python3 - <<'PY'
T=112
M=[(-2,5,-1),(-1,-4,3),(0,4,-3),(1,2,2),(2,-5,1),(-2,1,-4),(1,-4,-2),(2,3,-3)]
def md(a,m):
    return a-(a//m)*m
r=17
s=41
q=73
R=[]
S=[]
Q=[]
for i in range(72):
    r=md(5*r+3*s+7*i+11,97)
    s=md(2*r+7*s+q+5*i+13,89)
    q=md(3*r+s+5*q+11*i+17,83)
    R.append(r)
    S.append(s)
    Q.append(q)
t=[20+i+i//4 for i in range(72)]
x=[4+md(7*R[i]+3*S[i]+5*Q[i]+2*i,23) for i in range(72)]
y=[3+md(5*R[i]+2*S[i]+7*Q[i]+3*i,17) for i in range(72)]
p=[1 if md(R[i]+2*S[i]+Q[i]+i,6) in (0,1,4) else -1 for i in range(72)]
h=1
om,xi,eta=M[h]
P=[[0]*8 for a in range(11)]
N=[[0]*8 for a in range(11)]
LP=[[-1000]*8 for a in range(11)]
LM=[[-1000]*8 for a in range(11)]
Z=[0]*72
for i in range(72):
    u=x[i]+((T-t[i])*(om*(y[i]-11)+xi))//128
    v=y[i]+((T-t[i])*(-om*(x[i]-15)+eta))//128
    if u<0 or u>30 or v<0 or v>22:
        zz=0
    else:
        a=u//3
        b=v//3
        last=(LP if p[i]==1 else LM)[a][b]
        if t[i]-last<=7:
            zz=1 if p[i]==1 else 2
        else:
            zz=3 if p[i]==1 else 4
            if p[i]==1:
                P[a][b]+=1
                LP[a][b]=t[i]
            else:
                N[a][b]+=1
                LM[a][b]=t[i]
    Z[i]=zz
dx=1 if M[h][1]>0 else -1
dy=1 if M[h][2]>0 else -1
EE=[[-1000]*8 for a in range(11)]
EF=[[-1000]*8 for a in range(11)]
SS=0
def g(E,aa,bb):
    if aa<0 or aa>10 or bb<0 or bb>7:
        return -1000
    return E[aa][bb]
for i in range(72):
    if Z[i] not in (3,4):
        continue
    u=x[i]+((T-t[i])*(om*(y[i]-11)+xi))//128
    v=y[i]+((T-t[i])*(-om*(x[i]-15)+eta))//128
    a=u//3
    b=v//3
    ap=a-dx
    bp=b-dy
    ep=EE if p[i]==1 else EF
    eo=EF if p[i]==1 else EE
    qs=(1 if 4<=t[i]-g(ep,a,b)<=12 else 0)+(1 if 4<=t[i]-g(ep,ap,bp)<=12 else 0)
    qo=(1 if 1<=t[i]-g(eo,a,b)<=6 else 0)+(1 if 1<=t[i]-g(eo,ap,bp)<=6 else 0)
    inc=1 if qs>=1 and qo==0 else 0
    SS+=inc
    print(i,'z',Z[i],'t',t[i],'p',p[i],'uv',u,v,'ab',a,b,'apbp',ap,bp,'qs',qs,'qo',qo,'inc',inc,'S',SS)
    ep[a][b]=t[i]
print('S',SS)
PY