#!/usr/local/bin/python3
from itertools import combinations
L=(1,2,3,4,6,7,8,9,10,11,12,13)
KS=range(1,14)
ORDER=(15,14,16,13,17,12,18,11,19,10,20,9,21)
def vals(ps):
    return tuple((v if v<=9 else 10) for v in ps)
def sums_of(ps):
    a=vals(ps)
    return [sum(c) for r in range(1,6) for c in combinations(a,r)]
def seqpts(ps):
    D=set(ps)
    total=0
    for a in range(1,14):
        for b in range(a,15):
            ln=b-a
            if ln>=3:
                if all(j in D for j in range(a,b)):
                    if a==1 or (a-1) not in D:
                        if b==14 or b not in D:
                            ways=1
                            for j in range(a,b):
                                ways=ways*ps.count(j)
                            total=sum((total,ln*ways))
    return total
def profile(H):
    cnt=[0]*13
    for k in KS:
        ss=sums_of((*H,k))
        cs=[ss.count(m) for m in ORDER]
        best=max(cs)
        idx=cs.index(best)
        cnt[idx]=sum((cnt[idx],1))
    return tuple(cnt)
def targetscores(H,m):
    out=[]
    for k in KS:
        ps=(*H,k)
        ss=sums_of(ps)
        sc=sum((2*ss.count(m),seqpts(ps),(k in H)*2))
        out.append(sc)
    return out
def show(H):
    ts=targetscores(H,15)
    rng=max(ts)-min(ts)
    print('show',H,'profile',profile(H),'range',rng,'scores',ts,'sigma',sum(ts))
def main():
    print('example_start')
    show((2,3,5,8))
    print('example_end')
    tied=[]
    best=None
    for H in combinations(L,4):
        p=profile(H)
        if best is None or p>best:
            best=p
            tied=[H]
        elif p==best:
            tied.append(H)
    print('bestprofile',best)
    print('bestcount',len(tied))
    print('bestfirst',tied[:20])
    print('bestlast',tied[-20:])
    rbest=None
    rt=[]
    for H in tied:
        ts=targetscores(H,15)
        r=max(ts)-min(ts)
        if rbest is None or r>rbest:
            rbest=r
            rt=[H]
        elif r==rbest:
            rt.append(H)
    print('maxrange',rbest)
    print('rangecount',len(rt))
    print('rangetied',rt)
    cur=rt
    for level in range(1,14):
        withl=[H for H in cur if level in H]
        if len(withl)==1:
            cur=withl
            print('literalselected',level)
            break
    print('literalfinal',cur)
    cur2=rt
    for level in range(1,14):
        withl=[H for H in cur2 if level in H]
        if len(withl)>0:
            cur2=withl
    print('lexmaxfinal',cur2)
    print('finalstart')
    for H in cur:
        show(H)
    for H in cur2:
        if H not in cur:
            show(H)
main()