code: 
  
  import itertools
  
  
  
  
  def     UpperCAmelCase__       (    _A   :				int = 1_00_00_00							):
  
  
  
  
  
    '''simple docstring'''
  
  
  
  
  
  
  
    a__						=[1]
  
    for i in itertools.count(len(_A							)							):
      a__						=0
      for j in itertools.count(1							):
        a__						=-1 if j % 2 == 0 else +1
        a__						=(j * j * 3 - j) // 2
        if index > i:
          break
        item += partitions[i - index] * sign
        item %= number
        index += j
        if index > i:
          break
        item += partitions[i - index] * sign
        item %= number
  
      if item == 0:
        return i
      partitions.append(_A							)
  
    return 0
  
  
  if __name__ == "__main__":
         import doctest
  
         doctest.testmod()
  
         print(f"""{solution() = }""")
  
style_context: 
  
  from dataclasses import dataclass
  from typing import List, Optional, Union
  
  import numpy as np
  import PIL
  from PIL import Image
  
  from ...utils import BaseOutput, is_torch_available, is_transformers_available
  
  
  
  
  
  
  
  @dataclass
  # Copied from diffusers.pipelines.stable_diffusion.__init__.StableDiffusionPipelineOutput with Stable->Alt
  class 		__magic_name__    (							lowerCamelCase__							):
  
     '''simple docstring'''
  
  
  
  
     lowerCamelCase__				:			Union[List[PIL.Image.Image], np.ndarray]
     lowerCamelCase__				:			Optional[List[bool]]
  
  
  if is_transformers_available() and is_torch_available():
         from .modeling_roberta_series import RobertaSeriesModelWithTransformation
         from .pipeline_alt_diffusion import AltDiffusionPipeline
         from .pipeline_alt_diffusion_imgaimg import AltDiffusionImgaImgPipeline
  