#!/usr/local/bin/python3
from itertools import combinations
L=(1,2,3,4,6,7,8,9,10,11,12,13)
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 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 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 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 main():
    badseq=0
    firstseq=None
    badcomb=0
    firstcomb=None
    for H in combinations(L,4):
        for k in range(1,14):
            ps=(*H,k)
            s1=seqpts(ps)
            s2=seq2(ps)
            if s1!=s2:
                badseq=sum((badseq,1))
                if firstseq is None:
                    firstseq=(ps,s1,s2)
            ss=sums_of(ps)
            d=csums(ps)
            for m in range(9,22):
                if ss.count(m)!=d.get(m,0):
                    badcomb=sum((badcomb,1))
                    if firstcomb is None:
                        firstcomb=(ps,m,ss.count(m),d.get(m,0))
    print('badseq',badseq,'firstseq',firstseq)
    print('badcomb',badcomb,'firstcomb',firstcomb)
main()