3.1.16 \(\int \frac {A+B x}{(a+b x+c x^2)^2 (d+e x+f x^2)} \, dx\)

Optimal. Leaf size=1075 \[ -\frac {A c (2 a c e-b (c d+a f))+(A b-a B) \left (f b^2+2 c^2 d-c (b e+2 a f)\right )+c \left (A f b^2-(B c d+A c e+a B f) b+2 c (A c d+a B e-a A f)\right ) x}{\left (b^2-4 a c\right ) \left ((c d-a f)^2-(b d-a e) (c e-b f)\right ) \left (c x^2+b x+a\right )}-\frac {\left ((B d-A e) f^2 b^5-2 f \left (B c d e-A \left (c e^2+a f^2-c d f\right )\right ) b^4-\left (A c e \left (c e^2-4 a f^2-2 c d f\right )+B \left (a^2 f^3+4 a c d f^2-c^2 d \left (e^2+5 d f\right )\right )\right ) b^3-4 c \left (B c^2 e d^2+A f \left (2 c^2 d^2+3 a^2 f^2+3 a c \left (e^2-d f\right )\right )\right ) b^2+2 c \left (B \left (c^3 d^3+a c^2 \left (e^2-7 d f\right ) d+3 a^3 f^3+3 a^2 c f \left (e^2+d f\right )\right )+A c e \left (3 c^2 d^2+3 a^2 f^2+a c \left (3 e^2+2 d f\right )\right )\right ) b-4 c^2 \left (A \left (c^3 d^3+a c^2 \left (3 e^2-5 d f\right ) d-3 a^3 f^3-a^2 c f \left (e^2-7 d f\right )\right )-a B e \left (c^2 d^2-3 a^2 f^2-a c \left (e^2-2 d f\right )\right )\right )\right ) \tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{3/2} \left (c^2 d^2+f \left (f a^2-b e a+b^2 d\right )-c \left (b d e-a \left (e^2-2 d f\right )\right )\right )^2}+\frac {\left (B \left (d e \left (e^2-3 d f\right ) c^2-2 d f \left (b e^2-a f e-2 b d f\right ) c+f^2 \left (e f a^2-4 b d f a+b^2 d e\right )\right )-A \left (\left (e^4-4 d f e^2+2 d^2 f^2\right ) c^2+2 f \left (a f \left (e^2-2 d f\right )-b \left (e^3-3 d e f\right )\right ) c-f^2 \left (-\left (\left (e^2-2 d f\right ) b^2\right )+2 a e f b-2 a^2 f^2\right )\right )\right ) \tanh ^{-1}\left (\frac {e+2 f x}{\sqrt {e^2-4 d f}}\right )}{\sqrt {e^2-4 d f} \left (c^2 d^2+f \left (f a^2-b e a+b^2 d\right )-c \left (b d e-a \left (e^2-2 d f\right )\right )\right )^2}+\frac {\left (A (c e-b f) \left (f (b e-2 a f)-c \left (e^2-2 d f\right )\right )-B \left (-d \left (e^2-d f\right ) c^2+2 d f (b e-a f) c-f^2 \left (b^2 d-a^2 f\right )\right )\right ) \log \left (c x^2+b x+a\right )}{2 \left (c^2 d^2+f \left (f a^2-b e a+b^2 d\right )-c \left (b d e-a \left (e^2-2 d f\right )\right )\right )^2}-\frac {\left (A (c e-b f) \left (f (b e-2 a f)-c \left (e^2-2 d f\right )\right )-B \left (-d \left (e^2-d f\right ) c^2+2 d f (b e-a f) c-f^2 \left (b^2 d-a^2 f\right )\right )\right ) \log \left (f x^2+e x+d\right )}{2 \left (c^2 d^2+f \left (f a^2-b e a+b^2 d\right )-c \left (b d e-a \left (e^2-2 d f\right )\right )\right )^2} \]

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Rubi [A]  time = 4.18, antiderivative size = 1067, normalized size of antiderivative = 0.99, number of steps used = 10, number of rules used = 6, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {1016, 1072, 634, 618, 206, 628} \begin {gather*} -\frac {A c (2 a c e-b (c d+a f))+(A b-a B) \left (f b^2+2 c^2 d-c (b e+2 a f)\right )+c \left (A f b^2-(B c d+A c e+a B f) b+2 c (A c d+a B e-a A f)\right ) x}{\left (b^2-4 a c\right ) \left ((c d-a f)^2-(b d-a e) (c e-b f)\right ) \left (c x^2+b x+a\right )}-\frac {\left ((B d-A e) f^2 b^5-2 f \left (-a A f^2+B c d e-A c \left (e^2-d f\right )\right ) b^4-\left (A c e \left (c e^2-4 a f^2-2 c d f\right )+B \left (a^2 f^3+4 a c d f^2-c^2 d \left (e^2+5 d f\right )\right )\right ) b^3-4 \left (B d^2 e c^3+A f \left (2 c^2 d^2+3 a^2 f^2+3 a c \left (e^2-d f\right )\right ) c\right ) b^2+2 c \left (B \left (c^3 d^3+a c^2 \left (e^2-7 d f\right ) d+3 a^3 f^3+3 a^2 c f \left (e^2+d f\right )\right )+A c e \left (3 c^2 d^2+3 a^2 f^2+a c \left (3 e^2+2 d f\right )\right )\right ) b-4 c^2 \left (A \left (c^3 d^3+a c^2 \left (3 e^2-5 d f\right ) d-3 a^3 f^3-a^2 c f \left (e^2-7 d f\right )\right )-a B e \left (c^2 d^2-3 a^2 f^2-a c \left (e^2-2 d f\right )\right )\right )\right ) \tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{3/2} \left (c^2 d^2-b c e d+f \left (f a^2-b e a+b^2 d\right )+a c \left (e^2-2 d f\right )\right )^2}+\frac {\left (B \left (d e \left (e^2-3 d f\right ) c^2-2 d f \left (b e^2-a f e-2 b d f\right ) c+f^2 \left (e f a^2-4 b d f a+b^2 d e\right )\right )-A \left (\left (e^4-4 d f e^2+2 d^2 f^2\right ) c^2+2 f \left (a f \left (e^2-2 d f\right )-b \left (e^3-3 d e f\right )\right ) c-f^2 \left (-\left (e^2-2 d f\right ) b^2+2 a e f b-2 a^2 f^2\right )\right )\right ) \tanh ^{-1}\left (\frac {e+2 f x}{\sqrt {e^2-4 d f}}\right )}{\sqrt {e^2-4 d f} \left (c^2 d^2-b c e d+f \left (f a^2-b e a+b^2 d\right )+a c \left (e^2-2 d f\right )\right )^2}+\frac {\left (A (c e-b f) \left (f (b e-2 a f)-c \left (e^2-2 d f\right )\right )-B \left (-d \left (e^2-d f\right ) c^2+2 d f (b e-a f) c-f^2 \left (b^2 d-a^2 f\right )\right )\right ) \log \left (c x^2+b x+a\right )}{2 \left (c^2 d^2-b c e d+f \left (f a^2-b e a+b^2 d\right )+a c \left (e^2-2 d f\right )\right )^2}-\frac {\left (A (c e-b f) \left (f (b e-2 a f)-c \left (e^2-2 d f\right )\right )-B \left (-d \left (e^2-d f\right ) c^2+2 d f (b e-a f) c-f^2 \left (b^2 d-a^2 f\right )\right )\right ) \log \left (f x^2+e x+d\right )}{2 \left (c^2 d^2-b c e d+f \left (f a^2-b e a+b^2 d\right )+a c \left (e^2-2 d f\right )\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(A + B*x)/((a + b*x + c*x^2)^2*(d + e*x + f*x^2)),x]

[Out]

-((A*c*(2*a*c*e - b*(c*d + a*f)) + (A*b - a*B)*(2*c^2*d + b^2*f - c*(b*e + 2*a*f)) + c*(A*b^2*f + 2*c*(A*c*d +
a*B*e - a*A*f) - b*(B*c*d + A*c*e + a*B*f))*x)/((b^2 - 4*a*c)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(a +
b*x + c*x^2))) - ((b^5*(B*d - A*e)*f^2 - 2*b^4*f*(B*c*d*e - a*A*f^2 - A*c*(e^2 - d*f)) - 4*c^2*(A*(c^3*d^3 - 3
*a^3*f^3 - a^2*c*f*(e^2 - 7*d*f) + a*c^2*d*(3*e^2 - 5*d*f)) - a*B*e*(c^2*d^2 - 3*a^2*f^2 - a*c*(e^2 - 2*d*f)))
- 4*b^2*(B*c^3*d^2*e + A*c*f*(2*c^2*d^2 + 3*a^2*f^2 + 3*a*c*(e^2 - d*f))) + 2*b*c*(B*(c^3*d^3 + 3*a^3*f^3 + a
*c^2*d*(e^2 - 7*d*f) + 3*a^2*c*f*(e^2 + d*f)) + A*c*e*(3*c^2*d^2 + 3*a^2*f^2 + a*c*(3*e^2 + 2*d*f))) - b^3*(A*
c*e*(c*e^2 - 2*c*d*f - 4*a*f^2) + B*(4*a*c*d*f^2 + a^2*f^3 - c^2*d*(e^2 + 5*d*f))))*ArcTanh[(b + 2*c*x)/Sqrt[b
^2 - 4*a*c]])/((b^2 - 4*a*c)^(3/2)*(c^2*d^2 - b*c*d*e + f*(b^2*d - a*b*e + a^2*f) + a*c*(e^2 - 2*d*f))^2) + ((
B*(c^2*d*e*(e^2 - 3*d*f) - 2*c*d*f*(b*e^2 - 2*b*d*f - a*e*f) + f^2*(b^2*d*e - 4*a*b*d*f + a^2*e*f)) - A*(c^2*(
e^4 - 4*d*e^2*f + 2*d^2*f^2) - f^2*(2*a*b*e*f - 2*a^2*f^2 - b^2*(e^2 - 2*d*f)) + 2*c*f*(a*f*(e^2 - 2*d*f) - b*
(e^3 - 3*d*e*f))))*ArcTanh[(e + 2*f*x)/Sqrt[e^2 - 4*d*f]])/(Sqrt[e^2 - 4*d*f]*(c^2*d^2 - b*c*d*e + f*(b^2*d -
a*b*e + a^2*f) + a*c*(e^2 - 2*d*f))^2) + ((A*(c*e - b*f)*(f*(b*e - 2*a*f) - c*(e^2 - 2*d*f)) - B*(2*c*d*f*(b*e
- a*f) - f^2*(b^2*d - a^2*f) - c^2*d*(e^2 - d*f)))*Log[a + b*x + c*x^2])/(2*(c^2*d^2 - b*c*d*e + f*(b^2*d - a
*b*e + a^2*f) + a*c*(e^2 - 2*d*f))^2) - ((A*(c*e - b*f)*(f*(b*e - 2*a*f) - c*(e^2 - 2*d*f)) - B*(2*c*d*f*(b*e
- a*f) - f^2*(b^2*d - a^2*f) - c^2*d*(e^2 - d*f)))*Log[d + e*x + f*x^2])/(2*(c^2*d^2 - b*c*d*e + f*(b^2*d - a*
b*e + a^2*f) + a*c*(e^2 - 2*d*f))^2)

Rule 206

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rule 618

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> Dist[-2, Subst[Int[1/Simp[b^2 - 4*a*c - x^2, x], x]
, x, b + 2*c*x], x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 628

Int[((d_) + (e_.)*(x_))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[(d*Log[RemoveContent[a + b*x +
c*x^2, x]])/b, x] /; FreeQ[{a, b, c, d, e}, x] && EqQ[2*c*d - b*e, 0]

Rule 634

Int[((d_.) + (e_.)*(x_))/((a_) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Dist[(2*c*d - b*e)/(2*c), Int[1/(a +
b*x + c*x^2), x], x] + Dist[e/(2*c), Int[(b + 2*c*x)/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c, d, e}, x] &
& NeQ[2*c*d - b*e, 0] && NeQ[b^2 - 4*a*c, 0] &&  !NiceSqrtQ[b^2 - 4*a*c]

Rule 1016

Int[((g_.) + (h_.)*(x_))*((a_) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_)*((d_) + (e_.)*(x_) + (f_.)*(x_)^2)^(q_), x_Sy
mbol] :> Simp[((a + b*x + c*x^2)^(p + 1)*(d + e*x + f*x^2)^(q + 1)*(g*c*(2*a*c*e - b*(c*d + a*f)) + (g*b - a*h
)*(2*c^2*d + b^2*f - c*(b*e + 2*a*f)) + c*(g*(2*c^2*d + b^2*f - c*(b*e + 2*a*f)) - h*(b*c*d - 2*a*c*e + a*b*f)
)*x))/((b^2 - 4*a*c)*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(p + 1)), x] + Dist[1/((b^2 - 4*a*c)*((c*d - a*
f)^2 - (b*d - a*e)*(c*e - b*f))*(p + 1)), Int[(a + b*x + c*x^2)^(p + 1)*(d + e*x + f*x^2)^q*Simp[(b*h - 2*g*c)
*((c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f))*(p + 1) + (b^2*(g*f) - b*(h*c*d + g*c*e + a*h*f) + 2*(g*c*(c*d - a*
f) - a*(-(h*c*e))))*(a*f*(p + 1) - c*d*(p + 2)) - e*((g*c)*(2*a*c*e - b*(c*d + a*f)) + (g*b - a*h)*(2*c^2*d +
b^2*f - c*(b*e + 2*a*f)))*(p + q + 2) - (2*f*((g*c)*(2*a*c*e - b*(c*d + a*f)) + (g*b - a*h)*(2*c^2*d + b^2*f -
c*(b*e + 2*a*f)))*(p + q + 2) - (b^2*g*f - b*(h*c*d + g*c*e + a*h*f) + 2*(g*c*(c*d - a*f) - a*(-(h*c*e))))*(b
*f*(p + 1) - c*e*(2*p + q + 4)))*x - c*f*(b^2*(g*f) - b*(h*c*d + g*c*e + a*h*f) + 2*(g*c*(c*d - a*f) + a*h*c*e
))*(2*p + 2*q + 5)*x^2, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, h, q}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[e^2
- 4*d*f, 0] && LtQ[p, -1] && NeQ[(c*d - a*f)^2 - (b*d - a*e)*(c*e - b*f), 0] &&  !( !IntegerQ[p] && ILtQ[q, -1
])

Rule 1072

Int[((A_.) + (B_.)*(x_) + (C_.)*(x_)^2)/(((a_) + (b_.)*(x_) + (c_.)*(x_)^2)*((d_) + (e_.)*(x_) + (f_.)*(x_)^2)
), x_Symbol] :> With[{q = c^2*d^2 - b*c*d*e + a*c*e^2 + b^2*d*f - 2*a*c*d*f - a*b*e*f + a^2*f^2}, Dist[1/q, In
t[(A*c^2*d - a*c*C*d - A*b*c*e + a*B*c*e + A*b^2*f - a*b*B*f - a*A*c*f + a^2*C*f + c*(B*c*d - b*C*d - A*c*e +
a*C*e + A*b*f - a*B*f)*x)/(a + b*x + c*x^2), x], x] + Dist[1/q, Int[(c*C*d^2 - B*c*d*e + A*c*e^2 + b*B*d*f - A
*c*d*f - a*C*d*f - A*b*e*f + a*A*f^2 - f*(B*c*d - b*C*d - A*c*e + a*C*e + A*b*f - a*B*f)*x)/(d + e*x + f*x^2),
x], x] /; NeQ[q, 0]] /; FreeQ[{a, b, c, d, e, f, A, B, C}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[e^2 - 4*d*f, 0]

Rubi steps

\begin {align*} \int \frac {A+B x}{\left (a+b x+c x^2\right )^2 \left (d+e x+f x^2\right )} \, dx &=-\frac {A c (2 a c e-b (c d+a f))+(A b-a B) \left (2 c^2 d+b^2 f-c (b e+2 a f)\right )+c \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right ) x}{\left (b^2-4 a c\right ) \left ((c d-a f)^2-(b d-a e) (c e-b f)\right ) \left (a+b x+c x^2\right )}-\frac {\int \frac {-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )+\left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right ) x+c f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right ) x^2}{\left (a+b x+c x^2\right ) \left (d+e x+f x^2\right )} \, dx}{\left (b^2-4 a c\right ) \left ((c d-a f)^2-(b d-a e) (c e-b f)\right )}\\ &=-\frac {A c (2 a c e-b (c d+a f))+(A b-a B) \left (2 c^2 d+b^2 f-c (b e+2 a f)\right )+c \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right ) x}{\left (b^2-4 a c\right ) \left ((c d-a f)^2-(b d-a e) (c e-b f)\right ) \left (a+b x+c x^2\right )}-\frac {\int \frac {-a c^2 d f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+a^2 c f^2 \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+a c e \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )-a b f \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )+c^2 d \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )-b c e \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )+b^2 f \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )-a c f \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )+c \left (-b c d f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+a c e f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+c d \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )-a f \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )-c e \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )+b f \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )\right ) x}{a+b x+c x^2} \, dx}{\left (b^2-4 a c\right ) \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}-\frac {\int \frac {c^2 d^2 f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )-a c d f^2 \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )-c d e \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )+b d f \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )+c e^2 \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )-c d f \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )-b e f \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )+a f^2 \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )-f \left (-b c d f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+a c e f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+c d \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )-a f \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )-c e \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )+b f \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )\right ) x}{d+e x+f x^2} \, dx}{\left (b^2-4 a c\right ) \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}\\ &=-\frac {A c (2 a c e-b (c d+a f))+(A b-a B) \left (2 c^2 d+b^2 f-c (b e+2 a f)\right )+c \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right ) x}{\left (b^2-4 a c\right ) \left ((c d-a f)^2-(b d-a e) (c e-b f)\right ) \left (a+b x+c x^2\right )}+\frac {\left (A (c e-b f) \left (f (b e-2 a f)-c \left (e^2-2 d f\right )\right )-B \left (2 c d f (b e-a f)-f^2 \left (b^2 d-a^2 f\right )-c^2 d \left (e^2-d f\right )\right )\right ) \int \frac {b+2 c x}{a+b x+c x^2} \, dx}{2 \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}-\frac {\left (A (c e-b f) \left (f (b e-2 a f)-c \left (e^2-2 d f\right )\right )-B \left (2 c d f (b e-a f)-f^2 \left (b^2 d-a^2 f\right )-c^2 d \left (e^2-d f\right )\right )\right ) \int \frac {e+2 f x}{d+e x+f x^2} \, dx}{2 \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}-\frac {\left (B \left (c^2 d e \left (e^2-3 d f\right )-2 c d f \left (b e^2-2 b d f-a e f\right )+f^2 \left (b^2 d e-4 a b d f+a^2 e f\right )\right )-A \left (c^2 \left (e^4-4 d e^2 f+2 d^2 f^2\right )-f^2 \left (2 a b e f-2 a^2 f^2-b^2 \left (e^2-2 d f\right )\right )+2 c f \left (a f \left (e^2-2 d f\right )-b \left (e^3-3 d e f\right )\right )\right )\right ) \int \frac {1}{d+e x+f x^2} \, dx}{2 \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}-\frac {\left (-b c \left (-b c d f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+a c e f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+c d \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )-a f \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )-c e \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )+b f \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )\right )+2 c \left (-a c^2 d f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+a^2 c f^2 \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+a c e \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )-a b f \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )+c^2 d \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )-b c e \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )+b^2 f \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )-a c f \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )\right )\right ) \int \frac {1}{a+b x+c x^2} \, dx}{2 c \left (b^2-4 a c\right ) \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}\\ &=-\frac {A c (2 a c e-b (c d+a f))+(A b-a B) \left (2 c^2 d+b^2 f-c (b e+2 a f)\right )+c \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right ) x}{\left (b^2-4 a c\right ) \left ((c d-a f)^2-(b d-a e) (c e-b f)\right ) \left (a+b x+c x^2\right )}+\frac {\left (A (c e-b f) \left (f (b e-2 a f)-c \left (e^2-2 d f\right )\right )-B \left (2 c d f (b e-a f)-f^2 \left (b^2 d-a^2 f\right )-c^2 d \left (e^2-d f\right )\right )\right ) \log \left (a+b x+c x^2\right )}{2 \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}-\frac {\left (A (c e-b f) \left (f (b e-2 a f)-c \left (e^2-2 d f\right )\right )-B \left (2 c d f (b e-a f)-f^2 \left (b^2 d-a^2 f\right )-c^2 d \left (e^2-d f\right )\right )\right ) \log \left (d+e x+f x^2\right )}{2 \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}+\frac {\left (B \left (c^2 d e \left (e^2-3 d f\right )-2 c d f \left (b e^2-2 b d f-a e f\right )+f^2 \left (b^2 d e-4 a b d f+a^2 e f\right )\right )-A \left (c^2 \left (e^4-4 d e^2 f+2 d^2 f^2\right )-f^2 \left (2 a b e f-2 a^2 f^2-b^2 \left (e^2-2 d f\right )\right )+2 c f \left (a f \left (e^2-2 d f\right )-b \left (e^3-3 d e f\right )\right )\right )\right ) \operatorname {Subst}\left (\int \frac {1}{e^2-4 d f-x^2} \, dx,x,e+2 f x\right )}{\left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}+\frac {\left (-b c \left (-b c d f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+a c e f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+c d \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )-a f \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )-c e \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )+b f \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )\right )+2 c \left (-a c^2 d f \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+a^2 c f^2 \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right )+a c e \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )-a b f \left (A b^3 f^2+b^2 B f (c d-a f)-b c \left (B c d e+A c e^2+a B e f+4 a A f^2\right )+2 c \left (A c e (c d+a f)+a B \left (c e^2-2 c d f+2 a f^2\right )\right )\right )+c^2 d \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )-b c e \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )+b^2 f \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )-a c f \left (-b^3 (B d f-A e f)-b c (B d (c d-3 a f)+A e (c d+4 a f))+b^2 \left (B c d e-A \left (c e^2-2 c d f+a f^2\right )\right )-2 c \left (a B c d e-A \left (c^2 d^2+2 a c e^2-3 a c d f+2 a^2 f^2\right )\right )\right )\right )\right ) \operatorname {Subst}\left (\int \frac {1}{b^2-4 a c-x^2} \, dx,x,b+2 c x\right )}{c \left (b^2-4 a c\right ) \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}\\ &=-\frac {A c (2 a c e-b (c d+a f))+(A b-a B) \left (2 c^2 d+b^2 f-c (b e+2 a f)\right )+c \left (A b^2 f+2 c (A c d+a B e-a A f)-b (B c d+A c e+a B f)\right ) x}{\left (b^2-4 a c\right ) \left ((c d-a f)^2-(b d-a e) (c e-b f)\right ) \left (a+b x+c x^2\right )}-\frac {\left (b^5 (B d-A e) f^2-2 b^4 f \left (B c d e-a A f^2-A c \left (e^2-d f\right )\right )-4 c^2 \left (A \left (c^3 d^3-3 a^3 f^3-a^2 c f \left (e^2-7 d f\right )+a c^2 d \left (3 e^2-5 d f\right )\right )-a B e \left (c^2 d^2-3 a^2 f^2-a c \left (e^2-2 d f\right )\right )\right )-4 b^2 \left (B c^3 d^2 e+A c f \left (2 c^2 d^2+3 a^2 f^2+3 a c \left (e^2-d f\right )\right )\right )+2 b c \left (B \left (c^3 d^3+3 a^3 f^3+a c^2 d \left (e^2-7 d f\right )+3 a^2 c f \left (e^2+d f\right )\right )+A c e \left (3 c^2 d^2+3 a^2 f^2+a c \left (3 e^2+2 d f\right )\right )\right )-b^3 \left (A c e \left (c e^2-2 c d f-4 a f^2\right )+B \left (4 a c d f^2+a^2 f^3-c^2 d \left (e^2+5 d f\right )\right )\right )\right ) \tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right )}{\left (b^2-4 a c\right )^{3/2} \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}+\frac {\left (B \left (c^2 d e \left (e^2-3 d f\right )-2 c d f \left (b e^2-2 b d f-a e f\right )+f^2 \left (b^2 d e-4 a b d f+a^2 e f\right )\right )-A \left (c^2 \left (e^4-4 d e^2 f+2 d^2 f^2\right )-f^2 \left (2 a b e f-2 a^2 f^2-b^2 \left (e^2-2 d f\right )\right )+2 c f \left (a f \left (e^2-2 d f\right )-b \left (e^3-3 d e f\right )\right )\right )\right ) \tanh ^{-1}\left (\frac {e+2 f x}{\sqrt {e^2-4 d f}}\right )}{\sqrt {e^2-4 d f} \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}+\frac {\left (A (c e-b f) \left (f (b e-2 a f)-c \left (e^2-2 d f\right )\right )-B \left (2 c d f (b e-a f)-f^2 \left (b^2 d-a^2 f\right )-c^2 d \left (e^2-d f\right )\right )\right ) \log \left (a+b x+c x^2\right )}{2 \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}-\frac {\left (A (c e-b f) \left (f (b e-2 a f)-c \left (e^2-2 d f\right )\right )-B \left (2 c d f (b e-a f)-f^2 \left (b^2 d-a^2 f\right )-c^2 d \left (e^2-d f\right )\right )\right ) \log \left (d+e x+f x^2\right )}{2 \left (c^2 d^2-b c d e+f \left (b^2 d-a b e+a^2 f\right )+a c \left (e^2-2 d f\right )\right )^2}\\ \end {align*}

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Mathematica [A]  time = 6.70, size = 952, normalized size = 0.89 \begin {gather*} \frac {-\frac {2 \left (c^2 d^2-b c e d+f \left (f a^2-b e a+b^2 d\right )+a c \left (e^2-2 d f\right )\right ) \left (A \left (f b^3+c (f x-e) b^2+c (c (d-e x)-3 a f) b+2 c^2 (c d x+a (e-f x))\right )+B \left (2 c f a^2-\left (f b^2+c (f x-e) b+2 c^2 (d-e x)\right ) a-b c^2 d x\right )\right )}{\left (b^2-4 a c\right ) (a+x (b+c x))}-\frac {2 \left ((B d-A e) f^2 b^5+2 f \left (a A f^2-B c d e+A c \left (e^2-d f\right )\right ) b^4+\left (A c e \left (-c e^2+4 a f^2+2 c d f\right )+B \left (-a^2 f^3-4 a c d f^2+c^2 d \left (e^2+5 d f\right )\right )\right ) b^3-4 \left (B d^2 e c^3+A f \left (2 c^2 d^2+3 a^2 f^2+3 a c \left (e^2-d f\right )\right ) c\right ) b^2+2 c \left (B \left (c^3 d^3+a c^2 \left (e^2-7 d f\right ) d+3 a^3 f^3+3 a^2 c f \left (e^2+d f\right )\right )+A c e \left (3 c^2 d^2+3 a^2 f^2+a c \left (3 e^2+2 d f\right )\right )\right ) b+4 c^2 \left (a B e \left (c^2 d^2-3 a^2 f^2-a c \left (e^2-2 d f\right )\right )+A \left (-c^3 d^3+a c^2 \left (5 d f-3 e^2\right ) d+3 a^3 f^3+a^2 c f \left (e^2-7 d f\right )\right )\right )\right ) \tan ^{-1}\left (\frac {b+2 c x}{\sqrt {4 a c-b^2}}\right )}{\left (4 a c-b^2\right )^{3/2}}+\frac {2 \left (B \left (d e \left (3 d f-e^2\right ) c^2-2 d f \left (-b e^2+a f e+2 b d f\right ) c+f^2 \left (-e f a^2+4 b d f a-b^2 d e\right )\right )+A \left (\left (e^4-4 d f e^2+2 d^2 f^2\right ) c^2+2 f \left (a f \left (e^2-2 d f\right )-b \left (e^3-3 d e f\right )\right ) c+f^2 \left (\left (e^2-2 d f\right ) b^2-2 a e f b+2 a^2 f^2\right )\right )\right ) \tan ^{-1}\left (\frac {e+2 f x}{\sqrt {4 d f-e^2}}\right )}{\sqrt {4 d f-e^2}}-\left (A (c e-b f) \left (f (2 a f-b e)+c \left (e^2-2 d f\right )\right )+B \left (d \left (d f-e^2\right ) c^2+2 d f (b e-a f) c+f^2 \left (a^2 f-b^2 d\right )\right )\right ) \log (a+x (b+c x))+\left (A (c e-b f) \left (f (2 a f-b e)+c \left (e^2-2 d f\right )\right )+B \left (d \left (d f-e^2\right ) c^2+2 d f (b e-a f) c+f^2 \left (a^2 f-b^2 d\right )\right )\right ) \log (d+x (e+f x))}{2 \left (c^2 d^2-b c e d+f \left (f a^2-b e a+b^2 d\right )+a c \left (e^2-2 d f\right )\right )^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(A + B*x)/((a + b*x + c*x^2)^2*(d + e*x + f*x^2)),x]

[Out]

((-2*(c^2*d^2 - b*c*d*e + f*(b^2*d - a*b*e + a^2*f) + a*c*(e^2 - 2*d*f))*(A*(b^3*f + b^2*c*(-e + f*x) + b*c*(-
3*a*f + c*(d - e*x)) + 2*c^2*(c*d*x + a*(e - f*x))) + B*(2*a^2*c*f - b*c^2*d*x - a*(b^2*f + 2*c^2*(d - e*x) +
b*c*(-e + f*x)))))/((b^2 - 4*a*c)*(a + x*(b + c*x))) - (2*(b^5*(B*d - A*e)*f^2 + 2*b^4*f*(-(B*c*d*e) + a*A*f^2
+ A*c*(e^2 - d*f)) - 4*b^2*(B*c^3*d^2*e + A*c*f*(2*c^2*d^2 + 3*a^2*f^2 + 3*a*c*(e^2 - d*f))) + 2*b*c*(B*(c^3*
d^3 + 3*a^3*f^3 + a*c^2*d*(e^2 - 7*d*f) + 3*a^2*c*f*(e^2 + d*f)) + A*c*e*(3*c^2*d^2 + 3*a^2*f^2 + a*c*(3*e^2 +
2*d*f))) + 4*c^2*(a*B*e*(c^2*d^2 - 3*a^2*f^2 - a*c*(e^2 - 2*d*f)) + A*(-(c^3*d^3) + 3*a^3*f^3 + a^2*c*f*(e^2
- 7*d*f) + a*c^2*d*(-3*e^2 + 5*d*f))) + b^3*(A*c*e*(-(c*e^2) + 2*c*d*f + 4*a*f^2) + B*(-4*a*c*d*f^2 - a^2*f^3
+ c^2*d*(e^2 + 5*d*f))))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])/(-b^2 + 4*a*c)^(3/2) + (2*(B*(c^2*d*e*(-e^2 +
3*d*f) - 2*c*d*f*(-(b*e^2) + 2*b*d*f + a*e*f) + f^2*(-(b^2*d*e) + 4*a*b*d*f - a^2*e*f)) + A*(c^2*(e^4 - 4*d*e
^2*f + 2*d^2*f^2) + f^2*(-2*a*b*e*f + 2*a^2*f^2 + b^2*(e^2 - 2*d*f)) + 2*c*f*(a*f*(e^2 - 2*d*f) - b*(e^3 - 3*d
*e*f))))*ArcTan[(e + 2*f*x)/Sqrt[-e^2 + 4*d*f]])/Sqrt[-e^2 + 4*d*f] - (A*(c*e - b*f)*(f*(-(b*e) + 2*a*f) + c*(
e^2 - 2*d*f)) + B*(2*c*d*f*(b*e - a*f) + f^2*(-(b^2*d) + a^2*f) + c^2*d*(-e^2 + d*f)))*Log[a + x*(b + c*x)] +
(A*(c*e - b*f)*(f*(-(b*e) + 2*a*f) + c*(e^2 - 2*d*f)) + B*(2*c*d*f*(b*e - a*f) + f^2*(-(b^2*d) + a^2*f) + c^2*
d*(-e^2 + d*f)))*Log[d + x*(e + f*x)])/(2*(c^2*d^2 - b*c*d*e + f*(b^2*d - a*b*e + a^2*f) + a*c*(e^2 - 2*d*f))^
2)

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {A+B x}{\left (a+b x+c x^2\right )^2 \left (d+e x+f x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[(A + B*x)/((a + b*x + c*x^2)^2*(d + e*x + f*x^2)),x]

[Out]

IntegrateAlgebraic[(A + B*x)/((a + b*x + c*x^2)^2*(d + e*x + f*x^2)), x]

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fricas [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((B*x+A)/(c*x^2+b*x+a)^2/(f*x^2+e*x+d),x, algorithm="fricas")

[Out]

Timed out

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giac [B]  time = 0.45, size = 3226, normalized size = 3.00

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((B*x+A)/(c*x^2+b*x+a)^2/(f*x^2+e*x+d),x, algorithm="giac")

[Out]

-1/2*(B*c^2*d^2*f - B*b^2*d*f^2 - 2*B*a*c*d*f^2 + 2*A*b*c*d*f^2 + B*a^2*f^3 - 2*A*a*b*f^3 + 2*B*b*c*d*f*e - 2*
A*c^2*d*f*e + A*b^2*f^2*e + 2*A*a*c*f^2*e - B*c^2*d*e^2 - 2*A*b*c*f*e^2 + A*c^2*e^3)*log(c*x^2 + b*x + a)/(c^4
*d^4 + 2*b^2*c^2*d^3*f - 4*a*c^3*d^3*f + b^4*d^2*f^2 - 4*a*b^2*c*d^2*f^2 + 6*a^2*c^2*d^2*f^2 + 2*a^2*b^2*d*f^3
- 4*a^3*c*d*f^3 + a^4*f^4 - 2*b*c^3*d^3*e - 2*b^3*c*d^2*f*e + 2*a*b*c^2*d^2*f*e - 2*a*b^3*d*f^2*e + 2*a^2*b*c
*d*f^2*e - 2*a^3*b*f^3*e + b^2*c^2*d^2*e^2 + 2*a*c^3*d^2*e^2 + 4*a*b^2*c*d*f*e^2 - 4*a^2*c^2*d*f*e^2 + a^2*b^2
*f^2*e^2 + 2*a^3*c*f^2*e^2 - 2*a*b*c^2*d*e^3 - 2*a^2*b*c*f*e^3 + a^2*c^2*e^4) + 1/2*(B*c^2*d^2*f - B*b^2*d*f^2
- 2*B*a*c*d*f^2 + 2*A*b*c*d*f^2 + B*a^2*f^3 - 2*A*a*b*f^3 + 2*B*b*c*d*f*e - 2*A*c^2*d*f*e + A*b^2*f^2*e + 2*A
*a*c*f^2*e - B*c^2*d*e^2 - 2*A*b*c*f*e^2 + A*c^2*e^3)*log(f*x^2 + x*e + d)/(c^4*d^4 + 2*b^2*c^2*d^3*f - 4*a*c^
3*d^3*f + b^4*d^2*f^2 - 4*a*b^2*c*d^2*f^2 + 6*a^2*c^2*d^2*f^2 + 2*a^2*b^2*d*f^3 - 4*a^3*c*d*f^3 + a^4*f^4 - 2*
b*c^3*d^3*e - 2*b^3*c*d^2*f*e + 2*a*b*c^2*d^2*f*e - 2*a*b^3*d*f^2*e + 2*a^2*b*c*d*f^2*e - 2*a^3*b*f^3*e + b^2*
c^2*d^2*e^2 + 2*a*c^3*d^2*e^2 + 4*a*b^2*c*d*f*e^2 - 4*a^2*c^2*d*f*e^2 + a^2*b^2*f^2*e^2 + 2*a^3*c*f^2*e^2 - 2*
a*b*c^2*d*e^3 - 2*a^2*b*c*f*e^3 + a^2*c^2*e^4) + (2*B*b*c^4*d^3 - 4*A*c^5*d^3 + 5*B*b^3*c^2*d^2*f - 14*B*a*b*c
^3*d^2*f - 8*A*b^2*c^3*d^2*f + 20*A*a*c^4*d^2*f + B*b^5*d*f^2 - 4*B*a*b^3*c*d*f^2 - 2*A*b^4*c*d*f^2 + 6*B*a^2*
b*c^2*d*f^2 + 12*A*a*b^2*c^2*d*f^2 - 28*A*a^2*c^3*d*f^2 - B*a^2*b^3*f^3 + 2*A*a*b^4*f^3 + 6*B*a^3*b*c*f^3 - 12
*A*a^2*b^2*c*f^3 + 12*A*a^3*c^2*f^3 - 4*B*b^2*c^3*d^2*e + 4*B*a*c^4*d^2*e + 6*A*b*c^4*d^2*e - 2*B*b^4*c*d*f*e
+ 2*A*b^3*c^2*d*f*e + 8*B*a^2*c^3*d*f*e + 4*A*a*b*c^3*d*f*e - A*b^5*f^2*e + 4*A*a*b^3*c*f^2*e - 12*B*a^3*c^2*f
^2*e + 6*A*a^2*b*c^2*f^2*e + B*b^3*c^2*d*e^2 + 2*B*a*b*c^3*d*e^2 - 12*A*a*c^4*d*e^2 + 2*A*b^4*c*f*e^2 + 6*B*a^
2*b*c^2*f*e^2 - 12*A*a*b^2*c^2*f*e^2 + 4*A*a^2*c^3*f*e^2 - A*b^3*c^2*e^3 - 4*B*a^2*c^3*e^3 + 6*A*a*b*c^3*e^3)*
arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^2*c^4*d^4 - 4*a*c^5*d^4 + 2*b^4*c^2*d^3*f - 12*a*b^2*c^3*d^3*f + 16
*a^2*c^4*d^3*f + b^6*d^2*f^2 - 8*a*b^4*c*d^2*f^2 + 22*a^2*b^2*c^2*d^2*f^2 - 24*a^3*c^3*d^2*f^2 + 2*a^2*b^4*d*f
^3 - 12*a^3*b^2*c*d*f^3 + 16*a^4*c^2*d*f^3 + a^4*b^2*f^4 - 4*a^5*c*f^4 - 2*b^3*c^3*d^3*e + 8*a*b*c^4*d^3*e - 2
*b^5*c*d^2*f*e + 10*a*b^3*c^2*d^2*f*e - 8*a^2*b*c^3*d^2*f*e - 2*a*b^5*d*f^2*e + 10*a^2*b^3*c*d*f^2*e - 8*a^3*b
*c^2*d*f^2*e - 2*a^3*b^3*f^3*e + 8*a^4*b*c*f^3*e + b^4*c^2*d^2*e^2 - 2*a*b^2*c^3*d^2*e^2 - 8*a^2*c^4*d^2*e^2 +
4*a*b^4*c*d*f*e^2 - 20*a^2*b^2*c^2*d*f*e^2 + 16*a^3*c^3*d*f*e^2 + a^2*b^4*f^2*e^2 - 2*a^3*b^2*c*f^2*e^2 - 8*a
^4*c^2*f^2*e^2 - 2*a*b^3*c^2*d*e^3 + 8*a^2*b*c^3*d*e^3 - 2*a^2*b^3*c*f*e^3 + 8*a^3*b*c^2*f*e^3 + a^2*b^2*c^2*e
^4 - 4*a^3*c^3*e^4)*sqrt(-b^2 + 4*a*c)) - (4*B*b*c*d^2*f^2 - 2*A*c^2*d^2*f^2 - 4*B*a*b*d*f^3 + 2*A*b^2*d*f^3 +
4*A*a*c*d*f^3 - 2*A*a^2*f^4 - 3*B*c^2*d^2*f*e + B*b^2*d*f^2*e + 2*B*a*c*d*f^2*e - 6*A*b*c*d*f^2*e + B*a^2*f^3
*e + 2*A*a*b*f^3*e - 2*B*b*c*d*f*e^2 + 4*A*c^2*d*f*e^2 - A*b^2*f^2*e^2 - 2*A*a*c*f^2*e^2 + B*c^2*d*e^3 + 2*A*b
*c*f*e^3 - A*c^2*e^4)*arctan((2*f*x + e)/sqrt(4*d*f - e^2))/((c^4*d^4 + 2*b^2*c^2*d^3*f - 4*a*c^3*d^3*f + b^4*
d^2*f^2 - 4*a*b^2*c*d^2*f^2 + 6*a^2*c^2*d^2*f^2 + 2*a^2*b^2*d*f^3 - 4*a^3*c*d*f^3 + a^4*f^4 - 2*b*c^3*d^3*e -
2*b^3*c*d^2*f*e + 2*a*b*c^2*d^2*f*e - 2*a*b^3*d*f^2*e + 2*a^2*b*c*d*f^2*e - 2*a^3*b*f^3*e + b^2*c^2*d^2*e^2 +
2*a*c^3*d^2*e^2 + 4*a*b^2*c*d*f*e^2 - 4*a^2*c^2*d*f*e^2 + a^2*b^2*f^2*e^2 + 2*a^3*c*f^2*e^2 - 2*a*b*c^2*d*e^3
- 2*a^2*b*c*f*e^3 + a^2*c^2*e^4)*sqrt(4*d*f - e^2)) + (2*B*a*c^4*d^3 - A*b*c^4*d^3 + 3*B*a*b^2*c^2*d^2*f - 2*A
*b^3*c^2*d^2*f - 6*B*a^2*c^3*d^2*f + 5*A*a*b*c^3*d^2*f + B*a*b^4*d*f^2 - A*b^5*d*f^2 - 4*B*a^2*b^2*c*d*f^2 + 5
*A*a*b^3*c*d*f^2 + 6*B*a^3*c^2*d*f^2 - 7*A*a^2*b*c^2*d*f^2 + B*a^3*b^2*f^3 - A*a^2*b^3*f^3 - 2*B*a^4*c*f^3 + 3
*A*a^3*b*c*f^3 - 3*B*a*b*c^3*d^2*e + 2*A*b^2*c^3*d^2*e - 2*A*a*c^4*d^2*e - 2*B*a*b^3*c*d*f*e + 2*A*b^4*c*d*f*e
+ 2*B*a^2*b*c^2*d*f*e - 6*A*a*b^2*c^2*d*f*e + 4*A*a^2*c^3*d*f*e - B*a^2*b^3*f^2*e + A*a*b^4*f^2*e + B*a^3*b*c
*f^2*e - 2*A*a^2*b^2*c*f^2*e - 2*A*a^3*c^2*f^2*e + B*a*b^2*c^2*d*e^2 - A*b^3*c^2*d*e^2 + 2*B*a^2*c^3*d*e^2 + A
*a*b*c^3*d*e^2 + 2*B*a^2*b^2*c*f*e^2 - 2*A*a*b^3*c*f*e^2 - 2*B*a^3*c^2*f*e^2 + 5*A*a^2*b*c^2*f*e^2 - B*a^2*b*c
^2*e^3 + A*a*b^2*c^2*e^3 - 2*A*a^2*c^3*e^3 + (B*b*c^4*d^3 - 2*A*c^5*d^3 + B*b^3*c^2*d^2*f - B*a*b*c^3*d^2*f -
3*A*b^2*c^3*d^2*f + 6*A*a*c^4*d^2*f + B*a*b^3*c*d*f^2 - A*b^4*c*d*f^2 - B*a^2*b*c^2*d*f^2 + 4*A*a*b^2*c^2*d*f^
2 - 6*A*a^2*c^3*d*f^2 + B*a^3*b*c*f^3 - A*a^2*b^2*c*f^3 + 2*A*a^3*c^2*f^3 - B*b^2*c^3*d^2*e - 2*B*a*c^4*d^2*e
+ 3*A*b*c^4*d^2*e - 4*B*a*b^2*c^2*d*f*e + 2*A*b^3*c^2*d*f*e + 4*B*a^2*c^3*d*f*e - 2*A*a*b*c^3*d*f*e - B*a^2*b^
2*c*f^2*e + A*a*b^3*c*f^2*e - 2*B*a^3*c^2*f^2*e - A*a^2*b*c^2*f^2*e + 3*B*a*b*c^3*d*e^2 - A*b^2*c^3*d*e^2 - 2*
A*a*c^4*d*e^2 + 3*B*a^2*b*c^2*f*e^2 - 2*A*a*b^2*c^2*f*e^2 + 2*A*a^2*c^3*f*e^2 - 2*B*a^2*c^3*e^3 + A*a*b*c^3*e^
3)*x)/((c^2*d^2 + b^2*d*f - 2*a*c*d*f + a^2*f^2 - b*c*d*e - a*b*f*e + a*c*e^2)^2*(c*x^2 + b*x + a)*(b^2 - 4*a*
c))

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maple [B]  time = 0.05, size = 51470, normalized size = 47.88 \begin {gather*} \text {output too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((B*x+A)/(c*x^2+b*x+a)^2/(f*x^2+e*x+d),x)

[Out]

result too large to display

________________________________________________________________________________________

maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: ValueError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((B*x+A)/(c*x^2+b*x+a)^2/(f*x^2+e*x+d),x, algorithm="maxima")

[Out]

Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'a
ssume' command before evaluation *may* help (example of legal syntax is 'assume(4*d*f-e^2>0)', see `assume?` f
or more details)Is 4*d*f-e^2 positive or negative?

________________________________________________________________________________________

mupad [B]  time = 30.31, size = 118429, normalized size = 110.17

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((A + B*x)/((a + b*x + c*x^2)^2*(d + e*x + f*x^2)),x)

[Out]

symsum(log((x*(4*A^3*b^3*c^4*f^6 + 16*B^3*a^3*c^4*f^6 - 3*B^3*a^2*b^2*c^3*f^6 + 4*B^3*a^2*c^5*e^2*f^4 + B^3*b^
2*c^5*d^2*f^4 - 16*A^3*a*b*c^5*f^6 + 16*A^3*a*c^6*e*f^5 + 20*A^2*B*a^2*c^5*f^6 - 3*A^2*B*b^4*c^3*f^6 + 4*A^2*B
*c^7*d^2*f^4 - 16*B^3*a^2*c^5*d*f^5 - 4*A^3*b^2*c^5*e*f^5 + 6*B^3*a*b^2*c^4*d*f^5 - 4*B^3*a^2*b*c^4*e*f^5 + A^
2*B*b^2*c^5*e^2*f^4 - 24*A^2*B*a*c^6*d*f^5 + 6*A*B^2*a*b^3*c^3*f^6 - 28*A*B^2*a^2*b*c^4*f^6 + 8*A^2*B*a*b^2*c^
4*f^6 - 4*A*B^2*b*c^6*d^2*f^4 + 8*A*B^2*a^2*c^5*e*f^5 - 6*A*B^2*b^3*c^4*d*f^5 + 8*A^2*B*b^2*c^5*d*f^5 + 2*A^2*
B*b^3*c^4*e*f^5 - 4*B^3*a*b*c^5*d*e*f^4 - 4*A*B^2*a*b*c^5*e^2*f^4 + 2*A*B^2*a*b^2*c^4*e*f^5 + 2*A*B^2*b^2*c^5*
d*e*f^4 + 16*A*B^2*a*b*c^5*d*f^5 - 12*A^2*B*a*b*c^5*e*f^5 + 8*A*B^2*a*c^6*d*e*f^4 - 4*A^2*B*b*c^6*d*e*f^4))/(1
6*a^2*c^6*d^4 + a^4*b^4*f^4 + 16*a^4*c^4*e^4 + b^4*c^4*d^4 + 16*a^6*c^2*f^4 + b^8*d^2*f^2 - 8*a*b^2*c^5*d^4 -
8*a^5*b^2*c*f^4 + 2*a^2*b^6*d*f^3 - 2*a^3*b^5*e*f^3 - 64*a^3*c^5*d^3*f - 64*a^5*c^3*d*f^3 - 2*b^5*c^3*d^3*e +
2*b^6*c^2*d^3*f + a^2*b^4*c^2*e^4 - 8*a^3*b^2*c^3*e^4 + 32*a^3*c^5*d^2*e^2 + a^2*b^6*e^2*f^2 + 96*a^4*c^4*d^2*
f^2 + b^6*c^2*d^2*e^2 + 32*a^5*c^3*e^2*f^2 - 2*a*b^7*d*e*f^2 - 2*b^7*c*d^2*e*f + 54*a^2*b^4*c^2*d^2*f^2 - 112*
a^3*b^2*c^3*d^2*f^2 + 16*a*b^3*c^4*d^3*e - 2*a*b^5*c^2*d*e^3 - 32*a^2*b*c^5*d^3*e - 32*a^3*b*c^4*d*e^3 - 20*a*
b^4*c^3*d^3*f - 12*a*b^6*c*d^2*f^2 - 20*a^3*b^4*c*d*f^3 - 2*a^2*b^5*c*e^3*f - 32*a^4*b*c^3*e^3*f + 16*a^4*b^3*
c*e*f^3 - 32*a^5*b*c^2*e*f^3 - 64*a^4*c^4*d*e^2*f - 6*a*b^4*c^3*d^2*e^2 + 16*a^2*b^3*c^3*d*e^3 + 64*a^2*b^2*c^
4*d^3*f + 64*a^4*b^2*c^2*d*f^3 + 16*a^3*b^3*c^2*e^3*f - 6*a^3*b^4*c*e^2*f^2 - 48*a^2*b^3*c^3*d^2*e*f - 36*a^2*
b^4*c^2*d*e^2*f + 96*a^3*b^2*c^3*d*e^2*f - 48*a^3*b^3*c^2*d*e*f^2 + 4*a*b^6*c*d*e^2*f + 18*a*b^5*c^2*d^2*e*f +
18*a^2*b^5*c*d*e*f^2 + 32*a^3*b*c^4*d^2*e*f + 32*a^4*b*c^3*d*e*f^2) - root(48416*a^6*b^2*c^6*d^4*e^2*f^4*z^4
- 41544*a^5*b^4*c^5*d^4*e^2*f^4*z^4 - 31872*a^7*b^2*c^5*d^3*e^2*f^5*z^4 - 31872*a^5*b^2*c^7*d^5*e^2*f^3*z^4 -
29184*a^6*b^2*c^6*d^3*e^4*f^3*z^4 + 28800*a^5*b^4*c^5*d^3*e^4*f^3*z^4 + 21510*a^4*b^6*c^4*d^4*e^2*f^4*z^4 + 21
408*a^6*b^4*c^4*d^3*e^2*f^5*z^4 + 21408*a^4*b^4*c^6*d^5*e^2*f^3*z^4 - 18112*a^7*b^3*c^4*d^2*e^3*f^5*z^4 - 1811
2*a^4*b^3*c^7*d^5*e^3*f^2*z^4 - 15600*a^5*b^5*c^4*d^3*e^3*f^4*z^4 - 15600*a^4*b^5*c^5*d^4*e^3*f^3*z^4 + 15296*
a^6*b^3*c^5*d^3*e^3*f^4*z^4 + 15296*a^5*b^3*c^6*d^4*e^3*f^3*z^4 + 14016*a^7*b^2*c^5*d^2*e^4*f^4*z^4 + 14016*a^
5*b^2*c^7*d^4*e^4*f^2*z^4 - 13920*a^4*b^6*c^4*d^3*e^4*f^3*z^4 - 11648*a^6*b^3*c^5*d^2*e^5*f^3*z^4 - 11648*a^5*
b^3*c^6*d^3*e^5*f^2*z^4 + 10432*a^6*b^2*c^6*d^2*e^6*f^2*z^4 + 9008*a^6*b^5*c^3*d^2*e^3*f^5*z^4 + 9008*a^3*b^5*
c^6*d^5*e^3*f^2*z^4 + 8544*a^5*b^5*c^4*d^2*e^5*f^3*z^4 + 8544*a^4*b^5*c^5*d^3*e^5*f^2*z^4 - 8496*a^5*b^4*c^5*d
^2*e^6*f^2*z^4 + 7488*a^8*b^2*c^4*d^2*e^2*f^6*z^4 + 7488*a^4*b^2*c^8*d^6*e^2*f^2*z^4 + 7380*a^4*b^7*c^3*d^3*e^
3*f^4*z^4 + 7380*a^3*b^7*c^4*d^4*e^3*f^3*z^4 - 6720*a^3*b^8*c^3*d^4*e^2*f^4*z^4 - 5784*a^5*b^6*c^3*d^3*e^2*f^5
*z^4 - 5784*a^3*b^6*c^5*d^5*e^2*f^3*z^4 - 3440*a^6*b^4*c^4*d^2*e^4*f^4*z^4 - 3440*a^4*b^4*c^6*d^4*e^4*f^2*z^4
+ 3360*a^3*b^8*c^3*d^3*e^4*f^3*z^4 + 3140*a^4*b^6*c^4*d^2*e^6*f^2*z^4 - 2760*a^4*b^7*c^3*d^2*e^5*f^3*z^4 - 276
0*a^3*b^7*c^4*d^3*e^5*f^2*z^4 - 1764*a^5*b^7*c^2*d^2*e^3*f^5*z^4 - 1764*a^2*b^7*c^5*d^5*e^3*f^2*z^4 - 1640*a^3
*b^9*c^2*d^3*e^3*f^4*z^4 - 1640*a^2*b^9*c^3*d^4*e^3*f^3*z^4 - 1604*a^6*b^6*c^2*d^2*e^2*f^6*z^4 - 1604*a^2*b^6*
c^6*d^6*e^2*f^2*z^4 - 1500*a^5*b^6*c^3*d^2*e^4*f^4*z^4 - 1500*a^3*b^6*c^5*d^4*e^4*f^2*z^4 + 1140*a^2*b^10*c^2*
d^4*e^2*f^4*z^4 + 810*a^4*b^8*c^2*d^2*e^4*f^4*z^4 + 810*a^2*b^8*c^4*d^4*e^4*f^2*z^4 - 544*a^3*b^8*c^3*d^2*e^6*
f^2*z^4 + 416*a^3*b^9*c^2*d^2*e^5*f^3*z^4 + 416*a^2*b^9*c^3*d^3*e^5*f^2*z^4 - 384*a^2*b^10*c^2*d^3*e^4*f^3*z^4
+ 180*a^4*b^8*c^2*d^3*e^2*f^5*z^4 + 180*a^2*b^8*c^4*d^5*e^2*f^3*z^4 + 48*a^7*b^4*c^3*d^2*e^2*f^6*z^4 + 48*a^3
*b^4*c^7*d^6*e^2*f^2*z^4 + 36*a^2*b^10*c^2*d^2*e^6*f^2*z^4 - 1024*a^10*b*c^3*d*e*f^8*z^4 - 1024*a^3*b*c^10*d^8
*e*f*z^4 - 192*a^8*b^5*c*d*e*f^8*z^4 - 192*a*b^5*c^8*d^8*e*f*z^4 + 16128*a^7*b^3*c^4*d^3*e*f^6*z^4 + 16128*a^4
*b^3*c^7*d^6*e*f^3*z^4 - 11712*a^6*b^5*c^3*d^3*e*f^6*z^4 - 11712*a^3*b^5*c^6*d^6*e*f^3*z^4 + 11520*a^8*b*c^5*d
^2*e^3*f^5*z^4 + 11520*a^5*b*c^8*d^5*e^3*f^2*z^4 - 9984*a^6*b^3*c^5*d^4*e*f^5*z^4 - 9984*a^5*b^3*c^6*d^5*e*f^4
*z^4 + 8640*a^5*b^5*c^4*d^4*e*f^5*z^4 + 8640*a^4*b^5*c^5*d^5*e*f^4*z^4 - 7424*a^7*b*c^6*d^3*e^3*f^4*z^4 - 7424
*a^6*b*c^7*d^4*e^3*f^3*z^4 - 6912*a^8*b^3*c^3*d^2*e*f^7*z^4 - 6912*a^3*b^3*c^8*d^7*e*f^2*z^4 + 4800*a^7*b^3*c^
4*d*e^5*f^4*z^4 + 4800*a^4*b^3*c^7*d^4*e^5*f*z^4 + 4608*a^7*b*c^6*d^2*e^5*f^3*z^4 + 4608*a^6*b*c^7*d^3*e^5*f^2
*z^4 - 4560*a^4*b^7*c^3*d^4*e*f^5*z^4 - 4560*a^3*b^7*c^4*d^5*e*f^4*z^4 + 4176*a^5*b^7*c^2*d^3*e*f^6*z^4 + 4176
*a^2*b^7*c^5*d^6*e*f^3*z^4 + 3264*a^7*b^5*c^2*d^2*e*f^7*z^4 + 3264*a^2*b^5*c^7*d^7*e*f^2*z^4 + 3008*a^8*b^3*c^
3*d*e^3*f^6*z^4 + 3008*a^3*b^3*c^8*d^6*e^3*f*z^4 + 2880*a^6*b^3*c^5*d*e^7*f^2*z^4 + 2880*a^5*b^3*c^6*d^2*e^7*f
*z^4 - 2240*a^7*b^4*c^3*d*e^4*f^5*z^4 - 2240*a^3*b^4*c^7*d^5*e^4*f*z^4 - 1488*a^5*b^5*c^4*d*e^7*f^2*z^4 - 1488
*a^4*b^5*c^5*d^2*e^7*f*z^4 + 1440*a^3*b^9*c^2*d^4*e*f^5*z^4 + 1440*a^2*b^9*c^3*d^5*e*f^4*z^4 - 1328*a^6*b^5*c^
3*d*e^5*f^4*z^4 - 1328*a^3*b^5*c^6*d^4*e^5*f*z^4 - 1152*a^7*b^2*c^5*d*e^6*f^3*z^4 - 1152*a^5*b^2*c^7*d^3*e^6*f
*z^4 - 1120*a^6*b^4*c^4*d*e^6*f^3*z^4 - 1120*a^4*b^4*c^6*d^3*e^6*f*z^4 + 912*a^6*b^6*c^2*d*e^4*f^5*z^4 + 912*a
^2*b^6*c^6*d^5*e^4*f*z^4 + 872*a^5*b^6*c^3*d*e^6*f^3*z^4 + 872*a^3*b^6*c^5*d^3*e^6*f*z^4 + 768*a^8*b^2*c^4*d*e
^4*f^5*z^4 + 768*a^4*b^2*c^8*d^5*e^4*f*z^4 - 672*a^8*b^4*c^2*d*e^2*f^7*z^4 - 672*a^2*b^4*c^8*d^7*e^2*f*z^4 - 6
24*a^7*b^5*c^2*d*e^3*f^6*z^4 - 624*a^2*b^5*c^7*d^6*e^3*f*z^4 + 480*a^5*b^8*c*d^2*e^2*f^6*z^4 + 480*a*b^8*c^5*d
^6*e^2*f^2*z^4 + 316*a^4*b^7*c^3*d*e^7*f^2*z^4 + 316*a^3*b^7*c^4*d^2*e^7*f*z^4 - 204*a^4*b^8*c^2*d*e^6*f^3*z^4
- 204*a^2*b^8*c^4*d^3*e^6*f*z^4 + 168*a^3*b^10*c*d^3*e^2*f^5*z^4 + 168*a*b^10*c^3*d^5*e^2*f^3*z^4 + 156*a^2*b
^11*c*d^3*e^3*f^4*z^4 + 156*a*b^11*c^2*d^4*e^3*f^3*z^4 + 128*a^9*b^2*c^3*d*e^2*f^7*z^4 + 128*a^3*b^2*c^9*d^7*e
^2*f*z^4 - 124*a^3*b^10*c*d^2*e^4*f^4*z^4 - 124*a*b^10*c^3*d^4*e^4*f^2*z^4 + 100*a^4*b^9*c*d^2*e^3*f^5*z^4 + 1
00*a*b^9*c^4*d^5*e^3*f^2*z^4 + 36*a^5*b^7*c^2*d*e^5*f^4*z^4 + 36*a^2*b^7*c^5*d^4*e^5*f*z^4 - 24*a^3*b^9*c^2*d*
e^7*f^2*z^4 - 24*a^2*b^11*c*d^2*e^5*f^3*z^4 - 24*a^2*b^9*c^3*d^2*e^7*f*z^4 - 24*a*b^11*c^2*d^3*e^5*f^2*z^4 - 9
216*a^8*b*c^5*d^3*e*f^6*z^4 - 9216*a^5*b*c^8*d^6*e*f^3*z^4 - 5376*a^8*b*c^5*d*e^5*f^4*z^4 - 5376*a^5*b*c^8*d^4
*e^5*f*z^4 + 5120*a^9*b*c^4*d^2*e*f^7*z^4 + 5120*a^7*b*c^6*d^4*e*f^5*z^4 + 5120*a^6*b*c^7*d^5*e*f^4*z^4 + 5120
*a^4*b*c^9*d^7*e*f^2*z^4 - 4352*a^9*b*c^4*d*e^3*f^6*z^4 - 4352*a^4*b*c^9*d^6*e^3*f*z^4 - 1792*a^7*b*c^6*d*e^7*
f^2*z^4 - 1792*a^6*b*c^7*d^2*e^7*f*z^4 - 1600*a^6*b^2*c^6*d*e^8*f*z^4 + 912*a^5*b^4*c^5*d*e^8*f*z^4 + 768*a^9*
b^3*c^2*d*e*f^8*z^4 + 768*a^2*b^3*c^9*d^8*e*f*z^4 - 720*a^4*b^9*c*d^3*e*f^6*z^4 - 720*a*b^9*c^4*d^6*e*f^3*z^4
- 656*a^6*b^7*c*d^2*e*f^7*z^4 - 656*a*b^7*c^6*d^7*e*f^2*z^4 - 240*a^2*b^11*c*d^4*e*f^5*z^4 - 240*a*b^11*c^2*d^
5*e*f^4*z^4 + 216*a^7*b^6*c*d*e^2*f^7*z^4 + 216*a*b^6*c^7*d^7*e^2*f*z^4 - 204*a^4*b^6*c^4*d*e^8*f*z^4 - 144*a^
5*b^8*c*d*e^4*f^5*z^4 - 144*a*b^8*c^5*d^5*e^4*f*z^4 - 84*a*b^12*c*d^4*e^2*f^4*z^4 + 36*a^4*b^9*c*d*e^5*f^4*z^4
+ 36*a*b^9*c^4*d^4*e^5*f*z^4 + 20*a^6*b^7*c*d*e^3*f^6*z^4 + 20*a*b^7*c^6*d^6*e^3*f*z^4 + 16*a^3*b^10*c*d*e^6*
f^3*z^4 + 16*a^3*b^8*c^3*d*e^8*f*z^4 + 16*a*b^12*c*d^3*e^4*f^3*z^4 + 16*a*b^10*c^3*d^3*e^6*f*z^4 + 48*b^11*c^3
*d^6*e*f^3*z^4 + 48*b^9*c^5*d^7*e*f^2*z^4 - 20*b^8*c^6*d^7*e^2*f*z^4 + 8*b^10*c^4*d^5*e^4*f*z^4 - 4*b^13*c*d^4
*e^3*f^3*z^4 - 4*b^11*c^3*d^4*e^5*f*z^4 + 4*b^9*c^5*d^6*e^3*f*z^4 + 3072*a^9*c^5*d*e^4*f^5*z^4 + 3072*a^5*c^9*
d^5*e^4*f*z^4 + 2560*a^8*c^6*d*e^6*f^3*z^4 + 2560*a^6*c^8*d^3*e^6*f*z^4 + 1536*a^10*c^4*d*e^2*f^7*z^4 + 1536*a
^4*c^10*d^7*e^2*f*z^4 + 48*a^5*b^9*d^2*e*f^7*z^4 + 48*a^3*b^11*d^3*e*f^6*z^4 - 20*a^6*b^8*d*e^2*f^7*z^4 + 8*a^
4*b^10*d*e^4*f^5*z^4 + 4*a^5*b^9*d*e^3*f^6*z^4 - 4*a^3*b^11*d*e^5*f^4*z^4 - 4*a*b^13*d^3*e^3*f^4*z^4 + 768*a^9
*b*c^4*e^5*f^5*z^4 + 768*a^8*b*c^5*e^7*f^3*z^4 + 256*a^10*b*c^3*e^3*f^7*z^4 - 192*a^6*b^3*c^5*e^9*f*z^4 - 68*a
^7*b^6*c*e^4*f^6*z^4 + 48*a^8*b^5*c*e^3*f^7*z^4 + 48*a^5*b^5*c^4*e^9*f*z^4 + 36*a^6*b^7*c*e^5*f^5*z^4 - 12*a^9
*b^4*c*e^2*f^8*z^4 - 4*a^4*b^9*c*e^7*f^3*z^4 - 4*a^4*b^7*c^3*e^9*f*z^4 + 384*a^5*b^8*c*d^3*f^7*z^4 + 384*a*b^8
*c^5*d^7*f^3*z^4 + 288*a^3*b^10*c*d^4*f^6*z^4 + 288*a*b^10*c^3*d^6*f^4*z^4 + 224*a^7*b^6*c*d^2*f^8*z^4 + 224*a
*b^6*c^7*d^8*f^2*z^4 - 192*a^10*b^2*c^2*d*f^9*z^4 - 192*a^2*b^2*c^10*d^9*f*z^4 + 768*a^5*b*c^8*d^3*e^7*z^4 + 7
68*a^4*b*c^9*d^5*e^5*z^4 + 256*a^3*b*c^10*d^7*e^3*z^4 - 192*a^5*b^3*c^6*d*e^9*z^4 - 68*a*b^6*c^7*d^6*e^4*z^4 +
48*a^4*b^5*c^5*d*e^9*z^4 + 48*a*b^5*c^8*d^7*e^3*z^4 + 36*a*b^7*c^6*d^5*e^5*z^4 - 12*a*b^4*c^9*d^8*e^2*z^4 - 4
*a^3*b^7*c^4*d*e^9*z^4 - 4*a*b^9*c^4*d^3*e^7*z^4 + 16*b^13*c*d^5*e*f^4*z^4 + 16*b^7*c^7*d^8*e*f*z^4 + 768*a^7*
c^7*d*e^8*f*z^4 + 16*a^7*b^7*d*e*f^8*z^4 + 16*a*b^13*d^4*e*f^5*z^4 + 256*a^7*b*c^6*e^9*f*z^4 + 80*a*b^12*c*d^5
*f^5*z^4 + 48*a^9*b^4*c*d*f^9*z^4 + 48*a*b^4*c^9*d^9*f*z^4 + 256*a^6*b*c^7*d*e^9*z^4 - 42*b^10*c^4*d^6*e^2*f^2
*z^4 - 20*b^12*c^2*d^5*e^2*f^3*z^4 + 6*b^12*c^2*d^4*e^4*f^2*z^4 + 4*b^11*c^3*d^5*e^3*f^2*z^4 - 24960*a^7*c^7*d
^4*e^2*f^4*z^4 + 18944*a^8*c^6*d^3*e^2*f^5*z^4 + 18944*a^6*c^8*d^5*e^2*f^3*z^4 + 14336*a^7*c^7*d^3*e^4*f^3*z^4
- 9984*a^8*c^6*d^2*e^4*f^4*z^4 - 9984*a^6*c^8*d^4*e^4*f^2*z^4 - 7936*a^9*c^5*d^2*e^2*f^6*z^4 - 7936*a^5*c^9*d
^6*e^2*f^2*z^4 - 4352*a^7*c^7*d^2*e^6*f^2*z^4 - 42*a^4*b^10*d^2*e^2*f^6*z^4 - 20*a^2*b^12*d^3*e^2*f^5*z^4 + 6*
a^2*b^12*d^2*e^4*f^4*z^4 + 4*a^3*b^11*d^2*e^3*f^5*z^4 - 480*a^8*b^2*c^4*e^6*f^4*z^4 + 440*a^7*b^4*c^3*e^6*f^4*
z^4 - 320*a^8*b^3*c^3*e^5*f^5*z^4 - 320*a^7*b^3*c^4*e^7*f^3*z^4 + 240*a^8*b^4*c^2*e^4*f^6*z^4 + 240*a^6*b^4*c^
4*e^8*f^2*z^4 - 192*a^9*b^3*c^2*e^3*f^7*z^4 - 192*a^9*b^2*c^3*e^4*f^6*z^4 - 192*a^7*b^2*c^5*e^8*f^2*z^4 - 90*a
^6*b^6*c^2*e^6*f^4*z^4 - 68*a^5*b^6*c^3*e^8*f^2*z^4 + 48*a^10*b^2*c^2*e^2*f^8*z^4 - 48*a^7*b^5*c^2*e^5*f^5*z^4
- 48*a^6*b^5*c^3*e^7*f^3*z^4 + 36*a^5*b^7*c^2*e^7*f^3*z^4 + 6*a^4*b^8*c^2*e^8*f^2*z^4 - 33920*a^6*b^2*c^6*d^5
*f^5*z^4 + 27936*a^5*b^4*c^5*d^5*f^5*z^4 + 26112*a^7*b^2*c^5*d^4*f^6*z^4 + 26112*a^5*b^2*c^7*d^6*f^4*z^4 - 203
52*a^6*b^4*c^4*d^4*f^6*z^4 - 20352*a^4*b^4*c^6*d^6*f^4*z^4 - 13080*a^4*b^6*c^4*d^5*f^5*z^4 - 11520*a^8*b^2*c^4
*d^3*f^7*z^4 - 11520*a^4*b^2*c^8*d^7*f^3*z^4 + 8736*a^5*b^6*c^3*d^4*f^6*z^4 + 8736*a^3*b^6*c^5*d^6*f^4*z^4 + 7
488*a^7*b^4*c^3*d^3*f^7*z^4 + 7488*a^3*b^4*c^7*d^7*f^3*z^4 + 3840*a^3*b^8*c^3*d^5*f^5*z^4 + 2560*a^9*b^2*c^3*d
^2*f^8*z^4 + 2560*a^3*b^2*c^9*d^8*f^2*z^4 - 2416*a^6*b^6*c^2*d^3*f^7*z^4 - 2416*a^2*b^6*c^6*d^7*f^3*z^4 - 2160
*a^4*b^8*c^2*d^4*f^6*z^4 - 2160*a^2*b^8*c^4*d^6*f^4*z^4 - 1152*a^8*b^4*c^2*d^2*f^8*z^4 - 1152*a^2*b^4*c^8*d^8*
f^2*z^4 - 720*a^2*b^10*c^2*d^5*f^5*z^4 - 480*a^4*b^2*c^8*d^4*e^6*z^4 + 440*a^3*b^4*c^7*d^4*e^6*z^4 - 320*a^4*b
^3*c^7*d^3*e^7*z^4 - 320*a^3*b^3*c^8*d^5*e^5*z^4 + 240*a^4*b^4*c^6*d^2*e^8*z^4 + 240*a^2*b^4*c^8*d^6*e^4*z^4 -
192*a^5*b^2*c^7*d^2*e^8*z^4 - 192*a^3*b^2*c^9*d^6*e^4*z^4 - 192*a^2*b^3*c^9*d^7*e^3*z^4 - 90*a^2*b^6*c^6*d^4*
e^6*z^4 - 68*a^3*b^6*c^5*d^2*e^8*z^4 - 48*a^3*b^5*c^6*d^3*e^7*z^4 - 48*a^2*b^5*c^7*d^5*e^5*z^4 + 48*a^2*b^2*c^
10*d^8*e^2*z^4 + 36*a^2*b^7*c^5*d^3*e^7*z^4 + 6*a^2*b^8*c^4*d^2*e^8*z^4 - 4*b^6*c^8*d^9*f*z^4 + 256*a^11*c^3*d
*f^9*z^4 + 256*a^3*c^11*d^9*f*z^4 - 4*a^8*b^6*d*f^9*z^4 - 384*a^9*c^5*e^6*f^4*z^4 - 256*a^10*c^4*e^4*f^6*z^4 -
256*a^8*c^6*e^8*f^2*z^4 - 64*a^11*c^3*e^2*f^8*z^4 - 24*b^10*c^4*d^7*f^3*z^4 - 16*b^12*c^2*d^6*f^4*z^4 - 16*b^
8*c^6*d^8*f^2*z^4 + 17920*a^7*c^7*d^5*f^5*z^4 - 14336*a^8*c^6*d^4*f^6*z^4 - 14336*a^6*c^8*d^6*f^4*z^4 + 7168*a
^9*c^5*d^3*f^7*z^4 + 7168*a^5*c^9*d^7*f^3*z^4 - 2048*a^10*c^4*d^2*f^8*z^4 - 2048*a^4*c^10*d^8*f^2*z^4 + 6*b^8*
c^6*d^6*e^4*z^4 + 6*a^6*b^8*e^4*f^6*z^4 - 4*b^9*c^5*d^5*e^5*z^4 - 4*b^7*c^7*d^7*e^3*z^4 - 4*a^7*b^7*e^3*f^7*z^
4 - 4*a^5*b^9*e^5*f^5*z^4 - 384*a^5*c^9*d^4*e^6*z^4 - 256*a^6*c^8*d^2*e^8*z^4 - 256*a^4*c^10*d^6*e^4*z^4 - 64*
a^3*c^11*d^8*e^2*z^4 - 24*a^4*b^10*d^3*f^7*z^4 - 16*a^6*b^8*d^2*f^8*z^4 - 16*a^2*b^12*d^4*f^6*z^4 + 48*a^6*b^2
*c^6*e^10*z^4 - 12*a^5*b^4*c^5*e^10*z^4 - 4*b^14*d^5*f^5*z^4 - 64*a^7*c^7*e^10*z^4 + b^14*d^4*e^2*f^4*z^4 + b^
10*c^4*d^4*e^6*z^4 + b^6*c^8*d^8*e^2*z^4 + a^8*b^6*e^2*f^8*z^4 + a^4*b^10*e^6*f^4*z^4 + a^4*b^6*c^4*e^10*z^4 -
4820*A*B*a^4*b*c^5*d^2*e^2*f^4*z^2 + 2976*A*B*a^3*b*c^6*d^3*e^2*f^3*z^2 - 2328*A*B*a^3*b*c^6*d^2*e^4*f^2*z^2
+ 1848*A*B*a^2*b^4*c^4*d^3*e*f^4*z^2 - 1768*A*B*a^3*b^4*c^3*d^2*e*f^5*z^2 + 1528*A*B*a^4*b^2*c^4*d^2*e*f^5*z^2
- 1136*A*B*a^3*b^2*c^5*d^3*e*f^4*z^2 - 974*A*B*a^4*b^3*c^3*d*e^2*f^5*z^2 + 692*A*B*a^2*b*c^7*d^4*e^2*f^2*z^2
+ 588*A*B*a*b^6*c^3*d^2*e^3*f^3*z^2 - 580*A*B*a^3*b^3*c^4*d*e^4*f^3*z^2 + 488*A*B*a^3*b^4*c^3*d*e^3*f^4*z^2 -
444*A*B*a^2*b^2*c^6*d^2*e^5*f*z^2 - 412*A*B*a*b^5*c^4*d^2*e^4*f^2*z^2 + 366*A*B*a^2*b^6*c^2*d^2*e*f^5*z^2 - 35
2*A*B*a^2*b^2*c^6*d^4*e*f^3*z^2 + 326*A*B*a^2*b^4*c^4*d*e^5*f^2*z^2 + 324*A*B*a*b^5*c^4*d^3*e^2*f^3*z^2 - 302*
A*B*a*b^3*c^6*d^4*e^2*f^2*z^2 - 296*A*B*a*b^7*c^2*d^2*e^2*f^4*z^2 + 122*A*B*a^4*b^2*c^4*d*e^3*f^4*z^2 - 122*A*
B*a^2*b^6*c^2*d*e^3*f^4*z^2 - 84*A*B*a^3*b^2*c^5*d*e^5*f^2*z^2 + 72*A*B*a*b^4*c^5*d^3*e^3*f^2*z^2 - 64*A*B*a^2
*b^5*c^3*d*e^4*f^3*z^2 + 60*A*B*a^3*b^5*c^2*d*e^2*f^5*z^2 + 1312*A*B*a^5*b*c^4*d*e^2*f^5*z^2 + 1040*A*B*a^4*b*
c^5*d*e^4*f^3*z^2 - 500*A*B*a*b^6*c^3*d^3*e*f^4*z^2 - 376*A*B*a*b^2*c^7*d^5*e*f^2*z^2 + 276*A*B*a^4*b^4*c^2*d*
e*f^6*z^2 - 262*A*B*a^2*b^3*c^5*d*e^6*f*z^2 + 238*A*B*a*b^2*c^7*d^4*e^3*f*z^2 + 232*A*B*a^5*b^2*c^3*d*e*f^6*z^
2 - 176*A*B*a^2*b*c^7*d^3*e^4*f*z^2 - 120*A*B*a*b^6*c^3*d*e^5*f^2*z^2 - 108*A*B*a*b^4*c^5*d^4*e*f^3*z^2 + 68*A
*B*a*b^7*c^2*d*e^4*f^3*z^2 + 68*A*B*a*b^4*c^5*d^2*e^5*f*z^2 + 46*A*B*a^2*b^7*c*d*e^2*f^5*z^2 - 36*A*B*a*b^3*c^
6*d^3*e^4*f*z^2 - 1932*A*B*a^2*b^3*c^5*d^3*e^2*f^3*z^2 - 1818*A*B*a^2*b^4*c^4*d^2*e^3*f^3*z^2 + 1620*A*B*a^3*b
^3*c^4*d^2*e^2*f^4*z^2 + 1560*A*B*a^2*b^3*c^5*d^2*e^4*f^2*z^2 + 1244*A*B*a^3*b^2*c^5*d^2*e^3*f^3*z^2 + 820*A*B
*a^2*b^2*c^6*d^3*e^3*f^2*z^2 + 480*A*B*a^2*b^5*c^3*d^2*e^2*f^4*z^2 + 352*A*B*a^3*b*c^6*d*e^6*f*z^2 - 108*A*B*a
^3*b^6*c*d*e*f^6*z^2 + 82*A*B*a*b^5*c^4*d*e^6*f*z^2 - 64*A*B*a*b*c^8*d^5*e^2*f*z^2 + 16*A*B*a*b^8*c*d^2*e*f^5*
z^2 - 4*A*B*a*b^8*c*d*e^3*f^4*z^2 + 16*B^2*a*b*c^8*d^6*e*f*z^2 + 56*A*B*b^2*c^8*d^6*e*f*z^2 - 8*A*B*b^9*c*d*e^
4*f^3*z^2 - 8*A*B*b^7*c^3*d*e^6*f*z^2 - 800*A*B*a^6*c^4*d*e*f^6*z^2 + 10*A*B*a^2*b^8*d*e*f^6*z^2 - 6*A*B*a*b^9
*d*e^2*f^5*z^2 - 12*A*B*a^5*b^4*c*e*f^7*z^2 + 912*A*B*a^6*b*c^3*d*f^7*z^2 + 192*A*B*a^4*b^5*c*d*f^7*z^2 + 192*
A*B*a*b*c^8*d^6*f^2*z^2 - 20*A*B*a*b^4*c^5*d*e^7*z^2 + 4*A*B*a*b*c^8*d^4*e^4*z^2 + 2144*B^2*a^4*b*c^5*d^3*e*f^
4*z^2 - 1120*B^2*a^3*b*c^6*d^4*e*f^3*z^2 - 688*B^2*a^5*b*c^4*d^2*e*f^5*z^2 - 256*B^2*a^3*b*c^6*d^2*e^5*f*z^2 +
152*B^2*a*b^3*c^6*d^5*e*f^2*z^2 + 120*B^2*a^5*b^3*c^2*d*e*f^6*z^2 - 116*B^2*a^5*b*c^4*d*e^3*f^4*z^2 + 110*B^2
*a*b^7*c^2*d^3*e*f^4*z^2 - 80*B^2*a^2*b*c^7*d^5*e*f^2*z^2 - 72*B^2*a*b^5*c^4*d^4*e*f^3*z^2 - 48*B^2*a^4*b*c^5*
d*e^5*f^2*z^2 - 46*B^2*a*b^3*c^6*d^4*e^3*f*z^2 - 44*B^2*a*b^4*c^5*d^3*e^4*f*z^2 - 34*B^2*a*b^5*c^4*d^2*e^5*f*z
^2 + 20*B^2*a^2*b*c^7*d^4*e^3*f*z^2 - 10*B^2*a^3*b^6*c*d*e^2*f^5*z^2 - 10*B^2*a^2*b^7*c*d^2*e*f^5*z^2 - 10*B^2
*a*b^2*c^7*d^5*e^2*f*z^2 - 7*B^2*a^2*b^4*c^4*d*e^6*f*z^2 - 6*B^2*a^3*b^2*c^5*d*e^6*f*z^2 + 4*B^2*a*b^8*c*d^2*e
^2*f^4*z^2 - 2*B^2*a^2*b^7*c*d*e^3*f^4*z^2 + 3196*A^2*a^4*b*c^5*d*e^3*f^4*z^2 - 3184*A^2*a^4*b*c^5*d^2*e*f^5*z
^2 + 1568*A^2*a^3*b*c^6*d^3*e*f^4*z^2 + 1504*A^2*a^3*b*c^6*d*e^5*f^2*z^2 - 656*A^2*a^4*b^3*c^3*d*e*f^6*z^2 - 4
00*A^2*a*b^6*c^3*d*e^4*f^3*z^2 + 314*A^2*a*b^5*c^4*d*e^5*f^2*z^2 - 264*A^2*a^3*b^5*c^2*d*e*f^6*z^2 + 240*A^2*a
^2*b^2*c^6*d*e^6*f*z^2 - 224*A^2*a^2*b*c^7*d^4*e*f^3*z^2 + 216*A^2*a*b^5*c^4*d^3*e*f^4*z^2 - 192*A^2*a^2*b*c^7
*d^2*e^5*f*z^2 + 178*A^2*a*b^7*c^2*d*e^3*f^4*z^2 - 154*A^2*a*b^7*c^2*d^2*e*f^5*z^2 + 128*A^2*a*b^3*c^6*d^4*e*f
^3*z^2 + 106*A^2*a*b^3*c^6*d^2*e^5*f*z^2 - 12*A^2*a*b^2*c^7*d^3*e^4*f*z^2 - 58*A*B*b^8*c^2*d^2*e^3*f^3*z^2 + 4
0*A*B*b^7*c^3*d^2*e^4*f^2*z^2 - 28*A*B*b^7*c^3*d^3*e^2*f^3*z^2 - 24*A*B*b^5*c^5*d^4*e^2*f^2*z^2 - 20*A*B*b^6*c
^4*d^3*e^3*f^2*z^2 + 2768*A*B*a^4*c^6*d^2*e^3*f^3*z^2 - 1712*A*B*a^3*c^7*d^3*e^3*f^2*z^2 - 156*A*B*a^4*b^2*c^4
*e^5*f^3*z^2 + 146*A*B*a^4*b^3*c^3*e^4*f^4*z^2 - 106*A*B*a^5*b^2*c^3*e^3*f^5*z^2 + 90*A*B*a^5*b^3*c^2*e^2*f^6*
z^2 + 38*A*B*a^3*b^3*c^4*e^6*f^2*z^2 - 36*A*B*a^3*b^5*c^2*e^4*f^4*z^2 + 16*A*B*a^3*b^4*c^3*e^5*f^3*z^2 - 9*A*B
*a^4*b^4*c^2*e^3*f^5*z^2 - 8*A*B*a^2*b^5*c^3*e^6*f^2*z^2 + 2*A*B*a^2*b^6*c^2*e^5*f^3*z^2 + 920*A*B*a^4*b^3*c^3
*d^2*f^6*z^2 - 480*A*B*a^2*b^5*c^3*d^3*f^5*z^2 - 336*A*B*a^2*b^3*c^5*d^4*f^4*z^2 - 272*A*B*a^3*b^3*c^4*d^3*f^5
*z^2 + 240*A*B*a^3*b^5*c^2*d^2*f^6*z^2 - 32*A*B*a*c^9*d^6*e*f*z^2 - 792*B^2*a^2*b^3*c^5*d^3*e^3*f^2*z^2 + 714*
B^2*a^2*b^4*c^4*d^3*e^2*f^3*z^2 - 572*B^2*a^3*b^2*c^5*d^3*e^2*f^3*z^2 - 475*B^2*a^2*b^2*c^6*d^4*e^2*f^2*z^2 +
265*B^2*a^4*b^2*c^4*d^2*e^2*f^4*z^2 + 260*B^2*a^3*b^3*c^4*d^2*e^3*f^3*z^2 - 212*B^2*a^3*b^4*c^3*d^2*e^2*f^4*z^
2 + 180*B^2*a^3*b^2*c^5*d^2*e^4*f^2*z^2 - 158*B^2*a^2*b^4*c^4*d^2*e^4*f^2*z^2 + 47*B^2*a^2*b^6*c^2*d^2*e^2*f^4
*z^2 + 16*B^2*a^2*b^5*c^3*d^2*e^3*f^3*z^2 + 2752*A^2*a^3*b^2*c^5*d^2*e^2*f^4*z^2 - 2148*A^2*a^2*b^4*c^4*d^2*e^
2*f^4*z^2 + 2064*A^2*a^2*b^3*c^5*d^2*e^3*f^3*z^2 - 424*A^2*a^2*b^2*c^6*d^3*e^2*f^3*z^2 - 198*A^2*a^2*b^2*c^6*d
^2*e^4*f^2*z^2 - 272*B^2*a^6*b*c^3*d*e*f^6*z^2 - 24*B^2*a^4*b^5*c*d*e*f^6*z^2 + 1808*A^2*a^5*b*c^4*d*e*f^6*z^2
- 244*A^2*a*b*c^8*d^4*e^3*f*z^2 + 208*A^2*a*b*c^8*d^5*e*f^2*z^2 + 134*A^2*a^2*b^7*c*d*e*f^6*z^2 - 76*A^2*a*b^
4*c^5*d*e^6*f*z^2 + 4*A^2*a*b^8*c*d*e^2*f^5*z^2 + 148*A*B*b^4*c^6*d^5*e*f^2*z^2 + 65*A*B*b^6*c^4*d^4*e*f^3*z^2
+ 46*A*B*b^8*c^2*d^3*e*f^4*z^2 - 38*A*B*b^3*c^7*d^5*e^2*f*z^2 + 34*A*B*b^9*c*d^2*e^2*f^4*z^2 - 29*A*B*b^4*c^6
*d^4*e^3*f*z^2 + 20*A*B*b^5*c^5*d^3*e^4*f*z^2 + 12*A*B*b^8*c^2*d*e^5*f^2*z^2 - 7*A*B*b^6*c^4*d^2*e^5*f*z^2 - 2
880*A*B*a^4*c^6*d^3*e*f^4*z^2 + 2784*A*B*a^5*c^5*d^2*e*f^5*z^2 - 1112*A*B*a^5*c^5*d*e^3*f^4*z^2 + 896*A*B*a^3*
c^7*d^4*e*f^3*z^2 + 848*A*B*a^3*c^7*d^2*e^5*f*z^2 - 560*A*B*a^4*c^6*d*e^5*f^2*z^2 + 96*A*B*a^2*c^8*d^5*e*f^2*z
^2 - 88*A*B*a^2*c^8*d^4*e^3*f*z^2 - 100*A*B*a^6*b*c^3*e^2*f^6*z^2 - 76*A*B*a^5*b*c^4*e^4*f^4*z^2 + 48*A*B*a^6*
b^2*c^2*e*f^7*z^2 - 42*A*B*a^3*b^2*c^5*e^7*f*z^2 + 36*A*B*a^4*b*c^5*e^6*f^2*z^2 - 24*A*B*a^4*b^5*c*e^2*f^6*z^2
+ 10*A*B*a^3*b^6*c*e^3*f^5*z^2 + 7*A*B*a^2*b^4*c^4*e^7*f*z^2 + 2*A*B*a^2*b^7*c*e^4*f^4*z^2 - 2496*A*B*a^5*b*c
^4*d^2*f^6*z^2 + 1872*A*B*a^4*b*c^5*d^3*f^5*z^2 - 744*A*B*a^5*b^3*c^2*d*f^7*z^2 - 720*A*B*a^2*b*c^7*d^5*f^3*z^
2 + 504*A*B*a*b^3*c^6*d^5*f^3*z^2 + 256*A*B*a^3*b*c^6*d^4*f^4*z^2 + 168*A*B*a*b^7*c^2*d^3*f^5*z^2 - 144*A*B*a^
2*b^7*c*d^2*f^6*z^2 + 144*A*B*a*b^5*c^4*d^4*f^4*z^2 + 66*A*B*a^2*b^2*c^6*d*e^7*z^2 - 36*A*B*a*b^2*c^7*d^3*e^5*
z^2 + 20*A*B*a*b^3*c^6*d^2*e^6*z^2 + 12*A*B*a^2*b*c^7*d^2*e^6*z^2 + 1208*B^2*a^3*b*c^6*d^3*e^3*f^2*z^2 - 848*B
^2*a^3*b^3*c^4*d^3*e*f^4*z^2 + 672*B^2*a^2*b^3*c^5*d^4*e*f^3*z^2 - 632*B^2*a^4*b*c^5*d^2*e^3*f^3*z^2 + 432*B^2
*a^4*b^3*c^3*d^2*e*f^5*z^2 + 276*B^2*a^2*b^2*c^6*d^3*e^4*f*z^2 - 196*B^2*a*b^6*c^3*d^3*e^2*f^3*z^2 - 168*B^2*a
^2*b^5*c^3*d^3*e*f^4*z^2 + 154*B^2*a^2*b^3*c^5*d^2*e^5*f*z^2 + 148*B^2*a*b^5*c^4*d^3*e^3*f^2*z^2 + 96*B^2*a*b^
4*c^5*d^4*e^2*f^2*z^2 - 72*B^2*a^3*b^5*c^2*d^2*e*f^5*z^2 + 70*B^2*a^5*b^2*c^3*d*e^2*f^5*z^2 - 60*B^2*a^4*b^3*c
^3*d*e^3*f^4*z^2 + 52*B^2*a*b^6*c^3*d^2*e^4*f^2*z^2 + 36*B^2*a^4*b^2*c^4*d*e^4*f^3*z^2 - 32*B^2*a*b^7*c^2*d^2*
e^3*f^3*z^2 + 24*B^2*a^3*b^5*c^2*d*e^3*f^4*z^2 + 15*B^2*a^4*b^4*c^2*d*e^2*f^5*z^2 - 8*B^2*a^3*b^4*c^3*d*e^4*f^
3*z^2 + 8*B^2*a^2*b^5*c^3*d*e^5*f^2*z^2 - 2*B^2*a^3*b^3*c^4*d*e^5*f^2*z^2 - 2*B^2*a^2*b^6*c^2*d*e^4*f^3*z^2 -
3176*A^2*a^3*b*c^6*d^2*e^3*f^3*z^2 - 2252*A^2*a^4*b^2*c^4*d*e^2*f^5*z^2 + 1952*A^2*a^3*b^4*c^3*d*e^2*f^5*z^2 -
1496*A^2*a^3*b^3*c^4*d*e^3*f^4*z^2 + 1378*A^2*a^2*b^4*c^4*d*e^4*f^3*z^2 + 1184*A^2*a^3*b^3*c^4*d^2*e*f^5*z^2
- 1166*A^2*a^2*b^3*c^5*d*e^5*f^2*z^2 - 1164*A^2*a^3*b^2*c^5*d*e^4*f^3*z^2 - 1152*A^2*a^2*b^3*c^5*d^3*e*f^4*z^2
+ 578*A^2*a*b^6*c^3*d^2*e^2*f^4*z^2 - 548*A^2*a*b^5*c^4*d^2*e^3*f^3*z^2 + 440*A^2*a*b^2*c^7*d^4*e^2*f^2*z^2 -
412*A^2*a^2*b^6*c^2*d*e^2*f^5*z^2 - 360*A^2*a*b^3*c^6*d^3*e^3*f^2*z^2 + 312*A^2*a*b^4*c^5*d^3*e^2*f^3*z^2 + 2
48*A^2*a^2*b*c^7*d^3*e^3*f^2*z^2 - 224*A^2*a^2*b^5*c^3*d*e^3*f^4*z^2 + 216*A^2*a^2*b^5*c^3*d^2*e*f^5*z^2 + 52*
A^2*a*b^4*c^5*d^2*e^4*f^2*z^2 - 16*B^2*b^3*c^7*d^6*e*f*z^2 - 14*B^2*b^9*c*d^3*e*f^4*z^2 + 32*B^2*a^4*c^6*d*e^6
*f*z^2 - 20*A^2*b^9*c*d*e^3*f^4*z^2 + 18*A^2*b^9*c*d^2*e*f^5*z^2 + 8*A^2*b^6*c^4*d*e^6*f*z^2 - 360*A^2*a^3*c^7
*d*e^6*f*z^2 + 136*A^2*a*c^9*d^5*e^2*f*z^2 + 2*B^2*a^3*b^7*d*e*f^6*z^2 + 2*B^2*a*b^9*d^2*e*f^5*z^2 + 12*B^2*a^
4*b*c^5*e^7*f*z^2 - 204*A^2*a^3*b*c^6*e^7*f*z^2 - 128*A^2*a^6*b*c^3*e*f^7*z^2 - 48*A^2*a*b^5*c^4*e^7*f*z^2 - 3
6*B^2*a^5*b^4*c*d*f^7*z^2 - 24*A^2*a^4*b^5*c*e*f^7*z^2 - 16*B^2*a*b^8*c*d^3*f^5*z^2 - 164*A^2*a^3*b^6*c*d*f^7*
z^2 - 16*A^2*a*b^8*c*d^2*f^6*z^2 + 4*B^2*a^3*b*c^6*d*e^7*z^2 - 4*B^2*a*b*c^8*d^5*e^3*z^2 + 48*A^2*a*b*c^8*d^3*
e^5*z^2 + 36*A^2*a^2*b*c^7*d*e^7*z^2 - 6*A^2*a*b^3*c^6*d*e^7*z^2 + 136*A*B*a^6*c^4*e^3*f^5*z^2 - 96*A*B*b^5*c^
5*d^5*f^3*z^2 + 80*A*B*a^5*c^5*e^5*f^3*z^2 - 72*A*B*b^3*c^7*d^6*f^2*z^2 - 24*A*B*b^7*c^3*d^4*f^4*z^2 + 14*A*B*
b^3*c^7*d^4*e^4*z^2 - 14*A*B*b^2*c^8*d^5*e^3*z^2 - 2*A*B*b^5*c^5*d^2*e^6*z^2 - 2*A*B*b^4*c^6*d^3*e^5*z^2 + 2*A
*B*a^3*b^7*e^2*f^6*z^2 - A*B*a^2*b^8*e^3*f^5*z^2 + 16*A*B*a^2*c^8*d^3*e^5*z^2 - 2*A*B*a^2*b^3*c^5*e^8*z^2 + 22
*B^2*b^8*c^2*d^3*e^2*f^3*z^2 - 12*B^2*b^7*c^3*d^3*e^3*f^2*z^2 + 12*B^2*b^6*c^4*d^4*e^2*f^2*z^2 - 6*B^2*b^8*c^2
*d^2*e^4*f^2*z^2 - 864*B^2*a^4*c^6*d^3*e^2*f^3*z^2 + 496*B^2*a^3*c^7*d^4*e^2*f^2*z^2 + 224*B^2*a^5*c^5*d^2*e^2
*f^4*z^2 + 136*B^2*a^4*c^6*d^2*e^4*f^2*z^2 - 53*A^2*b^8*c^2*d^2*e^2*f^4*z^2 + 52*A^2*b^7*c^3*d^2*e^3*f^3*z^2 +
52*A^2*b^5*c^5*d^3*e^3*f^2*z^2 - 36*A^2*b^6*c^4*d^3*e^2*f^3*z^2 - 12*A^2*b^4*c^6*d^4*e^2*f^2*z^2 - 9*A^2*b^6*
c^4*d^2*e^4*f^2*z^2 + 836*A^2*a^4*c^6*d^2*e^2*f^4*z^2 - 668*A^2*a^2*c^8*d^4*e^2*f^2*z^2 + 656*A^2*a^3*c^7*d^2*
e^4*f^2*z^2 + 368*A^2*a^3*c^7*d^3*e^2*f^3*z^2 - 45*B^2*a^6*b^2*c^2*e^2*f^6*z^2 - 18*B^2*a^5*b^2*c^3*e^4*f^4*z^
2 - 9*B^2*a^4*b^2*c^4*e^6*f^2*z^2 - 6*B^2*a^5*b^3*c^2*e^3*f^5*z^2 + 3*B^2*a^4*b^4*c^2*e^4*f^4*z^2 - 2*B^2*a^4*
b^3*c^3*e^5*f^3*z^2 - 580*B^2*a^4*b^2*c^4*d^3*f^5*z^2 + 536*B^2*a^3*b^4*c^3*d^3*f^5*z^2 + 471*A^2*a^4*b^2*c^4*
e^4*f^4*z^2 - 436*A^2*a^3*b^4*c^3*e^4*f^4*z^2 - 348*B^2*a^4*b^4*c^2*d^2*f^6*z^2 + 316*B^2*a^2*b^2*c^6*d^5*f^3*
z^2 + 310*A^2*a^3*b^3*c^4*e^5*f^3*z^2 + 232*A^2*a^5*b^2*c^3*e^2*f^6*z^2 - 229*A^2*a^2*b^4*c^4*e^6*f^2*z^2 - 21
6*A^2*a^4*b^4*c^2*e^2*f^6*z^2 + 204*A^2*a^4*b^3*c^3*e^3*f^5*z^2 + 200*B^2*a^5*b^2*c^3*d^2*f^6*z^2 + 150*A^2*a^
3*b^2*c^5*e^6*f^2*z^2 - 120*B^2*a^2*b^4*c^4*d^4*f^4*z^2 + 91*A^2*a^2*b^6*c^2*e^4*f^4*z^2 + 72*A^2*a^3*b^5*c^2*
e^3*f^5*z^2 - 66*B^2*a^2*b^6*c^2*d^3*f^5*z^2 + 44*A^2*a^2*b^5*c^3*e^5*f^3*z^2 - 16*B^2*a^3*b^2*c^5*d^4*f^4*z^2
+ 1952*A^2*a^4*b^2*c^4*d^2*f^6*z^2 - 1792*A^2*a^3*b^2*c^5*d^3*f^5*z^2 - 1272*A^2*a^3*b^4*c^3*d^2*f^6*z^2 + 97
6*A^2*a^2*b^2*c^6*d^4*f^4*z^2 + 960*A^2*a^2*b^4*c^4*d^3*f^5*z^2 + 282*A^2*a^2*b^6*c^2*d^2*f^6*z^2 - 45*B^2*a^2
*b^2*c^6*d^2*e^6*z^2 - 48*A^2*b*c^9*d^6*e*f*z^2 - 14*A^2*a*b^9*d*e*f^6*z^2 - 7*A*B*b^10*d^2*e*f^5*z^2 + 2*A*B*
b^10*d*e^3*f^4*z^2 - 64*A*B*a^7*c^3*e*f^7*z^2 - 16*A*B*b^9*c*d^3*f^5*z^2 + 8*A*B*a^4*c^6*e^7*f*z^2 + 4*A*B*b*c
^9*d^6*e^2*z^2 + 2*A*B*b^6*c^4*d*e^7*z^2 - 120*A*B*a^3*c^7*d*e^7*z^2 - 16*A*B*a^3*b^7*d*f^7*z^2 + 16*A*B*a*b^9
*d^2*f^6*z^2 + 8*A*B*a*c^9*d^5*e^3*z^2 + 12*A*B*a^3*b*c^6*e^8*z^2 - 48*B^2*b^5*c^5*d^5*e*f^2*z^2 + 15*B^2*b^4*
c^6*d^5*e^2*f*z^2 - 14*B^2*b^7*c^3*d^4*e*f^3*z^2 + 4*B^2*b^9*c*d^2*e^3*f^3*z^2 + 4*B^2*b^7*c^3*d^2*e^5*f*z^2 +
4*B^2*b^5*c^5*d^4*e^3*f*z^2 - B^2*b^6*c^4*d^3*e^4*f*z^2 - 336*B^2*a^3*c^7*d^3*e^4*f*z^2 + 112*B^2*a^5*c^5*d*e
^4*f^3*z^2 - 112*A^2*b^3*c^7*d^5*e*f^2*z^2 + 80*B^2*a^6*c^4*d*e^2*f^5*z^2 - 48*A^2*b^5*c^5*d^4*e*f^3*z^2 + 36*
A^2*b^8*c^2*d*e^4*f^3*z^2 + 36*A^2*b^3*c^7*d^4*e^3*f*z^2 - 28*A^2*b^7*c^3*d*e^5*f^2*z^2 + 20*A^2*b^2*c^8*d^5*e
^2*f*z^2 + 16*B^2*a^2*c^8*d^5*e^2*f*z^2 - 14*A^2*b^7*c^3*d^3*e*f^4*z^2 - 14*A^2*b^4*c^6*d^3*e^4*f*z^2 - 10*A^2
*b^5*c^5*d^2*e^5*f*z^2 - 1008*A^2*a^4*c^6*d*e^4*f^3*z^2 - 760*A^2*a^5*c^5*d*e^2*f^5*z^2 + 272*A^2*a^2*c^8*d^3*
e^4*f*z^2 + 48*B^2*a^5*b*c^4*e^5*f^3*z^2 + 36*B^2*a^6*b*c^3*e^3*f^5*z^2 + 12*B^2*a^5*b^4*c*e^2*f^6*z^2 - 624*A
^2*a^4*b*c^5*e^5*f^3*z^2 - 548*A^2*a^5*b*c^4*e^3*f^5*z^2 + 182*A^2*a^2*b^3*c^5*e^7*f*z^2 - 180*B^2*a*b^4*c^5*d
^5*f^3*z^2 + 132*B^2*a^6*b^2*c^2*d*f^7*z^2 + 108*B^2*a^3*b^6*c*d^2*f^6*z^2 + 96*A^2*a^5*b^3*c^2*e*f^7*z^2 + 68
*A^2*a*b^6*c^3*e^6*f^2*z^2 + 58*A^2*a^3*b^6*c*e^2*f^6*z^2 - 56*B^2*a*b^2*c^7*d^6*f^2*z^2 - 38*A^2*a^2*b^7*c*e^
3*f^5*z^2 - 36*A^2*a*b^7*c^2*e^5*f^3*z^2 + 20*B^2*a*b^6*c^3*d^4*f^4*z^2 - 736*A^2*a^5*b^2*c^3*d*f^7*z^2 + 624*
A^2*a^4*b^4*c^2*d*f^7*z^2 - 416*A^2*a*b^2*c^7*d^5*f^3*z^2 - 276*A^2*a*b^4*c^5*d^4*f^4*z^2 - 196*A^2*a*b^6*c^3*
d^3*f^5*z^2 + 8*B^2*a*b^4*c^5*d^2*e^6*z^2 + 6*B^2*a*b^2*c^7*d^4*e^4*z^2 + 2*B^2*a^2*b^3*c^5*d*e^7*z^2 + 2*B^2*
a*b^3*c^6*d^3*e^5*z^2 - 18*A^2*a*b^2*c^7*d^2*e^6*z^2 - 16*A*B*b*c^9*d^7*f*z^2 - B^2*b^10*d^2*e^2*f^4*z^2 + 48*
B^2*a^7*c^3*e^2*f^6*z^2 - 36*B^2*a^6*c^4*e^4*f^4*z^2 + 31*B^2*b^6*c^4*d^5*f^3*z^2 - 24*B^2*a^5*c^5*e^6*f^2*z^2
+ 20*B^2*b^4*c^6*d^6*f^2*z^2 - 6*A^2*b^8*c^2*e^6*f^2*z^2 + 2*B^2*b^8*c^2*d^4*f^4*z^2 - 768*B^2*a^5*c^5*d^3*f^
5*z^2 + 512*B^2*a^6*c^4*d^2*f^6*z^2 + 512*B^2*a^4*c^6*d^4*f^4*z^2 + 232*A^2*a^5*c^5*e^4*f^4*z^2 + 188*A^2*a^4*
c^6*e^6*f^2*z^2 - 128*B^2*a^3*c^7*d^5*f^3*z^2 + 92*A^2*a^6*c^4*e^2*f^6*z^2 + 80*A^2*b^4*c^6*d^5*f^3*z^2 + 64*A
^2*b^2*c^8*d^6*f^2*z^2 + 31*A^2*b^6*c^4*d^4*f^4*z^2 + 14*A^2*b^8*c^2*d^3*f^5*z^2 - 5*B^2*b^4*c^6*d^4*e^4*z^2 +
4*B^2*b^3*c^7*d^5*e^3*z^2 + 2*B^2*b^5*c^5*d^3*e^5*z^2 - B^2*b^6*c^4*d^2*e^6*z^2 - B^2*b^2*c^8*d^6*e^2*z^2 - B
^2*a^4*b^6*e^2*f^6*z^2 - 1152*A^2*a^3*c^7*d^4*f^4*z^2 + 1008*A^2*a^4*c^6*d^3*f^5*z^2 + 624*A^2*a^2*c^8*d^5*f^3
*z^2 - 288*A^2*a^5*c^5*d^2*f^6*z^2 + 56*B^2*a^3*c^7*d^2*e^6*z^2 - 10*B^2*a^2*b^8*d^2*f^6*z^2 - 9*A^2*b^2*c^8*d
^4*e^4*z^2 - 5*A^2*a^2*b^8*e^2*f^6*z^2 - 4*B^2*a^2*c^8*d^4*e^4*z^2 + 3*A^2*b^4*c^6*d^2*e^6*z^2 - 2*A^2*b^3*c^7
*d^3*e^5*z^2 - 36*A^2*a^2*c^8*d^2*e^6*z^2 - 48*A^2*a^6*b^2*c^2*f^8*z^2 - 45*A^2*a^2*b^2*c^6*e^8*z^2 + 4*A^2*b^
10*d*e^2*f^5*z^2 + 4*B^2*b^2*c^8*d^7*f*z^2 + 4*A^2*b^9*c*e^5*f^3*z^2 + 4*A^2*b^7*c^3*e^7*f*z^2 - 128*B^2*a^7*c
^3*d*f^7*z^2 - 160*A^2*a*c^9*d^6*f^2*z^2 - 112*A^2*a^6*c^4*d*f^7*z^2 + 12*A^2*b*c^9*d^5*e^3*z^2 + 4*A^2*a*b^9*
e^3*f^5*z^2 + 3*B^2*a^4*b^6*d*f^7*z^2 + 2*A^2*a^3*b^7*e*f^7*z^2 - 24*A^2*a*c^9*d^4*e^4*z^2 + 14*A^2*a^2*b^8*d*
f^7*z^2 + 12*A^2*a^5*b^4*c*f^8*z^2 + 12*A^2*a*b^4*c^5*e^8*z^2 + A*B*a^4*b^6*e*f^7*z^2 + B^2*a^2*b^8*d*e^2*f^5*
z^2 + 16*A^2*c^10*d^7*f*z^2 + 3*B^2*b^10*d^3*f^5*z^2 - A^2*b^10*e^4*f^4*z^2 - 4*A^2*c^10*d^6*e^2*z^2 - A^2*b^1
0*d^2*f^6*z^2 + 64*A^2*a^7*c^3*f^8*z^2 - 4*B^2*a^4*c^6*e^8*z^2 - A^2*b^6*c^4*e^8*z^2 + 48*A^2*a^3*c^7*e^8*z^2
- A^2*a^4*b^6*f^8*z^2 + 720*A^2*B*a*b^2*c^5*d^2*e^2*f^3*z - 600*A^2*B*a^2*b^2*c^4*d*e^2*f^4*z + 576*A*B^2*a^2*
b^2*c^4*d^2*e*f^4*z + 348*A*B^2*a*b^2*c^5*d^2*e^3*f^2*z - 336*A*B^2*a^2*b*c^5*d^2*e^2*f^3*z - 260*A*B^2*a*b^3*
c^4*d^2*e^2*f^3*z - 240*A*B^2*a^2*b^2*c^4*d*e^3*f^3*z + 196*A*B^2*a^2*b^3*c^3*d*e^2*f^4*z + 172*A^2*B*a*b*c^6*
d*e^5*f*z + 20*A*B^2*a*b^6*c*d*e*f^5*z - 912*A^2*B*a^2*b*c^5*d^2*e*f^4*z - 644*A^2*B*a*b*c^6*d^2*e^3*f^2*z - 4
32*A*B^2*a*b^2*c^5*d^3*e*f^3*z + 372*A^2*B*a^2*b*c^5*d*e^3*f^3*z - 330*A^2*B*a*b^2*c^5*d*e^4*f^2*z + 312*A*B^2
*a*b*c^6*d^3*e^2*f^2*z - 208*A*B^2*a^3*b^2*c^3*d*e*f^5*z + 192*A^2*B*a^2*b^3*c^3*d*e*f^5*z + 172*A^2*B*a*b^3*c
^4*d*e^3*f^3*z + 108*A*B^2*a^2*b*c^5*d*e^4*f^2*z + 104*A*B^2*a^3*b*c^4*d*e^2*f^4*z - 80*A^2*B*a*b^3*c^4*d^2*e*
f^4*z + 68*A^2*B*a*b^4*c^3*d*e^2*f^4*z - 60*A*B^2*a*b^5*c^2*d*e^2*f^4*z + 58*A*B^2*a*b^3*c^4*d*e^4*f^2*z - 36*
A*B^2*a*b^4*c^3*d^2*e*f^4*z - 24*A*B^2*a^2*b^4*c^2*d*e*f^5*z + 24*A*B^2*a*b^4*c^3*d*e^3*f^3*z + 592*A^2*B*a*b*
c^6*d^3*e*f^3*z + 240*A^2*B*a^3*b*c^4*d*e*f^5*z - 132*A*B^2*a*b*c^6*d^2*e^4*f*z - 60*A*B^2*a*b^2*c^5*d*e^5*f*z
- 48*A^2*B*a*b^5*c^2*d*e*f^5*z + 20*B^3*a*b*c^6*d^3*e^3*f*z + 16*B^3*a^4*b*c^3*d*e*f^5*z - 16*B^3*a*b*c^6*d^4
*e*f^2*z + 12*B^3*a^2*b*c^5*d*e^5*f*z + 320*A^3*a*b*c^6*d*e^4*f^2*z + 40*A^3*a*b^4*c^3*d*e*f^5*z - 48*A^2*B*b*
c^7*d^4*e*f^2*z - 44*A^2*B*b^3*c^5*d*e^5*f*z - 20*A*B^2*b*c^7*d^4*e^2*f*z + 14*A*B^2*b^4*c^4*d*e^5*f*z + 12*A^
2*B*b*c^7*d^3*e^3*f*z + 4*A*B^2*b^7*c*d*e^2*f^4*z + 160*A*B^2*a^4*c^4*d*e*f^5*z + 152*A^2*B*a*c^7*d^2*e^4*f*z
- 40*A*B^2*a*c^7*d^3*e^3*f*z + 32*A*B^2*a*c^7*d^4*e*f^2*z - 16*A*B^2*a^2*c^6*d*e^5*f*z + 128*A^2*B*a^4*b*c^3*e
*f^6*z + 42*A^2*B*a*b^2*c^5*e^6*f*z + 24*A^2*B*a^2*b^5*c*e*f^6*z - 12*A*B^2*a^3*b^4*c*e*f^6*z - 12*A*B^2*a^2*b
*c^5*e^6*f*z - 10*A^2*B*a*b^6*c*e^2*f^5*z - 160*A*B^2*a*b*c^6*d^4*f^3*z + 112*A*B^2*a^4*b*c^3*d*f^6*z - 24*A*B
^2*a^2*b^5*c*d*f^6*z - 84*B^3*a*b^2*c^5*d^3*e^2*f^2*z - 80*B^3*a^2*b^3*c^3*d^2*e*f^4*z - 60*B^3*a^2*b*c^5*d^2*
e^3*f^2*z - 20*B^3*a^3*b^2*c^3*d*e^2*f^4*z - 20*B^3*a*b^3*c^4*d^2*e^3*f^2*z - 9*B^3*a^2*b^2*c^4*d*e^4*f^2*z -
8*B^3*a*b^4*c^3*d^2*e^2*f^3*z + 6*B^3*a^2*b^4*c^2*d*e^2*f^4*z - 4*B^3*a^2*b^3*c^3*d*e^3*f^3*z - 216*A^2*B*b^4*
c^4*d^2*e^2*f^3*z + 196*A^2*B*b^3*c^5*d^2*e^3*f^2*z - 108*A*B^2*b^3*c^5*d^3*e^2*f^2*z - 94*A*B^2*b^4*c^4*d^2*e
^3*f^2*z + 88*A^2*B*b^2*c^6*d^3*e^2*f^2*z + 80*A*B^2*b^5*c^3*d^2*e^2*f^3*z + 360*A^2*B*a^2*c^6*d^2*e^2*f^3*z +
8*A*B^2*a^2*c^6*d^2*e^3*f^2*z + 153*A^2*B*a^2*b^2*c^4*e^4*f^3*z - 144*A^2*B*a^2*b^3*c^3*e^3*f^4*z + 80*A^2*B*
a^3*b^2*c^3*e^2*f^5*z + 36*A*B^2*a^3*b^2*c^3*e^3*f^4*z + 12*A^2*B*a^2*b^4*c^2*e^2*f^5*z + 12*A*B^2*a^3*b^3*c^2
*e^2*f^5*z + 9*A*B^2*a^2*b^2*c^4*e^5*f^2*z - 6*A*B^2*a^2*b^4*c^2*e^3*f^4*z + 4*A*B^2*a^2*b^3*c^3*e^4*f^3*z + 4
80*A^2*B*a^2*b^2*c^4*d^2*f^5*z - 176*A*B^2*a^2*b^3*c^3*d^2*f^5*z - 10*A^2*B*a*b^6*c*d*f^6*z + 16*A*B^2*a*b*c^6
*d*e^6*z + 80*B^3*a*b^3*c^4*d^3*e*f^3*z - 48*B^3*a^3*b*c^4*d^2*e*f^4*z + 48*B^3*a^2*b*c^5*d^3*e*f^3*z + 44*B^3
*a^3*b*c^4*d*e^3*f^3*z + 24*B^3*a*b^5*c^2*d^2*e*f^4*z + 18*B^3*a*b^2*c^5*d^2*e^4*f*z + 696*A^3*a^2*b*c^5*d*e^2
*f^4*z - 504*A^3*a*b*c^6*d^2*e^2*f^3*z - 192*A^3*a*b^2*c^5*d*e^3*f^3*z - 144*A^3*a^2*b^2*c^4*d*e*f^5*z + 96*A^
3*a*b^2*c^5*d^2*e*f^4*z - 72*A^3*a*b^3*c^4*d*e^2*f^4*z - 208*A^2*B*b^3*c^5*d^3*e*f^3*z + 152*A*B^2*b^4*c^4*d^3
*e*f^3*z + 80*A^2*B*b^5*c^3*d^2*e*f^4*z + 75*A^2*B*b^4*c^4*d*e^4*f^2*z - 59*A^2*B*b^2*c^6*d^2*e^4*f*z - 52*A^2
*B*b^5*c^3*d*e^3*f^3*z + 42*A*B^2*b^3*c^5*d^2*e^4*f*z - 21*A*B^2*b^6*c^2*d^2*e*f^4*z - 16*A*B^2*b^5*c^3*d*e^4*
f^2*z + 16*A*B^2*b^2*c^6*d^4*e*f^2*z + 16*A*B^2*b^2*c^6*d^3*e^3*f*z + 11*A^2*B*b^6*c^2*d*e^2*f^4*z + 4*A*B^2*b
^6*c^2*d*e^3*f^3*z - 256*A^2*B*a*c^7*d^3*e^2*f^2*z - 96*A*B^2*a^3*c^5*d^2*e*f^4*z - 36*A^2*B*a^2*c^6*d*e^4*f^2
*z - 32*A^2*B*a^3*c^5*d*e^2*f^4*z - 32*A*B^2*a^2*c^6*d^3*e*f^3*z + 8*A*B^2*a^3*c^5*d*e^3*f^3*z - 96*A^2*B*a^3*
b^3*c^2*e*f^6*z + 68*A^2*B*a^3*b*c^4*e^3*f^4*z - 60*A*B^2*a^4*b*c^3*e^2*f^5*z - 60*A*B^2*a^3*b*c^4*e^4*f^3*z +
48*A*B^2*a^4*b^2*c^2*e*f^6*z - 38*A^2*B*a*b^3*c^4*e^5*f^2*z - 36*A^2*B*a^2*b*c^5*e^5*f^2*z + 36*A^2*B*a*b^5*c
^2*e^3*f^4*z - 16*A^2*B*a*b^4*c^3*e^4*f^3*z + 384*A*B^2*a^2*b*c^5*d^3*f^4*z - 352*A*B^2*a^3*b*c^4*d^2*f^5*z -
288*A^2*B*a*b^2*c^5*d^3*f^4*z - 160*A^2*B*a^3*b^2*c^3*d*f^6*z - 148*A^2*B*a*b^4*c^3*d^2*f^5*z + 112*A*B^2*a*b^
3*c^4*d^3*f^4*z + 72*A^2*B*a^2*b^4*c^2*d*f^6*z + 72*A*B^2*a*b^5*c^2*d^2*f^5*z + 48*A*B^2*a^3*b^3*c^2*d*f^6*z +
102*B^3*a^2*b^2*c^4*d^2*e^2*f^3*z - 32*B^3*b^5*c^3*d^3*e*f^3*z - 8*B^3*b^3*c^5*d^3*e^3*f*z - 7*B^3*b^4*c^4*d^
2*e^4*f*z + 5*B^3*b^2*c^6*d^4*e^2*f*z + 80*A^3*b^2*c^6*d^3*e*f^3*z - 74*A^3*b^3*c^5*d*e^4*f^2*z - 64*A^3*b^4*c
^4*d^2*e*f^4*z + 60*A^3*b^4*c^4*d*e^3*f^3*z - 48*B^3*a^4*c^4*d*e^2*f^4*z - 24*B^3*a^3*c^5*d*e^4*f^2*z + 20*B^3
*a^2*c^6*d^2*e^4*f*z - 16*A^3*b^5*c^3*d*e^2*f^4*z + 8*A^3*b*c^7*d^3*e^2*f^2*z + 480*A^3*a^2*c^6*d^2*e*f^4*z -
392*A^3*a^2*c^6*d*e^3*f^3*z + 280*A^3*a*c^7*d^2*e^3*f^2*z - 4*B^3*a^4*b*c^3*e^3*f^4*z - 200*A^3*a^3*b*c^4*e^2*
f^5*z - 144*A^3*a^2*b*c^5*e^4*f^3*z + 48*B^3*a*b^2*c^5*d^4*f^3*z + 42*A^3*a*b^2*c^5*e^5*f^2*z - 36*B^3*a^4*b^2
*c^2*d*f^6*z - 32*A^3*a^3*b^2*c^3*e*f^6*z - 24*A^3*a^2*b^4*c^2*e*f^6*z - 24*A^3*a*b^5*c^2*e^2*f^5*z + 10*A^3*a
*b^3*c^4*e^4*f^3*z - 4*B^3*a*b^4*c^3*d^3*f^4*z - 4*A^3*a*b^4*c^3*e^3*f^4*z - 480*A^3*a^2*b*c^5*d^2*f^5*z - 160
*A^3*a^2*b^3*c^3*d*f^6*z + 128*A^3*a*b^3*c^4*d^2*f^5*z + 8*A^2*B*b^5*c^3*e^5*f^2*z - 2*A^2*B*b^6*c^2*e^4*f^3*z
+ 112*A^2*B*b^4*c^4*d^3*f^4*z - 92*A^2*B*a^4*c^4*e^2*f^5*z - 64*A^2*B*a^3*c^5*e^4*f^3*z - 64*A*B^2*b^5*c^3*d^
3*f^4*z + 24*A*B^2*a^4*c^4*e^3*f^4*z + 24*A*B^2*a^3*c^5*e^5*f^2*z + 16*A^2*B*b^2*c^6*d^4*f^3*z + 16*A*B^2*b^3*
c^5*d^4*f^3*z - A^2*B*b^6*c^2*d^2*f^5*z + 448*A^2*B*a^3*c^5*d^2*f^5*z - 352*A^2*B*a^2*c^6*d^3*f^4*z - 5*A*B^2*
b^2*c^6*d^2*e^5*z - 48*A^2*B*a^4*b^2*c^2*f^7*z - 2*B^3*b^7*c*d^2*e*f^4*z + 34*A^3*b^2*c^6*d*e^5*f*z + 16*A^3*b
*c^7*d^2*e^4*f*z + 2*A^3*b^6*c^2*d*e*f^5*z - 416*A^3*a^3*c^5*d*e*f^5*z - 224*A^3*a*c^7*d^3*e*f^3*z + 12*B^3*a^
3*b^4*c*d*f^6*z - 10*B^3*a*b^6*c*d^2*f^5*z + 416*A^3*a^3*b*c^4*d*f^6*z + 224*A^3*a*b*c^6*d^3*f^4*z + 24*A^3*a*
b^5*c^2*d*f^6*z - 4*B^3*a*b*c^6*d^2*e^5*z + 20*A^2*B*c^8*d^4*e^2*f*z - 7*A^2*B*b^4*c^4*e^6*f*z - 2*A^2*B*b^7*c
*e^3*f^4*z - 64*A*B^2*a^5*c^3*e*f^6*z + 16*A*B^2*b*c^7*d^5*f^2*z - 8*A^2*B*a^2*c^6*e^6*f*z - 2*A*B^2*b^7*c*d^2
*f^5*z - 272*A^2*B*a^4*c^4*d*f^6*z + 128*A^2*B*a*c^7*d^4*f^3*z + 9*A^2*B*b^2*c^6*d*e^6*z - 4*A*B^2*b^3*c^5*d*e
^6*z + 4*A*B^2*b*c^7*d^3*e^4*z + 8*A*B^2*a*c^7*d^2*e^5*z + 12*A^2*B*a^3*b^4*c*f^7*z + 30*B^3*b^4*c^4*d^3*e^2*f
^2*z + 8*B^3*b^5*c^3*d^2*e^3*f^2*z - 2*B^3*b^6*c^2*d^2*e^2*f^3*z + 152*A^3*b^3*c^5*d^2*e^2*f^3*z - 108*A^3*b^2
*c^6*d^2*e^3*f^2*z + 48*B^3*a^3*c^5*d^2*e^2*f^3*z - 16*B^3*a^2*c^6*d^3*e^2*f^2*z - 3*B^3*a^4*b^2*c^2*e^2*f^5*z
- 120*B^3*a^2*b^2*c^4*d^3*f^4*z + 112*B^3*a^3*b^2*c^3*d^2*f^5*z + 112*A^3*a^2*b^3*c^3*e^2*f^5*z + 12*A^3*a^2*
b^2*c^4*e^3*f^4*z - 120*A^3*a*c^7*d*e^5*f*z - 52*A^3*a*b*c^6*e^6*f*z + 10*A^3*a*b^6*c*e*f^6*z - 2*A*B^2*b^8*d*
e*f^5*z - 2*A^2*B*a*b^7*e*f^6*z - 24*A^2*B*a*c^7*d*e^6*z + 2*A*B^2*a*b^7*d*f^6*z - 12*A^2*B*a*b*c^6*e^7*z - 2*
A^3*b^7*c*d*f^6*z - 4*A^3*b*c^7*d*e^6*z + 16*B^3*a^5*c^3*e^2*f^5*z + 11*B^3*b^6*c^2*d^3*f^4*z - 11*A^3*b^4*c^4
*e^5*f^2*z - 8*B^3*b^4*c^4*d^4*f^3*z - 4*B^3*b^2*c^6*d^5*f^2*z + 4*B^3*a^4*c^4*e^4*f^3*z + 4*A^3*b^5*c^3*e^4*f
^3*z - A^3*b^6*c^2*e^3*f^4*z + 136*A^3*a^3*c^5*e^3*f^4*z + 68*A^3*a^2*c^6*e^5*f^2*z - 64*A^3*b^3*c^5*d^3*f^4*z
+ 2*B^3*b^3*c^5*d^2*e^5*z - B^3*b^2*c^6*d^3*e^4*z + 96*A^3*a^3*b^3*c^2*f^7*z + A*B^2*a^2*b^6*e*f^6*z + 32*A^3
*c^8*d^4*e*f^2*z - 24*A^3*c^8*d^3*e^3*f*z + 10*A^3*b^3*c^5*e^6*f*z + 2*A^3*b^7*c*e^2*f^5*z + 128*A^3*a^4*c^4*e
*f^6*z - 32*A^3*b*c^7*d^4*f^3*z - 4*B^3*a^2*c^6*d*e^6*z - B^3*a^2*b^6*d*f^6*z - 128*A^3*a^4*b*c^3*f^7*z - 24*A
^3*a^2*b^5*c*f^7*z - 16*A^2*B*c^8*d^5*f^2*z - 4*A^2*B*c^8*d^3*e^4*z + 64*A^2*B*a^5*c^3*f^7*z + 2*A^2*B*b^3*c^5
*e^7*z + 4*A*B^2*a^2*c^6*e^7*z - A^2*B*a^2*b^6*f^7*z + 4*A^3*c^8*d^2*e^5*z - 3*A^3*b^2*c^6*e^7*z + A^2*B*b^8*d
*f^6*z - A^3*b^8*e*f^6*z + 16*A^3*a*c^7*e^7*z + 2*A^3*a*b^7*f^7*z + A^2*B*b^8*e^2*f^5*z + B^3*b^8*d^2*f^5*z -
48*A^2*B^2*a*b*c^4*d*e*f^4 + 28*A*B^3*a*b^2*c^3*d*e*f^4 - 16*A*B^3*a*b*c^4*d*e^2*f^3 + 16*A^3*B*a*c^5*d*e*f^4
+ 32*A^3*B*a*b*c^4*d*f^5 + 12*A^2*B^2*b^3*c^3*d*e*f^4 + 5*A*B^3*b^2*c^4*d^2*e*f^3 + 4*A*B^3*b^3*c^3*d*e^2*f^3
+ 24*A^2*B^2*a*c^5*d*e^2*f^3 + 24*A^2*B^2*a^2*b*c^3*e*f^5 + 12*A^2*B^2*a*b*c^4*e^3*f^3 - 6*A^2*B^2*a*b^3*c^2*e
*f^5 + 4*A*B^3*a^2*b*c^3*e^2*f^4 + 3*A*B^3*a^2*b^2*c^2*e*f^5 - 18*A^2*B^2*a*b^2*c^3*d*f^5 - 4*B^4*a^2*b*c^3*d*
e*f^4 + 4*B^4*a*b*c^4*d^2*e*f^3 - 6*A*B^3*b^4*c^2*d*e*f^4 + 4*A^3*B*b*c^5*d*e^2*f^3 - 2*A^3*B*b^2*c^4*d*e*f^4
- 8*A*B^3*a^2*c^4*d*e*f^4 - 8*A*B^3*a*c^5*d^2*e*f^3 + 26*A^3*B*a*b^2*c^3*e*f^5 + 8*A^3*B*a*b*c^4*e^2*f^4 + 32*
A*B^3*a*b*c^4*d^2*f^4 - 28*A*B^3*a^2*b*c^3*d*f^5 + 6*A*B^3*a*b^3*c^2*d*f^5 - 9*A^2*B^2*b^2*c^4*d*e^2*f^3 - 18*
A^2*B^2*a*b^2*c^3*e^2*f^4 - 4*A^3*B*c^6*d^2*e*f^3 - 3*A^3*B*b^4*c^2*e*f^5 - 44*A^3*B*a^2*c^4*e*f^5 - 16*A^3*B*
a*c^5*e^3*f^3 - 16*A*B^3*a^3*c^3*e*f^5 - 10*A^3*B*b^3*c^3*d*f^5 - 4*A^3*B*b*c^5*d^2*f^4 - 4*A*B^3*b*c^5*d^3*f^
3 - 28*A^3*B*a^2*b*c^3*f^6 + 6*A^3*B*a*b^3*c^2*f^6 - 4*A^4*b*c^5*d*e*f^4 - 20*A^4*a*b*c^4*e*f^5 + 3*A^2*B^2*b^
4*c^2*e^2*f^4 - 2*A^2*B^2*b^3*c^3*e^3*f^3 + 12*A^2*B^2*a^2*c^4*e^2*f^4 + 9*A^2*B^2*b^2*c^4*d^2*f^4 - 3*A^2*B^2
*a^2*b^2*c^2*f^6 - 2*B^4*b^3*c^3*d^2*e*f^3 + 4*B^4*a^2*c^4*d*e^2*f^3 - 10*B^4*a*b^2*c^3*d^2*f^4 - 3*B^4*a^2*b^
2*c^2*d*f^5 + 3*A^3*B*b^2*c^4*e^3*f^3 - 2*A^3*B*b^3*c^3*e^2*f^4 - 10*A*B^3*b^3*c^3*d^2*f^4 - 4*A*B^3*a^2*c^4*e
^3*f^3 + 3*A^2*B^2*b^4*c^2*d*f^5 + 36*A^2*B^2*a^2*c^4*d*f^5 - 24*A^2*B^2*a*c^5*d^2*f^4 + 4*A^2*B^2*c^6*d^3*f^3
+ 16*A^2*B^2*a^3*c^3*f^6 + 4*A^4*b^3*c^3*e*f^5 + 16*B^4*a^3*c^3*d*f^5 + 16*A^4*a*c^5*e^2*f^4 + 8*A^4*b^2*c^4*
d*f^5 - 8*A^4*a*b^2*c^3*f^6 - 24*A^4*a*c^5*d*f^5 + 3*B^4*b^4*c^2*d^2*f^4 - 3*A^4*b^2*c^4*e^2*f^4 + 4*A^4*c^6*d
^2*f^4 + 36*A^4*a^2*c^4*f^6 + B^4*b^2*c^4*d^3*f^3, z, k)*(root(48416*a^6*b^2*c^6*d^4*e^2*f^4*z^4 - 41544*a^5*b
^4*c^5*d^4*e^2*f^4*z^4 - 31872*a^7*b^2*c^5*d^3*e^2*f^5*z^4 - 31872*a^5*b^2*c^7*d^5*e^2*f^3*z^4 - 29184*a^6*b^2
*c^6*d^3*e^4*f^3*z^4 + 28800*a^5*b^4*c^5*d^3*e^4*f^3*z^4 + 21510*a^4*b^6*c^4*d^4*e^2*f^4*z^4 + 21408*a^6*b^4*c
^4*d^3*e^2*f^5*z^4 + 21408*a^4*b^4*c^6*d^5*e^2*f^3*z^4 - 18112*a^7*b^3*c^4*d^2*e^3*f^5*z^4 - 18112*a^4*b^3*c^7
*d^5*e^3*f^2*z^4 - 15600*a^5*b^5*c^4*d^3*e^3*f^4*z^4 - 15600*a^4*b^5*c^5*d^4*e^3*f^3*z^4 + 15296*a^6*b^3*c^5*d
^3*e^3*f^4*z^4 + 15296*a^5*b^3*c^6*d^4*e^3*f^3*z^4 + 14016*a^7*b^2*c^5*d^2*e^4*f^4*z^4 + 14016*a^5*b^2*c^7*d^4
*e^4*f^2*z^4 - 13920*a^4*b^6*c^4*d^3*e^4*f^3*z^4 - 11648*a^6*b^3*c^5*d^2*e^5*f^3*z^4 - 11648*a^5*b^3*c^6*d^3*e
^5*f^2*z^4 + 10432*a^6*b^2*c^6*d^2*e^6*f^2*z^4 + 9008*a^6*b^5*c^3*d^2*e^3*f^5*z^4 + 9008*a^3*b^5*c^6*d^5*e^3*f
^2*z^4 + 8544*a^5*b^5*c^4*d^2*e^5*f^3*z^4 + 8544*a^4*b^5*c^5*d^3*e^5*f^2*z^4 - 8496*a^5*b^4*c^5*d^2*e^6*f^2*z^
4 + 7488*a^8*b^2*c^4*d^2*e^2*f^6*z^4 + 7488*a^4*b^2*c^8*d^6*e^2*f^2*z^4 + 7380*a^4*b^7*c^3*d^3*e^3*f^4*z^4 + 7
380*a^3*b^7*c^4*d^4*e^3*f^3*z^4 - 6720*a^3*b^8*c^3*d^4*e^2*f^4*z^4 - 5784*a^5*b^6*c^3*d^3*e^2*f^5*z^4 - 5784*a
^3*b^6*c^5*d^5*e^2*f^3*z^4 - 3440*a^6*b^4*c^4*d^2*e^4*f^4*z^4 - 3440*a^4*b^4*c^6*d^4*e^4*f^2*z^4 + 3360*a^3*b^
8*c^3*d^3*e^4*f^3*z^4 + 3140*a^4*b^6*c^4*d^2*e^6*f^2*z^4 - 2760*a^4*b^7*c^3*d^2*e^5*f^3*z^4 - 2760*a^3*b^7*c^4
*d^3*e^5*f^2*z^4 - 1764*a^5*b^7*c^2*d^2*e^3*f^5*z^4 - 1764*a^2*b^7*c^5*d^5*e^3*f^2*z^4 - 1640*a^3*b^9*c^2*d^3*
e^3*f^4*z^4 - 1640*a^2*b^9*c^3*d^4*e^3*f^3*z^4 - 1604*a^6*b^6*c^2*d^2*e^2*f^6*z^4 - 1604*a^2*b^6*c^6*d^6*e^2*f
^2*z^4 - 1500*a^5*b^6*c^3*d^2*e^4*f^4*z^4 - 1500*a^3*b^6*c^5*d^4*e^4*f^2*z^4 + 1140*a^2*b^10*c^2*d^4*e^2*f^4*z
^4 + 810*a^4*b^8*c^2*d^2*e^4*f^4*z^4 + 810*a^2*b^8*c^4*d^4*e^4*f^2*z^4 - 544*a^3*b^8*c^3*d^2*e^6*f^2*z^4 + 416
*a^3*b^9*c^2*d^2*e^5*f^3*z^4 + 416*a^2*b^9*c^3*d^3*e^5*f^2*z^4 - 384*a^2*b^10*c^2*d^3*e^4*f^3*z^4 + 180*a^4*b^
8*c^2*d^3*e^2*f^5*z^4 + 180*a^2*b^8*c^4*d^5*e^2*f^3*z^4 + 48*a^7*b^4*c^3*d^2*e^2*f^6*z^4 + 48*a^3*b^4*c^7*d^6*
e^2*f^2*z^4 + 36*a^2*b^10*c^2*d^2*e^6*f^2*z^4 - 1024*a^10*b*c^3*d*e*f^8*z^4 - 1024*a^3*b*c^10*d^8*e*f*z^4 - 19
2*a^8*b^5*c*d*e*f^8*z^4 - 192*a*b^5*c^8*d^8*e*f*z^4 + 16128*a^7*b^3*c^4*d^3*e*f^6*z^4 + 16128*a^4*b^3*c^7*d^6*
e*f^3*z^4 - 11712*a^6*b^5*c^3*d^3*e*f^6*z^4 - 11712*a^3*b^5*c^6*d^6*e*f^3*z^4 + 11520*a^8*b*c^5*d^2*e^3*f^5*z^
4 + 11520*a^5*b*c^8*d^5*e^3*f^2*z^4 - 9984*a^6*b^3*c^5*d^4*e*f^5*z^4 - 9984*a^5*b^3*c^6*d^5*e*f^4*z^4 + 8640*a
^5*b^5*c^4*d^4*e*f^5*z^4 + 8640*a^4*b^5*c^5*d^5*e*f^4*z^4 - 7424*a^7*b*c^6*d^3*e^3*f^4*z^4 - 7424*a^6*b*c^7*d^
4*e^3*f^3*z^4 - 6912*a^8*b^3*c^3*d^2*e*f^7*z^4 - 6912*a^3*b^3*c^8*d^7*e*f^2*z^4 + 4800*a^7*b^3*c^4*d*e^5*f^4*z
^4 + 4800*a^4*b^3*c^7*d^4*e^5*f*z^4 + 4608*a^7*b*c^6*d^2*e^5*f^3*z^4 + 4608*a^6*b*c^7*d^3*e^5*f^2*z^4 - 4560*a
^4*b^7*c^3*d^4*e*f^5*z^4 - 4560*a^3*b^7*c^4*d^5*e*f^4*z^4 + 4176*a^5*b^7*c^2*d^3*e*f^6*z^4 + 4176*a^2*b^7*c^5*
d^6*e*f^3*z^4 + 3264*a^7*b^5*c^2*d^2*e*f^7*z^4 + 3264*a^2*b^5*c^7*d^7*e*f^2*z^4 + 3008*a^8*b^3*c^3*d*e^3*f^6*z
^4 + 3008*a^3*b^3*c^8*d^6*e^3*f*z^4 + 2880*a^6*b^3*c^5*d*e^7*f^2*z^4 + 2880*a^5*b^3*c^6*d^2*e^7*f*z^4 - 2240*a
^7*b^4*c^3*d*e^4*f^5*z^4 - 2240*a^3*b^4*c^7*d^5*e^4*f*z^4 - 1488*a^5*b^5*c^4*d*e^7*f^2*z^4 - 1488*a^4*b^5*c^5*
d^2*e^7*f*z^4 + 1440*a^3*b^9*c^2*d^4*e*f^5*z^4 + 1440*a^2*b^9*c^3*d^5*e*f^4*z^4 - 1328*a^6*b^5*c^3*d*e^5*f^4*z
^4 - 1328*a^3*b^5*c^6*d^4*e^5*f*z^4 - 1152*a^7*b^2*c^5*d*e^6*f^3*z^4 - 1152*a^5*b^2*c^7*d^3*e^6*f*z^4 - 1120*a
^6*b^4*c^4*d*e^6*f^3*z^4 - 1120*a^4*b^4*c^6*d^3*e^6*f*z^4 + 912*a^6*b^6*c^2*d*e^4*f^5*z^4 + 912*a^2*b^6*c^6*d^
5*e^4*f*z^4 + 872*a^5*b^6*c^3*d*e^6*f^3*z^4 + 872*a^3*b^6*c^5*d^3*e^6*f*z^4 + 768*a^8*b^2*c^4*d*e^4*f^5*z^4 +
768*a^4*b^2*c^8*d^5*e^4*f*z^4 - 672*a^8*b^4*c^2*d*e^2*f^7*z^4 - 672*a^2*b^4*c^8*d^7*e^2*f*z^4 - 624*a^7*b^5*c^
2*d*e^3*f^6*z^4 - 624*a^2*b^5*c^7*d^6*e^3*f*z^4 + 480*a^5*b^8*c*d^2*e^2*f^6*z^4 + 480*a*b^8*c^5*d^6*e^2*f^2*z^
4 + 316*a^4*b^7*c^3*d*e^7*f^2*z^4 + 316*a^3*b^7*c^4*d^2*e^7*f*z^4 - 204*a^4*b^8*c^2*d*e^6*f^3*z^4 - 204*a^2*b^
8*c^4*d^3*e^6*f*z^4 + 168*a^3*b^10*c*d^3*e^2*f^5*z^4 + 168*a*b^10*c^3*d^5*e^2*f^3*z^4 + 156*a^2*b^11*c*d^3*e^3
*f^4*z^4 + 156*a*b^11*c^2*d^4*e^3*f^3*z^4 + 128*a^9*b^2*c^3*d*e^2*f^7*z^4 + 128*a^3*b^2*c^9*d^7*e^2*f*z^4 - 12
4*a^3*b^10*c*d^2*e^4*f^4*z^4 - 124*a*b^10*c^3*d^4*e^4*f^2*z^4 + 100*a^4*b^9*c*d^2*e^3*f^5*z^4 + 100*a*b^9*c^4*
d^5*e^3*f^2*z^4 + 36*a^5*b^7*c^2*d*e^5*f^4*z^4 + 36*a^2*b^7*c^5*d^4*e^5*f*z^4 - 24*a^3*b^9*c^2*d*e^7*f^2*z^4 -
24*a^2*b^11*c*d^2*e^5*f^3*z^4 - 24*a^2*b^9*c^3*d^2*e^7*f*z^4 - 24*a*b^11*c^2*d^3*e^5*f^2*z^4 - 9216*a^8*b*c^5
*d^3*e*f^6*z^4 - 9216*a^5*b*c^8*d^6*e*f^3*z^4 - 5376*a^8*b*c^5*d*e^5*f^4*z^4 - 5376*a^5*b*c^8*d^4*e^5*f*z^4 +
5120*a^9*b*c^4*d^2*e*f^7*z^4 + 5120*a^7*b*c^6*d^4*e*f^5*z^4 + 5120*a^6*b*c^7*d^5*e*f^4*z^4 + 5120*a^4*b*c^9*d^
7*e*f^2*z^4 - 4352*a^9*b*c^4*d*e^3*f^6*z^4 - 4352*a^4*b*c^9*d^6*e^3*f*z^4 - 1792*a^7*b*c^6*d*e^7*f^2*z^4 - 179
2*a^6*b*c^7*d^2*e^7*f*z^4 - 1600*a^6*b^2*c^6*d*e^8*f*z^4 + 912*a^5*b^4*c^5*d*e^8*f*z^4 + 768*a^9*b^3*c^2*d*e*f
^8*z^4 + 768*a^2*b^3*c^9*d^8*e*f*z^4 - 720*a^4*b^9*c*d^3*e*f^6*z^4 - 720*a*b^9*c^4*d^6*e*f^3*z^4 - 656*a^6*b^7
*c*d^2*e*f^7*z^4 - 656*a*b^7*c^6*d^7*e*f^2*z^4 - 240*a^2*b^11*c*d^4*e*f^5*z^4 - 240*a*b^11*c^2*d^5*e*f^4*z^4 +
216*a^7*b^6*c*d*e^2*f^7*z^4 + 216*a*b^6*c^7*d^7*e^2*f*z^4 - 204*a^4*b^6*c^4*d*e^8*f*z^4 - 144*a^5*b^8*c*d*e^4
*f^5*z^4 - 144*a*b^8*c^5*d^5*e^4*f*z^4 - 84*a*b^12*c*d^4*e^2*f^4*z^4 + 36*a^4*b^9*c*d*e^5*f^4*z^4 + 36*a*b^9*c
^4*d^4*e^5*f*z^4 + 20*a^6*b^7*c*d*e^3*f^6*z^4 + 20*a*b^7*c^6*d^6*e^3*f*z^4 + 16*a^3*b^10*c*d*e^6*f^3*z^4 + 16*
a^3*b^8*c^3*d*e^8*f*z^4 + 16*a*b^12*c*d^3*e^4*f^3*z^4 + 16*a*b^10*c^3*d^3*e^6*f*z^4 + 48*b^11*c^3*d^6*e*f^3*z^
4 + 48*b^9*c^5*d^7*e*f^2*z^4 - 20*b^8*c^6*d^7*e^2*f*z^4 + 8*b^10*c^4*d^5*e^4*f*z^4 - 4*b^13*c*d^4*e^3*f^3*z^4
- 4*b^11*c^3*d^4*e^5*f*z^4 + 4*b^9*c^5*d^6*e^3*f*z^4 + 3072*a^9*c^5*d*e^4*f^5*z^4 + 3072*a^5*c^9*d^5*e^4*f*z^4
+ 2560*a^8*c^6*d*e^6*f^3*z^4 + 2560*a^6*c^8*d^3*e^6*f*z^4 + 1536*a^10*c^4*d*e^2*f^7*z^4 + 1536*a^4*c^10*d^7*e
^2*f*z^4 + 48*a^5*b^9*d^2*e*f^7*z^4 + 48*a^3*b^11*d^3*e*f^6*z^4 - 20*a^6*b^8*d*e^2*f^7*z^4 + 8*a^4*b^10*d*e^4*
f^5*z^4 + 4*a^5*b^9*d*e^3*f^6*z^4 - 4*a^3*b^11*d*e^5*f^4*z^4 - 4*a*b^13*d^3*e^3*f^4*z^4 + 768*a^9*b*c^4*e^5*f^
5*z^4 + 768*a^8*b*c^5*e^7*f^3*z^4 + 256*a^10*b*c^3*e^3*f^7*z^4 - 192*a^6*b^3*c^5*e^9*f*z^4 - 68*a^7*b^6*c*e^4*
f^6*z^4 + 48*a^8*b^5*c*e^3*f^7*z^4 + 48*a^5*b^5*c^4*e^9*f*z^4 + 36*a^6*b^7*c*e^5*f^5*z^4 - 12*a^9*b^4*c*e^2*f^
8*z^4 - 4*a^4*b^9*c*e^7*f^3*z^4 - 4*a^4*b^7*c^3*e^9*f*z^4 + 384*a^5*b^8*c*d^3*f^7*z^4 + 384*a*b^8*c^5*d^7*f^3*
z^4 + 288*a^3*b^10*c*d^4*f^6*z^4 + 288*a*b^10*c^3*d^6*f^4*z^4 + 224*a^7*b^6*c*d^2*f^8*z^4 + 224*a*b^6*c^7*d^8*
f^2*z^4 - 192*a^10*b^2*c^2*d*f^9*z^4 - 192*a^2*b^2*c^10*d^9*f*z^4 + 768*a^5*b*c^8*d^3*e^7*z^4 + 768*a^4*b*c^9*
d^5*e^5*z^4 + 256*a^3*b*c^10*d^7*e^3*z^4 - 192*a^5*b^3*c^6*d*e^9*z^4 - 68*a*b^6*c^7*d^6*e^4*z^4 + 48*a^4*b^5*c
^5*d*e^9*z^4 + 48*a*b^5*c^8*d^7*e^3*z^4 + 36*a*b^7*c^6*d^5*e^5*z^4 - 12*a*b^4*c^9*d^8*e^2*z^4 - 4*a^3*b^7*c^4*
d*e^9*z^4 - 4*a*b^9*c^4*d^3*e^7*z^4 + 16*b^13*c*d^5*e*f^4*z^4 + 16*b^7*c^7*d^8*e*f*z^4 + 768*a^7*c^7*d*e^8*f*z
^4 + 16*a^7*b^7*d*e*f^8*z^4 + 16*a*b^13*d^4*e*f^5*z^4 + 256*a^7*b*c^6*e^9*f*z^4 + 80*a*b^12*c*d^5*f^5*z^4 + 48
*a^9*b^4*c*d*f^9*z^4 + 48*a*b^4*c^9*d^9*f*z^4 + 256*a^6*b*c^7*d*e^9*z^4 - 42*b^10*c^4*d^6*e^2*f^2*z^4 - 20*b^1
2*c^2*d^5*e^2*f^3*z^4 + 6*b^12*c^2*d^4*e^4*f^2*z^4 + 4*b^11*c^3*d^5*e^3*f^2*z^4 - 24960*a^7*c^7*d^4*e^2*f^4*z^
4 + 18944*a^8*c^6*d^3*e^2*f^5*z^4 + 18944*a^6*c^8*d^5*e^2*f^3*z^4 + 14336*a^7*c^7*d^3*e^4*f^3*z^4 - 9984*a^8*c
^6*d^2*e^4*f^4*z^4 - 9984*a^6*c^8*d^4*e^4*f^2*z^4 - 7936*a^9*c^5*d^2*e^2*f^6*z^4 - 7936*a^5*c^9*d^6*e^2*f^2*z^
4 - 4352*a^7*c^7*d^2*e^6*f^2*z^4 - 42*a^4*b^10*d^2*e^2*f^6*z^4 - 20*a^2*b^12*d^3*e^2*f^5*z^4 + 6*a^2*b^12*d^2*
e^4*f^4*z^4 + 4*a^3*b^11*d^2*e^3*f^5*z^4 - 480*a^8*b^2*c^4*e^6*f^4*z^4 + 440*a^7*b^4*c^3*e^6*f^4*z^4 - 320*a^8
*b^3*c^3*e^5*f^5*z^4 - 320*a^7*b^3*c^4*e^7*f^3*z^4 + 240*a^8*b^4*c^2*e^4*f^6*z^4 + 240*a^6*b^4*c^4*e^8*f^2*z^4
- 192*a^9*b^3*c^2*e^3*f^7*z^4 - 192*a^9*b^2*c^3*e^4*f^6*z^4 - 192*a^7*b^2*c^5*e^8*f^2*z^4 - 90*a^6*b^6*c^2*e^
6*f^4*z^4 - 68*a^5*b^6*c^3*e^8*f^2*z^4 + 48*a^10*b^2*c^2*e^2*f^8*z^4 - 48*a^7*b^5*c^2*e^5*f^5*z^4 - 48*a^6*b^5
*c^3*e^7*f^3*z^4 + 36*a^5*b^7*c^2*e^7*f^3*z^4 + 6*a^4*b^8*c^2*e^8*f^2*z^4 - 33920*a^6*b^2*c^6*d^5*f^5*z^4 + 27
936*a^5*b^4*c^5*d^5*f^5*z^4 + 26112*a^7*b^2*c^5*d^4*f^6*z^4 + 26112*a^5*b^2*c^7*d^6*f^4*z^4 - 20352*a^6*b^4*c^
4*d^4*f^6*z^4 - 20352*a^4*b^4*c^6*d^6*f^4*z^4 - 13080*a^4*b^6*c^4*d^5*f^5*z^4 - 11520*a^8*b^2*c^4*d^3*f^7*z^4
- 11520*a^4*b^2*c^8*d^7*f^3*z^4 + 8736*a^5*b^6*c^3*d^4*f^6*z^4 + 8736*a^3*b^6*c^5*d^6*f^4*z^4 + 7488*a^7*b^4*c
^3*d^3*f^7*z^4 + 7488*a^3*b^4*c^7*d^7*f^3*z^4 + 3840*a^3*b^8*c^3*d^5*f^5*z^4 + 2560*a^9*b^2*c^3*d^2*f^8*z^4 +
2560*a^3*b^2*c^9*d^8*f^2*z^4 - 2416*a^6*b^6*c^2*d^3*f^7*z^4 - 2416*a^2*b^6*c^6*d^7*f^3*z^4 - 2160*a^4*b^8*c^2*
d^4*f^6*z^4 - 2160*a^2*b^8*c^4*d^6*f^4*z^4 - 1152*a^8*b^4*c^2*d^2*f^8*z^4 - 1152*a^2*b^4*c^8*d^8*f^2*z^4 - 720
*a^2*b^10*c^2*d^5*f^5*z^4 - 480*a^4*b^2*c^8*d^4*e^6*z^4 + 440*a^3*b^4*c^7*d^4*e^6*z^4 - 320*a^4*b^3*c^7*d^3*e^
7*z^4 - 320*a^3*b^3*c^8*d^5*e^5*z^4 + 240*a^4*b^4*c^6*d^2*e^8*z^4 + 240*a^2*b^4*c^8*d^6*e^4*z^4 - 192*a^5*b^2*
c^7*d^2*e^8*z^4 - 192*a^3*b^2*c^9*d^6*e^4*z^4 - 192*a^2*b^3*c^9*d^7*e^3*z^4 - 90*a^2*b^6*c^6*d^4*e^6*z^4 - 68*
a^3*b^6*c^5*d^2*e^8*z^4 - 48*a^3*b^5*c^6*d^3*e^7*z^4 - 48*a^2*b^5*c^7*d^5*e^5*z^4 + 48*a^2*b^2*c^10*d^8*e^2*z^
4 + 36*a^2*b^7*c^5*d^3*e^7*z^4 + 6*a^2*b^8*c^4*d^2*e^8*z^4 - 4*b^6*c^8*d^9*f*z^4 + 256*a^11*c^3*d*f^9*z^4 + 25
6*a^3*c^11*d^9*f*z^4 - 4*a^8*b^6*d*f^9*z^4 - 384*a^9*c^5*e^6*f^4*z^4 - 256*a^10*c^4*e^4*f^6*z^4 - 256*a^8*c^6*
e^8*f^2*z^4 - 64*a^11*c^3*e^2*f^8*z^4 - 24*b^10*c^4*d^7*f^3*z^4 - 16*b^12*c^2*d^6*f^4*z^4 - 16*b^8*c^6*d^8*f^2
*z^4 + 17920*a^7*c^7*d^5*f^5*z^4 - 14336*a^8*c^6*d^4*f^6*z^4 - 14336*a^6*c^8*d^6*f^4*z^4 + 7168*a^9*c^5*d^3*f^
7*z^4 + 7168*a^5*c^9*d^7*f^3*z^4 - 2048*a^10*c^4*d^2*f^8*z^4 - 2048*a^4*c^10*d^8*f^2*z^4 + 6*b^8*c^6*d^6*e^4*z
^4 + 6*a^6*b^8*e^4*f^6*z^4 - 4*b^9*c^5*d^5*e^5*z^4 - 4*b^7*c^7*d^7*e^3*z^4 - 4*a^7*b^7*e^3*f^7*z^4 - 4*a^5*b^9
*e^5*f^5*z^4 - 384*a^5*c^9*d^4*e^6*z^4 - 256*a^6*c^8*d^2*e^8*z^4 - 256*a^4*c^10*d^6*e^4*z^4 - 64*a^3*c^11*d^8*
e^2*z^4 - 24*a^4*b^10*d^3*f^7*z^4 - 16*a^6*b^8*d^2*f^8*z^4 - 16*a^2*b^12*d^4*f^6*z^4 + 48*a^6*b^2*c^6*e^10*z^4
- 12*a^5*b^4*c^5*e^10*z^4 - 4*b^14*d^5*f^5*z^4 - 64*a^7*c^7*e^10*z^4 + b^14*d^4*e^2*f^4*z^4 + b^10*c^4*d^4*e^
6*z^4 + b^6*c^8*d^8*e^2*z^4 + a^8*b^6*e^2*f^8*z^4 + a^4*b^10*e^6*f^4*z^4 + a^4*b^6*c^4*e^10*z^4 - 4820*A*B*a^4
*b*c^5*d^2*e^2*f^4*z^2 + 2976*A*B*a^3*b*c^6*d^3*e^2*f^3*z^2 - 2328*A*B*a^3*b*c^6*d^2*e^4*f^2*z^2 + 1848*A*B*a^
2*b^4*c^4*d^3*e*f^4*z^2 - 1768*A*B*a^3*b^4*c^3*d^2*e*f^5*z^2 + 1528*A*B*a^4*b^2*c^4*d^2*e*f^5*z^2 - 1136*A*B*a
^3*b^2*c^5*d^3*e*f^4*z^2 - 974*A*B*a^4*b^3*c^3*d*e^2*f^5*z^2 + 692*A*B*a^2*b*c^7*d^4*e^2*f^2*z^2 + 588*A*B*a*b
^6*c^3*d^2*e^3*f^3*z^2 - 580*A*B*a^3*b^3*c^4*d*e^4*f^3*z^2 + 488*A*B*a^3*b^4*c^3*d*e^3*f^4*z^2 - 444*A*B*a^2*b
^2*c^6*d^2*e^5*f*z^2 - 412*A*B*a*b^5*c^4*d^2*e^4*f^2*z^2 + 366*A*B*a^2*b^6*c^2*d^2*e*f^5*z^2 - 352*A*B*a^2*b^2
*c^6*d^4*e*f^3*z^2 + 326*A*B*a^2*b^4*c^4*d*e^5*f^2*z^2 + 324*A*B*a*b^5*c^4*d^3*e^2*f^3*z^2 - 302*A*B*a*b^3*c^6
*d^4*e^2*f^2*z^2 - 296*A*B*a*b^7*c^2*d^2*e^2*f^4*z^2 + 122*A*B*a^4*b^2*c^4*d*e^3*f^4*z^2 - 122*A*B*a^2*b^6*c^2
*d*e^3*f^4*z^2 - 84*A*B*a^3*b^2*c^5*d*e^5*f^2*z^2 + 72*A*B*a*b^4*c^5*d^3*e^3*f^2*z^2 - 64*A*B*a^2*b^5*c^3*d*e^
4*f^3*z^2 + 60*A*B*a^3*b^5*c^2*d*e^2*f^5*z^2 + 1312*A*B*a^5*b*c^4*d*e^2*f^5*z^2 + 1040*A*B*a^4*b*c^5*d*e^4*f^3
*z^2 - 500*A*B*a*b^6*c^3*d^3*e*f^4*z^2 - 376*A*B*a*b^2*c^7*d^5*e*f^2*z^2 + 276*A*B*a^4*b^4*c^2*d*e*f^6*z^2 - 2
62*A*B*a^2*b^3*c^5*d*e^6*f*z^2 + 238*A*B*a*b^2*c^7*d^4*e^3*f*z^2 + 232*A*B*a^5*b^2*c^3*d*e*f^6*z^2 - 176*A*B*a
^2*b*c^7*d^3*e^4*f*z^2 - 120*A*B*a*b^6*c^3*d*e^5*f^2*z^2 - 108*A*B*a*b^4*c^5*d^4*e*f^3*z^2 + 68*A*B*a*b^7*c^2*
d*e^4*f^3*z^2 + 68*A*B*a*b^4*c^5*d^2*e^5*f*z^2 + 46*A*B*a^2*b^7*c*d*e^2*f^5*z^2 - 36*A*B*a*b^3*c^6*d^3*e^4*f*z
^2 - 1932*A*B*a^2*b^3*c^5*d^3*e^2*f^3*z^2 - 1818*A*B*a^2*b^4*c^4*d^2*e^3*f^3*z^2 + 1620*A*B*a^3*b^3*c^4*d^2*e^
2*f^4*z^2 + 1560*A*B*a^2*b^3*c^5*d^2*e^4*f^2*z^2 + 1244*A*B*a^3*b^2*c^5*d^2*e^3*f^3*z^2 + 820*A*B*a^2*b^2*c^6*
d^3*e^3*f^2*z^2 + 480*A*B*a^2*b^5*c^3*d^2*e^2*f^4*z^2 + 352*A*B*a^3*b*c^6*d*e^6*f*z^2 - 108*A*B*a^3*b^6*c*d*e*
f^6*z^2 + 82*A*B*a*b^5*c^4*d*e^6*f*z^2 - 64*A*B*a*b*c^8*d^5*e^2*f*z^2 + 16*A*B*a*b^8*c*d^2*e*f^5*z^2 - 4*A*B*a
*b^8*c*d*e^3*f^4*z^2 + 16*B^2*a*b*c^8*d^6*e*f*z^2 + 56*A*B*b^2*c^8*d^6*e*f*z^2 - 8*A*B*b^9*c*d*e^4*f^3*z^2 - 8
*A*B*b^7*c^3*d*e^6*f*z^2 - 800*A*B*a^6*c^4*d*e*f^6*z^2 + 10*A*B*a^2*b^8*d*e*f^6*z^2 - 6*A*B*a*b^9*d*e^2*f^5*z^
2 - 12*A*B*a^5*b^4*c*e*f^7*z^2 + 912*A*B*a^6*b*c^3*d*f^7*z^2 + 192*A*B*a^4*b^5*c*d*f^7*z^2 + 192*A*B*a*b*c^8*d
^6*f^2*z^2 - 20*A*B*a*b^4*c^5*d*e^7*z^2 + 4*A*B*a*b*c^8*d^4*e^4*z^2 + 2144*B^2*a^4*b*c^5*d^3*e*f^4*z^2 - 1120*
B^2*a^3*b*c^6*d^4*e*f^3*z^2 - 688*B^2*a^5*b*c^4*d^2*e*f^5*z^2 - 256*B^2*a^3*b*c^6*d^2*e^5*f*z^2 + 152*B^2*a*b^
3*c^6*d^5*e*f^2*z^2 + 120*B^2*a^5*b^3*c^2*d*e*f^6*z^2 - 116*B^2*a^5*b*c^4*d*e^3*f^4*z^2 + 110*B^2*a*b^7*c^2*d^
3*e*f^4*z^2 - 80*B^2*a^2*b*c^7*d^5*e*f^2*z^2 - 72*B^2*a*b^5*c^4*d^4*e*f^3*z^2 - 48*B^2*a^4*b*c^5*d*e^5*f^2*z^2
- 46*B^2*a*b^3*c^6*d^4*e^3*f*z^2 - 44*B^2*a*b^4*c^5*d^3*e^4*f*z^2 - 34*B^2*a*b^5*c^4*d^2*e^5*f*z^2 + 20*B^2*a
^2*b*c^7*d^4*e^3*f*z^2 - 10*B^2*a^3*b^6*c*d*e^2*f^5*z^2 - 10*B^2*a^2*b^7*c*d^2*e*f^5*z^2 - 10*B^2*a*b^2*c^7*d^
5*e^2*f*z^2 - 7*B^2*a^2*b^4*c^4*d*e^6*f*z^2 - 6*B^2*a^3*b^2*c^5*d*e^6*f*z^2 + 4*B^2*a*b^8*c*d^2*e^2*f^4*z^2 -
2*B^2*a^2*b^7*c*d*e^3*f^4*z^2 + 3196*A^2*a^4*b*c^5*d*e^3*f^4*z^2 - 3184*A^2*a^4*b*c^5*d^2*e*f^5*z^2 + 1568*A^2
*a^3*b*c^6*d^3*e*f^4*z^2 + 1504*A^2*a^3*b*c^6*d*e^5*f^2*z^2 - 656*A^2*a^4*b^3*c^3*d*e*f^6*z^2 - 400*A^2*a*b^6*
c^3*d*e^4*f^3*z^2 + 314*A^2*a*b^5*c^4*d*e^5*f^2*z^2 - 264*A^2*a^3*b^5*c^2*d*e*f^6*z^2 + 240*A^2*a^2*b^2*c^6*d*
e^6*f*z^2 - 224*A^2*a^2*b*c^7*d^4*e*f^3*z^2 + 216*A^2*a*b^5*c^4*d^3*e*f^4*z^2 - 192*A^2*a^2*b*c^7*d^2*e^5*f*z^
2 + 178*A^2*a*b^7*c^2*d*e^3*f^4*z^2 - 154*A^2*a*b^7*c^2*d^2*e*f^5*z^2 + 128*A^2*a*b^3*c^6*d^4*e*f^3*z^2 + 106*
A^2*a*b^3*c^6*d^2*e^5*f*z^2 - 12*A^2*a*b^2*c^7*d^3*e^4*f*z^2 - 58*A*B*b^8*c^2*d^2*e^3*f^3*z^2 + 40*A*B*b^7*c^3
*d^2*e^4*f^2*z^2 - 28*A*B*b^7*c^3*d^3*e^2*f^3*z^2 - 24*A*B*b^5*c^5*d^4*e^2*f^2*z^2 - 20*A*B*b^6*c^4*d^3*e^3*f^
2*z^2 + 2768*A*B*a^4*c^6*d^2*e^3*f^3*z^2 - 1712*A*B*a^3*c^7*d^3*e^3*f^2*z^2 - 156*A*B*a^4*b^2*c^4*e^5*f^3*z^2
+ 146*A*B*a^4*b^3*c^3*e^4*f^4*z^2 - 106*A*B*a^5*b^2*c^3*e^3*f^5*z^2 + 90*A*B*a^5*b^3*c^2*e^2*f^6*z^2 + 38*A*B*
a^3*b^3*c^4*e^6*f^2*z^2 - 36*A*B*a^3*b^5*c^2*e^4*f^4*z^2 + 16*A*B*a^3*b^4*c^3*e^5*f^3*z^2 - 9*A*B*a^4*b^4*c^2*
e^3*f^5*z^2 - 8*A*B*a^2*b^5*c^3*e^6*f^2*z^2 + 2*A*B*a^2*b^6*c^2*e^5*f^3*z^2 + 920*A*B*a^4*b^3*c^3*d^2*f^6*z^2
- 480*A*B*a^2*b^5*c^3*d^3*f^5*z^2 - 336*A*B*a^2*b^3*c^5*d^4*f^4*z^2 - 272*A*B*a^3*b^3*c^4*d^3*f^5*z^2 + 240*A*
B*a^3*b^5*c^2*d^2*f^6*z^2 - 32*A*B*a*c^9*d^6*e*f*z^2 - 792*B^2*a^2*b^3*c^5*d^3*e^3*f^2*z^2 + 714*B^2*a^2*b^4*c
^4*d^3*e^2*f^3*z^2 - 572*B^2*a^3*b^2*c^5*d^3*e^2*f^3*z^2 - 475*B^2*a^2*b^2*c^6*d^4*e^2*f^2*z^2 + 265*B^2*a^4*b
^2*c^4*d^2*e^2*f^4*z^2 + 260*B^2*a^3*b^3*c^4*d^2*e^3*f^3*z^2 - 212*B^2*a^3*b^4*c^3*d^2*e^2*f^4*z^2 + 180*B^2*a
^3*b^2*c^5*d^2*e^4*f^2*z^2 - 158*B^2*a^2*b^4*c^4*d^2*e^4*f^2*z^2 + 47*B^2*a^2*b^6*c^2*d^2*e^2*f^4*z^2 + 16*B^2
*a^2*b^5*c^3*d^2*e^3*f^3*z^2 + 2752*A^2*a^3*b^2*c^5*d^2*e^2*f^4*z^2 - 2148*A^2*a^2*b^4*c^4*d^2*e^2*f^4*z^2 + 2
064*A^2*a^2*b^3*c^5*d^2*e^3*f^3*z^2 - 424*A^2*a^2*b^2*c^6*d^3*e^2*f^3*z^2 - 198*A^2*a^2*b^2*c^6*d^2*e^4*f^2*z^
2 - 272*B^2*a^6*b*c^3*d*e*f^6*z^2 - 24*B^2*a^4*b^5*c*d*e*f^6*z^2 + 1808*A^2*a^5*b*c^4*d*e*f^6*z^2 - 244*A^2*a*
b*c^8*d^4*e^3*f*z^2 + 208*A^2*a*b*c^8*d^5*e*f^2*z^2 + 134*A^2*a^2*b^7*c*d*e*f^6*z^2 - 76*A^2*a*b^4*c^5*d*e^6*f
*z^2 + 4*A^2*a*b^8*c*d*e^2*f^5*z^2 + 148*A*B*b^4*c^6*d^5*e*f^2*z^2 + 65*A*B*b^6*c^4*d^4*e*f^3*z^2 + 46*A*B*b^8
*c^2*d^3*e*f^4*z^2 - 38*A*B*b^3*c^7*d^5*e^2*f*z^2 + 34*A*B*b^9*c*d^2*e^2*f^4*z^2 - 29*A*B*b^4*c^6*d^4*e^3*f*z^
2 + 20*A*B*b^5*c^5*d^3*e^4*f*z^2 + 12*A*B*b^8*c^2*d*e^5*f^2*z^2 - 7*A*B*b^6*c^4*d^2*e^5*f*z^2 - 2880*A*B*a^4*c
^6*d^3*e*f^4*z^2 + 2784*A*B*a^5*c^5*d^2*e*f^5*z^2 - 1112*A*B*a^5*c^5*d*e^3*f^4*z^2 + 896*A*B*a^3*c^7*d^4*e*f^3
*z^2 + 848*A*B*a^3*c^7*d^2*e^5*f*z^2 - 560*A*B*a^4*c^6*d*e^5*f^2*z^2 + 96*A*B*a^2*c^8*d^5*e*f^2*z^2 - 88*A*B*a
^2*c^8*d^4*e^3*f*z^2 - 100*A*B*a^6*b*c^3*e^2*f^6*z^2 - 76*A*B*a^5*b*c^4*e^4*f^4*z^2 + 48*A*B*a^6*b^2*c^2*e*f^7
*z^2 - 42*A*B*a^3*b^2*c^5*e^7*f*z^2 + 36*A*B*a^4*b*c^5*e^6*f^2*z^2 - 24*A*B*a^4*b^5*c*e^2*f^6*z^2 + 10*A*B*a^3
*b^6*c*e^3*f^5*z^2 + 7*A*B*a^2*b^4*c^4*e^7*f*z^2 + 2*A*B*a^2*b^7*c*e^4*f^4*z^2 - 2496*A*B*a^5*b*c^4*d^2*f^6*z^
2 + 1872*A*B*a^4*b*c^5*d^3*f^5*z^2 - 744*A*B*a^5*b^3*c^2*d*f^7*z^2 - 720*A*B*a^2*b*c^7*d^5*f^3*z^2 + 504*A*B*a
*b^3*c^6*d^5*f^3*z^2 + 256*A*B*a^3*b*c^6*d^4*f^4*z^2 + 168*A*B*a*b^7*c^2*d^3*f^5*z^2 - 144*A*B*a^2*b^7*c*d^2*f
^6*z^2 + 144*A*B*a*b^5*c^4*d^4*f^4*z^2 + 66*A*B*a^2*b^2*c^6*d*e^7*z^2 - 36*A*B*a*b^2*c^7*d^3*e^5*z^2 + 20*A*B*
a*b^3*c^6*d^2*e^6*z^2 + 12*A*B*a^2*b*c^7*d^2*e^6*z^2 + 1208*B^2*a^3*b*c^6*d^3*e^3*f^2*z^2 - 848*B^2*a^3*b^3*c^
4*d^3*e*f^4*z^2 + 672*B^2*a^2*b^3*c^5*d^4*e*f^3*z^2 - 632*B^2*a^4*b*c^5*d^2*e^3*f^3*z^2 + 432*B^2*a^4*b^3*c^3*
d^2*e*f^5*z^2 + 276*B^2*a^2*b^2*c^6*d^3*e^4*f*z^2 - 196*B^2*a*b^6*c^3*d^3*e^2*f^3*z^2 - 168*B^2*a^2*b^5*c^3*d^
3*e*f^4*z^2 + 154*B^2*a^2*b^3*c^5*d^2*e^5*f*z^2 + 148*B^2*a*b^5*c^4*d^3*e^3*f^2*z^2 + 96*B^2*a*b^4*c^5*d^4*e^2
*f^2*z^2 - 72*B^2*a^3*b^5*c^2*d^2*e*f^5*z^2 + 70*B^2*a^5*b^2*c^3*d*e^2*f^5*z^2 - 60*B^2*a^4*b^3*c^3*d*e^3*f^4*
z^2 + 52*B^2*a*b^6*c^3*d^2*e^4*f^2*z^2 + 36*B^2*a^4*b^2*c^4*d*e^4*f^3*z^2 - 32*B^2*a*b^7*c^2*d^2*e^3*f^3*z^2 +
24*B^2*a^3*b^5*c^2*d*e^3*f^4*z^2 + 15*B^2*a^4*b^4*c^2*d*e^2*f^5*z^2 - 8*B^2*a^3*b^4*c^3*d*e^4*f^3*z^2 + 8*B^2
*a^2*b^5*c^3*d*e^5*f^2*z^2 - 2*B^2*a^3*b^3*c^4*d*e^5*f^2*z^2 - 2*B^2*a^2*b^6*c^2*d*e^4*f^3*z^2 - 3176*A^2*a^3*
b*c^6*d^2*e^3*f^3*z^2 - 2252*A^2*a^4*b^2*c^4*d*e^2*f^5*z^2 + 1952*A^2*a^3*b^4*c^3*d*e^2*f^5*z^2 - 1496*A^2*a^3
*b^3*c^4*d*e^3*f^4*z^2 + 1378*A^2*a^2*b^4*c^4*d*e^4*f^3*z^2 + 1184*A^2*a^3*b^3*c^4*d^2*e*f^5*z^2 - 1166*A^2*a^
2*b^3*c^5*d*e^5*f^2*z^2 - 1164*A^2*a^3*b^2*c^5*d*e^4*f^3*z^2 - 1152*A^2*a^2*b^3*c^5*d^3*e*f^4*z^2 + 578*A^2*a*
b^6*c^3*d^2*e^2*f^4*z^2 - 548*A^2*a*b^5*c^4*d^2*e^3*f^3*z^2 + 440*A^2*a*b^2*c^7*d^4*e^2*f^2*z^2 - 412*A^2*a^2*
b^6*c^2*d*e^2*f^5*z^2 - 360*A^2*a*b^3*c^6*d^3*e^3*f^2*z^2 + 312*A^2*a*b^4*c^5*d^3*e^2*f^3*z^2 + 248*A^2*a^2*b*
c^7*d^3*e^3*f^2*z^2 - 224*A^2*a^2*b^5*c^3*d*e^3*f^4*z^2 + 216*A^2*a^2*b^5*c^3*d^2*e*f^5*z^2 + 52*A^2*a*b^4*c^5
*d^2*e^4*f^2*z^2 - 16*B^2*b^3*c^7*d^6*e*f*z^2 - 14*B^2*b^9*c*d^3*e*f^4*z^2 + 32*B^2*a^4*c^6*d*e^6*f*z^2 - 20*A
^2*b^9*c*d*e^3*f^4*z^2 + 18*A^2*b^9*c*d^2*e*f^5*z^2 + 8*A^2*b^6*c^4*d*e^6*f*z^2 - 360*A^2*a^3*c^7*d*e^6*f*z^2
+ 136*A^2*a*c^9*d^5*e^2*f*z^2 + 2*B^2*a^3*b^7*d*e*f^6*z^2 + 2*B^2*a*b^9*d^2*e*f^5*z^2 + 12*B^2*a^4*b*c^5*e^7*f
*z^2 - 204*A^2*a^3*b*c^6*e^7*f*z^2 - 128*A^2*a^6*b*c^3*e*f^7*z^2 - 48*A^2*a*b^5*c^4*e^7*f*z^2 - 36*B^2*a^5*b^4
*c*d*f^7*z^2 - 24*A^2*a^4*b^5*c*e*f^7*z^2 - 16*B^2*a*b^8*c*d^3*f^5*z^2 - 164*A^2*a^3*b^6*c*d*f^7*z^2 - 16*A^2*
a*b^8*c*d^2*f^6*z^2 + 4*B^2*a^3*b*c^6*d*e^7*z^2 - 4*B^2*a*b*c^8*d^5*e^3*z^2 + 48*A^2*a*b*c^8*d^3*e^5*z^2 + 36*
A^2*a^2*b*c^7*d*e^7*z^2 - 6*A^2*a*b^3*c^6*d*e^7*z^2 + 136*A*B*a^6*c^4*e^3*f^5*z^2 - 96*A*B*b^5*c^5*d^5*f^3*z^2
+ 80*A*B*a^5*c^5*e^5*f^3*z^2 - 72*A*B*b^3*c^7*d^6*f^2*z^2 - 24*A*B*b^7*c^3*d^4*f^4*z^2 + 14*A*B*b^3*c^7*d^4*e
^4*z^2 - 14*A*B*b^2*c^8*d^5*e^3*z^2 - 2*A*B*b^5*c^5*d^2*e^6*z^2 - 2*A*B*b^4*c^6*d^3*e^5*z^2 + 2*A*B*a^3*b^7*e^
2*f^6*z^2 - A*B*a^2*b^8*e^3*f^5*z^2 + 16*A*B*a^2*c^8*d^3*e^5*z^2 - 2*A*B*a^2*b^3*c^5*e^8*z^2 + 22*B^2*b^8*c^2*
d^3*e^2*f^3*z^2 - 12*B^2*b^7*c^3*d^3*e^3*f^2*z^2 + 12*B^2*b^6*c^4*d^4*e^2*f^2*z^2 - 6*B^2*b^8*c^2*d^2*e^4*f^2*
z^2 - 864*B^2*a^4*c^6*d^3*e^2*f^3*z^2 + 496*B^2*a^3*c^7*d^4*e^2*f^2*z^2 + 224*B^2*a^5*c^5*d^2*e^2*f^4*z^2 + 13
6*B^2*a^4*c^6*d^2*e^4*f^2*z^2 - 53*A^2*b^8*c^2*d^2*e^2*f^4*z^2 + 52*A^2*b^7*c^3*d^2*e^3*f^3*z^2 + 52*A^2*b^5*c
^5*d^3*e^3*f^2*z^2 - 36*A^2*b^6*c^4*d^3*e^2*f^3*z^2 - 12*A^2*b^4*c^6*d^4*e^2*f^2*z^2 - 9*A^2*b^6*c^4*d^2*e^4*f
^2*z^2 + 836*A^2*a^4*c^6*d^2*e^2*f^4*z^2 - 668*A^2*a^2*c^8*d^4*e^2*f^2*z^2 + 656*A^2*a^3*c^7*d^2*e^4*f^2*z^2 +
368*A^2*a^3*c^7*d^3*e^2*f^3*z^2 - 45*B^2*a^6*b^2*c^2*e^2*f^6*z^2 - 18*B^2*a^5*b^2*c^3*e^4*f^4*z^2 - 9*B^2*a^4
*b^2*c^4*e^6*f^2*z^2 - 6*B^2*a^5*b^3*c^2*e^3*f^5*z^2 + 3*B^2*a^4*b^4*c^2*e^4*f^4*z^2 - 2*B^2*a^4*b^3*c^3*e^5*f
^3*z^2 - 580*B^2*a^4*b^2*c^4*d^3*f^5*z^2 + 536*B^2*a^3*b^4*c^3*d^3*f^5*z^2 + 471*A^2*a^4*b^2*c^4*e^4*f^4*z^2 -
436*A^2*a^3*b^4*c^3*e^4*f^4*z^2 - 348*B^2*a^4*b^4*c^2*d^2*f^6*z^2 + 316*B^2*a^2*b^2*c^6*d^5*f^3*z^2 + 310*A^2
*a^3*b^3*c^4*e^5*f^3*z^2 + 232*A^2*a^5*b^2*c^3*e^2*f^6*z^2 - 229*A^2*a^2*b^4*c^4*e^6*f^2*z^2 - 216*A^2*a^4*b^4
*c^2*e^2*f^6*z^2 + 204*A^2*a^4*b^3*c^3*e^3*f^5*z^2 + 200*B^2*a^5*b^2*c^3*d^2*f^6*z^2 + 150*A^2*a^3*b^2*c^5*e^6
*f^2*z^2 - 120*B^2*a^2*b^4*c^4*d^4*f^4*z^2 + 91*A^2*a^2*b^6*c^2*e^4*f^4*z^2 + 72*A^2*a^3*b^5*c^2*e^3*f^5*z^2 -
66*B^2*a^2*b^6*c^2*d^3*f^5*z^2 + 44*A^2*a^2*b^5*c^3*e^5*f^3*z^2 - 16*B^2*a^3*b^2*c^5*d^4*f^4*z^2 + 1952*A^2*a
^4*b^2*c^4*d^2*f^6*z^2 - 1792*A^2*a^3*b^2*c^5*d^3*f^5*z^2 - 1272*A^2*a^3*b^4*c^3*d^2*f^6*z^2 + 976*A^2*a^2*b^2
*c^6*d^4*f^4*z^2 + 960*A^2*a^2*b^4*c^4*d^3*f^5*z^2 + 282*A^2*a^2*b^6*c^2*d^2*f^6*z^2 - 45*B^2*a^2*b^2*c^6*d^2*
e^6*z^2 - 48*A^2*b*c^9*d^6*e*f*z^2 - 14*A^2*a*b^9*d*e*f^6*z^2 - 7*A*B*b^10*d^2*e*f^5*z^2 + 2*A*B*b^10*d*e^3*f^
4*z^2 - 64*A*B*a^7*c^3*e*f^7*z^2 - 16*A*B*b^9*c*d^3*f^5*z^2 + 8*A*B*a^4*c^6*e^7*f*z^2 + 4*A*B*b*c^9*d^6*e^2*z^
2 + 2*A*B*b^6*c^4*d*e^7*z^2 - 120*A*B*a^3*c^7*d*e^7*z^2 - 16*A*B*a^3*b^7*d*f^7*z^2 + 16*A*B*a*b^9*d^2*f^6*z^2
+ 8*A*B*a*c^9*d^5*e^3*z^2 + 12*A*B*a^3*b*c^6*e^8*z^2 - 48*B^2*b^5*c^5*d^5*e*f^2*z^2 + 15*B^2*b^4*c^6*d^5*e^2*f
*z^2 - 14*B^2*b^7*c^3*d^4*e*f^3*z^2 + 4*B^2*b^9*c*d^2*e^3*f^3*z^2 + 4*B^2*b^7*c^3*d^2*e^5*f*z^2 + 4*B^2*b^5*c^
5*d^4*e^3*f*z^2 - B^2*b^6*c^4*d^3*e^4*f*z^2 - 336*B^2*a^3*c^7*d^3*e^4*f*z^2 + 112*B^2*a^5*c^5*d*e^4*f^3*z^2 -
112*A^2*b^3*c^7*d^5*e*f^2*z^2 + 80*B^2*a^6*c^4*d*e^2*f^5*z^2 - 48*A^2*b^5*c^5*d^4*e*f^3*z^2 + 36*A^2*b^8*c^2*d
*e^4*f^3*z^2 + 36*A^2*b^3*c^7*d^4*e^3*f*z^2 - 28*A^2*b^7*c^3*d*e^5*f^2*z^2 + 20*A^2*b^2*c^8*d^5*e^2*f*z^2 + 16
*B^2*a^2*c^8*d^5*e^2*f*z^2 - 14*A^2*b^7*c^3*d^3*e*f^4*z^2 - 14*A^2*b^4*c^6*d^3*e^4*f*z^2 - 10*A^2*b^5*c^5*d^2*
e^5*f*z^2 - 1008*A^2*a^4*c^6*d*e^4*f^3*z^2 - 760*A^2*a^5*c^5*d*e^2*f^5*z^2 + 272*A^2*a^2*c^8*d^3*e^4*f*z^2 + 4
8*B^2*a^5*b*c^4*e^5*f^3*z^2 + 36*B^2*a^6*b*c^3*e^3*f^5*z^2 + 12*B^2*a^5*b^4*c*e^2*f^6*z^2 - 624*A^2*a^4*b*c^5*
e^5*f^3*z^2 - 548*A^2*a^5*b*c^4*e^3*f^5*z^2 + 182*A^2*a^2*b^3*c^5*e^7*f*z^2 - 180*B^2*a*b^4*c^5*d^5*f^3*z^2 +
132*B^2*a^6*b^2*c^2*d*f^7*z^2 + 108*B^2*a^3*b^6*c*d^2*f^6*z^2 + 96*A^2*a^5*b^3*c^2*e*f^7*z^2 + 68*A^2*a*b^6*c^
3*e^6*f^2*z^2 + 58*A^2*a^3*b^6*c*e^2*f^6*z^2 - 56*B^2*a*b^2*c^7*d^6*f^2*z^2 - 38*A^2*a^2*b^7*c*e^3*f^5*z^2 - 3
6*A^2*a*b^7*c^2*e^5*f^3*z^2 + 20*B^2*a*b^6*c^3*d^4*f^4*z^2 - 736*A^2*a^5*b^2*c^3*d*f^7*z^2 + 624*A^2*a^4*b^4*c
^2*d*f^7*z^2 - 416*A^2*a*b^2*c^7*d^5*f^3*z^2 - 276*A^2*a*b^4*c^5*d^4*f^4*z^2 - 196*A^2*a*b^6*c^3*d^3*f^5*z^2 +
8*B^2*a*b^4*c^5*d^2*e^6*z^2 + 6*B^2*a*b^2*c^7*d^4*e^4*z^2 + 2*B^2*a^2*b^3*c^5*d*e^7*z^2 + 2*B^2*a*b^3*c^6*d^3
*e^5*z^2 - 18*A^2*a*b^2*c^7*d^2*e^6*z^2 - 16*A*B*b*c^9*d^7*f*z^2 - B^2*b^10*d^2*e^2*f^4*z^2 + 48*B^2*a^7*c^3*e
^2*f^6*z^2 - 36*B^2*a^6*c^4*e^4*f^4*z^2 + 31*B^2*b^6*c^4*d^5*f^3*z^2 - 24*B^2*a^5*c^5*e^6*f^2*z^2 + 20*B^2*b^4
*c^6*d^6*f^2*z^2 - 6*A^2*b^8*c^2*e^6*f^2*z^2 + 2*B^2*b^8*c^2*d^4*f^4*z^2 - 768*B^2*a^5*c^5*d^3*f^5*z^2 + 512*B
^2*a^6*c^4*d^2*f^6*z^2 + 512*B^2*a^4*c^6*d^4*f^4*z^2 + 232*A^2*a^5*c^5*e^4*f^4*z^2 + 188*A^2*a^4*c^6*e^6*f^2*z
^2 - 128*B^2*a^3*c^7*d^5*f^3*z^2 + 92*A^2*a^6*c^4*e^2*f^6*z^2 + 80*A^2*b^4*c^6*d^5*f^3*z^2 + 64*A^2*b^2*c^8*d^
6*f^2*z^2 + 31*A^2*b^6*c^4*d^4*f^4*z^2 + 14*A^2*b^8*c^2*d^3*f^5*z^2 - 5*B^2*b^4*c^6*d^4*e^4*z^2 + 4*B^2*b^3*c^
7*d^5*e^3*z^2 + 2*B^2*b^5*c^5*d^3*e^5*z^2 - B^2*b^6*c^4*d^2*e^6*z^2 - B^2*b^2*c^8*d^6*e^2*z^2 - B^2*a^4*b^6*e^
2*f^6*z^2 - 1152*A^2*a^3*c^7*d^4*f^4*z^2 + 1008*A^2*a^4*c^6*d^3*f^5*z^2 + 624*A^2*a^2*c^8*d^5*f^3*z^2 - 288*A^
2*a^5*c^5*d^2*f^6*z^2 + 56*B^2*a^3*c^7*d^2*e^6*z^2 - 10*B^2*a^2*b^8*d^2*f^6*z^2 - 9*A^2*b^2*c^8*d^4*e^4*z^2 -
5*A^2*a^2*b^8*e^2*f^6*z^2 - 4*B^2*a^2*c^8*d^4*e^4*z^2 + 3*A^2*b^4*c^6*d^2*e^6*z^2 - 2*A^2*b^3*c^7*d^3*e^5*z^2
- 36*A^2*a^2*c^8*d^2*e^6*z^2 - 48*A^2*a^6*b^2*c^2*f^8*z^2 - 45*A^2*a^2*b^2*c^6*e^8*z^2 + 4*A^2*b^10*d*e^2*f^5*
z^2 + 4*B^2*b^2*c^8*d^7*f*z^2 + 4*A^2*b^9*c*e^5*f^3*z^2 + 4*A^2*b^7*c^3*e^7*f*z^2 - 128*B^2*a^7*c^3*d*f^7*z^2
- 160*A^2*a*c^9*d^6*f^2*z^2 - 112*A^2*a^6*c^4*d*f^7*z^2 + 12*A^2*b*c^9*d^5*e^3*z^2 + 4*A^2*a*b^9*e^3*f^5*z^2 +
3*B^2*a^4*b^6*d*f^7*z^2 + 2*A^2*a^3*b^7*e*f^7*z^2 - 24*A^2*a*c^9*d^4*e^4*z^2 + 14*A^2*a^2*b^8*d*f^7*z^2 + 12*
A^2*a^5*b^4*c*f^8*z^2 + 12*A^2*a*b^4*c^5*e^8*z^2 + A*B*a^4*b^6*e*f^7*z^2 + B^2*a^2*b^8*d*e^2*f^5*z^2 + 16*A^2*
c^10*d^7*f*z^2 + 3*B^2*b^10*d^3*f^5*z^2 - A^2*b^10*e^4*f^4*z^2 - 4*A^2*c^10*d^6*e^2*z^2 - A^2*b^10*d^2*f^6*z^2
+ 64*A^2*a^7*c^3*f^8*z^2 - 4*B^2*a^4*c^6*e^8*z^2 - A^2*b^6*c^4*e^8*z^2 + 48*A^2*a^3*c^7*e^8*z^2 - A^2*a^4*b^6
*f^8*z^2 + 720*A^2*B*a*b^2*c^5*d^2*e^2*f^3*z - 600*A^2*B*a^2*b^2*c^4*d*e^2*f^4*z + 576*A*B^2*a^2*b^2*c^4*d^2*e
*f^4*z + 348*A*B^2*a*b^2*c^5*d^2*e^3*f^2*z - 336*A*B^2*a^2*b*c^5*d^2*e^2*f^3*z - 260*A*B^2*a*b^3*c^4*d^2*e^2*f
^3*z - 240*A*B^2*a^2*b^2*c^4*d*e^3*f^3*z + 196*A*B^2*a^2*b^3*c^3*d*e^2*f^4*z + 172*A^2*B*a*b*c^6*d*e^5*f*z + 2
0*A*B^2*a*b^6*c*d*e*f^5*z - 912*A^2*B*a^2*b*c^5*d^2*e*f^4*z - 644*A^2*B*a*b*c^6*d^2*e^3*f^2*z - 432*A*B^2*a*b^
2*c^5*d^3*e*f^3*z + 372*A^2*B*a^2*b*c^5*d*e^3*f^3*z - 330*A^2*B*a*b^2*c^5*d*e^4*f^2*z + 312*A*B^2*a*b*c^6*d^3*
e^2*f^2*z - 208*A*B^2*a^3*b^2*c^3*d*e*f^5*z + 192*A^2*B*a^2*b^3*c^3*d*e*f^5*z + 172*A^2*B*a*b^3*c^4*d*e^3*f^3*
z + 108*A*B^2*a^2*b*c^5*d*e^4*f^2*z + 104*A*B^2*a^3*b*c^4*d*e^2*f^4*z - 80*A^2*B*a*b^3*c^4*d^2*e*f^4*z + 68*A^
2*B*a*b^4*c^3*d*e^2*f^4*z - 60*A*B^2*a*b^5*c^2*d*e^2*f^4*z + 58*A*B^2*a*b^3*c^4*d*e^4*f^2*z - 36*A*B^2*a*b^4*c
^3*d^2*e*f^4*z - 24*A*B^2*a^2*b^4*c^2*d*e*f^5*z + 24*A*B^2*a*b^4*c^3*d*e^3*f^3*z + 592*A^2*B*a*b*c^6*d^3*e*f^3
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*B^3*a^2*b*c^5*d*e^5*f*z + 320*A^3*a*b*c^6*d*e^4*f^2*z + 40*A^3*a*b^4*c^3*d*e*f^5*z - 48*A^2*B*b*c^7*d^4*e*f^2
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c^7*d^3*e^3*f*z + 32*A*B^2*a*c^7*d^4*e*f^2*z - 16*A*B^2*a^2*c^6*d*e^5*f*z + 128*A^2*B*a^4*b*c^3*e*f^6*z + 42*A
^2*B*a*b^2*c^5*e^6*f*z + 24*A^2*B*a^2*b^5*c*e*f^6*z - 12*A*B^2*a^3*b^4*c*e*f^6*z - 12*A*B^2*a^2*b*c^5*e^6*f*z
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d*f^6*z - 84*B^3*a*b^2*c^5*d^3*e^2*f^2*z - 80*B^3*a^2*b^3*c^3*d^2*e*f^4*z - 60*B^3*a^2*b*c^5*d^2*e^3*f^2*z - 2
0*B^3*a^3*b^2*c^3*d*e^2*f^4*z - 20*B^3*a*b^3*c^4*d^2*e^3*f^2*z - 9*B^3*a^2*b^2*c^4*d*e^4*f^2*z - 8*B^3*a*b^4*c
^3*d^2*e^2*f^3*z + 6*B^3*a^2*b^4*c^2*d*e^2*f^4*z - 4*B^3*a^2*b^3*c^3*d*e^3*f^3*z - 216*A^2*B*b^4*c^4*d^2*e^2*f
^3*z + 196*A^2*B*b^3*c^5*d^2*e^3*f^2*z - 108*A*B^2*b^3*c^5*d^3*e^2*f^2*z - 94*A*B^2*b^4*c^4*d^2*e^3*f^2*z + 88
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c^6*d^2*e^3*f^2*z + 153*A^2*B*a^2*b^2*c^4*e^4*f^3*z - 144*A^2*B*a^2*b^3*c^3*e^3*f^4*z + 80*A^2*B*a^3*b^2*c^3*e
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9*A*B^2*a^2*b^2*c^4*e^5*f^2*z - 6*A*B^2*a^2*b^4*c^2*e^3*f^4*z + 4*A*B^2*a^2*b^3*c^3*e^4*f^3*z + 480*A^2*B*a^2*
b^2*c^4*d^2*f^5*z - 176*A*B^2*a^2*b^3*c^3*d^2*f^5*z - 10*A^2*B*a*b^6*c*d*f^6*z + 16*A*B^2*a*b*c^6*d*e^6*z + 80
*B^3*a*b^3*c^4*d^3*e*f^3*z - 48*B^3*a^3*b*c^4*d^2*e*f^4*z + 48*B^3*a^2*b*c^5*d^3*e*f^3*z + 44*B^3*a^3*b*c^4*d*
e^3*f^3*z + 24*B^3*a*b^5*c^2*d^2*e*f^4*z + 18*B^3*a*b^2*c^5*d^2*e^4*f*z + 696*A^3*a^2*b*c^5*d*e^2*f^4*z - 504*
A^3*a*b*c^6*d^2*e^2*f^3*z - 192*A^3*a*b^2*c^5*d*e^3*f^3*z - 144*A^3*a^2*b^2*c^4*d*e*f^5*z + 96*A^3*a*b^2*c^5*d
^2*e*f^4*z - 72*A^3*a*b^3*c^4*d*e^2*f^4*z - 208*A^2*B*b^3*c^5*d^3*e*f^3*z + 152*A*B^2*b^4*c^4*d^3*e*f^3*z + 80
*A^2*B*b^5*c^3*d^2*e*f^4*z + 75*A^2*B*b^4*c^4*d*e^4*f^2*z - 59*A^2*B*b^2*c^6*d^2*e^4*f*z - 52*A^2*B*b^5*c^3*d*
e^3*f^3*z + 42*A*B^2*b^3*c^5*d^2*e^4*f*z - 21*A*B^2*b^6*c^2*d^2*e*f^4*z - 16*A*B^2*b^5*c^3*d*e^4*f^2*z + 16*A*
B^2*b^2*c^6*d^4*e*f^2*z + 16*A*B^2*b^2*c^6*d^3*e^3*f*z + 11*A^2*B*b^6*c^2*d*e^2*f^4*z + 4*A*B^2*b^6*c^2*d*e^3*
f^3*z - 256*A^2*B*a*c^7*d^3*e^2*f^2*z - 96*A*B^2*a^3*c^5*d^2*e*f^4*z - 36*A^2*B*a^2*c^6*d*e^4*f^2*z - 32*A^2*B
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^2*c^5*d^3*f^4*z - 160*A^2*B*a^3*b^2*c^3*d*f^6*z - 148*A^2*B*a*b^4*c^3*d^2*f^5*z + 112*A*B^2*a*b^3*c^4*d^3*f^4
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b^2*c^4*d^2*e^2*f^3*z - 32*B^3*b^5*c^3*d^3*e*f^3*z - 8*B^3*b^3*c^5*d^3*e^3*f*z - 7*B^3*b^4*c^4*d^2*e^4*f*z + 5
*B^3*b^2*c^6*d^4*e^2*f*z + 80*A^3*b^2*c^6*d^3*e*f^3*z - 74*A^3*b^3*c^5*d*e^4*f^2*z - 64*A^3*b^4*c^4*d^2*e*f^4*
z + 60*A^3*b^4*c^4*d*e^3*f^3*z - 48*B^3*a^4*c^4*d*e^2*f^4*z - 24*B^3*a^3*c^5*d*e^4*f^2*z + 20*B^3*a^2*c^6*d^2*
e^4*f*z - 16*A^3*b^5*c^3*d*e^2*f^4*z + 8*A^3*b*c^7*d^3*e^2*f^2*z + 480*A^3*a^2*c^6*d^2*e*f^4*z - 392*A^3*a^2*c
^6*d*e^3*f^3*z + 280*A^3*a*c^7*d^2*e^3*f^2*z - 4*B^3*a^4*b*c^3*e^3*f^4*z - 200*A^3*a^3*b*c^4*e^2*f^5*z - 144*A
^3*a^2*b*c^5*e^4*f^3*z + 48*B^3*a*b^2*c^5*d^4*f^3*z + 42*A^3*a*b^2*c^5*e^5*f^2*z - 36*B^3*a^4*b^2*c^2*d*f^6*z
- 32*A^3*a^3*b^2*c^3*e*f^6*z - 24*A^3*a^2*b^4*c^2*e*f^6*z - 24*A^3*a*b^5*c^2*e^2*f^5*z + 10*A^3*a*b^3*c^4*e^4*
f^3*z - 4*B^3*a*b^4*c^3*d^3*f^4*z - 4*A^3*a*b^4*c^3*e^3*f^4*z - 480*A^3*a^2*b*c^5*d^2*f^5*z - 160*A^3*a^2*b^3*
c^3*d*f^6*z + 128*A^3*a*b^3*c^4*d^2*f^5*z + 8*A^2*B*b^5*c^3*e^5*f^2*z - 2*A^2*B*b^6*c^2*e^4*f^3*z + 112*A^2*B*
b^4*c^4*d^3*f^4*z - 92*A^2*B*a^4*c^4*e^2*f^5*z - 64*A^2*B*a^3*c^5*e^4*f^3*z - 64*A*B^2*b^5*c^3*d^3*f^4*z + 24*
A*B^2*a^4*c^4*e^3*f^4*z + 24*A*B^2*a^3*c^5*e^5*f^2*z + 16*A^2*B*b^2*c^6*d^4*f^3*z + 16*A*B^2*b^3*c^5*d^4*f^3*z
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^5*z - 48*A^2*B*a^4*b^2*c^2*f^7*z - 2*B^3*b^7*c*d^2*e*f^4*z + 34*A^3*b^2*c^6*d*e^5*f*z + 16*A^3*b*c^7*d^2*e^4*
f*z + 2*A^3*b^6*c^2*d*e*f^5*z - 416*A^3*a^3*c^5*d*e*f^5*z - 224*A^3*a*c^7*d^3*e*f^3*z + 12*B^3*a^3*b^4*c*d*f^6
*z - 10*B^3*a*b^6*c*d^2*f^5*z + 416*A^3*a^3*b*c^4*d*f^6*z + 224*A^3*a*b*c^6*d^3*f^4*z + 24*A^3*a*b^5*c^2*d*f^6
*z - 4*B^3*a*b*c^6*d^2*e^5*z + 20*A^2*B*c^8*d^4*e^2*f*z - 7*A^2*B*b^4*c^4*e^6*f*z - 2*A^2*B*b^7*c*e^3*f^4*z -
64*A*B^2*a^5*c^3*e*f^6*z + 16*A*B^2*b*c^7*d^5*f^2*z - 8*A^2*B*a^2*c^6*e^6*f*z - 2*A*B^2*b^7*c*d^2*f^5*z - 272*
A^2*B*a^4*c^4*d*f^6*z + 128*A^2*B*a*c^7*d^4*f^3*z + 9*A^2*B*b^2*c^6*d*e^6*z - 4*A*B^2*b^3*c^5*d*e^6*z + 4*A*B^
2*b*c^7*d^3*e^4*z + 8*A*B^2*a*c^7*d^2*e^5*z + 12*A^2*B*a^3*b^4*c*f^7*z + 30*B^3*b^4*c^4*d^3*e^2*f^2*z + 8*B^3*
b^5*c^3*d^2*e^3*f^2*z - 2*B^3*b^6*c^2*d^2*e^2*f^3*z + 152*A^3*b^3*c^5*d^2*e^2*f^3*z - 108*A^3*b^2*c^6*d^2*e^3*
f^2*z + 48*B^3*a^3*c^5*d^2*e^2*f^3*z - 16*B^3*a^2*c^6*d^3*e^2*f^2*z - 3*B^3*a^4*b^2*c^2*e^2*f^5*z - 120*B^3*a^
2*b^2*c^4*d^3*f^4*z + 112*B^3*a^3*b^2*c^3*d^2*f^5*z + 112*A^3*a^2*b^3*c^3*e^2*f^5*z + 12*A^3*a^2*b^2*c^4*e^3*f
^4*z - 120*A^3*a*c^7*d*e^5*f*z - 52*A^3*a*b*c^6*e^6*f*z + 10*A^3*a*b^6*c*e*f^6*z - 2*A*B^2*b^8*d*e*f^5*z - 2*A
^2*B*a*b^7*e*f^6*z - 24*A^2*B*a*c^7*d*e^6*z + 2*A*B^2*a*b^7*d*f^6*z - 12*A^2*B*a*b*c^6*e^7*z - 2*A^3*b^7*c*d*f
^6*z - 4*A^3*b*c^7*d*e^6*z + 16*B^3*a^5*c^3*e^2*f^5*z + 11*B^3*b^6*c^2*d^3*f^4*z - 11*A^3*b^4*c^4*e^5*f^2*z -
8*B^3*b^4*c^4*d^4*f^3*z - 4*B^3*b^2*c^6*d^5*f^2*z + 4*B^3*a^4*c^4*e^4*f^3*z + 4*A^3*b^5*c^3*e^4*f^3*z - A^3*b^
6*c^2*e^3*f^4*z + 136*A^3*a^3*c^5*e^3*f^4*z + 68*A^3*a^2*c^6*e^5*f^2*z - 64*A^3*b^3*c^5*d^3*f^4*z + 2*B^3*b^3*
c^5*d^2*e^5*z - B^3*b^2*c^6*d^3*e^4*z + 96*A^3*a^3*b^3*c^2*f^7*z + A*B^2*a^2*b^6*e*f^6*z + 32*A^3*c^8*d^4*e*f^
2*z - 24*A^3*c^8*d^3*e^3*f*z + 10*A^3*b^3*c^5*e^6*f*z + 2*A^3*b^7*c*e^2*f^5*z + 128*A^3*a^4*c^4*e*f^6*z - 32*A
^3*b*c^7*d^4*f^3*z - 4*B^3*a^2*c^6*d*e^6*z - B^3*a^2*b^6*d*f^6*z - 128*A^3*a^4*b*c^3*f^7*z - 24*A^3*a^2*b^5*c*
f^7*z - 16*A^2*B*c^8*d^5*f^2*z - 4*A^2*B*c^8*d^3*e^4*z + 64*A^2*B*a^5*c^3*f^7*z + 2*A^2*B*b^3*c^5*e^7*z + 4*A*
B^2*a^2*c^6*e^7*z - A^2*B*a^2*b^6*f^7*z + 4*A^3*c^8*d^2*e^5*z - 3*A^3*b^2*c^6*e^7*z + A^2*B*b^8*d*f^6*z - A^3*
b^8*e*f^6*z + 16*A^3*a*c^7*e^7*z + 2*A^3*a*b^7*f^7*z + A^2*B*b^8*e^2*f^5*z + B^3*b^8*d^2*f^5*z - 48*A^2*B^2*a*
b*c^4*d*e*f^4 + 28*A*B^3*a*b^2*c^3*d*e*f^4 - 16*A*B^3*a*b*c^4*d*e^2*f^3 + 16*A^3*B*a*c^5*d*e*f^4 + 32*A^3*B*a*
b*c^4*d*f^5 + 12*A^2*B^2*b^3*c^3*d*e*f^4 + 5*A*B^3*b^2*c^4*d^2*e*f^3 + 4*A*B^3*b^3*c^3*d*e^2*f^3 + 24*A^2*B^2*
a*c^5*d*e^2*f^3 + 24*A^2*B^2*a^2*b*c^3*e*f^5 + 12*A^2*B^2*a*b*c^4*e^3*f^3 - 6*A^2*B^2*a*b^3*c^2*e*f^5 + 4*A*B^
3*a^2*b*c^3*e^2*f^4 + 3*A*B^3*a^2*b^2*c^2*e*f^5 - 18*A^2*B^2*a*b^2*c^3*d*f^5 - 4*B^4*a^2*b*c^3*d*e*f^4 + 4*B^4
*a*b*c^4*d^2*e*f^3 - 6*A*B^3*b^4*c^2*d*e*f^4 + 4*A^3*B*b*c^5*d*e^2*f^3 - 2*A^3*B*b^2*c^4*d*e*f^4 - 8*A*B^3*a^2
*c^4*d*e*f^4 - 8*A*B^3*a*c^5*d^2*e*f^3 + 26*A^3*B*a*b^2*c^3*e*f^5 + 8*A^3*B*a*b*c^4*e^2*f^4 + 32*A*B^3*a*b*c^4
*d^2*f^4 - 28*A*B^3*a^2*b*c^3*d*f^5 + 6*A*B^3*a*b^3*c^2*d*f^5 - 9*A^2*B^2*b^2*c^4*d*e^2*f^3 - 18*A^2*B^2*a*b^2
*c^3*e^2*f^4 - 4*A^3*B*c^6*d^2*e*f^3 - 3*A^3*B*b^4*c^2*e*f^5 - 44*A^3*B*a^2*c^4*e*f^5 - 16*A^3*B*a*c^5*e^3*f^3
- 16*A*B^3*a^3*c^3*e*f^5 - 10*A^3*B*b^3*c^3*d*f^5 - 4*A^3*B*b*c^5*d^2*f^4 - 4*A*B^3*b*c^5*d^3*f^3 - 28*A^3*B*
a^2*b*c^3*f^6 + 6*A^3*B*a*b^3*c^2*f^6 - 4*A^4*b*c^5*d*e*f^4 - 20*A^4*a*b*c^4*e*f^5 + 3*A^2*B^2*b^4*c^2*e^2*f^4
- 2*A^2*B^2*b^3*c^3*e^3*f^3 + 12*A^2*B^2*a^2*c^4*e^2*f^4 + 9*A^2*B^2*b^2*c^4*d^2*f^4 - 3*A^2*B^2*a^2*b^2*c^2*
f^6 - 2*B^4*b^3*c^3*d^2*e*f^3 + 4*B^4*a^2*c^4*d*e^2*f^3 - 10*B^4*a*b^2*c^3*d^2*f^4 - 3*B^4*a^2*b^2*c^2*d*f^5 +
3*A^3*B*b^2*c^4*e^3*f^3 - 2*A^3*B*b^3*c^3*e^2*f^4 - 10*A*B^3*b^3*c^3*d^2*f^4 - 4*A*B^3*a^2*c^4*e^3*f^3 + 3*A^
2*B^2*b^4*c^2*d*f^5 + 36*A^2*B^2*a^2*c^4*d*f^5 - 24*A^2*B^2*a*c^5*d^2*f^4 + 4*A^2*B^2*c^6*d^3*f^3 + 16*A^2*B^2
*a^3*c^3*f^6 + 4*A^4*b^3*c^3*e*f^5 + 16*B^4*a^3*c^3*d*f^5 + 16*A^4*a*c^5*e^2*f^4 + 8*A^4*b^2*c^4*d*f^5 - 8*A^4
*a*b^2*c^3*f^6 - 24*A^4*a*c^5*d*f^5 + 3*B^4*b^4*c^2*d^2*f^4 - 3*A^4*b^2*c^4*e^2*f^4 + 4*A^4*c^6*d^2*f^4 + 36*A
^4*a^2*c^4*f^6 + B^4*b^2*c^4*d^3*f^3, z, k)*(root(48416*a^6*b^2*c^6*d^4*e^2*f^4*z^4 - 41544*a^5*b^4*c^5*d^4*e^
2*f^4*z^4 - 31872*a^7*b^2*c^5*d^3*e^2*f^5*z^4 - 31872*a^5*b^2*c^7*d^5*e^2*f^3*z^4 - 29184*a^6*b^2*c^6*d^3*e^4*
f^3*z^4 + 28800*a^5*b^4*c^5*d^3*e^4*f^3*z^4 + 21510*a^4*b^6*c^4*d^4*e^2*f^4*z^4 + 21408*a^6*b^4*c^4*d^3*e^2*f^
5*z^4 + 21408*a^4*b^4*c^6*d^5*e^2*f^3*z^4 - 18112*a^7*b^3*c^4*d^2*e^3*f^5*z^4 - 18112*a^4*b^3*c^7*d^5*e^3*f^2*
z^4 - 15600*a^5*b^5*c^4*d^3*e^3*f^4*z^4 - 15600*a^4*b^5*c^5*d^4*e^3*f^3*z^4 + 15296*a^6*b^3*c^5*d^3*e^3*f^4*z^
4 + 15296*a^5*b^3*c^6*d^4*e^3*f^3*z^4 + 14016*a^7*b^2*c^5*d^2*e^4*f^4*z^4 + 14016*a^5*b^2*c^7*d^4*e^4*f^2*z^4
- 13920*a^4*b^6*c^4*d^3*e^4*f^3*z^4 - 11648*a^6*b^3*c^5*d^2*e^5*f^3*z^4 - 11648*a^5*b^3*c^6*d^3*e^5*f^2*z^4 +
10432*a^6*b^2*c^6*d^2*e^6*f^2*z^4 + 9008*a^6*b^5*c^3*d^2*e^3*f^5*z^4 + 9008*a^3*b^5*c^6*d^5*e^3*f^2*z^4 + 8544
*a^5*b^5*c^4*d^2*e^5*f^3*z^4 + 8544*a^4*b^5*c^5*d^3*e^5*f^2*z^4 - 8496*a^5*b^4*c^5*d^2*e^6*f^2*z^4 + 7488*a^8*
b^2*c^4*d^2*e^2*f^6*z^4 + 7488*a^4*b^2*c^8*d^6*e^2*f^2*z^4 + 7380*a^4*b^7*c^3*d^3*e^3*f^4*z^4 + 7380*a^3*b^7*c
^4*d^4*e^3*f^3*z^4 - 6720*a^3*b^8*c^3*d^4*e^2*f^4*z^4 - 5784*a^5*b^6*c^3*d^3*e^2*f^5*z^4 - 5784*a^3*b^6*c^5*d^
5*e^2*f^3*z^4 - 3440*a^6*b^4*c^4*d^2*e^4*f^4*z^4 - 3440*a^4*b^4*c^6*d^4*e^4*f^2*z^4 + 3360*a^3*b^8*c^3*d^3*e^4
*f^3*z^4 + 3140*a^4*b^6*c^4*d^2*e^6*f^2*z^4 - 2760*a^4*b^7*c^3*d^2*e^5*f^3*z^4 - 2760*a^3*b^7*c^4*d^3*e^5*f^2*
z^4 - 1764*a^5*b^7*c^2*d^2*e^3*f^5*z^4 - 1764*a^2*b^7*c^5*d^5*e^3*f^2*z^4 - 1640*a^3*b^9*c^2*d^3*e^3*f^4*z^4 -
1640*a^2*b^9*c^3*d^4*e^3*f^3*z^4 - 1604*a^6*b^6*c^2*d^2*e^2*f^6*z^4 - 1604*a^2*b^6*c^6*d^6*e^2*f^2*z^4 - 1500
*a^5*b^6*c^3*d^2*e^4*f^4*z^4 - 1500*a^3*b^6*c^5*d^4*e^4*f^2*z^4 + 1140*a^2*b^10*c^2*d^4*e^2*f^4*z^4 + 810*a^4*
b^8*c^2*d^2*e^4*f^4*z^4 + 810*a^2*b^8*c^4*d^4*e^4*f^2*z^4 - 544*a^3*b^8*c^3*d^2*e^6*f^2*z^4 + 416*a^3*b^9*c^2*
d^2*e^5*f^3*z^4 + 416*a^2*b^9*c^3*d^3*e^5*f^2*z^4 - 384*a^2*b^10*c^2*d^3*e^4*f^3*z^4 + 180*a^4*b^8*c^2*d^3*e^2
*f^5*z^4 + 180*a^2*b^8*c^4*d^5*e^2*f^3*z^4 + 48*a^7*b^4*c^3*d^2*e^2*f^6*z^4 + 48*a^3*b^4*c^7*d^6*e^2*f^2*z^4 +
36*a^2*b^10*c^2*d^2*e^6*f^2*z^4 - 1024*a^10*b*c^3*d*e*f^8*z^4 - 1024*a^3*b*c^10*d^8*e*f*z^4 - 192*a^8*b^5*c*d
*e*f^8*z^4 - 192*a*b^5*c^8*d^8*e*f*z^4 + 16128*a^7*b^3*c^4*d^3*e*f^6*z^4 + 16128*a^4*b^3*c^7*d^6*e*f^3*z^4 - 1
1712*a^6*b^5*c^3*d^3*e*f^6*z^4 - 11712*a^3*b^5*c^6*d^6*e*f^3*z^4 + 11520*a^8*b*c^5*d^2*e^3*f^5*z^4 + 11520*a^5
*b*c^8*d^5*e^3*f^2*z^4 - 9984*a^6*b^3*c^5*d^4*e*f^5*z^4 - 9984*a^5*b^3*c^6*d^5*e*f^4*z^4 + 8640*a^5*b^5*c^4*d^
4*e*f^5*z^4 + 8640*a^4*b^5*c^5*d^5*e*f^4*z^4 - 7424*a^7*b*c^6*d^3*e^3*f^4*z^4 - 7424*a^6*b*c^7*d^4*e^3*f^3*z^4
- 6912*a^8*b^3*c^3*d^2*e*f^7*z^4 - 6912*a^3*b^3*c^8*d^7*e*f^2*z^4 + 4800*a^7*b^3*c^4*d*e^5*f^4*z^4 + 4800*a^4
*b^3*c^7*d^4*e^5*f*z^4 + 4608*a^7*b*c^6*d^2*e^5*f^3*z^4 + 4608*a^6*b*c^7*d^3*e^5*f^2*z^4 - 4560*a^4*b^7*c^3*d^
4*e*f^5*z^4 - 4560*a^3*b^7*c^4*d^5*e*f^4*z^4 + 4176*a^5*b^7*c^2*d^3*e*f^6*z^4 + 4176*a^2*b^7*c^5*d^6*e*f^3*z^4
+ 3264*a^7*b^5*c^2*d^2*e*f^7*z^4 + 3264*a^2*b^5*c^7*d^7*e*f^2*z^4 + 3008*a^8*b^3*c^3*d*e^3*f^6*z^4 + 3008*a^3
*b^3*c^8*d^6*e^3*f*z^4 + 2880*a^6*b^3*c^5*d*e^7*f^2*z^4 + 2880*a^5*b^3*c^6*d^2*e^7*f*z^4 - 2240*a^7*b^4*c^3*d*
e^4*f^5*z^4 - 2240*a^3*b^4*c^7*d^5*e^4*f*z^4 - 1488*a^5*b^5*c^4*d*e^7*f^2*z^4 - 1488*a^4*b^5*c^5*d^2*e^7*f*z^4
+ 1440*a^3*b^9*c^2*d^4*e*f^5*z^4 + 1440*a^2*b^9*c^3*d^5*e*f^4*z^4 - 1328*a^6*b^5*c^3*d*e^5*f^4*z^4 - 1328*a^3
*b^5*c^6*d^4*e^5*f*z^4 - 1152*a^7*b^2*c^5*d*e^6*f^3*z^4 - 1152*a^5*b^2*c^7*d^3*e^6*f*z^4 - 1120*a^6*b^4*c^4*d*
e^6*f^3*z^4 - 1120*a^4*b^4*c^6*d^3*e^6*f*z^4 + 912*a^6*b^6*c^2*d*e^4*f^5*z^4 + 912*a^2*b^6*c^6*d^5*e^4*f*z^4 +
872*a^5*b^6*c^3*d*e^6*f^3*z^4 + 872*a^3*b^6*c^5*d^3*e^6*f*z^4 + 768*a^8*b^2*c^4*d*e^4*f^5*z^4 + 768*a^4*b^2*c
^8*d^5*e^4*f*z^4 - 672*a^8*b^4*c^2*d*e^2*f^7*z^4 - 672*a^2*b^4*c^8*d^7*e^2*f*z^4 - 624*a^7*b^5*c^2*d*e^3*f^6*z
^4 - 624*a^2*b^5*c^7*d^6*e^3*f*z^4 + 480*a^5*b^8*c*d^2*e^2*f^6*z^4 + 480*a*b^8*c^5*d^6*e^2*f^2*z^4 + 316*a^4*b
^7*c^3*d*e^7*f^2*z^4 + 316*a^3*b^7*c^4*d^2*e^7*f*z^4 - 204*a^4*b^8*c^2*d*e^6*f^3*z^4 - 204*a^2*b^8*c^4*d^3*e^6
*f*z^4 + 168*a^3*b^10*c*d^3*e^2*f^5*z^4 + 168*a*b^10*c^3*d^5*e^2*f^3*z^4 + 156*a^2*b^11*c*d^3*e^3*f^4*z^4 + 15
6*a*b^11*c^2*d^4*e^3*f^3*z^4 + 128*a^9*b^2*c^3*d*e^2*f^7*z^4 + 128*a^3*b^2*c^9*d^7*e^2*f*z^4 - 124*a^3*b^10*c*
d^2*e^4*f^4*z^4 - 124*a*b^10*c^3*d^4*e^4*f^2*z^4 + 100*a^4*b^9*c*d^2*e^3*f^5*z^4 + 100*a*b^9*c^4*d^5*e^3*f^2*z
^4 + 36*a^5*b^7*c^2*d*e^5*f^4*z^4 + 36*a^2*b^7*c^5*d^4*e^5*f*z^4 - 24*a^3*b^9*c^2*d*e^7*f^2*z^4 - 24*a^2*b^11*
c*d^2*e^5*f^3*z^4 - 24*a^2*b^9*c^3*d^2*e^7*f*z^4 - 24*a*b^11*c^2*d^3*e^5*f^2*z^4 - 9216*a^8*b*c^5*d^3*e*f^6*z^
4 - 9216*a^5*b*c^8*d^6*e*f^3*z^4 - 5376*a^8*b*c^5*d*e^5*f^4*z^4 - 5376*a^5*b*c^8*d^4*e^5*f*z^4 + 5120*a^9*b*c^
4*d^2*e*f^7*z^4 + 5120*a^7*b*c^6*d^4*e*f^5*z^4 + 5120*a^6*b*c^7*d^5*e*f^4*z^4 + 5120*a^4*b*c^9*d^7*e*f^2*z^4 -
4352*a^9*b*c^4*d*e^3*f^6*z^4 - 4352*a^4*b*c^9*d^6*e^3*f*z^4 - 1792*a^7*b*c^6*d*e^7*f^2*z^4 - 1792*a^6*b*c^7*d
^2*e^7*f*z^4 - 1600*a^6*b^2*c^6*d*e^8*f*z^4 + 912*a^5*b^4*c^5*d*e^8*f*z^4 + 768*a^9*b^3*c^2*d*e*f^8*z^4 + 768*
a^2*b^3*c^9*d^8*e*f*z^4 - 720*a^4*b^9*c*d^3*e*f^6*z^4 - 720*a*b^9*c^4*d^6*e*f^3*z^4 - 656*a^6*b^7*c*d^2*e*f^7*
z^4 - 656*a*b^7*c^6*d^7*e*f^2*z^4 - 240*a^2*b^11*c*d^4*e*f^5*z^4 - 240*a*b^11*c^2*d^5*e*f^4*z^4 + 216*a^7*b^6*
c*d*e^2*f^7*z^4 + 216*a*b^6*c^7*d^7*e^2*f*z^4 - 204*a^4*b^6*c^4*d*e^8*f*z^4 - 144*a^5*b^8*c*d*e^4*f^5*z^4 - 14
4*a*b^8*c^5*d^5*e^4*f*z^4 - 84*a*b^12*c*d^4*e^2*f^4*z^4 + 36*a^4*b^9*c*d*e^5*f^4*z^4 + 36*a*b^9*c^4*d^4*e^5*f*
z^4 + 20*a^6*b^7*c*d*e^3*f^6*z^4 + 20*a*b^7*c^6*d^6*e^3*f*z^4 + 16*a^3*b^10*c*d*e^6*f^3*z^4 + 16*a^3*b^8*c^3*d
*e^8*f*z^4 + 16*a*b^12*c*d^3*e^4*f^3*z^4 + 16*a*b^10*c^3*d^3*e^6*f*z^4 + 48*b^11*c^3*d^6*e*f^3*z^4 + 48*b^9*c^
5*d^7*e*f^2*z^4 - 20*b^8*c^6*d^7*e^2*f*z^4 + 8*b^10*c^4*d^5*e^4*f*z^4 - 4*b^13*c*d^4*e^3*f^3*z^4 - 4*b^11*c^3*
d^4*e^5*f*z^4 + 4*b^9*c^5*d^6*e^3*f*z^4 + 3072*a^9*c^5*d*e^4*f^5*z^4 + 3072*a^5*c^9*d^5*e^4*f*z^4 + 2560*a^8*c
^6*d*e^6*f^3*z^4 + 2560*a^6*c^8*d^3*e^6*f*z^4 + 1536*a^10*c^4*d*e^2*f^7*z^4 + 1536*a^4*c^10*d^7*e^2*f*z^4 + 48
*a^5*b^9*d^2*e*f^7*z^4 + 48*a^3*b^11*d^3*e*f^6*z^4 - 20*a^6*b^8*d*e^2*f^7*z^4 + 8*a^4*b^10*d*e^4*f^5*z^4 + 4*a
^5*b^9*d*e^3*f^6*z^4 - 4*a^3*b^11*d*e^5*f^4*z^4 - 4*a*b^13*d^3*e^3*f^4*z^4 + 768*a^9*b*c^4*e^5*f^5*z^4 + 768*a
^8*b*c^5*e^7*f^3*z^4 + 256*a^10*b*c^3*e^3*f^7*z^4 - 192*a^6*b^3*c^5*e^9*f*z^4 - 68*a^7*b^6*c*e^4*f^6*z^4 + 48*
a^8*b^5*c*e^3*f^7*z^4 + 48*a^5*b^5*c^4*e^9*f*z^4 + 36*a^6*b^7*c*e^5*f^5*z^4 - 12*a^9*b^4*c*e^2*f^8*z^4 - 4*a^4
*b^9*c*e^7*f^3*z^4 - 4*a^4*b^7*c^3*e^9*f*z^4 + 384*a^5*b^8*c*d^3*f^7*z^4 + 384*a*b^8*c^5*d^7*f^3*z^4 + 288*a^3
*b^10*c*d^4*f^6*z^4 + 288*a*b^10*c^3*d^6*f^4*z^4 + 224*a^7*b^6*c*d^2*f^8*z^4 + 224*a*b^6*c^7*d^8*f^2*z^4 - 192
*a^10*b^2*c^2*d*f^9*z^4 - 192*a^2*b^2*c^10*d^9*f*z^4 + 768*a^5*b*c^8*d^3*e^7*z^4 + 768*a^4*b*c^9*d^5*e^5*z^4 +
256*a^3*b*c^10*d^7*e^3*z^4 - 192*a^5*b^3*c^6*d*e^9*z^4 - 68*a*b^6*c^7*d^6*e^4*z^4 + 48*a^4*b^5*c^5*d*e^9*z^4
+ 48*a*b^5*c^8*d^7*e^3*z^4 + 36*a*b^7*c^6*d^5*e^5*z^4 - 12*a*b^4*c^9*d^8*e^2*z^4 - 4*a^3*b^7*c^4*d*e^9*z^4 - 4
*a*b^9*c^4*d^3*e^7*z^4 + 16*b^13*c*d^5*e*f^4*z^4 + 16*b^7*c^7*d^8*e*f*z^4 + 768*a^7*c^7*d*e^8*f*z^4 + 16*a^7*b
^7*d*e*f^8*z^4 + 16*a*b^13*d^4*e*f^5*z^4 + 256*a^7*b*c^6*e^9*f*z^4 + 80*a*b^12*c*d^5*f^5*z^4 + 48*a^9*b^4*c*d*
f^9*z^4 + 48*a*b^4*c^9*d^9*f*z^4 + 256*a^6*b*c^7*d*e^9*z^4 - 42*b^10*c^4*d^6*e^2*f^2*z^4 - 20*b^12*c^2*d^5*e^2
*f^3*z^4 + 6*b^12*c^2*d^4*e^4*f^2*z^4 + 4*b^11*c^3*d^5*e^3*f^2*z^4 - 24960*a^7*c^7*d^4*e^2*f^4*z^4 + 18944*a^8
*c^6*d^3*e^2*f^5*z^4 + 18944*a^6*c^8*d^5*e^2*f^3*z^4 + 14336*a^7*c^7*d^3*e^4*f^3*z^4 - 9984*a^8*c^6*d^2*e^4*f^
4*z^4 - 9984*a^6*c^8*d^4*e^4*f^2*z^4 - 7936*a^9*c^5*d^2*e^2*f^6*z^4 - 7936*a^5*c^9*d^6*e^2*f^2*z^4 - 4352*a^7*
c^7*d^2*e^6*f^2*z^4 - 42*a^4*b^10*d^2*e^2*f^6*z^4 - 20*a^2*b^12*d^3*e^2*f^5*z^4 + 6*a^2*b^12*d^2*e^4*f^4*z^4 +
4*a^3*b^11*d^2*e^3*f^5*z^4 - 480*a^8*b^2*c^4*e^6*f^4*z^4 + 440*a^7*b^4*c^3*e^6*f^4*z^4 - 320*a^8*b^3*c^3*e^5*
f^5*z^4 - 320*a^7*b^3*c^4*e^7*f^3*z^4 + 240*a^8*b^4*c^2*e^4*f^6*z^4 + 240*a^6*b^4*c^4*e^8*f^2*z^4 - 192*a^9*b^
3*c^2*e^3*f^7*z^4 - 192*a^9*b^2*c^3*e^4*f^6*z^4 - 192*a^7*b^2*c^5*e^8*f^2*z^4 - 90*a^6*b^6*c^2*e^6*f^4*z^4 - 6
8*a^5*b^6*c^3*e^8*f^2*z^4 + 48*a^10*b^2*c^2*e^2*f^8*z^4 - 48*a^7*b^5*c^2*e^5*f^5*z^4 - 48*a^6*b^5*c^3*e^7*f^3*
z^4 + 36*a^5*b^7*c^2*e^7*f^3*z^4 + 6*a^4*b^8*c^2*e^8*f^2*z^4 - 33920*a^6*b^2*c^6*d^5*f^5*z^4 + 27936*a^5*b^4*c
^5*d^5*f^5*z^4 + 26112*a^7*b^2*c^5*d^4*f^6*z^4 + 26112*a^5*b^2*c^7*d^6*f^4*z^4 - 20352*a^6*b^4*c^4*d^4*f^6*z^4
- 20352*a^4*b^4*c^6*d^6*f^4*z^4 - 13080*a^4*b^6*c^4*d^5*f^5*z^4 - 11520*a^8*b^2*c^4*d^3*f^7*z^4 - 11520*a^4*b
^2*c^8*d^7*f^3*z^4 + 8736*a^5*b^6*c^3*d^4*f^6*z^4 + 8736*a^3*b^6*c^5*d^6*f^4*z^4 + 7488*a^7*b^4*c^3*d^3*f^7*z^
4 + 7488*a^3*b^4*c^7*d^7*f^3*z^4 + 3840*a^3*b^8*c^3*d^5*f^5*z^4 + 2560*a^9*b^2*c^3*d^2*f^8*z^4 + 2560*a^3*b^2*
c^9*d^8*f^2*z^4 - 2416*a^6*b^6*c^2*d^3*f^7*z^4 - 2416*a^2*b^6*c^6*d^7*f^3*z^4 - 2160*a^4*b^8*c^2*d^4*f^6*z^4 -
2160*a^2*b^8*c^4*d^6*f^4*z^4 - 1152*a^8*b^4*c^2*d^2*f^8*z^4 - 1152*a^2*b^4*c^8*d^8*f^2*z^4 - 720*a^2*b^10*c^2
*d^5*f^5*z^4 - 480*a^4*b^2*c^8*d^4*e^6*z^4 + 440*a^3*b^4*c^7*d^4*e^6*z^4 - 320*a^4*b^3*c^7*d^3*e^7*z^4 - 320*a
^3*b^3*c^8*d^5*e^5*z^4 + 240*a^4*b^4*c^6*d^2*e^8*z^4 + 240*a^2*b^4*c^8*d^6*e^4*z^4 - 192*a^5*b^2*c^7*d^2*e^8*z
^4 - 192*a^3*b^2*c^9*d^6*e^4*z^4 - 192*a^2*b^3*c^9*d^7*e^3*z^4 - 90*a^2*b^6*c^6*d^4*e^6*z^4 - 68*a^3*b^6*c^5*d
^2*e^8*z^4 - 48*a^3*b^5*c^6*d^3*e^7*z^4 - 48*a^2*b^5*c^7*d^5*e^5*z^4 + 48*a^2*b^2*c^10*d^8*e^2*z^4 + 36*a^2*b^
7*c^5*d^3*e^7*z^4 + 6*a^2*b^8*c^4*d^2*e^8*z^4 - 4*b^6*c^8*d^9*f*z^4 + 256*a^11*c^3*d*f^9*z^4 + 256*a^3*c^11*d^
9*f*z^4 - 4*a^8*b^6*d*f^9*z^4 - 384*a^9*c^5*e^6*f^4*z^4 - 256*a^10*c^4*e^4*f^6*z^4 - 256*a^8*c^6*e^8*f^2*z^4 -
64*a^11*c^3*e^2*f^8*z^4 - 24*b^10*c^4*d^7*f^3*z^4 - 16*b^12*c^2*d^6*f^4*z^4 - 16*b^8*c^6*d^8*f^2*z^4 + 17920*
a^7*c^7*d^5*f^5*z^4 - 14336*a^8*c^6*d^4*f^6*z^4 - 14336*a^6*c^8*d^6*f^4*z^4 + 7168*a^9*c^5*d^3*f^7*z^4 + 7168*
a^5*c^9*d^7*f^3*z^4 - 2048*a^10*c^4*d^2*f^8*z^4 - 2048*a^4*c^10*d^8*f^2*z^4 + 6*b^8*c^6*d^6*e^4*z^4 + 6*a^6*b^
8*e^4*f^6*z^4 - 4*b^9*c^5*d^5*e^5*z^4 - 4*b^7*c^7*d^7*e^3*z^4 - 4*a^7*b^7*e^3*f^7*z^4 - 4*a^5*b^9*e^5*f^5*z^4
- 384*a^5*c^9*d^4*e^6*z^4 - 256*a^6*c^8*d^2*e^8*z^4 - 256*a^4*c^10*d^6*e^4*z^4 - 64*a^3*c^11*d^8*e^2*z^4 - 24*
a^4*b^10*d^3*f^7*z^4 - 16*a^6*b^8*d^2*f^8*z^4 - 16*a^2*b^12*d^4*f^6*z^4 + 48*a^6*b^2*c^6*e^10*z^4 - 12*a^5*b^4
*c^5*e^10*z^4 - 4*b^14*d^5*f^5*z^4 - 64*a^7*c^7*e^10*z^4 + b^14*d^4*e^2*f^4*z^4 + b^10*c^4*d^4*e^6*z^4 + b^6*c
^8*d^8*e^2*z^4 + a^8*b^6*e^2*f^8*z^4 + a^4*b^10*e^6*f^4*z^4 + a^4*b^6*c^4*e^10*z^4 - 4820*A*B*a^4*b*c^5*d^2*e^
2*f^4*z^2 + 2976*A*B*a^3*b*c^6*d^3*e^2*f^3*z^2 - 2328*A*B*a^3*b*c^6*d^2*e^4*f^2*z^2 + 1848*A*B*a^2*b^4*c^4*d^3
*e*f^4*z^2 - 1768*A*B*a^3*b^4*c^3*d^2*e*f^5*z^2 + 1528*A*B*a^4*b^2*c^4*d^2*e*f^5*z^2 - 1136*A*B*a^3*b^2*c^5*d^
3*e*f^4*z^2 - 974*A*B*a^4*b^3*c^3*d*e^2*f^5*z^2 + 692*A*B*a^2*b*c^7*d^4*e^2*f^2*z^2 + 588*A*B*a*b^6*c^3*d^2*e^
3*f^3*z^2 - 580*A*B*a^3*b^3*c^4*d*e^4*f^3*z^2 + 488*A*B*a^3*b^4*c^3*d*e^3*f^4*z^2 - 444*A*B*a^2*b^2*c^6*d^2*e^
5*f*z^2 - 412*A*B*a*b^5*c^4*d^2*e^4*f^2*z^2 + 366*A*B*a^2*b^6*c^2*d^2*e*f^5*z^2 - 352*A*B*a^2*b^2*c^6*d^4*e*f^
3*z^2 + 326*A*B*a^2*b^4*c^4*d*e^5*f^2*z^2 + 324*A*B*a*b^5*c^4*d^3*e^2*f^3*z^2 - 302*A*B*a*b^3*c^6*d^4*e^2*f^2*
z^2 - 296*A*B*a*b^7*c^2*d^2*e^2*f^4*z^2 + 122*A*B*a^4*b^2*c^4*d*e^3*f^4*z^2 - 122*A*B*a^2*b^6*c^2*d*e^3*f^4*z^
2 - 84*A*B*a^3*b^2*c^5*d*e^5*f^2*z^2 + 72*A*B*a*b^4*c^5*d^3*e^3*f^2*z^2 - 64*A*B*a^2*b^5*c^3*d*e^4*f^3*z^2 + 6
0*A*B*a^3*b^5*c^2*d*e^2*f^5*z^2 + 1312*A*B*a^5*b*c^4*d*e^2*f^5*z^2 + 1040*A*B*a^4*b*c^5*d*e^4*f^3*z^2 - 500*A*
B*a*b^6*c^3*d^3*e*f^4*z^2 - 376*A*B*a*b^2*c^7*d^5*e*f^2*z^2 + 276*A*B*a^4*b^4*c^2*d*e*f^6*z^2 - 262*A*B*a^2*b^
3*c^5*d*e^6*f*z^2 + 238*A*B*a*b^2*c^7*d^4*e^3*f*z^2 + 232*A*B*a^5*b^2*c^3*d*e*f^6*z^2 - 176*A*B*a^2*b*c^7*d^3*
e^4*f*z^2 - 120*A*B*a*b^6*c^3*d*e^5*f^2*z^2 - 108*A*B*a*b^4*c^5*d^4*e*f^3*z^2 + 68*A*B*a*b^7*c^2*d*e^4*f^3*z^2
+ 68*A*B*a*b^4*c^5*d^2*e^5*f*z^2 + 46*A*B*a^2*b^7*c*d*e^2*f^5*z^2 - 36*A*B*a*b^3*c^6*d^3*e^4*f*z^2 - 1932*A*B
*a^2*b^3*c^5*d^3*e^2*f^3*z^2 - 1818*A*B*a^2*b^4*c^4*d^2*e^3*f^3*z^2 + 1620*A*B*a^3*b^3*c^4*d^2*e^2*f^4*z^2 + 1
560*A*B*a^2*b^3*c^5*d^2*e^4*f^2*z^2 + 1244*A*B*a^3*b^2*c^5*d^2*e^3*f^3*z^2 + 820*A*B*a^2*b^2*c^6*d^3*e^3*f^2*z
^2 + 480*A*B*a^2*b^5*c^3*d^2*e^2*f^4*z^2 + 352*A*B*a^3*b*c^6*d*e^6*f*z^2 - 108*A*B*a^3*b^6*c*d*e*f^6*z^2 + 82*
A*B*a*b^5*c^4*d*e^6*f*z^2 - 64*A*B*a*b*c^8*d^5*e^2*f*z^2 + 16*A*B*a*b^8*c*d^2*e*f^5*z^2 - 4*A*B*a*b^8*c*d*e^3*
f^4*z^2 + 16*B^2*a*b*c^8*d^6*e*f*z^2 + 56*A*B*b^2*c^8*d^6*e*f*z^2 - 8*A*B*b^9*c*d*e^4*f^3*z^2 - 8*A*B*b^7*c^3*
d*e^6*f*z^2 - 800*A*B*a^6*c^4*d*e*f^6*z^2 + 10*A*B*a^2*b^8*d*e*f^6*z^2 - 6*A*B*a*b^9*d*e^2*f^5*z^2 - 12*A*B*a^
5*b^4*c*e*f^7*z^2 + 912*A*B*a^6*b*c^3*d*f^7*z^2 + 192*A*B*a^4*b^5*c*d*f^7*z^2 + 192*A*B*a*b*c^8*d^6*f^2*z^2 -
20*A*B*a*b^4*c^5*d*e^7*z^2 + 4*A*B*a*b*c^8*d^4*e^4*z^2 + 2144*B^2*a^4*b*c^5*d^3*e*f^4*z^2 - 1120*B^2*a^3*b*c^6
*d^4*e*f^3*z^2 - 688*B^2*a^5*b*c^4*d^2*e*f^5*z^2 - 256*B^2*a^3*b*c^6*d^2*e^5*f*z^2 + 152*B^2*a*b^3*c^6*d^5*e*f
^2*z^2 + 120*B^2*a^5*b^3*c^2*d*e*f^6*z^2 - 116*B^2*a^5*b*c^4*d*e^3*f^4*z^2 + 110*B^2*a*b^7*c^2*d^3*e*f^4*z^2 -
80*B^2*a^2*b*c^7*d^5*e*f^2*z^2 - 72*B^2*a*b^5*c^4*d^4*e*f^3*z^2 - 48*B^2*a^4*b*c^5*d*e^5*f^2*z^2 - 46*B^2*a*b
^3*c^6*d^4*e^3*f*z^2 - 44*B^2*a*b^4*c^5*d^3*e^4*f*z^2 - 34*B^2*a*b^5*c^4*d^2*e^5*f*z^2 + 20*B^2*a^2*b*c^7*d^4*
e^3*f*z^2 - 10*B^2*a^3*b^6*c*d*e^2*f^5*z^2 - 10*B^2*a^2*b^7*c*d^2*e*f^5*z^2 - 10*B^2*a*b^2*c^7*d^5*e^2*f*z^2 -
7*B^2*a^2*b^4*c^4*d*e^6*f*z^2 - 6*B^2*a^3*b^2*c^5*d*e^6*f*z^2 + 4*B^2*a*b^8*c*d^2*e^2*f^4*z^2 - 2*B^2*a^2*b^7
*c*d*e^3*f^4*z^2 + 3196*A^2*a^4*b*c^5*d*e^3*f^4*z^2 - 3184*A^2*a^4*b*c^5*d^2*e*f^5*z^2 + 1568*A^2*a^3*b*c^6*d^
3*e*f^4*z^2 + 1504*A^2*a^3*b*c^6*d*e^5*f^2*z^2 - 656*A^2*a^4*b^3*c^3*d*e*f^6*z^2 - 400*A^2*a*b^6*c^3*d*e^4*f^3
*z^2 + 314*A^2*a*b^5*c^4*d*e^5*f^2*z^2 - 264*A^2*a^3*b^5*c^2*d*e*f^6*z^2 + 240*A^2*a^2*b^2*c^6*d*e^6*f*z^2 - 2
24*A^2*a^2*b*c^7*d^4*e*f^3*z^2 + 216*A^2*a*b^5*c^4*d^3*e*f^4*z^2 - 192*A^2*a^2*b*c^7*d^2*e^5*f*z^2 + 178*A^2*a
*b^7*c^2*d*e^3*f^4*z^2 - 154*A^2*a*b^7*c^2*d^2*e*f^5*z^2 + 128*A^2*a*b^3*c^6*d^4*e*f^3*z^2 + 106*A^2*a*b^3*c^6
*d^2*e^5*f*z^2 - 12*A^2*a*b^2*c^7*d^3*e^4*f*z^2 - 58*A*B*b^8*c^2*d^2*e^3*f^3*z^2 + 40*A*B*b^7*c^3*d^2*e^4*f^2*
z^2 - 28*A*B*b^7*c^3*d^3*e^2*f^3*z^2 - 24*A*B*b^5*c^5*d^4*e^2*f^2*z^2 - 20*A*B*b^6*c^4*d^3*e^3*f^2*z^2 + 2768*
A*B*a^4*c^6*d^2*e^3*f^3*z^2 - 1712*A*B*a^3*c^7*d^3*e^3*f^2*z^2 - 156*A*B*a^4*b^2*c^4*e^5*f^3*z^2 + 146*A*B*a^4
*b^3*c^3*e^4*f^4*z^2 - 106*A*B*a^5*b^2*c^3*e^3*f^5*z^2 + 90*A*B*a^5*b^3*c^2*e^2*f^6*z^2 + 38*A*B*a^3*b^3*c^4*e
^6*f^2*z^2 - 36*A*B*a^3*b^5*c^2*e^4*f^4*z^2 + 16*A*B*a^3*b^4*c^3*e^5*f^3*z^2 - 9*A*B*a^4*b^4*c^2*e^3*f^5*z^2 -
8*A*B*a^2*b^5*c^3*e^6*f^2*z^2 + 2*A*B*a^2*b^6*c^2*e^5*f^3*z^2 + 920*A*B*a^4*b^3*c^3*d^2*f^6*z^2 - 480*A*B*a^2
*b^5*c^3*d^3*f^5*z^2 - 336*A*B*a^2*b^3*c^5*d^4*f^4*z^2 - 272*A*B*a^3*b^3*c^4*d^3*f^5*z^2 + 240*A*B*a^3*b^5*c^2
*d^2*f^6*z^2 - 32*A*B*a*c^9*d^6*e*f*z^2 - 792*B^2*a^2*b^3*c^5*d^3*e^3*f^2*z^2 + 714*B^2*a^2*b^4*c^4*d^3*e^2*f^
3*z^2 - 572*B^2*a^3*b^2*c^5*d^3*e^2*f^3*z^2 - 475*B^2*a^2*b^2*c^6*d^4*e^2*f^2*z^2 + 265*B^2*a^4*b^2*c^4*d^2*e^
2*f^4*z^2 + 260*B^2*a^3*b^3*c^4*d^2*e^3*f^3*z^2 - 212*B^2*a^3*b^4*c^3*d^2*e^2*f^4*z^2 + 180*B^2*a^3*b^2*c^5*d^
2*e^4*f^2*z^2 - 158*B^2*a^2*b^4*c^4*d^2*e^4*f^2*z^2 + 47*B^2*a^2*b^6*c^2*d^2*e^2*f^4*z^2 + 16*B^2*a^2*b^5*c^3*
d^2*e^3*f^3*z^2 + 2752*A^2*a^3*b^2*c^5*d^2*e^2*f^4*z^2 - 2148*A^2*a^2*b^4*c^4*d^2*e^2*f^4*z^2 + 2064*A^2*a^2*b
^3*c^5*d^2*e^3*f^3*z^2 - 424*A^2*a^2*b^2*c^6*d^3*e^2*f^3*z^2 - 198*A^2*a^2*b^2*c^6*d^2*e^4*f^2*z^2 - 272*B^2*a
^6*b*c^3*d*e*f^6*z^2 - 24*B^2*a^4*b^5*c*d*e*f^6*z^2 + 1808*A^2*a^5*b*c^4*d*e*f^6*z^2 - 244*A^2*a*b*c^8*d^4*e^3
*f*z^2 + 208*A^2*a*b*c^8*d^5*e*f^2*z^2 + 134*A^2*a^2*b^7*c*d*e*f^6*z^2 - 76*A^2*a*b^4*c^5*d*e^6*f*z^2 + 4*A^2*
a*b^8*c*d*e^2*f^5*z^2 + 148*A*B*b^4*c^6*d^5*e*f^2*z^2 + 65*A*B*b^6*c^4*d^4*e*f^3*z^2 + 46*A*B*b^8*c^2*d^3*e*f^
4*z^2 - 38*A*B*b^3*c^7*d^5*e^2*f*z^2 + 34*A*B*b^9*c*d^2*e^2*f^4*z^2 - 29*A*B*b^4*c^6*d^4*e^3*f*z^2 + 20*A*B*b^
5*c^5*d^3*e^4*f*z^2 + 12*A*B*b^8*c^2*d*e^5*f^2*z^2 - 7*A*B*b^6*c^4*d^2*e^5*f*z^2 - 2880*A*B*a^4*c^6*d^3*e*f^4*
z^2 + 2784*A*B*a^5*c^5*d^2*e*f^5*z^2 - 1112*A*B*a^5*c^5*d*e^3*f^4*z^2 + 896*A*B*a^3*c^7*d^4*e*f^3*z^2 + 848*A*
B*a^3*c^7*d^2*e^5*f*z^2 - 560*A*B*a^4*c^6*d*e^5*f^2*z^2 + 96*A*B*a^2*c^8*d^5*e*f^2*z^2 - 88*A*B*a^2*c^8*d^4*e^
3*f*z^2 - 100*A*B*a^6*b*c^3*e^2*f^6*z^2 - 76*A*B*a^5*b*c^4*e^4*f^4*z^2 + 48*A*B*a^6*b^2*c^2*e*f^7*z^2 - 42*A*B
*a^3*b^2*c^5*e^7*f*z^2 + 36*A*B*a^4*b*c^5*e^6*f^2*z^2 - 24*A*B*a^4*b^5*c*e^2*f^6*z^2 + 10*A*B*a^3*b^6*c*e^3*f^
5*z^2 + 7*A*B*a^2*b^4*c^4*e^7*f*z^2 + 2*A*B*a^2*b^7*c*e^4*f^4*z^2 - 2496*A*B*a^5*b*c^4*d^2*f^6*z^2 + 1872*A*B*
a^4*b*c^5*d^3*f^5*z^2 - 744*A*B*a^5*b^3*c^2*d*f^7*z^2 - 720*A*B*a^2*b*c^7*d^5*f^3*z^2 + 504*A*B*a*b^3*c^6*d^5*
f^3*z^2 + 256*A*B*a^3*b*c^6*d^4*f^4*z^2 + 168*A*B*a*b^7*c^2*d^3*f^5*z^2 - 144*A*B*a^2*b^7*c*d^2*f^6*z^2 + 144*
A*B*a*b^5*c^4*d^4*f^4*z^2 + 66*A*B*a^2*b^2*c^6*d*e^7*z^2 - 36*A*B*a*b^2*c^7*d^3*e^5*z^2 + 20*A*B*a*b^3*c^6*d^2
*e^6*z^2 + 12*A*B*a^2*b*c^7*d^2*e^6*z^2 + 1208*B^2*a^3*b*c^6*d^3*e^3*f^2*z^2 - 848*B^2*a^3*b^3*c^4*d^3*e*f^4*z
^2 + 672*B^2*a^2*b^3*c^5*d^4*e*f^3*z^2 - 632*B^2*a^4*b*c^5*d^2*e^3*f^3*z^2 + 432*B^2*a^4*b^3*c^3*d^2*e*f^5*z^2
+ 276*B^2*a^2*b^2*c^6*d^3*e^4*f*z^2 - 196*B^2*a*b^6*c^3*d^3*e^2*f^3*z^2 - 168*B^2*a^2*b^5*c^3*d^3*e*f^4*z^2 +
154*B^2*a^2*b^3*c^5*d^2*e^5*f*z^2 + 148*B^2*a*b^5*c^4*d^3*e^3*f^2*z^2 + 96*B^2*a*b^4*c^5*d^4*e^2*f^2*z^2 - 72
*B^2*a^3*b^5*c^2*d^2*e*f^5*z^2 + 70*B^2*a^5*b^2*c^3*d*e^2*f^5*z^2 - 60*B^2*a^4*b^3*c^3*d*e^3*f^4*z^2 + 52*B^2*
a*b^6*c^3*d^2*e^4*f^2*z^2 + 36*B^2*a^4*b^2*c^4*d*e^4*f^3*z^2 - 32*B^2*a*b^7*c^2*d^2*e^3*f^3*z^2 + 24*B^2*a^3*b
^5*c^2*d*e^3*f^4*z^2 + 15*B^2*a^4*b^4*c^2*d*e^2*f^5*z^2 - 8*B^2*a^3*b^4*c^3*d*e^4*f^3*z^2 + 8*B^2*a^2*b^5*c^3*
d*e^5*f^2*z^2 - 2*B^2*a^3*b^3*c^4*d*e^5*f^2*z^2 - 2*B^2*a^2*b^6*c^2*d*e^4*f^3*z^2 - 3176*A^2*a^3*b*c^6*d^2*e^3
*f^3*z^2 - 2252*A^2*a^4*b^2*c^4*d*e^2*f^5*z^2 + 1952*A^2*a^3*b^4*c^3*d*e^2*f^5*z^2 - 1496*A^2*a^3*b^3*c^4*d*e^
3*f^4*z^2 + 1378*A^2*a^2*b^4*c^4*d*e^4*f^3*z^2 + 1184*A^2*a^3*b^3*c^4*d^2*e*f^5*z^2 - 1166*A^2*a^2*b^3*c^5*d*e
^5*f^2*z^2 - 1164*A^2*a^3*b^2*c^5*d*e^4*f^3*z^2 - 1152*A^2*a^2*b^3*c^5*d^3*e*f^4*z^2 + 578*A^2*a*b^6*c^3*d^2*e
^2*f^4*z^2 - 548*A^2*a*b^5*c^4*d^2*e^3*f^3*z^2 + 440*A^2*a*b^2*c^7*d^4*e^2*f^2*z^2 - 412*A^2*a^2*b^6*c^2*d*e^2
*f^5*z^2 - 360*A^2*a*b^3*c^6*d^3*e^3*f^2*z^2 + 312*A^2*a*b^4*c^5*d^3*e^2*f^3*z^2 + 248*A^2*a^2*b*c^7*d^3*e^3*f
^2*z^2 - 224*A^2*a^2*b^5*c^3*d*e^3*f^4*z^2 + 216*A^2*a^2*b^5*c^3*d^2*e*f^5*z^2 + 52*A^2*a*b^4*c^5*d^2*e^4*f^2*
z^2 - 16*B^2*b^3*c^7*d^6*e*f*z^2 - 14*B^2*b^9*c*d^3*e*f^4*z^2 + 32*B^2*a^4*c^6*d*e^6*f*z^2 - 20*A^2*b^9*c*d*e^
3*f^4*z^2 + 18*A^2*b^9*c*d^2*e*f^5*z^2 + 8*A^2*b^6*c^4*d*e^6*f*z^2 - 360*A^2*a^3*c^7*d*e^6*f*z^2 + 136*A^2*a*c
^9*d^5*e^2*f*z^2 + 2*B^2*a^3*b^7*d*e*f^6*z^2 + 2*B^2*a*b^9*d^2*e*f^5*z^2 + 12*B^2*a^4*b*c^5*e^7*f*z^2 - 204*A^
2*a^3*b*c^6*e^7*f*z^2 - 128*A^2*a^6*b*c^3*e*f^7*z^2 - 48*A^2*a*b^5*c^4*e^7*f*z^2 - 36*B^2*a^5*b^4*c*d*f^7*z^2
- 24*A^2*a^4*b^5*c*e*f^7*z^2 - 16*B^2*a*b^8*c*d^3*f^5*z^2 - 164*A^2*a^3*b^6*c*d*f^7*z^2 - 16*A^2*a*b^8*c*d^2*f
^6*z^2 + 4*B^2*a^3*b*c^6*d*e^7*z^2 - 4*B^2*a*b*c^8*d^5*e^3*z^2 + 48*A^2*a*b*c^8*d^3*e^5*z^2 + 36*A^2*a^2*b*c^7
*d*e^7*z^2 - 6*A^2*a*b^3*c^6*d*e^7*z^2 + 136*A*B*a^6*c^4*e^3*f^5*z^2 - 96*A*B*b^5*c^5*d^5*f^3*z^2 + 80*A*B*a^5
*c^5*e^5*f^3*z^2 - 72*A*B*b^3*c^7*d^6*f^2*z^2 - 24*A*B*b^7*c^3*d^4*f^4*z^2 + 14*A*B*b^3*c^7*d^4*e^4*z^2 - 14*A
*B*b^2*c^8*d^5*e^3*z^2 - 2*A*B*b^5*c^5*d^2*e^6*z^2 - 2*A*B*b^4*c^6*d^3*e^5*z^2 + 2*A*B*a^3*b^7*e^2*f^6*z^2 - A
*B*a^2*b^8*e^3*f^5*z^2 + 16*A*B*a^2*c^8*d^3*e^5*z^2 - 2*A*B*a^2*b^3*c^5*e^8*z^2 + 22*B^2*b^8*c^2*d^3*e^2*f^3*z
^2 - 12*B^2*b^7*c^3*d^3*e^3*f^2*z^2 + 12*B^2*b^6*c^4*d^4*e^2*f^2*z^2 - 6*B^2*b^8*c^2*d^2*e^4*f^2*z^2 - 864*B^2
*a^4*c^6*d^3*e^2*f^3*z^2 + 496*B^2*a^3*c^7*d^4*e^2*f^2*z^2 + 224*B^2*a^5*c^5*d^2*e^2*f^4*z^2 + 136*B^2*a^4*c^6
*d^2*e^4*f^2*z^2 - 53*A^2*b^8*c^2*d^2*e^2*f^4*z^2 + 52*A^2*b^7*c^3*d^2*e^3*f^3*z^2 + 52*A^2*b^5*c^5*d^3*e^3*f^
2*z^2 - 36*A^2*b^6*c^4*d^3*e^2*f^3*z^2 - 12*A^2*b^4*c^6*d^4*e^2*f^2*z^2 - 9*A^2*b^6*c^4*d^2*e^4*f^2*z^2 + 836*
A^2*a^4*c^6*d^2*e^2*f^4*z^2 - 668*A^2*a^2*c^8*d^4*e^2*f^2*z^2 + 656*A^2*a^3*c^7*d^2*e^4*f^2*z^2 + 368*A^2*a^3*
c^7*d^3*e^2*f^3*z^2 - 45*B^2*a^6*b^2*c^2*e^2*f^6*z^2 - 18*B^2*a^5*b^2*c^3*e^4*f^4*z^2 - 9*B^2*a^4*b^2*c^4*e^6*
f^2*z^2 - 6*B^2*a^5*b^3*c^2*e^3*f^5*z^2 + 3*B^2*a^4*b^4*c^2*e^4*f^4*z^2 - 2*B^2*a^4*b^3*c^3*e^5*f^3*z^2 - 580*
B^2*a^4*b^2*c^4*d^3*f^5*z^2 + 536*B^2*a^3*b^4*c^3*d^3*f^5*z^2 + 471*A^2*a^4*b^2*c^4*e^4*f^4*z^2 - 436*A^2*a^3*
b^4*c^3*e^4*f^4*z^2 - 348*B^2*a^4*b^4*c^2*d^2*f^6*z^2 + 316*B^2*a^2*b^2*c^6*d^5*f^3*z^2 + 310*A^2*a^3*b^3*c^4*
e^5*f^3*z^2 + 232*A^2*a^5*b^2*c^3*e^2*f^6*z^2 - 229*A^2*a^2*b^4*c^4*e^6*f^2*z^2 - 216*A^2*a^4*b^4*c^2*e^2*f^6*
z^2 + 204*A^2*a^4*b^3*c^3*e^3*f^5*z^2 + 200*B^2*a^5*b^2*c^3*d^2*f^6*z^2 + 150*A^2*a^3*b^2*c^5*e^6*f^2*z^2 - 12
0*B^2*a^2*b^4*c^4*d^4*f^4*z^2 + 91*A^2*a^2*b^6*c^2*e^4*f^4*z^2 + 72*A^2*a^3*b^5*c^2*e^3*f^5*z^2 - 66*B^2*a^2*b
^6*c^2*d^3*f^5*z^2 + 44*A^2*a^2*b^5*c^3*e^5*f^3*z^2 - 16*B^2*a^3*b^2*c^5*d^4*f^4*z^2 + 1952*A^2*a^4*b^2*c^4*d^
2*f^6*z^2 - 1792*A^2*a^3*b^2*c^5*d^3*f^5*z^2 - 1272*A^2*a^3*b^4*c^3*d^2*f^6*z^2 + 976*A^2*a^2*b^2*c^6*d^4*f^4*
z^2 + 960*A^2*a^2*b^4*c^4*d^3*f^5*z^2 + 282*A^2*a^2*b^6*c^2*d^2*f^6*z^2 - 45*B^2*a^2*b^2*c^6*d^2*e^6*z^2 - 48*
A^2*b*c^9*d^6*e*f*z^2 - 14*A^2*a*b^9*d*e*f^6*z^2 - 7*A*B*b^10*d^2*e*f^5*z^2 + 2*A*B*b^10*d*e^3*f^4*z^2 - 64*A*
B*a^7*c^3*e*f^7*z^2 - 16*A*B*b^9*c*d^3*f^5*z^2 + 8*A*B*a^4*c^6*e^7*f*z^2 + 4*A*B*b*c^9*d^6*e^2*z^2 + 2*A*B*b^6
*c^4*d*e^7*z^2 - 120*A*B*a^3*c^7*d*e^7*z^2 - 16*A*B*a^3*b^7*d*f^7*z^2 + 16*A*B*a*b^9*d^2*f^6*z^2 + 8*A*B*a*c^9
*d^5*e^3*z^2 + 12*A*B*a^3*b*c^6*e^8*z^2 - 48*B^2*b^5*c^5*d^5*e*f^2*z^2 + 15*B^2*b^4*c^6*d^5*e^2*f*z^2 - 14*B^2
*b^7*c^3*d^4*e*f^3*z^2 + 4*B^2*b^9*c*d^2*e^3*f^3*z^2 + 4*B^2*b^7*c^3*d^2*e^5*f*z^2 + 4*B^2*b^5*c^5*d^4*e^3*f*z
^2 - B^2*b^6*c^4*d^3*e^4*f*z^2 - 336*B^2*a^3*c^7*d^3*e^4*f*z^2 + 112*B^2*a^5*c^5*d*e^4*f^3*z^2 - 112*A^2*b^3*c
^7*d^5*e*f^2*z^2 + 80*B^2*a^6*c^4*d*e^2*f^5*z^2 - 48*A^2*b^5*c^5*d^4*e*f^3*z^2 + 36*A^2*b^8*c^2*d*e^4*f^3*z^2
+ 36*A^2*b^3*c^7*d^4*e^3*f*z^2 - 28*A^2*b^7*c^3*d*e^5*f^2*z^2 + 20*A^2*b^2*c^8*d^5*e^2*f*z^2 + 16*B^2*a^2*c^8*
d^5*e^2*f*z^2 - 14*A^2*b^7*c^3*d^3*e*f^4*z^2 - 14*A^2*b^4*c^6*d^3*e^4*f*z^2 - 10*A^2*b^5*c^5*d^2*e^5*f*z^2 - 1
008*A^2*a^4*c^6*d*e^4*f^3*z^2 - 760*A^2*a^5*c^5*d*e^2*f^5*z^2 + 272*A^2*a^2*c^8*d^3*e^4*f*z^2 + 48*B^2*a^5*b*c
^4*e^5*f^3*z^2 + 36*B^2*a^6*b*c^3*e^3*f^5*z^2 + 12*B^2*a^5*b^4*c*e^2*f^6*z^2 - 624*A^2*a^4*b*c^5*e^5*f^3*z^2 -
548*A^2*a^5*b*c^4*e^3*f^5*z^2 + 182*A^2*a^2*b^3*c^5*e^7*f*z^2 - 180*B^2*a*b^4*c^5*d^5*f^3*z^2 + 132*B^2*a^6*b
^2*c^2*d*f^7*z^2 + 108*B^2*a^3*b^6*c*d^2*f^6*z^2 + 96*A^2*a^5*b^3*c^2*e*f^7*z^2 + 68*A^2*a*b^6*c^3*e^6*f^2*z^2
+ 58*A^2*a^3*b^6*c*e^2*f^6*z^2 - 56*B^2*a*b^2*c^7*d^6*f^2*z^2 - 38*A^2*a^2*b^7*c*e^3*f^5*z^2 - 36*A^2*a*b^7*c
^2*e^5*f^3*z^2 + 20*B^2*a*b^6*c^3*d^4*f^4*z^2 - 736*A^2*a^5*b^2*c^3*d*f^7*z^2 + 624*A^2*a^4*b^4*c^2*d*f^7*z^2
- 416*A^2*a*b^2*c^7*d^5*f^3*z^2 - 276*A^2*a*b^4*c^5*d^4*f^4*z^2 - 196*A^2*a*b^6*c^3*d^3*f^5*z^2 + 8*B^2*a*b^4*
c^5*d^2*e^6*z^2 + 6*B^2*a*b^2*c^7*d^4*e^4*z^2 + 2*B^2*a^2*b^3*c^5*d*e^7*z^2 + 2*B^2*a*b^3*c^6*d^3*e^5*z^2 - 18
*A^2*a*b^2*c^7*d^2*e^6*z^2 - 16*A*B*b*c^9*d^7*f*z^2 - B^2*b^10*d^2*e^2*f^4*z^2 + 48*B^2*a^7*c^3*e^2*f^6*z^2 -
36*B^2*a^6*c^4*e^4*f^4*z^2 + 31*B^2*b^6*c^4*d^5*f^3*z^2 - 24*B^2*a^5*c^5*e^6*f^2*z^2 + 20*B^2*b^4*c^6*d^6*f^2*
z^2 - 6*A^2*b^8*c^2*e^6*f^2*z^2 + 2*B^2*b^8*c^2*d^4*f^4*z^2 - 768*B^2*a^5*c^5*d^3*f^5*z^2 + 512*B^2*a^6*c^4*d^
2*f^6*z^2 + 512*B^2*a^4*c^6*d^4*f^4*z^2 + 232*A^2*a^5*c^5*e^4*f^4*z^2 + 188*A^2*a^4*c^6*e^6*f^2*z^2 - 128*B^2*
a^3*c^7*d^5*f^3*z^2 + 92*A^2*a^6*c^4*e^2*f^6*z^2 + 80*A^2*b^4*c^6*d^5*f^3*z^2 + 64*A^2*b^2*c^8*d^6*f^2*z^2 + 3
1*A^2*b^6*c^4*d^4*f^4*z^2 + 14*A^2*b^8*c^2*d^3*f^5*z^2 - 5*B^2*b^4*c^6*d^4*e^4*z^2 + 4*B^2*b^3*c^7*d^5*e^3*z^2
+ 2*B^2*b^5*c^5*d^3*e^5*z^2 - B^2*b^6*c^4*d^2*e^6*z^2 - B^2*b^2*c^8*d^6*e^2*z^2 - B^2*a^4*b^6*e^2*f^6*z^2 - 1
152*A^2*a^3*c^7*d^4*f^4*z^2 + 1008*A^2*a^4*c^6*d^3*f^5*z^2 + 624*A^2*a^2*c^8*d^5*f^3*z^2 - 288*A^2*a^5*c^5*d^2
*f^6*z^2 + 56*B^2*a^3*c^7*d^2*e^6*z^2 - 10*B^2*a^2*b^8*d^2*f^6*z^2 - 9*A^2*b^2*c^8*d^4*e^4*z^2 - 5*A^2*a^2*b^8
*e^2*f^6*z^2 - 4*B^2*a^2*c^8*d^4*e^4*z^2 + 3*A^2*b^4*c^6*d^2*e^6*z^2 - 2*A^2*b^3*c^7*d^3*e^5*z^2 - 36*A^2*a^2*
c^8*d^2*e^6*z^2 - 48*A^2*a^6*b^2*c^2*f^8*z^2 - 45*A^2*a^2*b^2*c^6*e^8*z^2 + 4*A^2*b^10*d*e^2*f^5*z^2 + 4*B^2*b
^2*c^8*d^7*f*z^2 + 4*A^2*b^9*c*e^5*f^3*z^2 + 4*A^2*b^7*c^3*e^7*f*z^2 - 128*B^2*a^7*c^3*d*f^7*z^2 - 160*A^2*a*c
^9*d^6*f^2*z^2 - 112*A^2*a^6*c^4*d*f^7*z^2 + 12*A^2*b*c^9*d^5*e^3*z^2 + 4*A^2*a*b^9*e^3*f^5*z^2 + 3*B^2*a^4*b^
6*d*f^7*z^2 + 2*A^2*a^3*b^7*e*f^7*z^2 - 24*A^2*a*c^9*d^4*e^4*z^2 + 14*A^2*a^2*b^8*d*f^7*z^2 + 12*A^2*a^5*b^4*c
*f^8*z^2 + 12*A^2*a*b^4*c^5*e^8*z^2 + A*B*a^4*b^6*e*f^7*z^2 + B^2*a^2*b^8*d*e^2*f^5*z^2 + 16*A^2*c^10*d^7*f*z^
2 + 3*B^2*b^10*d^3*f^5*z^2 - A^2*b^10*e^4*f^4*z^2 - 4*A^2*c^10*d^6*e^2*z^2 - A^2*b^10*d^2*f^6*z^2 + 64*A^2*a^7
*c^3*f^8*z^2 - 4*B^2*a^4*c^6*e^8*z^2 - A^2*b^6*c^4*e^8*z^2 + 48*A^2*a^3*c^7*e^8*z^2 - A^2*a^4*b^6*f^8*z^2 + 72
0*A^2*B*a*b^2*c^5*d^2*e^2*f^3*z - 600*A^2*B*a^2*b^2*c^4*d*e^2*f^4*z + 576*A*B^2*a^2*b^2*c^4*d^2*e*f^4*z + 348*
A*B^2*a*b^2*c^5*d^2*e^3*f^2*z - 336*A*B^2*a^2*b*c^5*d^2*e^2*f^3*z - 260*A*B^2*a*b^3*c^4*d^2*e^2*f^3*z - 240*A*
B^2*a^2*b^2*c^4*d*e^3*f^3*z + 196*A*B^2*a^2*b^3*c^3*d*e^2*f^4*z + 172*A^2*B*a*b*c^6*d*e^5*f*z + 20*A*B^2*a*b^6
*c*d*e*f^5*z - 912*A^2*B*a^2*b*c^5*d^2*e*f^4*z - 644*A^2*B*a*b*c^6*d^2*e^3*f^2*z - 432*A*B^2*a*b^2*c^5*d^3*e*f
^3*z + 372*A^2*B*a^2*b*c^5*d*e^3*f^3*z - 330*A^2*B*a*b^2*c^5*d*e^4*f^2*z + 312*A*B^2*a*b*c^6*d^3*e^2*f^2*z - 2
08*A*B^2*a^3*b^2*c^3*d*e*f^5*z + 192*A^2*B*a^2*b^3*c^3*d*e*f^5*z + 172*A^2*B*a*b^3*c^4*d*e^3*f^3*z + 108*A*B^2
*a^2*b*c^5*d*e^4*f^2*z + 104*A*B^2*a^3*b*c^4*d*e^2*f^4*z - 80*A^2*B*a*b^3*c^4*d^2*e*f^4*z + 68*A^2*B*a*b^4*c^3
*d*e^2*f^4*z - 60*A*B^2*a*b^5*c^2*d*e^2*f^4*z + 58*A*B^2*a*b^3*c^4*d*e^4*f^2*z - 36*A*B^2*a*b^4*c^3*d^2*e*f^4*
z - 24*A*B^2*a^2*b^4*c^2*d*e*f^5*z + 24*A*B^2*a*b^4*c^3*d*e^3*f^3*z + 592*A^2*B*a*b*c^6*d^3*e*f^3*z + 240*A^2*
B*a^3*b*c^4*d*e*f^5*z - 132*A*B^2*a*b*c^6*d^2*e^4*f*z - 60*A*B^2*a*b^2*c^5*d*e^5*f*z - 48*A^2*B*a*b^5*c^2*d*e*
f^5*z + 20*B^3*a*b*c^6*d^3*e^3*f*z + 16*B^3*a^4*b*c^3*d*e*f^5*z - 16*B^3*a*b*c^6*d^4*e*f^2*z + 12*B^3*a^2*b*c^
5*d*e^5*f*z + 320*A^3*a*b*c^6*d*e^4*f^2*z + 40*A^3*a*b^4*c^3*d*e*f^5*z - 48*A^2*B*b*c^7*d^4*e*f^2*z - 44*A^2*B
*b^3*c^5*d*e^5*f*z - 20*A*B^2*b*c^7*d^4*e^2*f*z + 14*A*B^2*b^4*c^4*d*e^5*f*z + 12*A^2*B*b*c^7*d^3*e^3*f*z + 4*
A*B^2*b^7*c*d*e^2*f^4*z + 160*A*B^2*a^4*c^4*d*e*f^5*z + 152*A^2*B*a*c^7*d^2*e^4*f*z - 40*A*B^2*a*c^7*d^3*e^3*f
*z + 32*A*B^2*a*c^7*d^4*e*f^2*z - 16*A*B^2*a^2*c^6*d*e^5*f*z + 128*A^2*B*a^4*b*c^3*e*f^6*z + 42*A^2*B*a*b^2*c^
5*e^6*f*z + 24*A^2*B*a^2*b^5*c*e*f^6*z - 12*A*B^2*a^3*b^4*c*e*f^6*z - 12*A*B^2*a^2*b*c^5*e^6*f*z - 10*A^2*B*a*
b^6*c*e^2*f^5*z - 160*A*B^2*a*b*c^6*d^4*f^3*z + 112*A*B^2*a^4*b*c^3*d*f^6*z - 24*A*B^2*a^2*b^5*c*d*f^6*z - 84*
B^3*a*b^2*c^5*d^3*e^2*f^2*z - 80*B^3*a^2*b^3*c^3*d^2*e*f^4*z - 60*B^3*a^2*b*c^5*d^2*e^3*f^2*z - 20*B^3*a^3*b^2
*c^3*d*e^2*f^4*z - 20*B^3*a*b^3*c^4*d^2*e^3*f^2*z - 9*B^3*a^2*b^2*c^4*d*e^4*f^2*z - 8*B^3*a*b^4*c^3*d^2*e^2*f^
3*z + 6*B^3*a^2*b^4*c^2*d*e^2*f^4*z - 4*B^3*a^2*b^3*c^3*d*e^3*f^3*z - 216*A^2*B*b^4*c^4*d^2*e^2*f^3*z + 196*A^
2*B*b^3*c^5*d^2*e^3*f^2*z - 108*A*B^2*b^3*c^5*d^3*e^2*f^2*z - 94*A*B^2*b^4*c^4*d^2*e^3*f^2*z + 88*A^2*B*b^2*c^
6*d^3*e^2*f^2*z + 80*A*B^2*b^5*c^3*d^2*e^2*f^3*z + 360*A^2*B*a^2*c^6*d^2*e^2*f^3*z + 8*A*B^2*a^2*c^6*d^2*e^3*f
^2*z + 153*A^2*B*a^2*b^2*c^4*e^4*f^3*z - 144*A^2*B*a^2*b^3*c^3*e^3*f^4*z + 80*A^2*B*a^3*b^2*c^3*e^2*f^5*z + 36
*A*B^2*a^3*b^2*c^3*e^3*f^4*z + 12*A^2*B*a^2*b^4*c^2*e^2*f^5*z + 12*A*B^2*a^3*b^3*c^2*e^2*f^5*z + 9*A*B^2*a^2*b
^2*c^4*e^5*f^2*z - 6*A*B^2*a^2*b^4*c^2*e^3*f^4*z + 4*A*B^2*a^2*b^3*c^3*e^4*f^3*z + 480*A^2*B*a^2*b^2*c^4*d^2*f
^5*z - 176*A*B^2*a^2*b^3*c^3*d^2*f^5*z - 10*A^2*B*a*b^6*c*d*f^6*z + 16*A*B^2*a*b*c^6*d*e^6*z + 80*B^3*a*b^3*c^
4*d^3*e*f^3*z - 48*B^3*a^3*b*c^4*d^2*e*f^4*z + 48*B^3*a^2*b*c^5*d^3*e*f^3*z + 44*B^3*a^3*b*c^4*d*e^3*f^3*z + 2
4*B^3*a*b^5*c^2*d^2*e*f^4*z + 18*B^3*a*b^2*c^5*d^2*e^4*f*z + 696*A^3*a^2*b*c^5*d*e^2*f^4*z - 504*A^3*a*b*c^6*d
^2*e^2*f^3*z - 192*A^3*a*b^2*c^5*d*e^3*f^3*z - 144*A^3*a^2*b^2*c^4*d*e*f^5*z + 96*A^3*a*b^2*c^5*d^2*e*f^4*z -
72*A^3*a*b^3*c^4*d*e^2*f^4*z - 208*A^2*B*b^3*c^5*d^3*e*f^3*z + 152*A*B^2*b^4*c^4*d^3*e*f^3*z + 80*A^2*B*b^5*c^
3*d^2*e*f^4*z + 75*A^2*B*b^4*c^4*d*e^4*f^2*z - 59*A^2*B*b^2*c^6*d^2*e^4*f*z - 52*A^2*B*b^5*c^3*d*e^3*f^3*z + 4
2*A*B^2*b^3*c^5*d^2*e^4*f*z - 21*A*B^2*b^6*c^2*d^2*e*f^4*z - 16*A*B^2*b^5*c^3*d*e^4*f^2*z + 16*A*B^2*b^2*c^6*d
^4*e*f^2*z + 16*A*B^2*b^2*c^6*d^3*e^3*f*z + 11*A^2*B*b^6*c^2*d*e^2*f^4*z + 4*A*B^2*b^6*c^2*d*e^3*f^3*z - 256*A
^2*B*a*c^7*d^3*e^2*f^2*z - 96*A*B^2*a^3*c^5*d^2*e*f^4*z - 36*A^2*B*a^2*c^6*d*e^4*f^2*z - 32*A^2*B*a^3*c^5*d*e^
2*f^4*z - 32*A*B^2*a^2*c^6*d^3*e*f^3*z + 8*A*B^2*a^3*c^5*d*e^3*f^3*z - 96*A^2*B*a^3*b^3*c^2*e*f^6*z + 68*A^2*B
*a^3*b*c^4*e^3*f^4*z - 60*A*B^2*a^4*b*c^3*e^2*f^5*z - 60*A*B^2*a^3*b*c^4*e^4*f^3*z + 48*A*B^2*a^4*b^2*c^2*e*f^
6*z - 38*A^2*B*a*b^3*c^4*e^5*f^2*z - 36*A^2*B*a^2*b*c^5*e^5*f^2*z + 36*A^2*B*a*b^5*c^2*e^3*f^4*z - 16*A^2*B*a*
b^4*c^3*e^4*f^3*z + 384*A*B^2*a^2*b*c^5*d^3*f^4*z - 352*A*B^2*a^3*b*c^4*d^2*f^5*z - 288*A^2*B*a*b^2*c^5*d^3*f^
4*z - 160*A^2*B*a^3*b^2*c^3*d*f^6*z - 148*A^2*B*a*b^4*c^3*d^2*f^5*z + 112*A*B^2*a*b^3*c^4*d^3*f^4*z + 72*A^2*B
*a^2*b^4*c^2*d*f^6*z + 72*A*B^2*a*b^5*c^2*d^2*f^5*z + 48*A*B^2*a^3*b^3*c^2*d*f^6*z + 102*B^3*a^2*b^2*c^4*d^2*e
^2*f^3*z - 32*B^3*b^5*c^3*d^3*e*f^3*z - 8*B^3*b^3*c^5*d^3*e^3*f*z - 7*B^3*b^4*c^4*d^2*e^4*f*z + 5*B^3*b^2*c^6*
d^4*e^2*f*z + 80*A^3*b^2*c^6*d^3*e*f^3*z - 74*A^3*b^3*c^5*d*e^4*f^2*z - 64*A^3*b^4*c^4*d^2*e*f^4*z + 60*A^3*b^
4*c^4*d*e^3*f^3*z - 48*B^3*a^4*c^4*d*e^2*f^4*z - 24*B^3*a^3*c^5*d*e^4*f^2*z + 20*B^3*a^2*c^6*d^2*e^4*f*z - 16*
A^3*b^5*c^3*d*e^2*f^4*z + 8*A^3*b*c^7*d^3*e^2*f^2*z + 480*A^3*a^2*c^6*d^2*e*f^4*z - 392*A^3*a^2*c^6*d*e^3*f^3*
z + 280*A^3*a*c^7*d^2*e^3*f^2*z - 4*B^3*a^4*b*c^3*e^3*f^4*z - 200*A^3*a^3*b*c^4*e^2*f^5*z - 144*A^3*a^2*b*c^5*
e^4*f^3*z + 48*B^3*a*b^2*c^5*d^4*f^3*z + 42*A^3*a*b^2*c^5*e^5*f^2*z - 36*B^3*a^4*b^2*c^2*d*f^6*z - 32*A^3*a^3*
b^2*c^3*e*f^6*z - 24*A^3*a^2*b^4*c^2*e*f^6*z - 24*A^3*a*b^5*c^2*e^2*f^5*z + 10*A^3*a*b^3*c^4*e^4*f^3*z - 4*B^3
*a*b^4*c^3*d^3*f^4*z - 4*A^3*a*b^4*c^3*e^3*f^4*z - 480*A^3*a^2*b*c^5*d^2*f^5*z - 160*A^3*a^2*b^3*c^3*d*f^6*z +
128*A^3*a*b^3*c^4*d^2*f^5*z + 8*A^2*B*b^5*c^3*e^5*f^2*z - 2*A^2*B*b^6*c^2*e^4*f^3*z + 112*A^2*B*b^4*c^4*d^3*f
^4*z - 92*A^2*B*a^4*c^4*e^2*f^5*z - 64*A^2*B*a^3*c^5*e^4*f^3*z - 64*A*B^2*b^5*c^3*d^3*f^4*z + 24*A*B^2*a^4*c^4
*e^3*f^4*z + 24*A*B^2*a^3*c^5*e^5*f^2*z + 16*A^2*B*b^2*c^6*d^4*f^3*z + 16*A*B^2*b^3*c^5*d^4*f^3*z - A^2*B*b^6*
c^2*d^2*f^5*z + 448*A^2*B*a^3*c^5*d^2*f^5*z - 352*A^2*B*a^2*c^6*d^3*f^4*z - 5*A*B^2*b^2*c^6*d^2*e^5*z - 48*A^2
*B*a^4*b^2*c^2*f^7*z - 2*B^3*b^7*c*d^2*e*f^4*z + 34*A^3*b^2*c^6*d*e^5*f*z + 16*A^3*b*c^7*d^2*e^4*f*z + 2*A^3*b
^6*c^2*d*e*f^5*z - 416*A^3*a^3*c^5*d*e*f^5*z - 224*A^3*a*c^7*d^3*e*f^3*z + 12*B^3*a^3*b^4*c*d*f^6*z - 10*B^3*a
*b^6*c*d^2*f^5*z + 416*A^3*a^3*b*c^4*d*f^6*z + 224*A^3*a*b*c^6*d^3*f^4*z + 24*A^3*a*b^5*c^2*d*f^6*z - 4*B^3*a*
b*c^6*d^2*e^5*z + 20*A^2*B*c^8*d^4*e^2*f*z - 7*A^2*B*b^4*c^4*e^6*f*z - 2*A^2*B*b^7*c*e^3*f^4*z - 64*A*B^2*a^5*
c^3*e*f^6*z + 16*A*B^2*b*c^7*d^5*f^2*z - 8*A^2*B*a^2*c^6*e^6*f*z - 2*A*B^2*b^7*c*d^2*f^5*z - 272*A^2*B*a^4*c^4
*d*f^6*z + 128*A^2*B*a*c^7*d^4*f^3*z + 9*A^2*B*b^2*c^6*d*e^6*z - 4*A*B^2*b^3*c^5*d*e^6*z + 4*A*B^2*b*c^7*d^3*e
^4*z + 8*A*B^2*a*c^7*d^2*e^5*z + 12*A^2*B*a^3*b^4*c*f^7*z + 30*B^3*b^4*c^4*d^3*e^2*f^2*z + 8*B^3*b^5*c^3*d^2*e
^3*f^2*z - 2*B^3*b^6*c^2*d^2*e^2*f^3*z + 152*A^3*b^3*c^5*d^2*e^2*f^3*z - 108*A^3*b^2*c^6*d^2*e^3*f^2*z + 48*B^
3*a^3*c^5*d^2*e^2*f^3*z - 16*B^3*a^2*c^6*d^3*e^2*f^2*z - 3*B^3*a^4*b^2*c^2*e^2*f^5*z - 120*B^3*a^2*b^2*c^4*d^3
*f^4*z + 112*B^3*a^3*b^2*c^3*d^2*f^5*z + 112*A^3*a^2*b^3*c^3*e^2*f^5*z + 12*A^3*a^2*b^2*c^4*e^3*f^4*z - 120*A^
3*a*c^7*d*e^5*f*z - 52*A^3*a*b*c^6*e^6*f*z + 10*A^3*a*b^6*c*e*f^6*z - 2*A*B^2*b^8*d*e*f^5*z - 2*A^2*B*a*b^7*e*
f^6*z - 24*A^2*B*a*c^7*d*e^6*z + 2*A*B^2*a*b^7*d*f^6*z - 12*A^2*B*a*b*c^6*e^7*z - 2*A^3*b^7*c*d*f^6*z - 4*A^3*
b*c^7*d*e^6*z + 16*B^3*a^5*c^3*e^2*f^5*z + 11*B^3*b^6*c^2*d^3*f^4*z - 11*A^3*b^4*c^4*e^5*f^2*z - 8*B^3*b^4*c^4
*d^4*f^3*z - 4*B^3*b^2*c^6*d^5*f^2*z + 4*B^3*a^4*c^4*e^4*f^3*z + 4*A^3*b^5*c^3*e^4*f^3*z - A^3*b^6*c^2*e^3*f^4
*z + 136*A^3*a^3*c^5*e^3*f^4*z + 68*A^3*a^2*c^6*e^5*f^2*z - 64*A^3*b^3*c^5*d^3*f^4*z + 2*B^3*b^3*c^5*d^2*e^5*z
- B^3*b^2*c^6*d^3*e^4*z + 96*A^3*a^3*b^3*c^2*f^7*z + A*B^2*a^2*b^6*e*f^6*z + 32*A^3*c^8*d^4*e*f^2*z - 24*A^3*
c^8*d^3*e^3*f*z + 10*A^3*b^3*c^5*e^6*f*z + 2*A^3*b^7*c*e^2*f^5*z + 128*A^3*a^4*c^4*e*f^6*z - 32*A^3*b*c^7*d^4*
f^3*z - 4*B^3*a^2*c^6*d*e^6*z - B^3*a^2*b^6*d*f^6*z - 128*A^3*a^4*b*c^3*f^7*z - 24*A^3*a^2*b^5*c*f^7*z - 16*A^
2*B*c^8*d^5*f^2*z - 4*A^2*B*c^8*d^3*e^4*z + 64*A^2*B*a^5*c^3*f^7*z + 2*A^2*B*b^3*c^5*e^7*z + 4*A*B^2*a^2*c^6*e
^7*z - A^2*B*a^2*b^6*f^7*z + 4*A^3*c^8*d^2*e^5*z - 3*A^3*b^2*c^6*e^7*z + A^2*B*b^8*d*f^6*z - A^3*b^8*e*f^6*z +
16*A^3*a*c^7*e^7*z + 2*A^3*a*b^7*f^7*z + A^2*B*b^8*e^2*f^5*z + B^3*b^8*d^2*f^5*z - 48*A^2*B^2*a*b*c^4*d*e*f^4
+ 28*A*B^3*a*b^2*c^3*d*e*f^4 - 16*A*B^3*a*b*c^4*d*e^2*f^3 + 16*A^3*B*a*c^5*d*e*f^4 + 32*A^3*B*a*b*c^4*d*f^5 +
12*A^2*B^2*b^3*c^3*d*e*f^4 + 5*A*B^3*b^2*c^4*d^2*e*f^3 + 4*A*B^3*b^3*c^3*d*e^2*f^3 + 24*A^2*B^2*a*c^5*d*e^2*f
^3 + 24*A^2*B^2*a^2*b*c^3*e*f^5 + 12*A^2*B^2*a*b*c^4*e^3*f^3 - 6*A^2*B^2*a*b^3*c^2*e*f^5 + 4*A*B^3*a^2*b*c^3*e
^2*f^4 + 3*A*B^3*a^2*b^2*c^2*e*f^5 - 18*A^2*B^2*a*b^2*c^3*d*f^5 - 4*B^4*a^2*b*c^3*d*e*f^4 + 4*B^4*a*b*c^4*d^2*
e*f^3 - 6*A*B^3*b^4*c^2*d*e*f^4 + 4*A^3*B*b*c^5*d*e^2*f^3 - 2*A^3*B*b^2*c^4*d*e*f^4 - 8*A*B^3*a^2*c^4*d*e*f^4
- 8*A*B^3*a*c^5*d^2*e*f^3 + 26*A^3*B*a*b^2*c^3*e*f^5 + 8*A^3*B*a*b*c^4*e^2*f^4 + 32*A*B^3*a*b*c^4*d^2*f^4 - 28
*A*B^3*a^2*b*c^3*d*f^5 + 6*A*B^3*a*b^3*c^2*d*f^5 - 9*A^2*B^2*b^2*c^4*d*e^2*f^3 - 18*A^2*B^2*a*b^2*c^3*e^2*f^4
- 4*A^3*B*c^6*d^2*e*f^3 - 3*A^3*B*b^4*c^2*e*f^5 - 44*A^3*B*a^2*c^4*e*f^5 - 16*A^3*B*a*c^5*e^3*f^3 - 16*A*B^3*a
^3*c^3*e*f^5 - 10*A^3*B*b^3*c^3*d*f^5 - 4*A^3*B*b*c^5*d^2*f^4 - 4*A*B^3*b*c^5*d^3*f^3 - 28*A^3*B*a^2*b*c^3*f^6
+ 6*A^3*B*a*b^3*c^2*f^6 - 4*A^4*b*c^5*d*e*f^4 - 20*A^4*a*b*c^4*e*f^5 + 3*A^2*B^2*b^4*c^2*e^2*f^4 - 2*A^2*B^2*
b^3*c^3*e^3*f^3 + 12*A^2*B^2*a^2*c^4*e^2*f^4 + 9*A^2*B^2*b^2*c^4*d^2*f^4 - 3*A^2*B^2*a^2*b^2*c^2*f^6 - 2*B^4*b
^3*c^3*d^2*e*f^3 + 4*B^4*a^2*c^4*d*e^2*f^3 - 10*B^4*a*b^2*c^3*d^2*f^4 - 3*B^4*a^2*b^2*c^2*d*f^5 + 3*A^3*B*b^2*
c^4*e^3*f^3 - 2*A^3*B*b^3*c^3*e^2*f^4 - 10*A*B^3*b^3*c^3*d^2*f^4 - 4*A*B^3*a^2*c^4*e^3*f^3 + 3*A^2*B^2*b^4*c^2
*d*f^5 + 36*A^2*B^2*a^2*c^4*d*f^5 - 24*A^2*B^2*a*c^5*d^2*f^4 + 4*A^2*B^2*c^6*d^3*f^3 + 16*A^2*B^2*a^3*c^3*f^6
+ 4*A^4*b^3*c^3*e*f^5 + 16*B^4*a^3*c^3*d*f^5 + 16*A^4*a*c^5*e^2*f^4 + 8*A^4*b^2*c^4*d*f^5 - 8*A^4*a*b^2*c^3*f^
6 - 24*A^4*a*c^5*d*f^5 + 3*B^4*b^4*c^2*d^2*f^4 - 3*A^4*b^2*c^4*e^2*f^4 + 4*A^4*c^6*d^2*f^4 + 36*A^4*a^2*c^4*f^
6 + B^4*b^2*c^4*d^3*f^3, z, k)*((64*a^9*c^4*e*f^8 - 64*a^6*c^7*e^7*f^2 - 64*a^7*c^6*e^5*f^4 + 64*a^8*c^5*e^3*f
^6 + 4*b^5*c^8*d^7*f^2 + 4*b^7*c^6*d^6*f^3 - 4*b^9*c^4*d^5*f^4 - 4*b^11*c^2*d^4*f^5 - 612*a^2*b^5*c^6*d^5*f^4
- 712*a^2*b^7*c^4*d^4*f^5 - 132*a^2*b^9*c^2*d^3*f^6 + 1696*a^3*b^3*c^7*d^5*f^4 + 2736*a^3*b^5*c^5*d^4*f^5 + 89
6*a^3*b^7*c^3*d^3*f^6 - 5120*a^4*b^3*c^6*d^4*f^5 - 3140*a^4*b^5*c^4*d^3*f^6 - 220*a^4*b^7*c^2*d^2*f^7 + 5664*a
^5*b^3*c^5*d^3*f^6 + 1128*a^5*b^5*c^3*d^2*f^7 - 2560*a^6*b^3*c^4*d^2*f^7 + 4*a^3*b^6*c^4*e^7*f^2 - 6*a^3*b^7*c
^3*e^6*f^3 + 4*a^3*b^8*c^2*e^5*f^4 - 36*a^4*b^4*c^5*e^7*f^2 + 57*a^4*b^5*c^4*e^6*f^3 - 37*a^4*b^6*c^3*e^5*f^4
+ 7*a^4*b^7*c^2*e^4*f^5 + 96*a^5*b^2*c^6*e^7*f^2 - 168*a^5*b^3*c^5*e^6*f^3 + 100*a^5*b^4*c^4*e^5*f^4 - 3*a^5*b
^5*c^3*e^4*f^5 - 10*a^5*b^6*c^2*e^3*f^6 - 48*a^6*b^2*c^5*e^5*f^4 - 56*a^6*b^3*c^4*e^4*f^5 + 36*a^6*b^4*c^3*e^3
*f^6 - 13*a^6*b^5*c^2*e^2*f^7 - 64*a^7*b^2*c^4*e^3*f^6 + 56*a^7*b^3*c^3*e^2*f^7 - 1472*a^4*c^9*d^4*e^3*f^2 - 1
088*a^5*c^8*d^2*e^5*f^2 + 3584*a^5*c^8*d^3*e^3*f^3 - 3200*a^6*c^7*d^2*e^3*f^4 - 2*b^7*c^6*d^5*e^2*f^2 - b^8*c^
5*d^4*e^3*f^2 + 4*b^9*c^4*d^3*e^4*f^2 - 5*b^9*c^4*d^4*e^2*f^3 - 6*b^10*c^3*d^3*e^3*f^3 + 4*b^11*c^2*d^3*e^2*f^
4 + 8*a*b^11*c*d^3*f^6 + 8*a^5*b^7*c*d*f^8 - 448*a^8*b*c^4*d*f^8 - 16*a^5*b*c^7*e^8*f - a^6*b^6*c*e*f^8 + 128*
a^5*c^8*d*e^7*f + 128*a^8*c^5*d*e*f^7 - b^12*c*d^3*e*f^5 - 32*a*b^3*c^9*d^7*f^2 - 24*a*b^5*c^7*d^6*f^3 + 88*a*
b^7*c^5*d^5*f^4 + 88*a*b^9*c^3*d^4*f^5 + 64*a^2*b*c^10*d^7*f^2 + 128*a^3*b*c^9*d^6*f^3 + 16*a^3*b^9*c*d^2*f^7
- 1600*a^4*b*c^8*d^5*f^4 + 3840*a^5*b*c^7*d^4*f^5 - 4160*a^6*b*c^6*d^3*f^6 - 92*a^6*b^5*c^2*d*f^8 + 2176*a^7*b
*c^5*d^2*f^7 + 352*a^7*b^3*c^3*d*f^8 - a^3*b^5*c^5*e^8*f - a^3*b^9*c*e^4*f^5 + 8*a^4*b^3*c^6*e^8*f + a^4*b^8*c
*e^3*f^6 + a^5*b^7*c*e^2*f^7 + 144*a^6*b*c^6*e^6*f^3 + 80*a^7*b*c^5*e^4*f^5 + 12*a^7*b^4*c^2*e*f^8 - 80*a^8*b*
c^4*e^2*f^7 - 48*a^8*b^2*c^3*e*f^8 + 128*a^3*c^10*d^5*e^3*f - 448*a^3*c^10*d^6*e*f^2 + 256*a^4*c^9*d^3*e^5*f +
2176*a^4*c^9*d^5*e*f^3 - 4160*a^5*c^8*d^4*e*f^4 + 896*a^6*c^7*d*e^5*f^3 + 3840*a^6*c^7*d^3*e*f^5 + 896*a^7*c^
6*d*e^3*f^5 - 1600*a^7*c^6*d^2*e*f^6 - b^5*c^8*d^6*e^2*f + b^6*c^7*d^5*e^3*f - 5*b^6*c^7*d^6*e*f^2 + b^7*c^6*d
^4*e^4*f - b^8*c^5*d^3*e^5*f + 5*b^8*c^5*d^5*e*f^3 + 9*b^10*c^3*d^4*e*f^4 + 8*a*b^3*c^9*d^6*e^2*f + 12*a*b^4*c
^8*d^6*e*f^2 - 27*a*b^5*c^7*d^4*e^4*f + 18*a*b^6*c^6*d^3*e^5*f - 154*a*b^6*c^6*d^5*e*f^3 + a*b^7*c^5*d^2*e^6*f
- 200*a*b^8*c^4*d^4*e*f^4 - 2*a*b^10*c^2*d^3*e*f^5 + a*b^11*c*d^2*e^2*f^5 - 16*a^2*b*c^10*d^6*e^2*f + a^2*b^6
*c^5*d*e^7*f + a^2*b^10*c*d*e^3*f^5 - 19*a^2*b^10*c*d^2*e*f^6 - 304*a^3*b*c^9*d^4*e^4*f + 10*a^3*b^9*c*d*e^2*f
^6 - 304*a^4*b*c^8*d^2*e^6*f - 48*a^4*b^2*c^7*d*e^7*f - 160*a^5*b*c^7*d*e^6*f^2 + 214*a^5*b^6*c^2*d*e*f^7 - 20
48*a^6*b*c^6*d*e^4*f^4 - 792*a^6*b^4*c^3*d*e*f^7 - 1824*a^7*b*c^5*d*e^2*f^6 + 928*a^7*b^2*c^4*d*e*f^7 + 78*a*b
^5*c^7*d^5*e^2*f^2 + 10*a*b^6*c^6*d^4*e^3*f^2 - 68*a*b^7*c^5*d^3*e^4*f^2 + 129*a*b^7*c^5*d^4*e^2*f^3 - 4*a*b^8
*c^4*d^2*e^5*f^2 + 96*a*b^8*c^4*d^3*e^3*f^3 + 6*a*b^9*c^3*d^2*e^4*f^3 - 52*a*b^9*c^3*d^3*e^2*f^4 - 4*a*b^10*c^
2*d^2*e^3*f^4 - 48*a^2*b^2*c^9*d^5*e^3*f + 144*a^2*b^2*c^9*d^6*e*f^2 + 168*a^2*b^3*c^8*d^4*e^4*f - 80*a^2*b^4*
c^7*d^3*e^5*f + 1128*a^2*b^4*c^7*d^5*e*f^3 - 27*a^2*b^5*c^6*d^2*e^6*f + 1481*a^2*b^6*c^5*d^4*e*f^4 - 4*a^2*b^7
*c^4*d*e^6*f^2 + 6*a^2*b^8*c^3*d*e^5*f^3 + 126*a^2*b^8*c^3*d^3*e*f^5 - 4*a^2*b^9*c^2*d*e^4*f^4 + 992*a^3*b*c^9
*d^5*e^2*f^2 + 32*a^3*b^2*c^8*d^3*e^5*f - 2912*a^3*b^2*c^8*d^5*e*f^3 + 168*a^3*b^3*c^7*d^2*e^6*f - 4812*a^3*b^
4*c^6*d^4*e*f^4 + 22*a^3*b^5*c^5*d*e^6*f^2 - 68*a^3*b^6*c^4*d*e^5*f^3 - 860*a^3*b^6*c^4*d^3*e*f^5 + 80*a^3*b^7
*c^3*d*e^4*f^4 - 44*a^3*b^8*c^2*d*e^3*f^5 + 232*a^3*b^8*c^2*d^2*e*f^6 + 1280*a^4*b*c^8*d^3*e^4*f^2 - 816*a^4*b
*c^8*d^4*e^2*f^3 + 7088*a^4*b^2*c^7*d^4*e*f^4 + 16*a^4*b^3*c^6*d*e^6*f^2 + 312*a^4*b^4*c^5*d*e^5*f^3 + 2864*a^
4*b^4*c^5*d^3*e*f^5 - 576*a^4*b^5*c^4*d*e^4*f^4 + 393*a^4*b^6*c^3*d*e^3*f^5 - 995*a^4*b^6*c^3*d^2*e*f^6 - 78*a
^4*b^7*c^2*d*e^2*f^6 + 992*a^5*b*c^7*d^2*e^4*f^3 - 3264*a^5*b*c^7*d^3*e^2*f^4 - 768*a^5*b^2*c^6*d*e^5*f^3 - 51
84*a^5*b^2*c^6*d^3*e*f^5 + 1792*a^5*b^3*c^5*d*e^4*f^4 - 1232*a^5*b^4*c^4*d*e^3*f^5 + 1588*a^5*b^4*c^4*d^2*e*f^
6 + 30*a^5*b^5*c^3*d*e^2*f^6 + 5008*a^6*b*c^6*d^2*e^2*f^5 + 976*a^6*b^2*c^5*d*e^3*f^5 - 16*a^6*b^2*c^5*d^2*e*f
^6 + 944*a^6*b^3*c^4*d*e^2*f^6 - 19*a^4*b^8*c*d*e*f^7 - 528*a^2*b^3*c^8*d^5*e^2*f^2 - 124*a^2*b^4*c^7*d^4*e^3*
f^2 + 432*a^2*b^5*c^6*d^3*e^4*f^2 - 843*a^2*b^5*c^6*d^4*e^2*f^3 + 83*a^2*b^6*c^5*d^2*e^5*f^2 - 722*a^2*b^6*c^5
*d^3*e^3*f^3 - 80*a^2*b^7*c^4*d^2*e^4*f^3 + 376*a^2*b^7*c^4*d^3*e^2*f^4 + 43*a^2*b^9*c^2*d^2*e^2*f^5 + 768*a^3
*b^2*c^8*d^4*e^3*f^2 - 1216*a^3*b^3*c^7*d^3*e^4*f^2 + 1832*a^3*b^3*c^7*d^4*e^2*f^3 - 540*a^3*b^4*c^6*d^2*e^5*f
^2 + 2928*a^3*b^4*c^6*d^3*e^3*f^3 + 414*a^3*b^5*c^5*d^2*e^4*f^3 - 1740*a^3*b^5*c^5*d^3*e^2*f^4 + 344*a^3*b^6*c
^4*d^2*e^3*f^4 - 634*a^3*b^7*c^3*d^2*e^2*f^5 + 1360*a^4*b^2*c^7*d^2*e^5*f^2 - 5664*a^4*b^2*c^7*d^3*e^3*f^3 - 1
008*a^4*b^3*c^6*d^2*e^4*f^3 + 4064*a^4*b^3*c^6*d^3*e^2*f^4 - 1928*a^4*b^4*c^5*d^2*e^3*f^4 + 3065*a^4*b^5*c^4*d
^2*e^2*f^5 + 4032*a^5*b^2*c^6*d^2*e^3*f^4 - 6376*a^5*b^3*c^5*d^2*e^2*f^5)/(16*a^2*c^6*d^4 + a^4*b^4*f^4 + 16*a
^4*c^4*e^4 + b^4*c^4*d^4 + 16*a^6*c^2*f^4 + b^8*d^2*f^2 - 8*a*b^2*c^5*d^4 - 8*a^5*b^2*c*f^4 + 2*a^2*b^6*d*f^3
- 2*a^3*b^5*e*f^3 - 64*a^3*c^5*d^3*f - 64*a^5*c^3*d*f^3 - 2*b^5*c^3*d^3*e + 2*b^6*c^2*d^3*f + a^2*b^4*c^2*e^4
- 8*a^3*b^2*c^3*e^4 + 32*a^3*c^5*d^2*e^2 + a^2*b^6*e^2*f^2 + 96*a^4*c^4*d^2*f^2 + b^6*c^2*d^2*e^2 + 32*a^5*c^3
*e^2*f^2 - 2*a*b^7*d*e*f^2 - 2*b^7*c*d^2*e*f + 54*a^2*b^4*c^2*d^2*f^2 - 112*a^3*b^2*c^3*d^2*f^2 + 16*a*b^3*c^4
*d^3*e - 2*a*b^5*c^2*d*e^3 - 32*a^2*b*c^5*d^3*e - 32*a^3*b*c^4*d*e^3 - 20*a*b^4*c^3*d^3*f - 12*a*b^6*c*d^2*f^2
- 20*a^3*b^4*c*d*f^3 - 2*a^2*b^5*c*e^3*f - 32*a^4*b*c^3*e^3*f + 16*a^4*b^3*c*e*f^3 - 32*a^5*b*c^2*e*f^3 - 64*
a^4*c^4*d*e^2*f - 6*a*b^4*c^3*d^2*e^2 + 16*a^2*b^3*c^3*d*e^3 + 64*a^2*b^2*c^4*d^3*f + 64*a^4*b^2*c^2*d*f^3 + 1
6*a^3*b^3*c^2*e^3*f - 6*a^3*b^4*c*e^2*f^2 - 48*a^2*b^3*c^3*d^2*e*f - 36*a^2*b^4*c^2*d*e^2*f + 96*a^3*b^2*c^3*d
*e^2*f - 48*a^3*b^3*c^2*d*e*f^2 + 4*a*b^6*c*d*e^2*f + 18*a*b^5*c^2*d^2*e*f + 18*a^2*b^5*c*d*e*f^2 + 32*a^3*b*c
^4*d^2*e*f + 32*a^4*b*c^3*d*e*f^2) + (x*(128*a^9*c^4*f^9 - 2*a^6*b^6*c*f^9 - 640*a^8*c^5*d*f^8 + 96*a^5*c^8*e^
8*f + 6*b^12*c*d^3*f^6 + 24*a^7*b^4*c^2*f^9 - 96*a^8*b^2*c^3*f^9 + 128*a^2*c^11*d^7*f^2 - 640*a^3*c^10*d^6*f^3
+ 1152*a^4*c^9*d^5*f^4 - 640*a^5*c^8*d^4*f^5 - 640*a^6*c^7*d^3*f^6 + 1152*a^7*c^6*d^2*f^7 + 288*a^6*c^7*e^6*f
^3 + 416*a^7*c^6*e^4*f^5 + 352*a^8*c^5*e^2*f^7 + 8*b^4*c^9*d^7*f^2 + 22*b^6*c^7*d^6*f^3 + 26*b^8*c^5*d^5*f^4 +
18*b^10*c^3*d^4*f^5 + 672*a^2*b^2*c^9*d^6*f^3 + 1224*a^2*b^4*c^7*d^5*f^4 + 1202*a^2*b^6*c^5*d^4*f^5 + 564*a^2
*b^8*c^3*d^3*f^6 - 2048*a^3*b^2*c^8*d^5*f^4 - 2744*a^3*b^4*c^6*d^4*f^5 - 1736*a^3*b^6*c^4*d^3*f^6 - 128*a^3*b^
8*c^2*d^2*f^7 + 2656*a^4*b^2*c^7*d^4*f^5 + 2648*a^4*b^4*c^5*d^3*f^6 + 570*a^4*b^6*c^3*d^2*f^7 - 1344*a^5*b^2*c
^6*d^3*f^6 - 904*a^5*b^4*c^4*d^2*f^7 - 160*a^6*b^2*c^5*d^2*f^7 + 8*a^2*b^7*c^4*e^7*f^2 - 12*a^2*b^8*c^3*e^6*f^
3 + 8*a^2*b^9*c^2*e^5*f^4 - 90*a^3*b^5*c^5*e^7*f^2 + 132*a^3*b^6*c^4*e^6*f^3 - 76*a^3*b^7*c^3*e^5*f^4 + 6*a^3*
b^8*c^2*e^4*f^5 + 336*a^4*b^3*c^6*e^7*f^2 - 462*a^4*b^4*c^5*e^6*f^3 + 164*a^4*b^5*c^4*e^5*f^4 + 106*a^4*b^6*c^
3*e^4*f^5 - 56*a^4*b^7*c^2*e^3*f^6 + 432*a^5*b^2*c^6*e^6*f^3 + 288*a^5*b^3*c^5*e^5*f^4 - 598*a^5*b^4*c^4*e^4*f
^5 + 102*a^5*b^5*c^3*e^3*f^6 + 90*a^5*b^6*c^2*e^2*f^7 + 720*a^6*b^2*c^5*e^4*f^5 + 336*a^6*b^3*c^4*e^3*f^6 - 31
4*a^6*b^4*c^3*e^2*f^7 + 240*a^7*b^2*c^4*e^2*f^7 + 64*a^3*c^10*d^5*e^2*f^2 - 768*a^4*c^9*d^3*e^4*f^2 + 416*a^4*
c^9*d^4*e^2*f^3 + 1856*a^5*c^8*d^2*e^4*f^3 - 1664*a^5*c^8*d^3*e^2*f^4 + 2336*a^6*c^7*d^2*e^2*f^5 + 26*b^6*c^7*
d^5*e^2*f^2 - 8*b^7*c^6*d^4*e^3*f^2 - 10*b^8*c^5*d^3*e^4*f^2 + 58*b^8*c^5*d^4*e^2*f^3 + 8*b^9*c^4*d^2*e^5*f^2
- 12*b^9*c^4*d^3*e^3*f^3 - 12*b^10*c^3*d^2*e^4*f^3 + 36*b^10*c^3*d^3*e^2*f^4 + 8*b^11*c^2*d^2*e^3*f^4 + 2*a^4*
b^8*c*d*f^8 + 6*a^5*b^7*c*e*f^8 - 384*a^8*b*c^4*e*f^8 - 64*a*b^2*c^10*d^7*f^2 - 216*a*b^4*c^8*d^6*f^3 - 300*a*
b^6*c^6*d^5*f^4 - 240*a*b^8*c^4*d^4*f^5 - 92*a*b^10*c^2*d^3*f^6 + 10*a^2*b^10*c*d^2*f^7 - 12*a^5*b^6*c^2*d*f^8
- 40*a^6*b^4*c^3*d*f^8 + 384*a^7*b^2*c^4*d*f^8 - 2*a^2*b^6*c^5*e^8*f - 2*a^2*b^10*c*e^4*f^5 + 22*a^3*b^4*c^6*
e^8*f + 6*a^3*b^9*c*e^3*f^6 - 80*a^4*b^2*c^7*e^8*f - 8*a^4*b^8*c*e^2*f^7 - 416*a^5*b*c^7*e^7*f^2 - 960*a^6*b*c
^6*e^5*f^4 - 72*a^6*b^5*c^2*e*f^8 - 928*a^7*b*c^5*e^3*f^6 + 288*a^7*b^3*c^3*e*f^8 - 32*a^2*c^11*d^6*e^2*f + 32
*a^3*c^10*d^4*e^4*f + 160*a^4*c^9*d^2*e^6*f - 704*a^5*c^8*d*e^6*f^2 - 1536*a^6*c^7*d*e^4*f^4 - 1472*a^7*c^6*d*
e^2*f^6 - 2*b^4*c^9*d^6*e^2*f + 6*b^5*c^8*d^5*e^3*f - 24*b^5*c^8*d^6*e*f^2 - 8*b^6*c^7*d^4*e^4*f + 6*b^7*c^6*d
^3*e^5*f - 58*b^7*c^6*d^5*e*f^3 - 2*b^8*c^5*d^2*e^6*f - 60*b^9*c^4*d^4*e*f^4 - 26*b^11*c^2*d^3*e*f^5 - 2*b^12*
c*d^2*e^2*f^5 + 16*a*b^2*c^10*d^6*e^2*f - 48*a*b^3*c^9*d^5*e^3*f + 192*a*b^3*c^9*d^6*e*f^2 + 66*a*b^4*c^8*d^4*
e^4*f - 52*a*b^5*c^7*d^3*e^5*f + 576*a*b^5*c^7*d^5*e*f^3 + 14*a*b^6*c^6*d^2*e^6*f + 718*a*b^7*c^5*d^4*e*f^4 -
16*a*b^8*c^4*d*e^6*f^2 + 24*a*b^9*c^3*d*e^5*f^3 + 356*a*b^9*c^3*d^3*e*f^5 - 16*a*b^10*c^2*d*e^4*f^4 + 96*a^2*b
*c^10*d^5*e^3*f - 384*a^2*b*c^10*d^6*e*f^2 - 42*a^2*b^5*c^6*d*e^7*f - 2*a^2*b^10*c*d*e^2*f^6 - 64*a^3*b*c^9*d^
3*e^5*f + 1792*a^3*b*c^9*d^5*e*f^3 + 144*a^3*b^3*c^7*d*e^7*f - 3712*a^4*b*c^8*d^4*e*f^4 + 14*a^4*b^7*c^2*d*e*f
^7 + 2368*a^5*b*c^7*d*e^5*f^3 + 4608*a^5*b*c^7*d^3*e*f^5 + 192*a^5*b^5*c^3*d*e*f^7 + 3808*a^6*b*c^6*d*e^3*f^5
- 3712*a^6*b*c^6*d^2*e*f^6 - 1184*a^6*b^3*c^4*d*e*f^7 - 204*a*b^4*c^8*d^5*e^2*f^2 + 46*a*b^5*c^7*d^4*e^3*f^2 +
132*a*b^6*c^6*d^3*e^4*f^2 - 590*a*b^6*c^6*d^4*e^2*f^3 - 90*a*b^7*c^5*d^2*e^5*f^2 + 64*a*b^7*c^5*d^3*e^3*f^3 +
196*a*b^8*c^4*d^2*e^4*f^3 - 408*a*b^8*c^4*d^3*e^2*f^4 - 188*a*b^9*c^3*d^2*e^3*f^4 + 78*a*b^10*c^2*d^2*e^2*f^5
- 144*a^2*b^2*c^9*d^4*e^4*f + 128*a^2*b^3*c^8*d^3*e^5*f - 1824*a^2*b^3*c^8*d^5*e*f^3 - 6*a^2*b^4*c^7*d^2*e^6*
f - 3096*a^2*b^5*c^6*d^4*e*f^4 + 190*a^2*b^6*c^5*d*e^6*f^2 - 316*a^2*b^7*c^4*d*e^5*f^3 - 1908*a^2*b^7*c^4*d^3*
e*f^5 + 228*a^2*b^8*c^3*d*e^4*f^4 - 58*a^2*b^9*c^2*d*e^3*f^5 + 92*a^2*b^9*c^2*d^2*e*f^6 - 288*a^3*b*c^9*d^4*e^
3*f^2 - 112*a^3*b^2*c^8*d^2*e^6*f + 5664*a^3*b^3*c^7*d^4*e*f^4 - 796*a^3*b^4*c^6*d*e^6*f^2 + 1524*a^3*b^5*c^5*
d*e^5*f^3 + 5120*a^3*b^5*c^5*d^3*e*f^5 - 1176*a^3*b^6*c^4*d*e^4*f^4 + 240*a^3*b^7*c^3*d*e^3*f^5 - 116*a^3*b^7*
c^3*d^2*e*f^6 + 68*a^3*b^8*c^2*d*e^2*f^6 + 192*a^4*b*c^8*d^2*e^5*f^2 + 2240*a^4*b*c^8*d^3*e^3*f^3 + 1344*a^4*b
^2*c^7*d*e^6*f^2 - 3168*a^4*b^3*c^6*d*e^5*f^3 - 7232*a^4*b^3*c^6*d^3*e*f^5 + 2464*a^4*b^4*c^5*d*e^4*f^4 + 78*a
^4*b^5*c^4*d*e^3*f^5 - 1160*a^4*b^5*c^4*d^2*e*f^6 - 574*a^4*b^6*c^3*d*e^2*f^6 - 4928*a^5*b*c^7*d^2*e^3*f^4 - 1
152*a^5*b^2*c^6*d*e^4*f^4 - 2416*a^5*b^3*c^5*d*e^3*f^5 + 4096*a^5*b^3*c^5*d^2*e*f^6 + 1748*a^5*b^4*c^4*d*e^2*f
^6 - 1280*a^6*b^2*c^5*d*e^2*f^6 + 4*a*b^7*c^5*d*e^7*f + 4*a*b^11*c*d*e^3*f^5 - 10*a*b^11*c*d^2*e*f^6 - 4*a^3*b
^9*c*d*e*f^7 - 160*a^4*b*c^8*d*e^7*f + 1792*a^7*b*c^5*d*e*f^7 + 384*a^2*b^2*c^9*d^5*e^2*f^2 + 16*a^2*b^3*c^8*d
^4*e^3*f^2 - 624*a^2*b^4*c^7*d^3*e^4*f^2 + 1962*a^2*b^4*c^7*d^4*e^2*f^3 + 348*a^2*b^5*c^6*d^2*e^5*f^2 + 204*a^
2*b^5*c^6*d^3*e^3*f^3 - 1214*a^2*b^6*c^5*d^2*e^4*f^3 + 1636*a^2*b^6*c^5*d^3*e^2*f^4 + 1520*a^2*b^7*c^4*d^2*e^3
*f^4 - 750*a^2*b^8*c^3*d^2*e^2*f^5 + 1216*a^3*b^2*c^8*d^3*e^4*f^2 - 2224*a^3*b^2*c^8*d^4*e^2*f^3 - 512*a^3*b^3
*c^7*d^2*e^5*f^2 - 1632*a^3*b^3*c^7*d^3*e^3*f^3 + 3492*a^3*b^4*c^6*d^2*e^4*f^3 - 2824*a^3*b^4*c^6*d^3*e^2*f^4
- 5492*a^3*b^5*c^5*d^2*e^3*f^4 + 2868*a^3*b^6*c^4*d^2*e^2*f^5 - 4480*a^4*b^2*c^7*d^2*e^4*f^3 + 2432*a^4*b^2*c^
7*d^3*e^2*f^4 + 8864*a^4*b^3*c^6*d^2*e^3*f^4 - 4206*a^4*b^4*c^5*d^2*e^2*f^5 + 432*a^5*b^2*c^6*d^2*e^2*f^5))/(1
6*a^2*c^6*d^4 + a^4*b^4*f^4 + 16*a^4*c^4*e^4 + b^4*c^4*d^4 + 16*a^6*c^2*f^4 + b^8*d^2*f^2 - 8*a*b^2*c^5*d^4 -
8*a^5*b^2*c*f^4 + 2*a^2*b^6*d*f^3 - 2*a^3*b^5*e*f^3 - 64*a^3*c^5*d^3*f - 64*a^5*c^3*d*f^3 - 2*b^5*c^3*d^3*e +
2*b^6*c^2*d^3*f + a^2*b^4*c^2*e^4 - 8*a^3*b^2*c^3*e^4 + 32*a^3*c^5*d^2*e^2 + a^2*b^6*e^2*f^2 + 96*a^4*c^4*d^2*
f^2 + b^6*c^2*d^2*e^2 + 32*a^5*c^3*e^2*f^2 - 2*a*b^7*d*e*f^2 - 2*b^7*c*d^2*e*f + 54*a^2*b^4*c^2*d^2*f^2 - 112*
a^3*b^2*c^3*d^2*f^2 + 16*a*b^3*c^4*d^3*e - 2*a*b^5*c^2*d*e^3 - 32*a^2*b*c^5*d^3*e - 32*a^3*b*c^4*d*e^3 - 20*a*
b^4*c^3*d^3*f - 12*a*b^6*c*d^2*f^2 - 20*a^3*b^4*c*d*f^3 - 2*a^2*b^5*c*e^3*f - 32*a^4*b*c^3*e^3*f + 16*a^4*b^3*
c*e*f^3 - 32*a^5*b*c^2*e*f^3 - 64*a^4*c^4*d*e^2*f - 6*a*b^4*c^3*d^2*e^2 + 16*a^2*b^3*c^3*d*e^3 + 64*a^2*b^2*c^
4*d^3*f + 64*a^4*b^2*c^2*d*f^3 + 16*a^3*b^3*c^2*e^3*f - 6*a^3*b^4*c*e^2*f^2 - 48*a^2*b^3*c^3*d^2*e*f - 36*a^2*
b^4*c^2*d*e^2*f + 96*a^3*b^2*c^3*d*e^2*f - 48*a^3*b^3*c^2*d*e*f^2 + 4*a*b^6*c*d*e^2*f + 18*a*b^5*c^2*d^2*e*f +
18*a^2*b^5*c*d*e*f^2 + 32*a^3*b*c^4*d^2*e*f + 32*a^4*b*c^3*d*e*f^2)) - (64*A*a^7*c^4*f^8 - A*a^4*b^6*c*f^8 +
32*A*a*c^10*d^6*f^2 - 352*A*a^6*c^5*d*f^7 - A*b^10*c*d^2*f^6 + 8*B*a^4*c^7*e^7*f - 64*B*a^7*c^4*e*f^7 + 12*A*a
^5*b^4*c^2*f^8 - 48*A*a^6*b^2*c^3*f^8 - 224*A*a^2*c^9*d^5*f^3 + 640*A*a^3*c^8*d^4*f^4 - 960*A*a^4*c^7*d^3*f^5
+ 800*A*a^5*c^6*d^2*f^6 - 40*A*a^4*c^7*e^6*f^2 - 80*A*a^5*c^6*e^4*f^4 + 24*A*a^6*c^5*e^2*f^6 - 8*A*b^2*c^9*d^6
*f^2 - 16*A*b^4*c^7*d^5*f^3 - A*b^6*c^5*d^4*f^4 + 6*A*b^8*c^3*d^3*f^5 + 16*B*a^5*c^6*e^5*f^3 - 56*B*a^6*c^5*e^
3*f^5 + 4*B*b^3*c^8*d^6*f^2 + 12*B*b^5*c^6*d^5*f^3 + 4*B*b^7*c^4*d^4*f^4 - 4*B*b^9*c^2*d^3*f^5 + 120*A*a*b^2*c
^8*d^5*f^3 + 60*A*a*b^4*c^6*d^4*f^4 - 36*A*a*b^6*c^4*d^3*f^5 + 8*A*a*b^8*c^2*d^2*f^6 + 20*A*a^3*b^6*c^2*d*f^7
- 80*A*a^4*b^4*c^3*d*f^7 + 216*A*a^5*b^2*c^4*d*f^7 + 4*A*a*b^6*c^4*e^6*f^2 - 6*A*a*b^7*c^3*e^5*f^3 + 4*A*a*b^8
*c^2*e^4*f^4 + 9*A*a^2*b^3*c^6*e^7*f + 2*A*a^2*b^8*c*e^2*f^6 + 88*A*a^4*b*c^6*e^5*f^3 + 172*A*a^5*b*c^5*e^3*f^
5 - 92*B*a*b^3*c^7*d^5*f^3 - 72*B*a*b^5*c^5*d^4*f^4 + 20*B*a*b^7*c^3*d^3*f^5 + 176*B*a^2*b*c^8*d^5*f^3 - 544*B
*a^3*b*c^7*d^4*f^4 + 736*B*a^4*b*c^6*d^3*f^5 + 4*B*a^4*b^5*c^2*d*f^7 - 464*B*a^5*b*c^5*d^2*f^6 - 44*B*a^5*b^3*
c^3*d*f^7 - 2*B*a^3*b^2*c^6*e^7*f - B*a^3*b^7*c*e^2*f^6 - 28*B*a^4*b*c^6*e^6*f^2 - 56*B*a^5*b*c^5*e^4*f^4 - 12
*B*a^5*b^4*c^2*e*f^7 + 36*B*a^6*b*c^4*e^2*f^6 + 48*B*a^6*b^2*c^3*e*f^7 - 16*A*a^2*c^9*d^3*e^4*f + 48*A*a^4*c^7
*d*e^4*f^3 - 168*A*a^5*c^6*d*e^2*f^5 + 2*A*b^2*c^9*d^5*e^2*f - 3*A*b^3*c^8*d^4*e^3*f + 12*A*b^3*c^8*d^5*e*f^2
- 4*A*b^7*c^4*d*e^5*f^2 - 12*A*b^7*c^4*d^3*e*f^4 + 6*A*b^8*c^3*d*e^4*f^3 - 4*A*b^9*c^2*d*e^3*f^4 + 8*A*b^9*c^2
*d^2*e*f^5 + 8*B*a^2*c^9*d^4*e^3*f - 32*B*a^2*c^9*d^5*e*f^2 + 16*B*a^3*c^8*d^2*e^5*f + 64*B*a^3*c^8*d^4*e*f^3
+ 64*B*a^4*c^7*d^3*e*f^4 + 96*B*a^5*c^6*d*e^3*f^4 - 256*B*a^5*c^6*d^2*e*f^5 - B*b^3*c^8*d^5*e^2*f + 2*B*b^4*c^
7*d^4*e^3*f - 8*B*b^4*c^7*d^5*e*f^2 - B*b^6*c^5*d^2*e^5*f - 3*B*b^6*c^5*d^4*e*f^3 + 12*B*b^8*c^3*d^3*e*f^4 - 3
84*A*a^2*b^2*c^7*d^4*f^4 - 32*A*a^2*b^4*c^5*d^3*f^5 - 14*A*a^2*b^6*c^3*d^2*f^6 + 560*A*a^3*b^2*c^6*d^3*f^5 + 5
6*A*a^3*b^4*c^4*d^2*f^6 - 456*A*a^4*b^2*c^5*d^2*f^6 - 38*A*a^2*b^4*c^5*e^6*f^2 + 58*A*a^2*b^5*c^4*e^5*f^3 - 36
*A*a^2*b^6*c^3*e^4*f^4 + 5*A*a^2*b^7*c^2*e^3*f^5 + 98*A*a^3*b^2*c^6*e^6*f^2 - 158*A*a^3*b^3*c^5*e^5*f^3 + 80*A
*a^3*b^4*c^4*e^4*f^4 + 22*A*a^3*b^5*c^3*e^3*f^5 - 22*A*a^3*b^6*c^2*e^2*f^6 + 20*A*a^4*b^2*c^5*e^4*f^4 - 147*A*
a^4*b^3*c^4*e^3*f^5 + 80*A*a^4*b^4*c^3*e^2*f^6 - 102*A*a^5*b^2*c^4*e^2*f^6 + 360*B*a^2*b^3*c^6*d^4*f^4 + 64*B*
a^2*b^5*c^4*d^3*f^5 - 504*B*a^3*b^3*c^5*d^3*f^5 - 40*B*a^3*b^5*c^3*d^2*f^6 + 276*B*a^4*b^3*c^4*d^2*f^6 + 7*B*a
^3*b^3*c^5*e^6*f^2 - 8*B*a^3*b^4*c^4*e^5*f^3 + 2*B*a^3*b^5*c^3*e^4*f^4 + 2*B*a^3*b^6*c^2*e^3*f^5 + 28*B*a^4*b^
2*c^5*e^5*f^3 + 6*B*a^4*b^3*c^4*e^4*f^4 - 26*B*a^4*b^4*c^3*e^3*f^5 + 11*B*a^4*b^5*c^2*e^2*f^6 + 86*B*a^5*b^2*c
^4*e^3*f^5 - 37*B*a^5*b^3*c^3*e^2*f^6 + 120*A*a^2*c^9*d^4*e^2*f^2 + 48*A*a^3*c^8*d^2*e^4*f^2 - 336*A*a^3*c^8*d
^3*e^2*f^3 + 368*A*a^4*c^7*d^2*e^2*f^4 + 4*A*b^4*c^7*d^4*e^2*f^2 - 5*A*b^6*c^5*d^2*e^4*f^2 + 6*A*b^6*c^5*d^3*e
^2*f^3 + 16*A*b^7*c^4*d^2*e^3*f^3 - 18*A*b^8*c^3*d^2*e^2*f^4 - 32*B*a^3*c^8*d^3*e^3*f^2 - 16*B*a^4*c^7*d^2*e^3
*f^3 - 3*B*b^5*c^6*d^4*e^2*f^2 + 4*B*b^6*c^5*d^3*e^3*f^2 + 4*B*b^7*c^4*d^2*e^4*f^2 - 12*B*b^7*c^4*d^3*e^2*f^3
- 6*B*b^8*c^3*d^2*e^3*f^3 + 4*B*b^9*c^2*d^2*e^2*f^4 - 2*A*a^2*b^8*c*d*f^7 - A*a*b^5*c^5*e^7*f - A*a*b^9*c*e^3*
f^5 - 20*A*a^3*b*c^7*e^7*f - 16*B*a*b*c^9*d^6*f^2 + 112*B*a^6*b*c^4*d*f^7 + B*a^4*b^6*c*e*f^7 - 8*A*a*c^10*d^5
*e^2*f - 8*A*a^3*c^8*d*e^6*f + A*b^6*c^5*d*e^6*f + A*b^10*c*d*e^2*f^5 + 224*B*a^6*c^5*d*e*f^6 - B*b^10*c*d^2*e
*f^5 + 12*A*a*b*c^9*d^4*e^3*f - 48*A*a*b*c^9*d^5*e*f^2 - 10*A*a*b^4*c^6*d*e^6*f + 80*A*a^5*b*c^5*d*e*f^6 + 4*B
*a*b*c^9*d^5*e^2*f + B*a*b^5*c^5*d*e^6*f + B*a*b^9*c*d*e^2*f^5 + 4*B*a^3*b*c^7*d*e^6*f - 92*A*a^2*b^2*c^7*d^2*
e^4*f^2 + 132*A*a^2*b^2*c^7*d^3*e^2*f^3 + 446*A*a^2*b^3*c^6*d^2*e^3*f^3 - 604*A*a^2*b^4*c^5*d^2*e^2*f^4 + 340*
A*a^3*b^2*c^6*d^2*e^2*f^4 + 72*B*a^2*b^2*c^7*d^3*e^3*f^2 + 134*B*a^2*b^3*c^6*d^2*e^4*f^2 - 306*B*a^2*b^3*c^6*d
^3*e^2*f^3 - 264*B*a^2*b^4*c^5*d^2*e^3*f^3 + 188*B*a^2*b^5*c^4*d^2*e^2*f^4 + 292*B*a^3*b^2*c^6*d^2*e^3*f^3 + 6
*B*a^3*b^3*c^5*d^2*e^2*f^4 + 4*A*a*b^2*c^8*d^3*e^4*f + 2*A*a*b^3*c^7*d^2*e^5*f - 16*A*a*b^3*c^7*d^4*e*f^3 + 48
*A*a*b^5*c^5*d*e^5*f^2 + 72*A*a*b^5*c^5*d^3*e*f^4 - 84*A*a*b^6*c^4*d*e^4*f^3 + 64*A*a*b^7*c^3*d*e^3*f^4 - 88*A
*a*b^7*c^3*d^2*e*f^5 - 18*A*a*b^8*c^2*d*e^2*f^5 - 8*A*a^2*b*c^8*d^2*e^5*f + 64*A*a^2*b*c^8*d^4*e*f^3 + 26*A*a^
2*b^2*c^7*d*e^6*f + 16*A*a^2*b^7*c^2*d*e*f^6 + 192*A*a^3*b*c^7*d*e^5*f^2 + 96*A*a^3*b*c^7*d^3*e*f^4 - 136*A*a^
3*b^5*c^3*d*e*f^6 + 80*A*a^4*b*c^6*d*e^3*f^4 - 192*A*a^4*b*c^6*d^2*e*f^5 + 268*A*a^4*b^3*c^4*d*e*f^6 - 10*B*a*
b^2*c^8*d^4*e^3*f + 40*B*a*b^2*c^8*d^5*e*f^2 - 2*B*a*b^3*c^7*d^3*e^4*f + 8*B*a*b^4*c^6*d^2*e^5*f + 36*B*a*b^4*
c^6*d^4*e*f^3 - 4*B*a*b^6*c^4*d*e^5*f^2 - 88*B*a*b^6*c^4*d^3*e*f^4 + 6*B*a*b^7*c^3*d*e^4*f^3 - 4*B*a*b^8*c^2*d
*e^3*f^4 + 16*B*a*b^8*c^2*d^2*e*f^5 + 8*B*a^2*b*c^8*d^3*e^4*f - 5*B*a^2*b^3*c^6*d*e^6*f - 8*B*a^3*b^6*c^2*d*e*
f^6 + 40*B*a^4*b*c^6*d*e^4*f^3 + 104*B*a^4*b^4*c^3*d*e*f^6 + 148*B*a^5*b*c^5*d*e^2*f^5 - 344*B*a^5*b^2*c^4*d*e
*f^6 - 46*A*a*b^2*c^8*d^4*e^2*f^2 - 4*A*a*b^3*c^7*d^3*e^3*f^2 + 40*A*a*b^4*c^6*d^2*e^4*f^2 - 36*A*a*b^4*c^6*d^
3*e^2*f^3 - 158*A*a*b^5*c^5*d^2*e^3*f^3 + 196*A*a*b^6*c^4*d^2*e^2*f^4 + 16*A*a^2*b*c^8*d^3*e^3*f^2 - 176*A*a^2
*b^3*c^6*d*e^5*f^2 - 120*A*a^2*b^3*c^6*d^3*e*f^4 + 380*A*a^2*b^4*c^5*d*e^4*f^3 - 324*A*a^2*b^5*c^4*d*e^3*f^4 +
272*A*a^2*b^5*c^4*d^2*e*f^5 + 80*A*a^2*b^6*c^3*d*e^2*f^5 - 280*A*a^3*b*c^7*d^2*e^3*f^3 - 572*A*a^3*b^2*c^6*d*
e^4*f^3 + 508*A*a^3*b^3*c^5*d*e^3*f^4 - 144*A*a^3*b^3*c^5*d^2*e*f^5 - 4*A*a^3*b^4*c^4*d*e^2*f^5 - 326*A*a^4*b^
2*c^5*d*e^2*f^5 + 31*B*a*b^3*c^7*d^4*e^2*f^2 - 32*B*a*b^4*c^6*d^3*e^3*f^2 - 40*B*a*b^5*c^5*d^2*e^4*f^2 + 102*B
*a*b^5*c^5*d^3*e^2*f^3 + 72*B*a*b^6*c^4*d^2*e^3*f^3 - 56*B*a*b^7*c^3*d^2*e^2*f^4 - 76*B*a^2*b*c^8*d^4*e^2*f^2
- 20*B*a^2*b^2*c^7*d^2*e^5*f - 112*B*a^2*b^2*c^7*d^4*e*f^3 + 24*B*a^2*b^4*c^5*d*e^5*f^2 + 192*B*a^2*b^4*c^5*d^
3*e*f^4 - 42*B*a^2*b^5*c^4*d*e^4*f^3 + 32*B*a^2*b^6*c^3*d*e^3*f^4 - 38*B*a^2*b^6*c^3*d^2*e*f^5 - 9*B*a^2*b^7*c
^2*d*e^2*f^5 - 152*B*a^3*b*c^7*d^2*e^4*f^2 + 360*B*a^3*b*c^7*d^3*e^2*f^3 - 32*B*a^3*b^2*c^6*d*e^5*f^2 - 144*B*
a^3*b^2*c^6*d^3*e*f^4 + 62*B*a^3*b^3*c^5*d*e^4*f^3 - 40*B*a^3*b^4*c^4*d*e^3*f^4 - 152*B*a^3*b^4*c^4*d^2*e*f^5
+ 14*B*a^3*b^5*c^3*d*e^2*f^5 - 472*B*a^4*b*c^6*d^2*e^2*f^4 - 120*B*a^4*b^2*c^5*d*e^3*f^4 + 512*B*a^4*b^2*c^5*d
^2*e*f^5 - 13*B*a^4*b^3*c^4*d*e^2*f^5)/(16*a^2*c^6*d^4 + a^4*b^4*f^4 + 16*a^4*c^4*e^4 + b^4*c^4*d^4 + 16*a^6*c
^2*f^4 + b^8*d^2*f^2 - 8*a*b^2*c^5*d^4 - 8*a^5*b^2*c*f^4 + 2*a^2*b^6*d*f^3 - 2*a^3*b^5*e*f^3 - 64*a^3*c^5*d^3*
f - 64*a^5*c^3*d*f^3 - 2*b^5*c^3*d^3*e + 2*b^6*c^2*d^3*f + a^2*b^4*c^2*e^4 - 8*a^3*b^2*c^3*e^4 + 32*a^3*c^5*d^
2*e^2 + a^2*b^6*e^2*f^2 + 96*a^4*c^4*d^2*f^2 + b^6*c^2*d^2*e^2 + 32*a^5*c^3*e^2*f^2 - 2*a*b^7*d*e*f^2 - 2*b^7*
c*d^2*e*f + 54*a^2*b^4*c^2*d^2*f^2 - 112*a^3*b^2*c^3*d^2*f^2 + 16*a*b^3*c^4*d^3*e - 2*a*b^5*c^2*d*e^3 - 32*a^2
*b*c^5*d^3*e - 32*a^3*b*c^4*d*e^3 - 20*a*b^4*c^3*d^3*f - 12*a*b^6*c*d^2*f^2 - 20*a^3*b^4*c*d*f^3 - 2*a^2*b^5*c
*e^3*f - 32*a^4*b*c^3*e^3*f + 16*a^4*b^3*c*e*f^3 - 32*a^5*b*c^2*e*f^3 - 64*a^4*c^4*d*e^2*f - 6*a*b^4*c^3*d^2*e
^2 + 16*a^2*b^3*c^3*d*e^3 + 64*a^2*b^2*c^4*d^3*f + 64*a^4*b^2*c^2*d*f^3 + 16*a^3*b^3*c^2*e^3*f - 6*a^3*b^4*c*e
^2*f^2 - 48*a^2*b^3*c^3*d^2*e*f - 36*a^2*b^4*c^2*d*e^2*f + 96*a^3*b^2*c^3*d*e^2*f - 48*a^3*b^3*c^2*d*e*f^2 + 4
*a*b^6*c*d*e^2*f + 18*a*b^5*c^2*d^2*e*f + 18*a^2*b^5*c*d*e*f^2 + 32*a^3*b*c^4*d^2*e*f + 32*a^4*b*c^3*d*e*f^2)
+ (x*(64*B*a^7*c^4*f^8 + 4*A*a^3*b^7*c*f^8 - 256*A*a^6*b*c^4*f^8 - B*a^4*b^6*c*f^8 + 48*A*a^3*c^8*e^7*f + 256*
A*a^6*c^5*e*f^7 - 320*B*a^6*c^5*d*f^7 + 3*B*b^10*c*d^2*f^6 - 48*A*a^4*b^5*c^2*f^8 + 192*A*a^5*b^3*c^3*f^8 + 12
*B*a^5*b^4*c^2*f^8 - 48*B*a^6*b^2*c^3*f^8 + 256*A*a^4*c^7*e^5*f^3 + 464*A*a^5*c^6*e^3*f^5 - 16*A*b^3*c^8*d^5*f
^3 - 48*A*b^5*c^6*d^4*f^4 - 36*A*b^7*c^4*d^3*f^5 - 4*A*b^9*c^2*d^2*f^6 - 64*B*a^2*c^9*d^5*f^3 + 320*B*a^3*c^8*
d^4*f^4 - 640*B*a^4*c^7*d^3*f^5 + 640*B*a^5*c^6*d^2*f^6 - 16*B*a^4*c^7*e^6*f^2 - 64*B*a^5*c^6*e^4*f^4 + 16*B*a
^6*c^5*e^2*f^6 + 4*B*b^4*c^7*d^5*f^3 + 23*B*b^6*c^5*d^4*f^4 + 22*B*b^8*c^3*d^3*f^5 + 320*A*a*b^3*c^7*d^4*f^4 +
352*A*a*b^5*c^5*d^3*f^5 + 76*A*a*b^7*c^3*d^2*f^6 - 512*A*a^2*b*c^8*d^4*f^4 - 60*A*a^2*b^7*c^2*d*f^7 + 1408*A*
a^3*b*c^7*d^3*f^5 + 352*A*a^3*b^5*c^3*d*f^7 - 1792*A*a^4*b*c^6*d^2*f^6 - 976*A*a^4*b^3*c^4*d*f^7 - 6*A*a*b^5*c
^5*e^6*f^2 + 4*A*a*b^6*c^4*e^5*f^3 + 4*A*a*b^7*c^3*e^4*f^4 - 6*A*a*b^8*c^2*e^3*f^5 - 20*A*a^2*b^2*c^7*e^7*f -
144*A*a^3*b*c^7*e^6*f^2 + 68*A*a^3*b^6*c^2*e*f^7 - 640*A*a^4*b*c^6*e^4*f^4 - 240*A*a^4*b^4*c^3*e*f^7 - 848*A*a
^5*b*c^5*e^2*f^6 + 192*A*a^5*b^2*c^4*e*f^7 - 132*B*a*b^4*c^6*d^4*f^4 - 196*B*a*b^6*c^4*d^3*f^5 - 40*B*a*b^8*c^
2*d^2*f^6 - 20*B*a^3*b^6*c^2*d*f^7 + 52*B*a^4*b^4*c^3*d*f^7 + 64*B*a^5*b^2*c^4*d*f^7 + 2*B*a^2*b^3*c^6*e^7*f +
B*a^2*b^8*c*e^2*f^6 + 16*B*a^4*b*c^6*e^5*f^3 + 120*B*a^5*b*c^5*e^3*f^5 + 64*A*a^2*c^9*d^2*e^5*f + 512*A*a^2*c
^9*d^4*e*f^3 - 384*A*a^3*c^8*d*e^5*f^2 - 1408*A*a^3*c^8*d^3*e*f^4 - 1280*A*a^4*c^7*d*e^3*f^4 + 1792*A*a^4*c^7*
d^2*e*f^5 - 4*A*b^2*c^9*d^4*e^3*f + 16*A*b^2*c^9*d^5*e*f^2 + 8*A*b^3*c^8*d^3*e^4*f - 2*A*b^4*c^7*d^2*e^5*f + 8
0*A*b^4*c^7*d^4*e*f^3 + 6*A*b^6*c^5*d*e^5*f^2 + 76*A*b^6*c^5*d^3*e*f^4 - 4*A*b^7*c^4*d*e^4*f^3 - 4*A*b^8*c^3*d
*e^3*f^4 - 2*A*b^8*c^3*d^2*e*f^5 + 6*A*b^9*c^2*d*e^2*f^5 - 32*B*a^2*c^9*d^3*e^4*f - 96*B*a^4*c^7*d*e^4*f^3 - 1
92*B*a^5*c^6*d*e^2*f^5 + 2*B*b^3*c^8*d^4*e^3*f - 8*B*b^3*c^8*d^5*e*f^2 - 6*B*b^4*c^7*d^3*e^4*f + 4*B*b^5*c^6*d
^2*e^5*f - 48*B*b^5*c^6*d^4*e*f^3 - 60*B*b^7*c^4*d^3*e*f^4 - 8*B*b^9*c^2*d^2*e*f^5 + 4*A*a*b^9*c*d*f^7 - 2*A*b
^10*c*d*e*f^6 - 1184*A*a^2*b^3*c^6*d^3*f^5 - 544*A*a^2*b^5*c^4*d^2*f^6 + 1664*A*a^3*b^3*c^5*d^2*f^6 + 60*A*a^2
*b^3*c^6*e^6*f^2 - 30*A*a^2*b^4*c^5*e^5*f^3 - 64*A*a^2*b^5*c^4*e^4*f^4 + 72*A*a^2*b^6*c^3*e^3*f^5 - 12*A*a^2*b
^7*c^2*e^2*f^6 - 8*A*a^3*b^2*c^6*e^5*f^3 + 352*A*a^3*b^3*c^5*e^4*f^4 - 268*A*a^3*b^4*c^4*e^3*f^5 - 52*A*a^3*b^
5*c^3*e^2*f^6 + 188*A*a^4*b^2*c^5*e^3*f^5 + 484*A*a^4*b^3*c^4*e^2*f^6 + 80*B*a^2*b^2*c^7*d^4*f^4 + 520*B*a^2*b
^4*c^5*d^3*f^5 + 210*B*a^2*b^6*c^3*d^2*f^6 - 192*B*a^3*b^2*c^6*d^3*f^5 - 456*B*a^3*b^4*c^4*d^2*f^6 + 96*B*a^4*
b^2*c^5*d^2*f^6 - 7*B*a^2*b^4*c^5*e^6*f^2 + 8*B*a^2*b^5*c^4*e^5*f^3 - 2*B*a^2*b^6*c^3*e^4*f^4 - 2*B*a^2*b^7*c^
2*e^3*f^5 + 32*B*a^3*b^2*c^6*e^6*f^2 - 36*B*a^3*b^3*c^5*e^5*f^3 - 4*B*a^3*b^4*c^4*e^4*f^4 + 28*B*a^3*b^5*c^3*e
^3*f^5 - 12*B*a^3*b^6*c^2*e^2*f^6 + 64*B*a^4*b^2*c^5*e^4*f^4 - 110*B*a^4*b^3*c^4*e^3*f^5 + 47*B*a^4*b^4*c^3*e^
2*f^6 - 64*B*a^5*b^2*c^4*e^2*f^6 - 384*A*a^2*c^9*d^3*e^3*f^2 + 1184*A*a^3*c^8*d^2*e^3*f^3 - 28*A*b^3*c^8*d^4*e
^2*f^2 - 12*A*b^4*c^7*d^3*e^3*f^2 + 20*A*b^5*c^6*d^2*e^4*f^2 - 36*A*b^5*c^6*d^3*e^2*f^3 - 44*A*b^6*c^5*d^2*e^3
*f^3 + 32*A*b^7*c^4*d^2*e^2*f^4 + 144*B*a^2*c^9*d^4*e^2*f^2 + 192*B*a^3*c^8*d^2*e^4*f^2 - 448*B*a^3*c^8*d^3*e^
2*f^3 + 480*B*a^4*c^7*d^2*e^2*f^4 + 23*B*b^4*c^7*d^4*e^2*f^2 - 4*B*b^5*c^6*d^3*e^3*f^2 - 13*B*b^6*c^5*d^2*e^4*
f^2 + 48*B*b^6*c^5*d^3*e^2*f^3 + 12*B*b^7*c^4*d^2*e^3*f^3 + 2*B*b^8*c^3*d^2*e^2*f^4 + 64*A*a*b*c^9*d^5*f^3 + 1
088*A*a^5*b*c^5*d*f^7 + 2*A*a*b^4*c^6*e^7*f + 2*A*a*b^9*c*e^2*f^6 - 6*A*a^2*b^8*c*e*f^7 + 2*B*a^2*b^8*c*d*f^7
- 8*B*a^3*b*c^7*e^7*f + 16*A*a*c^10*d^4*e^3*f - 64*A*a*c^10*d^5*e*f^2 - 1088*A*a^5*c^6*d*e*f^6 - 2*A*b^5*c^6*d
*e^6*f - 32*B*a^3*c^8*d*e^6*f - 32*A*a*b*c^9*d^3*e^4*f + 24*A*a*b^3*c^7*d*e^6*f + 24*A*a*b^8*c^2*d*e*f^6 - 64*
A*a^2*b*c^8*d*e^6*f - 8*B*a*b*c^9*d^4*e^3*f + 32*B*a*b*c^9*d^5*e*f^2 - 6*B*a*b^4*c^6*d*e^6*f + 288*B*a^5*b*c^5
*d*e*f^6 - 1496*A*a^2*b^2*c^7*d^2*e^3*f^3 + 1496*A*a^2*b^3*c^6*d^2*e^2*f^4 - 272*B*a^2*b^2*c^7*d^2*e^4*f^2 + 6
40*B*a^2*b^2*c^7*d^3*e^2*f^3 + 636*B*a^2*b^3*c^6*d^2*e^3*f^3 - 286*B*a^2*b^4*c^5*d^2*e^2*f^4 + 192*B*a^3*b^2*c
^6*d^2*e^2*f^4 + 112*A*a*b*c^9*d^4*e^2*f^2 - 8*A*a*b^2*c^8*d^2*e^5*f - 448*A*a*b^2*c^8*d^4*e*f^3 - 88*A*a*b^4*
c^6*d*e^5*f^2 - 576*A*a*b^4*c^6*d^3*e*f^4 + 84*A*a*b^5*c^5*d*e^4*f^3 + 32*A*a*b^6*c^4*d*e^3*f^4 + 12*A*a*b^6*c
^4*d^2*e*f^5 - 80*A*a*b^7*c^3*d*e^2*f^5 - 108*A*a^2*b^6*c^3*d*e*f^6 + 736*A*a^3*b*c^7*d*e^4*f^3 + 192*A*a^3*b^
4*c^4*d*e*f^6 + 2048*A*a^4*b*c^6*d*e^2*f^5 + 208*A*a^4*b^2*c^5*d*e*f^6 + 32*B*a*b^2*c^8*d^3*e^4*f - 20*B*a*b^3
*c^7*d^2*e^5*f + 288*B*a*b^3*c^7*d^4*e*f^3 + 20*B*a*b^5*c^5*d*e^5*f^2 + 480*B*a*b^5*c^5*d^3*e*f^4 - 20*B*a*b^6
*c^4*d*e^4*f^3 + 72*B*a*b^7*c^3*d^2*e*f^5 + 10*B*a*b^8*c^2*d*e^2*f^5 + 16*B*a^2*b*c^8*d^2*e^5*f - 384*B*a^2*b*
c^8*d^4*e*f^3 + 32*B*a^2*b^2*c^7*d*e^6*f + 44*B*a^2*b^7*c^2*d*e*f^6 + 192*B*a^3*b*c^7*d*e^5*f^2 + 960*B*a^3*b*
c^7*d^3*e*f^4 - 160*B*a^3*b^5*c^3*d*e*f^6 + 544*B*a^4*b*c^6*d*e^3*f^4 - 896*B*a^4*b*c^6*d^2*e*f^5 + 120*B*a^4*
b^3*c^4*d*e*f^6 - 4*B*a*b^9*c*d*e*f^6 + 144*A*a*b^2*c^8*d^3*e^3*f^2 - 144*A*a*b^3*c^7*d^2*e^4*f^2 + 112*A*a*b^
3*c^7*d^3*e^2*f^3 + 476*A*a*b^4*c^6*d^2*e^3*f^3 - 412*A*a*b^5*c^5*d^2*e^2*f^4 + 256*A*a^2*b*c^8*d^2*e^4*f^2 +
128*A*a^2*b*c^8*d^3*e^2*f^3 + 352*A*a^2*b^2*c^7*d*e^5*f^2 + 1440*A*a^2*b^2*c^7*d^3*e*f^4 - 456*A*a^2*b^3*c^6*d
*e^4*f^3 - 116*A*a^2*b^4*c^5*d*e^3*f^4 + 224*A*a^2*b^4*c^5*d^2*e*f^5 + 452*A*a^2*b^5*c^4*d*e^2*f^5 - 1440*A*a^
3*b*c^7*d^2*e^2*f^4 + 528*A*a^3*b^2*c^6*d*e^3*f^4 - 1408*A*a^3*b^2*c^6*d^2*e*f^5 - 1424*A*a^3*b^3*c^5*d*e^2*f^
5 - 128*B*a*b^2*c^8*d^4*e^2*f^2 + 8*B*a*b^3*c^7*d^3*e^3*f^2 + 108*B*a*b^4*c^6*d^2*e^4*f^2 - 324*B*a*b^4*c^6*d^
3*e^2*f^3 - 164*B*a*b^5*c^5*d^2*e^3*f^3 + 44*B*a*b^6*c^4*d^2*e^2*f^4 + 32*B*a^2*b*c^8*d^3*e^3*f^2 - 128*B*a^2*
b^3*c^6*d*e^5*f^2 - 1200*B*a^2*b^3*c^6*d^3*e*f^4 + 142*B*a^2*b^4*c^5*d*e^4*f^3 + 20*B*a^2*b^5*c^4*d*e^3*f^4 -
304*B*a^2*b^5*c^4*d^2*e*f^5 - 112*B*a^2*b^6*c^3*d*e^2*f^5 - 688*B*a^3*b*c^7*d^2*e^3*f^3 - 224*B*a^3*b^2*c^6*d*
e^4*f^3 - 216*B*a^3*b^3*c^5*d*e^3*f^4 + 800*B*a^3*b^3*c^5*d^2*e*f^5 + 460*B*a^3*b^4*c^4*d*e^2*f^5 - 640*B*a^4*
b^2*c^5*d*e^2*f^5))/(16*a^2*c^6*d^4 + a^4*b^4*f^4 + 16*a^4*c^4*e^4 + b^4*c^4*d^4 + 16*a^6*c^2*f^4 + b^8*d^2*f^
2 - 8*a*b^2*c^5*d^4 - 8*a^5*b^2*c*f^4 + 2*a^2*b^6*d*f^3 - 2*a^3*b^5*e*f^3 - 64*a^3*c^5*d^3*f - 64*a^5*c^3*d*f^
3 - 2*b^5*c^3*d^3*e + 2*b^6*c^2*d^3*f + a^2*b^4*c^2*e^4 - 8*a^3*b^2*c^3*e^4 + 32*a^3*c^5*d^2*e^2 + a^2*b^6*e^2
*f^2 + 96*a^4*c^4*d^2*f^2 + b^6*c^2*d^2*e^2 + 32*a^5*c^3*e^2*f^2 - 2*a*b^7*d*e*f^2 - 2*b^7*c*d^2*e*f + 54*a^2*
b^4*c^2*d^2*f^2 - 112*a^3*b^2*c^3*d^2*f^2 + 16*a*b^3*c^4*d^3*e - 2*a*b^5*c^2*d*e^3 - 32*a^2*b*c^5*d^3*e - 32*a
^3*b*c^4*d*e^3 - 20*a*b^4*c^3*d^3*f - 12*a*b^6*c*d^2*f^2 - 20*a^3*b^4*c*d*f^3 - 2*a^2*b^5*c*e^3*f - 32*a^4*b*c
^3*e^3*f + 16*a^4*b^3*c*e*f^3 - 32*a^5*b*c^2*e*f^3 - 64*a^4*c^4*d*e^2*f - 6*a*b^4*c^3*d^2*e^2 + 16*a^2*b^3*c^3
*d*e^3 + 64*a^2*b^2*c^4*d^3*f + 64*a^4*b^2*c^2*d*f^3 + 16*a^3*b^3*c^2*e^3*f - 6*a^3*b^4*c*e^2*f^2 - 48*a^2*b^3
*c^3*d^2*e*f - 36*a^2*b^4*c^2*d*e^2*f + 96*a^3*b^2*c^3*d*e^2*f - 48*a^3*b^3*c^2*d*e*f^2 + 4*a*b^6*c*d*e^2*f +
18*a*b^5*c^2*d^2*e*f + 18*a^2*b^5*c*d*e*f^2 + 32*a^3*b*c^4*d^2*e*f + 32*a^4*b*c^3*d*e*f^2)) - (56*A^2*a^3*b^3*
c^3*f^7 - 13*A^2*a^2*b^5*c^2*f^7 - 24*A^2*a^2*c^7*e^5*f^2 - 16*A^2*b^3*c^6*d^3*f^4 - A^2*b^5*c^4*d^2*f^5 + 2*A
^2*b^4*c^5*e^5*f^2 - A^2*b^5*c^4*e^4*f^3 - A^2*b^6*c^3*e^3*f^4 + 2*A^2*b^7*c^2*e^2*f^5 - 12*B^2*a^4*c^5*e^3*f^
4 - 8*B^2*b^3*c^6*d^4*f^3 - 9*B^2*b^5*c^4*d^3*f^4 + 64*A*B*a^5*c^4*f^7 + A^2*a*b^7*c*f^7 - A^2*b^8*c*e*f^6 - 8
0*A^2*a^4*b*c^4*f^7 - 16*A^2*b*c^8*d^4*f^3 + 28*A^2*a^4*c^5*e*f^6 - 2*A^2*b^7*c^2*d*f^6 - A^2*b^3*c^6*e^6*f -
16*B^2*a^5*c^4*e*f^6 - 4*A^2*c^9*d^3*e^3*f + 12*A^2*c^9*d^4*e*f^2 + 48*A^2*a*b*c^7*d^3*f^4 + 22*A^2*a*b^5*c^3*
d*f^6 + 48*A^2*a^3*b*c^5*d*f^6 + 12*A^2*a*b^6*c^2*e*f^6 + 16*B^2*a*b*c^7*d^4*f^3 + 64*B^2*a^4*b*c^4*d*f^6 - 16
*A^2*a*c^8*d^3*e*f^3 + 80*A^2*a^3*c^6*d*e*f^5 + 4*A^2*b*c^8*d^2*e^4*f + A^2*b^2*c^7*d*e^5*f + 2*A^2*b^6*c^3*d*
e*f^5 + 4*B^2*a^2*c^7*d*e^5*f - 64*B^2*a^4*c^5*d*e*f^5 + A*B*b^8*c*d*f^6 + 8*A^2*a*b^3*c^5*d^2*f^5 - 64*A^2*a^
2*b^3*c^4*d*f^6 - 2*A^2*a*b^2*c^6*e^5*f^2 - 10*A^2*a*b^3*c^5*e^4*f^3 + 20*A^2*a*b^4*c^4*e^3*f^4 - 25*A^2*a*b^5
*c^3*e^2*f^5 + 56*A^2*a^2*b*c^6*e^4*f^3 - 44*A^2*a^2*b^4*c^3*e*f^6 - 76*A^2*a^3*b*c^5*e^2*f^5 + 40*A^2*a^3*b^2
*c^4*e*f^6 + 56*B^2*a*b^3*c^5*d^3*f^4 - 2*B^2*a*b^5*c^3*d^2*f^5 - 96*B^2*a^2*b*c^6*d^3*f^4 + 11*B^2*a^2*b^5*c^
2*d*f^6 + 16*B^2*a^3*b*c^5*d^2*f^5 - 40*B^2*a^3*b^3*c^3*d*f^6 + 16*B^2*a^4*b*c^4*e^2*f^5 + 3*B^2*a^4*b^2*c^3*e
*f^6 + 24*A^2*a*c^8*d^2*e^3*f^2 + 92*A^2*a^2*c^7*d*e^3*f^3 - 104*A^2*a^2*c^7*d^2*e*f^4 - 4*A^2*b*c^8*d^3*e^2*f
^2 + 20*A^2*b^2*c^7*d^3*e*f^3 - A^2*b^4*c^5*d*e^3*f^3 - 8*A^2*b^4*c^5*d^2*e*f^4 + 32*B^2*a^2*c^7*d^3*e*f^3 - 8
*B^2*a^3*c^6*d*e^3*f^3 + 48*B^2*a^3*c^6*d^2*e*f^4 - B^2*b^2*c^7*d^3*e^3*f + 3*B^2*b^2*c^7*d^4*e*f^2 + B^2*b^3*
c^6*d^2*e^4*f + 8*B^2*b^4*c^5*d^3*e*f^3 - 3*B^2*b^6*c^3*d^2*e*f^4 - A*B*a^2*b^6*c*f^7 - 32*A*B*a*c^8*d^4*f^3 -
32*A*B*a^4*c^5*d*f^6 - 8*A*B*a^2*c^7*e^6*f + 4*A^2*a*b*c^7*e^6*f - B^2*a*b^7*c*d*f^6 - 8*A^2*a*c^8*d*e^5*f -
65*A^2*a^2*b^2*c^5*e^3*f^4 + 88*A^2*a^2*b^3*c^4*e^2*f^5 + 8*B^2*a^2*b^3*c^4*d^2*f^5 + 2*B^2*a^3*b^2*c^4*e^3*f^
4 - 3*B^2*a^3*b^3*c^3*e^2*f^5 - 13*A^2*b^2*c^7*d^2*e^3*f^2 + 16*A^2*b^3*c^6*d^2*e^2*f^3 - 28*B^2*a^2*c^7*d^2*e
^3*f^2 + B^2*b^3*c^6*d^3*e^2*f^2 - 5*B^2*b^4*c^5*d^2*e^3*f^2 + 7*B^2*b^5*c^4*d^2*e^2*f^3 + 12*A*B*a^3*b^4*c^2*
f^7 - 48*A*B*a^4*b^2*c^3*f^7 + 160*A*B*a^2*c^7*d^3*f^4 - 160*A*B*a^3*c^6*d^2*f^5 - 16*A*B*a^3*c^6*e^4*f^3 + 48
*A*B*a^4*c^5*e^2*f^5 + 24*A*B*b^2*c^7*d^4*f^3 + 24*A*B*b^4*c^5*d^3*f^4 - A*B*b^6*c^3*d^2*f^5 + 20*B^2*a*b^2*c^
6*d^2*e^3*f^2 - 49*B^2*a*b^3*c^5*d^2*e^2*f^3 + 96*B^2*a^2*b*c^6*d^2*e^2*f^3 + 19*B^2*a^2*b^2*c^5*d*e^3*f^3 - 1
02*B^2*a^2*b^2*c^5*d^2*e*f^4 + 3*B^2*a^2*b^3*c^4*d*e^2*f^4 - 120*A*B*a*b^2*c^6*d^3*f^4 + 4*A*B*a*b^4*c^4*d^2*f
^5 + 24*A*B*a^2*b^4*c^3*d*f^6 - 8*A*B*a^3*b^2*c^4*d*f^6 - 7*A*B*a*b^3*c^5*e^5*f^2 + 8*A*B*a*b^4*c^4*e^4*f^3 -
2*A*B*a*b^5*c^3*e^3*f^4 - 2*A*B*a*b^6*c^2*e^2*f^5 + 28*A*B*a^2*b*c^6*e^5*f^2 - 11*A*B*a^2*b^5*c^2*e*f^6 + 72*A
*B*a^3*b*c^5*e^3*f^4 + 34*A*B*a^3*b^3*c^3*e*f^6 + 16*A*B*a*c^8*d^3*e^2*f^2 + 80*A*B*a^2*c^7*d*e^4*f^2 + 16*A*B
*a^3*c^6*d*e^2*f^4 - 4*A*B*b^2*c^7*d^2*e^4*f - 22*A*B*b^3*c^6*d^3*e*f^3 + 3*A*B*b^4*c^5*d*e^4*f^2 - 6*A*B*b^5*
c^4*d*e^3*f^3 + 15*A*B*b^5*c^4*d^2*e*f^4 + 4*A*B*b^6*c^3*d*e^2*f^4 + 12*A^2*a*b*c^7*d*e^4*f^2 - 28*A^2*a*b^4*c
^4*d*e*f^5 - 2*B^2*a*b^2*c^6*d*e^5*f + 2*B^2*a*b^6*c^2*d*e*f^5 + A*B*a*b^7*c*e*f^6 + 24*A*B*a^2*b^2*c^5*d^2*f^
5 - 28*A*B*a^2*b^2*c^5*e^4*f^3 - 9*A*B*a^2*b^3*c^4*e^3*f^4 + 29*A*B*a^2*b^4*c^3*e^2*f^5 - 100*A*B*a^3*b^2*c^4*
e^2*f^5 - 208*A*B*a^2*c^7*d^2*e^2*f^3 + 13*A*B*b^3*c^6*d^2*e^3*f^2 - 23*A*B*b^4*c^5*d^2*e^2*f^3 - 52*A^2*a*b*c
^7*d^2*e^2*f^3 - 34*A^2*a*b^2*c^6*d*e^3*f^3 + 48*A^2*a*b^2*c^6*d^2*e*f^4 + 40*A^2*a*b^3*c^5*d*e^2*f^4 - 108*A^
2*a^2*b*c^6*d*e^2*f^4 + 36*A^2*a^2*b^2*c^5*d*e*f^5 - 8*B^2*a*b*c^7*d^3*e^2*f^2 - 24*B^2*a*b^2*c^6*d^3*e*f^3 +
7*B^2*a*b^3*c^5*d*e^4*f^2 - 8*B^2*a*b^4*c^4*d*e^3*f^3 + 32*B^2*a*b^4*c^4*d^2*e*f^4 + 2*B^2*a*b^5*c^3*d*e^2*f^4
- 16*B^2*a^2*b*c^6*d*e^4*f^2 - 20*B^2*a^2*b^4*c^3*d*e*f^5 + 8*B^2*a^3*b*c^5*d*e^2*f^4 + 40*B^2*a^3*b^2*c^4*d*
e*f^5 - 10*A*B*a*b^6*c^2*d*f^6 + 2*A*B*a*b^2*c^6*e^6*f - 20*A*B*a^4*b*c^4*e*f^6 + 4*A*B*b*c^8*d^3*e^3*f - 12*A
*B*b*c^8*d^4*e*f^2 - 2*A*B*b^7*c^2*d*e*f^5 + 132*A*B*a*b^2*c^6*d^2*e^2*f^3 + 96*A*B*a^2*b^2*c^5*d*e^2*f^4 + 24
*A*B*a*b*c^7*d^3*e*f^3 + 20*A*B*a*b^5*c^3*d*e*f^5 - 24*A*B*a^3*b*c^5*d*e*f^5 - 24*A*B*a*b*c^7*d^2*e^3*f^2 - 44
*A*B*a*b^2*c^6*d*e^4*f^2 + 84*A*B*a*b^3*c^5*d*e^3*f^3 - 122*A*B*a*b^3*c^5*d^2*e*f^4 - 54*A*B*a*b^4*c^4*d*e^2*f
^4 - 180*A*B*a^2*b*c^6*d*e^3*f^3 + 288*A*B*a^2*b*c^6*d^2*e*f^4 - 18*A*B*a^2*b^3*c^4*d*e*f^5 + 4*A*B*a*b*c^7*d*
e^5*f)/(16*a^2*c^6*d^4 + a^4*b^4*f^4 + 16*a^4*c^4*e^4 + b^4*c^4*d^4 + 16*a^6*c^2*f^4 + b^8*d^2*f^2 - 8*a*b^2*c
^5*d^4 - 8*a^5*b^2*c*f^4 + 2*a^2*b^6*d*f^3 - 2*a^3*b^5*e*f^3 - 64*a^3*c^5*d^3*f - 64*a^5*c^3*d*f^3 - 2*b^5*c^3
*d^3*e + 2*b^6*c^2*d^3*f + a^2*b^4*c^2*e^4 - 8*a^3*b^2*c^3*e^4 + 32*a^3*c^5*d^2*e^2 + a^2*b^6*e^2*f^2 + 96*a^4
*c^4*d^2*f^2 + b^6*c^2*d^2*e^2 + 32*a^5*c^3*e^2*f^2 - 2*a*b^7*d*e*f^2 - 2*b^7*c*d^2*e*f + 54*a^2*b^4*c^2*d^2*f
^2 - 112*a^3*b^2*c^3*d^2*f^2 + 16*a*b^3*c^4*d^3*e - 2*a*b^5*c^2*d*e^3 - 32*a^2*b*c^5*d^3*e - 32*a^3*b*c^4*d*e^
3 - 20*a*b^4*c^3*d^3*f - 12*a*b^6*c*d^2*f^2 - 20*a^3*b^4*c*d*f^3 - 2*a^2*b^5*c*e^3*f - 32*a^4*b*c^3*e^3*f + 16
*a^4*b^3*c*e*f^3 - 32*a^5*b*c^2*e*f^3 - 64*a^4*c^4*d*e^2*f - 6*a*b^4*c^3*d^2*e^2 + 16*a^2*b^3*c^3*d*e^3 + 64*a
^2*b^2*c^4*d^3*f + 64*a^4*b^2*c^2*d*f^3 + 16*a^3*b^3*c^2*e^3*f - 6*a^3*b^4*c*e^2*f^2 - 48*a^2*b^3*c^3*d^2*e*f
- 36*a^2*b^4*c^2*d*e^2*f + 96*a^3*b^2*c^3*d*e^2*f - 48*a^3*b^3*c^2*d*e*f^2 + 4*a*b^6*c*d*e^2*f + 18*a*b^5*c^2*
d^2*e*f + 18*a^2*b^5*c*d*e*f^2 + 32*a^3*b*c^4*d^2*e*f + 32*a^4*b*c^3*d*e*f^2) + (x*(104*A^2*a^4*c^5*f^7 - 32*B
^2*a^5*c^4*f^7 + 8*A^2*c^9*d^4*f^3 + A^2*b^8*c*f^7 + 50*A^2*a^2*b^4*c^3*f^7 - 96*A^2*a^3*b^2*c^4*f^7 - 12*B^2*
a^3*b^4*c^2*f^7 + 42*B^2*a^4*b^2*c^3*f^7 + 208*A^2*a^2*c^7*d^2*f^5 + 36*A^2*a^2*c^7*e^4*f^3 + 72*A^2*a^3*c^6*e
^2*f^5 + 8*A^2*b^2*c^7*d^3*f^4 + 18*A^2*b^4*c^5*d^2*f^5 - 32*B^2*a^2*c^7*d^3*f^4 + 32*B^2*a^3*c^6*d^2*f^5 - 2*
A^2*b^3*c^6*e^5*f^2 + A^2*b^4*c^5*e^4*f^3 + A^2*b^6*c^3*e^2*f^5 + 24*B^2*a^3*c^6*e^4*f^3 + 56*B^2*a^4*c^5*e^2*
f^5 + 2*B^2*b^2*c^7*d^4*f^3 - 6*B^2*b^4*c^5*d^3*f^4 + 9*B^2*b^6*c^3*d^2*f^5 - 16*A^2*c^9*d^3*e^2*f^2 - 12*A^2*
a*b^6*c^2*f^7 + B^2*a^2*b^6*c*f^7 - 64*A^2*a*c^8*d^3*f^4 - 256*A^2*a^3*c^6*d*f^6 + 2*A^2*b^6*c^3*d*f^6 + 32*B^
2*a^4*c^5*d*f^6 + A^2*b^2*c^7*e^6*f - 2*A^2*b^7*c^2*e*f^6 + 4*B^2*a^2*c^7*e^6*f + 4*A^2*c^9*d^2*e^4*f - 36*A^2
*a*b^4*c^4*d*f^6 - 4*A^2*a*b*c^7*e^5*f^2 + 22*A^2*a*b^5*c^3*e*f^6 - 16*A^2*a^3*b*c^5*e*f^6 - 2*B^2*a*b^6*c^2*d
*f^6 - 40*B^2*a^4*b*c^4*e*f^6 + 8*A^2*a*c^8*d*e^4*f^2 + 16*A^2*b*c^8*d^3*e*f^3 + 6*A^2*b^5*c^4*d*e*f^5 - 2*A*B
*a*b^7*c*f^7 - 144*A^2*a*b^2*c^6*d^2*f^5 + 168*A^2*a^2*b^2*c^5*d*f^6 + 2*A^2*a*b^2*c^6*e^4*f^3 + 10*A^2*a*b^3*
c^5*e^3*f^4 - 18*A^2*a*b^4*c^4*e^2*f^5 - 80*A^2*a^2*b*c^6*e^3*f^4 - 56*A^2*a^2*b^3*c^4*e*f^6 + 24*B^2*a*b^2*c^
6*d^3*f^4 - 64*B^2*a*b^4*c^4*d^2*f^5 + 26*B^2*a^2*b^4*c^3*d*f^6 - 88*B^2*a^3*b^2*c^4*d*f^6 - 12*B^2*a^2*b*c^6*
e^5*f^2 - 40*B^2*a^3*b*c^5*e^3*f^4 + 6*B^2*a^3*b^3*c^3*e*f^6 + 8*A^2*a*c^8*d^2*e^2*f^3 - 128*A^2*a^2*c^7*d*e^2
*f^4 + 8*A^2*b*c^8*d^2*e^3*f^2 + 4*A^2*b^2*c^7*d*e^4*f^2 + 10*A^2*b^3*c^6*d*e^3*f^3 - 18*A^2*b^4*c^5*d*e^2*f^4
- 32*B^2*a^2*c^7*d*e^4*f^2 - 80*B^2*a^3*c^6*d*e^2*f^4 + B^2*b^2*c^7*d^2*e^4*f + 10*B^2*b^3*c^6*d^3*e*f^3 - 12
*B^2*b^5*c^4*d^2*e*f^4 + 72*A*B*a^4*b*c^4*f^7 - 8*A*B*b*c^8*d^4*f^3 - 176*A*B*a^4*c^5*e*f^6 + 2*A*B*b^7*c^2*d*
f^6 - 4*A^2*b*c^8*d*e^5*f + 54*A^2*a^2*b^2*c^5*e^2*f^5 + 84*B^2*a^2*b^2*c^5*d^2*f^5 + 9*B^2*a^2*b^2*c^5*e^4*f^
3 + 2*B^2*a^3*b^2*c^4*e^2*f^5 - 26*A^2*b^2*c^7*d^2*e^2*f^3 + 88*B^2*a^2*c^7*d^2*e^2*f^3 - 4*B^2*b^2*c^7*d^3*e^
2*f^2 - 4*B^2*b^3*c^6*d^2*e^3*f^2 + 8*B^2*b^4*c^5*d^2*e^2*f^3 + 24*A*B*a^2*b^5*c^2*f^7 - 84*A*B*a^3*b^3*c^3*f^
7 + 8*A*B*a^2*c^7*e^5*f^2 - 32*A*B*a^3*c^6*e^3*f^4 + 4*A*B*b^3*c^6*d^3*f^4 - 20*A*B*b^5*c^4*d^2*f^5 - 4*B^2*a*
b*c^7*d*e^5*f - 78*B^2*a*b^2*c^6*d^2*e^2*f^3 - 48*B^2*a^2*b^2*c^5*d*e^2*f^4 + 148*A*B*a*b^3*c^5*d^2*f^5 - 192*
A*B*a^2*b*c^6*d^2*f^5 - 4*A*B*a^2*b^3*c^4*d*f^6 + 10*A*B*a*b^2*c^6*e^5*f^2 - 2*A*B*a*b^3*c^5*e^4*f^3 - 12*A*B*
a*b^4*c^4*e^3*f^4 + 8*A*B*a*b^5*c^3*e^2*f^5 - 52*A*B*a^2*b*c^6*e^4*f^3 - 44*A*B*a^2*b^4*c^3*e*f^6 - 48*A*B*a^3
*b*c^5*e^2*f^5 + 204*A*B*a^3*b^2*c^4*e*f^6 - 48*A*B*a*c^8*d^2*e^3*f^2 - 48*A*B*a^2*c^7*d*e^3*f^3 - 16*A*B*a^2*
c^7*d^2*e*f^4 + 16*A*B*b*c^8*d^3*e^2*f^2 - 28*A*B*b^2*c^7*d^3*e*f^3 - 6*A*B*b^3*c^6*d*e^4*f^2 + 8*A*B*b^4*c^5*
d^2*e*f^4 + 12*A*B*b^5*c^4*d*e^2*f^4 - 40*A^2*a*b*c^7*d*e^3*f^3 + 80*A^2*a*b*c^7*d^2*e*f^4 - 24*A^2*a*b^3*c^5*
d*e*f^5 + 48*A^2*a^2*b*c^6*d*e*f^5 - 24*B^2*a*b*c^7*d^3*e*f^3 - 8*B^2*a*b^5*c^3*d*e*f^5 + 56*B^2*a^3*b*c^5*d*e
*f^5 - 4*A*B*a*b*c^7*e^6*f + 8*A*B*a*c^8*d*e^5*f + 96*A*B*a^2*b^2*c^5*e^3*f^4 - 36*A*B*a^2*b^3*c^4*e^2*f^5 + 4
*A*B*b^2*c^7*d^2*e^3*f^2 + 8*A*B*b^3*c^6*d^2*e^2*f^3 + 84*A^2*a*b^2*c^6*d*e^2*f^4 + 24*B^2*a*b*c^7*d^2*e^3*f^2
+ 14*B^2*a*b^2*c^6*d*e^4*f^2 - 16*B^2*a*b^3*c^5*d*e^3*f^3 + 98*B^2*a*b^3*c^5*d^2*e*f^4 + 12*B^2*a*b^4*c^4*d*e
^2*f^4 + 64*B^2*a^2*b*c^6*d*e^3*f^3 - 120*B^2*a^2*b*c^6*d^2*e*f^4 + 30*B^2*a^2*b^3*c^4*d*e*f^5 + 16*A*B*a*b*c^
7*d^3*f^4 - 12*A*B*a*b^5*c^3*d*f^6 + 112*A*B*a^3*b*c^5*d*f^6 + 2*A*B*a*b^6*c^2*e*f^6 + 48*A*B*a*c^8*d^3*e*f^3
+ 144*A*B*a^3*c^6*d*e*f^5 - 4*A*B*b*c^8*d^2*e^4*f + 2*A*B*b^2*c^7*d*e^5*f - 10*A*B*b^6*c^3*d*e*f^5 + 100*A*B*a
*b^4*c^4*d*e*f^5 + 64*A*B*a*b*c^7*d^2*e^2*f^3 + 12*A*B*a*b^2*c^6*d*e^3*f^3 - 108*A*B*a*b^2*c^6*d^2*e*f^4 - 100
*A*B*a*b^3*c^5*d*e^2*f^4 + 288*A*B*a^2*b*c^6*d*e^2*f^4 - 324*A*B*a^2*b^2*c^5*d*e*f^5))/(16*a^2*c^6*d^4 + a^4*b
^4*f^4 + 16*a^4*c^4*e^4 + b^4*c^4*d^4 + 16*a^6*c^2*f^4 + b^8*d^2*f^2 - 8*a*b^2*c^5*d^4 - 8*a^5*b^2*c*f^4 + 2*a
^2*b^6*d*f^3 - 2*a^3*b^5*e*f^3 - 64*a^3*c^5*d^3*f - 64*a^5*c^3*d*f^3 - 2*b^5*c^3*d^3*e + 2*b^6*c^2*d^3*f + a^2
*b^4*c^2*e^4 - 8*a^3*b^2*c^3*e^4 + 32*a^3*c^5*d^2*e^2 + a^2*b^6*e^2*f^2 + 96*a^4*c^4*d^2*f^2 + b^6*c^2*d^2*e^2
+ 32*a^5*c^3*e^2*f^2 - 2*a*b^7*d*e*f^2 - 2*b^7*c*d^2*e*f + 54*a^2*b^4*c^2*d^2*f^2 - 112*a^3*b^2*c^3*d^2*f^2 +
16*a*b^3*c^4*d^3*e - 2*a*b^5*c^2*d*e^3 - 32*a^2*b*c^5*d^3*e - 32*a^3*b*c^4*d*e^3 - 20*a*b^4*c^3*d^3*f - 12*a*
b^6*c*d^2*f^2 - 20*a^3*b^4*c*d*f^3 - 2*a^2*b^5*c*e^3*f - 32*a^4*b*c^3*e^3*f + 16*a^4*b^3*c*e*f^3 - 32*a^5*b*c^
2*e*f^3 - 64*a^4*c^4*d*e^2*f - 6*a*b^4*c^3*d^2*e^2 + 16*a^2*b^3*c^3*d*e^3 + 64*a^2*b^2*c^4*d^3*f + 64*a^4*b^2*
c^2*d*f^3 + 16*a^3*b^3*c^2*e^3*f - 6*a^3*b^4*c*e^2*f^2 - 48*a^2*b^3*c^3*d^2*e*f - 36*a^2*b^4*c^2*d*e^2*f + 96*
a^3*b^2*c^3*d*e^2*f - 48*a^3*b^3*c^2*d*e*f^2 + 4*a*b^6*c*d*e^2*f + 18*a*b^5*c^2*d^2*e*f + 18*a^2*b^5*c*d*e*f^2
+ 32*a^3*b*c^4*d^2*e*f + 32*a^4*b*c^3*d*e*f^2)) - (3*A^3*b^2*c^5*e^2*f^4 - 4*A^3*c^7*d^2*f^4 - 12*A^3*a^2*c^5
*f^6 - B^3*b^3*c^4*d^2*f^4 + 16*A^3*a*c^6*d*f^5 - 16*A*B^2*a^3*c^4*f^6 + 2*A^3*a*b^2*c^4*f^6 - 16*A^3*a*c^6*e^
2*f^4 - 6*A^3*b^2*c^5*d*f^5 - 3*A^3*b^3*c^4*e*f^5 + 4*B^3*a*b*c^5*d^2*f^4 + 3*B^3*a*b^3*c^3*d*f^5 - 12*B^3*a^2
*b*c^4*d*f^5 + 8*B^3*a^2*c^5*d*e*f^4 + 3*A*B^2*a^2*b^2*c^3*f^6 - 12*A*B^2*a^2*c^5*e^2*f^4 + A*B^2*b^2*c^5*d^2*
f^4 - 3*A^2*B*b^3*c^4*e^2*f^4 + 16*A^3*a*b*c^5*e*f^5 + 4*A^3*b*c^6*d*e*f^4 - 3*A^2*B*a*b^3*c^3*f^6 + 16*A^2*B*
a^2*b*c^4*f^6 - 8*A*B^2*a*c^6*d^2*f^4 + 24*A*B^2*a^2*c^5*d*f^5 - 3*A*B^2*b^4*c^3*d*f^5 + 4*A^2*B*b*c^6*d^2*f^4
- 8*A^2*B*a^2*c^5*e*f^5 + 9*A^2*B*b^3*c^4*d*f^5 + 3*A^2*B*b^4*c^3*e*f^5 + 4*A*B^2*a*b^2*c^4*d*f^5 - 3*A*B^2*a
*b^3*c^3*e*f^5 + 16*A*B^2*a^2*b*c^4*e*f^5 + 16*A^2*B*a*b*c^5*e^2*f^4 - 14*A^2*B*a*b^2*c^4*e*f^5 + 4*A*B^2*b^3*
c^4*d*e*f^4 - 8*A^2*B*b^2*c^5*d*e*f^4 - 2*B^3*a*b^2*c^4*d*e*f^4 + 2*A*B^2*a*b^2*c^4*e^2*f^4 - 28*A^2*B*a*b*c^5
*d*f^5 + 16*A^2*B*a*c^6*d*e*f^4 - 12*A*B^2*a*b*c^5*d*e*f^4)/(16*a^2*c^6*d^4 + a^4*b^4*f^4 + 16*a^4*c^4*e^4 + b
^4*c^4*d^4 + 16*a^6*c^2*f^4 + b^8*d^2*f^2 - 8*a*b^2*c^5*d^4 - 8*a^5*b^2*c*f^4 + 2*a^2*b^6*d*f^3 - 2*a^3*b^5*e*
f^3 - 64*a^3*c^5*d^3*f - 64*a^5*c^3*d*f^3 - 2*b^5*c^3*d^3*e + 2*b^6*c^2*d^3*f + a^2*b^4*c^2*e^4 - 8*a^3*b^2*c^
3*e^4 + 32*a^3*c^5*d^2*e^2 + a^2*b^6*e^2*f^2 + 96*a^4*c^4*d^2*f^2 + b^6*c^2*d^2*e^2 + 32*a^5*c^3*e^2*f^2 - 2*a
*b^7*d*e*f^2 - 2*b^7*c*d^2*e*f + 54*a^2*b^4*c^2*d^2*f^2 - 112*a^3*b^2*c^3*d^2*f^2 + 16*a*b^3*c^4*d^3*e - 2*a*b
^5*c^2*d*e^3 - 32*a^2*b*c^5*d^3*e - 32*a^3*b*c^4*d*e^3 - 20*a*b^4*c^3*d^3*f - 12*a*b^6*c*d^2*f^2 - 20*a^3*b^4*
c*d*f^3 - 2*a^2*b^5*c*e^3*f - 32*a^4*b*c^3*e^3*f + 16*a^4*b^3*c*e*f^3 - 32*a^5*b*c^2*e*f^3 - 64*a^4*c^4*d*e^2*
f - 6*a*b^4*c^3*d^2*e^2 + 16*a^2*b^3*c^3*d*e^3 + 64*a^2*b^2*c^4*d^3*f + 64*a^4*b^2*c^2*d*f^3 + 16*a^3*b^3*c^2*
e^3*f - 6*a^3*b^4*c*e^2*f^2 - 48*a^2*b^3*c^3*d^2*e*f - 36*a^2*b^4*c^2*d*e^2*f + 96*a^3*b^2*c^3*d*e^2*f - 48*a^
3*b^3*c^2*d*e*f^2 + 4*a*b^6*c*d*e^2*f + 18*a*b^5*c^2*d^2*e*f + 18*a^2*b^5*c*d*e*f^2 + 32*a^3*b*c^4*d^2*e*f + 3
2*a^4*b*c^3*d*e*f^2))*root(48416*a^6*b^2*c^6*d^4*e^2*f^4*z^4 - 41544*a^5*b^4*c^5*d^4*e^2*f^4*z^4 - 31872*a^7*b
^2*c^5*d^3*e^2*f^5*z^4 - 31872*a^5*b^2*c^7*d^5*e^2*f^3*z^4 - 29184*a^6*b^2*c^6*d^3*e^4*f^3*z^4 + 28800*a^5*b^4
*c^5*d^3*e^4*f^3*z^4 + 21510*a^4*b^6*c^4*d^4*e^2*f^4*z^4 + 21408*a^6*b^4*c^4*d^3*e^2*f^5*z^4 + 21408*a^4*b^4*c
^6*d^5*e^2*f^3*z^4 - 18112*a^7*b^3*c^4*d^2*e^3*f^5*z^4 - 18112*a^4*b^3*c^7*d^5*e^3*f^2*z^4 - 15600*a^5*b^5*c^4
*d^3*e^3*f^4*z^4 - 15600*a^4*b^5*c^5*d^4*e^3*f^3*z^4 + 15296*a^6*b^3*c^5*d^3*e^3*f^4*z^4 + 15296*a^5*b^3*c^6*d
^4*e^3*f^3*z^4 + 14016*a^7*b^2*c^5*d^2*e^4*f^4*z^4 + 14016*a^5*b^2*c^7*d^4*e^4*f^2*z^4 - 13920*a^4*b^6*c^4*d^3
*e^4*f^3*z^4 - 11648*a^6*b^3*c^5*d^2*e^5*f^3*z^4 - 11648*a^5*b^3*c^6*d^3*e^5*f^2*z^4 + 10432*a^6*b^2*c^6*d^2*e
^6*f^2*z^4 + 9008*a^6*b^5*c^3*d^2*e^3*f^5*z^4 + 9008*a^3*b^5*c^6*d^5*e^3*f^2*z^4 + 8544*a^5*b^5*c^4*d^2*e^5*f^
3*z^4 + 8544*a^4*b^5*c^5*d^3*e^5*f^2*z^4 - 8496*a^5*b^4*c^5*d^2*e^6*f^2*z^4 + 7488*a^8*b^2*c^4*d^2*e^2*f^6*z^4
+ 7488*a^4*b^2*c^8*d^6*e^2*f^2*z^4 + 7380*a^4*b^7*c^3*d^3*e^3*f^4*z^4 + 7380*a^3*b^7*c^4*d^4*e^3*f^3*z^4 - 67
20*a^3*b^8*c^3*d^4*e^2*f^4*z^4 - 5784*a^5*b^6*c^3*d^3*e^2*f^5*z^4 - 5784*a^3*b^6*c^5*d^5*e^2*f^3*z^4 - 3440*a^
6*b^4*c^4*d^2*e^4*f^4*z^4 - 3440*a^4*b^4*c^6*d^4*e^4*f^2*z^4 + 3360*a^3*b^8*c^3*d^3*e^4*f^3*z^4 + 3140*a^4*b^6
*c^4*d^2*e^6*f^2*z^4 - 2760*a^4*b^7*c^3*d^2*e^5*f^3*z^4 - 2760*a^3*b^7*c^4*d^3*e^5*f^2*z^4 - 1764*a^5*b^7*c^2*
d^2*e^3*f^5*z^4 - 1764*a^2*b^7*c^5*d^5*e^3*f^2*z^4 - 1640*a^3*b^9*c^2*d^3*e^3*f^4*z^4 - 1640*a^2*b^9*c^3*d^4*e
^3*f^3*z^4 - 1604*a^6*b^6*c^2*d^2*e^2*f^6*z^4 - 1604*a^2*b^6*c^6*d^6*e^2*f^2*z^4 - 1500*a^5*b^6*c^3*d^2*e^4*f^
4*z^4 - 1500*a^3*b^6*c^5*d^4*e^4*f^2*z^4 + 1140*a^2*b^10*c^2*d^4*e^2*f^4*z^4 + 810*a^4*b^8*c^2*d^2*e^4*f^4*z^4
+ 810*a^2*b^8*c^4*d^4*e^4*f^2*z^4 - 544*a^3*b^8*c^3*d^2*e^6*f^2*z^4 + 416*a^3*b^9*c^2*d^2*e^5*f^3*z^4 + 416*a
^2*b^9*c^3*d^3*e^5*f^2*z^4 - 384*a^2*b^10*c^2*d^3*e^4*f^3*z^4 + 180*a^4*b^8*c^2*d^3*e^2*f^5*z^4 + 180*a^2*b^8*
c^4*d^5*e^2*f^3*z^4 + 48*a^7*b^4*c^3*d^2*e^2*f^6*z^4 + 48*a^3*b^4*c^7*d^6*e^2*f^2*z^4 + 36*a^2*b^10*c^2*d^2*e^
6*f^2*z^4 - 1024*a^10*b*c^3*d*e*f^8*z^4 - 1024*a^3*b*c^10*d^8*e*f*z^4 - 192*a^8*b^5*c*d*e*f^8*z^4 - 192*a*b^5*
c^8*d^8*e*f*z^4 + 16128*a^7*b^3*c^4*d^3*e*f^6*z^4 + 16128*a^4*b^3*c^7*d^6*e*f^3*z^4 - 11712*a^6*b^5*c^3*d^3*e*
f^6*z^4 - 11712*a^3*b^5*c^6*d^6*e*f^3*z^4 + 11520*a^8*b*c^5*d^2*e^3*f^5*z^4 + 11520*a^5*b*c^8*d^5*e^3*f^2*z^4
- 9984*a^6*b^3*c^5*d^4*e*f^5*z^4 - 9984*a^5*b^3*c^6*d^5*e*f^4*z^4 + 8640*a^5*b^5*c^4*d^4*e*f^5*z^4 + 8640*a^4*
b^5*c^5*d^5*e*f^4*z^4 - 7424*a^7*b*c^6*d^3*e^3*f^4*z^4 - 7424*a^6*b*c^7*d^4*e^3*f^3*z^4 - 6912*a^8*b^3*c^3*d^2
*e*f^7*z^4 - 6912*a^3*b^3*c^8*d^7*e*f^2*z^4 + 4800*a^7*b^3*c^4*d*e^5*f^4*z^4 + 4800*a^4*b^3*c^7*d^4*e^5*f*z^4
+ 4608*a^7*b*c^6*d^2*e^5*f^3*z^4 + 4608*a^6*b*c^7*d^3*e^5*f^2*z^4 - 4560*a^4*b^7*c^3*d^4*e*f^5*z^4 - 4560*a^3*
b^7*c^4*d^5*e*f^4*z^4 + 4176*a^5*b^7*c^2*d^3*e*f^6*z^4 + 4176*a^2*b^7*c^5*d^6*e*f^3*z^4 + 3264*a^7*b^5*c^2*d^2
*e*f^7*z^4 + 3264*a^2*b^5*c^7*d^7*e*f^2*z^4 + 3008*a^8*b^3*c^3*d*e^3*f^6*z^4 + 3008*a^3*b^3*c^8*d^6*e^3*f*z^4
+ 2880*a^6*b^3*c^5*d*e^7*f^2*z^4 + 2880*a^5*b^3*c^6*d^2*e^7*f*z^4 - 2240*a^7*b^4*c^3*d*e^4*f^5*z^4 - 2240*a^3*
b^4*c^7*d^5*e^4*f*z^4 - 1488*a^5*b^5*c^4*d*e^7*f^2*z^4 - 1488*a^4*b^5*c^5*d^2*e^7*f*z^4 + 1440*a^3*b^9*c^2*d^4
*e*f^5*z^4 + 1440*a^2*b^9*c^3*d^5*e*f^4*z^4 - 1328*a^6*b^5*c^3*d*e^5*f^4*z^4 - 1328*a^3*b^5*c^6*d^4*e^5*f*z^4
- 1152*a^7*b^2*c^5*d*e^6*f^3*z^4 - 1152*a^5*b^2*c^7*d^3*e^6*f*z^4 - 1120*a^6*b^4*c^4*d*e^6*f^3*z^4 - 1120*a^4*
b^4*c^6*d^3*e^6*f*z^4 + 912*a^6*b^6*c^2*d*e^4*f^5*z^4 + 912*a^2*b^6*c^6*d^5*e^4*f*z^4 + 872*a^5*b^6*c^3*d*e^6*
f^3*z^4 + 872*a^3*b^6*c^5*d^3*e^6*f*z^4 + 768*a^8*b^2*c^4*d*e^4*f^5*z^4 + 768*a^4*b^2*c^8*d^5*e^4*f*z^4 - 672*
a^8*b^4*c^2*d*e^2*f^7*z^4 - 672*a^2*b^4*c^8*d^7*e^2*f*z^4 - 624*a^7*b^5*c^2*d*e^3*f^6*z^4 - 624*a^2*b^5*c^7*d^
6*e^3*f*z^4 + 480*a^5*b^8*c*d^2*e^2*f^6*z^4 + 480*a*b^8*c^5*d^6*e^2*f^2*z^4 + 316*a^4*b^7*c^3*d*e^7*f^2*z^4 +
316*a^3*b^7*c^4*d^2*e^7*f*z^4 - 204*a^4*b^8*c^2*d*e^6*f^3*z^4 - 204*a^2*b^8*c^4*d^3*e^6*f*z^4 + 168*a^3*b^10*c
*d^3*e^2*f^5*z^4 + 168*a*b^10*c^3*d^5*e^2*f^3*z^4 + 156*a^2*b^11*c*d^3*e^3*f^4*z^4 + 156*a*b^11*c^2*d^4*e^3*f^
3*z^4 + 128*a^9*b^2*c^3*d*e^2*f^7*z^4 + 128*a^3*b^2*c^9*d^7*e^2*f*z^4 - 124*a^3*b^10*c*d^2*e^4*f^4*z^4 - 124*a
*b^10*c^3*d^4*e^4*f^2*z^4 + 100*a^4*b^9*c*d^2*e^3*f^5*z^4 + 100*a*b^9*c^4*d^5*e^3*f^2*z^4 + 36*a^5*b^7*c^2*d*e
^5*f^4*z^4 + 36*a^2*b^7*c^5*d^4*e^5*f*z^4 - 24*a^3*b^9*c^2*d*e^7*f^2*z^4 - 24*a^2*b^11*c*d^2*e^5*f^3*z^4 - 24*
a^2*b^9*c^3*d^2*e^7*f*z^4 - 24*a*b^11*c^2*d^3*e^5*f^2*z^4 - 9216*a^8*b*c^5*d^3*e*f^6*z^4 - 9216*a^5*b*c^8*d^6*
e*f^3*z^4 - 5376*a^8*b*c^5*d*e^5*f^4*z^4 - 5376*a^5*b*c^8*d^4*e^5*f*z^4 + 5120*a^9*b*c^4*d^2*e*f^7*z^4 + 5120*
a^7*b*c^6*d^4*e*f^5*z^4 + 5120*a^6*b*c^7*d^5*e*f^4*z^4 + 5120*a^4*b*c^9*d^7*e*f^2*z^4 - 4352*a^9*b*c^4*d*e^3*f
^6*z^4 - 4352*a^4*b*c^9*d^6*e^3*f*z^4 - 1792*a^7*b*c^6*d*e^7*f^2*z^4 - 1792*a^6*b*c^7*d^2*e^7*f*z^4 - 1600*a^6
*b^2*c^6*d*e^8*f*z^4 + 912*a^5*b^4*c^5*d*e^8*f*z^4 + 768*a^9*b^3*c^2*d*e*f^8*z^4 + 768*a^2*b^3*c^9*d^8*e*f*z^4
- 720*a^4*b^9*c*d^3*e*f^6*z^4 - 720*a*b^9*c^4*d^6*e*f^3*z^4 - 656*a^6*b^7*c*d^2*e*f^7*z^4 - 656*a*b^7*c^6*d^7
*e*f^2*z^4 - 240*a^2*b^11*c*d^4*e*f^5*z^4 - 240*a*b^11*c^2*d^5*e*f^4*z^4 + 216*a^7*b^6*c*d*e^2*f^7*z^4 + 216*a
*b^6*c^7*d^7*e^2*f*z^4 - 204*a^4*b^6*c^4*d*e^8*f*z^4 - 144*a^5*b^8*c*d*e^4*f^5*z^4 - 144*a*b^8*c^5*d^5*e^4*f*z
^4 - 84*a*b^12*c*d^4*e^2*f^4*z^4 + 36*a^4*b^9*c*d*e^5*f^4*z^4 + 36*a*b^9*c^4*d^4*e^5*f*z^4 + 20*a^6*b^7*c*d*e^
3*f^6*z^4 + 20*a*b^7*c^6*d^6*e^3*f*z^4 + 16*a^3*b^10*c*d*e^6*f^3*z^4 + 16*a^3*b^8*c^3*d*e^8*f*z^4 + 16*a*b^12*
c*d^3*e^4*f^3*z^4 + 16*a*b^10*c^3*d^3*e^6*f*z^4 + 48*b^11*c^3*d^6*e*f^3*z^4 + 48*b^9*c^5*d^7*e*f^2*z^4 - 20*b^
8*c^6*d^7*e^2*f*z^4 + 8*b^10*c^4*d^5*e^4*f*z^4 - 4*b^13*c*d^4*e^3*f^3*z^4 - 4*b^11*c^3*d^4*e^5*f*z^4 + 4*b^9*c
^5*d^6*e^3*f*z^4 + 3072*a^9*c^5*d*e^4*f^5*z^4 + 3072*a^5*c^9*d^5*e^4*f*z^4 + 2560*a^8*c^6*d*e^6*f^3*z^4 + 2560
*a^6*c^8*d^3*e^6*f*z^4 + 1536*a^10*c^4*d*e^2*f^7*z^4 + 1536*a^4*c^10*d^7*e^2*f*z^4 + 48*a^5*b^9*d^2*e*f^7*z^4
+ 48*a^3*b^11*d^3*e*f^6*z^4 - 20*a^6*b^8*d*e^2*f^7*z^4 + 8*a^4*b^10*d*e^4*f^5*z^4 + 4*a^5*b^9*d*e^3*f^6*z^4 -
4*a^3*b^11*d*e^5*f^4*z^4 - 4*a*b^13*d^3*e^3*f^4*z^4 + 768*a^9*b*c^4*e^5*f^5*z^4 + 768*a^8*b*c^5*e^7*f^3*z^4 +
256*a^10*b*c^3*e^3*f^7*z^4 - 192*a^6*b^3*c^5*e^9*f*z^4 - 68*a^7*b^6*c*e^4*f^6*z^4 + 48*a^8*b^5*c*e^3*f^7*z^4 +
48*a^5*b^5*c^4*e^9*f*z^4 + 36*a^6*b^7*c*e^5*f^5*z^4 - 12*a^9*b^4*c*e^2*f^8*z^4 - 4*a^4*b^9*c*e^7*f^3*z^4 - 4*
a^4*b^7*c^3*e^9*f*z^4 + 384*a^5*b^8*c*d^3*f^7*z^4 + 384*a*b^8*c^5*d^7*f^3*z^4 + 288*a^3*b^10*c*d^4*f^6*z^4 + 2
88*a*b^10*c^3*d^6*f^4*z^4 + 224*a^7*b^6*c*d^2*f^8*z^4 + 224*a*b^6*c^7*d^8*f^2*z^4 - 192*a^10*b^2*c^2*d*f^9*z^4
- 192*a^2*b^2*c^10*d^9*f*z^4 + 768*a^5*b*c^8*d^3*e^7*z^4 + 768*a^4*b*c^9*d^5*e^5*z^4 + 256*a^3*b*c^10*d^7*e^3
*z^4 - 192*a^5*b^3*c^6*d*e^9*z^4 - 68*a*b^6*c^7*d^6*e^4*z^4 + 48*a^4*b^5*c^5*d*e^9*z^4 + 48*a*b^5*c^8*d^7*e^3*
z^4 + 36*a*b^7*c^6*d^5*e^5*z^4 - 12*a*b^4*c^9*d^8*e^2*z^4 - 4*a^3*b^7*c^4*d*e^9*z^4 - 4*a*b^9*c^4*d^3*e^7*z^4
+ 16*b^13*c*d^5*e*f^4*z^4 + 16*b^7*c^7*d^8*e*f*z^4 + 768*a^7*c^7*d*e^8*f*z^4 + 16*a^7*b^7*d*e*f^8*z^4 + 16*a*b
^13*d^4*e*f^5*z^4 + 256*a^7*b*c^6*e^9*f*z^4 + 80*a*b^12*c*d^5*f^5*z^4 + 48*a^9*b^4*c*d*f^9*z^4 + 48*a*b^4*c^9*
d^9*f*z^4 + 256*a^6*b*c^7*d*e^9*z^4 - 42*b^10*c^4*d^6*e^2*f^2*z^4 - 20*b^12*c^2*d^5*e^2*f^3*z^4 + 6*b^12*c^2*d
^4*e^4*f^2*z^4 + 4*b^11*c^3*d^5*e^3*f^2*z^4 - 24960*a^7*c^7*d^4*e^2*f^4*z^4 + 18944*a^8*c^6*d^3*e^2*f^5*z^4 +
18944*a^6*c^8*d^5*e^2*f^3*z^4 + 14336*a^7*c^7*d^3*e^4*f^3*z^4 - 9984*a^8*c^6*d^2*e^4*f^4*z^4 - 9984*a^6*c^8*d^
4*e^4*f^2*z^4 - 7936*a^9*c^5*d^2*e^2*f^6*z^4 - 7936*a^5*c^9*d^6*e^2*f^2*z^4 - 4352*a^7*c^7*d^2*e^6*f^2*z^4 - 4
2*a^4*b^10*d^2*e^2*f^6*z^4 - 20*a^2*b^12*d^3*e^2*f^5*z^4 + 6*a^2*b^12*d^2*e^4*f^4*z^4 + 4*a^3*b^11*d^2*e^3*f^5
*z^4 - 480*a^8*b^2*c^4*e^6*f^4*z^4 + 440*a^7*b^4*c^3*e^6*f^4*z^4 - 320*a^8*b^3*c^3*e^5*f^5*z^4 - 320*a^7*b^3*c
^4*e^7*f^3*z^4 + 240*a^8*b^4*c^2*e^4*f^6*z^4 + 240*a^6*b^4*c^4*e^8*f^2*z^4 - 192*a^9*b^3*c^2*e^3*f^7*z^4 - 192
*a^9*b^2*c^3*e^4*f^6*z^4 - 192*a^7*b^2*c^5*e^8*f^2*z^4 - 90*a^6*b^6*c^2*e^6*f^4*z^4 - 68*a^5*b^6*c^3*e^8*f^2*z
^4 + 48*a^10*b^2*c^2*e^2*f^8*z^4 - 48*a^7*b^5*c^2*e^5*f^5*z^4 - 48*a^6*b^5*c^3*e^7*f^3*z^4 + 36*a^5*b^7*c^2*e^
7*f^3*z^4 + 6*a^4*b^8*c^2*e^8*f^2*z^4 - 33920*a^6*b^2*c^6*d^5*f^5*z^4 + 27936*a^5*b^4*c^5*d^5*f^5*z^4 + 26112*
a^7*b^2*c^5*d^4*f^6*z^4 + 26112*a^5*b^2*c^7*d^6*f^4*z^4 - 20352*a^6*b^4*c^4*d^4*f^6*z^4 - 20352*a^4*b^4*c^6*d^
6*f^4*z^4 - 13080*a^4*b^6*c^4*d^5*f^5*z^4 - 11520*a^8*b^2*c^4*d^3*f^7*z^4 - 11520*a^4*b^2*c^8*d^7*f^3*z^4 + 87
36*a^5*b^6*c^3*d^4*f^6*z^4 + 8736*a^3*b^6*c^5*d^6*f^4*z^4 + 7488*a^7*b^4*c^3*d^3*f^7*z^4 + 7488*a^3*b^4*c^7*d^
7*f^3*z^4 + 3840*a^3*b^8*c^3*d^5*f^5*z^4 + 2560*a^9*b^2*c^3*d^2*f^8*z^4 + 2560*a^3*b^2*c^9*d^8*f^2*z^4 - 2416*
a^6*b^6*c^2*d^3*f^7*z^4 - 2416*a^2*b^6*c^6*d^7*f^3*z^4 - 2160*a^4*b^8*c^2*d^4*f^6*z^4 - 2160*a^2*b^8*c^4*d^6*f
^4*z^4 - 1152*a^8*b^4*c^2*d^2*f^8*z^4 - 1152*a^2*b^4*c^8*d^8*f^2*z^4 - 720*a^2*b^10*c^2*d^5*f^5*z^4 - 480*a^4*
b^2*c^8*d^4*e^6*z^4 + 440*a^3*b^4*c^7*d^4*e^6*z^4 - 320*a^4*b^3*c^7*d^3*e^7*z^4 - 320*a^3*b^3*c^8*d^5*e^5*z^4
+ 240*a^4*b^4*c^6*d^2*e^8*z^4 + 240*a^2*b^4*c^8*d^6*e^4*z^4 - 192*a^5*b^2*c^7*d^2*e^8*z^4 - 192*a^3*b^2*c^9*d^
6*e^4*z^4 - 192*a^2*b^3*c^9*d^7*e^3*z^4 - 90*a^2*b^6*c^6*d^4*e^6*z^4 - 68*a^3*b^6*c^5*d^2*e^8*z^4 - 48*a^3*b^5
*c^6*d^3*e^7*z^4 - 48*a^2*b^5*c^7*d^5*e^5*z^4 + 48*a^2*b^2*c^10*d^8*e^2*z^4 + 36*a^2*b^7*c^5*d^3*e^7*z^4 + 6*a
^2*b^8*c^4*d^2*e^8*z^4 - 4*b^6*c^8*d^9*f*z^4 + 256*a^11*c^3*d*f^9*z^4 + 256*a^3*c^11*d^9*f*z^4 - 4*a^8*b^6*d*f
^9*z^4 - 384*a^9*c^5*e^6*f^4*z^4 - 256*a^10*c^4*e^4*f^6*z^4 - 256*a^8*c^6*e^8*f^2*z^4 - 64*a^11*c^3*e^2*f^8*z^
4 - 24*b^10*c^4*d^7*f^3*z^4 - 16*b^12*c^2*d^6*f^4*z^4 - 16*b^8*c^6*d^8*f^2*z^4 + 17920*a^7*c^7*d^5*f^5*z^4 - 1
4336*a^8*c^6*d^4*f^6*z^4 - 14336*a^6*c^8*d^6*f^4*z^4 + 7168*a^9*c^5*d^3*f^7*z^4 + 7168*a^5*c^9*d^7*f^3*z^4 - 2
048*a^10*c^4*d^2*f^8*z^4 - 2048*a^4*c^10*d^8*f^2*z^4 + 6*b^8*c^6*d^6*e^4*z^4 + 6*a^6*b^8*e^4*f^6*z^4 - 4*b^9*c
^5*d^5*e^5*z^4 - 4*b^7*c^7*d^7*e^3*z^4 - 4*a^7*b^7*e^3*f^7*z^4 - 4*a^5*b^9*e^5*f^5*z^4 - 384*a^5*c^9*d^4*e^6*z
^4 - 256*a^6*c^8*d^2*e^8*z^4 - 256*a^4*c^10*d^6*e^4*z^4 - 64*a^3*c^11*d^8*e^2*z^4 - 24*a^4*b^10*d^3*f^7*z^4 -
16*a^6*b^8*d^2*f^8*z^4 - 16*a^2*b^12*d^4*f^6*z^4 + 48*a^6*b^2*c^6*e^10*z^4 - 12*a^5*b^4*c^5*e^10*z^4 - 4*b^14*
d^5*f^5*z^4 - 64*a^7*c^7*e^10*z^4 + b^14*d^4*e^2*f^4*z^4 + b^10*c^4*d^4*e^6*z^4 + b^6*c^8*d^8*e^2*z^4 + a^8*b^
6*e^2*f^8*z^4 + a^4*b^10*e^6*f^4*z^4 + a^4*b^6*c^4*e^10*z^4 - 4820*A*B*a^4*b*c^5*d^2*e^2*f^4*z^2 + 2976*A*B*a^
3*b*c^6*d^3*e^2*f^3*z^2 - 2328*A*B*a^3*b*c^6*d^2*e^4*f^2*z^2 + 1848*A*B*a^2*b^4*c^4*d^3*e*f^4*z^2 - 1768*A*B*a
^3*b^4*c^3*d^2*e*f^5*z^2 + 1528*A*B*a^4*b^2*c^4*d^2*e*f^5*z^2 - 1136*A*B*a^3*b^2*c^5*d^3*e*f^4*z^2 - 974*A*B*a
^4*b^3*c^3*d*e^2*f^5*z^2 + 692*A*B*a^2*b*c^7*d^4*e^2*f^2*z^2 + 588*A*B*a*b^6*c^3*d^2*e^3*f^3*z^2 - 580*A*B*a^3
*b^3*c^4*d*e^4*f^3*z^2 + 488*A*B*a^3*b^4*c^3*d*e^3*f^4*z^2 - 444*A*B*a^2*b^2*c^6*d^2*e^5*f*z^2 - 412*A*B*a*b^5
*c^4*d^2*e^4*f^2*z^2 + 366*A*B*a^2*b^6*c^2*d^2*e*f^5*z^2 - 352*A*B*a^2*b^2*c^6*d^4*e*f^3*z^2 + 326*A*B*a^2*b^4
*c^4*d*e^5*f^2*z^2 + 324*A*B*a*b^5*c^4*d^3*e^2*f^3*z^2 - 302*A*B*a*b^3*c^6*d^4*e^2*f^2*z^2 - 296*A*B*a*b^7*c^2
*d^2*e^2*f^4*z^2 + 122*A*B*a^4*b^2*c^4*d*e^3*f^4*z^2 - 122*A*B*a^2*b^6*c^2*d*e^3*f^4*z^2 - 84*A*B*a^3*b^2*c^5*
d*e^5*f^2*z^2 + 72*A*B*a*b^4*c^5*d^3*e^3*f^2*z^2 - 64*A*B*a^2*b^5*c^3*d*e^4*f^3*z^2 + 60*A*B*a^3*b^5*c^2*d*e^2
*f^5*z^2 + 1312*A*B*a^5*b*c^4*d*e^2*f^5*z^2 + 1040*A*B*a^4*b*c^5*d*e^4*f^3*z^2 - 500*A*B*a*b^6*c^3*d^3*e*f^4*z
^2 - 376*A*B*a*b^2*c^7*d^5*e*f^2*z^2 + 276*A*B*a^4*b^4*c^2*d*e*f^6*z^2 - 262*A*B*a^2*b^3*c^5*d*e^6*f*z^2 + 238
*A*B*a*b^2*c^7*d^4*e^3*f*z^2 + 232*A*B*a^5*b^2*c^3*d*e*f^6*z^2 - 176*A*B*a^2*b*c^7*d^3*e^4*f*z^2 - 120*A*B*a*b
^6*c^3*d*e^5*f^2*z^2 - 108*A*B*a*b^4*c^5*d^4*e*f^3*z^2 + 68*A*B*a*b^7*c^2*d*e^4*f^3*z^2 + 68*A*B*a*b^4*c^5*d^2
*e^5*f*z^2 + 46*A*B*a^2*b^7*c*d*e^2*f^5*z^2 - 36*A*B*a*b^3*c^6*d^3*e^4*f*z^2 - 1932*A*B*a^2*b^3*c^5*d^3*e^2*f^
3*z^2 - 1818*A*B*a^2*b^4*c^4*d^2*e^3*f^3*z^2 + 1620*A*B*a^3*b^3*c^4*d^2*e^2*f^4*z^2 + 1560*A*B*a^2*b^3*c^5*d^2
*e^4*f^2*z^2 + 1244*A*B*a^3*b^2*c^5*d^2*e^3*f^3*z^2 + 820*A*B*a^2*b^2*c^6*d^3*e^3*f^2*z^2 + 480*A*B*a^2*b^5*c^
3*d^2*e^2*f^4*z^2 + 352*A*B*a^3*b*c^6*d*e^6*f*z^2 - 108*A*B*a^3*b^6*c*d*e*f^6*z^2 + 82*A*B*a*b^5*c^4*d*e^6*f*z
^2 - 64*A*B*a*b*c^8*d^5*e^2*f*z^2 + 16*A*B*a*b^8*c*d^2*e*f^5*z^2 - 4*A*B*a*b^8*c*d*e^3*f^4*z^2 + 16*B^2*a*b*c^
8*d^6*e*f*z^2 + 56*A*B*b^2*c^8*d^6*e*f*z^2 - 8*A*B*b^9*c*d*e^4*f^3*z^2 - 8*A*B*b^7*c^3*d*e^6*f*z^2 - 800*A*B*a
^6*c^4*d*e*f^6*z^2 + 10*A*B*a^2*b^8*d*e*f^6*z^2 - 6*A*B*a*b^9*d*e^2*f^5*z^2 - 12*A*B*a^5*b^4*c*e*f^7*z^2 + 912
*A*B*a^6*b*c^3*d*f^7*z^2 + 192*A*B*a^4*b^5*c*d*f^7*z^2 + 192*A*B*a*b*c^8*d^6*f^2*z^2 - 20*A*B*a*b^4*c^5*d*e^7*
z^2 + 4*A*B*a*b*c^8*d^4*e^4*z^2 + 2144*B^2*a^4*b*c^5*d^3*e*f^4*z^2 - 1120*B^2*a^3*b*c^6*d^4*e*f^3*z^2 - 688*B^
2*a^5*b*c^4*d^2*e*f^5*z^2 - 256*B^2*a^3*b*c^6*d^2*e^5*f*z^2 + 152*B^2*a*b^3*c^6*d^5*e*f^2*z^2 + 120*B^2*a^5*b^
3*c^2*d*e*f^6*z^2 - 116*B^2*a^5*b*c^4*d*e^3*f^4*z^2 + 110*B^2*a*b^7*c^2*d^3*e*f^4*z^2 - 80*B^2*a^2*b*c^7*d^5*e
*f^2*z^2 - 72*B^2*a*b^5*c^4*d^4*e*f^3*z^2 - 48*B^2*a^4*b*c^5*d*e^5*f^2*z^2 - 46*B^2*a*b^3*c^6*d^4*e^3*f*z^2 -
44*B^2*a*b^4*c^5*d^3*e^4*f*z^2 - 34*B^2*a*b^5*c^4*d^2*e^5*f*z^2 + 20*B^2*a^2*b*c^7*d^4*e^3*f*z^2 - 10*B^2*a^3*
b^6*c*d*e^2*f^5*z^2 - 10*B^2*a^2*b^7*c*d^2*e*f^5*z^2 - 10*B^2*a*b^2*c^7*d^5*e^2*f*z^2 - 7*B^2*a^2*b^4*c^4*d*e^
6*f*z^2 - 6*B^2*a^3*b^2*c^5*d*e^6*f*z^2 + 4*B^2*a*b^8*c*d^2*e^2*f^4*z^2 - 2*B^2*a^2*b^7*c*d*e^3*f^4*z^2 + 3196
*A^2*a^4*b*c^5*d*e^3*f^4*z^2 - 3184*A^2*a^4*b*c^5*d^2*e*f^5*z^2 + 1568*A^2*a^3*b*c^6*d^3*e*f^4*z^2 + 1504*A^2*
a^3*b*c^6*d*e^5*f^2*z^2 - 656*A^2*a^4*b^3*c^3*d*e*f^6*z^2 - 400*A^2*a*b^6*c^3*d*e^4*f^3*z^2 + 314*A^2*a*b^5*c^
4*d*e^5*f^2*z^2 - 264*A^2*a^3*b^5*c^2*d*e*f^6*z^2 + 240*A^2*a^2*b^2*c^6*d*e^6*f*z^2 - 224*A^2*a^2*b*c^7*d^4*e*
f^3*z^2 + 216*A^2*a*b^5*c^4*d^3*e*f^4*z^2 - 192*A^2*a^2*b*c^7*d^2*e^5*f*z^2 + 178*A^2*a*b^7*c^2*d*e^3*f^4*z^2
- 154*A^2*a*b^7*c^2*d^2*e*f^5*z^2 + 128*A^2*a*b^3*c^6*d^4*e*f^3*z^2 + 106*A^2*a*b^3*c^6*d^2*e^5*f*z^2 - 12*A^2
*a*b^2*c^7*d^3*e^4*f*z^2 - 58*A*B*b^8*c^2*d^2*e^3*f^3*z^2 + 40*A*B*b^7*c^3*d^2*e^4*f^2*z^2 - 28*A*B*b^7*c^3*d^
3*e^2*f^3*z^2 - 24*A*B*b^5*c^5*d^4*e^2*f^2*z^2 - 20*A*B*b^6*c^4*d^3*e^3*f^2*z^2 + 2768*A*B*a^4*c^6*d^2*e^3*f^3
*z^2 - 1712*A*B*a^3*c^7*d^3*e^3*f^2*z^2 - 156*A*B*a^4*b^2*c^4*e^5*f^3*z^2 + 146*A*B*a^4*b^3*c^3*e^4*f^4*z^2 -
106*A*B*a^5*b^2*c^3*e^3*f^5*z^2 + 90*A*B*a^5*b^3*c^2*e^2*f^6*z^2 + 38*A*B*a^3*b^3*c^4*e^6*f^2*z^2 - 36*A*B*a^3
*b^5*c^2*e^4*f^4*z^2 + 16*A*B*a^3*b^4*c^3*e^5*f^3*z^2 - 9*A*B*a^4*b^4*c^2*e^3*f^5*z^2 - 8*A*B*a^2*b^5*c^3*e^6*
f^2*z^2 + 2*A*B*a^2*b^6*c^2*e^5*f^3*z^2 + 920*A*B*a^4*b^3*c^3*d^2*f^6*z^2 - 480*A*B*a^2*b^5*c^3*d^3*f^5*z^2 -
336*A*B*a^2*b^3*c^5*d^4*f^4*z^2 - 272*A*B*a^3*b^3*c^4*d^3*f^5*z^2 + 240*A*B*a^3*b^5*c^2*d^2*f^6*z^2 - 32*A*B*a
*c^9*d^6*e*f*z^2 - 792*B^2*a^2*b^3*c^5*d^3*e^3*f^2*z^2 + 714*B^2*a^2*b^4*c^4*d^3*e^2*f^3*z^2 - 572*B^2*a^3*b^2
*c^5*d^3*e^2*f^3*z^2 - 475*B^2*a^2*b^2*c^6*d^4*e^2*f^2*z^2 + 265*B^2*a^4*b^2*c^4*d^2*e^2*f^4*z^2 + 260*B^2*a^3
*b^3*c^4*d^2*e^3*f^3*z^2 - 212*B^2*a^3*b^4*c^3*d^2*e^2*f^4*z^2 + 180*B^2*a^3*b^2*c^5*d^2*e^4*f^2*z^2 - 158*B^2
*a^2*b^4*c^4*d^2*e^4*f^2*z^2 + 47*B^2*a^2*b^6*c^2*d^2*e^2*f^4*z^2 + 16*B^2*a^2*b^5*c^3*d^2*e^3*f^3*z^2 + 2752*
A^2*a^3*b^2*c^5*d^2*e^2*f^4*z^2 - 2148*A^2*a^2*b^4*c^4*d^2*e^2*f^4*z^2 + 2064*A^2*a^2*b^3*c^5*d^2*e^3*f^3*z^2
- 424*A^2*a^2*b^2*c^6*d^3*e^2*f^3*z^2 - 198*A^2*a^2*b^2*c^6*d^2*e^4*f^2*z^2 - 272*B^2*a^6*b*c^3*d*e*f^6*z^2 -
24*B^2*a^4*b^5*c*d*e*f^6*z^2 + 1808*A^2*a^5*b*c^4*d*e*f^6*z^2 - 244*A^2*a*b*c^8*d^4*e^3*f*z^2 + 208*A^2*a*b*c^
8*d^5*e*f^2*z^2 + 134*A^2*a^2*b^7*c*d*e*f^6*z^2 - 76*A^2*a*b^4*c^5*d*e^6*f*z^2 + 4*A^2*a*b^8*c*d*e^2*f^5*z^2 +
148*A*B*b^4*c^6*d^5*e*f^2*z^2 + 65*A*B*b^6*c^4*d^4*e*f^3*z^2 + 46*A*B*b^8*c^2*d^3*e*f^4*z^2 - 38*A*B*b^3*c^7*
d^5*e^2*f*z^2 + 34*A*B*b^9*c*d^2*e^2*f^4*z^2 - 29*A*B*b^4*c^6*d^4*e^3*f*z^2 + 20*A*B*b^5*c^5*d^3*e^4*f*z^2 + 1
2*A*B*b^8*c^2*d*e^5*f^2*z^2 - 7*A*B*b^6*c^4*d^2*e^5*f*z^2 - 2880*A*B*a^4*c^6*d^3*e*f^4*z^2 + 2784*A*B*a^5*c^5*
d^2*e*f^5*z^2 - 1112*A*B*a^5*c^5*d*e^3*f^4*z^2 + 896*A*B*a^3*c^7*d^4*e*f^3*z^2 + 848*A*B*a^3*c^7*d^2*e^5*f*z^2
- 560*A*B*a^4*c^6*d*e^5*f^2*z^2 + 96*A*B*a^2*c^8*d^5*e*f^2*z^2 - 88*A*B*a^2*c^8*d^4*e^3*f*z^2 - 100*A*B*a^6*b
*c^3*e^2*f^6*z^2 - 76*A*B*a^5*b*c^4*e^4*f^4*z^2 + 48*A*B*a^6*b^2*c^2*e*f^7*z^2 - 42*A*B*a^3*b^2*c^5*e^7*f*z^2
+ 36*A*B*a^4*b*c^5*e^6*f^2*z^2 - 24*A*B*a^4*b^5*c*e^2*f^6*z^2 + 10*A*B*a^3*b^6*c*e^3*f^5*z^2 + 7*A*B*a^2*b^4*c
^4*e^7*f*z^2 + 2*A*B*a^2*b^7*c*e^4*f^4*z^2 - 2496*A*B*a^5*b*c^4*d^2*f^6*z^2 + 1872*A*B*a^4*b*c^5*d^3*f^5*z^2 -
744*A*B*a^5*b^3*c^2*d*f^7*z^2 - 720*A*B*a^2*b*c^7*d^5*f^3*z^2 + 504*A*B*a*b^3*c^6*d^5*f^3*z^2 + 256*A*B*a^3*b
*c^6*d^4*f^4*z^2 + 168*A*B*a*b^7*c^2*d^3*f^5*z^2 - 144*A*B*a^2*b^7*c*d^2*f^6*z^2 + 144*A*B*a*b^5*c^4*d^4*f^4*z
^2 + 66*A*B*a^2*b^2*c^6*d*e^7*z^2 - 36*A*B*a*b^2*c^7*d^3*e^5*z^2 + 20*A*B*a*b^3*c^6*d^2*e^6*z^2 + 12*A*B*a^2*b
*c^7*d^2*e^6*z^2 + 1208*B^2*a^3*b*c^6*d^3*e^3*f^2*z^2 - 848*B^2*a^3*b^3*c^4*d^3*e*f^4*z^2 + 672*B^2*a^2*b^3*c^
5*d^4*e*f^3*z^2 - 632*B^2*a^4*b*c^5*d^2*e^3*f^3*z^2 + 432*B^2*a^4*b^3*c^3*d^2*e*f^5*z^2 + 276*B^2*a^2*b^2*c^6*
d^3*e^4*f*z^2 - 196*B^2*a*b^6*c^3*d^3*e^2*f^3*z^2 - 168*B^2*a^2*b^5*c^3*d^3*e*f^4*z^2 + 154*B^2*a^2*b^3*c^5*d^
2*e^5*f*z^2 + 148*B^2*a*b^5*c^4*d^3*e^3*f^2*z^2 + 96*B^2*a*b^4*c^5*d^4*e^2*f^2*z^2 - 72*B^2*a^3*b^5*c^2*d^2*e*
f^5*z^2 + 70*B^2*a^5*b^2*c^3*d*e^2*f^5*z^2 - 60*B^2*a^4*b^3*c^3*d*e^3*f^4*z^2 + 52*B^2*a*b^6*c^3*d^2*e^4*f^2*z
^2 + 36*B^2*a^4*b^2*c^4*d*e^4*f^3*z^2 - 32*B^2*a*b^7*c^2*d^2*e^3*f^3*z^2 + 24*B^2*a^3*b^5*c^2*d*e^3*f^4*z^2 +
15*B^2*a^4*b^4*c^2*d*e^2*f^5*z^2 - 8*B^2*a^3*b^4*c^3*d*e^4*f^3*z^2 + 8*B^2*a^2*b^5*c^3*d*e^5*f^2*z^2 - 2*B^2*a
^3*b^3*c^4*d*e^5*f^2*z^2 - 2*B^2*a^2*b^6*c^2*d*e^4*f^3*z^2 - 3176*A^2*a^3*b*c^6*d^2*e^3*f^3*z^2 - 2252*A^2*a^4
*b^2*c^4*d*e^2*f^5*z^2 + 1952*A^2*a^3*b^4*c^3*d*e^2*f^5*z^2 - 1496*A^2*a^3*b^3*c^4*d*e^3*f^4*z^2 + 1378*A^2*a^
2*b^4*c^4*d*e^4*f^3*z^2 + 1184*A^2*a^3*b^3*c^4*d^2*e*f^5*z^2 - 1166*A^2*a^2*b^3*c^5*d*e^5*f^2*z^2 - 1164*A^2*a
^3*b^2*c^5*d*e^4*f^3*z^2 - 1152*A^2*a^2*b^3*c^5*d^3*e*f^4*z^2 + 578*A^2*a*b^6*c^3*d^2*e^2*f^4*z^2 - 548*A^2*a*
b^5*c^4*d^2*e^3*f^3*z^2 + 440*A^2*a*b^2*c^7*d^4*e^2*f^2*z^2 - 412*A^2*a^2*b^6*c^2*d*e^2*f^5*z^2 - 360*A^2*a*b^
3*c^6*d^3*e^3*f^2*z^2 + 312*A^2*a*b^4*c^5*d^3*e^2*f^3*z^2 + 248*A^2*a^2*b*c^7*d^3*e^3*f^2*z^2 - 224*A^2*a^2*b^
5*c^3*d*e^3*f^4*z^2 + 216*A^2*a^2*b^5*c^3*d^2*e*f^5*z^2 + 52*A^2*a*b^4*c^5*d^2*e^4*f^2*z^2 - 16*B^2*b^3*c^7*d^
6*e*f*z^2 - 14*B^2*b^9*c*d^3*e*f^4*z^2 + 32*B^2*a^4*c^6*d*e^6*f*z^2 - 20*A^2*b^9*c*d*e^3*f^4*z^2 + 18*A^2*b^9*
c*d^2*e*f^5*z^2 + 8*A^2*b^6*c^4*d*e^6*f*z^2 - 360*A^2*a^3*c^7*d*e^6*f*z^2 + 136*A^2*a*c^9*d^5*e^2*f*z^2 + 2*B^
2*a^3*b^7*d*e*f^6*z^2 + 2*B^2*a*b^9*d^2*e*f^5*z^2 + 12*B^2*a^4*b*c^5*e^7*f*z^2 - 204*A^2*a^3*b*c^6*e^7*f*z^2 -
128*A^2*a^6*b*c^3*e*f^7*z^2 - 48*A^2*a*b^5*c^4*e^7*f*z^2 - 36*B^2*a^5*b^4*c*d*f^7*z^2 - 24*A^2*a^4*b^5*c*e*f^
7*z^2 - 16*B^2*a*b^8*c*d^3*f^5*z^2 - 164*A^2*a^3*b^6*c*d*f^7*z^2 - 16*A^2*a*b^8*c*d^2*f^6*z^2 + 4*B^2*a^3*b*c^
6*d*e^7*z^2 - 4*B^2*a*b*c^8*d^5*e^3*z^2 + 48*A^2*a*b*c^8*d^3*e^5*z^2 + 36*A^2*a^2*b*c^7*d*e^7*z^2 - 6*A^2*a*b^
3*c^6*d*e^7*z^2 + 136*A*B*a^6*c^4*e^3*f^5*z^2 - 96*A*B*b^5*c^5*d^5*f^3*z^2 + 80*A*B*a^5*c^5*e^5*f^3*z^2 - 72*A
*B*b^3*c^7*d^6*f^2*z^2 - 24*A*B*b^7*c^3*d^4*f^4*z^2 + 14*A*B*b^3*c^7*d^4*e^4*z^2 - 14*A*B*b^2*c^8*d^5*e^3*z^2
- 2*A*B*b^5*c^5*d^2*e^6*z^2 - 2*A*B*b^4*c^6*d^3*e^5*z^2 + 2*A*B*a^3*b^7*e^2*f^6*z^2 - A*B*a^2*b^8*e^3*f^5*z^2
+ 16*A*B*a^2*c^8*d^3*e^5*z^2 - 2*A*B*a^2*b^3*c^5*e^8*z^2 + 22*B^2*b^8*c^2*d^3*e^2*f^3*z^2 - 12*B^2*b^7*c^3*d^3
*e^3*f^2*z^2 + 12*B^2*b^6*c^4*d^4*e^2*f^2*z^2 - 6*B^2*b^8*c^2*d^2*e^4*f^2*z^2 - 864*B^2*a^4*c^6*d^3*e^2*f^3*z^
2 + 496*B^2*a^3*c^7*d^4*e^2*f^2*z^2 + 224*B^2*a^5*c^5*d^2*e^2*f^4*z^2 + 136*B^2*a^4*c^6*d^2*e^4*f^2*z^2 - 53*A
^2*b^8*c^2*d^2*e^2*f^4*z^2 + 52*A^2*b^7*c^3*d^2*e^3*f^3*z^2 + 52*A^2*b^5*c^5*d^3*e^3*f^2*z^2 - 36*A^2*b^6*c^4*
d^3*e^2*f^3*z^2 - 12*A^2*b^4*c^6*d^4*e^2*f^2*z^2 - 9*A^2*b^6*c^4*d^2*e^4*f^2*z^2 + 836*A^2*a^4*c^6*d^2*e^2*f^4
*z^2 - 668*A^2*a^2*c^8*d^4*e^2*f^2*z^2 + 656*A^2*a^3*c^7*d^2*e^4*f^2*z^2 + 368*A^2*a^3*c^7*d^3*e^2*f^3*z^2 - 4
5*B^2*a^6*b^2*c^2*e^2*f^6*z^2 - 18*B^2*a^5*b^2*c^3*e^4*f^4*z^2 - 9*B^2*a^4*b^2*c^4*e^6*f^2*z^2 - 6*B^2*a^5*b^3
*c^2*e^3*f^5*z^2 + 3*B^2*a^4*b^4*c^2*e^4*f^4*z^2 - 2*B^2*a^4*b^3*c^3*e^5*f^3*z^2 - 580*B^2*a^4*b^2*c^4*d^3*f^5
*z^2 + 536*B^2*a^3*b^4*c^3*d^3*f^5*z^2 + 471*A^2*a^4*b^2*c^4*e^4*f^4*z^2 - 436*A^2*a^3*b^4*c^3*e^4*f^4*z^2 - 3
48*B^2*a^4*b^4*c^2*d^2*f^6*z^2 + 316*B^2*a^2*b^2*c^6*d^5*f^3*z^2 + 310*A^2*a^3*b^3*c^4*e^5*f^3*z^2 + 232*A^2*a
^5*b^2*c^3*e^2*f^6*z^2 - 229*A^2*a^2*b^4*c^4*e^6*f^2*z^2 - 216*A^2*a^4*b^4*c^2*e^2*f^6*z^2 + 204*A^2*a^4*b^3*c
^3*e^3*f^5*z^2 + 200*B^2*a^5*b^2*c^3*d^2*f^6*z^2 + 150*A^2*a^3*b^2*c^5*e^6*f^2*z^2 - 120*B^2*a^2*b^4*c^4*d^4*f
^4*z^2 + 91*A^2*a^2*b^6*c^2*e^4*f^4*z^2 + 72*A^2*a^3*b^5*c^2*e^3*f^5*z^2 - 66*B^2*a^2*b^6*c^2*d^3*f^5*z^2 + 44
*A^2*a^2*b^5*c^3*e^5*f^3*z^2 - 16*B^2*a^3*b^2*c^5*d^4*f^4*z^2 + 1952*A^2*a^4*b^2*c^4*d^2*f^6*z^2 - 1792*A^2*a^
3*b^2*c^5*d^3*f^5*z^2 - 1272*A^2*a^3*b^4*c^3*d^2*f^6*z^2 + 976*A^2*a^2*b^2*c^6*d^4*f^4*z^2 + 960*A^2*a^2*b^4*c
^4*d^3*f^5*z^2 + 282*A^2*a^2*b^6*c^2*d^2*f^6*z^2 - 45*B^2*a^2*b^2*c^6*d^2*e^6*z^2 - 48*A^2*b*c^9*d^6*e*f*z^2 -
14*A^2*a*b^9*d*e*f^6*z^2 - 7*A*B*b^10*d^2*e*f^5*z^2 + 2*A*B*b^10*d*e^3*f^4*z^2 - 64*A*B*a^7*c^3*e*f^7*z^2 - 1
6*A*B*b^9*c*d^3*f^5*z^2 + 8*A*B*a^4*c^6*e^7*f*z^2 + 4*A*B*b*c^9*d^6*e^2*z^2 + 2*A*B*b^6*c^4*d*e^7*z^2 - 120*A*
B*a^3*c^7*d*e^7*z^2 - 16*A*B*a^3*b^7*d*f^7*z^2 + 16*A*B*a*b^9*d^2*f^6*z^2 + 8*A*B*a*c^9*d^5*e^3*z^2 + 12*A*B*a
^3*b*c^6*e^8*z^2 - 48*B^2*b^5*c^5*d^5*e*f^2*z^2 + 15*B^2*b^4*c^6*d^5*e^2*f*z^2 - 14*B^2*b^7*c^3*d^4*e*f^3*z^2
+ 4*B^2*b^9*c*d^2*e^3*f^3*z^2 + 4*B^2*b^7*c^3*d^2*e^5*f*z^2 + 4*B^2*b^5*c^5*d^4*e^3*f*z^2 - B^2*b^6*c^4*d^3*e^
4*f*z^2 - 336*B^2*a^3*c^7*d^3*e^4*f*z^2 + 112*B^2*a^5*c^5*d*e^4*f^3*z^2 - 112*A^2*b^3*c^7*d^5*e*f^2*z^2 + 80*B
^2*a^6*c^4*d*e^2*f^5*z^2 - 48*A^2*b^5*c^5*d^4*e*f^3*z^2 + 36*A^2*b^8*c^2*d*e^4*f^3*z^2 + 36*A^2*b^3*c^7*d^4*e^
3*f*z^2 - 28*A^2*b^7*c^3*d*e^5*f^2*z^2 + 20*A^2*b^2*c^8*d^5*e^2*f*z^2 + 16*B^2*a^2*c^8*d^5*e^2*f*z^2 - 14*A^2*
b^7*c^3*d^3*e*f^4*z^2 - 14*A^2*b^4*c^6*d^3*e^4*f*z^2 - 10*A^2*b^5*c^5*d^2*e^5*f*z^2 - 1008*A^2*a^4*c^6*d*e^4*f
^3*z^2 - 760*A^2*a^5*c^5*d*e^2*f^5*z^2 + 272*A^2*a^2*c^8*d^3*e^4*f*z^2 + 48*B^2*a^5*b*c^4*e^5*f^3*z^2 + 36*B^2
*a^6*b*c^3*e^3*f^5*z^2 + 12*B^2*a^5*b^4*c*e^2*f^6*z^2 - 624*A^2*a^4*b*c^5*e^5*f^3*z^2 - 548*A^2*a^5*b*c^4*e^3*
f^5*z^2 + 182*A^2*a^2*b^3*c^5*e^7*f*z^2 - 180*B^2*a*b^4*c^5*d^5*f^3*z^2 + 132*B^2*a^6*b^2*c^2*d*f^7*z^2 + 108*
B^2*a^3*b^6*c*d^2*f^6*z^2 + 96*A^2*a^5*b^3*c^2*e*f^7*z^2 + 68*A^2*a*b^6*c^3*e^6*f^2*z^2 + 58*A^2*a^3*b^6*c*e^2
*f^6*z^2 - 56*B^2*a*b^2*c^7*d^6*f^2*z^2 - 38*A^2*a^2*b^7*c*e^3*f^5*z^2 - 36*A^2*a*b^7*c^2*e^5*f^3*z^2 + 20*B^2
*a*b^6*c^3*d^4*f^4*z^2 - 736*A^2*a^5*b^2*c^3*d*f^7*z^2 + 624*A^2*a^4*b^4*c^2*d*f^7*z^2 - 416*A^2*a*b^2*c^7*d^5
*f^3*z^2 - 276*A^2*a*b^4*c^5*d^4*f^4*z^2 - 196*A^2*a*b^6*c^3*d^3*f^5*z^2 + 8*B^2*a*b^4*c^5*d^2*e^6*z^2 + 6*B^2
*a*b^2*c^7*d^4*e^4*z^2 + 2*B^2*a^2*b^3*c^5*d*e^7*z^2 + 2*B^2*a*b^3*c^6*d^3*e^5*z^2 - 18*A^2*a*b^2*c^7*d^2*e^6*
z^2 - 16*A*B*b*c^9*d^7*f*z^2 - B^2*b^10*d^2*e^2*f^4*z^2 + 48*B^2*a^7*c^3*e^2*f^6*z^2 - 36*B^2*a^6*c^4*e^4*f^4*
z^2 + 31*B^2*b^6*c^4*d^5*f^3*z^2 - 24*B^2*a^5*c^5*e^6*f^2*z^2 + 20*B^2*b^4*c^6*d^6*f^2*z^2 - 6*A^2*b^8*c^2*e^6
*f^2*z^2 + 2*B^2*b^8*c^2*d^4*f^4*z^2 - 768*B^2*a^5*c^5*d^3*f^5*z^2 + 512*B^2*a^6*c^4*d^2*f^6*z^2 + 512*B^2*a^4
*c^6*d^4*f^4*z^2 + 232*A^2*a^5*c^5*e^4*f^4*z^2 + 188*A^2*a^4*c^6*e^6*f^2*z^2 - 128*B^2*a^3*c^7*d^5*f^3*z^2 + 9
2*A^2*a^6*c^4*e^2*f^6*z^2 + 80*A^2*b^4*c^6*d^5*f^3*z^2 + 64*A^2*b^2*c^8*d^6*f^2*z^2 + 31*A^2*b^6*c^4*d^4*f^4*z
^2 + 14*A^2*b^8*c^2*d^3*f^5*z^2 - 5*B^2*b^4*c^6*d^4*e^4*z^2 + 4*B^2*b^3*c^7*d^5*e^3*z^2 + 2*B^2*b^5*c^5*d^3*e^
5*z^2 - B^2*b^6*c^4*d^2*e^6*z^2 - B^2*b^2*c^8*d^6*e^2*z^2 - B^2*a^4*b^6*e^2*f^6*z^2 - 1152*A^2*a^3*c^7*d^4*f^4
*z^2 + 1008*A^2*a^4*c^6*d^3*f^5*z^2 + 624*A^2*a^2*c^8*d^5*f^3*z^2 - 288*A^2*a^5*c^5*d^2*f^6*z^2 + 56*B^2*a^3*c
^7*d^2*e^6*z^2 - 10*B^2*a^2*b^8*d^2*f^6*z^2 - 9*A^2*b^2*c^8*d^4*e^4*z^2 - 5*A^2*a^2*b^8*e^2*f^6*z^2 - 4*B^2*a^
2*c^8*d^4*e^4*z^2 + 3*A^2*b^4*c^6*d^2*e^6*z^2 - 2*A^2*b^3*c^7*d^3*e^5*z^2 - 36*A^2*a^2*c^8*d^2*e^6*z^2 - 48*A^
2*a^6*b^2*c^2*f^8*z^2 - 45*A^2*a^2*b^2*c^6*e^8*z^2 + 4*A^2*b^10*d*e^2*f^5*z^2 + 4*B^2*b^2*c^8*d^7*f*z^2 + 4*A^
2*b^9*c*e^5*f^3*z^2 + 4*A^2*b^7*c^3*e^7*f*z^2 - 128*B^2*a^7*c^3*d*f^7*z^2 - 160*A^2*a*c^9*d^6*f^2*z^2 - 112*A^
2*a^6*c^4*d*f^7*z^2 + 12*A^2*b*c^9*d^5*e^3*z^2 + 4*A^2*a*b^9*e^3*f^5*z^2 + 3*B^2*a^4*b^6*d*f^7*z^2 + 2*A^2*a^3
*b^7*e*f^7*z^2 - 24*A^2*a*c^9*d^4*e^4*z^2 + 14*A^2*a^2*b^8*d*f^7*z^2 + 12*A^2*a^5*b^4*c*f^8*z^2 + 12*A^2*a*b^4
*c^5*e^8*z^2 + A*B*a^4*b^6*e*f^7*z^2 + B^2*a^2*b^8*d*e^2*f^5*z^2 + 16*A^2*c^10*d^7*f*z^2 + 3*B^2*b^10*d^3*f^5*
z^2 - A^2*b^10*e^4*f^4*z^2 - 4*A^2*c^10*d^6*e^2*z^2 - A^2*b^10*d^2*f^6*z^2 + 64*A^2*a^7*c^3*f^8*z^2 - 4*B^2*a^
4*c^6*e^8*z^2 - A^2*b^6*c^4*e^8*z^2 + 48*A^2*a^3*c^7*e^8*z^2 - A^2*a^4*b^6*f^8*z^2 + 720*A^2*B*a*b^2*c^5*d^2*e
^2*f^3*z - 600*A^2*B*a^2*b^2*c^4*d*e^2*f^4*z + 576*A*B^2*a^2*b^2*c^4*d^2*e*f^4*z + 348*A*B^2*a*b^2*c^5*d^2*e^3
*f^2*z - 336*A*B^2*a^2*b*c^5*d^2*e^2*f^3*z - 260*A*B^2*a*b^3*c^4*d^2*e^2*f^3*z - 240*A*B^2*a^2*b^2*c^4*d*e^3*f
^3*z + 196*A*B^2*a^2*b^3*c^3*d*e^2*f^4*z + 172*A^2*B*a*b*c^6*d*e^5*f*z + 20*A*B^2*a*b^6*c*d*e*f^5*z - 912*A^2*
B*a^2*b*c^5*d^2*e*f^4*z - 644*A^2*B*a*b*c^6*d^2*e^3*f^2*z - 432*A*B^2*a*b^2*c^5*d^3*e*f^3*z + 372*A^2*B*a^2*b*
c^5*d*e^3*f^3*z - 330*A^2*B*a*b^2*c^5*d*e^4*f^2*z + 312*A*B^2*a*b*c^6*d^3*e^2*f^2*z - 208*A*B^2*a^3*b^2*c^3*d*
e*f^5*z + 192*A^2*B*a^2*b^3*c^3*d*e*f^5*z + 172*A^2*B*a*b^3*c^4*d*e^3*f^3*z + 108*A*B^2*a^2*b*c^5*d*e^4*f^2*z
+ 104*A*B^2*a^3*b*c^4*d*e^2*f^4*z - 80*A^2*B*a*b^3*c^4*d^2*e*f^4*z + 68*A^2*B*a*b^4*c^3*d*e^2*f^4*z - 60*A*B^2
*a*b^5*c^2*d*e^2*f^4*z + 58*A*B^2*a*b^3*c^4*d*e^4*f^2*z - 36*A*B^2*a*b^4*c^3*d^2*e*f^4*z - 24*A*B^2*a^2*b^4*c^
2*d*e*f^5*z + 24*A*B^2*a*b^4*c^3*d*e^3*f^3*z + 592*A^2*B*a*b*c^6*d^3*e*f^3*z + 240*A^2*B*a^3*b*c^4*d*e*f^5*z -
132*A*B^2*a*b*c^6*d^2*e^4*f*z - 60*A*B^2*a*b^2*c^5*d*e^5*f*z - 48*A^2*B*a*b^5*c^2*d*e*f^5*z + 20*B^3*a*b*c^6*
d^3*e^3*f*z + 16*B^3*a^4*b*c^3*d*e*f^5*z - 16*B^3*a*b*c^6*d^4*e*f^2*z + 12*B^3*a^2*b*c^5*d*e^5*f*z + 320*A^3*a
*b*c^6*d*e^4*f^2*z + 40*A^3*a*b^4*c^3*d*e*f^5*z - 48*A^2*B*b*c^7*d^4*e*f^2*z - 44*A^2*B*b^3*c^5*d*e^5*f*z - 20
*A*B^2*b*c^7*d^4*e^2*f*z + 14*A*B^2*b^4*c^4*d*e^5*f*z + 12*A^2*B*b*c^7*d^3*e^3*f*z + 4*A*B^2*b^7*c*d*e^2*f^4*z
+ 160*A*B^2*a^4*c^4*d*e*f^5*z + 152*A^2*B*a*c^7*d^2*e^4*f*z - 40*A*B^2*a*c^7*d^3*e^3*f*z + 32*A*B^2*a*c^7*d^4
*e*f^2*z - 16*A*B^2*a^2*c^6*d*e^5*f*z + 128*A^2*B*a^4*b*c^3*e*f^6*z + 42*A^2*B*a*b^2*c^5*e^6*f*z + 24*A^2*B*a^
2*b^5*c*e*f^6*z - 12*A*B^2*a^3*b^4*c*e*f^6*z - 12*A*B^2*a^2*b*c^5*e^6*f*z - 10*A^2*B*a*b^6*c*e^2*f^5*z - 160*A
*B^2*a*b*c^6*d^4*f^3*z + 112*A*B^2*a^4*b*c^3*d*f^6*z - 24*A*B^2*a^2*b^5*c*d*f^6*z - 84*B^3*a*b^2*c^5*d^3*e^2*f
^2*z - 80*B^3*a^2*b^3*c^3*d^2*e*f^4*z - 60*B^3*a^2*b*c^5*d^2*e^3*f^2*z - 20*B^3*a^3*b^2*c^3*d*e^2*f^4*z - 20*B
^3*a*b^3*c^4*d^2*e^3*f^2*z - 9*B^3*a^2*b^2*c^4*d*e^4*f^2*z - 8*B^3*a*b^4*c^3*d^2*e^2*f^3*z + 6*B^3*a^2*b^4*c^2
*d*e^2*f^4*z - 4*B^3*a^2*b^3*c^3*d*e^3*f^3*z - 216*A^2*B*b^4*c^4*d^2*e^2*f^3*z + 196*A^2*B*b^3*c^5*d^2*e^3*f^2
*z - 108*A*B^2*b^3*c^5*d^3*e^2*f^2*z - 94*A*B^2*b^4*c^4*d^2*e^3*f^2*z + 88*A^2*B*b^2*c^6*d^3*e^2*f^2*z + 80*A*
B^2*b^5*c^3*d^2*e^2*f^3*z + 360*A^2*B*a^2*c^6*d^2*e^2*f^3*z + 8*A*B^2*a^2*c^6*d^2*e^3*f^2*z + 153*A^2*B*a^2*b^
2*c^4*e^4*f^3*z - 144*A^2*B*a^2*b^3*c^3*e^3*f^4*z + 80*A^2*B*a^3*b^2*c^3*e^2*f^5*z + 36*A*B^2*a^3*b^2*c^3*e^3*
f^4*z + 12*A^2*B*a^2*b^4*c^2*e^2*f^5*z + 12*A*B^2*a^3*b^3*c^2*e^2*f^5*z + 9*A*B^2*a^2*b^2*c^4*e^5*f^2*z - 6*A*
B^2*a^2*b^4*c^2*e^3*f^4*z + 4*A*B^2*a^2*b^3*c^3*e^4*f^3*z + 480*A^2*B*a^2*b^2*c^4*d^2*f^5*z - 176*A*B^2*a^2*b^
3*c^3*d^2*f^5*z - 10*A^2*B*a*b^6*c*d*f^6*z + 16*A*B^2*a*b*c^6*d*e^6*z + 80*B^3*a*b^3*c^4*d^3*e*f^3*z - 48*B^3*
a^3*b*c^4*d^2*e*f^4*z + 48*B^3*a^2*b*c^5*d^3*e*f^3*z + 44*B^3*a^3*b*c^4*d*e^3*f^3*z + 24*B^3*a*b^5*c^2*d^2*e*f
^4*z + 18*B^3*a*b^2*c^5*d^2*e^4*f*z + 696*A^3*a^2*b*c^5*d*e^2*f^4*z - 504*A^3*a*b*c^6*d^2*e^2*f^3*z - 192*A^3*
a*b^2*c^5*d*e^3*f^3*z - 144*A^3*a^2*b^2*c^4*d*e*f^5*z + 96*A^3*a*b^2*c^5*d^2*e*f^4*z - 72*A^3*a*b^3*c^4*d*e^2*
f^4*z - 208*A^2*B*b^3*c^5*d^3*e*f^3*z + 152*A*B^2*b^4*c^4*d^3*e*f^3*z + 80*A^2*B*b^5*c^3*d^2*e*f^4*z + 75*A^2*
B*b^4*c^4*d*e^4*f^2*z - 59*A^2*B*b^2*c^6*d^2*e^4*f*z - 52*A^2*B*b^5*c^3*d*e^3*f^3*z + 42*A*B^2*b^3*c^5*d^2*e^4
*f*z - 21*A*B^2*b^6*c^2*d^2*e*f^4*z - 16*A*B^2*b^5*c^3*d*e^4*f^2*z + 16*A*B^2*b^2*c^6*d^4*e*f^2*z + 16*A*B^2*b
^2*c^6*d^3*e^3*f*z + 11*A^2*B*b^6*c^2*d*e^2*f^4*z + 4*A*B^2*b^6*c^2*d*e^3*f^3*z - 256*A^2*B*a*c^7*d^3*e^2*f^2*
z - 96*A*B^2*a^3*c^5*d^2*e*f^4*z - 36*A^2*B*a^2*c^6*d*e^4*f^2*z - 32*A^2*B*a^3*c^5*d*e^2*f^4*z - 32*A*B^2*a^2*
c^6*d^3*e*f^3*z + 8*A*B^2*a^3*c^5*d*e^3*f^3*z - 96*A^2*B*a^3*b^3*c^2*e*f^6*z + 68*A^2*B*a^3*b*c^4*e^3*f^4*z -
60*A*B^2*a^4*b*c^3*e^2*f^5*z - 60*A*B^2*a^3*b*c^4*e^4*f^3*z + 48*A*B^2*a^4*b^2*c^2*e*f^6*z - 38*A^2*B*a*b^3*c^
4*e^5*f^2*z - 36*A^2*B*a^2*b*c^5*e^5*f^2*z + 36*A^2*B*a*b^5*c^2*e^3*f^4*z - 16*A^2*B*a*b^4*c^3*e^4*f^3*z + 384
*A*B^2*a^2*b*c^5*d^3*f^4*z - 352*A*B^2*a^3*b*c^4*d^2*f^5*z - 288*A^2*B*a*b^2*c^5*d^3*f^4*z - 160*A^2*B*a^3*b^2
*c^3*d*f^6*z - 148*A^2*B*a*b^4*c^3*d^2*f^5*z + 112*A*B^2*a*b^3*c^4*d^3*f^4*z + 72*A^2*B*a^2*b^4*c^2*d*f^6*z +
72*A*B^2*a*b^5*c^2*d^2*f^5*z + 48*A*B^2*a^3*b^3*c^2*d*f^6*z + 102*B^3*a^2*b^2*c^4*d^2*e^2*f^3*z - 32*B^3*b^5*c
^3*d^3*e*f^3*z - 8*B^3*b^3*c^5*d^3*e^3*f*z - 7*B^3*b^4*c^4*d^2*e^4*f*z + 5*B^3*b^2*c^6*d^4*e^2*f*z + 80*A^3*b^
2*c^6*d^3*e*f^3*z - 74*A^3*b^3*c^5*d*e^4*f^2*z - 64*A^3*b^4*c^4*d^2*e*f^4*z + 60*A^3*b^4*c^4*d*e^3*f^3*z - 48*
B^3*a^4*c^4*d*e^2*f^4*z - 24*B^3*a^3*c^5*d*e^4*f^2*z + 20*B^3*a^2*c^6*d^2*e^4*f*z - 16*A^3*b^5*c^3*d*e^2*f^4*z
+ 8*A^3*b*c^7*d^3*e^2*f^2*z + 480*A^3*a^2*c^6*d^2*e*f^4*z - 392*A^3*a^2*c^6*d*e^3*f^3*z + 280*A^3*a*c^7*d^2*e
^3*f^2*z - 4*B^3*a^4*b*c^3*e^3*f^4*z - 200*A^3*a^3*b*c^4*e^2*f^5*z - 144*A^3*a^2*b*c^5*e^4*f^3*z + 48*B^3*a*b^
2*c^5*d^4*f^3*z + 42*A^3*a*b^2*c^5*e^5*f^2*z - 36*B^3*a^4*b^2*c^2*d*f^6*z - 32*A^3*a^3*b^2*c^3*e*f^6*z - 24*A^
3*a^2*b^4*c^2*e*f^6*z - 24*A^3*a*b^5*c^2*e^2*f^5*z + 10*A^3*a*b^3*c^4*e^4*f^3*z - 4*B^3*a*b^4*c^3*d^3*f^4*z -
4*A^3*a*b^4*c^3*e^3*f^4*z - 480*A^3*a^2*b*c^5*d^2*f^5*z - 160*A^3*a^2*b^3*c^3*d*f^6*z + 128*A^3*a*b^3*c^4*d^2*
f^5*z + 8*A^2*B*b^5*c^3*e^5*f^2*z - 2*A^2*B*b^6*c^2*e^4*f^3*z + 112*A^2*B*b^4*c^4*d^3*f^4*z - 92*A^2*B*a^4*c^4
*e^2*f^5*z - 64*A^2*B*a^3*c^5*e^4*f^3*z - 64*A*B^2*b^5*c^3*d^3*f^4*z + 24*A*B^2*a^4*c^4*e^3*f^4*z + 24*A*B^2*a
^3*c^5*e^5*f^2*z + 16*A^2*B*b^2*c^6*d^4*f^3*z + 16*A*B^2*b^3*c^5*d^4*f^3*z - A^2*B*b^6*c^2*d^2*f^5*z + 448*A^2
*B*a^3*c^5*d^2*f^5*z - 352*A^2*B*a^2*c^6*d^3*f^4*z - 5*A*B^2*b^2*c^6*d^2*e^5*z - 48*A^2*B*a^4*b^2*c^2*f^7*z -
2*B^3*b^7*c*d^2*e*f^4*z + 34*A^3*b^2*c^6*d*e^5*f*z + 16*A^3*b*c^7*d^2*e^4*f*z + 2*A^3*b^6*c^2*d*e*f^5*z - 416*
A^3*a^3*c^5*d*e*f^5*z - 224*A^3*a*c^7*d^3*e*f^3*z + 12*B^3*a^3*b^4*c*d*f^6*z - 10*B^3*a*b^6*c*d^2*f^5*z + 416*
A^3*a^3*b*c^4*d*f^6*z + 224*A^3*a*b*c^6*d^3*f^4*z + 24*A^3*a*b^5*c^2*d*f^6*z - 4*B^3*a*b*c^6*d^2*e^5*z + 20*A^
2*B*c^8*d^4*e^2*f*z - 7*A^2*B*b^4*c^4*e^6*f*z - 2*A^2*B*b^7*c*e^3*f^4*z - 64*A*B^2*a^5*c^3*e*f^6*z + 16*A*B^2*
b*c^7*d^5*f^2*z - 8*A^2*B*a^2*c^6*e^6*f*z - 2*A*B^2*b^7*c*d^2*f^5*z - 272*A^2*B*a^4*c^4*d*f^6*z + 128*A^2*B*a*
c^7*d^4*f^3*z + 9*A^2*B*b^2*c^6*d*e^6*z - 4*A*B^2*b^3*c^5*d*e^6*z + 4*A*B^2*b*c^7*d^3*e^4*z + 8*A*B^2*a*c^7*d^
2*e^5*z + 12*A^2*B*a^3*b^4*c*f^7*z + 30*B^3*b^4*c^4*d^3*e^2*f^2*z + 8*B^3*b^5*c^3*d^2*e^3*f^2*z - 2*B^3*b^6*c^
2*d^2*e^2*f^3*z + 152*A^3*b^3*c^5*d^2*e^2*f^3*z - 108*A^3*b^2*c^6*d^2*e^3*f^2*z + 48*B^3*a^3*c^5*d^2*e^2*f^3*z
- 16*B^3*a^2*c^6*d^3*e^2*f^2*z - 3*B^3*a^4*b^2*c^2*e^2*f^5*z - 120*B^3*a^2*b^2*c^4*d^3*f^4*z + 112*B^3*a^3*b^
2*c^3*d^2*f^5*z + 112*A^3*a^2*b^3*c^3*e^2*f^5*z + 12*A^3*a^2*b^2*c^4*e^3*f^4*z - 120*A^3*a*c^7*d*e^5*f*z - 52*
A^3*a*b*c^6*e^6*f*z + 10*A^3*a*b^6*c*e*f^6*z - 2*A*B^2*b^8*d*e*f^5*z - 2*A^2*B*a*b^7*e*f^6*z - 24*A^2*B*a*c^7*
d*e^6*z + 2*A*B^2*a*b^7*d*f^6*z - 12*A^2*B*a*b*c^6*e^7*z - 2*A^3*b^7*c*d*f^6*z - 4*A^3*b*c^7*d*e^6*z + 16*B^3*
a^5*c^3*e^2*f^5*z + 11*B^3*b^6*c^2*d^3*f^4*z - 11*A^3*b^4*c^4*e^5*f^2*z - 8*B^3*b^4*c^4*d^4*f^3*z - 4*B^3*b^2*
c^6*d^5*f^2*z + 4*B^3*a^4*c^4*e^4*f^3*z + 4*A^3*b^5*c^3*e^4*f^3*z - A^3*b^6*c^2*e^3*f^4*z + 136*A^3*a^3*c^5*e^
3*f^4*z + 68*A^3*a^2*c^6*e^5*f^2*z - 64*A^3*b^3*c^5*d^3*f^4*z + 2*B^3*b^3*c^5*d^2*e^5*z - B^3*b^2*c^6*d^3*e^4*
z + 96*A^3*a^3*b^3*c^2*f^7*z + A*B^2*a^2*b^6*e*f^6*z + 32*A^3*c^8*d^4*e*f^2*z - 24*A^3*c^8*d^3*e^3*f*z + 10*A^
3*b^3*c^5*e^6*f*z + 2*A^3*b^7*c*e^2*f^5*z + 128*A^3*a^4*c^4*e*f^6*z - 32*A^3*b*c^7*d^4*f^3*z - 4*B^3*a^2*c^6*d
*e^6*z - B^3*a^2*b^6*d*f^6*z - 128*A^3*a^4*b*c^3*f^7*z - 24*A^3*a^2*b^5*c*f^7*z - 16*A^2*B*c^8*d^5*f^2*z - 4*A
^2*B*c^8*d^3*e^4*z + 64*A^2*B*a^5*c^3*f^7*z + 2*A^2*B*b^3*c^5*e^7*z + 4*A*B^2*a^2*c^6*e^7*z - A^2*B*a^2*b^6*f^
7*z + 4*A^3*c^8*d^2*e^5*z - 3*A^3*b^2*c^6*e^7*z + A^2*B*b^8*d*f^6*z - A^3*b^8*e*f^6*z + 16*A^3*a*c^7*e^7*z + 2
*A^3*a*b^7*f^7*z + A^2*B*b^8*e^2*f^5*z + B^3*b^8*d^2*f^5*z - 48*A^2*B^2*a*b*c^4*d*e*f^4 + 28*A*B^3*a*b^2*c^3*d
*e*f^4 - 16*A*B^3*a*b*c^4*d*e^2*f^3 + 16*A^3*B*a*c^5*d*e*f^4 + 32*A^3*B*a*b*c^4*d*f^5 + 12*A^2*B^2*b^3*c^3*d*e
*f^4 + 5*A*B^3*b^2*c^4*d^2*e*f^3 + 4*A*B^3*b^3*c^3*d*e^2*f^3 + 24*A^2*B^2*a*c^5*d*e^2*f^3 + 24*A^2*B^2*a^2*b*c
^3*e*f^5 + 12*A^2*B^2*a*b*c^4*e^3*f^3 - 6*A^2*B^2*a*b^3*c^2*e*f^5 + 4*A*B^3*a^2*b*c^3*e^2*f^4 + 3*A*B^3*a^2*b^
2*c^2*e*f^5 - 18*A^2*B^2*a*b^2*c^3*d*f^5 - 4*B^4*a^2*b*c^3*d*e*f^4 + 4*B^4*a*b*c^4*d^2*e*f^3 - 6*A*B^3*b^4*c^2
*d*e*f^4 + 4*A^3*B*b*c^5*d*e^2*f^3 - 2*A^3*B*b^2*c^4*d*e*f^4 - 8*A*B^3*a^2*c^4*d*e*f^4 - 8*A*B^3*a*c^5*d^2*e*f
^3 + 26*A^3*B*a*b^2*c^3*e*f^5 + 8*A^3*B*a*b*c^4*e^2*f^4 + 32*A*B^3*a*b*c^4*d^2*f^4 - 28*A*B^3*a^2*b*c^3*d*f^5
+ 6*A*B^3*a*b^3*c^2*d*f^5 - 9*A^2*B^2*b^2*c^4*d*e^2*f^3 - 18*A^2*B^2*a*b^2*c^3*e^2*f^4 - 4*A^3*B*c^6*d^2*e*f^3
- 3*A^3*B*b^4*c^2*e*f^5 - 44*A^3*B*a^2*c^4*e*f^5 - 16*A^3*B*a*c^5*e^3*f^3 - 16*A*B^3*a^3*c^3*e*f^5 - 10*A^3*B
*b^3*c^3*d*f^5 - 4*A^3*B*b*c^5*d^2*f^4 - 4*A*B^3*b*c^5*d^3*f^3 - 28*A^3*B*a^2*b*c^3*f^6 + 6*A^3*B*a*b^3*c^2*f^
6 - 4*A^4*b*c^5*d*e*f^4 - 20*A^4*a*b*c^4*e*f^5 + 3*A^2*B^2*b^4*c^2*e^2*f^4 - 2*A^2*B^2*b^3*c^3*e^3*f^3 + 12*A^
2*B^2*a^2*c^4*e^2*f^4 + 9*A^2*B^2*b^2*c^4*d^2*f^4 - 3*A^2*B^2*a^2*b^2*c^2*f^6 - 2*B^4*b^3*c^3*d^2*e*f^3 + 4*B^
4*a^2*c^4*d*e^2*f^3 - 10*B^4*a*b^2*c^3*d^2*f^4 - 3*B^4*a^2*b^2*c^2*d*f^5 + 3*A^3*B*b^2*c^4*e^3*f^3 - 2*A^3*B*b
^3*c^3*e^2*f^4 - 10*A*B^3*b^3*c^3*d^2*f^4 - 4*A*B^3*a^2*c^4*e^3*f^3 + 3*A^2*B^2*b^4*c^2*d*f^5 + 36*A^2*B^2*a^2
*c^4*d*f^5 - 24*A^2*B^2*a*c^5*d^2*f^4 + 4*A^2*B^2*c^6*d^3*f^3 + 16*A^2*B^2*a^3*c^3*f^6 + 4*A^4*b^3*c^3*e*f^5 +
16*B^4*a^3*c^3*d*f^5 + 16*A^4*a*c^5*e^2*f^4 + 8*A^4*b^2*c^4*d*f^5 - 8*A^4*a*b^2*c^3*f^6 - 24*A^4*a*c^5*d*f^5
+ 3*B^4*b^4*c^2*d^2*f^4 - 3*A^4*b^2*c^4*e^2*f^4 + 4*A^4*c^6*d^2*f^4 + 36*A^4*a^2*c^4*f^6 + B^4*b^2*c^4*d^3*f^3
, z, k), k, 1, 4) - ((A*b^3*f + 2*A*a*c^2*e + A*b*c^2*d - 2*B*a*c^2*d - A*b^2*c*e - B*a*b^2*f + 2*B*a^2*c*f -
3*A*a*b*c*f + B*a*b*c*e)/(a^2*b^2*f^2 - 4*a^3*c*f^2 - 4*a*c^3*d^2 - 4*a^2*c^2*e^2 + b^2*c^2*d^2 + b^4*d*f - a*
b^3*e*f - b^3*c*d*e + a*b^2*c*e^2 + 8*a^2*c^2*d*f + 4*a*b*c^2*d*e - 6*a*b^2*c*d*f + 4*a^2*b*c*e*f) - (x*(2*A*a
*c^2*f - 2*A*c^3*d + A*b*c^2*e - 2*B*a*c^2*e + B*b*c^2*d - A*b^2*c*f + B*a*b*c*f))/(a^2*b^2*f^2 - 4*a^3*c*f^2
- 4*a*c^3*d^2 - 4*a^2*c^2*e^2 + b^2*c^2*d^2 + b^4*d*f - a*b^3*e*f - b^3*c*d*e + a*b^2*c*e^2 + 8*a^2*c^2*d*f +
4*a*b*c^2*d*e - 6*a*b^2*c*d*f + 4*a^2*b*c*e*f))/(a + b*x + c*x^2)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((B*x+A)/(c*x**2+b*x+a)**2/(f*x**2+e*x+d),x)

[Out]

Timed out

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