# coding: utf-8

# In[22]:

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[23]:

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[2]:

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[1]:

def allfunctions(m1,m2):
    return[[i for i in int2base(idx,m2+1,m1)] for idx in range((m2+1)^m1)]



# In[39]:

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

    for tmp1 in allfunctions(m1,m2):
        for tmp2 in allfunctions(m1,m2):
            tmp1=[0]+sorted(tmp1)
            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[40]:

print Opt
print OptSigma


# In[42]:

save_session('2ptsCvx_v2')