


"""simple docstring"""







def      lowercase			(				A_  ,   A_  ,   A_  ,   A_       )->      bool:
  '''simple docstring'''







  if graph[path[curr_ind - 1]][next_ver] == 0:
    return False

  # 2. Validate that next vertex is not already in path
  return not any(vertex == next_ver for vertex in path       )


def      lowercase			(				A_  ,   A_  ,   A_       )->      bool:
  '''simple docstring'''







  if curr_ind == len(A_       ):
    # return whether path exists between current and starting vertices
    return graph[path[curr_ind - 1]][path[0]] == 1

  # Recursive Step
  for next_ver in range(0  ,   len(A_       )       ):
    if valid_connection(A_  ,   A_  ,   A_  ,   A_       ):
      # Insert current vertex  into path as next transition
      a						:		List[Any]      							=			next_ver
      # Validate created path
      if util_hamilton_cycle(A_  ,   A_  ,   curr_ind + 1       ):
        return True
      # Backtrack
      a						:		List[str]      							=			-1
  return False







def      lowercase			(				A_  ,   A_ = 0       )->      list[int]:
  '''simple docstring'''







  a						:		Dict      							=			[-1] * (len(A_       ) + 1)
  # initialize start and end of path with starting index
  a						:		Union[str, Any]      							=			start_index
  # evaluate and if we find answer return path either return empty array
  return path if util_hamilton_cycle(A_  ,   A_  ,   1       ) else []









"""simple docstring"""





def   __SCREAMING_SNAKE_CASE  (      A_						,     A_ ):
	return numa ^ numa < 0


if __name__ == "__main__":
							import doctest

							doctest.testmod()




