#!/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 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 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 build_good():
    good=set()
    for a in combinations_with_replacement(range(1,11),5):
        d=make_dist(a)
        n15=d.get(15,0)
        ok=True
        for m in range(9,22):
            if d.get(m,0)>n15:
                ok=False
        if ok:
            good.add(tuple(a))
    return good
def aff(H,k):
    return tuple(sorted((v if v<=9 else 10 for v in (*H,k))))
def aligned_menus(good):
    out=[]
    for H in combinations(L,4):
        ok=True
        for k in range(1,14):
            if aff(H,k) not in good:
                ok=False
        if ok:
            out.append(H)
    return out
def scores3(H,m):
    out=[]
    for k in range(1,14):
        ps=(*H,k)
        d=make_dist(ps)
        sc=sum((2*d.get(m,0),seq3(ps),(k in H)*2))
        out.append(sc)
    return out
def main():
    good=build_good()
    print('goodcount',len(good))
    cand=aligned_menus(good)
    print('candcount',len(cand))
    print('cands',cand)
    rbest=None
    rt=[]
    for H in cand:
        ts=scores3(H,15)
        r=max(ts)-min(ts)
        print('chk',H,r,ts,sum(ts))
        if rbest is None or r>rbest:
            rbest=r
            rt=[H]
        elif r==rbest:
            rt.append(H)
    print('selrange',rbest,'selcount',len(rt),'seltied',rt)
main()