code: def cross_goal(state):
          
          centres, edges = state
          for edge in edges:
              if "D" not in edge.facings:
                  return False
              if edge["D"] != centres["D"]["D"]:
                  return False
              k = "".join(edge.facings.keys()).replace("D", "")
              if edge[k] != centres[k][k]:
                  return False
          return True
docs: The goal function for cross solving search.