def is_induced_path(G, p):
    for i in range(len(p)):
        N = G[p[i]]
        if any(p[j] in N for j in range(i+2, len(p))):
            return False
    return True

def induced_paths(G, u, v):
    for p in G.shortest_simple_paths(u, v):
        if is_induced_path(G, p):
            yield p

def monophonic_interval(G, u, v):
    return set(sum(list(induced_paths(G, u, v)), []))

def monophonic_closure(G, M):
    H = set(M)
    for u, v in Subsets(M, 2):
        H |= monophonic_interval(G, u, v)
    return H

def monophonic_hull(G, M):
    H = set(M)
    while True:
        C = monophonic_closure(G, H)
        if C == H:
            return C
        H = C

@cached_function
def statistic(G, value_only=True):
    V = set(G.vertices())
    for k in range(len(V)+1):
        for M in Subsets(V, k):
            if len(monophonic_hull(G, M)) == len(V):
                if value_only:
                    return k
                return M