# please improve me
def statistic(G):
    if not G.is_connected():
        return max(statistic(H) for H in G.connected_components_subgraphs())

    V = G.vertices()
    if len(V) <= 2:
        return len(V)
    max_len = 0
    for k in range(2, len(V)+1):
        for subV in Subsets(V, k):
            subG = G.subgraph(subV)
            degs = sorted(subG.degree())
            if degs[:2] == [1,1] and all(d == 2 for d in degs[2:]) and subG.is_connected():
                max_len = k
                break
    return max_len