# In[7]:

def SimpD(_f1,_f2,_g1,_g2,_m1,_m2):
    s=0
    for i in range(1,_m1+1):
        s+=binomial(_f1[i],2)+binomial(_f2[i]-_f1[i],2)+binomial(_m2-_f2[i],2)
    for j in range(1,_m2+1):
        s+=binomial(_g1[j],2)+binomial(_g2[j]-_g1[j],2)+binomial(_m1-_g2[j],2)
    return(binomial(_m1+_m2,3)-binomial(_m1,3)-binomial(_m2,3)-s)


# In[8]:

def g12(_f1,_f2,_m1,_m2):
    _g1=[0]+[max(i for i in range(_m1+1) if _f2[i]<j) for j in range(1,_m2+1)]
    _g2=[0]+[max(i for i in range(_m1+1) if _f1[i]<j) for j in range(1,_m2+1)]
    return [_g1,_g2]


# In[9]:

def int2base(x, base, length):
        digits = []

        k=0
        while k<length:
            digits.append(int(x % base))
            x = int(x / base)
            k+=1

        digits.reverse()

        return digits


# In[10]:

def allfunctions(_m1,_m2):
    return[[i for i in int2base(idx,_m2+1,_m1)] for idx in range((_m2+1)^_m1)]



# In[21]:

N=8
OptSigma=0
Optm1=0
Optm2=N
for m1 in range(N+1):
    m2=N-m1

    for tmp1 in allfunctions(m1,m2):
        tmp1=[0]+sorted(tmp1)                                               #Jetzt einen loop weiter aussen
        for tmp2 in allfunctions(m1,m2):
            tmp2=[0]+sorted(tmp2)
            f1=[min(tmp1[i],tmp2[i]) for i in range(m1+1)]
            f2=[max(tmp1[i],tmp2[i]) for i in range(m1+1)]
            [g1,g2]=g12(f1,f2,m1,m2)


            sigma=SimpD(f1,f2,g1,g2,m1,m2)

            if sigma>OptSigma or (sigma>=OptSigma and m1-m2>Optm1-Optm2):
                Opt=[f1,f2,g1,g2]
                OptSigma=sigma
                Optm1=m1
                Optm2=m2


# In[22]:

print Opt
print OptSigma



# Out[22]:

[[0, 0, 0, 1, 2], [0, 1, 2, 3, 4], [0, 0, 1, 2, 3], [0, 2, 3, 4, 4]]
32