




def    A						(__A   :    list[int]   ,				__A   :    list[int]   ,				__A   :    int       )   ->      bool:







     """simple docstring"""


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


def    A						(__A   :    list[list[int]]   ,				__A   :    int   ,				__A   :    list[int]   ,				__A   :    int       )   ->      bool:







     """simple docstring"""


     if index == len(__A       ):
          return True

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


def    A						(__A   :    list[list[int]]   ,				__A   :    int       )   ->      list[int]:







     """simple docstring"""


     UpperCAmelCase_          =							[-1] * len(__A       )

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

     return []












from diffusers.utils.testing_utils import require_onnxruntime







@require_onnxruntime
class __snake_case			:
   pass






