#!/usr/local/bin/python3
from itertools import combinations, combinations_with_replacement
from collections import Counter
L=(1,2,3,4,6,7,8,9,10,11,12,13)
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 make_dist(xs):
    c=Counter({0:1})
    for v in xs:
        vv=v if v<=9 else 10
        p=Counter()
        for s in list(c):
            p[sum((s,vv))]=c[s]
        c.update(p)
    return c
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 seq3(ps):
    D=sorted(set(ps))
    runs=[]
    start=None
    prev=None
    for v in D:
        if start is None:
            start=v
        elif v!=sum((prev,1)):
            runs.append((start,prev))
            start=v
        prev=v
    if start is not None:
        runs.append((start,prev))
    total=0
    for a,b in runs:
        ln=len(range(a,sum((b,1))))
        if ln>=3:
            ways=1
            for lev in range(a,sum((b,1))):
                ways=ways*ps.count(lev)
            total=sum((total,ln*ways))
    return total
def main():
    badcomb=0
    firstcomb=None
    for a in combinations_with_replacement(range(1,11),5):
        d1=csums(a)
        d2=make_dist(a)
        for m in range(9,22):
            if d1.get(m,0)!=d2.get(m,0):
                badcomb=sum((badcomb,1))
                if firstcomb is None:
                    firstcomb=(a,m,d1.get(m,0),d2.get(m,0))
    badseq=0
    firstseq=None
    for H in combinations(L,4):
        for k in range(1,14):
            ps=(*H,k)
            s2=seq2(ps)
            s3=seq3(ps)
            if s2!=s3:
                badseq=sum((badseq,1))
                if firstseq is None:
                    firstseq=(ps,s2,s3)
    print('badcomb_all',badcomb,'firstcomb',firstcomb)
    print('badseq_all',badseq,'firstseq',firstseq)
main()