





"""simple docstring"""




def 						UpperCAmelCase__		(     _UpperCAmelCase ,					_UpperCAmelCase ,					_UpperCAmelCase					):






  """simple docstring"""





  return not any(
      neighbour == 1 and colored_vertices[i] == color
      for i, neighbour in enumerate(_UpperCAmelCase					)					)





def 						UpperCAmelCase__		(     _UpperCAmelCase ,					_UpperCAmelCase ,					_UpperCAmelCase ,					_UpperCAmelCase					):






  """simple docstring"""





  if index == len(_UpperCAmelCase					):
    return True

  # Recursive Step
  for i in range(_UpperCAmelCase					):
    if valid_coloring(graph[index] ,					_UpperCAmelCase ,					_UpperCAmelCase					):
      # Color current vertex
      A_  :       int										=  i
      # Validate coloring
      if util_color(_UpperCAmelCase ,					_UpperCAmelCase ,					_UpperCAmelCase ,					index + 1					):
        return True
      # Backtrack
      A_  :       Tuple										=  -1
  return False





def 						UpperCAmelCase__		(     _UpperCAmelCase ,					_UpperCAmelCase					):






  """simple docstring"""





  A_  :       List[Any]										=  [-1] * len(_UpperCAmelCase					)

  if util_color(_UpperCAmelCase ,					_UpperCAmelCase ,					_UpperCAmelCase ,					0					):
    return colored_vertices

  return []






"""simple docstring"""




from typing import Optional, Union

import torch
from torch import nn

from ...configuration_utils import ConfigMixin, register_to_config
from ...models.modeling_utils import ModelMixin

class  _UpperCAmelCase  (   UpperCAmelCase__			,   UpperCAmelCase__		):



      '''simple docstring'''

      @register_to_config
      def __init__(     self					,      snake_case_ = 7_6_8					,      ):

        """simple docstring"""

        super().__init__()

        A_  :       Optional[int]										=  nn.Parameter(torch.zeros(1					,      snake_case_  )  )
        A_  :       Optional[int]										=  nn.Parameter(torch.ones(1					,      snake_case_  )  )

      def 					lowerCamelCase_			(     self					,      snake_case_ = None					,      snake_case_ = None					,      ):

        """simple docstring"""

        A_  :       str										=  nn.Parameter(self.mean.to(snake_case_  ).to(snake_case_  )  )
        A_  :       Optional[int]										=  nn.Parameter(self.std.to(snake_case_  ).to(snake_case_  )  )
        return self

      def 					lowerCamelCase_			(     self					,      snake_case_  ):

        """simple docstring"""

        A_  :       Tuple										=  (embeds - self.mean) * 1.0 / self.std
        return embeds

      def 					lowerCamelCase_			(     self					,      snake_case_  ):

        """simple docstring"""

        A_  :       List[str]										=  (embeds * self.std) + self.mean
        return embeds