






def     a_   (__A				,       __A				,       __A      )				->						bool:



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







def     a_   (__A				,       __A				,       __A				,       __A      )				->						bool:



					"""simple docstring"""

					# Base Case
					if index == len(__A      ):
										return True

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







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



					"""simple docstring"""
					__a					:						Optional[Any]      =					[-1] * len(__A      )

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

					return []













from abc import ABC, abstractmethod
from argparse import ArgumentParser




class 							snake_case_       (    __UpperCamelCase      ):

						"""simple docstring"""



						@staticmethod
						@abstractmethod
						def        UpperCAmelCase__					(__UpperCAmelCase:					ArgumentParser   )    ->     Tuple:




											'''simple docstring'''



											raise NotImplementedError()



						@abstractmethod
						def        UpperCAmelCase__					(self:					List[str]   )    ->     List[str]:




											'''simple docstring'''



											raise NotImplementedError()





