# coding: utf-8

# In[1]:

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[2]:

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[3]:

def All_Increasing_Sorted_Function_Pairs(_m1,_m2L,_m2U):
    if _m1==0: return[[[0],[0]]]
    return [[_f1+[i],_f2+[j]]
            for [_f1,_f2] in All_Increasing_Sorted_Function_Pairs(_m1-1,_m2L,_m2U)
            for i in range(max(_f1),_m2U+1)
            for j in range(max(_f2+[i]),_m2U+1)]



# In[ ]:

N=11
OptSigma=-1
Optm1=0
Optm2=N
Opt=set()
for m1 in range(N+1):
    m2=N-m1
    for [f1,f2] in All_Increasing_Sorted_Function_Pairs(m1,0,m2):
        [g1,g2]=g12(f1,f2,m1,m2)
        #print (f1,f2,g1,g2)

        sigma=SimpD(f1,f2,g1,g2,m1,m2)
        if sigma==OptSigma:
            if not ((f1,f2,g1,g2,m1,m2) in Opt):
                Opt+=[(f1,f2,g1,g2,m1,m2)]
                NOpt+=1
        if sigma>OptSigma:
            Opt=[(f1,f2,g1,g2,m1,m2)]
            OptSigma=sigma
            NOpt=1




# In[70]:

print NOpt


# In[71]:

Opt


# In[49]:

print OptSigma