#!/usr/local/bin/python3
from itertools import combinations
L=(1,2,3,4,6,7,8,9,10,11,12,13)
ORDER=(15,14,16,13,17,12,18,11,19,10,20,9,21)
def csums(ps):
    d={0:1}
    for v in ps:
        vv=v if v<=9 else 10
        nd=dict(d)
        for s in list(d):
            key=sum((s,vv))
            nd[key]=sum((nd.get(key,0),d[s]))
        d=nd
    return d
def seq2(ps):
    total=0
    for ln in range(3,6):
        for idx in combinations(range(5),ln):
            a=sorted(ps[i] for i in idx)
            ok=len(set(a))==ln
            if ok:
                for j in range(1,ln):
                    if a[j]!=sum((a[j-1],1)):
                        ok=False
            if ok:
                left=a[0]-1
                right=sum((a[-1],1))
                if not any(p==left for p in ps):
                    if not any(p==right for p in ps):
                        total=sum((total,ln))
    return total
def profile2(H):
    cnt=[0]*13
    for k in range(1,14):
        ps=(*H,k)
        d=csums(ps)
        cs=[d.get(m,0) for m in ORDER]
        best=max(cs)
        idx=cs.index(best)
        cnt[idx]=sum((cnt[idx],1))
    return tuple(cnt)
def scores2(H,m):
    out=[]
    for k in range(1,14):
        ps=(*H,k)
        d=csums(ps)
        sc=sum((2*d.get(m,0),seq2(ps),(k in H)*2))
        out.append(sc)
    return out
def better(p,q):
    for i in range(13):
        if p[i]>q[i]:
            return True
        if p[i]<q[i]:
            return False
    return False
def report(H):
    ts=scores2(H,15)
    total=0
    for x in ts:
        total=sum((total,x))
    print('reportH',H)
    print('reportprofile',profile2(H))
    print('reportscores',ts)
    print('reportrange',max(ts)-min(ts),'reportsigma',total)
def main():
    tied=[]
    best=None
    for H in combinations(L,4):
        p=profile2(H)
        if best is None or better(p,best):
            best=p
            tied=[H]
        elif p==best:
            tied.append(H)
    print('altbestprofile',best)
    print('altbestcount',len(tied))
    print('altbestfirst',tied[:20])
    print('altbestlast',tied[-20:])
    rbest=None
    rt=[]
    for H in tied:
        ts=scores2(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('altmaxrange',rbest)
    print('altrangecount',len(rt))
    print('altrangetied',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('altliteralselected',level)
            break
    print('altliteralfinal',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('altlexmaxfinal',cur2)
    for H in cur:
        report(H)
    for H in cur2:
        if H not in cur:
            report(H)
main()