowerCamelCase  ):
      if CHAINS[i] is None:
         chain(i + 1  )

   return CHAINS[:number].count(__lowerCamelCase  )


if __name__ == "__main__":
    import doctest

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









"""simple docstring"""



import unittest

import numpy as np
import requests

from transformers.testing_utils import require_torch, require_vision
from transformers.utils import is_torch_available, is_vision_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
       import torch

       from transformers.pytorch_utils import is_torch_greater_or_equal_than_1_11
else:
       a_ =			False

if is_vision_available():
       from PIL import Image

       from transformers import PixaStructImageProcessor






class 		__snake_case					(		unittest.TestCase     ):





 """simple docstring"""


 def __init__(    self					,						__lowerCamelCase					,						__lowerCamelCase=7					,						__lowerCamelCase=3					,						__lowerCamelCase=18					,						__lowerCamelCase=30					,						__lowerCamelCase=400					,						__lowerCamelCase=None					,						__lowerCamelCase=True					,						__lowerCamelCase=True					,						__lowerCamelCase=None					,						):



     '''simple docstring'''




     __A    :						str						 =     size if size is not None else {'''height''': 20, '''width''': 20}
     __A    :						Dict						 =     parent
     __A    :						Union[str, Any]						 =     batch_size
     __A    :						List[Any]						 =     num_channels
     __A    :						Union[str, Any]						 =     image_size
     __A    :						Any						 =     min_resolution
     __A    :						str						 =     max_resolution
     __A    :						Any						 =     size
     __A    :						Dict						 =     do_normalize
     __A    :						str						 =     do_convert_rgb
     __A    :						List[Any]						 =     [512, 1024, 2048, 4096]
     __A    :						Dict						 =     patch_size if patch_size is not None else {'''height''': 16, '''width''': 16}

 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     return {"do_normalize": self.do_normalize, "do_convert_rgb": self.do_convert_rgb}







 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						List[str]						 =     '''https://huggingface.co/datasets/huggingface/documentation-images/resolve/main/transformers/tasks/australia.jpg'''
     __A    :						Optional[Any]						 =     Image.open(requests.get(__lowerCamelCase					,						stream=__lowerCamelCase  ).raw  ).convert('''RGB'''  )
     return raw_image






@unittest.skipIf(
    not is_torch_greater_or_equal_than_1_11							,							reason="""`Pix2StructImageProcessor` requires `torch>=1.11.0`."""							,							)
@require_torch
@require_vision
class 		__snake_case					(		SCREAMING_SNAKE_CASE__							,							unittest.TestCase     ):





 """simple docstring"""


 _lowerCamelCase        =     PixaStructImageProcessor if is_vision_available() else None

 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						str						 =     PixaStructImageProcessingTester(self  )

 @property
 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     return self.image_processor_tester.prepare_image_processor_dict()

 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						Any						 =     self.image_processing_class(**self.image_processor_dict  )
     self.assertTrue(hasattr(__lowerCamelCase					,						'''do_normalize'''  )  )
     self.assertTrue(hasattr(__lowerCamelCase					,						'''do_convert_rgb'''  )  )

 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						Tuple						 =     self.image_processor_tester.prepare_dummy_image()

     __A    :						Optional[int]						 =     self.image_processing_class(**self.image_processor_dict  )
     __A    :						Dict						 =     2048

     __A    :						Any						 =     image_processor(__lowerCamelCase					,						return_tensors='''pt'''					,						max_patches=__lowerCamelCase  )
     self.assertTrue(torch.allclose(inputs.flattened_patches.mean()					,						torch.tensor(0.0_6_0_6  )					,						atol=1e-3					,						rtol=1e-3  )  )

 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						List[Any]						 =     self.image_processing_class(**self.image_processor_dict  )
     # create random PIL images
     __A    :						str						 =     prepare_image_inputs(self.image_processor_tester					,						equal_resolution=__lowerCamelCase  )
     for image in image_inputs:
         self.assertIsInstance(__lowerCamelCase					,						Image.Image  )

     # Test not batched input
     __A    :						List[str]						 =     (
         (self.image_processor_tester.patch_size['''height'''] * self.image_processor_tester.patch_size['''width'''])
         * self.image_processor_tester.num_channels
     ) + 2

     for max_patch in self.image_processor_tester.max_patches:
         # Test not batched input
         __A    :						Dict						 =     image_processor(
             image_inputs[0]					,						return_tensors='''pt'''					,						max_patches=__lowerCamelCase  ).flattened_patches
         self.assertEqual(
             encoded_images.shape					,						(1, max_patch, expected_hidden_dim)					,						)

         # Test batched
         __A    :						Tuple						 =     image_processor(
             __lowerCamelCase					,						return_tensors='''pt'''					,						max_patches=__lowerCamelCase  ).flattened_patches
         self.assertEqual(
             encoded_images.shape					,						(self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)					,						)

 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						List[str]						 =     self.image_processing_class(**self.image_processor_dict  )
     # create random PIL images
     __A    :						Union[str, Any]						 =     prepare_image_inputs(self.image_processor_tester					,						equal_resolution=__lowerCamelCase  )
     for image in image_inputs:
         self.assertIsInstance(__lowerCamelCase					,						Image.Image  )

     # Test not batched input
     __A    :						Tuple						 =     (
         (self.image_processor_tester.patch_size['''height'''] * self.image_processor_tester.patch_size['''width'''])
         * self.image_processor_tester.num_channels
     ) + 2

     __A    :						str						 =     True

     for max_patch in self.image_processor_tester.max_patches:
         # Test not batched input
         with self.assertRaises(__lowerCamelCase  ):
             __A    :						List[Any]						 =     image_processor(
                 image_inputs[0]					,						return_tensors='''pt'''					,						max_patches=__lowerCamelCase  ).flattened_patches

         __A    :						Any						 =     '''Hello'''

         __A    :						Tuple						 =     image_processor(
             image_inputs[0]					,						return_tensors='''pt'''					,						max_patches=__lowerCamelCase					,						header_text=__lowerCamelCase  ).flattened_patches
         self.assertEqual(
             encoded_images.shape					,						(1, max_patch, expected_hidden_dim)					,						)

         # Test batched
         __A    :						Union[str, Any]						 =     image_processor(
             __lowerCamelCase					,						return_tensors='''pt'''					,						max_patches=__lowerCamelCase					,						header_text=__lowerCamelCase  ).flattened_patches
         self.assertEqual(
             encoded_images.shape					,						(self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)					,						)

 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						int						 =     self.image_processing_class(**self.image_processor_dict  )
     # create random numpy tensors
     __A    :						Dict						 =     prepare_image_inputs(self.image_processor_tester					,						equal_resolution=__lowerCamelCase					,						numpify=__lowerCamelCase  )
     for image in image_inputs:
         self.assertIsInstance(__lowerCamelCase					,						np.ndarray  )

     __A    :						List[Any]						 =     (
         (self.image_processor_tester.patch_size['''height'''] * self.image_processor_tester.patch_size['''width'''])
         * self.image_processor_tester.num_channels
     ) + 2

     for max_patch in self.image_processor_tester.max_patches:
         # Test not batched input
         __A    :						List[str]						 =     image_processor(
             image_inputs[0]					,						return_tensors='''pt'''					,						max_patches=__lowerCamelCase  ).flattened_patches
         self.assertEqual(
             encoded_images.shape					,						(1, max_patch, expected_hidden_dim)					,						)

         # Test batched
         __A    :						Union[str, Any]						 =     image_processor(
             __lowerCamelCase					,						return_tensors='''pt'''					,						max_patches=__lowerCamelCase  ).flattened_patches
         self.assertEqual(
             encoded_images.shape					,						(self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)					,						)







 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						int						 =     self.image_processing_class(**self.image_processor_dict  )
     # create random PyTorch tensors
     __A    :						Optional[Any]						 =     prepare_image_inputs(self.image_processor_tester					,						equal_resolution=__lowerCamelCase					,						torchify=__lowerCamelCase  )
     for image in image_inputs:
         self.assertIsInstance(__lowerCamelCase					,						torch.Tensor  )

     # Test not batched input
     __A    :						int						 =     (
         (self.image_processor_tester.patch_size['''height'''] * self.image_processor_tester.patch_size['''width'''])
         * self.image_processor_tester.num_channels
     ) + 2

     for max_patch in self.image_processor_tester.max_patches:
         # Test not batched input
         __A    :						List[Any]						 =     image_processor(
             image_inputs[0]					,						return_tensors='''pt'''					,						max_patches=__lowerCamelCase  ).flattened_patches
         self.assertEqual(
             encoded_images.shape					,						(1, max_patch, expected_hidden_dim)					,						)

         # Test batched
         __A    :						Dict						 =     image_processor(
             __lowerCamelCase					,						return_tensors='''pt'''					,						max_patches=__lowerCamelCase  ).flattened_patches
         self.assertEqual(
             encoded_images.shape					,						(self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)					,						)






@unittest.skipIf(
    not is_torch_greater_or_equal_than_1_11							,							reason="""`Pix2StructImageProcessor` requires `torch>=1.11.0`."""							,							)
@require_torch
@require_vision
class 		__snake_case					(		SCREAMING_SNAKE_CASE__							,							unittest.TestCase     ):





 """simple docstring"""


 _lowerCamelCase        =     PixaStructImageProcessor if is_vision_available() else None

 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						int						 =     PixaStructImageProcessingTester(self					,						num_channels=4  )
     __A    :						Any						 =     3

 @property
 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     return self.image_processor_tester.prepare_image_processor_dict()

 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						Union[str, Any]						 =     self.image_processing_class(**self.image_processor_dict  )
     self.assertTrue(hasattr(__lowerCamelCase					,						'''do_normalize'''  )  )
     self.assertTrue(hasattr(__lowerCamelCase					,						'''do_convert_rgb'''  )  )







 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						Optional[int]						 =     self.image_processing_class(**self.image_processor_dict  )
     # create random PIL images
     __A    :						Dict						 =     prepare_image_inputs(self.image_processor_tester					,						equal_resolution=__lowerCamelCase  )
     for image in image_inputs:
         self.assertIsInstance(__lowerCamelCase					,						Image.Image  )

     # Test not batched input
     __A    :						List[Any]						 =     (
         (self.image_processor_tester.patch_size['''height'''] * self.image_processor_tester.patch_size['''width'''])
         * (self.image_processor_tester.num_channels - 1)
     ) + 2

     for max_patch in self.image_processor_tester.max_patches:
         # Test not batched input
         __A    :						Any						 =     image_processor(
             image_inputs[0]					,						return_tensors='''pt'''					,						max_patches=__lowerCamelCase  ).flattened_patches
         self.assertEqual(
             encoded_images.shape					,						(1, max_patch, expected_hidden_dim)					,						)

         # Test batched
         __A    :						int						 =     image_processor(
             __lowerCamelCase					,						return_tensors='''pt'''					,						max_patches=__lowerCamelCase  ).flattened_patches
         self.assertEqual(
             encoded_images.shape					,						(self.image_processor_tester.batch_size, max_patch, expected_hidden_dim)					,						)




