def statistic(G):
    G = G.copy(immutable=False)
    if not G.is_connected():
        l = [statistic(H) for H in G.connected_components_subgraphs()]
        if all(s is not None for s in l):
            return max(l)
        return
    
    if G.is_path():
        return 0
    if G.is_circular_planar():
        return 1
    if G.is_planar():
        if max(G.degree()) <= 4:
            return 2
        if G.is_hamiltonian():
            return 2
    
    if G.is_clique() and G.num_verts() >= 4:
        return (G.num_verts()+1)//2