python3 - <<'PY'
from itertools import product
A=5
B=6
C=9
N=A+B+C-2
mons=[]
for d in range(N+1):
    arr=[]
    for a in range(A):
        for b in range(B):
            for c in range(C):
                if a+b+c==d:
                    arr.append((a,b,c))
    mons.append(arr)
idx=[]
for M in mons:
    idx.append({m:i for i,m in enumerate(M)})
images=[]
for d in range(N):
    im=[]
    for a,b,c in mons[d]:
        mask=0
        if a+1<A:
            mask |= 1 << idx[d+1][(a+1,b,c)]
        if b+1<B:
            mask |= 1 << idx[d+1][(a,b+1,c)]
        if c+1<C:
            mask |= 1 << idx[d+1][(a,b,c+1)]
        im.append(mask)
    images.append(im)
def apply_c(d,v):
    r=0
    while v:
        lsb=v & -v
        j=lsb.bit_length()-1
        r ^= images[d][j]
        v ^= lsb
    return r
def rank(vs):
    b={}
    r=0
    for v in vs:
        x=v
        while x:
            p=x.bit_length()-1
            if p in b:
                x ^= b[p]
            else:
                b[p]=x
                r += 1
                break
    return r
rho=[[0]*18 for _ in range(18)]
for i in range(18):
    h=len(mons[i])
    for t in range(18-i):
        vs=[]
        for j in range(h):
            v=1<<j
            d=i
            for k in range(t):
                v=apply_c(d,v)
                d += 1
            vs.append(v)
        rho[i][i+t]=rank(vs)
def R(i,j):
    if i<0 or j>17 or i>j:
        return 0
    return rho[i][j]
m=[[0]*18 for _ in range(18)]
for i in range(18):
    for j in range(i,18):
        m[i][j]=R(i,j)-R(i-1,j)-R(i,j+1)+R(i-1,j+1)
n=[]
W=[]
for r in range(1,19):
    nr=0
    wr=0
    for i in range(0,19-r):
        val=m[i][i+r-1]
        nr += val
        wr += (i+1)**4 * val
    n.append(nr)
    W.append(wr)
terms=[]
for r in range(1,19):
    if n[r-1]>0:
        coeff=100000+7919*r+W[r-1]
        terms.append((r,coeff))
print('n=',n)
print('W=',W)
print('terms=',terms)
print('poly=','+'.join(str(c)+'V^'+str(r) for r,c in sorted(terms, reverse=True)))
PY