3.818 \(\int \frac {1}{(d+e x) (f+g x) (a+b x+c x^2)^2} \, dx\)

Optimal. Leaf size=644 \[ \frac {\tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right ) \left (2 c e g \left (a^2 e^2 g^2+a b e g (d g+e f)-b^2 (d g+e f)^2\right )+b^2 e^2 g^2 (-2 a e g+b d g+b e f)-c^2 \left (4 a d e^2 f g^2-b \left (d^3 g^3+5 d^2 e f g^2+5 d e^2 f^2 g+e^3 f^3\right )\right )-2 c^3 d f \left (d^2 g^2+d e f g+e^2 f^2\right )\right )}{\sqrt {b^2-4 a c} \left (a e^2-b d e+c d^2\right )^2 \left (c f^2-g (b f-a g)\right )^2}+\frac {2 c \tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right ) \left (-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right )}{\left (b^2-4 a c\right )^{3/2} \left (a e^2-b d e+c d^2\right ) \left (c f^2-g (b f-a g)\right )}-\frac {c x \left (-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right )+b c (c d f-3 a e g)+2 a c^2 (d g+e f)+b^3 e g-b^2 c (d g+e f)}{\left (b^2-4 a c\right ) \left (a+b x+c x^2\right ) \left (a e^2-b d e+c d^2\right ) \left (c f^2-g (b f-a g)\right )}-\frac {\log \left (a+b x+c x^2\right ) (-b e g+c d g+c e f) \left (e g (2 a e g-b (d g+e f))+c \left (d^2 g^2+e^2 f^2\right )\right )}{2 \left (a e^2-b d e+c d^2\right )^2 \left (c f^2-g (b f-a g)\right )^2}+\frac {e^4 \log (d+e x)}{(e f-d g) \left (a e^2-b d e+c d^2\right )^2}-\frac {g^4 \log (f+g x)}{(e f-d g) \left (a g^2-b f g+c f^2\right )^2} \]

[Out]

(-b^3*e*g+b^2*c*(d*g+e*f)-2*a*c^2*(d*g+e*f)-b*c*(-3*a*e*g+c*d*f)-c*(2*c^2*d*f+b^2*e*g-c*(2*a*e*g+b*d*g+b*e*f))
*x)/(-4*a*c+b^2)/(a*e^2-b*d*e+c*d^2)/(c*f^2-g*(-a*g+b*f))/(c*x^2+b*x+a)+2*c*(2*c^2*d*f+b^2*e*g-c*(2*a*e*g+b*d*
g+b*e*f))*arctanh((2*c*x+b)/(-4*a*c+b^2)^(1/2))/(-4*a*c+b^2)^(3/2)/(a*e^2-b*d*e+c*d^2)/(c*f^2-g*(-a*g+b*f))+e^
4*ln(e*x+d)/(a*e^2-b*d*e+c*d^2)^2/(-d*g+e*f)-g^4*ln(g*x+f)/(-d*g+e*f)/(a*g^2-b*f*g+c*f^2)^2-1/2*(-b*e*g+c*d*g+
c*e*f)*(c*(d^2*g^2+e^2*f^2)+e*g*(2*a*e*g-b*(d*g+e*f)))*ln(c*x^2+b*x+a)/(a*e^2-b*d*e+c*d^2)^2/(c*f^2-g*(-a*g+b*
f))^2+(b^2*e^2*g^2*(-2*a*e*g+b*d*g+b*e*f)-2*c^3*d*f*(d^2*g^2+d*e*f*g+e^2*f^2)+2*c*e*g*(a^2*e^2*g^2+a*b*e*g*(d*
g+e*f)-b^2*(d*g+e*f)^2)-c^2*(4*a*d*e^2*f*g^2-b*(d^3*g^3+5*d^2*e*f*g^2+5*d*e^2*f^2*g+e^3*f^3)))*arctanh((2*c*x+
b)/(-4*a*c+b^2)^(1/2))/(a*e^2-b*d*e+c*d^2)^2/(c*f^2-g*(-a*g+b*f))^2/(-4*a*c+b^2)^(1/2)

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Rubi [A]  time = 2.05, antiderivative size = 644, normalized size of antiderivative = 1.00, number of steps used = 9, number of rules used = 6, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {893, 638, 618, 206, 634, 628} \[ \frac {\tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right ) \left (2 c e g \left (a^2 e^2 g^2+a b e g (d g+e f)-b^2 (d g+e f)^2\right )+b^2 e^2 g^2 (-2 a e g+b d g+b e f)-c^2 \left (4 a d e^2 f g^2-b \left (5 d^2 e f g^2+d^3 g^3+5 d e^2 f^2 g+e^3 f^3\right )\right )-2 c^3 d f \left (d^2 g^2+d e f g+e^2 f^2\right )\right )}{\sqrt {b^2-4 a c} \left (a e^2-b d e+c d^2\right )^2 \left (c f^2-g (b f-a g)\right )^2}-\frac {c x \left (-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right )+b c (c d f-3 a e g)+2 a c^2 (d g+e f)-b^2 c (d g+e f)+b^3 e g}{\left (b^2-4 a c\right ) \left (a+b x+c x^2\right ) \left (a e^2-b d e+c d^2\right ) \left (c f^2-g (b f-a g)\right )}+\frac {2 c \tanh ^{-1}\left (\frac {b+2 c x}{\sqrt {b^2-4 a c}}\right ) \left (-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right )}{\left (b^2-4 a c\right )^{3/2} \left (a e^2-b d e+c d^2\right ) \left (c f^2-g (b f-a g)\right )}-\frac {\log \left (a+b x+c x^2\right ) (-b e g+c d g+c e f) \left (e g (2 a e g-b (d g+e f))+c \left (d^2 g^2+e^2 f^2\right )\right )}{2 \left (a e^2-b d e+c d^2\right )^2 \left (c f^2-g (b f-a g)\right )^2}+\frac {e^4 \log (d+e x)}{(e f-d g) \left (a e^2-b d e+c d^2\right )^2}-\frac {g^4 \log (f+g x)}{(e f-d g) \left (a g^2-b f g+c f^2\right )^2} \]

Antiderivative was successfully verified.

[In]

Int[1/((d + e*x)*(f + g*x)*(a + b*x + c*x^2)^2),x]

[Out]

-((b^3*e*g - b^2*c*(e*f + d*g) + 2*a*c^2*(e*f + d*g) + b*c*(c*d*f - 3*a*e*g) + c*(2*c^2*d*f + b^2*e*g - c*(b*e
*f + b*d*g + 2*a*e*g))*x)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(c*f^2 - g*(b*f - a*g))*(a + b*x + c*x^2))) +
(2*c*(2*c^2*d*f + b^2*e*g - c*(b*e*f + b*d*g + 2*a*e*g))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*
c)^(3/2)*(c*d^2 - b*d*e + a*e^2)*(c*f^2 - g*(b*f - a*g))) + ((b^2*e^2*g^2*(b*e*f + b*d*g - 2*a*e*g) - 2*c^3*d*
f*(e^2*f^2 + d*e*f*g + d^2*g^2) + 2*c*e*g*(a^2*e^2*g^2 + a*b*e*g*(e*f + d*g) - b^2*(e*f + d*g)^2) - c^2*(4*a*d
*e^2*f*g^2 - b*(e^3*f^3 + 5*d*e^2*f^2*g + 5*d^2*e*f*g^2 + d^3*g^3)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(
Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^2*(c*f^2 - g*(b*f - a*g))^2) + (e^4*Log[d + e*x])/((c*d^2 - b*d*e +
a*e^2)^2*(e*f - d*g)) - (g^4*Log[f + g*x])/((e*f - d*g)*(c*f^2 - b*f*g + a*g^2)^2) - ((c*e*f + c*d*g - b*e*g)*
(c*(e^2*f^2 + d^2*g^2) + e*g*(2*a*e*g - b*(e*f + d*g)))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^2*(c*
f^2 - g*(b*f - a*g))^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 638

Int[((d_.) + (e_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((b*d - 2*a*e + (2*c*d -
b*e)*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)), x] - Dist[((2*p + 3)*(2*c*d - b*e))/((p + 1)*(b^2
- 4*a*c)), Int[(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e}, x] && NeQ[2*c*d - b*e, 0] && NeQ[b^
2 - 4*a*c, 0] && LtQ[p, -1] && NeQ[p, -3/2]

Rule 893

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))^(n_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :
> Int[ExpandIntegrand[(d + e*x)^m*(f + g*x)^n*(a + b*x + c*x^2)^p, x], x] /; FreeQ[{a, b, c, d, e, f, g}, x] &
& NeQ[e*f - d*g, 0] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && IntegerQ[p] && ((EqQ[p, 1] && I
ntegersQ[m, n]) || (ILtQ[m, 0] && ILtQ[n, 0]))

Rubi steps

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

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Mathematica [A]  time = 2.63, size = 710, normalized size = 1.10 \[ \frac {\tan ^{-1}\left (\frac {b+2 c x}{\sqrt {4 a c-b^2}}\right ) \left (-2 c^3 \left (2 a^2 e g \left (d^2 g^2-5 d e f g+e^2 f^2\right )+a b \left (3 d^3 g^3+11 d^2 e f g^2+11 d e^2 f^2 g+3 e^3 f^3\right )-4 b^2 d^2 e f^2 g\right )-2 b^2 c e g \left (-6 a^2 e^2 g^2+2 a b e g (d g+e f)+b^2 \left (d^2 g^2+d e f g+e^2 f^2\right )\right )+c^2 \left (-12 a^3 e^3 g^3-6 a^2 b e^2 g^2 (d g+e f)+12 a b^2 e g \left (d^2 g^2+d e f g+e^2 f^2\right )+b^3 \left (d^3 g^3+d^2 e f g^2+d e^2 f^2 g+e^3 f^3\right )\right )+b^4 e^2 g^2 (-2 a e g+b d g+b e f)+2 c^4 d f \left (2 a \left (3 d^2 g^2+d e f g+3 e^2 f^2\right )-3 b d f (d g+e f)\right )+4 c^5 d^3 f^3\right )}{\left (4 a c-b^2\right )^{3/2} \left (e (a e-b d)+c d^2\right )^2 \left (g (a g-b f)+c f^2\right )^2}+\frac {b c (3 a e g+c (-d f+d g x+e f x))-2 c^2 (a d g+a e (f-g x)+c d f x)+b^3 (-e) g+b^2 c (d g+e (f-g x))}{\left (b^2-4 a c\right ) (a+x (b+c x)) \left (e (b d-a e)-c d^2\right ) \left (g (b f-a g)-c f^2\right )}+\frac {e^4 \log (d+e x)}{(e f-d g) \left (e (a e-b d)+c d^2\right )^2}-\frac {\log (a+x (b+c x)) (-b e g+c d g+c e f) \left (e g (2 a e g-b (d g+e f))+c \left (d^2 g^2+e^2 f^2\right )\right )}{2 \left (e (a e-b d)+c d^2\right )^2 \left (g (a g-b f)+c f^2\right )^2}-\frac {g^4 \log (f+g x)}{(e f-d g) \left (g (a g-b f)+c f^2\right )^2} \]

Antiderivative was successfully verified.

[In]

Integrate[1/((d + e*x)*(f + g*x)*(a + b*x + c*x^2)^2),x]

[Out]

(-(b^3*e*g) + b^2*c*(d*g + e*(f - g*x)) - 2*c^2*(a*d*g + c*d*f*x + a*e*(f - g*x)) + b*c*(3*a*e*g + c*(-(d*f) +
e*f*x + d*g*x)))/((b^2 - 4*a*c)*(-(c*d^2) + e*(b*d - a*e))*(-(c*f^2) + g*(b*f - a*g))*(a + x*(b + c*x))) + ((
4*c^5*d^3*f^3 + b^4*e^2*g^2*(b*e*f + b*d*g - 2*a*e*g) - 2*b^2*c*e*g*(-6*a^2*e^2*g^2 + 2*a*b*e*g*(e*f + d*g) +
b^2*(e^2*f^2 + d*e*f*g + d^2*g^2)) + 2*c^4*d*f*(-3*b*d*f*(e*f + d*g) + 2*a*(3*e^2*f^2 + d*e*f*g + 3*d^2*g^2))
+ c^2*(-12*a^3*e^3*g^3 - 6*a^2*b*e^2*g^2*(e*f + d*g) + 12*a*b^2*e*g*(e^2*f^2 + d*e*f*g + d^2*g^2) + b^3*(e^3*f
^3 + d*e^2*f^2*g + d^2*e*f*g^2 + d^3*g^3)) - 2*c^3*(-4*b^2*d^2*e*f^2*g + 2*a^2*e*g*(e^2*f^2 - 5*d*e*f*g + d^2*
g^2) + a*b*(3*e^3*f^3 + 11*d*e^2*f^2*g + 11*d^2*e*f*g^2 + 3*d^3*g^3)))*ArcTan[(b + 2*c*x)/Sqrt[-b^2 + 4*a*c]])
/((-b^2 + 4*a*c)^(3/2)*(c*d^2 + e*(-(b*d) + a*e))^2*(c*f^2 + g*(-(b*f) + a*g))^2) + (e^4*Log[d + e*x])/((c*d^2
+ e*(-(b*d) + a*e))^2*(e*f - d*g)) - (g^4*Log[f + g*x])/((e*f - d*g)*(c*f^2 + g*(-(b*f) + a*g))^2) - ((c*e*f
+ c*d*g - b*e*g)*(c*(e^2*f^2 + d^2*g^2) + e*g*(2*a*e*g - b*(e*f + d*g)))*Log[a + x*(b + c*x)])/(2*(c*d^2 + e*(
-(b*d) + a*e))^2*(c*f^2 + g*(-(b*f) + a*g))^2)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)/(g*x+f)/(c*x^2+b*x+a)^2,x, algorithm="fricas")

[Out]

Timed out

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giac [B]  time = 0.28, size = 3315, normalized size = 5.15 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)/(g*x+f)/(c*x^2+b*x+a)^2,x, algorithm="giac")

[Out]

g^5*log(abs(g*x + f))/(c^2*d*f^4*g^2 - 2*b*c*d*f^3*g^3 + b^2*d*f^2*g^4 + 2*a*c*d*f^2*g^4 - 2*a*b*d*f*g^5 + a^2
*d*g^6 - c^2*f^5*g*e + 2*b*c*f^4*g^2*e - b^2*f^3*g^3*e - 2*a*c*f^3*g^3*e + 2*a*b*f^2*g^4*e - a^2*f*g^5*e) - 1/
2*(c^2*d^3*g^3 + c^2*d^2*f*g^2*e - 2*b*c*d^2*g^3*e + c^2*d*f^2*g*e^2 - 2*b*c*d*f*g^2*e^2 + b^2*d*g^3*e^2 + 2*a
*c*d*g^3*e^2 + c^2*f^3*e^3 - 2*b*c*f^2*g*e^3 + b^2*f*g^2*e^3 + 2*a*c*f*g^2*e^3 - 2*a*b*g^3*e^3)*log(c*x^2 + b*
x + a)/(c^4*d^4*f^4 - 2*b*c^3*d^4*f^3*g + b^2*c^2*d^4*f^2*g^2 + 2*a*c^3*d^4*f^2*g^2 - 2*a*b*c^2*d^4*f*g^3 + a^
2*c^2*d^4*g^4 - 2*b*c^3*d^3*f^4*e + 4*b^2*c^2*d^3*f^3*g*e - 2*b^3*c*d^3*f^2*g^2*e - 4*a*b*c^2*d^3*f^2*g^2*e +
4*a*b^2*c*d^3*f*g^3*e - 2*a^2*b*c*d^3*g^4*e + b^2*c^2*d^2*f^4*e^2 + 2*a*c^3*d^2*f^4*e^2 - 2*b^3*c*d^2*f^3*g*e^
2 - 4*a*b*c^2*d^2*f^3*g*e^2 + b^4*d^2*f^2*g^2*e^2 + 4*a*b^2*c*d^2*f^2*g^2*e^2 + 4*a^2*c^2*d^2*f^2*g^2*e^2 - 2*
a*b^3*d^2*f*g^3*e^2 - 4*a^2*b*c*d^2*f*g^3*e^2 + a^2*b^2*d^2*g^4*e^2 + 2*a^3*c*d^2*g^4*e^2 - 2*a*b*c^2*d*f^4*e^
3 + 4*a*b^2*c*d*f^3*g*e^3 - 2*a*b^3*d*f^2*g^2*e^3 - 4*a^2*b*c*d*f^2*g^2*e^3 + 4*a^2*b^2*d*f*g^3*e^3 - 2*a^3*b*
d*g^4*e^3 + a^2*c^2*f^4*e^4 - 2*a^2*b*c*f^3*g*e^4 + a^2*b^2*f^2*g^2*e^4 + 2*a^3*c*f^2*g^2*e^4 - 2*a^3*b*f*g^3*
e^4 + a^4*g^4*e^4) - e^5*log(abs(x*e + d))/(c^2*d^5*g*e - c^2*d^4*f*e^2 - 2*b*c*d^4*g*e^2 + 2*b*c*d^3*f*e^3 +
b^2*d^3*g*e^3 + 2*a*c*d^3*g*e^3 - b^2*d^2*f*e^4 - 2*a*c*d^2*f*e^4 - 2*a*b*d^2*g*e^4 + 2*a*b*d*f*e^5 + a^2*d*g*
e^5 - a^2*f*e^6) - (4*c^5*d^3*f^3 - 6*b*c^4*d^3*f^2*g + 12*a*c^4*d^3*f*g^2 + b^3*c^2*d^3*g^3 - 6*a*b*c^3*d^3*g
^3 - 6*b*c^4*d^2*f^3*e + 8*b^2*c^3*d^2*f^2*g*e + 4*a*c^4*d^2*f^2*g*e + b^3*c^2*d^2*f*g^2*e - 22*a*b*c^3*d^2*f*
g^2*e - 2*b^4*c*d^2*g^3*e + 12*a*b^2*c^2*d^2*g^3*e - 4*a^2*c^3*d^2*g^3*e + 12*a*c^4*d*f^3*e^2 + b^3*c^2*d*f^2*
g*e^2 - 22*a*b*c^3*d*f^2*g*e^2 - 2*b^4*c*d*f*g^2*e^2 + 12*a*b^2*c^2*d*f*g^2*e^2 + 20*a^2*c^3*d*f*g^2*e^2 + b^5
*d*g^3*e^2 - 4*a*b^3*c*d*g^3*e^2 - 6*a^2*b*c^2*d*g^3*e^2 + b^3*c^2*f^3*e^3 - 6*a*b*c^3*f^3*e^3 - 2*b^4*c*f^2*g
*e^3 + 12*a*b^2*c^2*f^2*g*e^3 - 4*a^2*c^3*f^2*g*e^3 + b^5*f*g^2*e^3 - 4*a*b^3*c*f*g^2*e^3 - 6*a^2*b*c^2*f*g^2*
e^3 - 2*a*b^4*g^3*e^3 + 12*a^2*b^2*c*g^3*e^3 - 12*a^3*c^2*g^3*e^3)*arctan((2*c*x + b)/sqrt(-b^2 + 4*a*c))/((b^
2*c^4*d^4*f^4 - 4*a*c^5*d^4*f^4 - 2*b^3*c^3*d^4*f^3*g + 8*a*b*c^4*d^4*f^3*g + b^4*c^2*d^4*f^2*g^2 - 2*a*b^2*c^
3*d^4*f^2*g^2 - 8*a^2*c^4*d^4*f^2*g^2 - 2*a*b^3*c^2*d^4*f*g^3 + 8*a^2*b*c^3*d^4*f*g^3 + a^2*b^2*c^2*d^4*g^4 -
4*a^3*c^3*d^4*g^4 - 2*b^3*c^3*d^3*f^4*e + 8*a*b*c^4*d^3*f^4*e + 4*b^4*c^2*d^3*f^3*g*e - 16*a*b^2*c^3*d^3*f^3*g
*e - 2*b^5*c*d^3*f^2*g^2*e + 4*a*b^3*c^2*d^3*f^2*g^2*e + 16*a^2*b*c^3*d^3*f^2*g^2*e + 4*a*b^4*c*d^3*f*g^3*e -
16*a^2*b^2*c^2*d^3*f*g^3*e - 2*a^2*b^3*c*d^3*g^4*e + 8*a^3*b*c^2*d^3*g^4*e + b^4*c^2*d^2*f^4*e^2 - 2*a*b^2*c^3
*d^2*f^4*e^2 - 8*a^2*c^4*d^2*f^4*e^2 - 2*b^5*c*d^2*f^3*g*e^2 + 4*a*b^3*c^2*d^2*f^3*g*e^2 + 16*a^2*b*c^3*d^2*f^
3*g*e^2 + b^6*d^2*f^2*g^2*e^2 - 12*a^2*b^2*c^2*d^2*f^2*g^2*e^2 - 16*a^3*c^3*d^2*f^2*g^2*e^2 - 2*a*b^5*d^2*f*g^
3*e^2 + 4*a^2*b^3*c*d^2*f*g^3*e^2 + 16*a^3*b*c^2*d^2*f*g^3*e^2 + a^2*b^4*d^2*g^4*e^2 - 2*a^3*b^2*c*d^2*g^4*e^2
- 8*a^4*c^2*d^2*g^4*e^2 - 2*a*b^3*c^2*d*f^4*e^3 + 8*a^2*b*c^3*d*f^4*e^3 + 4*a*b^4*c*d*f^3*g*e^3 - 16*a^2*b^2*
c^2*d*f^3*g*e^3 - 2*a*b^5*d*f^2*g^2*e^3 + 4*a^2*b^3*c*d*f^2*g^2*e^3 + 16*a^3*b*c^2*d*f^2*g^2*e^3 + 4*a^2*b^4*d
*f*g^3*e^3 - 16*a^3*b^2*c*d*f*g^3*e^3 - 2*a^3*b^3*d*g^4*e^3 + 8*a^4*b*c*d*g^4*e^3 + a^2*b^2*c^2*f^4*e^4 - 4*a^
3*c^3*f^4*e^4 - 2*a^2*b^3*c*f^3*g*e^4 + 8*a^3*b*c^2*f^3*g*e^4 + a^2*b^4*f^2*g^2*e^4 - 2*a^3*b^2*c*f^2*g^2*e^4
- 8*a^4*c^2*f^2*g^2*e^4 - 2*a^3*b^3*f*g^3*e^4 + 8*a^4*b*c*f*g^3*e^4 + a^4*b^2*g^4*e^4 - 4*a^5*c*g^4*e^4)*sqrt(
-b^2 + 4*a*c)) - (b*c^4*d^3*f^3 - 2*b^2*c^3*d^3*f^2*g + 2*a*c^4*d^3*f^2*g + b^3*c^2*d^3*f*g^2 - a*b*c^3*d^3*f*
g^2 - a*b^2*c^2*d^3*g^3 + 2*a^2*c^3*d^3*g^3 - 2*b^2*c^3*d^2*f^3*e + 2*a*c^4*d^2*f^3*e + 4*b^3*c^2*d^2*f^2*g*e
- 7*a*b*c^3*d^2*f^2*g*e - 2*b^4*c*d^2*f*g^2*e + 3*a*b^2*c^2*d^2*f*g^2*e + 2*a^2*c^3*d^2*f*g^2*e + 2*a*b^3*c*d^
2*g^3*e - 5*a^2*b*c^2*d^2*g^3*e + b^3*c^2*d*f^3*e^2 - a*b*c^3*d*f^3*e^2 - 2*b^4*c*d*f^2*g*e^2 + 3*a*b^2*c^2*d*
f^2*g*e^2 + 2*a^2*c^3*d*f^2*g*e^2 + b^5*d*f*g^2*e^2 - a*b^3*c*d*f*g^2*e^2 - 3*a^2*b*c^2*d*f*g^2*e^2 - a*b^4*d*
g^3*e^2 + 2*a^2*b^2*c*d*g^3*e^2 + 2*a^3*c^2*d*g^3*e^2 - a*b^2*c^2*f^3*e^3 + 2*a^2*c^3*f^3*e^3 + 2*a*b^3*c*f^2*
g*e^3 - 5*a^2*b*c^2*f^2*g*e^3 - a*b^4*f*g^2*e^3 + 2*a^2*b^2*c*f*g^2*e^3 + 2*a^3*c^2*f*g^2*e^3 + a^2*b^3*g^3*e^
3 - 3*a^3*b*c*g^3*e^3 + (2*c^5*d^3*f^3 - 3*b*c^4*d^3*f^2*g + b^2*c^3*d^3*f*g^2 + 2*a*c^4*d^3*f*g^2 - a*b*c^3*d
^3*g^3 - 3*b*c^4*d^2*f^3*e + 5*b^2*c^3*d^2*f^2*g*e - 2*a*c^4*d^2*f^2*g*e - 2*b^3*c^2*d^2*f*g^2*e - a*b*c^3*d^2
*f*g^2*e + 2*a*b^2*c^2*d^2*g^3*e - 2*a^2*c^3*d^2*g^3*e + b^2*c^3*d*f^3*e^2 + 2*a*c^4*d*f^3*e^2 - 2*b^3*c^2*d*f
^2*g*e^2 - a*b*c^3*d*f^2*g*e^2 + b^4*c*d*f*g^2*e^2 + 2*a^2*c^3*d*f*g^2*e^2 - a*b^3*c*d*g^3*e^2 + a^2*b*c^2*d*g
^3*e^2 - a*b*c^3*f^3*e^3 + 2*a*b^2*c^2*f^2*g*e^3 - 2*a^2*c^3*f^2*g*e^3 - a*b^3*c*f*g^2*e^3 + a^2*b*c^2*f*g^2*e
^3 + a^2*b^2*c*g^3*e^3 - 2*a^3*c^2*g^3*e^3)*x)/((c*d^2 - b*d*e + a*e^2)^2*(c*f^2 - b*f*g + a*g^2)^2*(c*x^2 + b
*x + a)*(b^2 - 4*a*c))

________________________________________________________________________________________

maple [B]  time = 0.05, size = 9103, normalized size = 14.14 \[ \text {output too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(e*x+d)/(g*x+f)/(c*x^2+b*x+a)^2,x)

[Out]

result too large to display

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)/(g*x+f)/(c*x^2+b*x+a)^2,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*a*c-b^2>0)', see `assume?` f
or more details)Is 4*a*c-b^2 positive or negative?

________________________________________________________________________________________

mupad [B]  time = 32.63, size = 130035, normalized size = 201.92 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((f + g*x)*(d + e*x)*(a + b*x + c*x^2)^2),x)

[Out]

((b^3*e*g + 2*a*c^2*d*g + 2*a*c^2*e*f + b*c^2*d*f - b^2*c*d*g - b^2*c*e*f - 3*a*b*c*e*g)/(4*a*c^3*d^2*f^2 + 4*
a^3*c*e^2*g^2 - a^2*b^2*e^2*g^2 + 4*a^2*c^2*d^2*g^2 + 4*a^2*c^2*e^2*f^2 - b^2*c^2*d^2*f^2 + a*b^3*d*e*g^2 + b^
3*c*d*e*f^2 + a*b^3*e^2*f*g + b^3*c*d^2*f*g - a*b^2*c*d^2*g^2 - a*b^2*c*e^2*f^2 - b^4*d*e*f*g - 4*a*b*c^2*d*e*
f^2 - 4*a^2*b*c*d*e*g^2 - 4*a*b*c^2*d^2*f*g - 4*a^2*b*c*e^2*f*g + 4*a*b^2*c*d*e*f*g) - (x*(2*a*c^2*e*g - 2*c^3
*d*f + b*c^2*d*g + b*c^2*e*f - b^2*c*e*g))/(4*a*c^3*d^2*f^2 + 4*a^3*c*e^2*g^2 - a^2*b^2*e^2*g^2 + 4*a^2*c^2*d^
2*g^2 + 4*a^2*c^2*e^2*f^2 - b^2*c^2*d^2*f^2 + a*b^3*d*e*g^2 + b^3*c*d*e*f^2 + a*b^3*e^2*f*g + b^3*c*d^2*f*g -
a*b^2*c*d^2*g^2 - a*b^2*c*e^2*f^2 - b^4*d*e*f*g - 4*a*b*c^2*d*e*f^2 - 4*a^2*b*c*d*e*g^2 - 4*a*b*c^2*d^2*f*g -
4*a^2*b*c*e^2*f*g + 4*a*b^2*c*d*e*f*g))/(a + b*x + c*x^2) + symsum(log((12*a^2*c^5*e^6*g^6 - 3*b^2*c^5*d^2*e^4
*g^6 - 3*b^2*c^5*e^6*f^2*g^4 + 4*c^7*d^2*e^4*f^2*g^4 - 2*a*b^2*c^4*e^6*g^6 + 16*a*c^6*d^2*e^4*g^6 + 3*b^3*c^4*
d*e^5*g^6 + 16*a*c^6*e^6*f^2*g^4 + 3*b^3*c^4*e^6*f*g^5 - 4*b*c^6*d*e^5*f^2*g^4 - 4*b*c^6*d^2*e^4*f*g^5 - 16*a*
b*c^5*d*e^5*g^6 - 16*a*b*c^5*e^6*f*g^5 + 16*a*c^6*d*e^5*f*g^5)/(16*a^2*c^6*d^4*f^4 + a^4*b^4*e^4*g^4 + 16*a^4*
c^4*d^4*g^4 + 16*a^4*c^4*e^4*f^4 + b^4*c^4*d^4*f^4 + 16*a^6*c^2*e^4*g^4 + a^2*b^4*c^2*d^4*g^4 + a^2*b^4*c^2*e^
4*f^4 - 8*a^3*b^2*c^3*d^4*g^4 - 8*a^3*b^2*c^3*e^4*f^4 + a^2*b^6*d^2*e^2*g^4 + 32*a^3*c^5*d^2*e^2*f^4 + 32*a^5*
c^3*d^2*e^2*g^4 + b^6*c^2*d^2*e^2*f^4 + a^2*b^6*e^4*f^2*g^2 + 32*a^3*c^5*d^4*f^2*g^2 + 32*a^5*c^3*e^4*f^2*g^2
+ b^6*c^2*d^4*f^2*g^2 + b^8*d^2*e^2*f^2*g^2 - 8*a*b^2*c^5*d^4*f^4 - 8*a^5*b^2*c*e^4*g^4 - 2*a^3*b^5*d*e^3*g^4
- 2*b^5*c^3*d^3*e*f^4 - 2*a^3*b^5*e^4*f*g^3 - 2*b^5*c^3*d^4*f^3*g + 16*a*b^3*c^4*d^3*e*f^4 - 2*a*b^5*c^2*d*e^3
*f^4 - 32*a^2*b*c^5*d^3*e*f^4 - 32*a^3*b*c^4*d*e^3*f^4 - 2*a^2*b^5*c*d^3*e*g^4 - 32*a^4*b*c^3*d^3*e*g^4 + 16*a
^4*b^3*c*d*e^3*g^4 - 32*a^5*b*c^2*d*e^3*g^4 + 16*a*b^3*c^4*d^4*f^3*g - 2*a*b^5*c^2*d^4*f*g^3 - 32*a^2*b*c^5*d^
4*f^3*g - 32*a^3*b*c^4*d^4*f*g^3 - 2*a^2*b^5*c*e^4*f^3*g - 32*a^4*b*c^3*e^4*f^3*g + 16*a^4*b^3*c*e^4*f*g^3 - 3
2*a^5*b*c^2*e^4*f*g^3 - 2*a*b^7*d*e^3*f^2*g^2 - 2*a*b^7*d^2*e^2*f*g^3 + 4*a^2*b^6*d*e^3*f*g^3 + 4*b^6*c^2*d^3*
e*f^3*g - 2*b^7*c*d^2*e^2*f^3*g - 2*b^7*c*d^3*e*f^2*g^2 - 6*a*b^4*c^3*d^2*e^2*f^4 + 16*a^2*b^3*c^3*d*e^3*f^4 +
16*a^3*b^3*c^2*d^3*e*g^4 - 6*a^3*b^4*c*d^2*e^2*g^4 - 6*a*b^4*c^3*d^4*f^2*g^2 + 16*a^2*b^3*c^3*d^4*f*g^3 + 16*
a^3*b^3*c^2*e^4*f^3*g - 6*a^3*b^4*c*e^4*f^2*g^2 + 64*a^4*c^4*d^2*e^2*f^2*g^2 + 4*a*b^6*c*d*e^3*f^3*g + 4*a*b^6
*c*d^3*e*f*g^3 - 32*a*b^4*c^3*d^3*e*f^3*g - 32*a^3*b^4*c*d*e^3*f*g^3 - 12*a^2*b^4*c^2*d^2*e^2*f^2*g^2 + 32*a^3
*b^2*c^3*d^2*e^2*f^2*g^2 + 12*a*b^5*c^2*d^2*e^2*f^3*g + 12*a*b^5*c^2*d^3*e*f^2*g^2 - 4*a*b^6*c*d^2*e^2*f^2*g^2
+ 64*a^2*b^2*c^4*d^3*e*f^3*g - 32*a^2*b^4*c^2*d*e^3*f^3*g - 32*a^2*b^4*c^2*d^3*e*f*g^3 + 12*a^2*b^5*c*d*e^3*f
^2*g^2 + 12*a^2*b^5*c*d^2*e^2*f*g^3 - 64*a^3*b*c^4*d^2*e^2*f^3*g - 64*a^3*b*c^4*d^3*e*f^2*g^2 + 64*a^3*b^2*c^3
*d*e^3*f^3*g + 64*a^3*b^2*c^3*d^3*e*f*g^3 - 64*a^4*b*c^3*d*e^3*f^2*g^2 - 64*a^4*b*c^3*d^2*e^2*f*g^3 + 64*a^4*b
^2*c^2*d*e^3*f*g^3) - root(1120*a^6*b^2*c^6*d^9*e*f*g^9*z^4 + 1120*a^6*b^2*c^6*d*e^9*f^9*g*z^4 - 792*a^5*b^4*c
^5*d^9*e*f*g^9*z^4 - 792*a^5*b^4*c^5*d*e^9*f^9*g*z^4 + 512*a^9*b*c^4*d^4*e^6*f*g^9*z^4 + 512*a^9*b*c^4*d*e^9*f
^4*g^6*z^4 - 512*a^7*b*c^6*d^8*e^2*f*g^9*z^4 - 512*a^7*b*c^6*d*e^9*f^8*g^2*z^4 - 512*a^6*b*c^7*d^9*e*f^2*g^8*z
^4 - 512*a^6*b*c^7*d^2*e^8*f^9*g*z^4 + 512*a^4*b*c^9*d^9*e*f^6*g^4*z^4 + 512*a^4*b*c^9*d^6*e^4*f^9*g*z^4 + 256
*a^10*b*c^3*d^2*e^8*f*g^9*z^4 + 256*a^10*b*c^3*d*e^9*f^2*g^8*z^4 + 256*a^3*b*c^10*d^9*e*f^8*g^2*z^4 + 256*a^3*
b*c^10*d^8*e^2*f^9*g*z^4 - 200*a^6*b^7*c*d^4*e^6*f*g^9*z^4 - 200*a^6*b^7*c*d*e^9*f^4*g^6*z^4 - 200*a*b^7*c^6*d
^9*e*f^6*g^4*z^4 - 200*a*b^7*c^6*d^6*e^4*f^9*g*z^4 + 194*a^4*b^6*c^4*d^9*e*f*g^9*z^4 + 194*a^4*b^6*c^4*d*e^9*f
^9*g*z^4 + 144*a^5*b^8*c*d^5*e^5*f*g^9*z^4 + 144*a^5*b^8*c*d*e^9*f^5*g^5*z^4 + 144*a*b^8*c^5*d^9*e*f^5*g^5*z^4
+ 144*a*b^8*c^5*d^5*e^5*f^9*g*z^4 + 96*a^10*b^2*c^2*d*e^9*f*g^9*z^4 + 96*a^2*b^2*c^10*d^9*e*f^9*g*z^4 + 56*a^
7*b^6*c*d^3*e^7*f*g^9*z^4 + 56*a^7*b^6*c*d*e^9*f^3*g^7*z^4 + 56*a*b^6*c^7*d^9*e*f^7*g^3*z^4 + 56*a*b^6*c^7*d^7
*e^3*f^9*g*z^4 + 48*a^8*b^5*c*d^2*e^8*f*g^9*z^4 + 48*a^8*b^5*c*d*e^9*f^2*g^8*z^4 + 48*a*b^5*c^8*d^9*e*f^8*g^2*
z^4 + 48*a*b^5*c^8*d^8*e^2*f^9*g*z^4 + 20*a*b^12*c*d^6*e^4*f^4*g^6*z^4 + 20*a*b^12*c*d^4*e^6*f^6*g^4*z^4 - 16*
a^3*b^10*c*d^7*e^3*f*g^9*z^4 - 16*a^3*b^10*c*d*e^9*f^7*g^3*z^4 - 16*a^3*b^8*c^3*d^9*e*f*g^9*z^4 - 16*a^3*b^8*c
^3*d*e^9*f^9*g*z^4 - 16*a*b^12*c*d^7*e^3*f^3*g^7*z^4 - 16*a*b^12*c*d^3*e^7*f^7*g^3*z^4 - 16*a*b^10*c^3*d^9*e*f
^3*g^7*z^4 - 16*a*b^10*c^3*d^3*e^7*f^9*g*z^4 - 8*a^4*b^9*c*d^6*e^4*f*g^9*z^4 - 8*a^4*b^9*c*d*e^9*f^6*g^4*z^4 -
8*a*b^12*c*d^5*e^5*f^5*g^5*z^4 - 8*a*b^9*c^4*d^9*e*f^4*g^6*z^4 - 8*a*b^9*c^4*d^4*e^6*f^9*g*z^4 - 9984*a^7*b^2
*c^5*d^4*e^6*f^4*g^6*z^4 - 9984*a^5*b^2*c^7*d^6*e^4*f^6*g^4*z^4 - 8640*a^6*b^2*c^6*d^6*e^4*f^4*g^6*z^4 - 8640*
a^6*b^2*c^6*d^4*e^6*f^6*g^4*z^4 - 8544*a^5*b^4*c^5*d^5*e^5*f^5*g^5*z^4 + 5632*a^6*b^2*c^6*d^7*e^3*f^3*g^7*z^4
+ 5632*a^6*b^2*c^6*d^3*e^7*f^7*g^3*z^4 + 5232*a^5*b^4*c^5*d^6*e^4*f^4*g^6*z^4 + 5232*a^5*b^4*c^5*d^4*e^6*f^6*g
^4*z^4 + 4808*a^4*b^6*c^4*d^5*e^5*f^5*g^5*z^4 - 4288*a^6*b^4*c^4*d^5*e^5*f^3*g^7*z^4 - 4288*a^6*b^4*c^4*d^3*e^
7*f^5*g^5*z^4 - 4288*a^4*b^4*c^6*d^7*e^3*f^5*g^5*z^4 - 4288*a^4*b^4*c^6*d^5*e^5*f^7*g^3*z^4 + 3968*a^6*b^3*c^5
*d^5*e^5*f^4*g^6*z^4 + 3968*a^6*b^3*c^5*d^4*e^6*f^5*g^5*z^4 + 3968*a^5*b^3*c^6*d^6*e^4*f^5*g^5*z^4 + 3968*a^5*
b^3*c^6*d^5*e^5*f^6*g^4*z^4 + 3840*a^7*b^2*c^5*d^5*e^5*f^3*g^7*z^4 + 3840*a^7*b^2*c^5*d^3*e^7*f^5*g^5*z^4 + 38
40*a^5*b^2*c^7*d^7*e^3*f^5*g^5*z^4 + 3840*a^5*b^2*c^7*d^5*e^5*f^7*g^3*z^4 + 3776*a^6*b^4*c^4*d^4*e^6*f^4*g^6*z
^4 + 3776*a^4*b^4*c^6*d^6*e^4*f^6*g^4*z^4 + 3456*a^6*b^2*c^6*d^5*e^5*f^5*g^5*z^4 + 3440*a^6*b^4*c^4*d^6*e^4*f^
2*g^8*z^4 + 3440*a^6*b^4*c^4*d^2*e^8*f^6*g^4*z^4 + 3440*a^4*b^4*c^6*d^8*e^2*f^4*g^6*z^4 + 3440*a^4*b^4*c^6*d^4
*e^6*f^8*g^2*z^4 - 3360*a^8*b^2*c^4*d^4*e^6*f^2*g^8*z^4 - 3360*a^8*b^2*c^4*d^2*e^8*f^4*g^6*z^4 - 3360*a^4*b^2*
c^8*d^8*e^2*f^6*g^4*z^4 - 3360*a^4*b^2*c^8*d^6*e^4*f^8*g^2*z^4 - 2944*a^7*b^4*c^3*d^3*e^7*f^3*g^7*z^4 - 2944*a
^3*b^4*c^7*d^7*e^3*f^7*g^3*z^4 + 2512*a^5*b^6*c^3*d^5*e^5*f^3*g^7*z^4 + 2512*a^5*b^6*c^3*d^3*e^7*f^5*g^5*z^4 +
2512*a^3*b^6*c^5*d^7*e^3*f^5*g^5*z^4 + 2512*a^3*b^6*c^5*d^5*e^5*f^7*g^3*z^4 + 2312*a^7*b^4*c^3*d^4*e^6*f^2*g^
8*z^4 + 2312*a^7*b^4*c^3*d^2*e^8*f^4*g^6*z^4 + 2312*a^3*b^4*c^7*d^8*e^2*f^6*g^4*z^4 + 2312*a^3*b^4*c^7*d^6*e^4
*f^8*g^2*z^4 + 1952*a^6*b^6*c^2*d^3*e^7*f^3*g^7*z^4 + 1952*a^2*b^6*c^6*d^7*e^3*f^7*g^3*z^4 - 1920*a^5*b^4*c^5*
d^7*e^3*f^3*g^7*z^4 - 1920*a^5*b^4*c^5*d^3*e^7*f^7*g^3*z^4 - 1828*a^5*b^6*c^3*d^6*e^4*f^2*g^8*z^4 - 1828*a^5*b
^6*c^3*d^2*e^8*f^6*g^4*z^4 - 1828*a^3*b^6*c^5*d^8*e^2*f^4*g^6*z^4 - 1828*a^3*b^6*c^5*d^4*e^6*f^8*g^2*z^4 + 174
0*a^5*b^4*c^5*d^8*e^2*f^2*g^8*z^4 + 1740*a^5*b^4*c^5*d^2*e^8*f^8*g^2*z^4 - 1728*a^7*b^2*c^5*d^6*e^4*f^2*g^8*z^
4 - 1728*a^7*b^2*c^5*d^2*e^8*f^6*g^4*z^4 - 1728*a^5*b^2*c^7*d^8*e^2*f^4*g^6*z^4 - 1728*a^5*b^2*c^7*d^4*e^6*f^8
*g^2*z^4 - 1716*a^4*b^6*c^4*d^6*e^4*f^4*g^6*z^4 - 1716*a^4*b^6*c^4*d^4*e^6*f^6*g^4*z^4 - 1664*a^9*b^2*c^3*d^2*
e^8*f^2*g^8*z^4 - 1664*a^3*b^2*c^9*d^8*e^2*f^8*g^2*z^4 - 1600*a^6*b^3*c^5*d^7*e^3*f^2*g^8*z^4 - 1600*a^6*b^3*c
^5*d^2*e^8*f^7*g^3*z^4 - 1600*a^5*b^3*c^6*d^8*e^2*f^3*g^7*z^4 - 1600*a^5*b^3*c^6*d^3*e^7*f^8*g^2*z^4 - 1553*a^
4*b^6*c^4*d^8*e^2*f^2*g^8*z^4 - 1553*a^4*b^6*c^4*d^2*e^8*f^8*g^2*z^4 + 1536*a^8*b^2*c^4*d^3*e^7*f^3*g^7*z^4 +
1536*a^4*b^2*c^8*d^7*e^3*f^7*g^3*z^4 + 1408*a^7*b^3*c^4*d^4*e^6*f^3*g^7*z^4 + 1408*a^7*b^3*c^4*d^3*e^7*f^4*g^6
*z^4 - 1408*a^6*b^3*c^5*d^6*e^4*f^3*g^7*z^4 - 1408*a^6*b^3*c^5*d^3*e^7*f^6*g^4*z^4 - 1408*a^5*b^3*c^6*d^7*e^3*
f^4*g^6*z^4 - 1408*a^5*b^3*c^6*d^4*e^6*f^7*g^3*z^4 + 1408*a^4*b^3*c^7*d^7*e^3*f^6*g^4*z^4 + 1408*a^4*b^3*c^7*d
^6*e^4*f^7*g^3*z^4 - 1360*a^6*b^5*c^3*d^5*e^5*f^2*g^8*z^4 - 1360*a^6*b^5*c^3*d^2*e^8*f^5*g^5*z^4 - 1360*a^3*b^
5*c^6*d^8*e^2*f^5*g^5*z^4 - 1360*a^3*b^5*c^6*d^5*e^5*f^8*g^2*z^4 - 1248*a^5*b^5*c^4*d^5*e^5*f^4*g^6*z^4 - 1248
*a^5*b^5*c^4*d^4*e^6*f^5*g^5*z^4 - 1248*a^4*b^5*c^5*d^6*e^4*f^5*g^5*z^4 - 1248*a^4*b^5*c^5*d^5*e^5*f^6*g^4*z^4
+ 1088*a^8*b^3*c^3*d^3*e^7*f^2*g^8*z^4 + 1088*a^8*b^3*c^3*d^2*e^8*f^3*g^7*z^4 + 1088*a^3*b^3*c^8*d^8*e^2*f^7*
g^3*z^4 + 1088*a^3*b^3*c^8*d^7*e^3*f^8*g^2*z^4 + 1056*a^8*b^4*c^2*d^2*e^8*f^2*g^8*z^4 + 1056*a^2*b^4*c^8*d^8*e
^2*f^8*g^2*z^4 - 912*a^7*b^5*c^2*d^3*e^7*f^2*g^8*z^4 - 912*a^7*b^5*c^2*d^2*e^8*f^3*g^7*z^4 - 912*a^2*b^5*c^7*d
^8*e^2*f^7*g^3*z^4 - 912*a^2*b^5*c^7*d^7*e^3*f^8*g^2*z^4 - 848*a^5*b^6*c^3*d^4*e^6*f^4*g^6*z^4 - 848*a^3*b^6*c
^5*d^6*e^4*f^6*g^4*z^4 + 832*a^7*b^3*c^4*d^5*e^5*f^2*g^8*z^4 + 832*a^7*b^3*c^4*d^2*e^8*f^5*g^5*z^4 + 832*a^4*b
^3*c^7*d^8*e^2*f^5*g^5*z^4 + 832*a^4*b^3*c^7*d^5*e^5*f^8*g^2*z^4 + 828*a^5*b^7*c^2*d^5*e^5*f^2*g^8*z^4 + 828*a
^5*b^7*c^2*d^2*e^8*f^5*g^5*z^4 + 828*a^2*b^7*c^5*d^8*e^2*f^5*g^5*z^4 + 828*a^2*b^7*c^5*d^5*e^5*f^8*g^2*z^4 - 8
00*a^3*b^8*c^3*d^5*e^5*f^5*g^5*z^4 - 696*a^4*b^8*c^2*d^5*e^5*f^3*g^7*z^4 - 696*a^4*b^8*c^2*d^3*e^7*f^5*g^5*z^4
- 696*a^2*b^8*c^4*d^7*e^3*f^5*g^5*z^4 - 696*a^2*b^8*c^4*d^5*e^5*f^7*g^3*z^4 - 694*a^6*b^6*c^2*d^4*e^6*f^2*g^8
*z^4 - 694*a^6*b^6*c^2*d^2*e^8*f^4*g^6*z^4 - 694*a^2*b^6*c^6*d^8*e^2*f^6*g^4*z^4 - 694*a^2*b^6*c^6*d^6*e^4*f^8
*g^2*z^4 + 692*a^4*b^7*c^3*d^7*e^3*f^2*g^8*z^4 + 692*a^4*b^7*c^3*d^2*e^8*f^7*g^3*z^4 + 692*a^3*b^7*c^4*d^8*e^2
*f^3*g^7*z^4 + 692*a^3*b^7*c^4*d^3*e^7*f^8*g^2*z^4 + 672*a^4*b^6*c^4*d^7*e^3*f^3*g^7*z^4 + 672*a^4*b^6*c^4*d^3
*e^7*f^7*g^3*z^4 + 600*a^4*b^8*c^2*d^4*e^6*f^4*g^6*z^4 + 600*a^2*b^8*c^4*d^6*e^4*f^6*g^4*z^4 - 544*a^3*b^8*c^3
*d^7*e^3*f^3*g^7*z^4 + 544*a^3*b^8*c^3*d^6*e^4*f^4*g^6*z^4 + 544*a^3*b^8*c^3*d^4*e^6*f^6*g^4*z^4 - 544*a^3*b^8
*c^3*d^3*e^7*f^7*g^3*z^4 - 536*a^4*b^7*c^3*d^5*e^5*f^4*g^6*z^4 - 536*a^4*b^7*c^3*d^4*e^6*f^5*g^5*z^4 - 536*a^3
*b^7*c^4*d^6*e^4*f^5*g^5*z^4 - 536*a^3*b^7*c^4*d^5*e^5*f^6*g^4*z^4 - 504*a^5*b^7*c^2*d^4*e^6*f^3*g^7*z^4 - 504
*a^5*b^7*c^2*d^3*e^7*f^4*g^6*z^4 - 504*a^2*b^7*c^5*d^7*e^3*f^6*g^4*z^4 - 504*a^2*b^7*c^5*d^6*e^4*f^7*g^3*z^4 +
416*a^3*b^8*c^3*d^8*e^2*f^2*g^8*z^4 + 416*a^3*b^8*c^3*d^2*e^8*f^8*g^2*z^4 - 352*a^6*b^5*c^3*d^4*e^6*f^3*g^7*z
^4 - 352*a^6*b^5*c^3*d^3*e^7*f^4*g^6*z^4 - 352*a^3*b^5*c^6*d^7*e^3*f^6*g^4*z^4 - 352*a^3*b^5*c^6*d^6*e^4*f^7*g
^3*z^4 - 248*a^3*b^9*c^2*d^7*e^3*f^2*g^8*z^4 - 248*a^3*b^9*c^2*d^2*e^8*f^7*g^3*z^4 - 248*a^2*b^9*c^3*d^8*e^2*f
^3*g^7*z^4 - 248*a^2*b^9*c^3*d^3*e^7*f^8*g^2*z^4 + 246*a^4*b^8*c^2*d^6*e^4*f^2*g^8*z^4 + 246*a^4*b^8*c^2*d^2*e
^8*f^6*g^4*z^4 + 246*a^2*b^8*c^4*d^8*e^2*f^4*g^6*z^4 + 246*a^2*b^8*c^4*d^4*e^6*f^8*g^2*z^4 + 208*a^6*b^2*c^6*d
^8*e^2*f^2*g^8*z^4 + 208*a^6*b^2*c^6*d^2*e^8*f^8*g^2*z^4 + 168*a^2*b^10*c^2*d^7*e^3*f^3*g^7*z^4 + 168*a^2*b^10
*c^2*d^3*e^7*f^7*g^3*z^4 + 160*a^3*b^9*c^2*d^5*e^5*f^4*g^6*z^4 + 160*a^3*b^9*c^2*d^4*e^6*f^5*g^5*z^4 + 160*a^2
*b^9*c^3*d^6*e^4*f^5*g^5*z^4 + 160*a^2*b^9*c^3*d^5*e^5*f^6*g^4*z^4 + 144*a^5*b^5*c^4*d^7*e^3*f^2*g^8*z^4 + 144
*a^5*b^5*c^4*d^2*e^8*f^7*g^3*z^4 + 144*a^4*b^5*c^5*d^8*e^2*f^3*g^7*z^4 + 144*a^4*b^5*c^5*d^3*e^7*f^8*g^2*z^4 -
144*a^2*b^10*c^2*d^6*e^4*f^4*g^6*z^4 - 144*a^2*b^10*c^2*d^4*e^6*f^6*g^4*z^4 + 120*a^4*b^7*c^3*d^6*e^4*f^3*g^7
*z^4 + 120*a^4*b^7*c^3*d^3*e^7*f^6*g^4*z^4 + 120*a^3*b^7*c^4*d^7*e^3*f^4*g^6*z^4 + 120*a^3*b^7*c^4*d^4*e^6*f^7
*g^3*z^4 + 96*a^5*b^5*c^4*d^6*e^4*f^3*g^7*z^4 + 96*a^5*b^5*c^4*d^3*e^7*f^6*g^4*z^4 + 96*a^4*b^5*c^5*d^7*e^3*f^
4*g^6*z^4 + 96*a^4*b^5*c^5*d^4*e^6*f^7*g^3*z^4 + 64*a^3*b^9*c^2*d^6*e^4*f^3*g^7*z^4 + 64*a^3*b^9*c^2*d^3*e^7*f
^6*g^4*z^4 + 64*a^2*b^9*c^3*d^7*e^3*f^4*g^6*z^4 + 64*a^2*b^9*c^3*d^4*e^6*f^7*g^3*z^4 - 36*a^2*b^10*c^2*d^8*e^2
*f^2*g^8*z^4 - 36*a^2*b^10*c^2*d^2*e^8*f^8*g^2*z^4 + 24*a^2*b^10*c^2*d^5*e^5*f^5*g^5*z^4 - 24*a^9*b^4*c*d*e^9*
f*g^9*z^4 - 24*a*b^4*c^9*d^9*e*f^9*g*z^4 + 2688*a^7*b^2*c^5*d^7*e^3*f*g^9*z^4 + 2688*a^7*b^2*c^5*d*e^9*f^7*g^3
*z^4 + 2688*a^5*b^2*c^7*d^9*e*f^3*g^7*z^4 + 2688*a^5*b^2*c^7*d^3*e^7*f^9*g*z^4 - 2560*a^7*b^3*c^4*d^6*e^4*f*g^
9*z^4 - 2560*a^7*b^3*c^4*d*e^9*f^6*g^4*z^4 - 2560*a^4*b^3*c^7*d^9*e*f^4*g^6*z^4 - 2560*a^4*b^3*c^7*d^4*e^6*f^9
*g*z^4 + 2112*a^8*b^2*c^4*d^5*e^5*f*g^9*z^4 + 2112*a^8*b^2*c^4*d*e^9*f^5*g^5*z^4 + 2112*a^4*b^2*c^8*d^9*e*f^5*
g^5*z^4 + 2112*a^4*b^2*c^8*d^5*e^5*f^9*g*z^4 + 1664*a^6*b^5*c^3*d^6*e^4*f*g^9*z^4 + 1664*a^6*b^5*c^3*d*e^9*f^6
*g^4*z^4 + 1664*a^3*b^5*c^6*d^9*e*f^4*g^6*z^4 + 1664*a^3*b^5*c^6*d^4*e^6*f^9*g*z^4 + 1536*a^8*b*c^5*d^4*e^6*f^
3*g^7*z^4 + 1536*a^8*b*c^5*d^3*e^7*f^4*g^6*z^4 + 1536*a^7*b*c^6*d^5*e^5*f^4*g^6*z^4 + 1536*a^7*b*c^6*d^4*e^6*f
^5*g^5*z^4 + 1536*a^6*b*c^7*d^6*e^4*f^5*g^5*z^4 + 1536*a^6*b*c^7*d^5*e^5*f^6*g^4*z^4 + 1536*a^5*b*c^8*d^7*e^3*
f^6*g^4*z^4 + 1536*a^5*b*c^8*d^6*e^4*f^7*g^3*z^4 - 1408*a^8*b^3*c^3*d^4*e^6*f*g^9*z^4 - 1408*a^8*b^3*c^3*d*e^9
*f^4*g^6*z^4 - 1408*a^3*b^3*c^8*d^9*e*f^6*g^4*z^4 - 1408*a^3*b^3*c^8*d^6*e^4*f^9*g*z^4 - 1280*a^7*b*c^6*d^7*e^
3*f^2*g^8*z^4 - 1280*a^7*b*c^6*d^2*e^8*f^7*g^3*z^4 - 1280*a^6*b*c^7*d^8*e^2*f^3*g^7*z^4 - 1280*a^6*b*c^7*d^3*e
^7*f^8*g^2*z^4 - 1152*a^6*b^3*c^5*d^8*e^2*f*g^9*z^4 - 1152*a^6*b^3*c^5*d*e^9*f^8*g^2*z^4 - 1152*a^5*b^3*c^6*d^
9*e*f^2*g^8*z^4 - 1152*a^5*b^3*c^6*d^2*e^8*f^9*g*z^4 + 1056*a^5*b^5*c^4*d^8*e^2*f*g^9*z^4 + 1056*a^5*b^5*c^4*d
*e^9*f^8*g^2*z^4 + 1056*a^4*b^5*c^5*d^9*e*f^2*g^8*z^4 + 1056*a^4*b^5*c^5*d^2*e^8*f^9*g*z^4 + 864*a^7*b^5*c^2*d
^4*e^6*f*g^9*z^4 + 864*a^7*b^5*c^2*d*e^9*f^4*g^6*z^4 + 864*a^2*b^5*c^7*d^9*e*f^6*g^4*z^4 + 864*a^2*b^5*c^7*d^6
*e^4*f^9*g*z^4 - 800*a^6*b^4*c^4*d^7*e^3*f*g^9*z^4 - 800*a^6*b^4*c^4*d*e^9*f^7*g^3*z^4 - 800*a^4*b^4*c^6*d^9*e
*f^3*g^7*z^4 - 800*a^4*b^4*c^6*d^3*e^7*f^9*g*z^4 - 768*a^8*b*c^5*d^5*e^5*f^2*g^8*z^4 - 768*a^8*b*c^5*d^2*e^8*f
^5*g^5*z^4 - 768*a^5*b*c^8*d^8*e^2*f^5*g^5*z^4 - 768*a^5*b*c^8*d^5*e^5*f^8*g^2*z^4 + 640*a^9*b^2*c^3*d^3*e^7*f
*g^9*z^4 + 640*a^9*b^2*c^3*d*e^9*f^3*g^7*z^4 + 640*a^3*b^2*c^9*d^9*e*f^7*g^3*z^4 + 640*a^3*b^2*c^9*d^7*e^3*f^9
*g*z^4 + 512*a^7*b*c^6*d^6*e^4*f^3*g^7*z^4 + 512*a^7*b*c^6*d^3*e^7*f^6*g^4*z^4 + 512*a^6*b*c^7*d^7*e^3*f^4*g^6
*z^4 + 512*a^6*b*c^7*d^4*e^6*f^7*g^3*z^4 - 480*a^5*b^8*c*d^3*e^7*f^3*g^7*z^4 - 480*a*b^8*c^5*d^7*e^3*f^7*g^3*z
^4 - 400*a^7*b^4*c^3*d^5*e^5*f*g^9*z^4 - 400*a^7*b^4*c^3*d*e^9*f^5*g^5*z^4 - 400*a^3*b^4*c^7*d^9*e*f^5*g^5*z^4
- 400*a^3*b^4*c^7*d^5*e^5*f^9*g*z^4 - 372*a^6*b^6*c^2*d^5*e^5*f*g^9*z^4 - 372*a^6*b^6*c^2*d*e^9*f^5*g^5*z^4 -
372*a^2*b^6*c^6*d^9*e*f^5*g^5*z^4 - 372*a^2*b^6*c^6*d^5*e^5*f^9*g*z^4 - 328*a^5*b^6*c^3*d^7*e^3*f*g^9*z^4 - 3
28*a^5*b^6*c^3*d*e^9*f^7*g^3*z^4 - 328*a^3*b^6*c^5*d^9*e*f^3*g^7*z^4 - 328*a^3*b^6*c^5*d^3*e^7*f^9*g*z^4 - 288
*a^8*b^4*c^2*d^3*e^7*f*g^9*z^4 - 288*a^8*b^4*c^2*d*e^9*f^3*g^7*z^4 - 288*a^5*b^7*c^2*d^6*e^4*f*g^9*z^4 - 288*a
^5*b^7*c^2*d*e^9*f^6*g^4*z^4 - 288*a^2*b^7*c^5*d^9*e*f^4*g^6*z^4 - 288*a^2*b^7*c^5*d^4*e^6*f^9*g*z^4 - 288*a^2
*b^4*c^8*d^9*e*f^7*g^3*z^4 - 288*a^2*b^4*c^8*d^7*e^3*f^9*g*z^4 - 280*a^4*b^7*c^3*d^8*e^2*f*g^9*z^4 - 280*a^4*b
^7*c^3*d*e^9*f^8*g^2*z^4 - 280*a^3*b^7*c^4*d^9*e*f^2*g^8*z^4 - 280*a^3*b^7*c^4*d^2*e^8*f^9*g*z^4 + 256*a^9*b*c
^4*d^3*e^7*f^2*g^8*z^4 + 256*a^9*b*c^4*d^2*e^8*f^3*g^7*z^4 + 256*a^4*b*c^9*d^8*e^2*f^7*g^3*z^4 + 256*a^4*b*c^9
*d^7*e^3*f^8*g^2*z^4 - 248*a^7*b^6*c*d^2*e^8*f^2*g^8*z^4 - 248*a*b^6*c^7*d^8*e^2*f^8*g^2*z^4 + 236*a^6*b^7*c*d
^3*e^7*f^2*g^8*z^4 + 236*a^6*b^7*c*d^2*e^8*f^3*g^7*z^4 + 236*a*b^7*c^6*d^8*e^2*f^7*g^3*z^4 + 236*a*b^7*c^6*d^7
*e^3*f^8*g^2*z^4 + 200*a^4*b^9*c*d^4*e^6*f^3*g^7*z^4 + 200*a^4*b^9*c*d^3*e^7*f^4*g^6*z^4 - 200*a^3*b^10*c*d^4*
e^6*f^4*g^6*z^4 - 200*a*b^10*c^3*d^6*e^4*f^6*g^4*z^4 + 200*a*b^9*c^4*d^7*e^3*f^6*g^4*z^4 + 200*a*b^9*c^4*d^6*e
^4*f^7*g^3*z^4 - 196*a^4*b^9*c*d^5*e^5*f^2*g^8*z^4 - 196*a^4*b^9*c*d^2*e^8*f^5*g^5*z^4 - 196*a*b^9*c^4*d^8*e^2
*f^5*g^5*z^4 - 196*a*b^9*c^4*d^5*e^5*f^8*g^2*z^4 - 192*a^9*b^3*c^2*d^2*e^8*f*g^9*z^4 - 192*a^9*b^3*c^2*d*e^9*f
^2*g^8*z^4 - 192*a^2*b^3*c^9*d^9*e*f^8*g^2*z^4 - 192*a^2*b^3*c^9*d^8*e^2*f^9*g*z^4 + 156*a^4*b^8*c^2*d^7*e^3*f
*g^9*z^4 + 156*a^4*b^8*c^2*d*e^9*f^7*g^3*z^4 + 156*a^2*b^8*c^4*d^9*e*f^3*g^7*z^4 + 156*a^2*b^8*c^4*d^3*e^7*f^9
*g*z^4 + 96*a^5*b^8*c*d^4*e^6*f^2*g^8*z^4 + 96*a^5*b^8*c*d^2*e^8*f^4*g^6*z^4 + 96*a*b^8*c^5*d^8*e^2*f^6*g^4*z^
4 + 96*a*b^8*c^5*d^6*e^4*f^8*g^2*z^4 + 88*a^3*b^10*c*d^5*e^5*f^3*g^7*z^4 + 88*a^3*b^10*c*d^3*e^7*f^5*g^5*z^4 +
88*a*b^10*c^3*d^7*e^3*f^5*g^5*z^4 + 88*a*b^10*c^3*d^5*e^5*f^7*g^3*z^4 - 36*a^2*b^11*c*d^6*e^4*f^3*g^7*z^4 - 3
6*a^2*b^11*c*d^3*e^7*f^6*g^4*z^4 - 36*a*b^11*c^2*d^7*e^3*f^4*g^6*z^4 - 36*a*b^11*c^2*d^4*e^6*f^7*g^3*z^4 + 28*
a^3*b^10*c*d^6*e^4*f^2*g^8*z^4 + 28*a^3*b^10*c*d^2*e^8*f^6*g^4*z^4 + 28*a*b^10*c^3*d^8*e^2*f^4*g^6*z^4 + 28*a*
b^10*c^3*d^4*e^6*f^8*g^2*z^4 + 24*a^3*b^9*c^2*d^8*e^2*f*g^9*z^4 + 24*a^3*b^9*c^2*d*e^9*f^8*g^2*z^4 + 24*a^2*b^
11*c*d^7*e^3*f^2*g^8*z^4 + 24*a^2*b^11*c*d^2*e^8*f^7*g^3*z^4 + 24*a^2*b^9*c^3*d^9*e*f^2*g^8*z^4 + 24*a^2*b^9*c
^3*d^2*e^8*f^9*g*z^4 + 24*a*b^11*c^2*d^8*e^2*f^3*g^7*z^4 + 24*a*b^11*c^2*d^3*e^7*f^8*g^2*z^4 + 12*a^2*b^11*c*d
^5*e^5*f^4*g^6*z^4 + 12*a^2*b^11*c*d^4*e^6*f^5*g^5*z^4 + 12*a*b^11*c^2*d^6*e^4*f^5*g^5*z^4 + 12*a*b^11*c^2*d^5
*e^5*f^6*g^4*z^4 + 40*b^10*c^4*d^7*e^3*f^7*g^3*z^4 + 20*b^12*c^2*d^6*e^4*f^6*g^4*z^4 - 20*b^11*c^3*d^7*e^3*f^6
*g^4*z^4 - 20*b^11*c^3*d^6*e^4*f^7*g^3*z^4 - 20*b^9*c^5*d^8*e^2*f^7*g^3*z^4 - 20*b^9*c^5*d^7*e^3*f^8*g^2*z^4 +
20*b^8*c^6*d^8*e^2*f^8*g^2*z^4 + 16*b^11*c^3*d^8*e^2*f^5*g^5*z^4 + 16*b^11*c^3*d^5*e^5*f^8*g^2*z^4 - 6*b^12*c
^2*d^8*e^2*f^4*g^6*z^4 - 6*b^12*c^2*d^4*e^6*f^8*g^2*z^4 - 5*b^10*c^4*d^8*e^2*f^6*g^4*z^4 - 5*b^10*c^4*d^6*e^4*
f^8*g^2*z^4 - 4*b^12*c^2*d^7*e^3*f^5*g^5*z^4 - 4*b^12*c^2*d^5*e^5*f^7*g^3*z^4 - 4608*a^7*c^7*d^5*e^5*f^5*g^5*z
^4 + 3328*a^7*c^7*d^6*e^4*f^4*g^6*z^4 + 3328*a^7*c^7*d^4*e^6*f^6*g^4*z^4 - 3072*a^8*c^6*d^5*e^5*f^3*g^7*z^4 +
3072*a^8*c^6*d^4*e^6*f^4*g^6*z^4 - 3072*a^8*c^6*d^3*e^7*f^5*g^5*z^4 - 3072*a^6*c^8*d^7*e^3*f^5*g^5*z^4 + 3072*
a^6*c^8*d^6*e^4*f^6*g^4*z^4 - 3072*a^6*c^8*d^5*e^5*f^7*g^3*z^4 - 2048*a^9*c^5*d^3*e^7*f^3*g^7*z^4 - 2048*a^7*c
^7*d^7*e^3*f^3*g^7*z^4 - 2048*a^7*c^7*d^3*e^7*f^7*g^3*z^4 - 2048*a^5*c^9*d^7*e^3*f^7*g^3*z^4 + 1792*a^8*c^6*d^
6*e^4*f^2*g^8*z^4 + 1792*a^8*c^6*d^2*e^8*f^6*g^4*z^4 + 1792*a^6*c^8*d^8*e^2*f^4*g^6*z^4 + 1792*a^6*c^8*d^4*e^6
*f^8*g^2*z^4 + 1408*a^9*c^5*d^4*e^6*f^2*g^8*z^4 + 1408*a^9*c^5*d^2*e^8*f^4*g^6*z^4 + 1408*a^5*c^9*d^8*e^2*f^6*
g^4*z^4 + 1408*a^5*c^9*d^6*e^4*f^8*g^2*z^4 + 1088*a^7*c^7*d^8*e^2*f^2*g^8*z^4 + 1088*a^7*c^7*d^2*e^8*f^8*g^2*z
^4 + 512*a^10*c^4*d^2*e^8*f^2*g^8*z^4 + 512*a^4*c^10*d^8*e^2*f^8*g^2*z^4 + 40*a^4*b^10*d^3*e^7*f^3*g^7*z^4 + 2
0*a^6*b^8*d^2*e^8*f^2*g^8*z^4 - 20*a^5*b^9*d^3*e^7*f^2*g^8*z^4 - 20*a^5*b^9*d^2*e^8*f^3*g^7*z^4 - 20*a^3*b^11*
d^4*e^6*f^3*g^7*z^4 - 20*a^3*b^11*d^3*e^7*f^4*g^6*z^4 + 20*a^2*b^12*d^4*e^6*f^4*g^6*z^4 + 16*a^3*b^11*d^5*e^5*
f^2*g^8*z^4 + 16*a^3*b^11*d^2*e^8*f^5*g^5*z^4 - 6*a^2*b^12*d^6*e^4*f^2*g^8*z^4 - 6*a^2*b^12*d^2*e^8*f^6*g^4*z^
4 - 5*a^4*b^10*d^4*e^6*f^2*g^8*z^4 - 5*a^4*b^10*d^2*e^8*f^4*g^6*z^4 - 4*a^2*b^12*d^5*e^5*f^3*g^7*z^4 - 4*a^2*b
^12*d^3*e^7*f^5*g^5*z^4 + 480*a^8*b^2*c^4*e^10*f^6*g^4*z^4 - 440*a^7*b^4*c^3*e^10*f^6*g^4*z^4 + 320*a^8*b^3*c^
3*e^10*f^5*g^5*z^4 + 320*a^7*b^3*c^4*e^10*f^7*g^3*z^4 - 240*a^8*b^4*c^2*e^10*f^4*g^6*z^4 - 240*a^6*b^4*c^4*e^1
0*f^8*g^2*z^4 + 192*a^9*b^3*c^2*e^10*f^3*g^7*z^4 + 192*a^9*b^2*c^3*e^10*f^4*g^6*z^4 + 192*a^7*b^2*c^5*e^10*f^8
*g^2*z^4 + 90*a^6*b^6*c^2*e^10*f^6*g^4*z^4 + 68*a^5*b^6*c^3*e^10*f^8*g^2*z^4 - 48*a^10*b^2*c^2*e^10*f^2*g^8*z^
4 + 48*a^7*b^5*c^2*e^10*f^5*g^5*z^4 + 48*a^6*b^5*c^3*e^10*f^7*g^3*z^4 - 36*a^5*b^7*c^2*e^10*f^7*g^3*z^4 - 6*a^
4*b^8*c^2*e^10*f^8*g^2*z^4 + 480*a^4*b^2*c^8*d^10*f^4*g^6*z^4 - 440*a^3*b^4*c^7*d^10*f^4*g^6*z^4 + 320*a^4*b^3
*c^7*d^10*f^3*g^7*z^4 + 320*a^3*b^3*c^8*d^10*f^5*g^5*z^4 - 240*a^4*b^4*c^6*d^10*f^2*g^8*z^4 - 240*a^2*b^4*c^8*
d^10*f^6*g^4*z^4 + 192*a^5*b^2*c^7*d^10*f^2*g^8*z^4 + 192*a^3*b^2*c^9*d^10*f^6*g^4*z^4 + 192*a^2*b^3*c^9*d^10*
f^7*g^3*z^4 + 90*a^2*b^6*c^6*d^10*f^4*g^6*z^4 + 68*a^3*b^6*c^5*d^10*f^2*g^8*z^4 + 48*a^3*b^5*c^6*d^10*f^3*g^7*
z^4 + 48*a^2*b^5*c^7*d^10*f^5*g^5*z^4 - 48*a^2*b^2*c^10*d^10*f^8*g^2*z^4 - 36*a^2*b^7*c^5*d^10*f^3*g^7*z^4 - 6
*a^2*b^8*c^4*d^10*f^2*g^8*z^4 + 480*a^8*b^2*c^4*d^6*e^4*g^10*z^4 - 440*a^7*b^4*c^3*d^6*e^4*g^10*z^4 + 320*a^8*
b^3*c^3*d^5*e^5*g^10*z^4 + 320*a^7*b^3*c^4*d^7*e^3*g^10*z^4 - 240*a^8*b^4*c^2*d^4*e^6*g^10*z^4 - 240*a^6*b^4*c
^4*d^8*e^2*g^10*z^4 + 192*a^9*b^3*c^2*d^3*e^7*g^10*z^4 + 192*a^9*b^2*c^3*d^4*e^6*g^10*z^4 + 192*a^7*b^2*c^5*d^
8*e^2*g^10*z^4 + 90*a^6*b^6*c^2*d^6*e^4*g^10*z^4 + 68*a^5*b^6*c^3*d^8*e^2*g^10*z^4 - 48*a^10*b^2*c^2*d^2*e^8*g
^10*z^4 + 48*a^7*b^5*c^2*d^5*e^5*g^10*z^4 + 48*a^6*b^5*c^3*d^7*e^3*g^10*z^4 - 36*a^5*b^7*c^2*d^7*e^3*g^10*z^4
- 6*a^4*b^8*c^2*d^8*e^2*g^10*z^4 + 480*a^4*b^2*c^8*d^4*e^6*f^10*z^4 - 440*a^3*b^4*c^7*d^4*e^6*f^10*z^4 + 320*a
^4*b^3*c^7*d^3*e^7*f^10*z^4 + 320*a^3*b^3*c^8*d^5*e^5*f^10*z^4 - 240*a^4*b^4*c^6*d^2*e^8*f^10*z^4 - 240*a^2*b^
4*c^8*d^6*e^4*f^10*z^4 + 192*a^5*b^2*c^7*d^2*e^8*f^10*z^4 + 192*a^3*b^2*c^9*d^6*e^4*f^10*z^4 + 192*a^2*b^3*c^9
*d^7*e^3*f^10*z^4 + 90*a^2*b^6*c^6*d^4*e^6*f^10*z^4 + 68*a^3*b^6*c^5*d^2*e^8*f^10*z^4 + 48*a^3*b^5*c^6*d^3*e^7
*f^10*z^4 + 48*a^2*b^5*c^7*d^5*e^5*f^10*z^4 - 48*a^2*b^2*c^10*d^8*e^2*f^10*z^4 - 36*a^2*b^7*c^5*d^3*e^7*f^10*z
^4 - 6*a^2*b^8*c^4*d^2*e^8*f^10*z^4 + 16*b^9*c^5*d^9*e*f^6*g^4*z^4 + 16*b^9*c^5*d^6*e^4*f^9*g*z^4 - 14*b^10*c^
4*d^9*e*f^5*g^5*z^4 - 14*b^10*c^4*d^5*e^5*f^9*g*z^4 + 4*b^13*c*d^7*e^3*f^4*g^6*z^4 - 4*b^13*c*d^6*e^4*f^5*g^5*
z^4 - 4*b^13*c*d^5*e^5*f^6*g^4*z^4 + 4*b^13*c*d^4*e^6*f^7*g^3*z^4 + 4*b^11*c^3*d^9*e*f^4*g^6*z^4 + 4*b^11*c^3*
d^4*e^6*f^9*g*z^4 - 4*b^8*c^6*d^9*e*f^7*g^3*z^4 - 4*b^8*c^6*d^7*e^3*f^9*g*z^4 - 4*b^7*c^7*d^9*e*f^8*g^2*z^4 -
4*b^7*c^7*d^8*e^2*f^9*g*z^4 - 768*a^9*c^5*d^5*e^5*f*g^9*z^4 - 768*a^9*c^5*d*e^9*f^5*g^5*z^4 - 768*a^5*c^9*d^9*
e*f^5*g^5*z^4 - 768*a^5*c^9*d^5*e^5*f^9*g*z^4 - 512*a^10*c^4*d^3*e^7*f*g^9*z^4 - 512*a^10*c^4*d*e^9*f^3*g^7*z^
4 - 512*a^8*c^6*d^7*e^3*f*g^9*z^4 - 512*a^8*c^6*d*e^9*f^7*g^3*z^4 - 512*a^6*c^8*d^9*e*f^3*g^7*z^4 - 512*a^6*c^
8*d^3*e^7*f^9*g*z^4 - 512*a^4*c^10*d^9*e*f^7*g^3*z^4 - 512*a^4*c^10*d^7*e^3*f^9*g*z^4 + 16*a^5*b^9*d^4*e^6*f*g
^9*z^4 + 16*a^5*b^9*d*e^9*f^4*g^6*z^4 - 14*a^4*b^10*d^5*e^5*f*g^9*z^4 - 14*a^4*b^10*d*e^9*f^5*g^5*z^4 - 4*a^7*
b^7*d^2*e^8*f*g^9*z^4 - 4*a^7*b^7*d*e^9*f^2*g^8*z^4 - 4*a^6*b^8*d^3*e^7*f*g^9*z^4 - 4*a^6*b^8*d*e^9*f^3*g^7*z^
4 + 4*a^3*b^11*d^6*e^4*f*g^9*z^4 + 4*a^3*b^11*d*e^9*f^6*g^4*z^4 + 4*a*b^13*d^6*e^4*f^3*g^7*z^4 - 4*a*b^13*d^5*
e^5*f^4*g^6*z^4 - 4*a*b^13*d^4*e^6*f^5*g^5*z^4 + 4*a*b^13*d^3*e^7*f^6*g^4*z^4 - 768*a^9*b*c^4*e^10*f^5*g^5*z^4
- 768*a^8*b*c^5*e^10*f^7*g^3*z^4 - 256*a^10*b*c^3*e^10*f^3*g^7*z^4 + 192*a^6*b^3*c^5*e^10*f^9*g*z^4 + 68*a^7*
b^6*c*e^10*f^4*g^6*z^4 - 48*a^8*b^5*c*e^10*f^3*g^7*z^4 - 48*a^5*b^5*c^4*e^10*f^9*g*z^4 - 36*a^6*b^7*c*e^10*f^5
*g^5*z^4 + 12*a^9*b^4*c*e^10*f^2*g^8*z^4 + 4*a^4*b^9*c*e^10*f^7*g^3*z^4 + 4*a^4*b^7*c^3*e^10*f^9*g*z^4 - 768*a
^5*b*c^8*d^10*f^3*g^7*z^4 - 768*a^4*b*c^9*d^10*f^5*g^5*z^4 - 256*a^3*b*c^10*d^10*f^7*g^3*z^4 + 192*a^5*b^3*c^6
*d^10*f*g^9*z^4 + 68*a*b^6*c^7*d^10*f^6*g^4*z^4 - 48*a^4*b^5*c^5*d^10*f*g^9*z^4 - 48*a*b^5*c^8*d^10*f^7*g^3*z^
4 - 36*a*b^7*c^6*d^10*f^5*g^5*z^4 + 12*a*b^4*c^9*d^10*f^8*g^2*z^4 + 4*a^3*b^7*c^4*d^10*f*g^9*z^4 + 4*a*b^9*c^4
*d^10*f^3*g^7*z^4 - 768*a^9*b*c^4*d^5*e^5*g^10*z^4 - 768*a^8*b*c^5*d^7*e^3*g^10*z^4 - 256*a^10*b*c^3*d^3*e^7*g
^10*z^4 + 192*a^6*b^3*c^5*d^9*e*g^10*z^4 + 68*a^7*b^6*c*d^4*e^6*g^10*z^4 - 48*a^8*b^5*c*d^3*e^7*g^10*z^4 - 48*
a^5*b^5*c^4*d^9*e*g^10*z^4 - 36*a^6*b^7*c*d^5*e^5*g^10*z^4 + 12*a^9*b^4*c*d^2*e^8*g^10*z^4 + 4*a^4*b^9*c*d^7*e
^3*g^10*z^4 + 4*a^4*b^7*c^3*d^9*e*g^10*z^4 - 768*a^5*b*c^8*d^3*e^7*f^10*z^4 - 768*a^4*b*c^9*d^5*e^5*f^10*z^4 -
256*a^3*b*c^10*d^7*e^3*f^10*z^4 + 192*a^5*b^3*c^6*d*e^9*f^10*z^4 + 68*a*b^6*c^7*d^6*e^4*f^10*z^4 - 48*a^4*b^5
*c^5*d*e^9*f^10*z^4 - 48*a*b^5*c^8*d^7*e^3*f^10*z^4 - 36*a*b^7*c^6*d^5*e^5*f^10*z^4 + 12*a*b^4*c^9*d^8*e^2*f^1
0*z^4 + 4*a^3*b^7*c^4*d*e^9*f^10*z^4 + 4*a*b^9*c^4*d^3*e^7*f^10*z^4 + 2*b^6*c^8*d^9*e*f^9*g*z^4 - 128*a^11*c^3
*d*e^9*f*g^9*z^4 - 128*a^7*c^7*d^9*e*f*g^9*z^4 - 128*a^7*c^7*d*e^9*f^9*g*z^4 - 128*a^3*c^11*d^9*e*f^9*g*z^4 +
2*a^8*b^6*d*e^9*f*g^9*z^4 - 256*a^7*b*c^6*e^10*f^9*g*z^4 - 256*a^6*b*c^7*d^10*f*g^9*z^4 - 256*a^7*b*c^6*d^9*e*
g^10*z^4 - 256*a^6*b*c^7*d*e^9*f^10*z^4 + 2*b^14*d^5*e^5*f^5*g^5*z^4 + 384*a^9*c^5*e^10*f^6*g^4*z^4 + 256*a^10
*c^4*e^10*f^4*g^6*z^4 + 256*a^8*c^6*e^10*f^8*g^2*z^4 + 64*a^11*c^3*e^10*f^2*g^8*z^4 - 6*b^8*c^6*d^10*f^6*g^4*z
^4 + 4*b^9*c^5*d^10*f^5*g^5*z^4 + 4*b^7*c^7*d^10*f^7*g^3*z^4 + 384*a^5*c^9*d^10*f^4*g^6*z^4 + 256*a^6*c^8*d^10
*f^2*g^8*z^4 + 256*a^4*c^10*d^10*f^6*g^4*z^4 + 64*a^3*c^11*d^10*f^8*g^2*z^4 - 6*a^6*b^8*e^10*f^4*g^6*z^4 + 4*a
^7*b^7*e^10*f^3*g^7*z^4 + 4*a^5*b^9*e^10*f^5*g^5*z^4 + 384*a^9*c^5*d^6*e^4*g^10*z^4 + 256*a^10*c^4*d^4*e^6*g^1
0*z^4 + 256*a^8*c^6*d^8*e^2*g^10*z^4 + 64*a^11*c^3*d^2*e^8*g^10*z^4 - 6*b^8*c^6*d^6*e^4*f^10*z^4 + 4*b^9*c^5*d
^5*e^5*f^10*z^4 + 4*b^7*c^7*d^7*e^3*f^10*z^4 + 384*a^5*c^9*d^4*e^6*f^10*z^4 + 256*a^6*c^8*d^2*e^8*f^10*z^4 + 2
56*a^4*c^10*d^6*e^4*f^10*z^4 + 64*a^3*c^11*d^8*e^2*f^10*z^4 - 6*a^6*b^8*d^4*e^6*g^10*z^4 + 4*a^7*b^7*d^3*e^7*g
^10*z^4 + 4*a^5*b^9*d^5*e^5*g^10*z^4 - 48*a^6*b^2*c^6*e^10*f^10*z^4 - 48*a^6*b^2*c^6*d^10*g^10*z^4 + 12*a^5*b^
4*c^5*e^10*f^10*z^4 + 12*a^5*b^4*c^5*d^10*g^10*z^4 + 64*a^7*c^7*e^10*f^10*z^4 + 64*a^7*c^7*d^10*g^10*z^4 - b^1
4*d^6*e^4*f^4*g^6*z^4 - b^14*d^4*e^6*f^6*g^4*z^4 - b^10*c^4*d^10*f^4*g^6*z^4 - b^6*c^8*d^10*f^8*g^2*z^4 - a^8*
b^6*e^10*f^2*g^8*z^4 - a^4*b^10*e^10*f^6*g^4*z^4 - b^10*c^4*d^4*e^6*f^10*z^4 - b^6*c^8*d^8*e^2*f^10*z^4 - a^8*
b^6*d^2*e^8*g^10*z^4 - a^4*b^10*d^6*e^4*g^10*z^4 - a^4*b^6*c^4*e^10*f^10*z^4 - a^4*b^6*c^4*d^10*g^10*z^4 + 272
*a^5*b^2*c^3*d*e^7*f*g^7*z^2 - 192*a^4*b^4*c^2*d*e^7*f*g^7*z^2 - 164*a^5*b*c^4*d^2*e^6*f*g^7*z^2 - 164*a^5*b*c
^4*d*e^7*f^2*g^6*z^2 + 120*a^2*b^2*c^6*d^7*e*f*g^7*z^2 + 120*a^2*b^2*c^6*d*e^7*f^7*g*z^2 + 120*a*b^2*c^7*d^7*e
*f^3*g^5*z^2 + 120*a*b^2*c^7*d^3*e^5*f^7*g*z^2 - 76*a^4*b*c^5*d^4*e^4*f*g^7*z^2 - 76*a^4*b*c^5*d*e^7*f^4*g^4*z
^2 - 76*a^3*b*c^6*d^6*e^2*f*g^7*z^2 - 76*a^3*b*c^6*d*e^7*f^6*g^2*z^2 - 64*a*b^3*c^6*d^7*e*f^2*g^6*z^2 - 64*a*b
^3*c^6*d^2*e^6*f^7*g*z^2 - 60*a^2*b*c^7*d^7*e*f^2*g^6*z^2 - 60*a^2*b*c^7*d^2*e^6*f^7*g*z^2 + 44*a*b*c^8*d^6*e^
2*f^5*g^3*z^2 + 44*a*b*c^8*d^5*e^3*f^6*g^2*z^2 + 22*a*b^5*c^4*d^6*e^2*f*g^7*z^2 + 22*a*b^5*c^4*d*e^7*f^6*g^2*z
^2 - 20*a^2*b^7*c*d^2*e^6*f*g^7*z^2 - 20*a^2*b^7*c*d*e^7*f^2*g^6*z^2 + 8*a*b^8*c*d^2*e^6*f^2*g^6*z^2 - 8*a*b^6
*c^3*d^5*e^3*f*g^7*z^2 - 8*a*b^6*c^3*d*e^7*f^5*g^3*z^2 + 2*a*b^7*c^2*d^4*e^4*f*g^7*z^2 + 2*a*b^7*c^2*d*e^7*f^4
*g^4*z^2 - 590*a^2*b^2*c^6*d^4*e^4*f^4*g^4*z^2 - 352*a^2*b^4*c^4*d^3*e^5*f^3*g^5*z^2 - 346*a^3*b^2*c^5*d^4*e^4
*f^2*g^6*z^2 - 346*a^3*b^2*c^5*d^2*e^6*f^4*g^4*z^2 - 274*a^4*b^2*c^4*d^2*e^6*f^2*g^6*z^2 + 272*a^3*b^2*c^5*d^3
*e^5*f^3*g^5*z^2 + 250*a^2*b^3*c^5*d^4*e^4*f^3*g^5*z^2 + 250*a^2*b^3*c^5*d^3*e^5*f^4*g^4*z^2 + 204*a^3*b^3*c^4
*d^3*e^5*f^2*g^6*z^2 + 204*a^3*b^3*c^4*d^2*e^6*f^3*g^5*z^2 + 136*a^2*b^2*c^6*d^5*e^3*f^3*g^5*z^2 + 136*a^2*b^2
*c^6*d^3*e^5*f^5*g^3*z^2 + 71*a^2*b^4*c^4*d^4*e^4*f^2*g^6*z^2 + 71*a^2*b^4*c^4*d^2*e^6*f^4*g^4*z^2 - 56*a^2*b^
3*c^5*d^5*e^3*f^2*g^6*z^2 - 56*a^2*b^3*c^5*d^2*e^6*f^5*g^3*z^2 + 18*a^2*b^2*c^6*d^6*e^2*f^2*g^6*z^2 + 18*a^2*b
^2*c^6*d^2*e^6*f^6*g^2*z^2 - 16*a^3*b^4*c^3*d^2*e^6*f^2*g^6*z^2 + 16*a^2*b^5*c^3*d^3*e^5*f^2*g^6*z^2 + 16*a^2*
b^5*c^3*d^2*e^6*f^3*g^5*z^2 - 4*a^2*b^6*c^2*d^2*e^6*f^2*g^6*z^2 + 48*a^3*b^6*c*d*e^7*f*g^7*z^2 - 20*a*b^4*c^5*
d^7*e*f*g^7*z^2 - 20*a*b^4*c^5*d*e^7*f^7*g*z^2 - 4*a*b^8*c*d^3*e^5*f*g^7*z^2 - 4*a*b^8*c*d*e^7*f^3*g^5*z^2 + 4
*a*b*c^8*d^7*e*f^4*g^4*z^2 + 4*a*b*c^8*d^4*e^4*f^7*g*z^2 + 368*a^4*b^2*c^4*d^3*e^5*f*g^7*z^2 + 368*a^4*b^2*c^4
*d*e^7*f^3*g^5*z^2 + 264*a^3*b^2*c^5*d^5*e^3*f*g^7*z^2 + 264*a^3*b^2*c^5*d*e^7*f^5*g^3*z^2 - 208*a^3*b^4*c^3*d
^3*e^5*f*g^7*z^2 - 208*a^3*b^4*c^3*d*e^7*f^3*g^5*z^2 - 164*a^4*b*c^5*d^3*e^5*f^2*g^6*z^2 - 164*a^4*b*c^5*d^2*e
^6*f^3*g^5*z^2 + 140*a^2*b*c^7*d^5*e^3*f^4*g^4*z^2 + 140*a^2*b*c^7*d^4*e^4*f^5*g^3*z^2 - 122*a*b^2*c^7*d^6*e^2
*f^4*g^4*z^2 - 122*a*b^2*c^7*d^4*e^4*f^6*g^2*z^2 - 108*a^2*b^3*c^5*d^6*e^2*f*g^7*z^2 - 108*a^2*b^3*c^5*d*e^7*f
^6*g^2*z^2 + 102*a*b^3*c^6*d^5*e^3*f^4*g^4*z^2 + 102*a*b^3*c^6*d^4*e^4*f^5*g^3*z^2 + 80*a*b^6*c^3*d^3*e^5*f^3*
g^5*z^2 + 68*a*b^4*c^5*d^6*e^2*f^2*g^6*z^2 + 68*a*b^4*c^5*d^2*e^6*f^6*g^2*z^2 - 60*a^3*b*c^6*d^5*e^3*f^2*g^6*z
^2 + 60*a^3*b*c^6*d^4*e^4*f^3*g^5*z^2 + 60*a^3*b*c^6*d^3*e^5*f^4*g^4*z^2 - 60*a^3*b*c^6*d^2*e^6*f^5*g^3*z^2 -
54*a^3*b^3*c^4*d^4*e^4*f*g^7*z^2 - 54*a^3*b^3*c^4*d*e^7*f^4*g^4*z^2 - 52*a*b^4*c^5*d^5*e^3*f^3*g^5*z^2 - 52*a*
b^4*c^5*d^3*e^5*f^5*g^3*z^2 + 48*a^3*b^5*c^2*d^2*e^6*f*g^7*z^2 + 48*a^3*b^5*c^2*d*e^7*f^2*g^6*z^2 + 48*a^2*b^6
*c^2*d^3*e^5*f*g^7*z^2 + 48*a^2*b^6*c^2*d*e^7*f^3*g^5*z^2 + 44*a^4*b^3*c^3*d^2*e^6*f*g^7*z^2 + 44*a^4*b^3*c^3*
d*e^7*f^2*g^6*z^2 - 44*a^2*b*c^7*d^6*e^2*f^3*g^5*z^2 - 44*a^2*b*c^7*d^3*e^5*f^6*g^2*z^2 - 44*a*b^3*c^6*d^6*e^2
*f^3*g^5*z^2 - 44*a*b^3*c^6*d^3*e^5*f^6*g^2*z^2 - 32*a*b^5*c^4*d^4*e^4*f^3*g^5*z^2 - 32*a*b^5*c^4*d^3*e^5*f^4*
g^4*z^2 - 32*a*b^2*c^7*d^5*e^3*f^5*g^3*z^2 - 20*a*b^7*c^2*d^3*e^5*f^2*g^6*z^2 - 20*a*b^7*c^2*d^2*e^6*f^3*g^5*z
^2 + 20*a*b^4*c^5*d^4*e^4*f^4*g^4*z^2 - 14*a*b^5*c^4*d^5*e^3*f^2*g^6*z^2 - 14*a*b^5*c^4*d^2*e^6*f^5*g^3*z^2 +
4*a^2*b^5*c^3*d^4*e^4*f*g^7*z^2 + 4*a^2*b^5*c^3*d*e^7*f^4*g^4*z^2 - 4*a^2*b^4*c^4*d^5*e^3*f*g^7*z^2 - 4*a^2*b^
4*c^4*d*e^7*f^5*g^3*z^2 + 2*a*b^6*c^3*d^4*e^4*f^2*g^6*z^2 + 2*a*b^6*c^3*d^2*e^6*f^4*g^4*z^2 - 50*b^2*c^8*d^6*e
^2*f^6*g^2*z^2 - 32*b^4*c^6*d^5*e^3*f^5*g^3*z^2 + 24*b^3*c^7*d^6*e^2*f^5*g^3*z^2 + 24*b^3*c^7*d^5*e^3*f^6*g^2*
z^2 + 23*b^4*c^6*d^6*e^2*f^4*g^4*z^2 + 23*b^4*c^6*d^4*e^4*f^6*g^2*z^2 - 11*b^6*c^4*d^6*e^2*f^2*g^6*z^2 - 11*b^
6*c^4*d^2*e^6*f^6*g^2*z^2 + 8*b^6*c^4*d^5*e^3*f^3*g^5*z^2 + 8*b^6*c^4*d^3*e^5*f^5*g^3*z^2 - 8*b^5*c^5*d^5*e^3*
f^4*g^4*z^2 - 8*b^5*c^5*d^4*e^4*f^5*g^3*z^2 + 5*b^6*c^4*d^4*e^4*f^4*g^4*z^2 - 4*b^8*c^2*d^3*e^5*f^3*g^5*z^2 +
4*b^7*c^3*d^5*e^3*f^2*g^6*z^2 + 4*b^7*c^3*d^2*e^6*f^5*g^3*z^2 - 2*b^7*c^3*d^4*e^4*f^3*g^5*z^2 - 2*b^7*c^3*d^3*
e^5*f^4*g^4*z^2 - 2*b^5*c^5*d^6*e^2*f^3*g^5*z^2 - 2*b^5*c^5*d^3*e^5*f^6*g^2*z^2 + 416*a^5*c^5*d^2*e^6*f^2*g^6*
z^2 - 392*a^4*c^6*d^3*e^5*f^3*g^5*z^2 + 376*a^4*c^6*d^4*e^4*f^2*g^6*z^2 + 376*a^4*c^6*d^2*e^6*f^4*g^4*z^2 + 32
0*a^3*c^7*d^4*e^4*f^4*g^4*z^2 - 280*a^3*c^7*d^5*e^3*f^3*g^5*z^2 - 280*a^3*c^7*d^3*e^5*f^5*g^3*z^2 - 200*a^2*c^
8*d^5*e^3*f^5*g^3*z^2 + 160*a^3*c^7*d^6*e^2*f^2*g^6*z^2 + 160*a^3*c^7*d^2*e^6*f^6*g^2*z^2 + 120*a^2*c^8*d^6*e^
2*f^4*g^4*z^2 + 120*a^2*c^8*d^4*e^4*f^6*g^2*z^2 - 471*a^4*b^2*c^4*e^8*f^4*g^4*z^2 + 436*a^3*b^4*c^3*e^8*f^4*g^
4*z^2 - 310*a^3*b^3*c^4*e^8*f^5*g^3*z^2 - 232*a^5*b^2*c^3*e^8*f^2*g^6*z^2 + 229*a^2*b^4*c^4*e^8*f^6*g^2*z^2 +
216*a^4*b^4*c^2*e^8*f^2*g^6*z^2 - 204*a^4*b^3*c^3*e^8*f^3*g^5*z^2 - 150*a^3*b^2*c^5*e^8*f^6*g^2*z^2 - 91*a^2*b
^6*c^2*e^8*f^4*g^4*z^2 - 72*a^3*b^5*c^2*e^8*f^3*g^5*z^2 - 44*a^2*b^5*c^3*e^8*f^5*g^3*z^2 - 471*a^4*b^2*c^4*d^4
*e^4*g^8*z^2 + 436*a^3*b^4*c^3*d^4*e^4*g^8*z^2 - 310*a^3*b^3*c^4*d^5*e^3*g^8*z^2 - 232*a^5*b^2*c^3*d^2*e^6*g^8
*z^2 + 229*a^2*b^4*c^4*d^6*e^2*g^8*z^2 + 216*a^4*b^4*c^2*d^2*e^6*g^8*z^2 - 204*a^4*b^3*c^3*d^3*e^5*g^8*z^2 - 1
50*a^3*b^2*c^5*d^6*e^2*g^8*z^2 - 91*a^2*b^6*c^2*d^4*e^4*g^8*z^2 - 72*a^3*b^5*c^2*d^3*e^5*g^8*z^2 - 44*a^2*b^5*
c^3*d^5*e^3*g^8*z^2 - 26*b^3*c^7*d^7*e*f^4*g^4*z^2 - 26*b^3*c^7*d^4*e^4*f^7*g*z^2 + 16*b^2*c^8*d^7*e*f^5*g^3*z
^2 + 16*b^2*c^8*d^5*e^3*f^7*g*z^2 + 10*b^5*c^5*d^7*e*f^2*g^6*z^2 + 10*b^5*c^5*d^2*e^6*f^7*g*z^2 - 4*b^4*c^6*d^
7*e*f^3*g^5*z^2 - 4*b^4*c^6*d^3*e^5*f^7*g*z^2 + 2*b^9*c*d^3*e^5*f^2*g^6*z^2 + 2*b^9*c*d^2*e^6*f^3*g^5*z^2 - 16
8*a^5*c^5*d^3*e^5*f*g^7*z^2 - 168*a^5*c^5*d*e^7*f^3*g^5*z^2 - 120*a^4*c^6*d^5*e^3*f*g^7*z^2 - 120*a^4*c^6*d*e^
7*f^5*g^3*z^2 - 56*a^2*c^8*d^7*e*f^3*g^5*z^2 - 56*a^2*c^8*d^3*e^5*f^7*g*z^2 + 32*a*c^9*d^6*e^2*f^6*g^2*z^2 + 6
24*a^4*b*c^5*e^8*f^5*g^3*z^2 + 548*a^5*b*c^4*e^8*f^3*g^5*z^2 - 182*a^2*b^3*c^5*e^8*f^7*g*z^2 - 96*a^5*b^3*c^2*
e^8*f*g^7*z^2 - 68*a*b^6*c^3*e^8*f^6*g^2*z^2 - 58*a^3*b^6*c*e^8*f^2*g^6*z^2 + 38*a^2*b^7*c*e^8*f^3*g^5*z^2 + 3
6*a*b^7*c^2*e^8*f^5*g^3*z^2 + 18*a*b^2*c^7*d^8*f^2*g^6*z^2 + 624*a^4*b*c^5*d^5*e^3*g^8*z^2 + 548*a^5*b*c^4*d^3
*e^5*g^8*z^2 - 182*a^2*b^3*c^5*d^7*e*g^8*z^2 - 96*a^5*b^3*c^2*d*e^7*g^8*z^2 - 68*a*b^6*c^3*d^6*e^2*g^8*z^2 - 5
8*a^3*b^6*c*d^2*e^6*g^8*z^2 + 38*a^2*b^7*c*d^3*e^5*g^8*z^2 + 36*a*b^7*c^2*d^5*e^3*g^8*z^2 + 18*a*b^2*c^7*d^2*e
^6*f^8*z^2 + 12*b*c^9*d^7*e*f^6*g^2*z^2 + 12*b*c^9*d^6*e^2*f^7*g*z^2 - 72*a^6*c^4*d*e^7*f*g^7*z^2 - 40*a*c^9*d
^7*e*f^5*g^3*z^2 - 40*a*c^9*d^5*e^3*f^7*g*z^2 - 24*a^3*c^7*d^7*e*f*g^7*z^2 - 24*a^3*c^7*d*e^7*f^7*g*z^2 - 4*a^
2*b^8*d*e^7*f*g^7*z^2 + 2*a*b^9*d^2*e^6*f*g^7*z^2 + 2*a*b^9*d*e^7*f^2*g^6*z^2 + 204*a^3*b*c^6*e^8*f^7*g*z^2 +
128*a^6*b*c^3*e^8*f*g^7*z^2 + 48*a*b^5*c^4*e^8*f^7*g*z^2 + 24*a^4*b^5*c*e^8*f*g^7*z^2 - 48*a*b*c^8*d^8*f^3*g^5
*z^2 - 36*a^2*b*c^7*d^8*f*g^7*z^2 + 6*a*b^3*c^6*d^8*f*g^7*z^2 + 204*a^3*b*c^6*d^7*e*g^8*z^2 + 128*a^6*b*c^3*d*
e^7*g^8*z^2 + 48*a*b^5*c^4*d^7*e*g^8*z^2 + 24*a^4*b^5*c*d*e^7*g^8*z^2 - 48*a*b*c^8*d^3*e^5*f^8*z^2 - 36*a^2*b*
c^7*d*e^7*f^8*z^2 + 6*a*b^3*c^6*d*e^7*f^8*z^2 - b^8*c^2*d^4*e^4*f^2*g^6*z^2 - b^8*c^2*d^2*e^6*f^4*g^4*z^2 - 4*
b^9*c*e^8*f^5*g^3*z^2 - 4*b^7*c^3*e^8*f^7*g*z^2 - 12*b*c^9*d^8*f^5*g^3*z^2 + 24*a*c^9*d^8*f^4*g^4*z^2 - 4*b^9*
c*d^5*e^3*g^8*z^2 - 4*b^7*c^3*d^7*e*g^8*z^2 - 4*a*b^9*e^8*f^3*g^5*z^2 - 2*a^3*b^7*e^8*f*g^7*z^2 - 12*b*c^9*d^5
*e^3*f^8*z^2 + 24*a*c^9*d^4*e^4*f^8*z^2 - 4*a*b^9*d^3*e^5*g^8*z^2 - 2*a^3*b^7*d*e^7*g^8*z^2 - 12*a^5*b^4*c*e^8
*g^8*z^2 - 12*a*b^4*c^5*e^8*f^8*z^2 - 12*a*b^4*c^5*d^8*g^8*z^2 - 8*c^10*d^7*e*f^7*g*z^2 + 6*b^8*c^2*e^8*f^6*g^
2*z^2 - 232*a^5*c^5*e^8*f^4*g^4*z^2 - 188*a^4*c^6*e^8*f^6*g^2*z^2 - 92*a^6*c^4*e^8*f^2*g^6*z^2 + 9*b^2*c^8*d^8
*f^4*g^4*z^2 - 3*b^4*c^6*d^8*f^2*g^6*z^2 + 2*b^3*c^7*d^8*f^3*g^5*z^2 + 36*a^2*c^8*d^8*f^2*g^6*z^2 + 6*b^8*c^2*
d^6*e^2*g^8*z^2 + 5*a^2*b^8*e^8*f^2*g^6*z^2 - 232*a^5*c^5*d^4*e^4*g^8*z^2 - 188*a^4*c^6*d^6*e^2*g^8*z^2 - 92*a
^6*c^4*d^2*e^6*g^8*z^2 + 9*b^2*c^8*d^4*e^4*f^8*z^2 - 3*b^4*c^6*d^2*e^6*f^8*z^2 + 2*b^3*c^7*d^3*e^5*f^8*z^2 + 3
6*a^2*c^8*d^2*e^6*f^8*z^2 + 5*a^2*b^8*d^2*e^6*g^8*z^2 + 48*a^6*b^2*c^2*e^8*g^8*z^2 + 45*a^2*b^2*c^6*e^8*f^8*z^
2 + 45*a^2*b^2*c^6*d^8*g^8*z^2 + 4*c^10*d^8*f^6*g^2*z^2 + b^10*e^8*f^4*g^4*z^2 + 4*c^10*d^6*e^2*f^8*z^2 + b^10
*d^4*e^4*g^8*z^2 - 64*a^7*c^3*e^8*g^8*z^2 + b^6*c^4*e^8*f^8*z^2 + b^6*c^4*d^8*g^8*z^2 - 48*a^3*c^7*e^8*f^8*z^2
- 48*a^3*c^7*d^8*g^8*z^2 + a^4*b^6*e^8*g^8*z^2 - b^10*d^2*e^6*f^2*g^6*z^2 + 108*a^2*b^2*c^4*d^2*e^5*f*g^6*z +
108*a^2*b^2*c^4*d*e^6*f^2*g^5*z + 60*a*b^2*c^5*d^3*e^4*f^2*g^5*z + 60*a*b^2*c^5*d^2*e^5*f^3*g^4*z - 48*a^2*b*
c^5*d^2*e^5*f^2*g^5*z - 44*a*b^3*c^4*d^2*e^5*f^2*g^5*z - 120*a^2*b*c^5*d^3*e^4*f*g^6*z - 120*a^2*b*c^5*d*e^6*f
^3*g^4*z - 96*a*b*c^6*d^3*e^4*f^3*g^4*z - 64*a^2*b^3*c^3*d*e^6*f*g^6*z + 32*a*b^3*c^4*d^3*e^4*f*g^6*z + 32*a*b
^3*c^4*d*e^6*f^3*g^4*z - 28*a*b^4*c^3*d^2*e^5*f*g^6*z - 28*a*b^4*c^3*d*e^6*f^2*g^5*z - 18*a*b^2*c^5*d^4*e^3*f*
g^6*z - 18*a*b^2*c^5*d*e^6*f^4*g^3*z + 4*a*b*c^6*d^4*e^3*f^2*g^5*z + 4*a*b*c^6*d^2*e^5*f^4*g^3*z + 24*a*b^5*c^
2*d*e^6*f*g^6*z - 16*a^3*b*c^4*d*e^6*f*g^6*z - 8*a*b*c^6*d^5*e^2*f*g^6*z - 8*a*b*c^6*d*e^6*f^5*g^2*z - 13*b^2*
c^6*d^6*e*f*g^6*z - 13*b^2*c^6*d*e^6*f^6*g*z + 8*b*c^7*d^6*e*f^2*g^5*z + 8*b*c^7*d^2*e^5*f^6*g*z + 9*b^2*c^6*d
^4*e^3*f^3*g^4*z + 9*b^2*c^6*d^3*e^4*f^4*g^3*z + 8*b^5*c^3*d^2*e^5*f^2*g^5*z - 6*b^4*c^4*d^3*e^4*f^2*g^5*z - 6
*b^4*c^4*d^2*e^5*f^3*g^4*z - 6*b^3*c^5*d^4*e^3*f^2*g^5*z - 6*b^3*c^5*d^2*e^5*f^4*g^3*z + 4*b^3*c^5*d^3*e^4*f^3
*g^4*z + b^2*c^6*d^5*e^2*f^2*g^5*z + b^2*c^6*d^2*e^5*f^5*g^2*z + 16*a^2*c^6*d^3*e^4*f^2*g^5*z + 16*a^2*c^6*d^2
*e^5*f^3*g^4*z - 112*a^2*b^3*c^3*e^7*f^2*g^5*z - 12*a^2*b^2*c^4*e^7*f^3*g^4*z - 112*a^2*b^3*c^3*d^2*e^5*g^7*z
- 12*a^2*b^2*c^4*d^3*e^4*g^7*z - 2*b^7*c*d*e^6*f*g^6*z + 8*a*c^7*d^6*e*f*g^6*z + 8*a*c^7*d*e^6*f^6*g*z + 52*a*
b*c^6*e^7*f^6*g*z - 10*a*b^6*c*e^7*f*g^6*z + 52*a*b*c^6*d^6*e*g^7*z - 10*a*b^6*c*d*e^6*g^7*z + 14*b^3*c^5*d^5*
e^2*f*g^6*z + 14*b^3*c^5*d*e^6*f^5*g^2*z - 12*b*c^7*d^5*e^2*f^3*g^4*z - 12*b*c^7*d^3*e^4*f^5*g^2*z - 5*b^4*c^4
*d^4*e^3*f*g^6*z - 5*b^4*c^4*d*e^6*f^4*g^3*z + b^6*c^2*d^2*e^5*f*g^6*z + b^6*c^2*d*e^6*f^2*g^5*z + 52*a^2*c^6*
d^4*e^3*f*g^6*z + 52*a^2*c^6*d*e^6*f^4*g^3*z + 24*a*c^7*d^4*e^3*f^3*g^4*z + 24*a*c^7*d^3*e^4*f^4*g^3*z - 16*a*
c^7*d^5*e^2*f^2*g^5*z - 16*a*c^7*d^2*e^5*f^5*g^2*z + 8*a^3*c^5*d^2*e^5*f*g^6*z + 8*a^3*c^5*d*e^6*f^2*g^5*z + 2
00*a^3*b*c^4*e^7*f^2*g^5*z + 144*a^2*b*c^5*e^7*f^4*g^3*z - 42*a*b^2*c^5*e^7*f^5*g^2*z + 32*a^3*b^2*c^3*e^7*f*g
^6*z + 24*a^2*b^4*c^2*e^7*f*g^6*z + 24*a*b^5*c^2*e^7*f^2*g^5*z - 10*a*b^3*c^4*e^7*f^4*g^3*z + 4*a*b^4*c^3*e^7*
f^3*g^4*z + 200*a^3*b*c^4*d^2*e^5*g^7*z + 144*a^2*b*c^5*d^4*e^3*g^7*z - 42*a*b^2*c^5*d^5*e^2*g^7*z + 32*a^3*b^
2*c^3*d*e^6*g^7*z + 24*a^2*b^4*c^2*d*e^6*g^7*z + 24*a*b^5*c^2*d^2*e^5*g^7*z - 10*a*b^3*c^4*d^4*e^3*g^7*z + 4*a
*b^4*c^3*d^3*e^4*g^7*z + 4*b*c^7*d^7*f*g^6*z + 4*b*c^7*d*e^6*f^7*z + 11*b^4*c^4*e^7*f^5*g^2*z - 4*b^5*c^3*e^7*
f^4*g^3*z + b^6*c^2*e^7*f^3*g^4*z - 136*a^3*c^5*e^7*f^3*g^4*z - 68*a^2*c^6*e^7*f^5*g^2*z + 11*b^4*c^4*d^5*e^2*
g^7*z - 4*b^5*c^3*d^4*e^3*g^7*z + b^6*c^2*d^3*e^4*g^7*z - 136*a^3*c^5*d^3*e^4*g^7*z - 68*a^2*c^6*d^5*e^2*g^7*z
- 96*a^3*b^3*c^2*e^7*g^7*z + 4*c^8*d^6*e*f^3*g^4*z + 4*c^8*d^3*e^4*f^6*g*z - 10*b^3*c^5*e^7*f^6*g*z - 2*b^7*c
*e^7*f^2*g^5*z - 128*a^4*c^4*e^7*f*g^6*z - 10*b^3*c^5*d^6*e*g^7*z - 2*b^7*c*d^2*e^5*g^7*z - 128*a^4*c^4*d*e^6*
g^7*z + 128*a^4*b*c^3*e^7*g^7*z + 24*a^2*b^5*c*e^7*g^7*z - 4*c^8*d^7*f^2*g^5*z - 4*c^8*d^2*e^5*f^7*z + 3*b^2*c
^6*e^7*f^7*z + 3*b^2*c^6*d^7*g^7*z + b^8*e^7*f*g^6*z + b^8*d*e^6*g^7*z - 16*a*c^7*e^7*f^7*z - 16*a*c^7*d^7*g^7
*z - 2*a*b^7*e^7*g^7*z - 8*a*c^5*d*e^5*f*g^5 + 20*a*b*c^4*e^6*f*g^5 + 20*a*b*c^4*d*e^5*g^6 + 4*b*c^5*d^2*e^4*f
*g^5 + 4*b*c^5*d*e^5*f^2*g^4 - 2*b^2*c^4*d*e^5*f*g^5 - 4*b^3*c^3*e^6*f*g^5 - 16*a*c^5*e^6*f^2*g^4 - 4*b^3*c^3*
d*e^5*g^6 - 16*a*c^5*d^2*e^4*g^6 + 8*a*b^2*c^3*e^6*g^6 - 4*c^6*d^2*e^4*f^2*g^4 + 3*b^2*c^4*e^6*f^2*g^4 + 3*b^2
*c^4*d^2*e^4*g^6 - 36*a^2*c^4*e^6*g^6, z, k)*((13*a^2*b^5*c^2*e^7*g^7 - 56*a^3*b^3*c^3*e^7*g^7 + 24*a^2*c^7*d^
5*e^2*g^7 - 2*b^4*c^5*d^5*e^2*g^7 + b^5*c^4*d^4*e^3*g^7 + b^6*c^3*d^3*e^4*g^7 - 2*b^7*c^2*d^2*e^5*g^7 + 24*a^2
*c^7*e^7*f^5*g^2 - 2*b^4*c^5*e^7*f^5*g^2 + b^5*c^4*e^7*f^4*g^3 + b^6*c^3*e^7*f^3*g^4 - 2*b^7*c^2*e^7*f^2*g^5 -
a*b^7*c*e^7*g^7 + b^8*c*d*e^6*g^7 + b^8*c*e^7*f*g^6 + 80*a^4*b*c^4*e^7*g^7 - 28*a^4*c^5*d*e^6*g^7 + b^3*c^6*d
^6*e*g^7 - 28*a^4*c^5*e^7*f*g^6 + b^3*c^6*e^7*f^6*g + 4*c^9*d^3*e^4*f^6*g + 4*c^9*d^6*e*f^3*g^4 - 12*a*b^6*c^2
*d*e^6*g^7 - 12*a*b^6*c^2*e^7*f*g^6 - 4*b*c^8*d^2*e^5*f^6*g - 4*b*c^8*d^6*e*f^2*g^5 - b^2*c^7*d*e^6*f^6*g - b^
2*c^7*d^6*e*f*g^6 - 2*b^7*c^2*d*e^6*f*g^6 + 2*a*b^2*c^6*d^5*e^2*g^7 + 10*a*b^3*c^5*d^4*e^3*g^7 - 20*a*b^4*c^4*
d^3*e^4*g^7 + 25*a*b^5*c^3*d^2*e^5*g^7 - 56*a^2*b*c^6*d^4*e^3*g^7 + 44*a^2*b^4*c^3*d*e^6*g^7 + 76*a^3*b*c^5*d^
2*e^5*g^7 - 40*a^3*b^2*c^4*d*e^6*g^7 + 2*a*b^2*c^6*e^7*f^5*g^2 + 10*a*b^3*c^5*e^7*f^4*g^3 - 20*a*b^4*c^4*e^7*f
^3*g^4 + 25*a*b^5*c^3*e^7*f^2*g^5 - 56*a^2*b*c^6*e^7*f^4*g^3 + 44*a^2*b^4*c^3*e^7*f*g^6 + 76*a^3*b*c^5*e^7*f^2
*g^5 - 40*a^3*b^2*c^4*e^7*f*g^6 + 16*a*c^8*d^2*e^5*f^5*g^2 + 24*a*c^8*d^3*e^4*f^4*g^3 + 24*a*c^8*d^4*e^3*f^3*g
^4 + 16*a*c^8*d^5*e^2*f^2*g^5 + 28*a^2*c^7*d*e^6*f^4*g^3 + 28*a^2*c^7*d^4*e^3*f*g^6 - 80*a^3*c^6*d*e^6*f^2*g^5
- 80*a^3*c^6*d^2*e^5*f*g^6 - 12*b*c^8*d^3*e^4*f^5*g^2 - 12*b*c^8*d^5*e^2*f^3*g^4 + 6*b^3*c^6*d*e^6*f^5*g^2 +
6*b^3*c^6*d^5*e^2*f*g^6 - 9*b^4*c^5*d*e^6*f^4*g^3 - 9*b^4*c^5*d^4*e^3*f*g^6 + 4*b^5*c^4*d*e^6*f^3*g^4 + 4*b^5*
c^4*d^3*e^4*f*g^6 + b^6*c^3*d*e^6*f^2*g^5 + b^6*c^3*d^2*e^5*f*g^6 - 4*a*b*c^7*d^6*e*g^7 - 4*a*b*c^7*e^7*f^6*g
+ 8*a*c^8*d*e^6*f^6*g + 8*a*c^8*d^6*e*f*g^6 + 65*a^2*b^2*c^5*d^3*e^4*g^7 - 88*a^2*b^3*c^4*d^2*e^5*g^7 + 65*a^2
*b^2*c^5*e^7*f^3*g^4 - 88*a^2*b^3*c^4*e^7*f^2*g^5 + 68*a^2*c^7*d^2*e^5*f^3*g^4 + 68*a^2*c^7*d^3*e^4*f^2*g^5 +
8*b^2*c^7*d^2*e^5*f^5*g^2 + 9*b^2*c^7*d^3*e^4*f^4*g^3 + 9*b^2*c^7*d^4*e^3*f^3*g^4 + 8*b^2*c^7*d^5*e^2*f^2*g^5
- b^3*c^6*d^2*e^5*f^4*g^3 + 4*b^3*c^6*d^3*e^4*f^3*g^4 - b^3*c^6*d^4*e^3*f^2*g^5 - 9*b^4*c^5*d^2*e^5*f^3*g^4 -
9*b^4*c^5*d^3*e^4*f^2*g^5 + 7*b^5*c^4*d^2*e^5*f^2*g^5 + 74*a*b^2*c^6*d^2*e^5*f^3*g^4 + 74*a*b^2*c^6*d^3*e^4*f^
2*g^5 - 28*a*b^3*c^5*d^2*e^5*f^2*g^5 - 120*a^2*b*c^6*d^2*e^5*f^2*g^5 + 159*a^2*b^2*c^5*d*e^6*f^2*g^5 + 159*a^2
*b^2*c^5*d^2*e^5*f*g^6 - 36*a*b*c^7*d*e^6*f^5*g^2 - 36*a*b*c^7*d^5*e^2*f*g^6 + 28*a*b^5*c^3*d*e^6*f*g^6 + 104*
a^3*b*c^5*d*e^6*f*g^6 - 56*a*b*c^7*d^2*e^5*f^4*g^3 - 96*a*b*c^7*d^3*e^4*f^3*g^4 - 56*a*b*c^7*d^4*e^3*f^2*g^5 +
44*a*b^2*c^6*d*e^6*f^4*g^3 + 44*a*b^2*c^6*d^4*e^3*f*g^6 - 32*a*b^4*c^4*d*e^6*f^2*g^5 - 32*a*b^4*c^4*d^2*e^5*f
*g^6 - 116*a^2*b*c^6*d*e^6*f^3*g^4 - 116*a^2*b*c^6*d^3*e^4*f*g^6 - 112*a^2*b^3*c^4*d*e^6*f*g^6)/(16*a^2*c^6*d^
4*f^4 + a^4*b^4*e^4*g^4 + 16*a^4*c^4*d^4*g^4 + 16*a^4*c^4*e^4*f^4 + b^4*c^4*d^4*f^4 + 16*a^6*c^2*e^4*g^4 + a^2
*b^4*c^2*d^4*g^4 + a^2*b^4*c^2*e^4*f^4 - 8*a^3*b^2*c^3*d^4*g^4 - 8*a^3*b^2*c^3*e^4*f^4 + a^2*b^6*d^2*e^2*g^4 +
32*a^3*c^5*d^2*e^2*f^4 + 32*a^5*c^3*d^2*e^2*g^4 + b^6*c^2*d^2*e^2*f^4 + a^2*b^6*e^4*f^2*g^2 + 32*a^3*c^5*d^4*
f^2*g^2 + 32*a^5*c^3*e^4*f^2*g^2 + b^6*c^2*d^4*f^2*g^2 + b^8*d^2*e^2*f^2*g^2 - 8*a*b^2*c^5*d^4*f^4 - 8*a^5*b^2
*c*e^4*g^4 - 2*a^3*b^5*d*e^3*g^4 - 2*b^5*c^3*d^3*e*f^4 - 2*a^3*b^5*e^4*f*g^3 - 2*b^5*c^3*d^4*f^3*g + 16*a*b^3*
c^4*d^3*e*f^4 - 2*a*b^5*c^2*d*e^3*f^4 - 32*a^2*b*c^5*d^3*e*f^4 - 32*a^3*b*c^4*d*e^3*f^4 - 2*a^2*b^5*c*d^3*e*g^
4 - 32*a^4*b*c^3*d^3*e*g^4 + 16*a^4*b^3*c*d*e^3*g^4 - 32*a^5*b*c^2*d*e^3*g^4 + 16*a*b^3*c^4*d^4*f^3*g - 2*a*b^
5*c^2*d^4*f*g^3 - 32*a^2*b*c^5*d^4*f^3*g - 32*a^3*b*c^4*d^4*f*g^3 - 2*a^2*b^5*c*e^4*f^3*g - 32*a^4*b*c^3*e^4*f
^3*g + 16*a^4*b^3*c*e^4*f*g^3 - 32*a^5*b*c^2*e^4*f*g^3 - 2*a*b^7*d*e^3*f^2*g^2 - 2*a*b^7*d^2*e^2*f*g^3 + 4*a^2
*b^6*d*e^3*f*g^3 + 4*b^6*c^2*d^3*e*f^3*g - 2*b^7*c*d^2*e^2*f^3*g - 2*b^7*c*d^3*e*f^2*g^2 - 6*a*b^4*c^3*d^2*e^2
*f^4 + 16*a^2*b^3*c^3*d*e^3*f^4 + 16*a^3*b^3*c^2*d^3*e*g^4 - 6*a^3*b^4*c*d^2*e^2*g^4 - 6*a*b^4*c^3*d^4*f^2*g^2
+ 16*a^2*b^3*c^3*d^4*f*g^3 + 16*a^3*b^3*c^2*e^4*f^3*g - 6*a^3*b^4*c*e^4*f^2*g^2 + 64*a^4*c^4*d^2*e^2*f^2*g^2
+ 4*a*b^6*c*d*e^3*f^3*g + 4*a*b^6*c*d^3*e*f*g^3 - 32*a*b^4*c^3*d^3*e*f^3*g - 32*a^3*b^4*c*d*e^3*f*g^3 - 12*a^2
*b^4*c^2*d^2*e^2*f^2*g^2 + 32*a^3*b^2*c^3*d^2*e^2*f^2*g^2 + 12*a*b^5*c^2*d^2*e^2*f^3*g + 12*a*b^5*c^2*d^3*e*f^
2*g^2 - 4*a*b^6*c*d^2*e^2*f^2*g^2 + 64*a^2*b^2*c^4*d^3*e*f^3*g - 32*a^2*b^4*c^2*d*e^3*f^3*g - 32*a^2*b^4*c^2*d
^3*e*f*g^3 + 12*a^2*b^5*c*d*e^3*f^2*g^2 + 12*a^2*b^5*c*d^2*e^2*f*g^3 - 64*a^3*b*c^4*d^2*e^2*f^3*g - 64*a^3*b*c
^4*d^3*e*f^2*g^2 + 64*a^3*b^2*c^3*d*e^3*f^3*g + 64*a^3*b^2*c^3*d^3*e*f*g^3 - 64*a^4*b*c^3*d*e^3*f^2*g^2 - 64*a
^4*b*c^3*d^2*e^2*f*g^3 + 64*a^4*b^2*c^2*d*e^3*f*g^3) - root(1120*a^6*b^2*c^6*d^9*e*f*g^9*z^4 + 1120*a^6*b^2*c^
6*d*e^9*f^9*g*z^4 - 792*a^5*b^4*c^5*d^9*e*f*g^9*z^4 - 792*a^5*b^4*c^5*d*e^9*f^9*g*z^4 + 512*a^9*b*c^4*d^4*e^6*
f*g^9*z^4 + 512*a^9*b*c^4*d*e^9*f^4*g^6*z^4 - 512*a^7*b*c^6*d^8*e^2*f*g^9*z^4 - 512*a^7*b*c^6*d*e^9*f^8*g^2*z^
4 - 512*a^6*b*c^7*d^9*e*f^2*g^8*z^4 - 512*a^6*b*c^7*d^2*e^8*f^9*g*z^4 + 512*a^4*b*c^9*d^9*e*f^6*g^4*z^4 + 512*
a^4*b*c^9*d^6*e^4*f^9*g*z^4 + 256*a^10*b*c^3*d^2*e^8*f*g^9*z^4 + 256*a^10*b*c^3*d*e^9*f^2*g^8*z^4 + 256*a^3*b*
c^10*d^9*e*f^8*g^2*z^4 + 256*a^3*b*c^10*d^8*e^2*f^9*g*z^4 - 200*a^6*b^7*c*d^4*e^6*f*g^9*z^4 - 200*a^6*b^7*c*d*
e^9*f^4*g^6*z^4 - 200*a*b^7*c^6*d^9*e*f^6*g^4*z^4 - 200*a*b^7*c^6*d^6*e^4*f^9*g*z^4 + 194*a^4*b^6*c^4*d^9*e*f*
g^9*z^4 + 194*a^4*b^6*c^4*d*e^9*f^9*g*z^4 + 144*a^5*b^8*c*d^5*e^5*f*g^9*z^4 + 144*a^5*b^8*c*d*e^9*f^5*g^5*z^4
+ 144*a*b^8*c^5*d^9*e*f^5*g^5*z^4 + 144*a*b^8*c^5*d^5*e^5*f^9*g*z^4 + 96*a^10*b^2*c^2*d*e^9*f*g^9*z^4 + 96*a^2
*b^2*c^10*d^9*e*f^9*g*z^4 + 56*a^7*b^6*c*d^3*e^7*f*g^9*z^4 + 56*a^7*b^6*c*d*e^9*f^3*g^7*z^4 + 56*a*b^6*c^7*d^9
*e*f^7*g^3*z^4 + 56*a*b^6*c^7*d^7*e^3*f^9*g*z^4 + 48*a^8*b^5*c*d^2*e^8*f*g^9*z^4 + 48*a^8*b^5*c*d*e^9*f^2*g^8*
z^4 + 48*a*b^5*c^8*d^9*e*f^8*g^2*z^4 + 48*a*b^5*c^8*d^8*e^2*f^9*g*z^4 + 20*a*b^12*c*d^6*e^4*f^4*g^6*z^4 + 20*a
*b^12*c*d^4*e^6*f^6*g^4*z^4 - 16*a^3*b^10*c*d^7*e^3*f*g^9*z^4 - 16*a^3*b^10*c*d*e^9*f^7*g^3*z^4 - 16*a^3*b^8*c
^3*d^9*e*f*g^9*z^4 - 16*a^3*b^8*c^3*d*e^9*f^9*g*z^4 - 16*a*b^12*c*d^7*e^3*f^3*g^7*z^4 - 16*a*b^12*c*d^3*e^7*f^
7*g^3*z^4 - 16*a*b^10*c^3*d^9*e*f^3*g^7*z^4 - 16*a*b^10*c^3*d^3*e^7*f^9*g*z^4 - 8*a^4*b^9*c*d^6*e^4*f*g^9*z^4
- 8*a^4*b^9*c*d*e^9*f^6*g^4*z^4 - 8*a*b^12*c*d^5*e^5*f^5*g^5*z^4 - 8*a*b^9*c^4*d^9*e*f^4*g^6*z^4 - 8*a*b^9*c^4
*d^4*e^6*f^9*g*z^4 - 9984*a^7*b^2*c^5*d^4*e^6*f^4*g^6*z^4 - 9984*a^5*b^2*c^7*d^6*e^4*f^6*g^4*z^4 - 8640*a^6*b^
2*c^6*d^6*e^4*f^4*g^6*z^4 - 8640*a^6*b^2*c^6*d^4*e^6*f^6*g^4*z^4 - 8544*a^5*b^4*c^5*d^5*e^5*f^5*g^5*z^4 + 5632
*a^6*b^2*c^6*d^7*e^3*f^3*g^7*z^4 + 5632*a^6*b^2*c^6*d^3*e^7*f^7*g^3*z^4 + 5232*a^5*b^4*c^5*d^6*e^4*f^4*g^6*z^4
+ 5232*a^5*b^4*c^5*d^4*e^6*f^6*g^4*z^4 + 4808*a^4*b^6*c^4*d^5*e^5*f^5*g^5*z^4 - 4288*a^6*b^4*c^4*d^5*e^5*f^3*
g^7*z^4 - 4288*a^6*b^4*c^4*d^3*e^7*f^5*g^5*z^4 - 4288*a^4*b^4*c^6*d^7*e^3*f^5*g^5*z^4 - 4288*a^4*b^4*c^6*d^5*e
^5*f^7*g^3*z^4 + 3968*a^6*b^3*c^5*d^5*e^5*f^4*g^6*z^4 + 3968*a^6*b^3*c^5*d^4*e^6*f^5*g^5*z^4 + 3968*a^5*b^3*c^
6*d^6*e^4*f^5*g^5*z^4 + 3968*a^5*b^3*c^6*d^5*e^5*f^6*g^4*z^4 + 3840*a^7*b^2*c^5*d^5*e^5*f^3*g^7*z^4 + 3840*a^7
*b^2*c^5*d^3*e^7*f^5*g^5*z^4 + 3840*a^5*b^2*c^7*d^7*e^3*f^5*g^5*z^4 + 3840*a^5*b^2*c^7*d^5*e^5*f^7*g^3*z^4 + 3
776*a^6*b^4*c^4*d^4*e^6*f^4*g^6*z^4 + 3776*a^4*b^4*c^6*d^6*e^4*f^6*g^4*z^4 + 3456*a^6*b^2*c^6*d^5*e^5*f^5*g^5*
z^4 + 3440*a^6*b^4*c^4*d^6*e^4*f^2*g^8*z^4 + 3440*a^6*b^4*c^4*d^2*e^8*f^6*g^4*z^4 + 3440*a^4*b^4*c^6*d^8*e^2*f
^4*g^6*z^4 + 3440*a^4*b^4*c^6*d^4*e^6*f^8*g^2*z^4 - 3360*a^8*b^2*c^4*d^4*e^6*f^2*g^8*z^4 - 3360*a^8*b^2*c^4*d^
2*e^8*f^4*g^6*z^4 - 3360*a^4*b^2*c^8*d^8*e^2*f^6*g^4*z^4 - 3360*a^4*b^2*c^8*d^6*e^4*f^8*g^2*z^4 - 2944*a^7*b^4
*c^3*d^3*e^7*f^3*g^7*z^4 - 2944*a^3*b^4*c^7*d^7*e^3*f^7*g^3*z^4 + 2512*a^5*b^6*c^3*d^5*e^5*f^3*g^7*z^4 + 2512*
a^5*b^6*c^3*d^3*e^7*f^5*g^5*z^4 + 2512*a^3*b^6*c^5*d^7*e^3*f^5*g^5*z^4 + 2512*a^3*b^6*c^5*d^5*e^5*f^7*g^3*z^4
+ 2312*a^7*b^4*c^3*d^4*e^6*f^2*g^8*z^4 + 2312*a^7*b^4*c^3*d^2*e^8*f^4*g^6*z^4 + 2312*a^3*b^4*c^7*d^8*e^2*f^6*g
^4*z^4 + 2312*a^3*b^4*c^7*d^6*e^4*f^8*g^2*z^4 + 1952*a^6*b^6*c^2*d^3*e^7*f^3*g^7*z^4 + 1952*a^2*b^6*c^6*d^7*e^
3*f^7*g^3*z^4 - 1920*a^5*b^4*c^5*d^7*e^3*f^3*g^7*z^4 - 1920*a^5*b^4*c^5*d^3*e^7*f^7*g^3*z^4 - 1828*a^5*b^6*c^3
*d^6*e^4*f^2*g^8*z^4 - 1828*a^5*b^6*c^3*d^2*e^8*f^6*g^4*z^4 - 1828*a^3*b^6*c^5*d^8*e^2*f^4*g^6*z^4 - 1828*a^3*
b^6*c^5*d^4*e^6*f^8*g^2*z^4 + 1740*a^5*b^4*c^5*d^8*e^2*f^2*g^8*z^4 + 1740*a^5*b^4*c^5*d^2*e^8*f^8*g^2*z^4 - 17
28*a^7*b^2*c^5*d^6*e^4*f^2*g^8*z^4 - 1728*a^7*b^2*c^5*d^2*e^8*f^6*g^4*z^4 - 1728*a^5*b^2*c^7*d^8*e^2*f^4*g^6*z
^4 - 1728*a^5*b^2*c^7*d^4*e^6*f^8*g^2*z^4 - 1716*a^4*b^6*c^4*d^6*e^4*f^4*g^6*z^4 - 1716*a^4*b^6*c^4*d^4*e^6*f^
6*g^4*z^4 - 1664*a^9*b^2*c^3*d^2*e^8*f^2*g^8*z^4 - 1664*a^3*b^2*c^9*d^8*e^2*f^8*g^2*z^4 - 1600*a^6*b^3*c^5*d^7
*e^3*f^2*g^8*z^4 - 1600*a^6*b^3*c^5*d^2*e^8*f^7*g^3*z^4 - 1600*a^5*b^3*c^6*d^8*e^2*f^3*g^7*z^4 - 1600*a^5*b^3*
c^6*d^3*e^7*f^8*g^2*z^4 - 1553*a^4*b^6*c^4*d^8*e^2*f^2*g^8*z^4 - 1553*a^4*b^6*c^4*d^2*e^8*f^8*g^2*z^4 + 1536*a
^8*b^2*c^4*d^3*e^7*f^3*g^7*z^4 + 1536*a^4*b^2*c^8*d^7*e^3*f^7*g^3*z^4 + 1408*a^7*b^3*c^4*d^4*e^6*f^3*g^7*z^4 +
1408*a^7*b^3*c^4*d^3*e^7*f^4*g^6*z^4 - 1408*a^6*b^3*c^5*d^6*e^4*f^3*g^7*z^4 - 1408*a^6*b^3*c^5*d^3*e^7*f^6*g^
4*z^4 - 1408*a^5*b^3*c^6*d^7*e^3*f^4*g^6*z^4 - 1408*a^5*b^3*c^6*d^4*e^6*f^7*g^3*z^4 + 1408*a^4*b^3*c^7*d^7*e^3
*f^6*g^4*z^4 + 1408*a^4*b^3*c^7*d^6*e^4*f^7*g^3*z^4 - 1360*a^6*b^5*c^3*d^5*e^5*f^2*g^8*z^4 - 1360*a^6*b^5*c^3*
d^2*e^8*f^5*g^5*z^4 - 1360*a^3*b^5*c^6*d^8*e^2*f^5*g^5*z^4 - 1360*a^3*b^5*c^6*d^5*e^5*f^8*g^2*z^4 - 1248*a^5*b
^5*c^4*d^5*e^5*f^4*g^6*z^4 - 1248*a^5*b^5*c^4*d^4*e^6*f^5*g^5*z^4 - 1248*a^4*b^5*c^5*d^6*e^4*f^5*g^5*z^4 - 124
8*a^4*b^5*c^5*d^5*e^5*f^6*g^4*z^4 + 1088*a^8*b^3*c^3*d^3*e^7*f^2*g^8*z^4 + 1088*a^8*b^3*c^3*d^2*e^8*f^3*g^7*z^
4 + 1088*a^3*b^3*c^8*d^8*e^2*f^7*g^3*z^4 + 1088*a^3*b^3*c^8*d^7*e^3*f^8*g^2*z^4 + 1056*a^8*b^4*c^2*d^2*e^8*f^2
*g^8*z^4 + 1056*a^2*b^4*c^8*d^8*e^2*f^8*g^2*z^4 - 912*a^7*b^5*c^2*d^3*e^7*f^2*g^8*z^4 - 912*a^7*b^5*c^2*d^2*e^
8*f^3*g^7*z^4 - 912*a^2*b^5*c^7*d^8*e^2*f^7*g^3*z^4 - 912*a^2*b^5*c^7*d^7*e^3*f^8*g^2*z^4 - 848*a^5*b^6*c^3*d^
4*e^6*f^4*g^6*z^4 - 848*a^3*b^6*c^5*d^6*e^4*f^6*g^4*z^4 + 832*a^7*b^3*c^4*d^5*e^5*f^2*g^8*z^4 + 832*a^7*b^3*c^
4*d^2*e^8*f^5*g^5*z^4 + 832*a^4*b^3*c^7*d^8*e^2*f^5*g^5*z^4 + 832*a^4*b^3*c^7*d^5*e^5*f^8*g^2*z^4 + 828*a^5*b^
7*c^2*d^5*e^5*f^2*g^8*z^4 + 828*a^5*b^7*c^2*d^2*e^8*f^5*g^5*z^4 + 828*a^2*b^7*c^5*d^8*e^2*f^5*g^5*z^4 + 828*a^
2*b^7*c^5*d^5*e^5*f^8*g^2*z^4 - 800*a^3*b^8*c^3*d^5*e^5*f^5*g^5*z^4 - 696*a^4*b^8*c^2*d^5*e^5*f^3*g^7*z^4 - 69
6*a^4*b^8*c^2*d^3*e^7*f^5*g^5*z^4 - 696*a^2*b^8*c^4*d^7*e^3*f^5*g^5*z^4 - 696*a^2*b^8*c^4*d^5*e^5*f^7*g^3*z^4
- 694*a^6*b^6*c^2*d^4*e^6*f^2*g^8*z^4 - 694*a^6*b^6*c^2*d^2*e^8*f^4*g^6*z^4 - 694*a^2*b^6*c^6*d^8*e^2*f^6*g^4*
z^4 - 694*a^2*b^6*c^6*d^6*e^4*f^8*g^2*z^4 + 692*a^4*b^7*c^3*d^7*e^3*f^2*g^8*z^4 + 692*a^4*b^7*c^3*d^2*e^8*f^7*
g^3*z^4 + 692*a^3*b^7*c^4*d^8*e^2*f^3*g^7*z^4 + 692*a^3*b^7*c^4*d^3*e^7*f^8*g^2*z^4 + 672*a^4*b^6*c^4*d^7*e^3*
f^3*g^7*z^4 + 672*a^4*b^6*c^4*d^3*e^7*f^7*g^3*z^4 + 600*a^4*b^8*c^2*d^4*e^6*f^4*g^6*z^4 + 600*a^2*b^8*c^4*d^6*
e^4*f^6*g^4*z^4 - 544*a^3*b^8*c^3*d^7*e^3*f^3*g^7*z^4 + 544*a^3*b^8*c^3*d^6*e^4*f^4*g^6*z^4 + 544*a^3*b^8*c^3*
d^4*e^6*f^6*g^4*z^4 - 544*a^3*b^8*c^3*d^3*e^7*f^7*g^3*z^4 - 536*a^4*b^7*c^3*d^5*e^5*f^4*g^6*z^4 - 536*a^4*b^7*
c^3*d^4*e^6*f^5*g^5*z^4 - 536*a^3*b^7*c^4*d^6*e^4*f^5*g^5*z^4 - 536*a^3*b^7*c^4*d^5*e^5*f^6*g^4*z^4 - 504*a^5*
b^7*c^2*d^4*e^6*f^3*g^7*z^4 - 504*a^5*b^7*c^2*d^3*e^7*f^4*g^6*z^4 - 504*a^2*b^7*c^5*d^7*e^3*f^6*g^4*z^4 - 504*
a^2*b^7*c^5*d^6*e^4*f^7*g^3*z^4 + 416*a^3*b^8*c^3*d^8*e^2*f^2*g^8*z^4 + 416*a^3*b^8*c^3*d^2*e^8*f^8*g^2*z^4 -
352*a^6*b^5*c^3*d^4*e^6*f^3*g^7*z^4 - 352*a^6*b^5*c^3*d^3*e^7*f^4*g^6*z^4 - 352*a^3*b^5*c^6*d^7*e^3*f^6*g^4*z^
4 - 352*a^3*b^5*c^6*d^6*e^4*f^7*g^3*z^4 - 248*a^3*b^9*c^2*d^7*e^3*f^2*g^8*z^4 - 248*a^3*b^9*c^2*d^2*e^8*f^7*g^
3*z^4 - 248*a^2*b^9*c^3*d^8*e^2*f^3*g^7*z^4 - 248*a^2*b^9*c^3*d^3*e^7*f^8*g^2*z^4 + 246*a^4*b^8*c^2*d^6*e^4*f^
2*g^8*z^4 + 246*a^4*b^8*c^2*d^2*e^8*f^6*g^4*z^4 + 246*a^2*b^8*c^4*d^8*e^2*f^4*g^6*z^4 + 246*a^2*b^8*c^4*d^4*e^
6*f^8*g^2*z^4 + 208*a^6*b^2*c^6*d^8*e^2*f^2*g^8*z^4 + 208*a^6*b^2*c^6*d^2*e^8*f^8*g^2*z^4 + 168*a^2*b^10*c^2*d
^7*e^3*f^3*g^7*z^4 + 168*a^2*b^10*c^2*d^3*e^7*f^7*g^3*z^4 + 160*a^3*b^9*c^2*d^5*e^5*f^4*g^6*z^4 + 160*a^3*b^9*
c^2*d^4*e^6*f^5*g^5*z^4 + 160*a^2*b^9*c^3*d^6*e^4*f^5*g^5*z^4 + 160*a^2*b^9*c^3*d^5*e^5*f^6*g^4*z^4 + 144*a^5*
b^5*c^4*d^7*e^3*f^2*g^8*z^4 + 144*a^5*b^5*c^4*d^2*e^8*f^7*g^3*z^4 + 144*a^4*b^5*c^5*d^8*e^2*f^3*g^7*z^4 + 144*
a^4*b^5*c^5*d^3*e^7*f^8*g^2*z^4 - 144*a^2*b^10*c^2*d^6*e^4*f^4*g^6*z^4 - 144*a^2*b^10*c^2*d^4*e^6*f^6*g^4*z^4
+ 120*a^4*b^7*c^3*d^6*e^4*f^3*g^7*z^4 + 120*a^4*b^7*c^3*d^3*e^7*f^6*g^4*z^4 + 120*a^3*b^7*c^4*d^7*e^3*f^4*g^6*
z^4 + 120*a^3*b^7*c^4*d^4*e^6*f^7*g^3*z^4 + 96*a^5*b^5*c^4*d^6*e^4*f^3*g^7*z^4 + 96*a^5*b^5*c^4*d^3*e^7*f^6*g^
4*z^4 + 96*a^4*b^5*c^5*d^7*e^3*f^4*g^6*z^4 + 96*a^4*b^5*c^5*d^4*e^6*f^7*g^3*z^4 + 64*a^3*b^9*c^2*d^6*e^4*f^3*g
^7*z^4 + 64*a^3*b^9*c^2*d^3*e^7*f^6*g^4*z^4 + 64*a^2*b^9*c^3*d^7*e^3*f^4*g^6*z^4 + 64*a^2*b^9*c^3*d^4*e^6*f^7*
g^3*z^4 - 36*a^2*b^10*c^2*d^8*e^2*f^2*g^8*z^4 - 36*a^2*b^10*c^2*d^2*e^8*f^8*g^2*z^4 + 24*a^2*b^10*c^2*d^5*e^5*
f^5*g^5*z^4 - 24*a^9*b^4*c*d*e^9*f*g^9*z^4 - 24*a*b^4*c^9*d^9*e*f^9*g*z^4 + 2688*a^7*b^2*c^5*d^7*e^3*f*g^9*z^4
+ 2688*a^7*b^2*c^5*d*e^9*f^7*g^3*z^4 + 2688*a^5*b^2*c^7*d^9*e*f^3*g^7*z^4 + 2688*a^5*b^2*c^7*d^3*e^7*f^9*g*z^
4 - 2560*a^7*b^3*c^4*d^6*e^4*f*g^9*z^4 - 2560*a^7*b^3*c^4*d*e^9*f^6*g^4*z^4 - 2560*a^4*b^3*c^7*d^9*e*f^4*g^6*z
^4 - 2560*a^4*b^3*c^7*d^4*e^6*f^9*g*z^4 + 2112*a^8*b^2*c^4*d^5*e^5*f*g^9*z^4 + 2112*a^8*b^2*c^4*d*e^9*f^5*g^5*
z^4 + 2112*a^4*b^2*c^8*d^9*e*f^5*g^5*z^4 + 2112*a^4*b^2*c^8*d^5*e^5*f^9*g*z^4 + 1664*a^6*b^5*c^3*d^6*e^4*f*g^9
*z^4 + 1664*a^6*b^5*c^3*d*e^9*f^6*g^4*z^4 + 1664*a^3*b^5*c^6*d^9*e*f^4*g^6*z^4 + 1664*a^3*b^5*c^6*d^4*e^6*f^9*
g*z^4 + 1536*a^8*b*c^5*d^4*e^6*f^3*g^7*z^4 + 1536*a^8*b*c^5*d^3*e^7*f^4*g^6*z^4 + 1536*a^7*b*c^6*d^5*e^5*f^4*g
^6*z^4 + 1536*a^7*b*c^6*d^4*e^6*f^5*g^5*z^4 + 1536*a^6*b*c^7*d^6*e^4*f^5*g^5*z^4 + 1536*a^6*b*c^7*d^5*e^5*f^6*
g^4*z^4 + 1536*a^5*b*c^8*d^7*e^3*f^6*g^4*z^4 + 1536*a^5*b*c^8*d^6*e^4*f^7*g^3*z^4 - 1408*a^8*b^3*c^3*d^4*e^6*f
*g^9*z^4 - 1408*a^8*b^3*c^3*d*e^9*f^4*g^6*z^4 - 1408*a^3*b^3*c^8*d^9*e*f^6*g^4*z^4 - 1408*a^3*b^3*c^8*d^6*e^4*
f^9*g*z^4 - 1280*a^7*b*c^6*d^7*e^3*f^2*g^8*z^4 - 1280*a^7*b*c^6*d^2*e^8*f^7*g^3*z^4 - 1280*a^6*b*c^7*d^8*e^2*f
^3*g^7*z^4 - 1280*a^6*b*c^7*d^3*e^7*f^8*g^2*z^4 - 1152*a^6*b^3*c^5*d^8*e^2*f*g^9*z^4 - 1152*a^6*b^3*c^5*d*e^9*
f^8*g^2*z^4 - 1152*a^5*b^3*c^6*d^9*e*f^2*g^8*z^4 - 1152*a^5*b^3*c^6*d^2*e^8*f^9*g*z^4 + 1056*a^5*b^5*c^4*d^8*e
^2*f*g^9*z^4 + 1056*a^5*b^5*c^4*d*e^9*f^8*g^2*z^4 + 1056*a^4*b^5*c^5*d^9*e*f^2*g^8*z^4 + 1056*a^4*b^5*c^5*d^2*
e^8*f^9*g*z^4 + 864*a^7*b^5*c^2*d^4*e^6*f*g^9*z^4 + 864*a^7*b^5*c^2*d*e^9*f^4*g^6*z^4 + 864*a^2*b^5*c^7*d^9*e*
f^6*g^4*z^4 + 864*a^2*b^5*c^7*d^6*e^4*f^9*g*z^4 - 800*a^6*b^4*c^4*d^7*e^3*f*g^9*z^4 - 800*a^6*b^4*c^4*d*e^9*f^
7*g^3*z^4 - 800*a^4*b^4*c^6*d^9*e*f^3*g^7*z^4 - 800*a^4*b^4*c^6*d^3*e^7*f^9*g*z^4 - 768*a^8*b*c^5*d^5*e^5*f^2*
g^8*z^4 - 768*a^8*b*c^5*d^2*e^8*f^5*g^5*z^4 - 768*a^5*b*c^8*d^8*e^2*f^5*g^5*z^4 - 768*a^5*b*c^8*d^5*e^5*f^8*g^
2*z^4 + 640*a^9*b^2*c^3*d^3*e^7*f*g^9*z^4 + 640*a^9*b^2*c^3*d*e^9*f^3*g^7*z^4 + 640*a^3*b^2*c^9*d^9*e*f^7*g^3*
z^4 + 640*a^3*b^2*c^9*d^7*e^3*f^9*g*z^4 + 512*a^7*b*c^6*d^6*e^4*f^3*g^7*z^4 + 512*a^7*b*c^6*d^3*e^7*f^6*g^4*z^
4 + 512*a^6*b*c^7*d^7*e^3*f^4*g^6*z^4 + 512*a^6*b*c^7*d^4*e^6*f^7*g^3*z^4 - 480*a^5*b^8*c*d^3*e^7*f^3*g^7*z^4
- 480*a*b^8*c^5*d^7*e^3*f^7*g^3*z^4 - 400*a^7*b^4*c^3*d^5*e^5*f*g^9*z^4 - 400*a^7*b^4*c^3*d*e^9*f^5*g^5*z^4 -
400*a^3*b^4*c^7*d^9*e*f^5*g^5*z^4 - 400*a^3*b^4*c^7*d^5*e^5*f^9*g*z^4 - 372*a^6*b^6*c^2*d^5*e^5*f*g^9*z^4 - 37
2*a^6*b^6*c^2*d*e^9*f^5*g^5*z^4 - 372*a^2*b^6*c^6*d^9*e*f^5*g^5*z^4 - 372*a^2*b^6*c^6*d^5*e^5*f^9*g*z^4 - 328*
a^5*b^6*c^3*d^7*e^3*f*g^9*z^4 - 328*a^5*b^6*c^3*d*e^9*f^7*g^3*z^4 - 328*a^3*b^6*c^5*d^9*e*f^3*g^7*z^4 - 328*a^
3*b^6*c^5*d^3*e^7*f^9*g*z^4 - 288*a^8*b^4*c^2*d^3*e^7*f*g^9*z^4 - 288*a^8*b^4*c^2*d*e^9*f^3*g^7*z^4 - 288*a^5*
b^7*c^2*d^6*e^4*f*g^9*z^4 - 288*a^5*b^7*c^2*d*e^9*f^6*g^4*z^4 - 288*a^2*b^7*c^5*d^9*e*f^4*g^6*z^4 - 288*a^2*b^
7*c^5*d^4*e^6*f^9*g*z^4 - 288*a^2*b^4*c^8*d^9*e*f^7*g^3*z^4 - 288*a^2*b^4*c^8*d^7*e^3*f^9*g*z^4 - 280*a^4*b^7*
c^3*d^8*e^2*f*g^9*z^4 - 280*a^4*b^7*c^3*d*e^9*f^8*g^2*z^4 - 280*a^3*b^7*c^4*d^9*e*f^2*g^8*z^4 - 280*a^3*b^7*c^
4*d^2*e^8*f^9*g*z^4 + 256*a^9*b*c^4*d^3*e^7*f^2*g^8*z^4 + 256*a^9*b*c^4*d^2*e^8*f^3*g^7*z^4 + 256*a^4*b*c^9*d^
8*e^2*f^7*g^3*z^4 + 256*a^4*b*c^9*d^7*e^3*f^8*g^2*z^4 - 248*a^7*b^6*c*d^2*e^8*f^2*g^8*z^4 - 248*a*b^6*c^7*d^8*
e^2*f^8*g^2*z^4 + 236*a^6*b^7*c*d^3*e^7*f^2*g^8*z^4 + 236*a^6*b^7*c*d^2*e^8*f^3*g^7*z^4 + 236*a*b^7*c^6*d^8*e^
2*f^7*g^3*z^4 + 236*a*b^7*c^6*d^7*e^3*f^8*g^2*z^4 + 200*a^4*b^9*c*d^4*e^6*f^3*g^7*z^4 + 200*a^4*b^9*c*d^3*e^7*
f^4*g^6*z^4 - 200*a^3*b^10*c*d^4*e^6*f^4*g^6*z^4 - 200*a*b^10*c^3*d^6*e^4*f^6*g^4*z^4 + 200*a*b^9*c^4*d^7*e^3*
f^6*g^4*z^4 + 200*a*b^9*c^4*d^6*e^4*f^7*g^3*z^4 - 196*a^4*b^9*c*d^5*e^5*f^2*g^8*z^4 - 196*a^4*b^9*c*d^2*e^8*f^
5*g^5*z^4 - 196*a*b^9*c^4*d^8*e^2*f^5*g^5*z^4 - 196*a*b^9*c^4*d^5*e^5*f^8*g^2*z^4 - 192*a^9*b^3*c^2*d^2*e^8*f*
g^9*z^4 - 192*a^9*b^3*c^2*d*e^9*f^2*g^8*z^4 - 192*a^2*b^3*c^9*d^9*e*f^8*g^2*z^4 - 192*a^2*b^3*c^9*d^8*e^2*f^9*
g*z^4 + 156*a^4*b^8*c^2*d^7*e^3*f*g^9*z^4 + 156*a^4*b^8*c^2*d*e^9*f^7*g^3*z^4 + 156*a^2*b^8*c^4*d^9*e*f^3*g^7*
z^4 + 156*a^2*b^8*c^4*d^3*e^7*f^9*g*z^4 + 96*a^5*b^8*c*d^4*e^6*f^2*g^8*z^4 + 96*a^5*b^8*c*d^2*e^8*f^4*g^6*z^4
+ 96*a*b^8*c^5*d^8*e^2*f^6*g^4*z^4 + 96*a*b^8*c^5*d^6*e^4*f^8*g^2*z^4 + 88*a^3*b^10*c*d^5*e^5*f^3*g^7*z^4 + 88
*a^3*b^10*c*d^3*e^7*f^5*g^5*z^4 + 88*a*b^10*c^3*d^7*e^3*f^5*g^5*z^4 + 88*a*b^10*c^3*d^5*e^5*f^7*g^3*z^4 - 36*a
^2*b^11*c*d^6*e^4*f^3*g^7*z^4 - 36*a^2*b^11*c*d^3*e^7*f^6*g^4*z^4 - 36*a*b^11*c^2*d^7*e^3*f^4*g^6*z^4 - 36*a*b
^11*c^2*d^4*e^6*f^7*g^3*z^4 + 28*a^3*b^10*c*d^6*e^4*f^2*g^8*z^4 + 28*a^3*b^10*c*d^2*e^8*f^6*g^4*z^4 + 28*a*b^1
0*c^3*d^8*e^2*f^4*g^6*z^4 + 28*a*b^10*c^3*d^4*e^6*f^8*g^2*z^4 + 24*a^3*b^9*c^2*d^8*e^2*f*g^9*z^4 + 24*a^3*b^9*
c^2*d*e^9*f^8*g^2*z^4 + 24*a^2*b^11*c*d^7*e^3*f^2*g^8*z^4 + 24*a^2*b^11*c*d^2*e^8*f^7*g^3*z^4 + 24*a^2*b^9*c^3
*d^9*e*f^2*g^8*z^4 + 24*a^2*b^9*c^3*d^2*e^8*f^9*g*z^4 + 24*a*b^11*c^2*d^8*e^2*f^3*g^7*z^4 + 24*a*b^11*c^2*d^3*
e^7*f^8*g^2*z^4 + 12*a^2*b^11*c*d^5*e^5*f^4*g^6*z^4 + 12*a^2*b^11*c*d^4*e^6*f^5*g^5*z^4 + 12*a*b^11*c^2*d^6*e^
4*f^5*g^5*z^4 + 12*a*b^11*c^2*d^5*e^5*f^6*g^4*z^4 + 40*b^10*c^4*d^7*e^3*f^7*g^3*z^4 + 20*b^12*c^2*d^6*e^4*f^6*
g^4*z^4 - 20*b^11*c^3*d^7*e^3*f^6*g^4*z^4 - 20*b^11*c^3*d^6*e^4*f^7*g^3*z^4 - 20*b^9*c^5*d^8*e^2*f^7*g^3*z^4 -
20*b^9*c^5*d^7*e^3*f^8*g^2*z^4 + 20*b^8*c^6*d^8*e^2*f^8*g^2*z^4 + 16*b^11*c^3*d^8*e^2*f^5*g^5*z^4 + 16*b^11*c
^3*d^5*e^5*f^8*g^2*z^4 - 6*b^12*c^2*d^8*e^2*f^4*g^6*z^4 - 6*b^12*c^2*d^4*e^6*f^8*g^2*z^4 - 5*b^10*c^4*d^8*e^2*
f^6*g^4*z^4 - 5*b^10*c^4*d^6*e^4*f^8*g^2*z^4 - 4*b^12*c^2*d^7*e^3*f^5*g^5*z^4 - 4*b^12*c^2*d^5*e^5*f^7*g^3*z^4
- 4608*a^7*c^7*d^5*e^5*f^5*g^5*z^4 + 3328*a^7*c^7*d^6*e^4*f^4*g^6*z^4 + 3328*a^7*c^7*d^4*e^6*f^6*g^4*z^4 - 30
72*a^8*c^6*d^5*e^5*f^3*g^7*z^4 + 3072*a^8*c^6*d^4*e^6*f^4*g^6*z^4 - 3072*a^8*c^6*d^3*e^7*f^5*g^5*z^4 - 3072*a^
6*c^8*d^7*e^3*f^5*g^5*z^4 + 3072*a^6*c^8*d^6*e^4*f^6*g^4*z^4 - 3072*a^6*c^8*d^5*e^5*f^7*g^3*z^4 - 2048*a^9*c^5
*d^3*e^7*f^3*g^7*z^4 - 2048*a^7*c^7*d^7*e^3*f^3*g^7*z^4 - 2048*a^7*c^7*d^3*e^7*f^7*g^3*z^4 - 2048*a^5*c^9*d^7*
e^3*f^7*g^3*z^4 + 1792*a^8*c^6*d^6*e^4*f^2*g^8*z^4 + 1792*a^8*c^6*d^2*e^8*f^6*g^4*z^4 + 1792*a^6*c^8*d^8*e^2*f
^4*g^6*z^4 + 1792*a^6*c^8*d^4*e^6*f^8*g^2*z^4 + 1408*a^9*c^5*d^4*e^6*f^2*g^8*z^4 + 1408*a^9*c^5*d^2*e^8*f^4*g^
6*z^4 + 1408*a^5*c^9*d^8*e^2*f^6*g^4*z^4 + 1408*a^5*c^9*d^6*e^4*f^8*g^2*z^4 + 1088*a^7*c^7*d^8*e^2*f^2*g^8*z^4
+ 1088*a^7*c^7*d^2*e^8*f^8*g^2*z^4 + 512*a^10*c^4*d^2*e^8*f^2*g^8*z^4 + 512*a^4*c^10*d^8*e^2*f^8*g^2*z^4 + 40
*a^4*b^10*d^3*e^7*f^3*g^7*z^4 + 20*a^6*b^8*d^2*e^8*f^2*g^8*z^4 - 20*a^5*b^9*d^3*e^7*f^2*g^8*z^4 - 20*a^5*b^9*d
^2*e^8*f^3*g^7*z^4 - 20*a^3*b^11*d^4*e^6*f^3*g^7*z^4 - 20*a^3*b^11*d^3*e^7*f^4*g^6*z^4 + 20*a^2*b^12*d^4*e^6*f
^4*g^6*z^4 + 16*a^3*b^11*d^5*e^5*f^2*g^8*z^4 + 16*a^3*b^11*d^2*e^8*f^5*g^5*z^4 - 6*a^2*b^12*d^6*e^4*f^2*g^8*z^
4 - 6*a^2*b^12*d^2*e^8*f^6*g^4*z^4 - 5*a^4*b^10*d^4*e^6*f^2*g^8*z^4 - 5*a^4*b^10*d^2*e^8*f^4*g^6*z^4 - 4*a^2*b
^12*d^5*e^5*f^3*g^7*z^4 - 4*a^2*b^12*d^3*e^7*f^5*g^5*z^4 + 480*a^8*b^2*c^4*e^10*f^6*g^4*z^4 - 440*a^7*b^4*c^3*
e^10*f^6*g^4*z^4 + 320*a^8*b^3*c^3*e^10*f^5*g^5*z^4 + 320*a^7*b^3*c^4*e^10*f^7*g^3*z^4 - 240*a^8*b^4*c^2*e^10*
f^4*g^6*z^4 - 240*a^6*b^4*c^4*e^10*f^8*g^2*z^4 + 192*a^9*b^3*c^2*e^10*f^3*g^7*z^4 + 192*a^9*b^2*c^3*e^10*f^4*g
^6*z^4 + 192*a^7*b^2*c^5*e^10*f^8*g^2*z^4 + 90*a^6*b^6*c^2*e^10*f^6*g^4*z^4 + 68*a^5*b^6*c^3*e^10*f^8*g^2*z^4
- 48*a^10*b^2*c^2*e^10*f^2*g^8*z^4 + 48*a^7*b^5*c^2*e^10*f^5*g^5*z^4 + 48*a^6*b^5*c^3*e^10*f^7*g^3*z^4 - 36*a^
5*b^7*c^2*e^10*f^7*g^3*z^4 - 6*a^4*b^8*c^2*e^10*f^8*g^2*z^4 + 480*a^4*b^2*c^8*d^10*f^4*g^6*z^4 - 440*a^3*b^4*c
^7*d^10*f^4*g^6*z^4 + 320*a^4*b^3*c^7*d^10*f^3*g^7*z^4 + 320*a^3*b^3*c^8*d^10*f^5*g^5*z^4 - 240*a^4*b^4*c^6*d^
10*f^2*g^8*z^4 - 240*a^2*b^4*c^8*d^10*f^6*g^4*z^4 + 192*a^5*b^2*c^7*d^10*f^2*g^8*z^4 + 192*a^3*b^2*c^9*d^10*f^
6*g^4*z^4 + 192*a^2*b^3*c^9*d^10*f^7*g^3*z^4 + 90*a^2*b^6*c^6*d^10*f^4*g^6*z^4 + 68*a^3*b^6*c^5*d^10*f^2*g^8*z
^4 + 48*a^3*b^5*c^6*d^10*f^3*g^7*z^4 + 48*a^2*b^5*c^7*d^10*f^5*g^5*z^4 - 48*a^2*b^2*c^10*d^10*f^8*g^2*z^4 - 36
*a^2*b^7*c^5*d^10*f^3*g^7*z^4 - 6*a^2*b^8*c^4*d^10*f^2*g^8*z^4 + 480*a^8*b^2*c^4*d^6*e^4*g^10*z^4 - 440*a^7*b^
4*c^3*d^6*e^4*g^10*z^4 + 320*a^8*b^3*c^3*d^5*e^5*g^10*z^4 + 320*a^7*b^3*c^4*d^7*e^3*g^10*z^4 - 240*a^8*b^4*c^2
*d^4*e^6*g^10*z^4 - 240*a^6*b^4*c^4*d^8*e^2*g^10*z^4 + 192*a^9*b^3*c^2*d^3*e^7*g^10*z^4 + 192*a^9*b^2*c^3*d^4*
e^6*g^10*z^4 + 192*a^7*b^2*c^5*d^8*e^2*g^10*z^4 + 90*a^6*b^6*c^2*d^6*e^4*g^10*z^4 + 68*a^5*b^6*c^3*d^8*e^2*g^1
0*z^4 - 48*a^10*b^2*c^2*d^2*e^8*g^10*z^4 + 48*a^7*b^5*c^2*d^5*e^5*g^10*z^4 + 48*a^6*b^5*c^3*d^7*e^3*g^10*z^4 -
36*a^5*b^7*c^2*d^7*e^3*g^10*z^4 - 6*a^4*b^8*c^2*d^8*e^2*g^10*z^4 + 480*a^4*b^2*c^8*d^4*e^6*f^10*z^4 - 440*a^3
*b^4*c^7*d^4*e^6*f^10*z^4 + 320*a^4*b^3*c^7*d^3*e^7*f^10*z^4 + 320*a^3*b^3*c^8*d^5*e^5*f^10*z^4 - 240*a^4*b^4*
c^6*d^2*e^8*f^10*z^4 - 240*a^2*b^4*c^8*d^6*e^4*f^10*z^4 + 192*a^5*b^2*c^7*d^2*e^8*f^10*z^4 + 192*a^3*b^2*c^9*d
^6*e^4*f^10*z^4 + 192*a^2*b^3*c^9*d^7*e^3*f^10*z^4 + 90*a^2*b^6*c^6*d^4*e^6*f^10*z^4 + 68*a^3*b^6*c^5*d^2*e^8*
f^10*z^4 + 48*a^3*b^5*c^6*d^3*e^7*f^10*z^4 + 48*a^2*b^5*c^7*d^5*e^5*f^10*z^4 - 48*a^2*b^2*c^10*d^8*e^2*f^10*z^
4 - 36*a^2*b^7*c^5*d^3*e^7*f^10*z^4 - 6*a^2*b^8*c^4*d^2*e^8*f^10*z^4 + 16*b^9*c^5*d^9*e*f^6*g^4*z^4 + 16*b^9*c
^5*d^6*e^4*f^9*g*z^4 - 14*b^10*c^4*d^9*e*f^5*g^5*z^4 - 14*b^10*c^4*d^5*e^5*f^9*g*z^4 + 4*b^13*c*d^7*e^3*f^4*g^
6*z^4 - 4*b^13*c*d^6*e^4*f^5*g^5*z^4 - 4*b^13*c*d^5*e^5*f^6*g^4*z^4 + 4*b^13*c*d^4*e^6*f^7*g^3*z^4 + 4*b^11*c^
3*d^9*e*f^4*g^6*z^4 + 4*b^11*c^3*d^4*e^6*f^9*g*z^4 - 4*b^8*c^6*d^9*e*f^7*g^3*z^4 - 4*b^8*c^6*d^7*e^3*f^9*g*z^4
- 4*b^7*c^7*d^9*e*f^8*g^2*z^4 - 4*b^7*c^7*d^8*e^2*f^9*g*z^4 - 768*a^9*c^5*d^5*e^5*f*g^9*z^4 - 768*a^9*c^5*d*e
^9*f^5*g^5*z^4 - 768*a^5*c^9*d^9*e*f^5*g^5*z^4 - 768*a^5*c^9*d^5*e^5*f^9*g*z^4 - 512*a^10*c^4*d^3*e^7*f*g^9*z^
4 - 512*a^10*c^4*d*e^9*f^3*g^7*z^4 - 512*a^8*c^6*d^7*e^3*f*g^9*z^4 - 512*a^8*c^6*d*e^9*f^7*g^3*z^4 - 512*a^6*c
^8*d^9*e*f^3*g^7*z^4 - 512*a^6*c^8*d^3*e^7*f^9*g*z^4 - 512*a^4*c^10*d^9*e*f^7*g^3*z^4 - 512*a^4*c^10*d^7*e^3*f
^9*g*z^4 + 16*a^5*b^9*d^4*e^6*f*g^9*z^4 + 16*a^5*b^9*d*e^9*f^4*g^6*z^4 - 14*a^4*b^10*d^5*e^5*f*g^9*z^4 - 14*a^
4*b^10*d*e^9*f^5*g^5*z^4 - 4*a^7*b^7*d^2*e^8*f*g^9*z^4 - 4*a^7*b^7*d*e^9*f^2*g^8*z^4 - 4*a^6*b^8*d^3*e^7*f*g^9
*z^4 - 4*a^6*b^8*d*e^9*f^3*g^7*z^4 + 4*a^3*b^11*d^6*e^4*f*g^9*z^4 + 4*a^3*b^11*d*e^9*f^6*g^4*z^4 + 4*a*b^13*d^
6*e^4*f^3*g^7*z^4 - 4*a*b^13*d^5*e^5*f^4*g^6*z^4 - 4*a*b^13*d^4*e^6*f^5*g^5*z^4 + 4*a*b^13*d^3*e^7*f^6*g^4*z^4
- 768*a^9*b*c^4*e^10*f^5*g^5*z^4 - 768*a^8*b*c^5*e^10*f^7*g^3*z^4 - 256*a^10*b*c^3*e^10*f^3*g^7*z^4 + 192*a^6
*b^3*c^5*e^10*f^9*g*z^4 + 68*a^7*b^6*c*e^10*f^4*g^6*z^4 - 48*a^8*b^5*c*e^10*f^3*g^7*z^4 - 48*a^5*b^5*c^4*e^10*
f^9*g*z^4 - 36*a^6*b^7*c*e^10*f^5*g^5*z^4 + 12*a^9*b^4*c*e^10*f^2*g^8*z^4 + 4*a^4*b^9*c*e^10*f^7*g^3*z^4 + 4*a
^4*b^7*c^3*e^10*f^9*g*z^4 - 768*a^5*b*c^8*d^10*f^3*g^7*z^4 - 768*a^4*b*c^9*d^10*f^5*g^5*z^4 - 256*a^3*b*c^10*d
^10*f^7*g^3*z^4 + 192*a^5*b^3*c^6*d^10*f*g^9*z^4 + 68*a*b^6*c^7*d^10*f^6*g^4*z^4 - 48*a^4*b^5*c^5*d^10*f*g^9*z
^4 - 48*a*b^5*c^8*d^10*f^7*g^3*z^4 - 36*a*b^7*c^6*d^10*f^5*g^5*z^4 + 12*a*b^4*c^9*d^10*f^8*g^2*z^4 + 4*a^3*b^7
*c^4*d^10*f*g^9*z^4 + 4*a*b^9*c^4*d^10*f^3*g^7*z^4 - 768*a^9*b*c^4*d^5*e^5*g^10*z^4 - 768*a^8*b*c^5*d^7*e^3*g^
10*z^4 - 256*a^10*b*c^3*d^3*e^7*g^10*z^4 + 192*a^6*b^3*c^5*d^9*e*g^10*z^4 + 68*a^7*b^6*c*d^4*e^6*g^10*z^4 - 48
*a^8*b^5*c*d^3*e^7*g^10*z^4 - 48*a^5*b^5*c^4*d^9*e*g^10*z^4 - 36*a^6*b^7*c*d^5*e^5*g^10*z^4 + 12*a^9*b^4*c*d^2
*e^8*g^10*z^4 + 4*a^4*b^9*c*d^7*e^3*g^10*z^4 + 4*a^4*b^7*c^3*d^9*e*g^10*z^4 - 768*a^5*b*c^8*d^3*e^7*f^10*z^4 -
768*a^4*b*c^9*d^5*e^5*f^10*z^4 - 256*a^3*b*c^10*d^7*e^3*f^10*z^4 + 192*a^5*b^3*c^6*d*e^9*f^10*z^4 + 68*a*b^6*
c^7*d^6*e^4*f^10*z^4 - 48*a^4*b^5*c^5*d*e^9*f^10*z^4 - 48*a*b^5*c^8*d^7*e^3*f^10*z^4 - 36*a*b^7*c^6*d^5*e^5*f^
10*z^4 + 12*a*b^4*c^9*d^8*e^2*f^10*z^4 + 4*a^3*b^7*c^4*d*e^9*f^10*z^4 + 4*a*b^9*c^4*d^3*e^7*f^10*z^4 + 2*b^6*c
^8*d^9*e*f^9*g*z^4 - 128*a^11*c^3*d*e^9*f*g^9*z^4 - 128*a^7*c^7*d^9*e*f*g^9*z^4 - 128*a^7*c^7*d*e^9*f^9*g*z^4
- 128*a^3*c^11*d^9*e*f^9*g*z^4 + 2*a^8*b^6*d*e^9*f*g^9*z^4 - 256*a^7*b*c^6*e^10*f^9*g*z^4 - 256*a^6*b*c^7*d^10
*f*g^9*z^4 - 256*a^7*b*c^6*d^9*e*g^10*z^4 - 256*a^6*b*c^7*d*e^9*f^10*z^4 + 2*b^14*d^5*e^5*f^5*g^5*z^4 + 384*a^
9*c^5*e^10*f^6*g^4*z^4 + 256*a^10*c^4*e^10*f^4*g^6*z^4 + 256*a^8*c^6*e^10*f^8*g^2*z^4 + 64*a^11*c^3*e^10*f^2*g
^8*z^4 - 6*b^8*c^6*d^10*f^6*g^4*z^4 + 4*b^9*c^5*d^10*f^5*g^5*z^4 + 4*b^7*c^7*d^10*f^7*g^3*z^4 + 384*a^5*c^9*d^
10*f^4*g^6*z^4 + 256*a^6*c^8*d^10*f^2*g^8*z^4 + 256*a^4*c^10*d^10*f^6*g^4*z^4 + 64*a^3*c^11*d^10*f^8*g^2*z^4 -
6*a^6*b^8*e^10*f^4*g^6*z^4 + 4*a^7*b^7*e^10*f^3*g^7*z^4 + 4*a^5*b^9*e^10*f^5*g^5*z^4 + 384*a^9*c^5*d^6*e^4*g^
10*z^4 + 256*a^10*c^4*d^4*e^6*g^10*z^4 + 256*a^8*c^6*d^8*e^2*g^10*z^4 + 64*a^11*c^3*d^2*e^8*g^10*z^4 - 6*b^8*c
^6*d^6*e^4*f^10*z^4 + 4*b^9*c^5*d^5*e^5*f^10*z^4 + 4*b^7*c^7*d^7*e^3*f^10*z^4 + 384*a^5*c^9*d^4*e^6*f^10*z^4 +
256*a^6*c^8*d^2*e^8*f^10*z^4 + 256*a^4*c^10*d^6*e^4*f^10*z^4 + 64*a^3*c^11*d^8*e^2*f^10*z^4 - 6*a^6*b^8*d^4*e
^6*g^10*z^4 + 4*a^7*b^7*d^3*e^7*g^10*z^4 + 4*a^5*b^9*d^5*e^5*g^10*z^4 - 48*a^6*b^2*c^6*e^10*f^10*z^4 - 48*a^6*
b^2*c^6*d^10*g^10*z^4 + 12*a^5*b^4*c^5*e^10*f^10*z^4 + 12*a^5*b^4*c^5*d^10*g^10*z^4 + 64*a^7*c^7*e^10*f^10*z^4
+ 64*a^7*c^7*d^10*g^10*z^4 - b^14*d^6*e^4*f^4*g^6*z^4 - b^14*d^4*e^6*f^6*g^4*z^4 - b^10*c^4*d^10*f^4*g^6*z^4
- b^6*c^8*d^10*f^8*g^2*z^4 - a^8*b^6*e^10*f^2*g^8*z^4 - a^4*b^10*e^10*f^6*g^4*z^4 - b^10*c^4*d^4*e^6*f^10*z^4
- b^6*c^8*d^8*e^2*f^10*z^4 - a^8*b^6*d^2*e^8*g^10*z^4 - a^4*b^10*d^6*e^4*g^10*z^4 - a^4*b^6*c^4*e^10*f^10*z^4
- a^4*b^6*c^4*d^10*g^10*z^4 + 272*a^5*b^2*c^3*d*e^7*f*g^7*z^2 - 192*a^4*b^4*c^2*d*e^7*f*g^7*z^2 - 164*a^5*b*c^
4*d^2*e^6*f*g^7*z^2 - 164*a^5*b*c^4*d*e^7*f^2*g^6*z^2 + 120*a^2*b^2*c^6*d^7*e*f*g^7*z^2 + 120*a^2*b^2*c^6*d*e^
7*f^7*g*z^2 + 120*a*b^2*c^7*d^7*e*f^3*g^5*z^2 + 120*a*b^2*c^7*d^3*e^5*f^7*g*z^2 - 76*a^4*b*c^5*d^4*e^4*f*g^7*z
^2 - 76*a^4*b*c^5*d*e^7*f^4*g^4*z^2 - 76*a^3*b*c^6*d^6*e^2*f*g^7*z^2 - 76*a^3*b*c^6*d*e^7*f^6*g^2*z^2 - 64*a*b
^3*c^6*d^7*e*f^2*g^6*z^2 - 64*a*b^3*c^6*d^2*e^6*f^7*g*z^2 - 60*a^2*b*c^7*d^7*e*f^2*g^6*z^2 - 60*a^2*b*c^7*d^2*
e^6*f^7*g*z^2 + 44*a*b*c^8*d^6*e^2*f^5*g^3*z^2 + 44*a*b*c^8*d^5*e^3*f^6*g^2*z^2 + 22*a*b^5*c^4*d^6*e^2*f*g^7*z
^2 + 22*a*b^5*c^4*d*e^7*f^6*g^2*z^2 - 20*a^2*b^7*c*d^2*e^6*f*g^7*z^2 - 20*a^2*b^7*c*d*e^7*f^2*g^6*z^2 + 8*a*b^
8*c*d^2*e^6*f^2*g^6*z^2 - 8*a*b^6*c^3*d^5*e^3*f*g^7*z^2 - 8*a*b^6*c^3*d*e^7*f^5*g^3*z^2 + 2*a*b^7*c^2*d^4*e^4*
f*g^7*z^2 + 2*a*b^7*c^2*d*e^7*f^4*g^4*z^2 - 590*a^2*b^2*c^6*d^4*e^4*f^4*g^4*z^2 - 352*a^2*b^4*c^4*d^3*e^5*f^3*
g^5*z^2 - 346*a^3*b^2*c^5*d^4*e^4*f^2*g^6*z^2 - 346*a^3*b^2*c^5*d^2*e^6*f^4*g^4*z^2 - 274*a^4*b^2*c^4*d^2*e^6*
f^2*g^6*z^2 + 272*a^3*b^2*c^5*d^3*e^5*f^3*g^5*z^2 + 250*a^2*b^3*c^5*d^4*e^4*f^3*g^5*z^2 + 250*a^2*b^3*c^5*d^3*
e^5*f^4*g^4*z^2 + 204*a^3*b^3*c^4*d^3*e^5*f^2*g^6*z^2 + 204*a^3*b^3*c^4*d^2*e^6*f^3*g^5*z^2 + 136*a^2*b^2*c^6*
d^5*e^3*f^3*g^5*z^2 + 136*a^2*b^2*c^6*d^3*e^5*f^5*g^3*z^2 + 71*a^2*b^4*c^4*d^4*e^4*f^2*g^6*z^2 + 71*a^2*b^4*c^
4*d^2*e^6*f^4*g^4*z^2 - 56*a^2*b^3*c^5*d^5*e^3*f^2*g^6*z^2 - 56*a^2*b^3*c^5*d^2*e^6*f^5*g^3*z^2 + 18*a^2*b^2*c
^6*d^6*e^2*f^2*g^6*z^2 + 18*a^2*b^2*c^6*d^2*e^6*f^6*g^2*z^2 - 16*a^3*b^4*c^3*d^2*e^6*f^2*g^6*z^2 + 16*a^2*b^5*
c^3*d^3*e^5*f^2*g^6*z^2 + 16*a^2*b^5*c^3*d^2*e^6*f^3*g^5*z^2 - 4*a^2*b^6*c^2*d^2*e^6*f^2*g^6*z^2 + 48*a^3*b^6*
c*d*e^7*f*g^7*z^2 - 20*a*b^4*c^5*d^7*e*f*g^7*z^2 - 20*a*b^4*c^5*d*e^7*f^7*g*z^2 - 4*a*b^8*c*d^3*e^5*f*g^7*z^2
- 4*a*b^8*c*d*e^7*f^3*g^5*z^2 + 4*a*b*c^8*d^7*e*f^4*g^4*z^2 + 4*a*b*c^8*d^4*e^4*f^7*g*z^2 + 368*a^4*b^2*c^4*d^
3*e^5*f*g^7*z^2 + 368*a^4*b^2*c^4*d*e^7*f^3*g^5*z^2 + 264*a^3*b^2*c^5*d^5*e^3*f*g^7*z^2 + 264*a^3*b^2*c^5*d*e^
7*f^5*g^3*z^2 - 208*a^3*b^4*c^3*d^3*e^5*f*g^7*z^2 - 208*a^3*b^4*c^3*d*e^7*f^3*g^5*z^2 - 164*a^4*b*c^5*d^3*e^5*
f^2*g^6*z^2 - 164*a^4*b*c^5*d^2*e^6*f^3*g^5*z^2 + 140*a^2*b*c^7*d^5*e^3*f^4*g^4*z^2 + 140*a^2*b*c^7*d^4*e^4*f^
5*g^3*z^2 - 122*a*b^2*c^7*d^6*e^2*f^4*g^4*z^2 - 122*a*b^2*c^7*d^4*e^4*f^6*g^2*z^2 - 108*a^2*b^3*c^5*d^6*e^2*f*
g^7*z^2 - 108*a^2*b^3*c^5*d*e^7*f^6*g^2*z^2 + 102*a*b^3*c^6*d^5*e^3*f^4*g^4*z^2 + 102*a*b^3*c^6*d^4*e^4*f^5*g^
3*z^2 + 80*a*b^6*c^3*d^3*e^5*f^3*g^5*z^2 + 68*a*b^4*c^5*d^6*e^2*f^2*g^6*z^2 + 68*a*b^4*c^5*d^2*e^6*f^6*g^2*z^2
- 60*a^3*b*c^6*d^5*e^3*f^2*g^6*z^2 + 60*a^3*b*c^6*d^4*e^4*f^3*g^5*z^2 + 60*a^3*b*c^6*d^3*e^5*f^4*g^4*z^2 - 60
*a^3*b*c^6*d^2*e^6*f^5*g^3*z^2 - 54*a^3*b^3*c^4*d^4*e^4*f*g^7*z^2 - 54*a^3*b^3*c^4*d*e^7*f^4*g^4*z^2 - 52*a*b^
4*c^5*d^5*e^3*f^3*g^5*z^2 - 52*a*b^4*c^5*d^3*e^5*f^5*g^3*z^2 + 48*a^3*b^5*c^2*d^2*e^6*f*g^7*z^2 + 48*a^3*b^5*c
^2*d*e^7*f^2*g^6*z^2 + 48*a^2*b^6*c^2*d^3*e^5*f*g^7*z^2 + 48*a^2*b^6*c^2*d*e^7*f^3*g^5*z^2 + 44*a^4*b^3*c^3*d^
2*e^6*f*g^7*z^2 + 44*a^4*b^3*c^3*d*e^7*f^2*g^6*z^2 - 44*a^2*b*c^7*d^6*e^2*f^3*g^5*z^2 - 44*a^2*b*c^7*d^3*e^5*f
^6*g^2*z^2 - 44*a*b^3*c^6*d^6*e^2*f^3*g^5*z^2 - 44*a*b^3*c^6*d^3*e^5*f^6*g^2*z^2 - 32*a*b^5*c^4*d^4*e^4*f^3*g^
5*z^2 - 32*a*b^5*c^4*d^3*e^5*f^4*g^4*z^2 - 32*a*b^2*c^7*d^5*e^3*f^5*g^3*z^2 - 20*a*b^7*c^2*d^3*e^5*f^2*g^6*z^2
- 20*a*b^7*c^2*d^2*e^6*f^3*g^5*z^2 + 20*a*b^4*c^5*d^4*e^4*f^4*g^4*z^2 - 14*a*b^5*c^4*d^5*e^3*f^2*g^6*z^2 - 14
*a*b^5*c^4*d^2*e^6*f^5*g^3*z^2 + 4*a^2*b^5*c^3*d^4*e^4*f*g^7*z^2 + 4*a^2*b^5*c^3*d*e^7*f^4*g^4*z^2 - 4*a^2*b^4
*c^4*d^5*e^3*f*g^7*z^2 - 4*a^2*b^4*c^4*d*e^7*f^5*g^3*z^2 + 2*a*b^6*c^3*d^4*e^4*f^2*g^6*z^2 + 2*a*b^6*c^3*d^2*e
^6*f^4*g^4*z^2 - 50*b^2*c^8*d^6*e^2*f^6*g^2*z^2 - 32*b^4*c^6*d^5*e^3*f^5*g^3*z^2 + 24*b^3*c^7*d^6*e^2*f^5*g^3*
z^2 + 24*b^3*c^7*d^5*e^3*f^6*g^2*z^2 + 23*b^4*c^6*d^6*e^2*f^4*g^4*z^2 + 23*b^4*c^6*d^4*e^4*f^6*g^2*z^2 - 11*b^
6*c^4*d^6*e^2*f^2*g^6*z^2 - 11*b^6*c^4*d^2*e^6*f^6*g^2*z^2 + 8*b^6*c^4*d^5*e^3*f^3*g^5*z^2 + 8*b^6*c^4*d^3*e^5
*f^5*g^3*z^2 - 8*b^5*c^5*d^5*e^3*f^4*g^4*z^2 - 8*b^5*c^5*d^4*e^4*f^5*g^3*z^2 + 5*b^6*c^4*d^4*e^4*f^4*g^4*z^2 -
4*b^8*c^2*d^3*e^5*f^3*g^5*z^2 + 4*b^7*c^3*d^5*e^3*f^2*g^6*z^2 + 4*b^7*c^3*d^2*e^6*f^5*g^3*z^2 - 2*b^7*c^3*d^4
*e^4*f^3*g^5*z^2 - 2*b^7*c^3*d^3*e^5*f^4*g^4*z^2 - 2*b^5*c^5*d^6*e^2*f^3*g^5*z^2 - 2*b^5*c^5*d^3*e^5*f^6*g^2*z
^2 + 416*a^5*c^5*d^2*e^6*f^2*g^6*z^2 - 392*a^4*c^6*d^3*e^5*f^3*g^5*z^2 + 376*a^4*c^6*d^4*e^4*f^2*g^6*z^2 + 376
*a^4*c^6*d^2*e^6*f^4*g^4*z^2 + 320*a^3*c^7*d^4*e^4*f^4*g^4*z^2 - 280*a^3*c^7*d^5*e^3*f^3*g^5*z^2 - 280*a^3*c^7
*d^3*e^5*f^5*g^3*z^2 - 200*a^2*c^8*d^5*e^3*f^5*g^3*z^2 + 160*a^3*c^7*d^6*e^2*f^2*g^6*z^2 + 160*a^3*c^7*d^2*e^6
*f^6*g^2*z^2 + 120*a^2*c^8*d^6*e^2*f^4*g^4*z^2 + 120*a^2*c^8*d^4*e^4*f^6*g^2*z^2 - 471*a^4*b^2*c^4*e^8*f^4*g^4
*z^2 + 436*a^3*b^4*c^3*e^8*f^4*g^4*z^2 - 310*a^3*b^3*c^4*e^8*f^5*g^3*z^2 - 232*a^5*b^2*c^3*e^8*f^2*g^6*z^2 + 2
29*a^2*b^4*c^4*e^8*f^6*g^2*z^2 + 216*a^4*b^4*c^2*e^8*f^2*g^6*z^2 - 204*a^4*b^3*c^3*e^8*f^3*g^5*z^2 - 150*a^3*b
^2*c^5*e^8*f^6*g^2*z^2 - 91*a^2*b^6*c^2*e^8*f^4*g^4*z^2 - 72*a^3*b^5*c^2*e^8*f^3*g^5*z^2 - 44*a^2*b^5*c^3*e^8*
f^5*g^3*z^2 - 471*a^4*b^2*c^4*d^4*e^4*g^8*z^2 + 436*a^3*b^4*c^3*d^4*e^4*g^8*z^2 - 310*a^3*b^3*c^4*d^5*e^3*g^8*
z^2 - 232*a^5*b^2*c^3*d^2*e^6*g^8*z^2 + 229*a^2*b^4*c^4*d^6*e^2*g^8*z^2 + 216*a^4*b^4*c^2*d^2*e^6*g^8*z^2 - 20
4*a^4*b^3*c^3*d^3*e^5*g^8*z^2 - 150*a^3*b^2*c^5*d^6*e^2*g^8*z^2 - 91*a^2*b^6*c^2*d^4*e^4*g^8*z^2 - 72*a^3*b^5*
c^2*d^3*e^5*g^8*z^2 - 44*a^2*b^5*c^3*d^5*e^3*g^8*z^2 - 26*b^3*c^7*d^7*e*f^4*g^4*z^2 - 26*b^3*c^7*d^4*e^4*f^7*g
*z^2 + 16*b^2*c^8*d^7*e*f^5*g^3*z^2 + 16*b^2*c^8*d^5*e^3*f^7*g*z^2 + 10*b^5*c^5*d^7*e*f^2*g^6*z^2 + 10*b^5*c^5
*d^2*e^6*f^7*g*z^2 - 4*b^4*c^6*d^7*e*f^3*g^5*z^2 - 4*b^4*c^6*d^3*e^5*f^7*g*z^2 + 2*b^9*c*d^3*e^5*f^2*g^6*z^2 +
2*b^9*c*d^2*e^6*f^3*g^5*z^2 - 168*a^5*c^5*d^3*e^5*f*g^7*z^2 - 168*a^5*c^5*d*e^7*f^3*g^5*z^2 - 120*a^4*c^6*d^5
*e^3*f*g^7*z^2 - 120*a^4*c^6*d*e^7*f^5*g^3*z^2 - 56*a^2*c^8*d^7*e*f^3*g^5*z^2 - 56*a^2*c^8*d^3*e^5*f^7*g*z^2 +
32*a*c^9*d^6*e^2*f^6*g^2*z^2 + 624*a^4*b*c^5*e^8*f^5*g^3*z^2 + 548*a^5*b*c^4*e^8*f^3*g^5*z^2 - 182*a^2*b^3*c^
5*e^8*f^7*g*z^2 - 96*a^5*b^3*c^2*e^8*f*g^7*z^2 - 68*a*b^6*c^3*e^8*f^6*g^2*z^2 - 58*a^3*b^6*c*e^8*f^2*g^6*z^2 +
38*a^2*b^7*c*e^8*f^3*g^5*z^2 + 36*a*b^7*c^2*e^8*f^5*g^3*z^2 + 18*a*b^2*c^7*d^8*f^2*g^6*z^2 + 624*a^4*b*c^5*d^
5*e^3*g^8*z^2 + 548*a^5*b*c^4*d^3*e^5*g^8*z^2 - 182*a^2*b^3*c^5*d^7*e*g^8*z^2 - 96*a^5*b^3*c^2*d*e^7*g^8*z^2 -
68*a*b^6*c^3*d^6*e^2*g^8*z^2 - 58*a^3*b^6*c*d^2*e^6*g^8*z^2 + 38*a^2*b^7*c*d^3*e^5*g^8*z^2 + 36*a*b^7*c^2*d^5
*e^3*g^8*z^2 + 18*a*b^2*c^7*d^2*e^6*f^8*z^2 + 12*b*c^9*d^7*e*f^6*g^2*z^2 + 12*b*c^9*d^6*e^2*f^7*g*z^2 - 72*a^6
*c^4*d*e^7*f*g^7*z^2 - 40*a*c^9*d^7*e*f^5*g^3*z^2 - 40*a*c^9*d^5*e^3*f^7*g*z^2 - 24*a^3*c^7*d^7*e*f*g^7*z^2 -
24*a^3*c^7*d*e^7*f^7*g*z^2 - 4*a^2*b^8*d*e^7*f*g^7*z^2 + 2*a*b^9*d^2*e^6*f*g^7*z^2 + 2*a*b^9*d*e^7*f^2*g^6*z^2
+ 204*a^3*b*c^6*e^8*f^7*g*z^2 + 128*a^6*b*c^3*e^8*f*g^7*z^2 + 48*a*b^5*c^4*e^8*f^7*g*z^2 + 24*a^4*b^5*c*e^8*f
*g^7*z^2 - 48*a*b*c^8*d^8*f^3*g^5*z^2 - 36*a^2*b*c^7*d^8*f*g^7*z^2 + 6*a*b^3*c^6*d^8*f*g^7*z^2 + 204*a^3*b*c^6
*d^7*e*g^8*z^2 + 128*a^6*b*c^3*d*e^7*g^8*z^2 + 48*a*b^5*c^4*d^7*e*g^8*z^2 + 24*a^4*b^5*c*d*e^7*g^8*z^2 - 48*a*
b*c^8*d^3*e^5*f^8*z^2 - 36*a^2*b*c^7*d*e^7*f^8*z^2 + 6*a*b^3*c^6*d*e^7*f^8*z^2 - b^8*c^2*d^4*e^4*f^2*g^6*z^2 -
b^8*c^2*d^2*e^6*f^4*g^4*z^2 - 4*b^9*c*e^8*f^5*g^3*z^2 - 4*b^7*c^3*e^8*f^7*g*z^2 - 12*b*c^9*d^8*f^5*g^3*z^2 +
24*a*c^9*d^8*f^4*g^4*z^2 - 4*b^9*c*d^5*e^3*g^8*z^2 - 4*b^7*c^3*d^7*e*g^8*z^2 - 4*a*b^9*e^8*f^3*g^5*z^2 - 2*a^3
*b^7*e^8*f*g^7*z^2 - 12*b*c^9*d^5*e^3*f^8*z^2 + 24*a*c^9*d^4*e^4*f^8*z^2 - 4*a*b^9*d^3*e^5*g^8*z^2 - 2*a^3*b^7
*d*e^7*g^8*z^2 - 12*a^5*b^4*c*e^8*g^8*z^2 - 12*a*b^4*c^5*e^8*f^8*z^2 - 12*a*b^4*c^5*d^8*g^8*z^2 - 8*c^10*d^7*e
*f^7*g*z^2 + 6*b^8*c^2*e^8*f^6*g^2*z^2 - 232*a^5*c^5*e^8*f^4*g^4*z^2 - 188*a^4*c^6*e^8*f^6*g^2*z^2 - 92*a^6*c^
4*e^8*f^2*g^6*z^2 + 9*b^2*c^8*d^8*f^4*g^4*z^2 - 3*b^4*c^6*d^8*f^2*g^6*z^2 + 2*b^3*c^7*d^8*f^3*g^5*z^2 + 36*a^2
*c^8*d^8*f^2*g^6*z^2 + 6*b^8*c^2*d^6*e^2*g^8*z^2 + 5*a^2*b^8*e^8*f^2*g^6*z^2 - 232*a^5*c^5*d^4*e^4*g^8*z^2 - 1
88*a^4*c^6*d^6*e^2*g^8*z^2 - 92*a^6*c^4*d^2*e^6*g^8*z^2 + 9*b^2*c^8*d^4*e^4*f^8*z^2 - 3*b^4*c^6*d^2*e^6*f^8*z^
2 + 2*b^3*c^7*d^3*e^5*f^8*z^2 + 36*a^2*c^8*d^2*e^6*f^8*z^2 + 5*a^2*b^8*d^2*e^6*g^8*z^2 + 48*a^6*b^2*c^2*e^8*g^
8*z^2 + 45*a^2*b^2*c^6*e^8*f^8*z^2 + 45*a^2*b^2*c^6*d^8*g^8*z^2 + 4*c^10*d^8*f^6*g^2*z^2 + b^10*e^8*f^4*g^4*z^
2 + 4*c^10*d^6*e^2*f^8*z^2 + b^10*d^4*e^4*g^8*z^2 - 64*a^7*c^3*e^8*g^8*z^2 + b^6*c^4*e^8*f^8*z^2 + b^6*c^4*d^8
*g^8*z^2 - 48*a^3*c^7*e^8*f^8*z^2 - 48*a^3*c^7*d^8*g^8*z^2 + a^4*b^6*e^8*g^8*z^2 - b^10*d^2*e^6*f^2*g^6*z^2 +
108*a^2*b^2*c^4*d^2*e^5*f*g^6*z + 108*a^2*b^2*c^4*d*e^6*f^2*g^5*z + 60*a*b^2*c^5*d^3*e^4*f^2*g^5*z + 60*a*b^2*
c^5*d^2*e^5*f^3*g^4*z - 48*a^2*b*c^5*d^2*e^5*f^2*g^5*z - 44*a*b^3*c^4*d^2*e^5*f^2*g^5*z - 120*a^2*b*c^5*d^3*e^
4*f*g^6*z - 120*a^2*b*c^5*d*e^6*f^3*g^4*z - 96*a*b*c^6*d^3*e^4*f^3*g^4*z - 64*a^2*b^3*c^3*d*e^6*f*g^6*z + 32*a
*b^3*c^4*d^3*e^4*f*g^6*z + 32*a*b^3*c^4*d*e^6*f^3*g^4*z - 28*a*b^4*c^3*d^2*e^5*f*g^6*z - 28*a*b^4*c^3*d*e^6*f^
2*g^5*z - 18*a*b^2*c^5*d^4*e^3*f*g^6*z - 18*a*b^2*c^5*d*e^6*f^4*g^3*z + 4*a*b*c^6*d^4*e^3*f^2*g^5*z + 4*a*b*c^
6*d^2*e^5*f^4*g^3*z + 24*a*b^5*c^2*d*e^6*f*g^6*z - 16*a^3*b*c^4*d*e^6*f*g^6*z - 8*a*b*c^6*d^5*e^2*f*g^6*z - 8*
a*b*c^6*d*e^6*f^5*g^2*z - 13*b^2*c^6*d^6*e*f*g^6*z - 13*b^2*c^6*d*e^6*f^6*g*z + 8*b*c^7*d^6*e*f^2*g^5*z + 8*b*
c^7*d^2*e^5*f^6*g*z + 9*b^2*c^6*d^4*e^3*f^3*g^4*z + 9*b^2*c^6*d^3*e^4*f^4*g^3*z + 8*b^5*c^3*d^2*e^5*f^2*g^5*z
- 6*b^4*c^4*d^3*e^4*f^2*g^5*z - 6*b^4*c^4*d^2*e^5*f^3*g^4*z - 6*b^3*c^5*d^4*e^3*f^2*g^5*z - 6*b^3*c^5*d^2*e^5*
f^4*g^3*z + 4*b^3*c^5*d^3*e^4*f^3*g^4*z + b^2*c^6*d^5*e^2*f^2*g^5*z + b^2*c^6*d^2*e^5*f^5*g^2*z + 16*a^2*c^6*d
^3*e^4*f^2*g^5*z + 16*a^2*c^6*d^2*e^5*f^3*g^4*z - 112*a^2*b^3*c^3*e^7*f^2*g^5*z - 12*a^2*b^2*c^4*e^7*f^3*g^4*z
- 112*a^2*b^3*c^3*d^2*e^5*g^7*z - 12*a^2*b^2*c^4*d^3*e^4*g^7*z - 2*b^7*c*d*e^6*f*g^6*z + 8*a*c^7*d^6*e*f*g^6*
z + 8*a*c^7*d*e^6*f^6*g*z + 52*a*b*c^6*e^7*f^6*g*z - 10*a*b^6*c*e^7*f*g^6*z + 52*a*b*c^6*d^6*e*g^7*z - 10*a*b^
6*c*d*e^6*g^7*z + 14*b^3*c^5*d^5*e^2*f*g^6*z + 14*b^3*c^5*d*e^6*f^5*g^2*z - 12*b*c^7*d^5*e^2*f^3*g^4*z - 12*b*
c^7*d^3*e^4*f^5*g^2*z - 5*b^4*c^4*d^4*e^3*f*g^6*z - 5*b^4*c^4*d*e^6*f^4*g^3*z + b^6*c^2*d^2*e^5*f*g^6*z + b^6*
c^2*d*e^6*f^2*g^5*z + 52*a^2*c^6*d^4*e^3*f*g^6*z + 52*a^2*c^6*d*e^6*f^4*g^3*z + 24*a*c^7*d^4*e^3*f^3*g^4*z + 2
4*a*c^7*d^3*e^4*f^4*g^3*z - 16*a*c^7*d^5*e^2*f^2*g^5*z - 16*a*c^7*d^2*e^5*f^5*g^2*z + 8*a^3*c^5*d^2*e^5*f*g^6*
z + 8*a^3*c^5*d*e^6*f^2*g^5*z + 200*a^3*b*c^4*e^7*f^2*g^5*z + 144*a^2*b*c^5*e^7*f^4*g^3*z - 42*a*b^2*c^5*e^7*f
^5*g^2*z + 32*a^3*b^2*c^3*e^7*f*g^6*z + 24*a^2*b^4*c^2*e^7*f*g^6*z + 24*a*b^5*c^2*e^7*f^2*g^5*z - 10*a*b^3*c^4
*e^7*f^4*g^3*z + 4*a*b^4*c^3*e^7*f^3*g^4*z + 200*a^3*b*c^4*d^2*e^5*g^7*z + 144*a^2*b*c^5*d^4*e^3*g^7*z - 42*a*
b^2*c^5*d^5*e^2*g^7*z + 32*a^3*b^2*c^3*d*e^6*g^7*z + 24*a^2*b^4*c^2*d*e^6*g^7*z + 24*a*b^5*c^2*d^2*e^5*g^7*z -
10*a*b^3*c^4*d^4*e^3*g^7*z + 4*a*b^4*c^3*d^3*e^4*g^7*z + 4*b*c^7*d^7*f*g^6*z + 4*b*c^7*d*e^6*f^7*z + 11*b^4*c
^4*e^7*f^5*g^2*z - 4*b^5*c^3*e^7*f^4*g^3*z + b^6*c^2*e^7*f^3*g^4*z - 136*a^3*c^5*e^7*f^3*g^4*z - 68*a^2*c^6*e^
7*f^5*g^2*z + 11*b^4*c^4*d^5*e^2*g^7*z - 4*b^5*c^3*d^4*e^3*g^7*z + b^6*c^2*d^3*e^4*g^7*z - 136*a^3*c^5*d^3*e^4
*g^7*z - 68*a^2*c^6*d^5*e^2*g^7*z - 96*a^3*b^3*c^2*e^7*g^7*z + 4*c^8*d^6*e*f^3*g^4*z + 4*c^8*d^3*e^4*f^6*g*z -
10*b^3*c^5*e^7*f^6*g*z - 2*b^7*c*e^7*f^2*g^5*z - 128*a^4*c^4*e^7*f*g^6*z - 10*b^3*c^5*d^6*e*g^7*z - 2*b^7*c*d
^2*e^5*g^7*z - 128*a^4*c^4*d*e^6*g^7*z + 128*a^4*b*c^3*e^7*g^7*z + 24*a^2*b^5*c*e^7*g^7*z - 4*c^8*d^7*f^2*g^5*
z - 4*c^8*d^2*e^5*f^7*z + 3*b^2*c^6*e^7*f^7*z + 3*b^2*c^6*d^7*g^7*z + b^8*e^7*f*g^6*z + b^8*d*e^6*g^7*z - 16*a
*c^7*e^7*f^7*z - 16*a*c^7*d^7*g^7*z - 2*a*b^7*e^7*g^7*z - 8*a*c^5*d*e^5*f*g^5 + 20*a*b*c^4*e^6*f*g^5 + 20*a*b*
c^4*d*e^5*g^6 + 4*b*c^5*d^2*e^4*f*g^5 + 4*b*c^5*d*e^5*f^2*g^4 - 2*b^2*c^4*d*e^5*f*g^5 - 4*b^3*c^3*e^6*f*g^5 -
16*a*c^5*e^6*f^2*g^4 - 4*b^3*c^3*d*e^5*g^6 - 16*a*c^5*d^2*e^4*g^6 + 8*a*b^2*c^3*e^6*g^6 - 4*c^6*d^2*e^4*f^2*g^
4 + 3*b^2*c^4*e^6*f^2*g^4 + 3*b^2*c^4*d^2*e^4*g^6 - 36*a^2*c^4*e^6*g^6, z, k)*(root(1120*a^6*b^2*c^6*d^9*e*f*g
^9*z^4 + 1120*a^6*b^2*c^6*d*e^9*f^9*g*z^4 - 792*a^5*b^4*c^5*d^9*e*f*g^9*z^4 - 792*a^5*b^4*c^5*d*e^9*f^9*g*z^4
+ 512*a^9*b*c^4*d^4*e^6*f*g^9*z^4 + 512*a^9*b*c^4*d*e^9*f^4*g^6*z^4 - 512*a^7*b*c^6*d^8*e^2*f*g^9*z^4 - 512*a^
7*b*c^6*d*e^9*f^8*g^2*z^4 - 512*a^6*b*c^7*d^9*e*f^2*g^8*z^4 - 512*a^6*b*c^7*d^2*e^8*f^9*g*z^4 + 512*a^4*b*c^9*
d^9*e*f^6*g^4*z^4 + 512*a^4*b*c^9*d^6*e^4*f^9*g*z^4 + 256*a^10*b*c^3*d^2*e^8*f*g^9*z^4 + 256*a^10*b*c^3*d*e^9*
f^2*g^8*z^4 + 256*a^3*b*c^10*d^9*e*f^8*g^2*z^4 + 256*a^3*b*c^10*d^8*e^2*f^9*g*z^4 - 200*a^6*b^7*c*d^4*e^6*f*g^
9*z^4 - 200*a^6*b^7*c*d*e^9*f^4*g^6*z^4 - 200*a*b^7*c^6*d^9*e*f^6*g^4*z^4 - 200*a*b^7*c^6*d^6*e^4*f^9*g*z^4 +
194*a^4*b^6*c^4*d^9*e*f*g^9*z^4 + 194*a^4*b^6*c^4*d*e^9*f^9*g*z^4 + 144*a^5*b^8*c*d^5*e^5*f*g^9*z^4 + 144*a^5*
b^8*c*d*e^9*f^5*g^5*z^4 + 144*a*b^8*c^5*d^9*e*f^5*g^5*z^4 + 144*a*b^8*c^5*d^5*e^5*f^9*g*z^4 + 96*a^10*b^2*c^2*
d*e^9*f*g^9*z^4 + 96*a^2*b^2*c^10*d^9*e*f^9*g*z^4 + 56*a^7*b^6*c*d^3*e^7*f*g^9*z^4 + 56*a^7*b^6*c*d*e^9*f^3*g^
7*z^4 + 56*a*b^6*c^7*d^9*e*f^7*g^3*z^4 + 56*a*b^6*c^7*d^7*e^3*f^9*g*z^4 + 48*a^8*b^5*c*d^2*e^8*f*g^9*z^4 + 48*
a^8*b^5*c*d*e^9*f^2*g^8*z^4 + 48*a*b^5*c^8*d^9*e*f^8*g^2*z^4 + 48*a*b^5*c^8*d^8*e^2*f^9*g*z^4 + 20*a*b^12*c*d^
6*e^4*f^4*g^6*z^4 + 20*a*b^12*c*d^4*e^6*f^6*g^4*z^4 - 16*a^3*b^10*c*d^7*e^3*f*g^9*z^4 - 16*a^3*b^10*c*d*e^9*f^
7*g^3*z^4 - 16*a^3*b^8*c^3*d^9*e*f*g^9*z^4 - 16*a^3*b^8*c^3*d*e^9*f^9*g*z^4 - 16*a*b^12*c*d^7*e^3*f^3*g^7*z^4
- 16*a*b^12*c*d^3*e^7*f^7*g^3*z^4 - 16*a*b^10*c^3*d^9*e*f^3*g^7*z^4 - 16*a*b^10*c^3*d^3*e^7*f^9*g*z^4 - 8*a^4*
b^9*c*d^6*e^4*f*g^9*z^4 - 8*a^4*b^9*c*d*e^9*f^6*g^4*z^4 - 8*a*b^12*c*d^5*e^5*f^5*g^5*z^4 - 8*a*b^9*c^4*d^9*e*f
^4*g^6*z^4 - 8*a*b^9*c^4*d^4*e^6*f^9*g*z^4 - 9984*a^7*b^2*c^5*d^4*e^6*f^4*g^6*z^4 - 9984*a^5*b^2*c^7*d^6*e^4*f
^6*g^4*z^4 - 8640*a^6*b^2*c^6*d^6*e^4*f^4*g^6*z^4 - 8640*a^6*b^2*c^6*d^4*e^6*f^6*g^4*z^4 - 8544*a^5*b^4*c^5*d^
5*e^5*f^5*g^5*z^4 + 5632*a^6*b^2*c^6*d^7*e^3*f^3*g^7*z^4 + 5632*a^6*b^2*c^6*d^3*e^7*f^7*g^3*z^4 + 5232*a^5*b^4
*c^5*d^6*e^4*f^4*g^6*z^4 + 5232*a^5*b^4*c^5*d^4*e^6*f^6*g^4*z^4 + 4808*a^4*b^6*c^4*d^5*e^5*f^5*g^5*z^4 - 4288*
a^6*b^4*c^4*d^5*e^5*f^3*g^7*z^4 - 4288*a^6*b^4*c^4*d^3*e^7*f^5*g^5*z^4 - 4288*a^4*b^4*c^6*d^7*e^3*f^5*g^5*z^4
- 4288*a^4*b^4*c^6*d^5*e^5*f^7*g^3*z^4 + 3968*a^6*b^3*c^5*d^5*e^5*f^4*g^6*z^4 + 3968*a^6*b^3*c^5*d^4*e^6*f^5*g
^5*z^4 + 3968*a^5*b^3*c^6*d^6*e^4*f^5*g^5*z^4 + 3968*a^5*b^3*c^6*d^5*e^5*f^6*g^4*z^4 + 3840*a^7*b^2*c^5*d^5*e^
5*f^3*g^7*z^4 + 3840*a^7*b^2*c^5*d^3*e^7*f^5*g^5*z^4 + 3840*a^5*b^2*c^7*d^7*e^3*f^5*g^5*z^4 + 3840*a^5*b^2*c^7
*d^5*e^5*f^7*g^3*z^4 + 3776*a^6*b^4*c^4*d^4*e^6*f^4*g^6*z^4 + 3776*a^4*b^4*c^6*d^6*e^4*f^6*g^4*z^4 + 3456*a^6*
b^2*c^6*d^5*e^5*f^5*g^5*z^4 + 3440*a^6*b^4*c^4*d^6*e^4*f^2*g^8*z^4 + 3440*a^6*b^4*c^4*d^2*e^8*f^6*g^4*z^4 + 34
40*a^4*b^4*c^6*d^8*e^2*f^4*g^6*z^4 + 3440*a^4*b^4*c^6*d^4*e^6*f^8*g^2*z^4 - 3360*a^8*b^2*c^4*d^4*e^6*f^2*g^8*z
^4 - 3360*a^8*b^2*c^4*d^2*e^8*f^4*g^6*z^4 - 3360*a^4*b^2*c^8*d^8*e^2*f^6*g^4*z^4 - 3360*a^4*b^2*c^8*d^6*e^4*f^
8*g^2*z^4 - 2944*a^7*b^4*c^3*d^3*e^7*f^3*g^7*z^4 - 2944*a^3*b^4*c^7*d^7*e^3*f^7*g^3*z^4 + 2512*a^5*b^6*c^3*d^5
*e^5*f^3*g^7*z^4 + 2512*a^5*b^6*c^3*d^3*e^7*f^5*g^5*z^4 + 2512*a^3*b^6*c^5*d^7*e^3*f^5*g^5*z^4 + 2512*a^3*b^6*
c^5*d^5*e^5*f^7*g^3*z^4 + 2312*a^7*b^4*c^3*d^4*e^6*f^2*g^8*z^4 + 2312*a^7*b^4*c^3*d^2*e^8*f^4*g^6*z^4 + 2312*a
^3*b^4*c^7*d^8*e^2*f^6*g^4*z^4 + 2312*a^3*b^4*c^7*d^6*e^4*f^8*g^2*z^4 + 1952*a^6*b^6*c^2*d^3*e^7*f^3*g^7*z^4 +
1952*a^2*b^6*c^6*d^7*e^3*f^7*g^3*z^4 - 1920*a^5*b^4*c^5*d^7*e^3*f^3*g^7*z^4 - 1920*a^5*b^4*c^5*d^3*e^7*f^7*g^
3*z^4 - 1828*a^5*b^6*c^3*d^6*e^4*f^2*g^8*z^4 - 1828*a^5*b^6*c^3*d^2*e^8*f^6*g^4*z^4 - 1828*a^3*b^6*c^5*d^8*e^2
*f^4*g^6*z^4 - 1828*a^3*b^6*c^5*d^4*e^6*f^8*g^2*z^4 + 1740*a^5*b^4*c^5*d^8*e^2*f^2*g^8*z^4 + 1740*a^5*b^4*c^5*
d^2*e^8*f^8*g^2*z^4 - 1728*a^7*b^2*c^5*d^6*e^4*f^2*g^8*z^4 - 1728*a^7*b^2*c^5*d^2*e^8*f^6*g^4*z^4 - 1728*a^5*b
^2*c^7*d^8*e^2*f^4*g^6*z^4 - 1728*a^5*b^2*c^7*d^4*e^6*f^8*g^2*z^4 - 1716*a^4*b^6*c^4*d^6*e^4*f^4*g^6*z^4 - 171
6*a^4*b^6*c^4*d^4*e^6*f^6*g^4*z^4 - 1664*a^9*b^2*c^3*d^2*e^8*f^2*g^8*z^4 - 1664*a^3*b^2*c^9*d^8*e^2*f^8*g^2*z^
4 - 1600*a^6*b^3*c^5*d^7*e^3*f^2*g^8*z^4 - 1600*a^6*b^3*c^5*d^2*e^8*f^7*g^3*z^4 - 1600*a^5*b^3*c^6*d^8*e^2*f^3
*g^7*z^4 - 1600*a^5*b^3*c^6*d^3*e^7*f^8*g^2*z^4 - 1553*a^4*b^6*c^4*d^8*e^2*f^2*g^8*z^4 - 1553*a^4*b^6*c^4*d^2*
e^8*f^8*g^2*z^4 + 1536*a^8*b^2*c^4*d^3*e^7*f^3*g^7*z^4 + 1536*a^4*b^2*c^8*d^7*e^3*f^7*g^3*z^4 + 1408*a^7*b^3*c
^4*d^4*e^6*f^3*g^7*z^4 + 1408*a^7*b^3*c^4*d^3*e^7*f^4*g^6*z^4 - 1408*a^6*b^3*c^5*d^6*e^4*f^3*g^7*z^4 - 1408*a^
6*b^3*c^5*d^3*e^7*f^6*g^4*z^4 - 1408*a^5*b^3*c^6*d^7*e^3*f^4*g^6*z^4 - 1408*a^5*b^3*c^6*d^4*e^6*f^7*g^3*z^4 +
1408*a^4*b^3*c^7*d^7*e^3*f^6*g^4*z^4 + 1408*a^4*b^3*c^7*d^6*e^4*f^7*g^3*z^4 - 1360*a^6*b^5*c^3*d^5*e^5*f^2*g^8
*z^4 - 1360*a^6*b^5*c^3*d^2*e^8*f^5*g^5*z^4 - 1360*a^3*b^5*c^6*d^8*e^2*f^5*g^5*z^4 - 1360*a^3*b^5*c^6*d^5*e^5*
f^8*g^2*z^4 - 1248*a^5*b^5*c^4*d^5*e^5*f^4*g^6*z^4 - 1248*a^5*b^5*c^4*d^4*e^6*f^5*g^5*z^4 - 1248*a^4*b^5*c^5*d
^6*e^4*f^5*g^5*z^4 - 1248*a^4*b^5*c^5*d^5*e^5*f^6*g^4*z^4 + 1088*a^8*b^3*c^3*d^3*e^7*f^2*g^8*z^4 + 1088*a^8*b^
3*c^3*d^2*e^8*f^3*g^7*z^4 + 1088*a^3*b^3*c^8*d^8*e^2*f^7*g^3*z^4 + 1088*a^3*b^3*c^8*d^7*e^3*f^8*g^2*z^4 + 1056
*a^8*b^4*c^2*d^2*e^8*f^2*g^8*z^4 + 1056*a^2*b^4*c^8*d^8*e^2*f^8*g^2*z^4 - 912*a^7*b^5*c^2*d^3*e^7*f^2*g^8*z^4
- 912*a^7*b^5*c^2*d^2*e^8*f^3*g^7*z^4 - 912*a^2*b^5*c^7*d^8*e^2*f^7*g^3*z^4 - 912*a^2*b^5*c^7*d^7*e^3*f^8*g^2*
z^4 - 848*a^5*b^6*c^3*d^4*e^6*f^4*g^6*z^4 - 848*a^3*b^6*c^5*d^6*e^4*f^6*g^4*z^4 + 832*a^7*b^3*c^4*d^5*e^5*f^2*
g^8*z^4 + 832*a^7*b^3*c^4*d^2*e^8*f^5*g^5*z^4 + 832*a^4*b^3*c^7*d^8*e^2*f^5*g^5*z^4 + 832*a^4*b^3*c^7*d^5*e^5*
f^8*g^2*z^4 + 828*a^5*b^7*c^2*d^5*e^5*f^2*g^8*z^4 + 828*a^5*b^7*c^2*d^2*e^8*f^5*g^5*z^4 + 828*a^2*b^7*c^5*d^8*
e^2*f^5*g^5*z^4 + 828*a^2*b^7*c^5*d^5*e^5*f^8*g^2*z^4 - 800*a^3*b^8*c^3*d^5*e^5*f^5*g^5*z^4 - 696*a^4*b^8*c^2*
d^5*e^5*f^3*g^7*z^4 - 696*a^4*b^8*c^2*d^3*e^7*f^5*g^5*z^4 - 696*a^2*b^8*c^4*d^7*e^3*f^5*g^5*z^4 - 696*a^2*b^8*
c^4*d^5*e^5*f^7*g^3*z^4 - 694*a^6*b^6*c^2*d^4*e^6*f^2*g^8*z^4 - 694*a^6*b^6*c^2*d^2*e^8*f^4*g^6*z^4 - 694*a^2*
b^6*c^6*d^8*e^2*f^6*g^4*z^4 - 694*a^2*b^6*c^6*d^6*e^4*f^8*g^2*z^4 + 692*a^4*b^7*c^3*d^7*e^3*f^2*g^8*z^4 + 692*
a^4*b^7*c^3*d^2*e^8*f^7*g^3*z^4 + 692*a^3*b^7*c^4*d^8*e^2*f^3*g^7*z^4 + 692*a^3*b^7*c^4*d^3*e^7*f^8*g^2*z^4 +
672*a^4*b^6*c^4*d^7*e^3*f^3*g^7*z^4 + 672*a^4*b^6*c^4*d^3*e^7*f^7*g^3*z^4 + 600*a^4*b^8*c^2*d^4*e^6*f^4*g^6*z^
4 + 600*a^2*b^8*c^4*d^6*e^4*f^6*g^4*z^4 - 544*a^3*b^8*c^3*d^7*e^3*f^3*g^7*z^4 + 544*a^3*b^8*c^3*d^6*e^4*f^4*g^
6*z^4 + 544*a^3*b^8*c^3*d^4*e^6*f^6*g^4*z^4 - 544*a^3*b^8*c^3*d^3*e^7*f^7*g^3*z^4 - 536*a^4*b^7*c^3*d^5*e^5*f^
4*g^6*z^4 - 536*a^4*b^7*c^3*d^4*e^6*f^5*g^5*z^4 - 536*a^3*b^7*c^4*d^6*e^4*f^5*g^5*z^4 - 536*a^3*b^7*c^4*d^5*e^
5*f^6*g^4*z^4 - 504*a^5*b^7*c^2*d^4*e^6*f^3*g^7*z^4 - 504*a^5*b^7*c^2*d^3*e^7*f^4*g^6*z^4 - 504*a^2*b^7*c^5*d^
7*e^3*f^6*g^4*z^4 - 504*a^2*b^7*c^5*d^6*e^4*f^7*g^3*z^4 + 416*a^3*b^8*c^3*d^8*e^2*f^2*g^8*z^4 + 416*a^3*b^8*c^
3*d^2*e^8*f^8*g^2*z^4 - 352*a^6*b^5*c^3*d^4*e^6*f^3*g^7*z^4 - 352*a^6*b^5*c^3*d^3*e^7*f^4*g^6*z^4 - 352*a^3*b^
5*c^6*d^7*e^3*f^6*g^4*z^4 - 352*a^3*b^5*c^6*d^6*e^4*f^7*g^3*z^4 - 248*a^3*b^9*c^2*d^7*e^3*f^2*g^8*z^4 - 248*a^
3*b^9*c^2*d^2*e^8*f^7*g^3*z^4 - 248*a^2*b^9*c^3*d^8*e^2*f^3*g^7*z^4 - 248*a^2*b^9*c^3*d^3*e^7*f^8*g^2*z^4 + 24
6*a^4*b^8*c^2*d^6*e^4*f^2*g^8*z^4 + 246*a^4*b^8*c^2*d^2*e^8*f^6*g^4*z^4 + 246*a^2*b^8*c^4*d^8*e^2*f^4*g^6*z^4
+ 246*a^2*b^8*c^4*d^4*e^6*f^8*g^2*z^4 + 208*a^6*b^2*c^6*d^8*e^2*f^2*g^8*z^4 + 208*a^6*b^2*c^6*d^2*e^8*f^8*g^2*
z^4 + 168*a^2*b^10*c^2*d^7*e^3*f^3*g^7*z^4 + 168*a^2*b^10*c^2*d^3*e^7*f^7*g^3*z^4 + 160*a^3*b^9*c^2*d^5*e^5*f^
4*g^6*z^4 + 160*a^3*b^9*c^2*d^4*e^6*f^5*g^5*z^4 + 160*a^2*b^9*c^3*d^6*e^4*f^5*g^5*z^4 + 160*a^2*b^9*c^3*d^5*e^
5*f^6*g^4*z^4 + 144*a^5*b^5*c^4*d^7*e^3*f^2*g^8*z^4 + 144*a^5*b^5*c^4*d^2*e^8*f^7*g^3*z^4 + 144*a^4*b^5*c^5*d^
8*e^2*f^3*g^7*z^4 + 144*a^4*b^5*c^5*d^3*e^7*f^8*g^2*z^4 - 144*a^2*b^10*c^2*d^6*e^4*f^4*g^6*z^4 - 144*a^2*b^10*
c^2*d^4*e^6*f^6*g^4*z^4 + 120*a^4*b^7*c^3*d^6*e^4*f^3*g^7*z^4 + 120*a^4*b^7*c^3*d^3*e^7*f^6*g^4*z^4 + 120*a^3*
b^7*c^4*d^7*e^3*f^4*g^6*z^4 + 120*a^3*b^7*c^4*d^4*e^6*f^7*g^3*z^4 + 96*a^5*b^5*c^4*d^6*e^4*f^3*g^7*z^4 + 96*a^
5*b^5*c^4*d^3*e^7*f^6*g^4*z^4 + 96*a^4*b^5*c^5*d^7*e^3*f^4*g^6*z^4 + 96*a^4*b^5*c^5*d^4*e^6*f^7*g^3*z^4 + 64*a
^3*b^9*c^2*d^6*e^4*f^3*g^7*z^4 + 64*a^3*b^9*c^2*d^3*e^7*f^6*g^4*z^4 + 64*a^2*b^9*c^3*d^7*e^3*f^4*g^6*z^4 + 64*
a^2*b^9*c^3*d^4*e^6*f^7*g^3*z^4 - 36*a^2*b^10*c^2*d^8*e^2*f^2*g^8*z^4 - 36*a^2*b^10*c^2*d^2*e^8*f^8*g^2*z^4 +
24*a^2*b^10*c^2*d^5*e^5*f^5*g^5*z^4 - 24*a^9*b^4*c*d*e^9*f*g^9*z^4 - 24*a*b^4*c^9*d^9*e*f^9*g*z^4 + 2688*a^7*b
^2*c^5*d^7*e^3*f*g^9*z^4 + 2688*a^7*b^2*c^5*d*e^9*f^7*g^3*z^4 + 2688*a^5*b^2*c^7*d^9*e*f^3*g^7*z^4 + 2688*a^5*
b^2*c^7*d^3*e^7*f^9*g*z^4 - 2560*a^7*b^3*c^4*d^6*e^4*f*g^9*z^4 - 2560*a^7*b^3*c^4*d*e^9*f^6*g^4*z^4 - 2560*a^4
*b^3*c^7*d^9*e*f^4*g^6*z^4 - 2560*a^4*b^3*c^7*d^4*e^6*f^9*g*z^4 + 2112*a^8*b^2*c^4*d^5*e^5*f*g^9*z^4 + 2112*a^
8*b^2*c^4*d*e^9*f^5*g^5*z^4 + 2112*a^4*b^2*c^8*d^9*e*f^5*g^5*z^4 + 2112*a^4*b^2*c^8*d^5*e^5*f^9*g*z^4 + 1664*a
^6*b^5*c^3*d^6*e^4*f*g^9*z^4 + 1664*a^6*b^5*c^3*d*e^9*f^6*g^4*z^4 + 1664*a^3*b^5*c^6*d^9*e*f^4*g^6*z^4 + 1664*
a^3*b^5*c^6*d^4*e^6*f^9*g*z^4 + 1536*a^8*b*c^5*d^4*e^6*f^3*g^7*z^4 + 1536*a^8*b*c^5*d^3*e^7*f^4*g^6*z^4 + 1536
*a^7*b*c^6*d^5*e^5*f^4*g^6*z^4 + 1536*a^7*b*c^6*d^4*e^6*f^5*g^5*z^4 + 1536*a^6*b*c^7*d^6*e^4*f^5*g^5*z^4 + 153
6*a^6*b*c^7*d^5*e^5*f^6*g^4*z^4 + 1536*a^5*b*c^8*d^7*e^3*f^6*g^4*z^4 + 1536*a^5*b*c^8*d^6*e^4*f^7*g^3*z^4 - 14
08*a^8*b^3*c^3*d^4*e^6*f*g^9*z^4 - 1408*a^8*b^3*c^3*d*e^9*f^4*g^6*z^4 - 1408*a^3*b^3*c^8*d^9*e*f^6*g^4*z^4 - 1
408*a^3*b^3*c^8*d^6*e^4*f^9*g*z^4 - 1280*a^7*b*c^6*d^7*e^3*f^2*g^8*z^4 - 1280*a^7*b*c^6*d^2*e^8*f^7*g^3*z^4 -
1280*a^6*b*c^7*d^8*e^2*f^3*g^7*z^4 - 1280*a^6*b*c^7*d^3*e^7*f^8*g^2*z^4 - 1152*a^6*b^3*c^5*d^8*e^2*f*g^9*z^4 -
1152*a^6*b^3*c^5*d*e^9*f^8*g^2*z^4 - 1152*a^5*b^3*c^6*d^9*e*f^2*g^8*z^4 - 1152*a^5*b^3*c^6*d^2*e^8*f^9*g*z^4
+ 1056*a^5*b^5*c^4*d^8*e^2*f*g^9*z^4 + 1056*a^5*b^5*c^4*d*e^9*f^8*g^2*z^4 + 1056*a^4*b^5*c^5*d^9*e*f^2*g^8*z^4
+ 1056*a^4*b^5*c^5*d^2*e^8*f^9*g*z^4 + 864*a^7*b^5*c^2*d^4*e^6*f*g^9*z^4 + 864*a^7*b^5*c^2*d*e^9*f^4*g^6*z^4
+ 864*a^2*b^5*c^7*d^9*e*f^6*g^4*z^4 + 864*a^2*b^5*c^7*d^6*e^4*f^9*g*z^4 - 800*a^6*b^4*c^4*d^7*e^3*f*g^9*z^4 -
800*a^6*b^4*c^4*d*e^9*f^7*g^3*z^4 - 800*a^4*b^4*c^6*d^9*e*f^3*g^7*z^4 - 800*a^4*b^4*c^6*d^3*e^7*f^9*g*z^4 - 76
8*a^8*b*c^5*d^5*e^5*f^2*g^8*z^4 - 768*a^8*b*c^5*d^2*e^8*f^5*g^5*z^4 - 768*a^5*b*c^8*d^8*e^2*f^5*g^5*z^4 - 768*
a^5*b*c^8*d^5*e^5*f^8*g^2*z^4 + 640*a^9*b^2*c^3*d^3*e^7*f*g^9*z^4 + 640*a^9*b^2*c^3*d*e^9*f^3*g^7*z^4 + 640*a^
3*b^2*c^9*d^9*e*f^7*g^3*z^4 + 640*a^3*b^2*c^9*d^7*e^3*f^9*g*z^4 + 512*a^7*b*c^6*d^6*e^4*f^3*g^7*z^4 + 512*a^7*
b*c^6*d^3*e^7*f^6*g^4*z^4 + 512*a^6*b*c^7*d^7*e^3*f^4*g^6*z^4 + 512*a^6*b*c^7*d^4*e^6*f^7*g^3*z^4 - 480*a^5*b^
8*c*d^3*e^7*f^3*g^7*z^4 - 480*a*b^8*c^5*d^7*e^3*f^7*g^3*z^4 - 400*a^7*b^4*c^3*d^5*e^5*f*g^9*z^4 - 400*a^7*b^4*
c^3*d*e^9*f^5*g^5*z^4 - 400*a^3*b^4*c^7*d^9*e*f^5*g^5*z^4 - 400*a^3*b^4*c^7*d^5*e^5*f^9*g*z^4 - 372*a^6*b^6*c^
2*d^5*e^5*f*g^9*z^4 - 372*a^6*b^6*c^2*d*e^9*f^5*g^5*z^4 - 372*a^2*b^6*c^6*d^9*e*f^5*g^5*z^4 - 372*a^2*b^6*c^6*
d^5*e^5*f^9*g*z^4 - 328*a^5*b^6*c^3*d^7*e^3*f*g^9*z^4 - 328*a^5*b^6*c^3*d*e^9*f^7*g^3*z^4 - 328*a^3*b^6*c^5*d^
9*e*f^3*g^7*z^4 - 328*a^3*b^6*c^5*d^3*e^7*f^9*g*z^4 - 288*a^8*b^4*c^2*d^3*e^7*f*g^9*z^4 - 288*a^8*b^4*c^2*d*e^
9*f^3*g^7*z^4 - 288*a^5*b^7*c^2*d^6*e^4*f*g^9*z^4 - 288*a^5*b^7*c^2*d*e^9*f^6*g^4*z^4 - 288*a^2*b^7*c^5*d^9*e*
f^4*g^6*z^4 - 288*a^2*b^7*c^5*d^4*e^6*f^9*g*z^4 - 288*a^2*b^4*c^8*d^9*e*f^7*g^3*z^4 - 288*a^2*b^4*c^8*d^7*e^3*
f^9*g*z^4 - 280*a^4*b^7*c^3*d^8*e^2*f*g^9*z^4 - 280*a^4*b^7*c^3*d*e^9*f^8*g^2*z^4 - 280*a^3*b^7*c^4*d^9*e*f^2*
g^8*z^4 - 280*a^3*b^7*c^4*d^2*e^8*f^9*g*z^4 + 256*a^9*b*c^4*d^3*e^7*f^2*g^8*z^4 + 256*a^9*b*c^4*d^2*e^8*f^3*g^
7*z^4 + 256*a^4*b*c^9*d^8*e^2*f^7*g^3*z^4 + 256*a^4*b*c^9*d^7*e^3*f^8*g^2*z^4 - 248*a^7*b^6*c*d^2*e^8*f^2*g^8*
z^4 - 248*a*b^6*c^7*d^8*e^2*f^8*g^2*z^4 + 236*a^6*b^7*c*d^3*e^7*f^2*g^8*z^4 + 236*a^6*b^7*c*d^2*e^8*f^3*g^7*z^
4 + 236*a*b^7*c^6*d^8*e^2*f^7*g^3*z^4 + 236*a*b^7*c^6*d^7*e^3*f^8*g^2*z^4 + 200*a^4*b^9*c*d^4*e^6*f^3*g^7*z^4
+ 200*a^4*b^9*c*d^3*e^7*f^4*g^6*z^4 - 200*a^3*b^10*c*d^4*e^6*f^4*g^6*z^4 - 200*a*b^10*c^3*d^6*e^4*f^6*g^4*z^4
+ 200*a*b^9*c^4*d^7*e^3*f^6*g^4*z^4 + 200*a*b^9*c^4*d^6*e^4*f^7*g^3*z^4 - 196*a^4*b^9*c*d^5*e^5*f^2*g^8*z^4 -
196*a^4*b^9*c*d^2*e^8*f^5*g^5*z^4 - 196*a*b^9*c^4*d^8*e^2*f^5*g^5*z^4 - 196*a*b^9*c^4*d^5*e^5*f^8*g^2*z^4 - 19
2*a^9*b^3*c^2*d^2*e^8*f*g^9*z^4 - 192*a^9*b^3*c^2*d*e^9*f^2*g^8*z^4 - 192*a^2*b^3*c^9*d^9*e*f^8*g^2*z^4 - 192*
a^2*b^3*c^9*d^8*e^2*f^9*g*z^4 + 156*a^4*b^8*c^2*d^7*e^3*f*g^9*z^4 + 156*a^4*b^8*c^2*d*e^9*f^7*g^3*z^4 + 156*a^
2*b^8*c^4*d^9*e*f^3*g^7*z^4 + 156*a^2*b^8*c^4*d^3*e^7*f^9*g*z^4 + 96*a^5*b^8*c*d^4*e^6*f^2*g^8*z^4 + 96*a^5*b^
8*c*d^2*e^8*f^4*g^6*z^4 + 96*a*b^8*c^5*d^8*e^2*f^6*g^4*z^4 + 96*a*b^8*c^5*d^6*e^4*f^8*g^2*z^4 + 88*a^3*b^10*c*
d^5*e^5*f^3*g^7*z^4 + 88*a^3*b^10*c*d^3*e^7*f^5*g^5*z^4 + 88*a*b^10*c^3*d^7*e^3*f^5*g^5*z^4 + 88*a*b^10*c^3*d^
5*e^5*f^7*g^3*z^4 - 36*a^2*b^11*c*d^6*e^4*f^3*g^7*z^4 - 36*a^2*b^11*c*d^3*e^7*f^6*g^4*z^4 - 36*a*b^11*c^2*d^7*
e^3*f^4*g^6*z^4 - 36*a*b^11*c^2*d^4*e^6*f^7*g^3*z^4 + 28*a^3*b^10*c*d^6*e^4*f^2*g^8*z^4 + 28*a^3*b^10*c*d^2*e^
8*f^6*g^4*z^4 + 28*a*b^10*c^3*d^8*e^2*f^4*g^6*z^4 + 28*a*b^10*c^3*d^4*e^6*f^8*g^2*z^4 + 24*a^3*b^9*c^2*d^8*e^2
*f*g^9*z^4 + 24*a^3*b^9*c^2*d*e^9*f^8*g^2*z^4 + 24*a^2*b^11*c*d^7*e^3*f^2*g^8*z^4 + 24*a^2*b^11*c*d^2*e^8*f^7*
g^3*z^4 + 24*a^2*b^9*c^3*d^9*e*f^2*g^8*z^4 + 24*a^2*b^9*c^3*d^2*e^8*f^9*g*z^4 + 24*a*b^11*c^2*d^8*e^2*f^3*g^7*
z^4 + 24*a*b^11*c^2*d^3*e^7*f^8*g^2*z^4 + 12*a^2*b^11*c*d^5*e^5*f^4*g^6*z^4 + 12*a^2*b^11*c*d^4*e^6*f^5*g^5*z^
4 + 12*a*b^11*c^2*d^6*e^4*f^5*g^5*z^4 + 12*a*b^11*c^2*d^5*e^5*f^6*g^4*z^4 + 40*b^10*c^4*d^7*e^3*f^7*g^3*z^4 +
20*b^12*c^2*d^6*e^4*f^6*g^4*z^4 - 20*b^11*c^3*d^7*e^3*f^6*g^4*z^4 - 20*b^11*c^3*d^6*e^4*f^7*g^3*z^4 - 20*b^9*c
^5*d^8*e^2*f^7*g^3*z^4 - 20*b^9*c^5*d^7*e^3*f^8*g^2*z^4 + 20*b^8*c^6*d^8*e^2*f^8*g^2*z^4 + 16*b^11*c^3*d^8*e^2
*f^5*g^5*z^4 + 16*b^11*c^3*d^5*e^5*f^8*g^2*z^4 - 6*b^12*c^2*d^8*e^2*f^4*g^6*z^4 - 6*b^12*c^2*d^4*e^6*f^8*g^2*z
^4 - 5*b^10*c^4*d^8*e^2*f^6*g^4*z^4 - 5*b^10*c^4*d^6*e^4*f^8*g^2*z^4 - 4*b^12*c^2*d^7*e^3*f^5*g^5*z^4 - 4*b^12
*c^2*d^5*e^5*f^7*g^3*z^4 - 4608*a^7*c^7*d^5*e^5*f^5*g^5*z^4 + 3328*a^7*c^7*d^6*e^4*f^4*g^6*z^4 + 3328*a^7*c^7*
d^4*e^6*f^6*g^4*z^4 - 3072*a^8*c^6*d^5*e^5*f^3*g^7*z^4 + 3072*a^8*c^6*d^4*e^6*f^4*g^6*z^4 - 3072*a^8*c^6*d^3*e
^7*f^5*g^5*z^4 - 3072*a^6*c^8*d^7*e^3*f^5*g^5*z^4 + 3072*a^6*c^8*d^6*e^4*f^6*g^4*z^4 - 3072*a^6*c^8*d^5*e^5*f^
7*g^3*z^4 - 2048*a^9*c^5*d^3*e^7*f^3*g^7*z^4 - 2048*a^7*c^7*d^7*e^3*f^3*g^7*z^4 - 2048*a^7*c^7*d^3*e^7*f^7*g^3
*z^4 - 2048*a^5*c^9*d^7*e^3*f^7*g^3*z^4 + 1792*a^8*c^6*d^6*e^4*f^2*g^8*z^4 + 1792*a^8*c^6*d^2*e^8*f^6*g^4*z^4
+ 1792*a^6*c^8*d^8*e^2*f^4*g^6*z^4 + 1792*a^6*c^8*d^4*e^6*f^8*g^2*z^4 + 1408*a^9*c^5*d^4*e^6*f^2*g^8*z^4 + 140
8*a^9*c^5*d^2*e^8*f^4*g^6*z^4 + 1408*a^5*c^9*d^8*e^2*f^6*g^4*z^4 + 1408*a^5*c^9*d^6*e^4*f^8*g^2*z^4 + 1088*a^7
*c^7*d^8*e^2*f^2*g^8*z^4 + 1088*a^7*c^7*d^2*e^8*f^8*g^2*z^4 + 512*a^10*c^4*d^2*e^8*f^2*g^8*z^4 + 512*a^4*c^10*
d^8*e^2*f^8*g^2*z^4 + 40*a^4*b^10*d^3*e^7*f^3*g^7*z^4 + 20*a^6*b^8*d^2*e^8*f^2*g^8*z^4 - 20*a^5*b^9*d^3*e^7*f^
2*g^8*z^4 - 20*a^5*b^9*d^2*e^8*f^3*g^7*z^4 - 20*a^3*b^11*d^4*e^6*f^3*g^7*z^4 - 20*a^3*b^11*d^3*e^7*f^4*g^6*z^4
+ 20*a^2*b^12*d^4*e^6*f^4*g^6*z^4 + 16*a^3*b^11*d^5*e^5*f^2*g^8*z^4 + 16*a^3*b^11*d^2*e^8*f^5*g^5*z^4 - 6*a^2
*b^12*d^6*e^4*f^2*g^8*z^4 - 6*a^2*b^12*d^2*e^8*f^6*g^4*z^4 - 5*a^4*b^10*d^4*e^6*f^2*g^8*z^4 - 5*a^4*b^10*d^2*e
^8*f^4*g^6*z^4 - 4*a^2*b^12*d^5*e^5*f^3*g^7*z^4 - 4*a^2*b^12*d^3*e^7*f^5*g^5*z^4 + 480*a^8*b^2*c^4*e^10*f^6*g^
4*z^4 - 440*a^7*b^4*c^3*e^10*f^6*g^4*z^4 + 320*a^8*b^3*c^3*e^10*f^5*g^5*z^4 + 320*a^7*b^3*c^4*e^10*f^7*g^3*z^4
- 240*a^8*b^4*c^2*e^10*f^4*g^6*z^4 - 240*a^6*b^4*c^4*e^10*f^8*g^2*z^4 + 192*a^9*b^3*c^2*e^10*f^3*g^7*z^4 + 19
2*a^9*b^2*c^3*e^10*f^4*g^6*z^4 + 192*a^7*b^2*c^5*e^10*f^8*g^2*z^4 + 90*a^6*b^6*c^2*e^10*f^6*g^4*z^4 + 68*a^5*b
^6*c^3*e^10*f^8*g^2*z^4 - 48*a^10*b^2*c^2*e^10*f^2*g^8*z^4 + 48*a^7*b^5*c^2*e^10*f^5*g^5*z^4 + 48*a^6*b^5*c^3*
e^10*f^7*g^3*z^4 - 36*a^5*b^7*c^2*e^10*f^7*g^3*z^4 - 6*a^4*b^8*c^2*e^10*f^8*g^2*z^4 + 480*a^4*b^2*c^8*d^10*f^4
*g^6*z^4 - 440*a^3*b^4*c^7*d^10*f^4*g^6*z^4 + 320*a^4*b^3*c^7*d^10*f^3*g^7*z^4 + 320*a^3*b^3*c^8*d^10*f^5*g^5*
z^4 - 240*a^4*b^4*c^6*d^10*f^2*g^8*z^4 - 240*a^2*b^4*c^8*d^10*f^6*g^4*z^4 + 192*a^5*b^2*c^7*d^10*f^2*g^8*z^4 +
192*a^3*b^2*c^9*d^10*f^6*g^4*z^4 + 192*a^2*b^3*c^9*d^10*f^7*g^3*z^4 + 90*a^2*b^6*c^6*d^10*f^4*g^6*z^4 + 68*a^
3*b^6*c^5*d^10*f^2*g^8*z^4 + 48*a^3*b^5*c^6*d^10*f^3*g^7*z^4 + 48*a^2*b^5*c^7*d^10*f^5*g^5*z^4 - 48*a^2*b^2*c^
10*d^10*f^8*g^2*z^4 - 36*a^2*b^7*c^5*d^10*f^3*g^7*z^4 - 6*a^2*b^8*c^4*d^10*f^2*g^8*z^4 + 480*a^8*b^2*c^4*d^6*e
^4*g^10*z^4 - 440*a^7*b^4*c^3*d^6*e^4*g^10*z^4 + 320*a^8*b^3*c^3*d^5*e^5*g^10*z^4 + 320*a^7*b^3*c^4*d^7*e^3*g^
10*z^4 - 240*a^8*b^4*c^2*d^4*e^6*g^10*z^4 - 240*a^6*b^4*c^4*d^8*e^2*g^10*z^4 + 192*a^9*b^3*c^2*d^3*e^7*g^10*z^
4 + 192*a^9*b^2*c^3*d^4*e^6*g^10*z^4 + 192*a^7*b^2*c^5*d^8*e^2*g^10*z^4 + 90*a^6*b^6*c^2*d^6*e^4*g^10*z^4 + 68
*a^5*b^6*c^3*d^8*e^2*g^10*z^4 - 48*a^10*b^2*c^2*d^2*e^8*g^10*z^4 + 48*a^7*b^5*c^2*d^5*e^5*g^10*z^4 + 48*a^6*b^
5*c^3*d^7*e^3*g^10*z^4 - 36*a^5*b^7*c^2*d^7*e^3*g^10*z^4 - 6*a^4*b^8*c^2*d^8*e^2*g^10*z^4 + 480*a^4*b^2*c^8*d^
4*e^6*f^10*z^4 - 440*a^3*b^4*c^7*d^4*e^6*f^10*z^4 + 320*a^4*b^3*c^7*d^3*e^7*f^10*z^4 + 320*a^3*b^3*c^8*d^5*e^5
*f^10*z^4 - 240*a^4*b^4*c^6*d^2*e^8*f^10*z^4 - 240*a^2*b^4*c^8*d^6*e^4*f^10*z^4 + 192*a^5*b^2*c^7*d^2*e^8*f^10
*z^4 + 192*a^3*b^2*c^9*d^6*e^4*f^10*z^4 + 192*a^2*b^3*c^9*d^7*e^3*f^10*z^4 + 90*a^2*b^6*c^6*d^4*e^6*f^10*z^4 +
68*a^3*b^6*c^5*d^2*e^8*f^10*z^4 + 48*a^3*b^5*c^6*d^3*e^7*f^10*z^4 + 48*a^2*b^5*c^7*d^5*e^5*f^10*z^4 - 48*a^2*
b^2*c^10*d^8*e^2*f^10*z^4 - 36*a^2*b^7*c^5*d^3*e^7*f^10*z^4 - 6*a^2*b^8*c^4*d^2*e^8*f^10*z^4 + 16*b^9*c^5*d^9*
e*f^6*g^4*z^4 + 16*b^9*c^5*d^6*e^4*f^9*g*z^4 - 14*b^10*c^4*d^9*e*f^5*g^5*z^4 - 14*b^10*c^4*d^5*e^5*f^9*g*z^4 +
4*b^13*c*d^7*e^3*f^4*g^6*z^4 - 4*b^13*c*d^6*e^4*f^5*g^5*z^4 - 4*b^13*c*d^5*e^5*f^6*g^4*z^4 + 4*b^13*c*d^4*e^6
*f^7*g^3*z^4 + 4*b^11*c^3*d^9*e*f^4*g^6*z^4 + 4*b^11*c^3*d^4*e^6*f^9*g*z^4 - 4*b^8*c^6*d^9*e*f^7*g^3*z^4 - 4*b
^8*c^6*d^7*e^3*f^9*g*z^4 - 4*b^7*c^7*d^9*e*f^8*g^2*z^4 - 4*b^7*c^7*d^8*e^2*f^9*g*z^4 - 768*a^9*c^5*d^5*e^5*f*g
^9*z^4 - 768*a^9*c^5*d*e^9*f^5*g^5*z^4 - 768*a^5*c^9*d^9*e*f^5*g^5*z^4 - 768*a^5*c^9*d^5*e^5*f^9*g*z^4 - 512*a
^10*c^4*d^3*e^7*f*g^9*z^4 - 512*a^10*c^4*d*e^9*f^3*g^7*z^4 - 512*a^8*c^6*d^7*e^3*f*g^9*z^4 - 512*a^8*c^6*d*e^9
*f^7*g^3*z^4 - 512*a^6*c^8*d^9*e*f^3*g^7*z^4 - 512*a^6*c^8*d^3*e^7*f^9*g*z^4 - 512*a^4*c^10*d^9*e*f^7*g^3*z^4
- 512*a^4*c^10*d^7*e^3*f^9*g*z^4 + 16*a^5*b^9*d^4*e^6*f*g^9*z^4 + 16*a^5*b^9*d*e^9*f^4*g^6*z^4 - 14*a^4*b^10*d
^5*e^5*f*g^9*z^4 - 14*a^4*b^10*d*e^9*f^5*g^5*z^4 - 4*a^7*b^7*d^2*e^8*f*g^9*z^4 - 4*a^7*b^7*d*e^9*f^2*g^8*z^4 -
4*a^6*b^8*d^3*e^7*f*g^9*z^4 - 4*a^6*b^8*d*e^9*f^3*g^7*z^4 + 4*a^3*b^11*d^6*e^4*f*g^9*z^4 + 4*a^3*b^11*d*e^9*f
^6*g^4*z^4 + 4*a*b^13*d^6*e^4*f^3*g^7*z^4 - 4*a*b^13*d^5*e^5*f^4*g^6*z^4 - 4*a*b^13*d^4*e^6*f^5*g^5*z^4 + 4*a*
b^13*d^3*e^7*f^6*g^4*z^4 - 768*a^9*b*c^4*e^10*f^5*g^5*z^4 - 768*a^8*b*c^5*e^10*f^7*g^3*z^4 - 256*a^10*b*c^3*e^
10*f^3*g^7*z^4 + 192*a^6*b^3*c^5*e^10*f^9*g*z^4 + 68*a^7*b^6*c*e^10*f^4*g^6*z^4 - 48*a^8*b^5*c*e^10*f^3*g^7*z^
4 - 48*a^5*b^5*c^4*e^10*f^9*g*z^4 - 36*a^6*b^7*c*e^10*f^5*g^5*z^4 + 12*a^9*b^4*c*e^10*f^2*g^8*z^4 + 4*a^4*b^9*
c*e^10*f^7*g^3*z^4 + 4*a^4*b^7*c^3*e^10*f^9*g*z^4 - 768*a^5*b*c^8*d^10*f^3*g^7*z^4 - 768*a^4*b*c^9*d^10*f^5*g^
5*z^4 - 256*a^3*b*c^10*d^10*f^7*g^3*z^4 + 192*a^5*b^3*c^6*d^10*f*g^9*z^4 + 68*a*b^6*c^7*d^10*f^6*g^4*z^4 - 48*
a^4*b^5*c^5*d^10*f*g^9*z^4 - 48*a*b^5*c^8*d^10*f^7*g^3*z^4 - 36*a*b^7*c^6*d^10*f^5*g^5*z^4 + 12*a*b^4*c^9*d^10
*f^8*g^2*z^4 + 4*a^3*b^7*c^4*d^10*f*g^9*z^4 + 4*a*b^9*c^4*d^10*f^3*g^7*z^4 - 768*a^9*b*c^4*d^5*e^5*g^10*z^4 -
768*a^8*b*c^5*d^7*e^3*g^10*z^4 - 256*a^10*b*c^3*d^3*e^7*g^10*z^4 + 192*a^6*b^3*c^5*d^9*e*g^10*z^4 + 68*a^7*b^6
*c*d^4*e^6*g^10*z^4 - 48*a^8*b^5*c*d^3*e^7*g^10*z^4 - 48*a^5*b^5*c^4*d^9*e*g^10*z^4 - 36*a^6*b^7*c*d^5*e^5*g^1
0*z^4 + 12*a^9*b^4*c*d^2*e^8*g^10*z^4 + 4*a^4*b^9*c*d^7*e^3*g^10*z^4 + 4*a^4*b^7*c^3*d^9*e*g^10*z^4 - 768*a^5*
b*c^8*d^3*e^7*f^10*z^4 - 768*a^4*b*c^9*d^5*e^5*f^10*z^4 - 256*a^3*b*c^10*d^7*e^3*f^10*z^4 + 192*a^5*b^3*c^6*d*
e^9*f^10*z^4 + 68*a*b^6*c^7*d^6*e^4*f^10*z^4 - 48*a^4*b^5*c^5*d*e^9*f^10*z^4 - 48*a*b^5*c^8*d^7*e^3*f^10*z^4 -
36*a*b^7*c^6*d^5*e^5*f^10*z^4 + 12*a*b^4*c^9*d^8*e^2*f^10*z^4 + 4*a^3*b^7*c^4*d*e^9*f^10*z^4 + 4*a*b^9*c^4*d^
3*e^7*f^10*z^4 + 2*b^6*c^8*d^9*e*f^9*g*z^4 - 128*a^11*c^3*d*e^9*f*g^9*z^4 - 128*a^7*c^7*d^9*e*f*g^9*z^4 - 128*
a^7*c^7*d*e^9*f^9*g*z^4 - 128*a^3*c^11*d^9*e*f^9*g*z^4 + 2*a^8*b^6*d*e^9*f*g^9*z^4 - 256*a^7*b*c^6*e^10*f^9*g*
z^4 - 256*a^6*b*c^7*d^10*f*g^9*z^4 - 256*a^7*b*c^6*d^9*e*g^10*z^4 - 256*a^6*b*c^7*d*e^9*f^10*z^4 + 2*b^14*d^5*
e^5*f^5*g^5*z^4 + 384*a^9*c^5*e^10*f^6*g^4*z^4 + 256*a^10*c^4*e^10*f^4*g^6*z^4 + 256*a^8*c^6*e^10*f^8*g^2*z^4
+ 64*a^11*c^3*e^10*f^2*g^8*z^4 - 6*b^8*c^6*d^10*f^6*g^4*z^4 + 4*b^9*c^5*d^10*f^5*g^5*z^4 + 4*b^7*c^7*d^10*f^7*
g^3*z^4 + 384*a^5*c^9*d^10*f^4*g^6*z^4 + 256*a^6*c^8*d^10*f^2*g^8*z^4 + 256*a^4*c^10*d^10*f^6*g^4*z^4 + 64*a^3
*c^11*d^10*f^8*g^2*z^4 - 6*a^6*b^8*e^10*f^4*g^6*z^4 + 4*a^7*b^7*e^10*f^3*g^7*z^4 + 4*a^5*b^9*e^10*f^5*g^5*z^4
+ 384*a^9*c^5*d^6*e^4*g^10*z^4 + 256*a^10*c^4*d^4*e^6*g^10*z^4 + 256*a^8*c^6*d^8*e^2*g^10*z^4 + 64*a^11*c^3*d^
2*e^8*g^10*z^4 - 6*b^8*c^6*d^6*e^4*f^10*z^4 + 4*b^9*c^5*d^5*e^5*f^10*z^4 + 4*b^7*c^7*d^7*e^3*f^10*z^4 + 384*a^
5*c^9*d^4*e^6*f^10*z^4 + 256*a^6*c^8*d^2*e^8*f^10*z^4 + 256*a^4*c^10*d^6*e^4*f^10*z^4 + 64*a^3*c^11*d^8*e^2*f^
10*z^4 - 6*a^6*b^8*d^4*e^6*g^10*z^4 + 4*a^7*b^7*d^3*e^7*g^10*z^4 + 4*a^5*b^9*d^5*e^5*g^10*z^4 - 48*a^6*b^2*c^6
*e^10*f^10*z^4 - 48*a^6*b^2*c^6*d^10*g^10*z^4 + 12*a^5*b^4*c^5*e^10*f^10*z^4 + 12*a^5*b^4*c^5*d^10*g^10*z^4 +
64*a^7*c^7*e^10*f^10*z^4 + 64*a^7*c^7*d^10*g^10*z^4 - b^14*d^6*e^4*f^4*g^6*z^4 - b^14*d^4*e^6*f^6*g^4*z^4 - b^
10*c^4*d^10*f^4*g^6*z^4 - b^6*c^8*d^10*f^8*g^2*z^4 - a^8*b^6*e^10*f^2*g^8*z^4 - a^4*b^10*e^10*f^6*g^4*z^4 - b^
10*c^4*d^4*e^6*f^10*z^4 - b^6*c^8*d^8*e^2*f^10*z^4 - a^8*b^6*d^2*e^8*g^10*z^4 - a^4*b^10*d^6*e^4*g^10*z^4 - a^
4*b^6*c^4*e^10*f^10*z^4 - a^4*b^6*c^4*d^10*g^10*z^4 + 272*a^5*b^2*c^3*d*e^7*f*g^7*z^2 - 192*a^4*b^4*c^2*d*e^7*
f*g^7*z^2 - 164*a^5*b*c^4*d^2*e^6*f*g^7*z^2 - 164*a^5*b*c^4*d*e^7*f^2*g^6*z^2 + 120*a^2*b^2*c^6*d^7*e*f*g^7*z^
2 + 120*a^2*b^2*c^6*d*e^7*f^7*g*z^2 + 120*a*b^2*c^7*d^7*e*f^3*g^5*z^2 + 120*a*b^2*c^7*d^3*e^5*f^7*g*z^2 - 76*a
^4*b*c^5*d^4*e^4*f*g^7*z^2 - 76*a^4*b*c^5*d*e^7*f^4*g^4*z^2 - 76*a^3*b*c^6*d^6*e^2*f*g^7*z^2 - 76*a^3*b*c^6*d*
e^7*f^6*g^2*z^2 - 64*a*b^3*c^6*d^7*e*f^2*g^6*z^2 - 64*a*b^3*c^6*d^2*e^6*f^7*g*z^2 - 60*a^2*b*c^7*d^7*e*f^2*g^6
*z^2 - 60*a^2*b*c^7*d^2*e^6*f^7*g*z^2 + 44*a*b*c^8*d^6*e^2*f^5*g^3*z^2 + 44*a*b*c^8*d^5*e^3*f^6*g^2*z^2 + 22*a
*b^5*c^4*d^6*e^2*f*g^7*z^2 + 22*a*b^5*c^4*d*e^7*f^6*g^2*z^2 - 20*a^2*b^7*c*d^2*e^6*f*g^7*z^2 - 20*a^2*b^7*c*d*
e^7*f^2*g^6*z^2 + 8*a*b^8*c*d^2*e^6*f^2*g^6*z^2 - 8*a*b^6*c^3*d^5*e^3*f*g^7*z^2 - 8*a*b^6*c^3*d*e^7*f^5*g^3*z^
2 + 2*a*b^7*c^2*d^4*e^4*f*g^7*z^2 + 2*a*b^7*c^2*d*e^7*f^4*g^4*z^2 - 590*a^2*b^2*c^6*d^4*e^4*f^4*g^4*z^2 - 352*
a^2*b^4*c^4*d^3*e^5*f^3*g^5*z^2 - 346*a^3*b^2*c^5*d^4*e^4*f^2*g^6*z^2 - 346*a^3*b^2*c^5*d^2*e^6*f^4*g^4*z^2 -
274*a^4*b^2*c^4*d^2*e^6*f^2*g^6*z^2 + 272*a^3*b^2*c^5*d^3*e^5*f^3*g^5*z^2 + 250*a^2*b^3*c^5*d^4*e^4*f^3*g^5*z^
2 + 250*a^2*b^3*c^5*d^3*e^5*f^4*g^4*z^2 + 204*a^3*b^3*c^4*d^3*e^5*f^2*g^6*z^2 + 204*a^3*b^3*c^4*d^2*e^6*f^3*g^
5*z^2 + 136*a^2*b^2*c^6*d^5*e^3*f^3*g^5*z^2 + 136*a^2*b^2*c^6*d^3*e^5*f^5*g^3*z^2 + 71*a^2*b^4*c^4*d^4*e^4*f^2
*g^6*z^2 + 71*a^2*b^4*c^4*d^2*e^6*f^4*g^4*z^2 - 56*a^2*b^3*c^5*d^5*e^3*f^2*g^6*z^2 - 56*a^2*b^3*c^5*d^2*e^6*f^
5*g^3*z^2 + 18*a^2*b^2*c^6*d^6*e^2*f^2*g^6*z^2 + 18*a^2*b^2*c^6*d^2*e^6*f^6*g^2*z^2 - 16*a^3*b^4*c^3*d^2*e^6*f
^2*g^6*z^2 + 16*a^2*b^5*c^3*d^3*e^5*f^2*g^6*z^2 + 16*a^2*b^5*c^3*d^2*e^6*f^3*g^5*z^2 - 4*a^2*b^6*c^2*d^2*e^6*f
^2*g^6*z^2 + 48*a^3*b^6*c*d*e^7*f*g^7*z^2 - 20*a*b^4*c^5*d^7*e*f*g^7*z^2 - 20*a*b^4*c^5*d*e^7*f^7*g*z^2 - 4*a*
b^8*c*d^3*e^5*f*g^7*z^2 - 4*a*b^8*c*d*e^7*f^3*g^5*z^2 + 4*a*b*c^8*d^7*e*f^4*g^4*z^2 + 4*a*b*c^8*d^4*e^4*f^7*g*
z^2 + 368*a^4*b^2*c^4*d^3*e^5*f*g^7*z^2 + 368*a^4*b^2*c^4*d*e^7*f^3*g^5*z^2 + 264*a^3*b^2*c^5*d^5*e^3*f*g^7*z^
2 + 264*a^3*b^2*c^5*d*e^7*f^5*g^3*z^2 - 208*a^3*b^4*c^3*d^3*e^5*f*g^7*z^2 - 208*a^3*b^4*c^3*d*e^7*f^3*g^5*z^2
- 164*a^4*b*c^5*d^3*e^5*f^2*g^6*z^2 - 164*a^4*b*c^5*d^2*e^6*f^3*g^5*z^2 + 140*a^2*b*c^7*d^5*e^3*f^4*g^4*z^2 +
140*a^2*b*c^7*d^4*e^4*f^5*g^3*z^2 - 122*a*b^2*c^7*d^6*e^2*f^4*g^4*z^2 - 122*a*b^2*c^7*d^4*e^4*f^6*g^2*z^2 - 10
8*a^2*b^3*c^5*d^6*e^2*f*g^7*z^2 - 108*a^2*b^3*c^5*d*e^7*f^6*g^2*z^2 + 102*a*b^3*c^6*d^5*e^3*f^4*g^4*z^2 + 102*
a*b^3*c^6*d^4*e^4*f^5*g^3*z^2 + 80*a*b^6*c^3*d^3*e^5*f^3*g^5*z^2 + 68*a*b^4*c^5*d^6*e^2*f^2*g^6*z^2 + 68*a*b^4
*c^5*d^2*e^6*f^6*g^2*z^2 - 60*a^3*b*c^6*d^5*e^3*f^2*g^6*z^2 + 60*a^3*b*c^6*d^4*e^4*f^3*g^5*z^2 + 60*a^3*b*c^6*
d^3*e^5*f^4*g^4*z^2 - 60*a^3*b*c^6*d^2*e^6*f^5*g^3*z^2 - 54*a^3*b^3*c^4*d^4*e^4*f*g^7*z^2 - 54*a^3*b^3*c^4*d*e
^7*f^4*g^4*z^2 - 52*a*b^4*c^5*d^5*e^3*f^3*g^5*z^2 - 52*a*b^4*c^5*d^3*e^5*f^5*g^3*z^2 + 48*a^3*b^5*c^2*d^2*e^6*
f*g^7*z^2 + 48*a^3*b^5*c^2*d*e^7*f^2*g^6*z^2 + 48*a^2*b^6*c^2*d^3*e^5*f*g^7*z^2 + 48*a^2*b^6*c^2*d*e^7*f^3*g^5
*z^2 + 44*a^4*b^3*c^3*d^2*e^6*f*g^7*z^2 + 44*a^4*b^3*c^3*d*e^7*f^2*g^6*z^2 - 44*a^2*b*c^7*d^6*e^2*f^3*g^5*z^2
- 44*a^2*b*c^7*d^3*e^5*f^6*g^2*z^2 - 44*a*b^3*c^6*d^6*e^2*f^3*g^5*z^2 - 44*a*b^3*c^6*d^3*e^5*f^6*g^2*z^2 - 32*
a*b^5*c^4*d^4*e^4*f^3*g^5*z^2 - 32*a*b^5*c^4*d^3*e^5*f^4*g^4*z^2 - 32*a*b^2*c^7*d^5*e^3*f^5*g^3*z^2 - 20*a*b^7
*c^2*d^3*e^5*f^2*g^6*z^2 - 20*a*b^7*c^2*d^2*e^6*f^3*g^5*z^2 + 20*a*b^4*c^5*d^4*e^4*f^4*g^4*z^2 - 14*a*b^5*c^4*
d^5*e^3*f^2*g^6*z^2 - 14*a*b^5*c^4*d^2*e^6*f^5*g^3*z^2 + 4*a^2*b^5*c^3*d^4*e^4*f*g^7*z^2 + 4*a^2*b^5*c^3*d*e^7
*f^4*g^4*z^2 - 4*a^2*b^4*c^4*d^5*e^3*f*g^7*z^2 - 4*a^2*b^4*c^4*d*e^7*f^5*g^3*z^2 + 2*a*b^6*c^3*d^4*e^4*f^2*g^6
*z^2 + 2*a*b^6*c^3*d^2*e^6*f^4*g^4*z^2 - 50*b^2*c^8*d^6*e^2*f^6*g^2*z^2 - 32*b^4*c^6*d^5*e^3*f^5*g^3*z^2 + 24*
b^3*c^7*d^6*e^2*f^5*g^3*z^2 + 24*b^3*c^7*d^5*e^3*f^6*g^2*z^2 + 23*b^4*c^6*d^6*e^2*f^4*g^4*z^2 + 23*b^4*c^6*d^4
*e^4*f^6*g^2*z^2 - 11*b^6*c^4*d^6*e^2*f^2*g^6*z^2 - 11*b^6*c^4*d^2*e^6*f^6*g^2*z^2 + 8*b^6*c^4*d^5*e^3*f^3*g^5
*z^2 + 8*b^6*c^4*d^3*e^5*f^5*g^3*z^2 - 8*b^5*c^5*d^5*e^3*f^4*g^4*z^2 - 8*b^5*c^5*d^4*e^4*f^5*g^3*z^2 + 5*b^6*c
^4*d^4*e^4*f^4*g^4*z^2 - 4*b^8*c^2*d^3*e^5*f^3*g^5*z^2 + 4*b^7*c^3*d^5*e^3*f^2*g^6*z^2 + 4*b^7*c^3*d^2*e^6*f^5
*g^3*z^2 - 2*b^7*c^3*d^4*e^4*f^3*g^5*z^2 - 2*b^7*c^3*d^3*e^5*f^4*g^4*z^2 - 2*b^5*c^5*d^6*e^2*f^3*g^5*z^2 - 2*b
^5*c^5*d^3*e^5*f^6*g^2*z^2 + 416*a^5*c^5*d^2*e^6*f^2*g^6*z^2 - 392*a^4*c^6*d^3*e^5*f^3*g^5*z^2 + 376*a^4*c^6*d
^4*e^4*f^2*g^6*z^2 + 376*a^4*c^6*d^2*e^6*f^4*g^4*z^2 + 320*a^3*c^7*d^4*e^4*f^4*g^4*z^2 - 280*a^3*c^7*d^5*e^3*f
^3*g^5*z^2 - 280*a^3*c^7*d^3*e^5*f^5*g^3*z^2 - 200*a^2*c^8*d^5*e^3*f^5*g^3*z^2 + 160*a^3*c^7*d^6*e^2*f^2*g^6*z
^2 + 160*a^3*c^7*d^2*e^6*f^6*g^2*z^2 + 120*a^2*c^8*d^6*e^2*f^4*g^4*z^2 + 120*a^2*c^8*d^4*e^4*f^6*g^2*z^2 - 471
*a^4*b^2*c^4*e^8*f^4*g^4*z^2 + 436*a^3*b^4*c^3*e^8*f^4*g^4*z^2 - 310*a^3*b^3*c^4*e^8*f^5*g^3*z^2 - 232*a^5*b^2
*c^3*e^8*f^2*g^6*z^2 + 229*a^2*b^4*c^4*e^8*f^6*g^2*z^2 + 216*a^4*b^4*c^2*e^8*f^2*g^6*z^2 - 204*a^4*b^3*c^3*e^8
*f^3*g^5*z^2 - 150*a^3*b^2*c^5*e^8*f^6*g^2*z^2 - 91*a^2*b^6*c^2*e^8*f^4*g^4*z^2 - 72*a^3*b^5*c^2*e^8*f^3*g^5*z
^2 - 44*a^2*b^5*c^3*e^8*f^5*g^3*z^2 - 471*a^4*b^2*c^4*d^4*e^4*g^8*z^2 + 436*a^3*b^4*c^3*d^4*e^4*g^8*z^2 - 310*
a^3*b^3*c^4*d^5*e^3*g^8*z^2 - 232*a^5*b^2*c^3*d^2*e^6*g^8*z^2 + 229*a^2*b^4*c^4*d^6*e^2*g^8*z^2 + 216*a^4*b^4*
c^2*d^2*e^6*g^8*z^2 - 204*a^4*b^3*c^3*d^3*e^5*g^8*z^2 - 150*a^3*b^2*c^5*d^6*e^2*g^8*z^2 - 91*a^2*b^6*c^2*d^4*e
^4*g^8*z^2 - 72*a^3*b^5*c^2*d^3*e^5*g^8*z^2 - 44*a^2*b^5*c^3*d^5*e^3*g^8*z^2 - 26*b^3*c^7*d^7*e*f^4*g^4*z^2 -
26*b^3*c^7*d^4*e^4*f^7*g*z^2 + 16*b^2*c^8*d^7*e*f^5*g^3*z^2 + 16*b^2*c^8*d^5*e^3*f^7*g*z^2 + 10*b^5*c^5*d^7*e*
f^2*g^6*z^2 + 10*b^5*c^5*d^2*e^6*f^7*g*z^2 - 4*b^4*c^6*d^7*e*f^3*g^5*z^2 - 4*b^4*c^6*d^3*e^5*f^7*g*z^2 + 2*b^9
*c*d^3*e^5*f^2*g^6*z^2 + 2*b^9*c*d^2*e^6*f^3*g^5*z^2 - 168*a^5*c^5*d^3*e^5*f*g^7*z^2 - 168*a^5*c^5*d*e^7*f^3*g
^5*z^2 - 120*a^4*c^6*d^5*e^3*f*g^7*z^2 - 120*a^4*c^6*d*e^7*f^5*g^3*z^2 - 56*a^2*c^8*d^7*e*f^3*g^5*z^2 - 56*a^2
*c^8*d^3*e^5*f^7*g*z^2 + 32*a*c^9*d^6*e^2*f^6*g^2*z^2 + 624*a^4*b*c^5*e^8*f^5*g^3*z^2 + 548*a^5*b*c^4*e^8*f^3*
g^5*z^2 - 182*a^2*b^3*c^5*e^8*f^7*g*z^2 - 96*a^5*b^3*c^2*e^8*f*g^7*z^2 - 68*a*b^6*c^3*e^8*f^6*g^2*z^2 - 58*a^3
*b^6*c*e^8*f^2*g^6*z^2 + 38*a^2*b^7*c*e^8*f^3*g^5*z^2 + 36*a*b^7*c^2*e^8*f^5*g^3*z^2 + 18*a*b^2*c^7*d^8*f^2*g^
6*z^2 + 624*a^4*b*c^5*d^5*e^3*g^8*z^2 + 548*a^5*b*c^4*d^3*e^5*g^8*z^2 - 182*a^2*b^3*c^5*d^7*e*g^8*z^2 - 96*a^5
*b^3*c^2*d*e^7*g^8*z^2 - 68*a*b^6*c^3*d^6*e^2*g^8*z^2 - 58*a^3*b^6*c*d^2*e^6*g^8*z^2 + 38*a^2*b^7*c*d^3*e^5*g^
8*z^2 + 36*a*b^7*c^2*d^5*e^3*g^8*z^2 + 18*a*b^2*c^7*d^2*e^6*f^8*z^2 + 12*b*c^9*d^7*e*f^6*g^2*z^2 + 12*b*c^9*d^
6*e^2*f^7*g*z^2 - 72*a^6*c^4*d*e^7*f*g^7*z^2 - 40*a*c^9*d^7*e*f^5*g^3*z^2 - 40*a*c^9*d^5*e^3*f^7*g*z^2 - 24*a^
3*c^7*d^7*e*f*g^7*z^2 - 24*a^3*c^7*d*e^7*f^7*g*z^2 - 4*a^2*b^8*d*e^7*f*g^7*z^2 + 2*a*b^9*d^2*e^6*f*g^7*z^2 + 2
*a*b^9*d*e^7*f^2*g^6*z^2 + 204*a^3*b*c^6*e^8*f^7*g*z^2 + 128*a^6*b*c^3*e^8*f*g^7*z^2 + 48*a*b^5*c^4*e^8*f^7*g*
z^2 + 24*a^4*b^5*c*e^8*f*g^7*z^2 - 48*a*b*c^8*d^8*f^3*g^5*z^2 - 36*a^2*b*c^7*d^8*f*g^7*z^2 + 6*a*b^3*c^6*d^8*f
*g^7*z^2 + 204*a^3*b*c^6*d^7*e*g^8*z^2 + 128*a^6*b*c^3*d*e^7*g^8*z^2 + 48*a*b^5*c^4*d^7*e*g^8*z^2 + 24*a^4*b^5
*c*d*e^7*g^8*z^2 - 48*a*b*c^8*d^3*e^5*f^8*z^2 - 36*a^2*b*c^7*d*e^7*f^8*z^2 + 6*a*b^3*c^6*d*e^7*f^8*z^2 - b^8*c
^2*d^4*e^4*f^2*g^6*z^2 - b^8*c^2*d^2*e^6*f^4*g^4*z^2 - 4*b^9*c*e^8*f^5*g^3*z^2 - 4*b^7*c^3*e^8*f^7*g*z^2 - 12*
b*c^9*d^8*f^5*g^3*z^2 + 24*a*c^9*d^8*f^4*g^4*z^2 - 4*b^9*c*d^5*e^3*g^8*z^2 - 4*b^7*c^3*d^7*e*g^8*z^2 - 4*a*b^9
*e^8*f^3*g^5*z^2 - 2*a^3*b^7*e^8*f*g^7*z^2 - 12*b*c^9*d^5*e^3*f^8*z^2 + 24*a*c^9*d^4*e^4*f^8*z^2 - 4*a*b^9*d^3
*e^5*g^8*z^2 - 2*a^3*b^7*d*e^7*g^8*z^2 - 12*a^5*b^4*c*e^8*g^8*z^2 - 12*a*b^4*c^5*e^8*f^8*z^2 - 12*a*b^4*c^5*d^
8*g^8*z^2 - 8*c^10*d^7*e*f^7*g*z^2 + 6*b^8*c^2*e^8*f^6*g^2*z^2 - 232*a^5*c^5*e^8*f^4*g^4*z^2 - 188*a^4*c^6*e^8
*f^6*g^2*z^2 - 92*a^6*c^4*e^8*f^2*g^6*z^2 + 9*b^2*c^8*d^8*f^4*g^4*z^2 - 3*b^4*c^6*d^8*f^2*g^6*z^2 + 2*b^3*c^7*
d^8*f^3*g^5*z^2 + 36*a^2*c^8*d^8*f^2*g^6*z^2 + 6*b^8*c^2*d^6*e^2*g^8*z^2 + 5*a^2*b^8*e^8*f^2*g^6*z^2 - 232*a^5
*c^5*d^4*e^4*g^8*z^2 - 188*a^4*c^6*d^6*e^2*g^8*z^2 - 92*a^6*c^4*d^2*e^6*g^8*z^2 + 9*b^2*c^8*d^4*e^4*f^8*z^2 -
3*b^4*c^6*d^2*e^6*f^8*z^2 + 2*b^3*c^7*d^3*e^5*f^8*z^2 + 36*a^2*c^8*d^2*e^6*f^8*z^2 + 5*a^2*b^8*d^2*e^6*g^8*z^2
+ 48*a^6*b^2*c^2*e^8*g^8*z^2 + 45*a^2*b^2*c^6*e^8*f^8*z^2 + 45*a^2*b^2*c^6*d^8*g^8*z^2 + 4*c^10*d^8*f^6*g^2*z
^2 + b^10*e^8*f^4*g^4*z^2 + 4*c^10*d^6*e^2*f^8*z^2 + b^10*d^4*e^4*g^8*z^2 - 64*a^7*c^3*e^8*g^8*z^2 + b^6*c^4*e
^8*f^8*z^2 + b^6*c^4*d^8*g^8*z^2 - 48*a^3*c^7*e^8*f^8*z^2 - 48*a^3*c^7*d^8*g^8*z^2 + a^4*b^6*e^8*g^8*z^2 - b^1
0*d^2*e^6*f^2*g^6*z^2 + 108*a^2*b^2*c^4*d^2*e^5*f*g^6*z + 108*a^2*b^2*c^4*d*e^6*f^2*g^5*z + 60*a*b^2*c^5*d^3*e
^4*f^2*g^5*z + 60*a*b^2*c^5*d^2*e^5*f^3*g^4*z - 48*a^2*b*c^5*d^2*e^5*f^2*g^5*z - 44*a*b^3*c^4*d^2*e^5*f^2*g^5*
z - 120*a^2*b*c^5*d^3*e^4*f*g^6*z - 120*a^2*b*c^5*d*e^6*f^3*g^4*z - 96*a*b*c^6*d^3*e^4*f^3*g^4*z - 64*a^2*b^3*
c^3*d*e^6*f*g^6*z + 32*a*b^3*c^4*d^3*e^4*f*g^6*z + 32*a*b^3*c^4*d*e^6*f^3*g^4*z - 28*a*b^4*c^3*d^2*e^5*f*g^6*z
- 28*a*b^4*c^3*d*e^6*f^2*g^5*z - 18*a*b^2*c^5*d^4*e^3*f*g^6*z - 18*a*b^2*c^5*d*e^6*f^4*g^3*z + 4*a*b*c^6*d^4*
e^3*f^2*g^5*z + 4*a*b*c^6*d^2*e^5*f^4*g^3*z + 24*a*b^5*c^2*d*e^6*f*g^6*z - 16*a^3*b*c^4*d*e^6*f*g^6*z - 8*a*b*
c^6*d^5*e^2*f*g^6*z - 8*a*b*c^6*d*e^6*f^5*g^2*z - 13*b^2*c^6*d^6*e*f*g^6*z - 13*b^2*c^6*d*e^6*f^6*g*z + 8*b*c^
7*d^6*e*f^2*g^5*z + 8*b*c^7*d^2*e^5*f^6*g*z + 9*b^2*c^6*d^4*e^3*f^3*g^4*z + 9*b^2*c^6*d^3*e^4*f^4*g^3*z + 8*b^
5*c^3*d^2*e^5*f^2*g^5*z - 6*b^4*c^4*d^3*e^4*f^2*g^5*z - 6*b^4*c^4*d^2*e^5*f^3*g^4*z - 6*b^3*c^5*d^4*e^3*f^2*g^
5*z - 6*b^3*c^5*d^2*e^5*f^4*g^3*z + 4*b^3*c^5*d^3*e^4*f^3*g^4*z + b^2*c^6*d^5*e^2*f^2*g^5*z + b^2*c^6*d^2*e^5*
f^5*g^2*z + 16*a^2*c^6*d^3*e^4*f^2*g^5*z + 16*a^2*c^6*d^2*e^5*f^3*g^4*z - 112*a^2*b^3*c^3*e^7*f^2*g^5*z - 12*a
^2*b^2*c^4*e^7*f^3*g^4*z - 112*a^2*b^3*c^3*d^2*e^5*g^7*z - 12*a^2*b^2*c^4*d^3*e^4*g^7*z - 2*b^7*c*d*e^6*f*g^6*
z + 8*a*c^7*d^6*e*f*g^6*z + 8*a*c^7*d*e^6*f^6*g*z + 52*a*b*c^6*e^7*f^6*g*z - 10*a*b^6*c*e^7*f*g^6*z + 52*a*b*c
^6*d^6*e*g^7*z - 10*a*b^6*c*d*e^6*g^7*z + 14*b^3*c^5*d^5*e^2*f*g^6*z + 14*b^3*c^5*d*e^6*f^5*g^2*z - 12*b*c^7*d
^5*e^2*f^3*g^4*z - 12*b*c^7*d^3*e^4*f^5*g^2*z - 5*b^4*c^4*d^4*e^3*f*g^6*z - 5*b^4*c^4*d*e^6*f^4*g^3*z + b^6*c^
2*d^2*e^5*f*g^6*z + b^6*c^2*d*e^6*f^2*g^5*z + 52*a^2*c^6*d^4*e^3*f*g^6*z + 52*a^2*c^6*d*e^6*f^4*g^3*z + 24*a*c
^7*d^4*e^3*f^3*g^4*z + 24*a*c^7*d^3*e^4*f^4*g^3*z - 16*a*c^7*d^5*e^2*f^2*g^5*z - 16*a*c^7*d^2*e^5*f^5*g^2*z +
8*a^3*c^5*d^2*e^5*f*g^6*z + 8*a^3*c^5*d*e^6*f^2*g^5*z + 200*a^3*b*c^4*e^7*f^2*g^5*z + 144*a^2*b*c^5*e^7*f^4*g^
3*z - 42*a*b^2*c^5*e^7*f^5*g^2*z + 32*a^3*b^2*c^3*e^7*f*g^6*z + 24*a^2*b^4*c^2*e^7*f*g^6*z + 24*a*b^5*c^2*e^7*
f^2*g^5*z - 10*a*b^3*c^4*e^7*f^4*g^3*z + 4*a*b^4*c^3*e^7*f^3*g^4*z + 200*a^3*b*c^4*d^2*e^5*g^7*z + 144*a^2*b*c
^5*d^4*e^3*g^7*z - 42*a*b^2*c^5*d^5*e^2*g^7*z + 32*a^3*b^2*c^3*d*e^6*g^7*z + 24*a^2*b^4*c^2*d*e^6*g^7*z + 24*a
*b^5*c^2*d^2*e^5*g^7*z - 10*a*b^3*c^4*d^4*e^3*g^7*z + 4*a*b^4*c^3*d^3*e^4*g^7*z + 4*b*c^7*d^7*f*g^6*z + 4*b*c^
7*d*e^6*f^7*z + 11*b^4*c^4*e^7*f^5*g^2*z - 4*b^5*c^3*e^7*f^4*g^3*z + b^6*c^2*e^7*f^3*g^4*z - 136*a^3*c^5*e^7*f
^3*g^4*z - 68*a^2*c^6*e^7*f^5*g^2*z + 11*b^4*c^4*d^5*e^2*g^7*z - 4*b^5*c^3*d^4*e^3*g^7*z + b^6*c^2*d^3*e^4*g^7
*z - 136*a^3*c^5*d^3*e^4*g^7*z - 68*a^2*c^6*d^5*e^2*g^7*z - 96*a^3*b^3*c^2*e^7*g^7*z + 4*c^8*d^6*e*f^3*g^4*z +
4*c^8*d^3*e^4*f^6*g*z - 10*b^3*c^5*e^7*f^6*g*z - 2*b^7*c*e^7*f^2*g^5*z - 128*a^4*c^4*e^7*f*g^6*z - 10*b^3*c^5
*d^6*e*g^7*z - 2*b^7*c*d^2*e^5*g^7*z - 128*a^4*c^4*d*e^6*g^7*z + 128*a^4*b*c^3*e^7*g^7*z + 24*a^2*b^5*c*e^7*g^
7*z - 4*c^8*d^7*f^2*g^5*z - 4*c^8*d^2*e^5*f^7*z + 3*b^2*c^6*e^7*f^7*z + 3*b^2*c^6*d^7*g^7*z + b^8*e^7*f*g^6*z
+ b^8*d*e^6*g^7*z - 16*a*c^7*e^7*f^7*z - 16*a*c^7*d^7*g^7*z - 2*a*b^7*e^7*g^7*z - 8*a*c^5*d*e^5*f*g^5 + 20*a*b
*c^4*e^6*f*g^5 + 20*a*b*c^4*d*e^5*g^6 + 4*b*c^5*d^2*e^4*f*g^5 + 4*b*c^5*d*e^5*f^2*g^4 - 2*b^2*c^4*d*e^5*f*g^5
- 4*b^3*c^3*e^6*f*g^5 - 16*a*c^5*e^6*f^2*g^4 - 4*b^3*c^3*d*e^5*g^6 - 16*a*c^5*d^2*e^4*g^6 + 8*a*b^2*c^3*e^6*g^
6 - 4*c^6*d^2*e^4*f^2*g^4 + 3*b^2*c^4*e^6*f^2*g^4 + 3*b^2*c^4*d^2*e^4*g^6 - 36*a^2*c^4*e^6*g^6, z, k)*((64*a^6
*c^7*d^7*e^2*g^9 + 64*a^7*c^6*d^5*e^4*g^9 - 64*a^8*c^5*d^3*e^6*g^9 + 64*a^6*c^7*e^9*f^7*g^2 + 64*a^7*c^6*e^9*f
^5*g^4 - 64*a^8*c^5*e^9*f^3*g^6 - 64*a^9*c^4*d*e^8*g^9 - 64*a^9*c^4*e^9*f*g^8 + 16*a^5*b*c^7*d^8*e*g^9 + a^6*b
^6*c*d*e^8*g^9 + 16*a^5*b*c^7*e^9*f^8*g + a^6*b^6*c*e^9*f*g^8 - 128*a^5*c^8*d*e^8*f^8*g - 128*a^5*c^8*d^8*e*f*
g^8 + a^3*b^5*c^5*d^8*e*g^9 + a^3*b^9*c*d^4*e^5*g^9 - 8*a^4*b^3*c^6*d^8*e*g^9 - a^4*b^8*c*d^3*e^6*g^9 - a^5*b^
7*c*d^2*e^7*g^9 - 144*a^6*b*c^6*d^6*e^3*g^9 - 80*a^7*b*c^5*d^4*e^5*g^9 - 12*a^7*b^4*c^2*d*e^8*g^9 + 80*a^8*b*c
^4*d^2*e^7*g^9 + 48*a^8*b^2*c^3*d*e^8*g^9 + a^3*b^5*c^5*e^9*f^8*g + a^3*b^9*c*e^9*f^4*g^5 - 8*a^4*b^3*c^6*e^9*
f^8*g - a^4*b^8*c*e^9*f^3*g^6 - a^5*b^7*c*e^9*f^2*g^7 - 144*a^6*b*c^6*e^9*f^6*g^3 - 80*a^7*b*c^5*e^9*f^4*g^5 -
12*a^7*b^4*c^2*e^9*f*g^8 + 80*a^8*b*c^4*e^9*f^2*g^7 + 48*a^8*b^2*c^3*e^9*f*g^8 - 128*a^3*c^10*d^5*e^4*f^8*g -
128*a^3*c^10*d^8*e*f^5*g^4 - 256*a^4*c^9*d^3*e^6*f^8*g - 256*a^4*c^9*d^8*e*f^3*g^6 - 448*a^6*c^7*d*e^8*f^6*g^
3 - 448*a^6*c^7*d^6*e^3*f*g^8 - 576*a^7*c^6*d*e^8*f^4*g^5 - 576*a^7*c^6*d^4*e^5*f*g^8 - 320*a^8*c^5*d*e^8*f^2*
g^7 - 320*a^8*c^5*d^2*e^7*f*g^8 + b^5*c^8*d^6*e^3*f^8*g + b^5*c^8*d^8*e*f^6*g^3 - b^6*c^7*d^5*e^4*f^8*g - b^6*
c^7*d^8*e*f^5*g^4 - b^7*c^6*d^4*e^5*f^8*g - b^7*c^6*d^8*e*f^4*g^5 + b^8*c^5*d^3*e^6*f^8*g + b^8*c^5*d^8*e*f^3*
g^6 + b^12*c*d^3*e^6*f^4*g^5 + b^12*c*d^4*e^5*f^3*g^6 - 4*a^3*b^6*c^4*d^7*e^2*g^9 + 6*a^3*b^7*c^3*d^6*e^3*g^9
- 4*a^3*b^8*c^2*d^5*e^4*g^9 + 36*a^4*b^4*c^5*d^7*e^2*g^9 - 57*a^4*b^5*c^4*d^6*e^3*g^9 + 37*a^4*b^6*c^3*d^5*e^4
*g^9 - 7*a^4*b^7*c^2*d^4*e^5*g^9 - 96*a^5*b^2*c^6*d^7*e^2*g^9 + 168*a^5*b^3*c^5*d^6*e^3*g^9 - 100*a^5*b^4*c^4*
d^5*e^4*g^9 + 3*a^5*b^5*c^3*d^4*e^5*g^9 + 10*a^5*b^6*c^2*d^3*e^6*g^9 + 48*a^6*b^2*c^5*d^5*e^4*g^9 + 56*a^6*b^3
*c^4*d^4*e^5*g^9 - 36*a^6*b^4*c^3*d^3*e^6*g^9 + 13*a^6*b^5*c^2*d^2*e^7*g^9 + 64*a^7*b^2*c^4*d^3*e^6*g^9 - 56*a
^7*b^3*c^3*d^2*e^7*g^9 - 4*a^3*b^6*c^4*e^9*f^7*g^2 + 6*a^3*b^7*c^3*e^9*f^6*g^3 - 4*a^3*b^8*c^2*e^9*f^5*g^4 + 3
6*a^4*b^4*c^5*e^9*f^7*g^2 - 57*a^4*b^5*c^4*e^9*f^6*g^3 + 37*a^4*b^6*c^3*e^9*f^5*g^4 - 7*a^4*b^7*c^2*e^9*f^4*g^
5 - 96*a^5*b^2*c^6*e^9*f^7*g^2 + 168*a^5*b^3*c^5*e^9*f^6*g^3 - 100*a^5*b^4*c^4*e^9*f^5*g^4 + 3*a^5*b^5*c^3*e^9
*f^4*g^5 + 10*a^5*b^6*c^2*e^9*f^3*g^6 + 48*a^6*b^2*c^5*e^9*f^5*g^4 + 56*a^6*b^3*c^4*e^9*f^4*g^5 - 36*a^6*b^4*c
^3*e^9*f^3*g^6 + 13*a^6*b^5*c^2*e^9*f^2*g^7 + 64*a^7*b^2*c^4*e^9*f^3*g^6 - 56*a^7*b^3*c^3*e^9*f^2*g^7 + 64*a^3
*c^10*d^6*e^3*f^7*g^2 + 64*a^3*c^10*d^7*e^2*f^6*g^3 + 192*a^4*c^9*d^4*e^5*f^7*g^2 - 320*a^4*c^9*d^5*e^4*f^6*g^
3 - 320*a^4*c^9*d^6*e^3*f^5*g^4 + 192*a^4*c^9*d^7*e^2*f^4*g^5 + 192*a^5*c^8*d^2*e^7*f^7*g^2 - 832*a^5*c^8*d^3*
e^6*f^6*g^3 - 192*a^5*c^8*d^4*e^5*f^5*g^4 - 192*a^5*c^8*d^5*e^4*f^4*g^5 - 832*a^5*c^8*d^6*e^3*f^3*g^6 + 192*a^
5*c^8*d^7*e^2*f^2*g^7 + 64*a^6*c^7*d^2*e^7*f^5*g^4 - 960*a^6*c^7*d^3*e^6*f^4*g^5 - 960*a^6*c^7*d^4*e^5*f^3*g^6
+ 64*a^6*c^7*d^5*e^4*f^2*g^7 - 448*a^7*c^6*d^2*e^7*f^3*g^6 - 448*a^7*c^6*d^3*e^6*f^2*g^7 - 2*b^5*c^8*d^7*e^2*
f^7*g^2 + 2*b^6*c^7*d^6*e^3*f^7*g^2 + 2*b^6*c^7*d^7*e^2*f^6*g^3 - 2*b^7*c^6*d^5*e^4*f^7*g^2 - 6*b^7*c^6*d^6*e^
3*f^6*g^3 - 2*b^7*c^6*d^7*e^2*f^5*g^4 + 6*b^8*c^5*d^4*e^5*f^7*g^2 + 8*b^8*c^5*d^5*e^4*f^6*g^3 + 8*b^8*c^5*d^6*
e^3*f^5*g^4 + 6*b^8*c^5*d^7*e^2*f^4*g^5 - 4*b^9*c^4*d^3*e^6*f^7*g^2 - 11*b^9*c^4*d^4*e^5*f^6*g^3 - 10*b^9*c^4*
d^5*e^4*f^5*g^4 - 11*b^9*c^4*d^6*e^3*f^4*g^5 - 4*b^9*c^4*d^7*e^2*f^3*g^6 + 6*b^10*c^3*d^3*e^6*f^6*g^3 + 9*b^10
*c^3*d^4*e^5*f^5*g^4 + 9*b^10*c^3*d^5*e^4*f^4*g^5 + 6*b^10*c^3*d^6*e^3*f^3*g^6 - 4*b^11*c^2*d^3*e^6*f^5*g^4 -
4*b^11*c^2*d^4*e^5*f^4*g^5 - 4*b^11*c^2*d^5*e^4*f^3*g^6 + 16*a*b^3*c^9*d^7*e^2*f^7*g^2 - 12*a*b^4*c^8*d^6*e^3*
f^7*g^2 - 12*a*b^4*c^8*d^7*e^2*f^6*g^3 + 30*a*b^5*c^7*d^5*e^4*f^7*g^2 + 30*a*b^5*c^7*d^6*e^3*f^6*g^3 + 30*a*b^
5*c^7*d^7*e^2*f^5*g^4 - 100*a*b^6*c^6*d^4*e^5*f^7*g^2 - 56*a*b^6*c^6*d^5*e^4*f^6*g^3 - 56*a*b^6*c^6*d^6*e^3*f^
5*g^4 - 100*a*b^6*c^6*d^7*e^2*f^4*g^5 + 62*a*b^7*c^5*d^3*e^6*f^7*g^2 + 128*a*b^7*c^5*d^4*e^5*f^6*g^3 + 42*a*b^
7*c^5*d^5*e^4*f^5*g^4 + 128*a*b^7*c^5*d^6*e^3*f^4*g^5 + 62*a*b^7*c^5*d^7*e^2*f^3*g^6 + 4*a*b^8*c^4*d^2*e^7*f^7
*g^2 - 76*a*b^8*c^4*d^3*e^6*f^6*g^3 - 48*a*b^8*c^4*d^4*e^5*f^5*g^4 - 48*a*b^8*c^4*d^5*e^4*f^4*g^5 - 76*a*b^8*c
^4*d^6*e^3*f^3*g^6 + 4*a*b^8*c^4*d^7*e^2*f^2*g^7 - 6*a*b^9*c^3*d^2*e^7*f^6*g^3 + 28*a*b^9*c^3*d^3*e^6*f^5*g^4
- 20*a*b^9*c^3*d^4*e^5*f^4*g^5 + 28*a*b^9*c^3*d^5*e^4*f^3*g^6 - 6*a*b^9*c^3*d^6*e^3*f^2*g^7 + 4*a*b^10*c^2*d^2
*e^7*f^5*g^4 + 14*a*b^10*c^2*d^3*e^6*f^4*g^5 + 14*a*b^10*c^2*d^4*e^5*f^3*g^6 + 4*a*b^10*c^2*d^5*e^4*f^2*g^7 -
32*a^2*b*c^10*d^7*e^2*f^7*g^2 + 48*a^2*b^2*c^9*d^5*e^4*f^8*g + 48*a^2*b^2*c^9*d^8*e*f^5*g^4 - 168*a^2*b^3*c^8*
d^4*e^5*f^8*g - 168*a^2*b^3*c^8*d^8*e*f^4*g^5 + 80*a^2*b^4*c^7*d^3*e^6*f^8*g + 80*a^2*b^4*c^7*d^8*e*f^3*g^6 +
27*a^2*b^5*c^6*d^2*e^7*f^8*g + 27*a^2*b^5*c^6*d^8*e*f^2*g^7 + 4*a^2*b^7*c^4*d*e^8*f^7*g^2 + 4*a^2*b^7*c^4*d^7*
e^2*f*g^8 - 6*a^2*b^8*c^3*d*e^8*f^6*g^3 - 6*a^2*b^8*c^3*d^6*e^3*f*g^8 + 4*a^2*b^9*c^2*d*e^8*f^5*g^4 + 4*a^2*b^
9*c^2*d^5*e^4*f*g^8 + 16*a^2*b^10*c*d^2*e^7*f^3*g^6 + 16*a^2*b^10*c*d^3*e^6*f^2*g^7 + 224*a^3*b*c^9*d^5*e^4*f^
7*g^2 - 288*a^3*b*c^9*d^6*e^3*f^6*g^3 + 224*a^3*b*c^9*d^7*e^2*f^5*g^4 - 32*a^3*b^2*c^8*d^3*e^6*f^8*g - 32*a^3*
b^2*c^8*d^8*e*f^3*g^6 - 168*a^3*b^3*c^7*d^2*e^7*f^8*g - 168*a^3*b^3*c^7*d^8*e*f^2*g^7 - 14*a^3*b^5*c^5*d*e^8*f
^7*g^2 - 14*a^3*b^5*c^5*d^7*e^2*f*g^8 + 40*a^3*b^6*c^4*d*e^8*f^6*g^3 + 40*a^3*b^6*c^4*d^6*e^3*f*g^8 - 44*a^3*b
^7*c^3*d*e^8*f^5*g^4 - 44*a^3*b^7*c^3*d^5*e^4*f*g^8 + 24*a^3*b^8*c^2*d*e^8*f^4*g^5 + 24*a^3*b^8*c^2*d^4*e^5*f*
g^8 - 30*a^3*b^9*c*d^2*e^7*f^2*g^7 + 544*a^4*b*c^8*d^3*e^6*f^7*g^2 + 256*a^4*b*c^8*d^4*e^5*f^6*g^3 + 1632*a^4*
b*c^8*d^5*e^4*f^5*g^4 + 256*a^4*b*c^8*d^6*e^3*f^4*g^5 + 544*a^4*b*c^8*d^7*e^2*f^3*g^6 - 80*a^4*b^3*c^6*d*e^8*f
^7*g^2 - 80*a^4*b^3*c^6*d^7*e^2*f*g^8 - 60*a^4*b^4*c^5*d*e^8*f^6*g^3 - 60*a^4*b^4*c^5*d^6*e^3*f*g^8 + 234*a^4*
b^5*c^4*d*e^8*f^5*g^4 + 234*a^4*b^5*c^4*d^5*e^4*f*g^8 - 208*a^4*b^6*c^3*d*e^8*f^4*g^5 - 208*a^4*b^6*c^3*d^4*e^
5*f*g^8 + 50*a^4*b^7*c^2*d*e^8*f^3*g^6 + 50*a^4*b^7*c^2*d^3*e^6*f*g^8 + 416*a^5*b*c^7*d^2*e^7*f^6*g^3 + 2592*a
^5*b*c^7*d^3*e^6*f^5*g^4 + 1056*a^5*b*c^7*d^4*e^5*f^4*g^5 + 2592*a^5*b*c^7*d^5*e^4*f^3*g^6 + 416*a^5*b*c^7*d^6
*e^3*f^2*g^7 + 96*a^5*b^2*c^6*d*e^8*f^6*g^3 + 96*a^5*b^2*c^6*d^6*e^3*f*g^8 - 784*a^5*b^3*c^5*d*e^8*f^5*g^4 - 7
84*a^5*b^3*c^5*d^5*e^4*f*g^8 + 732*a^5*b^4*c^4*d*e^8*f^4*g^5 + 732*a^5*b^4*c^4*d^4*e^5*f*g^8 - 18*a^5*b^5*c^3*
d*e^8*f^3*g^6 - 18*a^5*b^5*c^3*d^3*e^6*f*g^8 - 184*a^5*b^6*c^2*d*e^8*f^2*g^7 - 184*a^5*b^6*c^2*d^2*e^7*f*g^8 +
1024*a^6*b*c^6*d^2*e^7*f^4*g^5 + 3552*a^6*b*c^6*d^3*e^6*f^3*g^6 + 1024*a^6*b*c^6*d^4*e^5*f^2*g^7 - 736*a^6*b^
2*c^5*d*e^8*f^4*g^5 - 736*a^6*b^2*c^5*d^4*e^5*f*g^8 - 720*a^6*b^3*c^4*d*e^8*f^3*g^6 - 720*a^6*b^3*c^4*d^3*e^6*
f*g^8 + 684*a^6*b^4*c^3*d*e^8*f^2*g^7 + 684*a^6*b^4*c^3*d^2*e^7*f*g^8 + 992*a^7*b*c^5*d^2*e^7*f^2*g^7 - 736*a^
7*b^2*c^4*d*e^8*f^2*g^7 - 736*a^7*b^2*c^4*d^2*e^7*f*g^8 - 10*a^5*b^7*c*d*e^8*f*g^8 + 608*a^8*b*c^4*d*e^8*f*g^8
- 144*a^2*b^3*c^8*d^5*e^4*f^7*g^2 + 48*a^2*b^3*c^8*d^6*e^3*f^6*g^3 - 144*a^2*b^3*c^8*d^7*e^2*f^5*g^4 + 524*a^
2*b^4*c^7*d^4*e^5*f^7*g^2 + 44*a^2*b^4*c^7*d^5*e^4*f^6*g^3 + 44*a^2*b^4*c^7*d^6*e^3*f^5*g^4 + 524*a^2*b^4*c^7*
d^7*e^2*f^4*g^5 - 270*a^2*b^5*c^6*d^3*e^6*f^7*g^2 - 480*a^2*b^5*c^6*d^4*e^5*f^6*g^3 + 246*a^2*b^5*c^6*d^5*e^4*
f^5*g^4 - 480*a^2*b^5*c^6*d^6*e^3*f^4*g^5 - 270*a^2*b^5*c^6*d^7*e^2*f^3*g^6 - 90*a^2*b^6*c^5*d^2*e^7*f^7*g^2 +
286*a^2*b^6*c^5*d^3*e^6*f^6*g^3 - 180*a^2*b^6*c^5*d^4*e^5*f^5*g^4 - 180*a^2*b^6*c^5*d^5*e^4*f^4*g^5 + 286*a^2
*b^6*c^5*d^6*e^3*f^3*g^6 - 90*a^2*b^6*c^5*d^7*e^2*f^2*g^7 + 104*a^2*b^7*c^4*d^2*e^7*f^6*g^3 + 4*a^2*b^7*c^4*d^
3*e^6*f^5*g^4 + 520*a^2*b^7*c^4*d^4*e^5*f^4*g^5 + 4*a^2*b^7*c^4*d^5*e^4*f^3*g^6 + 104*a^2*b^7*c^4*d^6*e^3*f^2*
g^7 - 30*a^2*b^8*c^3*d^2*e^7*f^5*g^4 - 186*a^2*b^8*c^3*d^3*e^6*f^4*g^5 - 186*a^2*b^8*c^3*d^4*e^5*f^3*g^6 - 30*
a^2*b^8*c^3*d^5*e^4*f^2*g^7 - 27*a^2*b^9*c^2*d^2*e^7*f^4*g^5 + 70*a^2*b^9*c^2*d^3*e^6*f^3*g^6 - 27*a^2*b^9*c^2
*d^4*e^5*f^2*g^7 - 928*a^3*b^2*c^8*d^4*e^5*f^7*g^2 + 288*a^3*b^2*c^8*d^5*e^4*f^6*g^3 + 288*a^3*b^2*c^8*d^6*e^3
*f^5*g^4 - 928*a^3*b^2*c^8*d^7*e^2*f^4*g^5 + 208*a^3*b^3*c^7*d^3*e^6*f^7*g^2 + 512*a^3*b^3*c^7*d^4*e^5*f^6*g^3
- 1424*a^3*b^3*c^7*d^5*e^4*f^5*g^4 + 512*a^3*b^3*c^7*d^6*e^3*f^4*g^5 + 208*a^3*b^3*c^7*d^7*e^2*f^3*g^6 + 540*
a^3*b^4*c^6*d^2*e^7*f^7*g^2 - 228*a^3*b^4*c^6*d^3*e^6*f^6*g^3 + 1428*a^3*b^4*c^6*d^4*e^5*f^5*g^4 + 1428*a^3*b^
4*c^6*d^5*e^4*f^4*g^5 - 228*a^3*b^4*c^6*d^6*e^3*f^3*g^6 + 540*a^3*b^4*c^6*d^7*e^2*f^2*g^7 - 518*a^3*b^5*c^5*d^
2*e^7*f^6*g^3 - 190*a^3*b^5*c^5*d^3*e^6*f^5*g^4 - 2110*a^3*b^5*c^5*d^4*e^5*f^4*g^5 - 190*a^3*b^5*c^5*d^5*e^4*f
^3*g^6 - 518*a^3*b^5*c^5*d^6*e^3*f^2*g^7 - 88*a^3*b^6*c^4*d^2*e^7*f^5*g^4 + 368*a^3*b^6*c^4*d^3*e^6*f^4*g^5 +
368*a^3*b^6*c^4*d^4*e^5*f^3*g^6 - 88*a^3*b^6*c^4*d^5*e^4*f^2*g^7 + 404*a^3*b^7*c^3*d^2*e^7*f^4*g^5 + 12*a^3*b^
7*c^3*d^3*e^6*f^3*g^6 + 404*a^3*b^7*c^3*d^4*e^5*f^2*g^7 - 140*a^3*b^8*c^2*d^2*e^7*f^3*g^6 - 140*a^3*b^8*c^2*d^
3*e^6*f^2*g^7 - 1024*a^4*b^2*c^7*d^2*e^7*f^7*g^2 - 128*a^4*b^2*c^7*d^3*e^6*f^6*g^3 - 2016*a^4*b^2*c^7*d^4*e^5*
f^5*g^4 - 2016*a^4*b^2*c^7*d^5*e^4*f^4*g^5 - 128*a^4*b^2*c^7*d^6*e^3*f^3*g^6 - 1024*a^4*b^2*c^7*d^7*e^2*f^2*g^
7 + 688*a^4*b^3*c^6*d^2*e^7*f^6*g^3 - 720*a^4*b^3*c^6*d^3*e^6*f^5*g^4 + 2160*a^4*b^3*c^6*d^4*e^5*f^4*g^5 - 720
*a^4*b^3*c^6*d^5*e^4*f^3*g^6 + 688*a^4*b^3*c^6*d^6*e^3*f^2*g^7 + 1124*a^4*b^4*c^5*d^2*e^7*f^5*g^4 + 1060*a^4*b
^4*c^5*d^3*e^6*f^4*g^5 + 1060*a^4*b^4*c^5*d^4*e^5*f^3*g^6 + 1124*a^4*b^4*c^5*d^5*e^4*f^2*g^7 - 1616*a^4*b^5*c^
4*d^2*e^7*f^4*g^5 - 674*a^4*b^5*c^4*d^3*e^6*f^3*g^6 - 1616*a^4*b^5*c^4*d^4*e^5*f^2*g^7 + 186*a^4*b^6*c^3*d^2*e
^7*f^3*g^6 + 186*a^4*b^6*c^3*d^3*e^6*f^2*g^7 + 334*a^4*b^7*c^2*d^2*e^7*f^2*g^7 - 2208*a^5*b^2*c^6*d^2*e^7*f^5*
g^4 - 2592*a^5*b^2*c^6*d^3*e^6*f^4*g^5 - 2592*a^5*b^2*c^6*d^4*e^5*f^3*g^6 - 2208*a^5*b^2*c^6*d^5*e^4*f^2*g^7 +
1728*a^5*b^3*c^5*d^2*e^7*f^4*g^5 - 304*a^5*b^3*c^5*d^3*e^6*f^3*g^6 + 1728*a^5*b^3*c^5*d^4*e^5*f^2*g^7 + 1108*
a^5*b^4*c^4*d^2*e^7*f^3*g^6 + 1108*a^5*b^4*c^4*d^3*e^6*f^2*g^7 - 1170*a^5*b^5*c^3*d^2*e^7*f^2*g^7 - 2432*a^6*b
^2*c^5*d^2*e^7*f^3*g^6 - 2432*a^6*b^2*c^5*d^3*e^6*f^2*g^7 + 1008*a^6*b^3*c^4*d^2*e^7*f^2*g^7 - 8*a*b^3*c^9*d^6
*e^3*f^8*g - 8*a*b^3*c^9*d^8*e*f^6*g^3 + 27*a*b^5*c^7*d^4*e^5*f^8*g + 27*a*b^5*c^7*d^8*e*f^4*g^5 - 18*a*b^6*c^
6*d^3*e^6*f^8*g - 18*a*b^6*c^6*d^8*e*f^3*g^6 - a*b^7*c^5*d^2*e^7*f^8*g - a*b^7*c^5*d^8*e*f^2*g^7 - a*b^11*c*d^
2*e^7*f^4*g^5 - 10*a*b^11*c*d^3*e^6*f^3*g^6 - a*b^11*c*d^4*e^5*f^2*g^7 + 16*a^2*b*c^10*d^6*e^3*f^8*g + 16*a^2*
b*c^10*d^8*e*f^6*g^3 - a^2*b^6*c^5*d*e^8*f^8*g - a^2*b^6*c^5*d^8*e*f*g^8 - a^2*b^10*c*d*e^8*f^4*g^5 - a^2*b^10
*c*d^4*e^5*f*g^8 + 304*a^3*b*c^9*d^4*e^5*f^8*g + 304*a^3*b*c^9*d^8*e*f^4*g^5 - 6*a^3*b^9*c*d*e^8*f^3*g^6 - 6*a
^3*b^9*c*d^3*e^6*f*g^8 + 304*a^4*b*c^8*d^2*e^7*f^8*g + 304*a^4*b*c^8*d^8*e*f^2*g^7 + 48*a^4*b^2*c^7*d*e^8*f^8*
g + 48*a^4*b^2*c^7*d^8*e*f*g^8 + 16*a^4*b^8*c*d*e^8*f^2*g^7 + 16*a^4*b^8*c*d^2*e^7*f*g^8 + 288*a^5*b*c^7*d*e^8
*f^7*g^2 + 288*a^5*b*c^7*d^7*e^2*f*g^8 + 1184*a^6*b*c^6*d*e^8*f^5*g^4 + 1184*a^6*b*c^6*d^5*e^4*f*g^8 + 118*a^6
*b^5*c^2*d*e^8*f*g^8 + 1504*a^7*b*c^5*d*e^8*f^3*g^6 + 1504*a^7*b*c^5*d^3*e^6*f*g^8 - 464*a^7*b^3*c^3*d*e^8*f*g
^8)/(16*a^2*c^6*d^4*f^4 + a^4*b^4*e^4*g^4 + 16*a^4*c^4*d^4*g^4 + 16*a^4*c^4*e^4*f^4 + b^4*c^4*d^4*f^4 + 16*a^6
*c^2*e^4*g^4 + a^2*b^4*c^2*d^4*g^4 + a^2*b^4*c^2*e^4*f^4 - 8*a^3*b^2*c^3*d^4*g^4 - 8*a^3*b^2*c^3*e^4*f^4 + a^2
*b^6*d^2*e^2*g^4 + 32*a^3*c^5*d^2*e^2*f^4 + 32*a^5*c^3*d^2*e^2*g^4 + b^6*c^2*d^2*e^2*f^4 + a^2*b^6*e^4*f^2*g^2
+ 32*a^3*c^5*d^4*f^2*g^2 + 32*a^5*c^3*e^4*f^2*g^2 + b^6*c^2*d^4*f^2*g^2 + b^8*d^2*e^2*f^2*g^2 - 8*a*b^2*c^5*d
^4*f^4 - 8*a^5*b^2*c*e^4*g^4 - 2*a^3*b^5*d*e^3*g^4 - 2*b^5*c^3*d^3*e*f^4 - 2*a^3*b^5*e^4*f*g^3 - 2*b^5*c^3*d^4
*f^3*g + 16*a*b^3*c^4*d^3*e*f^4 - 2*a*b^5*c^2*d*e^3*f^4 - 32*a^2*b*c^5*d^3*e*f^4 - 32*a^3*b*c^4*d*e^3*f^4 - 2*
a^2*b^5*c*d^3*e*g^4 - 32*a^4*b*c^3*d^3*e*g^4 + 16*a^4*b^3*c*d*e^3*g^4 - 32*a^5*b*c^2*d*e^3*g^4 + 16*a*b^3*c^4*
d^4*f^3*g - 2*a*b^5*c^2*d^4*f*g^3 - 32*a^2*b*c^5*d^4*f^3*g - 32*a^3*b*c^4*d^4*f*g^3 - 2*a^2*b^5*c*e^4*f^3*g -
32*a^4*b*c^3*e^4*f^3*g + 16*a^4*b^3*c*e^4*f*g^3 - 32*a^5*b*c^2*e^4*f*g^3 - 2*a*b^7*d*e^3*f^2*g^2 - 2*a*b^7*d^2
*e^2*f*g^3 + 4*a^2*b^6*d*e^3*f*g^3 + 4*b^6*c^2*d^3*e*f^3*g - 2*b^7*c*d^2*e^2*f^3*g - 2*b^7*c*d^3*e*f^2*g^2 - 6
*a*b^4*c^3*d^2*e^2*f^4 + 16*a^2*b^3*c^3*d*e^3*f^4 + 16*a^3*b^3*c^2*d^3*e*g^4 - 6*a^3*b^4*c*d^2*e^2*g^4 - 6*a*b
^4*c^3*d^4*f^2*g^2 + 16*a^2*b^3*c^3*d^4*f*g^3 + 16*a^3*b^3*c^2*e^4*f^3*g - 6*a^3*b^4*c*e^4*f^2*g^2 + 64*a^4*c^
4*d^2*e^2*f^2*g^2 + 4*a*b^6*c*d*e^3*f^3*g + 4*a*b^6*c*d^3*e*f*g^3 - 32*a*b^4*c^3*d^3*e*f^3*g - 32*a^3*b^4*c*d*
e^3*f*g^3 - 12*a^2*b^4*c^2*d^2*e^2*f^2*g^2 + 32*a^3*b^2*c^3*d^2*e^2*f^2*g^2 + 12*a*b^5*c^2*d^2*e^2*f^3*g + 12*
a*b^5*c^2*d^3*e*f^2*g^2 - 4*a*b^6*c*d^2*e^2*f^2*g^2 + 64*a^2*b^2*c^4*d^3*e*f^3*g - 32*a^2*b^4*c^2*d*e^3*f^3*g
- 32*a^2*b^4*c^2*d^3*e*f*g^3 + 12*a^2*b^5*c*d*e^3*f^2*g^2 + 12*a^2*b^5*c*d^2*e^2*f*g^3 - 64*a^3*b*c^4*d^2*e^2*
f^3*g - 64*a^3*b*c^4*d^3*e*f^2*g^2 + 64*a^3*b^2*c^3*d*e^3*f^3*g + 64*a^3*b^2*c^3*d^3*e*f*g^3 - 64*a^4*b*c^3*d*
e^3*f^2*g^2 - 64*a^4*b*c^3*d^2*e^2*f*g^3 + 64*a^4*b^2*c^2*d*e^3*f*g^3) - (x*(128*a^9*c^4*e^9*g^9 + 24*a^7*b^4*
c^2*e^9*g^9 - 96*a^8*b^2*c^3*e^9*g^9 + 288*a^6*c^7*d^6*e^3*g^9 + 416*a^7*c^6*d^4*e^5*g^9 + 352*a^8*c^5*d^2*e^7
*g^9 + 288*a^6*c^7*e^9*f^6*g^3 + 416*a^7*c^6*e^9*f^4*g^5 + 352*a^8*c^5*e^9*f^2*g^7 - 2*a^6*b^6*c*e^9*g^9 + 96*
a^5*c^8*d^8*e*g^9 + 96*a^5*c^8*e^9*f^8*g + 6*a^5*b^7*c*d*e^8*g^9 - 384*a^8*b*c^4*d*e^8*g^9 + 6*a^5*b^7*c*e^9*f
*g^8 - 384*a^8*b*c^4*e^9*f*g^8 + 64*a^8*c^5*d*e^8*f*g^8 - 2*a^2*b^6*c^5*d^8*e*g^9 - 2*a^2*b^10*c*d^4*e^5*g^9 +
22*a^3*b^4*c^6*d^8*e*g^9 + 6*a^3*b^9*c*d^3*e^6*g^9 - 80*a^4*b^2*c^7*d^8*e*g^9 - 8*a^4*b^8*c*d^2*e^7*g^9 - 416
*a^5*b*c^7*d^7*e^2*g^9 - 960*a^6*b*c^6*d^5*e^4*g^9 - 72*a^6*b^5*c^2*d*e^8*g^9 - 928*a^7*b*c^5*d^3*e^6*g^9 + 28
8*a^7*b^3*c^3*d*e^8*g^9 - 2*a^2*b^6*c^5*e^9*f^8*g - 2*a^2*b^10*c*e^9*f^4*g^5 + 22*a^3*b^4*c^6*e^9*f^8*g + 6*a^
3*b^9*c*e^9*f^3*g^6 - 80*a^4*b^2*c^7*e^9*f^8*g - 8*a^4*b^8*c*e^9*f^2*g^7 - 416*a^5*b*c^7*e^9*f^7*g^2 - 960*a^6
*b*c^6*e^9*f^5*g^4 - 72*a^6*b^5*c^2*e^9*f*g^8 - 928*a^7*b*c^5*e^9*f^3*g^6 + 288*a^7*b^3*c^3*e^9*f*g^8 - 32*a^2
*c^11*d^6*e^3*f^8*g - 32*a^2*c^11*d^8*e*f^6*g^3 + 32*a^3*c^10*d^4*e^5*f^8*g + 32*a^3*c^10*d^8*e*f^4*g^5 + 160*
a^4*c^9*d^2*e^7*f^8*g + 160*a^4*c^9*d^8*e*f^2*g^7 + 64*a^5*c^8*d*e^8*f^7*g^2 + 64*a^5*c^8*d^7*e^2*f*g^8 + 192*
a^6*c^7*d*e^8*f^5*g^4 + 192*a^6*c^7*d^5*e^4*f*g^8 + 192*a^7*c^6*d*e^8*f^3*g^6 + 192*a^7*c^6*d^3*e^6*f*g^8 - 2*
b^4*c^9*d^6*e^3*f^8*g - 2*b^4*c^9*d^8*e*f^6*g^3 + 6*b^5*c^8*d^5*e^4*f^8*g + 6*b^5*c^8*d^8*e*f^5*g^4 - 8*b^6*c^
7*d^4*e^5*f^8*g - 8*b^6*c^7*d^8*e*f^4*g^5 + 6*b^7*c^6*d^3*e^6*f^8*g + 6*b^7*c^6*d^8*e*f^3*g^6 - 2*b^8*c^5*d^2*
e^7*f^8*g - 2*b^8*c^5*d^8*e*f^2*g^7 - 2*b^12*c*d^2*e^7*f^4*g^5 + 2*b^12*c*d^3*e^6*f^3*g^6 - 2*b^12*c*d^4*e^5*f
^2*g^7 + 8*a^2*b^7*c^4*d^7*e^2*g^9 - 12*a^2*b^8*c^3*d^6*e^3*g^9 + 8*a^2*b^9*c^2*d^5*e^4*g^9 - 90*a^3*b^5*c^5*d
^7*e^2*g^9 + 132*a^3*b^6*c^4*d^6*e^3*g^9 - 76*a^3*b^7*c^3*d^5*e^4*g^9 + 6*a^3*b^8*c^2*d^4*e^5*g^9 + 336*a^4*b^
3*c^6*d^7*e^2*g^9 - 462*a^4*b^4*c^5*d^6*e^3*g^9 + 164*a^4*b^5*c^4*d^5*e^4*g^9 + 106*a^4*b^6*c^3*d^4*e^5*g^9 -
56*a^4*b^7*c^2*d^3*e^6*g^9 + 432*a^5*b^2*c^6*d^6*e^3*g^9 + 288*a^5*b^3*c^5*d^5*e^4*g^9 - 598*a^5*b^4*c^4*d^4*e
^5*g^9 + 102*a^5*b^5*c^3*d^3*e^6*g^9 + 90*a^5*b^6*c^2*d^2*e^7*g^9 + 720*a^6*b^2*c^5*d^4*e^5*g^9 + 336*a^6*b^3*
c^4*d^3*e^6*g^9 - 314*a^6*b^4*c^3*d^2*e^7*g^9 + 240*a^7*b^2*c^4*d^2*e^7*g^9 + 8*a^2*b^7*c^4*e^9*f^7*g^2 - 12*a
^2*b^8*c^3*e^9*f^6*g^3 + 8*a^2*b^9*c^2*e^9*f^5*g^4 - 90*a^3*b^5*c^5*e^9*f^7*g^2 + 132*a^3*b^6*c^4*e^9*f^6*g^3
- 76*a^3*b^7*c^3*e^9*f^5*g^4 + 6*a^3*b^8*c^2*e^9*f^4*g^5 + 336*a^4*b^3*c^6*e^9*f^7*g^2 - 462*a^4*b^4*c^5*e^9*f
^6*g^3 + 164*a^4*b^5*c^4*e^9*f^5*g^4 + 106*a^4*b^6*c^3*e^9*f^4*g^5 - 56*a^4*b^7*c^2*e^9*f^3*g^6 + 432*a^5*b^2*
c^6*e^9*f^6*g^3 + 288*a^5*b^3*c^5*e^9*f^5*g^4 - 598*a^5*b^4*c^4*e^9*f^4*g^5 + 102*a^5*b^5*c^3*e^9*f^3*g^6 + 90
*a^5*b^6*c^2*e^9*f^2*g^7 + 720*a^6*b^2*c^5*e^9*f^4*g^5 + 336*a^6*b^3*c^4*e^9*f^3*g^6 - 314*a^6*b^4*c^3*e^9*f^2
*g^7 + 240*a^7*b^2*c^4*e^9*f^2*g^7 + 64*a^2*c^11*d^7*e^2*f^7*g^2 + 192*a^3*c^10*d^5*e^4*f^7*g^2 - 320*a^3*c^10
*d^6*e^3*f^6*g^3 + 192*a^3*c^10*d^7*e^2*f^5*g^4 + 192*a^4*c^9*d^3*e^6*f^7*g^2 - 256*a^4*c^9*d^4*e^5*f^6*g^3 +
576*a^4*c^9*d^5*e^4*f^5*g^4 - 256*a^4*c^9*d^6*e^3*f^4*g^5 + 192*a^4*c^9*d^7*e^2*f^3*g^6 + 320*a^5*c^8*d^2*e^7*
f^6*g^3 + 576*a^5*c^8*d^3*e^6*f^5*g^4 - 192*a^5*c^8*d^4*e^5*f^4*g^5 + 576*a^5*c^8*d^5*e^4*f^3*g^6 + 320*a^5*c^
8*d^6*e^3*f^2*g^7 + 512*a^6*c^7*d^2*e^7*f^4*g^5 + 576*a^6*c^7*d^3*e^6*f^3*g^6 + 512*a^6*c^7*d^4*e^5*f^2*g^7 +
704*a^7*c^6*d^2*e^7*f^2*g^7 + 4*b^4*c^9*d^7*e^2*f^7*g^2 - 6*b^5*c^8*d^6*e^3*f^7*g^2 - 6*b^5*c^8*d^7*e^2*f^6*g^
3 - 6*b^6*c^7*d^5*e^4*f^7*g^2 + 26*b^6*c^7*d^6*e^3*f^6*g^3 - 6*b^6*c^7*d^7*e^2*f^5*g^4 + 22*b^7*c^6*d^4*e^5*f^
7*g^2 - 22*b^7*c^6*d^5*e^4*f^6*g^3 - 22*b^7*c^6*d^6*e^3*f^5*g^4 + 22*b^7*c^6*d^7*e^2*f^4*g^5 - 22*b^8*c^5*d^3*
e^6*f^7*g^2 - 12*b^8*c^5*d^4*e^5*f^6*g^3 + 42*b^8*c^5*d^5*e^4*f^5*g^4 - 12*b^8*c^5*d^6*e^3*f^4*g^5 - 22*b^8*c^
5*d^7*e^2*f^3*g^6 + 8*b^9*c^4*d^2*e^7*f^7*g^2 + 28*b^9*c^4*d^3*e^6*f^6*g^3 - 16*b^9*c^4*d^4*e^5*f^5*g^4 - 16*b
^9*c^4*d^5*e^4*f^4*g^5 + 28*b^9*c^4*d^6*e^3*f^3*g^6 + 8*b^9*c^4*d^7*e^2*f^2*g^7 - 12*b^10*c^3*d^2*e^7*f^6*g^3
- 12*b^10*c^3*d^3*e^6*f^5*g^4 + 18*b^10*c^3*d^4*e^5*f^4*g^5 - 12*b^10*c^3*d^5*e^4*f^3*g^6 - 12*b^10*c^3*d^6*e^
3*f^2*g^7 + 8*b^11*c^2*d^2*e^7*f^5*g^4 - 2*b^11*c^2*d^3*e^6*f^4*g^5 - 2*b^11*c^2*d^4*e^5*f^3*g^6 + 8*b^11*c^2*
d^5*e^4*f^2*g^7 - 32*a*b^2*c^10*d^7*e^2*f^7*g^2 + 48*a*b^3*c^9*d^6*e^3*f^7*g^2 + 48*a*b^3*c^9*d^7*e^2*f^6*g^3
+ 60*a*b^4*c^8*d^5*e^4*f^7*g^2 - 228*a*b^4*c^8*d^6*e^3*f^6*g^3 + 60*a*b^4*c^8*d^7*e^2*f^5*g^4 - 214*a*b^5*c^7*
d^4*e^5*f^7*g^2 + 194*a*b^5*c^7*d^5*e^4*f^6*g^3 + 194*a*b^5*c^7*d^6*e^3*f^5*g^4 - 214*a*b^5*c^7*d^7*e^2*f^4*g^
5 + 216*a*b^6*c^6*d^3*e^6*f^7*g^2 + 148*a*b^6*c^6*d^4*e^5*f^6*g^3 - 408*a*b^6*c^6*d^5*e^4*f^5*g^4 + 148*a*b^6*
c^6*d^6*e^3*f^4*g^5 + 216*a*b^6*c^6*d^7*e^2*f^3*g^6 - 62*a*b^7*c^5*d^2*e^7*f^7*g^2 - 302*a*b^7*c^5*d^3*e^6*f^6
*g^3 + 150*a*b^7*c^5*d^4*e^5*f^5*g^4 + 150*a*b^7*c^5*d^5*e^4*f^4*g^5 - 302*a*b^7*c^5*d^6*e^3*f^3*g^6 - 62*a*b^
7*c^5*d^7*e^2*f^2*g^7 + 100*a*b^8*c^4*d^2*e^7*f^6*g^3 + 136*a*b^8*c^4*d^3*e^6*f^5*g^4 - 200*a*b^8*c^4*d^4*e^5*
f^4*g^5 + 136*a*b^8*c^4*d^5*e^4*f^3*g^6 + 100*a*b^8*c^4*d^6*e^3*f^2*g^7 - 68*a*b^9*c^3*d^2*e^7*f^5*g^4 + 32*a*
b^9*c^3*d^3*e^6*f^4*g^5 + 32*a*b^9*c^3*d^4*e^5*f^3*g^6 - 68*a*b^9*c^3*d^5*e^4*f^2*g^7 + 14*a*b^10*c^2*d^2*e^7*
f^4*g^5 - 32*a*b^10*c^2*d^3*e^6*f^3*g^6 + 14*a*b^10*c^2*d^4*e^5*f^2*g^7 - 96*a^2*b*c^10*d^6*e^3*f^7*g^2 - 96*a
^2*b*c^10*d^7*e^2*f^6*g^3 - 144*a^2*b^2*c^9*d^4*e^5*f^8*g - 144*a^2*b^2*c^9*d^8*e*f^4*g^5 + 128*a^2*b^3*c^8*d^
3*e^6*f^8*g + 128*a^2*b^3*c^8*d^8*e*f^3*g^6 - 6*a^2*b^4*c^7*d^2*e^7*f^8*g - 6*a^2*b^4*c^7*d^8*e*f^2*g^7 + 174*
a^2*b^6*c^5*d*e^8*f^7*g^2 + 174*a^2*b^6*c^5*d^7*e^2*f*g^8 - 260*a^2*b^7*c^4*d*e^8*f^6*g^3 - 260*a^2*b^7*c^4*d^
6*e^3*f*g^8 + 156*a^2*b^8*c^3*d*e^8*f^5*g^4 + 156*a^2*b^8*c^3*d^5*e^4*f*g^8 - 18*a^2*b^9*c^2*d*e^8*f^4*g^5 - 1
8*a^2*b^9*c^2*d^4*e^5*f*g^8 - 6*a^2*b^10*c*d^2*e^7*f^2*g^7 - 608*a^3*b*c^9*d^4*e^5*f^7*g^2 + 288*a^3*b*c^9*d^5
*e^4*f^6*g^3 + 288*a^3*b*c^9*d^6*e^3*f^5*g^4 - 608*a^3*b*c^9*d^7*e^2*f^4*g^5 - 112*a^3*b^2*c^8*d^2*e^7*f^8*g -
112*a^3*b^2*c^8*d^8*e*f^2*g^7 - 620*a^3*b^4*c^6*d*e^8*f^7*g^2 - 620*a^3*b^4*c^6*d^7*e^2*f*g^8 + 894*a^3*b^5*c
^5*d*e^8*f^6*g^3 + 894*a^3*b^5*c^5*d^6*e^3*f*g^8 - 384*a^3*b^6*c^4*d*e^8*f^5*g^4 - 384*a^3*b^6*c^4*d^5*e^4*f*g
^8 - 140*a^3*b^7*c^3*d*e^8*f^4*g^5 - 140*a^3*b^7*c^3*d^4*e^5*f*g^8 + 92*a^3*b^8*c^2*d*e^8*f^3*g^6 + 92*a^3*b^8
*c^2*d^3*e^6*f*g^8 - 928*a^4*b*c^8*d^2*e^7*f^7*g^2 - 160*a^4*b*c^8*d^3*e^6*f^6*g^3 - 672*a^4*b*c^8*d^4*e^5*f^5
*g^4 - 672*a^4*b*c^8*d^5*e^4*f^4*g^5 - 160*a^4*b*c^8*d^6*e^3*f^3*g^6 - 928*a^4*b*c^8*d^7*e^2*f^2*g^7 + 704*a^4
*b^2*c^7*d*e^8*f^7*g^2 + 704*a^4*b^2*c^7*d^7*e^2*f*g^8 - 816*a^4*b^3*c^6*d*e^8*f^6*g^3 - 816*a^4*b^3*c^6*d^6*e
^3*f*g^8 - 308*a^4*b^4*c^5*d*e^8*f^5*g^4 - 308*a^4*b^4*c^5*d^5*e^4*f*g^8 + 898*a^4*b^5*c^4*d*e^8*f^4*g^5 + 898
*a^4*b^5*c^4*d^4*e^5*f*g^8 - 150*a^4*b^6*c^3*d*e^8*f^3*g^6 - 150*a^4*b^6*c^3*d^3*e^6*f*g^8 - 154*a^4*b^7*c^2*d
*e^8*f^2*g^7 - 154*a^4*b^7*c^2*d^2*e^7*f*g^8 - 1824*a^5*b*c^7*d^2*e^7*f^5*g^4 - 1056*a^5*b*c^7*d^3*e^6*f^4*g^5
- 1056*a^5*b*c^7*d^4*e^5*f^3*g^6 - 1824*a^5*b*c^7*d^5*e^4*f^2*g^7 + 1440*a^5*b^2*c^6*d*e^8*f^5*g^4 + 1440*a^5
*b^2*c^6*d^5*e^4*f*g^8 - 976*a^5*b^3*c^5*d*e^8*f^4*g^5 - 976*a^5*b^3*c^5*d^4*e^5*f*g^8 - 644*a^5*b^4*c^4*d*e^8
*f^3*g^6 - 644*a^5*b^4*c^4*d^3*e^6*f*g^8 + 498*a^5*b^5*c^3*d*e^8*f^2*g^7 + 498*a^5*b^5*c^3*d^2*e^7*f*g^8 - 188
8*a^6*b*c^6*d^2*e^7*f^3*g^6 - 1888*a^6*b*c^6*d^3*e^6*f^2*g^7 + 1600*a^6*b^2*c^5*d*e^8*f^3*g^6 + 1600*a^6*b^2*c
^5*d^3*e^6*f*g^8 - 176*a^6*b^3*c^4*d*e^8*f^2*g^7 - 176*a^6*b^3*c^4*d^2*e^7*f*g^8 + 4*a*b^7*c^5*d*e^8*f^8*g + 4
*a*b^7*c^5*d^8*e*f*g^8 + 4*a*b^11*c*d*e^8*f^4*g^5 + 4*a*b^11*c*d^4*e^5*f*g^8 - 160*a^4*b*c^8*d*e^8*f^8*g - 160
*a^4*b*c^8*d^8*e*f*g^8 - 14*a^4*b^8*c*d*e^8*f*g^8 - 192*a^2*b^2*c^9*d^5*e^4*f^7*g^2 + 576*a^2*b^2*c^9*d^6*e^3*
f^6*g^3 - 192*a^2*b^2*c^9*d^7*e^2*f^5*g^4 + 656*a^2*b^3*c^8*d^4*e^5*f^7*g^2 - 496*a^2*b^3*c^8*d^5*e^4*f^6*g^3
- 496*a^2*b^3*c^8*d^6*e^3*f^5*g^4 + 656*a^2*b^3*c^8*d^7*e^2*f^4*g^5 - 660*a^2*b^4*c^7*d^3*e^6*f^7*g^2 - 624*a^
2*b^4*c^7*d^4*e^5*f^6*g^3 + 1284*a^2*b^4*c^7*d^5*e^4*f^5*g^4 - 624*a^2*b^4*c^7*d^6*e^3*f^4*g^5 - 660*a^2*b^4*c
^7*d^7*e^2*f^3*g^6 + 54*a^2*b^5*c^6*d^2*e^7*f^7*g^2 + 1062*a^2*b^5*c^6*d^3*e^6*f^6*g^3 - 474*a^2*b^5*c^6*d^4*e
^5*f^5*g^4 - 474*a^2*b^5*c^6*d^5*e^4*f^4*g^5 + 1062*a^2*b^5*c^6*d^6*e^3*f^3*g^6 + 54*a^2*b^5*c^6*d^7*e^2*f^2*g
^7 - 130*a^2*b^6*c^5*d^2*e^7*f^6*g^3 - 482*a^2*b^6*c^5*d^3*e^6*f^5*g^4 + 850*a^2*b^6*c^5*d^4*e^5*f^4*g^5 - 482
*a^2*b^6*c^5*d^5*e^4*f^3*g^6 - 130*a^2*b^6*c^5*d^6*e^3*f^2*g^7 + 108*a^2*b^7*c^4*d^2*e^7*f^5*g^4 - 228*a^2*b^7
*c^4*d^3*e^6*f^4*g^5 - 228*a^2*b^7*c^4*d^4*e^5*f^3*g^6 + 108*a^2*b^7*c^4*d^5*e^4*f^2*g^7 - 18*a^2*b^8*c^3*d^2*
e^7*f^4*g^5 + 192*a^2*b^8*c^3*d^3*e^6*f^3*g^6 - 18*a^2*b^8*c^3*d^4*e^5*f^2*g^7 - 2*a^2*b^9*c^2*d^2*e^7*f^3*g^6
- 2*a^2*b^9*c^2*d^3*e^6*f^2*g^7 + 544*a^3*b^2*c^8*d^3*e^6*f^7*g^2 + 960*a^3*b^2*c^8*d^4*e^5*f^6*g^3 - 1440*a^
3*b^2*c^8*d^5*e^4*f^5*g^4 + 960*a^3*b^2*c^8*d^6*e^3*f^4*g^5 + 544*a^3*b^2*c^8*d^7*e^2*f^3*g^6 + 496*a^3*b^3*c^
7*d^2*e^7*f^7*g^2 - 1168*a^3*b^3*c^7*d^3*e^6*f^6*g^3 + 688*a^3*b^3*c^7*d^4*e^5*f^5*g^4 + 688*a^3*b^3*c^7*d^5*e
^4*f^4*g^5 - 1168*a^3*b^3*c^7*d^6*e^3*f^3*g^6 + 496*a^3*b^3*c^7*d^7*e^2*f^2*g^7 - 668*a^3*b^4*c^6*d^2*e^7*f^6*
g^3 + 436*a^3*b^4*c^6*d^3*e^6*f^5*g^4 - 1820*a^3*b^4*c^6*d^4*e^5*f^4*g^5 + 436*a^3*b^4*c^6*d^5*e^4*f^3*g^6 - 6
68*a^3*b^4*c^6*d^6*e^3*f^2*g^7 + 238*a^3*b^5*c^5*d^2*e^7*f^5*g^4 + 734*a^3*b^5*c^5*d^3*e^6*f^4*g^5 + 734*a^3*b
^5*c^5*d^4*e^5*f^3*g^6 + 238*a^3*b^5*c^5*d^5*e^4*f^2*g^7 + 144*a^3*b^6*c^4*d^2*e^7*f^4*g^5 - 416*a^3*b^6*c^4*d
^3*e^6*f^3*g^6 + 144*a^3*b^6*c^4*d^4*e^5*f^2*g^7 - 156*a^3*b^7*c^3*d^2*e^7*f^3*g^6 - 156*a^3*b^7*c^3*d^3*e^6*f
^2*g^7 + 44*a^3*b^8*c^2*d^2*e^7*f^2*g^7 + 1344*a^4*b^2*c^7*d^2*e^7*f^6*g^3 + 192*a^4*b^2*c^7*d^3*e^6*f^5*g^4 +
1920*a^4*b^2*c^7*d^4*e^5*f^4*g^5 + 192*a^4*b^2*c^7*d^5*e^4*f^3*g^6 + 1344*a^4*b^2*c^7*d^6*e^3*f^2*g^7 + 80*a^
4*b^3*c^6*d^2*e^7*f^5*g^4 - 560*a^4*b^3*c^6*d^3*e^6*f^4*g^5 - 560*a^4*b^3*c^6*d^4*e^5*f^3*g^6 + 80*a^4*b^3*c^6
*d^5*e^4*f^2*g^7 - 1280*a^4*b^4*c^5*d^2*e^7*f^4*g^5 - 220*a^4*b^4*c^5*d^3*e^6*f^3*g^6 - 1280*a^4*b^4*c^5*d^4*e
^5*f^2*g^7 + 714*a^4*b^5*c^4*d^2*e^7*f^3*g^6 + 714*a^4*b^5*c^4*d^3*e^6*f^2*g^7 + 58*a^4*b^6*c^3*d^2*e^7*f^2*g^
7 + 2304*a^5*b^2*c^6*d^2*e^7*f^4*g^5 + 1248*a^5*b^2*c^6*d^3*e^6*f^3*g^6 + 2304*a^5*b^2*c^6*d^4*e^5*f^2*g^7 - 2
72*a^5*b^3*c^5*d^2*e^7*f^3*g^6 - 272*a^5*b^3*c^5*d^3*e^6*f^2*g^7 - 996*a^5*b^4*c^4*d^2*e^7*f^2*g^7 + 1600*a^6*
b^2*c^5*d^2*e^7*f^2*g^7 + 16*a*b^2*c^10*d^6*e^3*f^8*g + 16*a*b^2*c^10*d^8*e*f^6*g^3 - 48*a*b^3*c^9*d^5*e^4*f^8
*g - 48*a*b^3*c^9*d^8*e*f^5*g^4 + 66*a*b^4*c^8*d^4*e^5*f^8*g + 66*a*b^4*c^8*d^8*e*f^4*g^5 - 52*a*b^5*c^7*d^3*e
^6*f^8*g - 52*a*b^5*c^7*d^8*e*f^3*g^6 + 14*a*b^6*c^6*d^2*e^7*f^8*g + 14*a*b^6*c^6*d^8*e*f^2*g^7 - 16*a*b^8*c^4
*d*e^8*f^7*g^2 - 16*a*b^8*c^4*d^7*e^2*f*g^8 + 24*a*b^9*c^3*d*e^8*f^6*g^3 + 24*a*b^9*c^3*d^6*e^3*f*g^8 - 16*a*b
^10*c^2*d*e^8*f^5*g^4 - 16*a*b^10*c^2*d^5*e^4*f*g^8 + 2*a*b^11*c*d^2*e^7*f^3*g^6 + 2*a*b^11*c*d^3*e^6*f^2*g^7
+ 96*a^2*b*c^10*d^5*e^4*f^8*g + 96*a^2*b*c^10*d^8*e*f^5*g^4 - 42*a^2*b^5*c^6*d*e^8*f^8*g - 42*a^2*b^5*c^6*d^8*
e*f*g^8 - 10*a^2*b^10*c*d*e^8*f^3*g^6 - 10*a^2*b^10*c*d^3*e^6*f*g^8 - 64*a^3*b*c^9*d^3*e^6*f^8*g - 64*a^3*b*c^
9*d^8*e*f^3*g^6 + 144*a^3*b^3*c^7*d*e^8*f^8*g + 144*a^3*b^3*c^7*d^8*e*f*g^8 + 14*a^3*b^9*c*d*e^8*f^2*g^7 + 14*
a^3*b^9*c*d^2*e^7*f*g^8 - 544*a^5*b*c^7*d*e^8*f^6*g^3 - 544*a^5*b*c^7*d^6*e^3*f*g^8 + 168*a^5*b^6*c^2*d*e^8*f*
g^8 - 992*a^6*b*c^6*d*e^8*f^4*g^5 - 992*a^6*b*c^6*d^4*e^5*f*g^8 - 668*a^6*b^4*c^3*d*e^8*f*g^8 - 992*a^7*b*c^5*
d*e^8*f^2*g^7 - 992*a^7*b*c^5*d^2*e^7*f*g^8 + 864*a^7*b^2*c^4*d*e^8*f*g^8))/(16*a^2*c^6*d^4*f^4 + a^4*b^4*e^4*
g^4 + 16*a^4*c^4*d^4*g^4 + 16*a^4*c^4*e^4*f^4 + b^4*c^4*d^4*f^4 + 16*a^6*c^2*e^4*g^4 + a^2*b^4*c^2*d^4*g^4 + a
^2*b^4*c^2*e^4*f^4 - 8*a^3*b^2*c^3*d^4*g^4 - 8*a^3*b^2*c^3*e^4*f^4 + a^2*b^6*d^2*e^2*g^4 + 32*a^3*c^5*d^2*e^2*
f^4 + 32*a^5*c^3*d^2*e^2*g^4 + b^6*c^2*d^2*e^2*f^4 + a^2*b^6*e^4*f^2*g^2 + 32*a^3*c^5*d^4*f^2*g^2 + 32*a^5*c^3
*e^4*f^2*g^2 + b^6*c^2*d^4*f^2*g^2 + b^8*d^2*e^2*f^2*g^2 - 8*a*b^2*c^5*d^4*f^4 - 8*a^5*b^2*c*e^4*g^4 - 2*a^3*b
^5*d*e^3*g^4 - 2*b^5*c^3*d^3*e*f^4 - 2*a^3*b^5*e^4*f*g^3 - 2*b^5*c^3*d^4*f^3*g + 16*a*b^3*c^4*d^3*e*f^4 - 2*a*
b^5*c^2*d*e^3*f^4 - 32*a^2*b*c^5*d^3*e*f^4 - 32*a^3*b*c^4*d*e^3*f^4 - 2*a^2*b^5*c*d^3*e*g^4 - 32*a^4*b*c^3*d^3
*e*g^4 + 16*a^4*b^3*c*d*e^3*g^4 - 32*a^5*b*c^2*d*e^3*g^4 + 16*a*b^3*c^4*d^4*f^3*g - 2*a*b^5*c^2*d^4*f*g^3 - 32
*a^2*b*c^5*d^4*f^3*g - 32*a^3*b*c^4*d^4*f*g^3 - 2*a^2*b^5*c*e^4*f^3*g - 32*a^4*b*c^3*e^4*f^3*g + 16*a^4*b^3*c*
e^4*f*g^3 - 32*a^5*b*c^2*e^4*f*g^3 - 2*a*b^7*d*e^3*f^2*g^2 - 2*a*b^7*d^2*e^2*f*g^3 + 4*a^2*b^6*d*e^3*f*g^3 + 4
*b^6*c^2*d^3*e*f^3*g - 2*b^7*c*d^2*e^2*f^3*g - 2*b^7*c*d^3*e*f^2*g^2 - 6*a*b^4*c^3*d^2*e^2*f^4 + 16*a^2*b^3*c^
3*d*e^3*f^4 + 16*a^3*b^3*c^2*d^3*e*g^4 - 6*a^3*b^4*c*d^2*e^2*g^4 - 6*a*b^4*c^3*d^4*f^2*g^2 + 16*a^2*b^3*c^3*d^
4*f*g^3 + 16*a^3*b^3*c^2*e^4*f^3*g - 6*a^3*b^4*c*e^4*f^2*g^2 + 64*a^4*c^4*d^2*e^2*f^2*g^2 + 4*a*b^6*c*d*e^3*f^
3*g + 4*a*b^6*c*d^3*e*f*g^3 - 32*a*b^4*c^3*d^3*e*f^3*g - 32*a^3*b^4*c*d*e^3*f*g^3 - 12*a^2*b^4*c^2*d^2*e^2*f^2
*g^2 + 32*a^3*b^2*c^3*d^2*e^2*f^2*g^2 + 12*a*b^5*c^2*d^2*e^2*f^3*g + 12*a*b^5*c^2*d^3*e*f^2*g^2 - 4*a*b^6*c*d^
2*e^2*f^2*g^2 + 64*a^2*b^2*c^4*d^3*e*f^3*g - 32*a^2*b^4*c^2*d*e^3*f^3*g - 32*a^2*b^4*c^2*d^3*e*f*g^3 + 12*a^2*
b^5*c*d*e^3*f^2*g^2 + 12*a^2*b^5*c*d^2*e^2*f*g^3 - 64*a^3*b*c^4*d^2*e^2*f^3*g - 64*a^3*b*c^4*d^3*e*f^2*g^2 + 6
4*a^3*b^2*c^3*d*e^3*f^3*g + 64*a^3*b^2*c^3*d^3*e*f*g^3 - 64*a^4*b*c^3*d*e^3*f^2*g^2 - 64*a^4*b*c^3*d^2*e^2*f*g
^3 + 64*a^4*b^2*c^2*d*e^3*f*g^3)) - (48*a^6*b^2*c^3*e^8*g^8 - 12*a^5*b^4*c^2*e^8*g^8 - 64*a^7*c^4*e^8*g^8 + 40
*a^4*c^7*d^6*e^2*g^8 + 80*a^5*c^6*d^4*e^4*g^8 - 24*a^6*c^5*d^2*e^6*g^8 + 40*a^4*c^7*e^8*f^6*g^2 + 80*a^5*c^6*e
^8*f^4*g^4 - 24*a^6*c^5*e^8*f^2*g^6 + a^4*b^6*c*e^8*g^8 + a*b^5*c^5*d^7*e*g^8 + a*b^9*c*d^3*e^5*g^8 + 20*a^3*b
*c^7*d^7*e*g^8 + a*b^5*c^5*e^8*f^7*g + a*b^9*c*e^8*f^3*g^5 + 20*a^3*b*c^7*e^8*f^7*g + 8*a*c^10*d^5*e^3*f^7*g +
8*a*c^10*d^7*e*f^5*g^3 + 8*a^3*c^8*d*e^7*f^7*g + 8*a^3*c^8*d^7*e*f*g^7 + 304*a^6*c^5*d*e^7*f*g^7 - b^6*c^5*d*
e^7*f^7*g - b^6*c^5*d^7*e*f*g^7 - b^10*c*d*e^7*f^3*g^5 - b^10*c*d^3*e^5*f*g^7 - 4*a*b^6*c^4*d^6*e^2*g^8 + 6*a*
b^7*c^3*d^5*e^3*g^8 - 4*a*b^8*c^2*d^4*e^4*g^8 - 9*a^2*b^3*c^6*d^7*e*g^8 - 2*a^2*b^8*c*d^2*e^6*g^8 - 88*a^4*b*c
^6*d^5*e^3*g^8 - 172*a^5*b*c^5*d^3*e^5*g^8 - 4*a*b^6*c^4*e^8*f^6*g^2 + 6*a*b^7*c^3*e^8*f^5*g^3 - 4*a*b^8*c^2*e
^8*f^4*g^4 - 9*a^2*b^3*c^6*e^8*f^7*g - 2*a^2*b^8*c*e^8*f^2*g^6 - 88*a^4*b*c^6*e^8*f^5*g^3 - 172*a^5*b*c^5*e^8*
f^3*g^5 - 16*a*c^10*d^6*e^2*f^6*g^2 + 16*a^2*c^9*d^3*e^5*f^7*g + 16*a^2*c^9*d^7*e*f^3*g^5 + 192*a^4*c^7*d*e^7*
f^5*g^3 + 192*a^4*c^7*d^5*e^3*f*g^7 + 488*a^5*c^6*d*e^7*f^3*g^5 + 488*a^5*c^6*d^3*e^5*f*g^7 - 2*b^2*c^9*d^5*e^
3*f^7*g - 2*b^2*c^9*d^7*e*f^5*g^3 + 3*b^3*c^8*d^4*e^4*f^7*g + 3*b^3*c^8*d^7*e*f^4*g^4 + 4*b^7*c^4*d*e^7*f^6*g^
2 + 4*b^7*c^4*d^6*e^2*f*g^7 - 6*b^8*c^3*d*e^7*f^5*g^3 - 6*b^8*c^3*d^5*e^3*f*g^7 + 4*b^9*c^2*d*e^7*f^4*g^4 + 4*
b^9*c^2*d^4*e^4*f*g^7 - b^10*c*d^2*e^6*f^2*g^6 + 38*a^2*b^4*c^5*d^6*e^2*g^8 - 58*a^2*b^5*c^4*d^5*e^3*g^8 + 36*
a^2*b^6*c^3*d^4*e^4*g^8 - 5*a^2*b^7*c^2*d^3*e^5*g^8 - 98*a^3*b^2*c^6*d^6*e^2*g^8 + 158*a^3*b^3*c^5*d^5*e^3*g^8
- 80*a^3*b^4*c^4*d^4*e^4*g^8 - 22*a^3*b^5*c^3*d^3*e^5*g^8 + 22*a^3*b^6*c^2*d^2*e^6*g^8 - 20*a^4*b^2*c^5*d^4*e
^4*g^8 + 147*a^4*b^3*c^4*d^3*e^5*g^8 - 80*a^4*b^4*c^3*d^2*e^6*g^8 + 102*a^5*b^2*c^4*d^2*e^6*g^8 + 38*a^2*b^4*c
^5*e^8*f^6*g^2 - 58*a^2*b^5*c^4*e^8*f^5*g^3 + 36*a^2*b^6*c^3*e^8*f^4*g^4 - 5*a^2*b^7*c^2*e^8*f^3*g^5 - 98*a^3*
b^2*c^6*e^8*f^6*g^2 + 158*a^3*b^3*c^5*e^8*f^5*g^3 - 80*a^3*b^4*c^4*e^8*f^4*g^4 - 22*a^3*b^5*c^3*e^8*f^3*g^5 +
22*a^3*b^6*c^2*e^8*f^2*g^6 - 20*a^4*b^2*c^5*e^8*f^4*g^4 + 147*a^4*b^3*c^4*e^8*f^3*g^5 - 80*a^4*b^4*c^3*e^8*f^2
*g^6 + 102*a^5*b^2*c^4*e^8*f^2*g^6 - 56*a^2*c^9*d^4*e^4*f^6*g^2 + 80*a^2*c^9*d^5*e^3*f^5*g^3 - 56*a^2*c^9*d^6*
e^2*f^4*g^4 + 264*a^3*c^8*d^3*e^5*f^5*g^3 - 96*a^3*c^8*d^4*e^4*f^4*g^4 + 264*a^3*c^8*d^5*e^3*f^3*g^5 + 40*a^4*
c^7*d^2*e^6*f^4*g^4 + 736*a^4*c^7*d^3*e^5*f^3*g^5 + 40*a^4*c^7*d^4*e^4*f^2*g^6 + 16*a^5*c^6*d^2*e^6*f^2*g^6 +
4*b^2*c^9*d^6*e^2*f^6*g^2 - 3*b^3*c^8*d^5*e^3*f^6*g^2 - 3*b^3*c^8*d^6*e^2*f^5*g^3 - 4*b^4*c^7*d^4*e^4*f^6*g^2
+ 8*b^4*c^7*d^5*e^3*f^5*g^3 - 4*b^4*c^7*d^6*e^2*f^4*g^4 - b^6*c^5*d^2*e^6*f^6*g^2 - b^6*c^5*d^3*e^5*f^5*g^3 -
b^6*c^5*d^4*e^4*f^4*g^4 - b^6*c^5*d^5*e^3*f^3*g^5 - b^6*c^5*d^6*e^2*f^2*g^6 + 4*b^7*c^4*d^2*e^6*f^5*g^3 + 4*b^
7*c^4*d^3*e^5*f^4*g^4 + 4*b^7*c^4*d^4*e^4*f^3*g^5 + 4*b^7*c^4*d^5*e^3*f^2*g^6 - 6*b^8*c^3*d^2*e^6*f^4*g^4 - 6*
b^8*c^3*d^3*e^5*f^3*g^5 - 6*b^8*c^3*d^4*e^4*f^2*g^6 + 4*b^9*c^2*d^2*e^6*f^3*g^5 + 4*b^9*c^2*d^3*e^5*f^2*g^6 +
30*a*b^2*c^8*d^4*e^4*f^6*g^2 - 52*a*b^2*c^8*d^5*e^3*f^5*g^3 + 30*a*b^2*c^8*d^6*e^2*f^4*g^4 - 6*a*b^3*c^7*d^3*e
^5*f^6*g^2 + 8*a*b^3*c^7*d^4*e^4*f^5*g^3 + 8*a*b^3*c^7*d^5*e^3*f^4*g^4 - 6*a*b^3*c^7*d^6*e^2*f^3*g^5 + 20*a*b^
4*c^6*d^2*e^6*f^6*g^2 + 26*a*b^4*c^6*d^3*e^5*f^5*g^3 - 28*a*b^4*c^6*d^4*e^4*f^4*g^4 + 26*a*b^4*c^6*d^5*e^3*f^3
*g^5 + 20*a*b^4*c^6*d^6*e^2*f^2*g^6 - 61*a*b^5*c^5*d^2*e^6*f^5*g^3 - 43*a*b^5*c^5*d^3*e^5*f^4*g^4 - 43*a*b^5*c
^5*d^4*e^4*f^3*g^5 - 61*a*b^5*c^5*d^5*e^3*f^2*g^6 + 80*a*b^6*c^4*d^2*e^6*f^4*g^4 + 68*a*b^6*c^4*d^3*e^5*f^3*g^
5 + 80*a*b^6*c^4*d^4*e^4*f^2*g^6 - 44*a*b^7*c^3*d^2*e^6*f^3*g^5 - 44*a*b^7*c^3*d^3*e^5*f^2*g^6 + 4*a*b^8*c^2*d
^2*e^6*f^2*g^6 + 24*a^2*b*c^8*d^3*e^5*f^6*g^2 - 32*a^2*b*c^8*d^4*e^4*f^5*g^3 - 32*a^2*b*c^8*d^5*e^3*f^4*g^4 +
24*a^2*b*c^8*d^6*e^2*f^3*g^5 + 113*a^2*b^3*c^6*d*e^7*f^6*g^2 + 113*a^2*b^3*c^6*d^6*e^2*f*g^7 - 152*a^2*b^4*c^5
*d*e^7*f^5*g^3 - 152*a^2*b^4*c^5*d^5*e^3*f*g^7 + 34*a^2*b^5*c^4*d*e^7*f^4*g^4 + 34*a^2*b^5*c^4*d^4*e^4*f*g^7 +
64*a^2*b^6*c^3*d*e^7*f^3*g^5 + 64*a^2*b^6*c^3*d^3*e^5*f*g^7 - 31*a^2*b^7*c^2*d*e^7*f^2*g^6 - 31*a^2*b^7*c^2*d
^2*e^6*f*g^7 - 260*a^3*b*c^7*d^2*e^6*f^5*g^3 - 476*a^3*b*c^7*d^3*e^5*f^4*g^4 - 476*a^3*b*c^7*d^4*e^4*f^3*g^5 -
260*a^3*b*c^7*d^5*e^3*f^2*g^6 - 16*a^3*b^2*c^6*d*e^7*f^5*g^3 - 16*a^3*b^2*c^6*d^5*e^3*f*g^7 + 282*a^3*b^3*c^5
*d*e^7*f^4*g^4 + 282*a^3*b^3*c^5*d^4*e^4*f*g^7 - 316*a^3*b^4*c^4*d*e^7*f^3*g^5 - 316*a^3*b^4*c^4*d^3*e^5*f*g^7
+ 70*a^3*b^5*c^3*d*e^7*f^2*g^6 + 70*a^3*b^5*c^3*d^2*e^6*f*g^7 - 928*a^4*b*c^6*d^2*e^6*f^3*g^5 - 928*a^4*b*c^6
*d^3*e^5*f^2*g^6 + 246*a^4*b^2*c^5*d*e^7*f^3*g^5 + 246*a^4*b^2*c^5*d^3*e^5*f*g^7 + 173*a^4*b^3*c^4*d*e^7*f^2*g
^6 + 173*a^4*b^3*c^4*d^2*e^6*f*g^7 - 12*a*b*c^9*d^4*e^4*f^7*g - 12*a*b*c^9*d^7*e*f^4*g^4 + 10*a*b^4*c^6*d*e^7*
f^7*g + 10*a*b^4*c^6*d^7*e*f*g^7 + 3*a*b^9*c*d*e^7*f^2*g^6 + 3*a*b^9*c*d^2*e^6*f*g^7 - 2*a^2*b^8*c*d*e^7*f*g^7
- 64*a^2*b^2*c^7*d^2*e^6*f^6*g^2 - 154*a^2*b^2*c^7*d^3*e^5*f^5*g^3 + 152*a^2*b^2*c^7*d^4*e^4*f^4*g^4 - 154*a^
2*b^2*c^7*d^5*e^3*f^3*g^5 - 64*a^2*b^2*c^7*d^6*e^2*f^2*g^6 + 245*a^2*b^3*c^6*d^2*e^6*f^5*g^3 + 227*a^2*b^3*c^6
*d^3*e^5*f^4*g^4 + 227*a^2*b^3*c^6*d^4*e^4*f^3*g^5 + 245*a^2*b^3*c^6*d^5*e^3*f^2*g^6 - 346*a^2*b^4*c^5*d^2*e^6
*f^4*g^4 - 280*a^2*b^4*c^5*d^3*e^5*f^3*g^5 - 346*a^2*b^4*c^5*d^4*e^4*f^2*g^6 + 120*a^2*b^5*c^4*d^2*e^6*f^3*g^5
+ 120*a^2*b^5*c^4*d^3*e^5*f^2*g^6 + 70*a^2*b^6*c^3*d^2*e^6*f^2*g^6 + 478*a^3*b^2*c^6*d^2*e^6*f^4*g^4 + 232*a^
3*b^2*c^6*d^3*e^5*f^3*g^5 + 478*a^3*b^2*c^6*d^4*e^4*f^2*g^6 + 200*a^3*b^3*c^5*d^2*e^6*f^3*g^5 + 200*a^3*b^3*c^
5*d^3*e^5*f^2*g^6 - 528*a^3*b^4*c^4*d^2*e^6*f^2*g^6 + 988*a^4*b^2*c^5*d^2*e^6*f^2*g^6 + 12*a*b*c^9*d^5*e^3*f^6
*g^2 + 12*a*b*c^9*d^6*e^2*f^5*g^3 - 4*a*b^2*c^8*d^3*e^5*f^7*g - 4*a*b^2*c^8*d^7*e*f^3*g^5 - 2*a*b^3*c^7*d^2*e^
6*f^7*g - 2*a*b^3*c^7*d^7*e*f^2*g^6 - 41*a*b^5*c^5*d*e^7*f^6*g^2 - 41*a*b^5*c^5*d^6*e^2*f*g^7 + 60*a*b^6*c^4*d
*e^7*f^5*g^3 + 60*a*b^6*c^4*d^5*e^3*f*g^7 - 34*a*b^7*c^3*d*e^7*f^4*g^4 - 34*a*b^7*c^3*d^4*e^4*f*g^7 + 2*a*b^8*
c^2*d*e^7*f^3*g^5 + 2*a*b^8*c^2*d^3*e^5*f*g^7 + 8*a^2*b*c^8*d^2*e^6*f^7*g + 8*a^2*b*c^8*d^7*e*f^2*g^6 - 26*a^2
*b^2*c^7*d*e^7*f^7*g - 26*a^2*b^2*c^7*d^7*e*f*g^7 - 52*a^3*b*c^7*d*e^7*f^6*g^2 - 52*a^3*b*c^7*d^6*e^2*f*g^7 +
24*a^3*b^6*c^2*d*e^7*f*g^7 - 520*a^4*b*c^6*d*e^7*f^4*g^4 - 520*a^4*b*c^6*d^4*e^4*f*g^7 - 80*a^4*b^4*c^3*d*e^7*
f*g^7 - 596*a^5*b*c^5*d*e^7*f^2*g^6 - 596*a^5*b*c^5*d^2*e^6*f*g^7 - 12*a^5*b^2*c^4*d*e^7*f*g^7)/(16*a^2*c^6*d^
4*f^4 + a^4*b^4*e^4*g^4 + 16*a^4*c^4*d^4*g^4 + 16*a^4*c^4*e^4*f^4 + b^4*c^4*d^4*f^4 + 16*a^6*c^2*e^4*g^4 + a^2
*b^4*c^2*d^4*g^4 + a^2*b^4*c^2*e^4*f^4 - 8*a^3*b^2*c^3*d^4*g^4 - 8*a^3*b^2*c^3*e^4*f^4 + a^2*b^6*d^2*e^2*g^4 +
32*a^3*c^5*d^2*e^2*f^4 + 32*a^5*c^3*d^2*e^2*g^4 + b^6*c^2*d^2*e^2*f^4 + a^2*b^6*e^4*f^2*g^2 + 32*a^3*c^5*d^4*
f^2*g^2 + 32*a^5*c^3*e^4*f^2*g^2 + b^6*c^2*d^4*f^2*g^2 + b^8*d^2*e^2*f^2*g^2 - 8*a*b^2*c^5*d^4*f^4 - 8*a^5*b^2
*c*e^4*g^4 - 2*a^3*b^5*d*e^3*g^4 - 2*b^5*c^3*d^3*e*f^4 - 2*a^3*b^5*e^4*f*g^3 - 2*b^5*c^3*d^4*f^3*g + 16*a*b^3*
c^4*d^3*e*f^4 - 2*a*b^5*c^2*d*e^3*f^4 - 32*a^2*b*c^5*d^3*e*f^4 - 32*a^3*b*c^4*d*e^3*f^4 - 2*a^2*b^5*c*d^3*e*g^
4 - 32*a^4*b*c^3*d^3*e*g^4 + 16*a^4*b^3*c*d*e^3*g^4 - 32*a^5*b*c^2*d*e^3*g^4 + 16*a*b^3*c^4*d^4*f^3*g - 2*a*b^
5*c^2*d^4*f*g^3 - 32*a^2*b*c^5*d^4*f^3*g - 32*a^3*b*c^4*d^4*f*g^3 - 2*a^2*b^5*c*e^4*f^3*g - 32*a^4*b*c^3*e^4*f
^3*g + 16*a^4*b^3*c*e^4*f*g^3 - 32*a^5*b*c^2*e^4*f*g^3 - 2*a*b^7*d*e^3*f^2*g^2 - 2*a*b^7*d^2*e^2*f*g^3 + 4*a^2
*b^6*d*e^3*f*g^3 + 4*b^6*c^2*d^3*e*f^3*g - 2*b^7*c*d^2*e^2*f^3*g - 2*b^7*c*d^3*e*f^2*g^2 - 6*a*b^4*c^3*d^2*e^2
*f^4 + 16*a^2*b^3*c^3*d*e^3*f^4 + 16*a^3*b^3*c^2*d^3*e*g^4 - 6*a^3*b^4*c*d^2*e^2*g^4 - 6*a*b^4*c^3*d^4*f^2*g^2
+ 16*a^2*b^3*c^3*d^4*f*g^3 + 16*a^3*b^3*c^2*e^4*f^3*g - 6*a^3*b^4*c*e^4*f^2*g^2 + 64*a^4*c^4*d^2*e^2*f^2*g^2
+ 4*a*b^6*c*d*e^3*f^3*g + 4*a*b^6*c*d^3*e*f*g^3 - 32*a*b^4*c^3*d^3*e*f^3*g - 32*a^3*b^4*c*d*e^3*f*g^3 - 12*a^2
*b^4*c^2*d^2*e^2*f^2*g^2 + 32*a^3*b^2*c^3*d^2*e^2*f^2*g^2 + 12*a*b^5*c^2*d^2*e^2*f^3*g + 12*a*b^5*c^2*d^3*e*f^
2*g^2 - 4*a*b^6*c*d^2*e^2*f^2*g^2 + 64*a^2*b^2*c^4*d^3*e*f^3*g - 32*a^2*b^4*c^2*d*e^3*f^3*g - 32*a^2*b^4*c^2*d
^3*e*f*g^3 + 12*a^2*b^5*c*d*e^3*f^2*g^2 + 12*a^2*b^5*c*d^2*e^2*f*g^3 - 64*a^3*b*c^4*d^2*e^2*f^3*g - 64*a^3*b*c
^4*d^3*e*f^2*g^2 + 64*a^3*b^2*c^3*d*e^3*f^3*g + 64*a^3*b^2*c^3*d^3*e*f*g^3 - 64*a^4*b*c^3*d*e^3*f^2*g^2 - 64*a
^4*b*c^3*d^2*e^2*f*g^3 + 64*a^4*b^2*c^2*d*e^3*f*g^3) + (x*(48*a^4*b^5*c^2*e^8*g^8 - 192*a^5*b^3*c^3*e^8*g^8 -
256*a^4*c^7*d^5*e^3*g^8 - 464*a^5*c^6*d^3*e^5*g^8 - 256*a^4*c^7*e^8*f^5*g^3 - 464*a^5*c^6*e^8*f^3*g^5 - 4*a^3*
b^7*c*e^8*g^8 + 256*a^6*b*c^4*e^8*g^8 - 48*a^3*c^8*d^7*e*g^8 - 256*a^6*c^5*d*e^7*g^8 - 48*a^3*c^8*e^8*f^7*g -
256*a^6*c^5*e^8*f*g^7 - 2*a*b^4*c^6*d^7*e*g^8 - 2*a*b^9*c*d^2*e^6*g^8 + 6*a^2*b^8*c*d*e^7*g^8 - 2*a*b^4*c^6*e^
8*f^7*g - 2*a*b^9*c*e^8*f^2*g^6 + 6*a^2*b^8*c*e^8*f*g^7 - 16*a*c^10*d^4*e^4*f^7*g - 16*a*c^10*d^7*e*f^4*g^4 +
2*b^5*c^6*d*e^7*f^7*g + 2*b^5*c^6*d^7*e*f*g^7 + 2*b^10*c*d*e^7*f^2*g^6 + 2*b^10*c*d^2*e^6*f*g^7 + 6*a*b^5*c^5*
d^6*e^2*g^8 - 4*a*b^6*c^4*d^5*e^3*g^8 - 4*a*b^7*c^3*d^4*e^4*g^8 + 6*a*b^8*c^2*d^3*e^5*g^8 + 20*a^2*b^2*c^7*d^7
*e*g^8 + 144*a^3*b*c^7*d^6*e^2*g^8 - 68*a^3*b^6*c^2*d*e^7*g^8 + 640*a^4*b*c^6*d^4*e^4*g^8 + 240*a^4*b^4*c^3*d*
e^7*g^8 + 848*a^5*b*c^5*d^2*e^6*g^8 - 192*a^5*b^2*c^4*d*e^7*g^8 + 6*a*b^5*c^5*e^8*f^6*g^2 - 4*a*b^6*c^4*e^8*f^
5*g^3 - 4*a*b^7*c^3*e^8*f^4*g^4 + 6*a*b^8*c^2*e^8*f^3*g^5 + 20*a^2*b^2*c^7*e^8*f^7*g + 144*a^3*b*c^7*e^8*f^6*g
^2 - 68*a^3*b^6*c^2*e^8*f*g^7 + 640*a^4*b*c^6*e^8*f^4*g^4 + 240*a^4*b^4*c^3*e^8*f*g^7 + 848*a^5*b*c^5*e^8*f^2*
g^6 - 192*a^5*b^2*c^4*e^8*f*g^7 + 16*a*c^10*d^5*e^3*f^6*g^2 + 16*a*c^10*d^6*e^2*f^5*g^3 - 64*a^2*c^9*d^2*e^6*f
^7*g - 64*a^2*c^9*d^7*e*f^2*g^6 + 48*a^3*c^8*d*e^7*f^6*g^2 + 48*a^3*c^8*d^6*e^2*f*g^7 - 304*a^5*c^6*d*e^7*f^2*
g^6 - 304*a^5*c^6*d^2*e^6*f*g^7 + 4*b^2*c^9*d^4*e^4*f^7*g + 4*b^2*c^9*d^7*e*f^4*g^4 - 8*b^3*c^8*d^3*e^5*f^7*g
- 8*b^3*c^8*d^7*e*f^3*g^5 + 2*b^4*c^7*d^2*e^6*f^7*g + 2*b^4*c^7*d^7*e*f^2*g^6 - 6*b^6*c^5*d*e^7*f^6*g^2 - 6*b^
6*c^5*d^6*e^2*f*g^7 + 4*b^7*c^4*d*e^7*f^5*g^3 + 4*b^7*c^4*d^5*e^3*f*g^7 + 4*b^8*c^3*d*e^7*f^4*g^4 + 4*b^8*c^3*
d^4*e^4*f*g^7 - 6*b^9*c^2*d*e^7*f^3*g^5 - 6*b^9*c^2*d^3*e^5*f*g^7 - 60*a^2*b^3*c^6*d^6*e^2*g^8 + 30*a^2*b^4*c^
5*d^5*e^3*g^8 + 64*a^2*b^5*c^4*d^4*e^4*g^8 - 72*a^2*b^6*c^3*d^3*e^5*g^8 + 12*a^2*b^7*c^2*d^2*e^6*g^8 + 8*a^3*b
^2*c^6*d^5*e^3*g^8 - 352*a^3*b^3*c^5*d^4*e^4*g^8 + 268*a^3*b^4*c^4*d^3*e^5*g^8 + 52*a^3*b^5*c^3*d^2*e^6*g^8 -
188*a^4*b^2*c^5*d^3*e^5*g^8 - 484*a^4*b^3*c^4*d^2*e^6*g^8 - 60*a^2*b^3*c^6*e^8*f^6*g^2 + 30*a^2*b^4*c^5*e^8*f^
5*g^3 + 64*a^2*b^5*c^4*e^8*f^4*g^4 - 72*a^2*b^6*c^3*e^8*f^3*g^5 + 12*a^2*b^7*c^2*e^8*f^2*g^6 + 8*a^3*b^2*c^6*e
^8*f^5*g^3 - 352*a^3*b^3*c^5*e^8*f^4*g^4 + 268*a^3*b^4*c^4*e^8*f^3*g^5 + 52*a^3*b^5*c^3*e^8*f^2*g^6 - 188*a^4*
b^2*c^5*e^8*f^3*g^5 - 484*a^4*b^3*c^4*e^8*f^2*g^6 + 64*a^2*c^9*d^3*e^5*f^6*g^2 + 64*a^2*c^9*d^6*e^2*f^3*g^5 -
272*a^3*c^8*d^2*e^6*f^5*g^3 + 16*a^3*c^8*d^3*e^5*f^4*g^4 + 16*a^3*c^8*d^4*e^4*f^3*g^5 - 272*a^3*c^8*d^5*e^3*f^
2*g^6 - 512*a^4*c^7*d^2*e^6*f^3*g^5 - 512*a^4*c^7*d^3*e^5*f^2*g^6 - 4*b^2*c^9*d^5*e^3*f^6*g^2 - 4*b^2*c^9*d^6*
e^2*f^5*g^3 - 4*b^3*c^8*d^4*e^4*f^6*g^2 + 24*b^3*c^8*d^5*e^3*f^5*g^3 - 4*b^3*c^8*d^6*e^2*f^4*g^4 + 22*b^4*c^7*
d^3*e^5*f^6*g^2 - 24*b^4*c^7*d^4*e^4*f^5*g^3 - 24*b^4*c^7*d^5*e^3*f^4*g^4 + 22*b^4*c^7*d^6*e^2*f^3*g^5 - 8*b^5
*c^6*d^2*e^6*f^6*g^2 - 14*b^5*c^6*d^3*e^5*f^5*g^3 + 40*b^5*c^6*d^4*e^4*f^4*g^4 - 14*b^5*c^6*d^5*e^3*f^3*g^5 -
8*b^5*c^6*d^6*e^2*f^2*g^6 + 14*b^6*c^5*d^2*e^6*f^5*g^3 - 4*b^6*c^5*d^3*e^5*f^4*g^4 - 4*b^6*c^5*d^4*e^4*f^3*g^5
+ 14*b^6*c^5*d^5*e^3*f^2*g^6 - 16*b^7*c^4*d^2*e^6*f^4*g^4 - 4*b^7*c^4*d^3*e^5*f^3*g^5 - 16*b^7*c^4*d^4*e^4*f^
2*g^6 + 14*b^8*c^3*d^2*e^6*f^3*g^5 + 14*b^8*c^3*d^3*e^5*f^2*g^6 - 8*b^9*c^2*d^2*e^6*f^2*g^6 - 8*a*b^9*c*d*e^7*
f*g^7 - 104*a*b^2*c^8*d^3*e^5*f^6*g^2 + 96*a*b^2*c^8*d^4*e^4*f^5*g^3 + 96*a*b^2*c^8*d^5*e^3*f^4*g^4 - 104*a*b^
2*c^8*d^6*e^2*f^3*g^5 + 104*a*b^3*c^7*d^3*e^5*f^5*g^3 - 160*a*b^3*c^7*d^4*e^4*f^4*g^4 + 104*a*b^3*c^7*d^5*e^3*
f^3*g^5 - 78*a*b^4*c^6*d^2*e^6*f^5*g^3 - 42*a*b^4*c^6*d^3*e^5*f^4*g^4 - 42*a*b^4*c^6*d^4*e^4*f^3*g^5 - 78*a*b^
4*c^6*d^5*e^3*f^2*g^6 + 166*a*b^5*c^5*d^2*e^6*f^4*g^4 + 88*a*b^5*c^5*d^3*e^5*f^3*g^5 + 166*a*b^5*c^5*d^4*e^4*f
^2*g^6 - 148*a*b^6*c^4*d^2*e^6*f^3*g^5 - 148*a*b^6*c^4*d^3*e^5*f^2*g^6 + 60*a*b^7*c^3*d^2*e^6*f^2*g^6 + 128*a^
2*b*c^8*d^2*e^6*f^6*g^2 - 192*a^2*b*c^8*d^3*e^5*f^5*g^3 - 192*a^2*b*c^8*d^5*e^3*f^3*g^5 + 128*a^2*b*c^8*d^6*e^
2*f^2*g^6 - 212*a^2*b^2*c^7*d*e^7*f^6*g^2 - 212*a^2*b^2*c^7*d^6*e^2*f*g^7 + 96*a^2*b^3*c^6*d*e^7*f^5*g^3 + 96*
a^2*b^3*c^6*d^5*e^3*f*g^7 + 266*a^2*b^4*c^5*d*e^7*f^4*g^4 + 266*a^2*b^4*c^5*d^4*e^4*f*g^7 - 196*a^2*b^5*c^4*d*
e^7*f^3*g^5 - 196*a^2*b^5*c^4*d^3*e^5*f*g^7 - 108*a^2*b^6*c^3*d*e^7*f^2*g^6 - 108*a^2*b^6*c^3*d^2*e^6*f*g^7 +
656*a^3*b*c^7*d^2*e^6*f^4*g^4 - 64*a^3*b*c^7*d^3*e^5*f^3*g^5 + 656*a^3*b*c^7*d^4*e^4*f^2*g^6 - 488*a^3*b^2*c^6
*d*e^7*f^4*g^4 - 488*a^3*b^2*c^6*d^4*e^4*f*g^7 + 16*a^3*b^3*c^5*d*e^7*f^3*g^5 + 16*a^3*b^3*c^5*d^3*e^5*f*g^7 +
612*a^3*b^4*c^4*d*e^7*f^2*g^6 + 612*a^3*b^4*c^4*d^2*e^6*f*g^7 + 1536*a^4*b*c^6*d^2*e^6*f^2*g^6 - 772*a^4*b^2*
c^5*d*e^7*f^2*g^6 - 772*a^4*b^2*c^5*d^2*e^6*f*g^7 + 32*a*b*c^9*d^3*e^5*f^7*g + 32*a*b*c^9*d^7*e*f^3*g^5 - 24*a
*b^3*c^7*d*e^7*f^7*g - 24*a*b^3*c^7*d^7*e*f*g^7 + 64*a^2*b*c^8*d*e^7*f^7*g + 64*a^2*b*c^8*d^7*e*f*g^7 + 608*a^
5*b*c^5*d*e^7*f*g^7 + 156*a^2*b^2*c^7*d^2*e^6*f^5*g^3 + 228*a^2*b^2*c^7*d^3*e^5*f^4*g^4 + 228*a^2*b^2*c^7*d^4*
e^4*f^3*g^5 + 156*a^2*b^2*c^7*d^5*e^3*f^2*g^6 - 572*a^2*b^3*c^6*d^2*e^6*f^4*g^4 - 272*a^2*b^3*c^6*d^3*e^5*f^3*
g^5 - 572*a^2*b^3*c^6*d^4*e^4*f^2*g^6 + 424*a^2*b^4*c^5*d^2*e^6*f^3*g^5 + 424*a^2*b^4*c^5*d^3*e^5*f^2*g^6 + 24
*a^2*b^5*c^4*d^2*e^6*f^2*g^6 - 96*a^3*b^2*c^6*d^2*e^6*f^3*g^5 - 96*a^3*b^2*c^6*d^3*e^5*f^2*g^6 - 928*a^3*b^3*c
^5*d^2*e^6*f^2*g^6 + 16*a*b*c^9*d^4*e^4*f^6*g^2 - 96*a*b*c^9*d^5*e^3*f^5*g^3 + 16*a*b*c^9*d^6*e^2*f^4*g^4 + 8*
a*b^2*c^8*d^2*e^6*f^7*g + 8*a*b^2*c^8*d^7*e*f^2*g^6 + 74*a*b^4*c^6*d*e^7*f^6*g^2 + 74*a*b^4*c^6*d^6*e^2*f*g^7
- 48*a*b^5*c^5*d*e^7*f^5*g^3 - 48*a*b^5*c^5*d^5*e^3*f*g^7 - 52*a*b^6*c^4*d*e^7*f^4*g^4 - 52*a*b^6*c^4*d^4*e^4*
f*g^7 + 64*a*b^7*c^3*d*e^7*f^3*g^5 + 64*a*b^7*c^3*d^3*e^5*f*g^7 - 6*a*b^8*c^2*d*e^7*f^2*g^6 - 6*a*b^8*c^2*d^2*
e^6*f*g^7 + 84*a^2*b^7*c^2*d*e^7*f*g^7 + 128*a^3*b*c^7*d*e^7*f^5*g^3 + 128*a^3*b*c^7*d^5*e^3*f*g^7 - 248*a^3*b
^5*c^3*d*e^7*f*g^7 + 512*a^4*b*c^6*d*e^7*f^3*g^5 + 512*a^4*b*c^6*d^3*e^5*f*g^7 + 8*a^4*b^3*c^4*d*e^7*f*g^7))/(
16*a^2*c^6*d^4*f^4 + a^4*b^4*e^4*g^4 + 16*a^4*c^4*d^4*g^4 + 16*a^4*c^4*e^4*f^4 + b^4*c^4*d^4*f^4 + 16*a^6*c^2*
e^4*g^4 + a^2*b^4*c^2*d^4*g^4 + a^2*b^4*c^2*e^4*f^4 - 8*a^3*b^2*c^3*d^4*g^4 - 8*a^3*b^2*c^3*e^4*f^4 + a^2*b^6*
d^2*e^2*g^4 + 32*a^3*c^5*d^2*e^2*f^4 + 32*a^5*c^3*d^2*e^2*g^4 + b^6*c^2*d^2*e^2*f^4 + a^2*b^6*e^4*f^2*g^2 + 32
*a^3*c^5*d^4*f^2*g^2 + 32*a^5*c^3*e^4*f^2*g^2 + b^6*c^2*d^4*f^2*g^2 + b^8*d^2*e^2*f^2*g^2 - 8*a*b^2*c^5*d^4*f^
4 - 8*a^5*b^2*c*e^4*g^4 - 2*a^3*b^5*d*e^3*g^4 - 2*b^5*c^3*d^3*e*f^4 - 2*a^3*b^5*e^4*f*g^3 - 2*b^5*c^3*d^4*f^3*
g + 16*a*b^3*c^4*d^3*e*f^4 - 2*a*b^5*c^2*d*e^3*f^4 - 32*a^2*b*c^5*d^3*e*f^4 - 32*a^3*b*c^4*d*e^3*f^4 - 2*a^2*b
^5*c*d^3*e*g^4 - 32*a^4*b*c^3*d^3*e*g^4 + 16*a^4*b^3*c*d*e^3*g^4 - 32*a^5*b*c^2*d*e^3*g^4 + 16*a*b^3*c^4*d^4*f
^3*g - 2*a*b^5*c^2*d^4*f*g^3 - 32*a^2*b*c^5*d^4*f^3*g - 32*a^3*b*c^4*d^4*f*g^3 - 2*a^2*b^5*c*e^4*f^3*g - 32*a^
4*b*c^3*e^4*f^3*g + 16*a^4*b^3*c*e^4*f*g^3 - 32*a^5*b*c^2*e^4*f*g^3 - 2*a*b^7*d*e^3*f^2*g^2 - 2*a*b^7*d^2*e^2*
f*g^3 + 4*a^2*b^6*d*e^3*f*g^3 + 4*b^6*c^2*d^3*e*f^3*g - 2*b^7*c*d^2*e^2*f^3*g - 2*b^7*c*d^3*e*f^2*g^2 - 6*a*b^
4*c^3*d^2*e^2*f^4 + 16*a^2*b^3*c^3*d*e^3*f^4 + 16*a^3*b^3*c^2*d^3*e*g^4 - 6*a^3*b^4*c*d^2*e^2*g^4 - 6*a*b^4*c^
3*d^4*f^2*g^2 + 16*a^2*b^3*c^3*d^4*f*g^3 + 16*a^3*b^3*c^2*e^4*f^3*g - 6*a^3*b^4*c*e^4*f^2*g^2 + 64*a^4*c^4*d^2
*e^2*f^2*g^2 + 4*a*b^6*c*d*e^3*f^3*g + 4*a*b^6*c*d^3*e*f*g^3 - 32*a*b^4*c^3*d^3*e*f^3*g - 32*a^3*b^4*c*d*e^3*f
*g^3 - 12*a^2*b^4*c^2*d^2*e^2*f^2*g^2 + 32*a^3*b^2*c^3*d^2*e^2*f^2*g^2 + 12*a*b^5*c^2*d^2*e^2*f^3*g + 12*a*b^5
*c^2*d^3*e*f^2*g^2 - 4*a*b^6*c*d^2*e^2*f^2*g^2 + 64*a^2*b^2*c^4*d^3*e*f^3*g - 32*a^2*b^4*c^2*d*e^3*f^3*g - 32*
a^2*b^4*c^2*d^3*e*f*g^3 + 12*a^2*b^5*c*d*e^3*f^2*g^2 + 12*a^2*b^5*c*d^2*e^2*f*g^3 - 64*a^3*b*c^4*d^2*e^2*f^3*g
- 64*a^3*b*c^4*d^3*e*f^2*g^2 + 64*a^3*b^2*c^3*d*e^3*f^3*g + 64*a^3*b^2*c^3*d^3*e*f*g^3 - 64*a^4*b*c^3*d*e^3*f
^2*g^2 - 64*a^4*b*c^3*d^2*e^2*f*g^3 + 64*a^4*b^2*c^2*d*e^3*f*g^3)) + (x*(b^8*c*e^7*g^7 + 104*a^4*c^5*e^7*g^7 +
50*a^2*b^4*c^3*e^7*g^7 - 96*a^3*b^2*c^4*e^7*g^7 + 36*a^2*c^7*d^4*e^3*g^7 + 72*a^3*c^6*d^2*e^5*g^7 - 2*b^3*c^6
*d^5*e^2*g^7 + b^4*c^5*d^4*e^3*g^7 + b^6*c^3*d^2*e^5*g^7 + 36*a^2*c^7*e^7*f^4*g^3 + 72*a^3*c^6*e^7*f^2*g^5 - 2
*b^3*c^6*e^7*f^5*g^2 + b^4*c^5*e^7*f^4*g^3 + b^6*c^3*e^7*f^2*g^5 - 12*a*b^6*c^2*e^7*g^7 + b^2*c^7*d^6*e*g^7 -
2*b^7*c^2*d*e^6*g^7 + b^2*c^7*e^7*f^6*g - 2*b^7*c^2*e^7*f*g^6 + 4*c^9*d^2*e^5*f^6*g + 4*c^9*d^6*e*f^2*g^5 - 4*
a*b*c^7*d^5*e^2*g^7 + 22*a*b^5*c^3*d*e^6*g^7 - 16*a^3*b*c^5*d*e^6*g^7 - 4*a*b*c^7*e^7*f^5*g^2 + 22*a*b^5*c^3*e
^7*f*g^6 - 16*a^3*b*c^5*e^7*f*g^6 + 8*a*c^8*d*e^6*f^5*g^2 + 8*a*c^8*d^5*e^2*f*g^6 - 112*a^3*c^6*d*e^6*f*g^6 +
4*b^6*c^3*d*e^6*f*g^6 + 2*a*b^2*c^6*d^4*e^3*g^7 + 10*a*b^3*c^5*d^3*e^4*g^7 - 18*a*b^4*c^4*d^2*e^5*g^7 - 80*a^2
*b*c^6*d^3*e^4*g^7 - 56*a^2*b^3*c^4*d*e^6*g^7 + 2*a*b^2*c^6*e^7*f^4*g^3 + 10*a*b^3*c^5*e^7*f^3*g^4 - 18*a*b^4*
c^4*e^7*f^2*g^5 - 80*a^2*b*c^6*e^7*f^3*g^4 - 56*a^2*b^3*c^4*e^7*f*g^6 + 40*a*c^8*d^2*e^5*f^4*g^3 + 40*a*c^8*d^
4*e^3*f^2*g^5 + 16*a^2*c^7*d*e^6*f^3*g^4 + 16*a^2*c^7*d^3*e^4*f*g^6 - 12*b*c^8*d^2*e^5*f^5*g^2 - 12*b*c^8*d^5*
e^2*f^2*g^5 + 10*b^2*c^7*d*e^6*f^5*g^2 + 10*b^2*c^7*d^5*e^2*f*g^6 - 14*b^4*c^5*d*e^6*f^3*g^4 - 14*b^4*c^5*d^3*
e^4*f*g^6 + 6*b^5*c^4*d*e^6*f^2*g^5 + 6*b^5*c^4*d^2*e^5*f*g^6 - 4*b*c^8*d*e^6*f^6*g - 4*b*c^8*d^6*e*f*g^6 + 54
*a^2*b^2*c^5*d^2*e^5*g^7 + 54*a^2*b^2*c^5*e^7*f^2*g^5 + 168*a^2*c^7*d^2*e^5*f^2*g^5 + 5*b^2*c^7*d^2*e^5*f^4*g^
3 + 5*b^2*c^7*d^4*e^3*f^2*g^5 + 10*b^3*c^6*d^2*e^5*f^3*g^4 + 10*b^3*c^6*d^3*e^4*f^2*g^5 - 12*b^4*c^5*d^2*e^5*f
^2*g^5 + 36*a*b^2*c^6*d^2*e^5*f^2*g^5 - 60*a*b*c^7*d*e^6*f^4*g^3 - 60*a*b*c^7*d^4*e^3*f*g^6 - 72*a*b^4*c^4*d*e
^6*f*g^6 - 80*a*b*c^7*d^2*e^5*f^3*g^4 - 80*a*b*c^7*d^3*e^4*f^2*g^5 + 92*a*b^2*c^6*d*e^6*f^3*g^4 + 92*a*b^2*c^6
*d^3*e^4*f*g^6 + 6*a*b^3*c^5*d*e^6*f^2*g^5 + 6*a*b^3*c^5*d^2*e^5*f*g^6 - 192*a^2*b*c^6*d*e^6*f^2*g^5 - 192*a^2
*b*c^6*d^2*e^5*f*g^6 + 276*a^2*b^2*c^5*d*e^6*f*g^6))/(16*a^2*c^6*d^4*f^4 + a^4*b^4*e^4*g^4 + 16*a^4*c^4*d^4*g^
4 + 16*a^4*c^4*e^4*f^4 + b^4*c^4*d^4*f^4 + 16*a^6*c^2*e^4*g^4 + a^2*b^4*c^2*d^4*g^4 + a^2*b^4*c^2*e^4*f^4 - 8*
a^3*b^2*c^3*d^4*g^4 - 8*a^3*b^2*c^3*e^4*f^4 + a^2*b^6*d^2*e^2*g^4 + 32*a^3*c^5*d^2*e^2*f^4 + 32*a^5*c^3*d^2*e^
2*g^4 + b^6*c^2*d^2*e^2*f^4 + a^2*b^6*e^4*f^2*g^2 + 32*a^3*c^5*d^4*f^2*g^2 + 32*a^5*c^3*e^4*f^2*g^2 + b^6*c^2*
d^4*f^2*g^2 + b^8*d^2*e^2*f^2*g^2 - 8*a*b^2*c^5*d^4*f^4 - 8*a^5*b^2*c*e^4*g^4 - 2*a^3*b^5*d*e^3*g^4 - 2*b^5*c^
3*d^3*e*f^4 - 2*a^3*b^5*e^4*f*g^3 - 2*b^5*c^3*d^4*f^3*g + 16*a*b^3*c^4*d^3*e*f^4 - 2*a*b^5*c^2*d*e^3*f^4 - 32*
a^2*b*c^5*d^3*e*f^4 - 32*a^3*b*c^4*d*e^3*f^4 - 2*a^2*b^5*c*d^3*e*g^4 - 32*a^4*b*c^3*d^3*e*g^4 + 16*a^4*b^3*c*d
*e^3*g^4 - 32*a^5*b*c^2*d*e^3*g^4 + 16*a*b^3*c^4*d^4*f^3*g - 2*a*b^5*c^2*d^4*f*g^3 - 32*a^2*b*c^5*d^4*f^3*g -
32*a^3*b*c^4*d^4*f*g^3 - 2*a^2*b^5*c*e^4*f^3*g - 32*a^4*b*c^3*e^4*f^3*g + 16*a^4*b^3*c*e^4*f*g^3 - 32*a^5*b*c^
2*e^4*f*g^3 - 2*a*b^7*d*e^3*f^2*g^2 - 2*a*b^7*d^2*e^2*f*g^3 + 4*a^2*b^6*d*e^3*f*g^3 + 4*b^6*c^2*d^3*e*f^3*g -
2*b^7*c*d^2*e^2*f^3*g - 2*b^7*c*d^3*e*f^2*g^2 - 6*a*b^4*c^3*d^2*e^2*f^4 + 16*a^2*b^3*c^3*d*e^3*f^4 + 16*a^3*b^
3*c^2*d^3*e*g^4 - 6*a^3*b^4*c*d^2*e^2*g^4 - 6*a*b^4*c^3*d^4*f^2*g^2 + 16*a^2*b^3*c^3*d^4*f*g^3 + 16*a^3*b^3*c^
2*e^4*f^3*g - 6*a^3*b^4*c*e^4*f^2*g^2 + 64*a^4*c^4*d^2*e^2*f^2*g^2 + 4*a*b^6*c*d*e^3*f^3*g + 4*a*b^6*c*d^3*e*f
*g^3 - 32*a*b^4*c^3*d^3*e*f^3*g - 32*a^3*b^4*c*d*e^3*f*g^3 - 12*a^2*b^4*c^2*d^2*e^2*f^2*g^2 + 32*a^3*b^2*c^3*d
^2*e^2*f^2*g^2 + 12*a*b^5*c^2*d^2*e^2*f^3*g + 12*a*b^5*c^2*d^3*e*f^2*g^2 - 4*a*b^6*c*d^2*e^2*f^2*g^2 + 64*a^2*
b^2*c^4*d^3*e*f^3*g - 32*a^2*b^4*c^2*d*e^3*f^3*g - 32*a^2*b^4*c^2*d^3*e*f*g^3 + 12*a^2*b^5*c*d*e^3*f^2*g^2 + 1
2*a^2*b^5*c*d^2*e^2*f*g^3 - 64*a^3*b*c^4*d^2*e^2*f^3*g - 64*a^3*b*c^4*d^3*e*f^2*g^2 + 64*a^3*b^2*c^3*d*e^3*f^3
*g + 64*a^3*b^2*c^3*d^3*e*f*g^3 - 64*a^4*b*c^3*d*e^3*f^2*g^2 - 64*a^4*b*c^3*d^2*e^2*f*g^3 + 64*a^4*b^2*c^2*d*e
^3*f*g^3)) + (x*(4*b^3*c^4*e^6*g^6 - 16*a*b*c^5*e^6*g^6 + 16*a*c^6*d*e^5*g^6 + 16*a*c^6*e^6*f*g^5 - 4*b^2*c^5*
d*e^5*g^6 - 4*b^2*c^5*e^6*f*g^5))/(16*a^2*c^6*d^4*f^4 + a^4*b^4*e^4*g^4 + 16*a^4*c^4*d^4*g^4 + 16*a^4*c^4*e^4*
f^4 + b^4*c^4*d^4*f^4 + 16*a^6*c^2*e^4*g^4 + a^2*b^4*c^2*d^4*g^4 + a^2*b^4*c^2*e^4*f^4 - 8*a^3*b^2*c^3*d^4*g^4
- 8*a^3*b^2*c^3*e^4*f^4 + a^2*b^6*d^2*e^2*g^4 + 32*a^3*c^5*d^2*e^2*f^4 + 32*a^5*c^3*d^2*e^2*g^4 + b^6*c^2*d^2
*e^2*f^4 + a^2*b^6*e^4*f^2*g^2 + 32*a^3*c^5*d^4*f^2*g^2 + 32*a^5*c^3*e^4*f^2*g^2 + b^6*c^2*d^4*f^2*g^2 + b^8*d
^2*e^2*f^2*g^2 - 8*a*b^2*c^5*d^4*f^4 - 8*a^5*b^2*c*e^4*g^4 - 2*a^3*b^5*d*e^3*g^4 - 2*b^5*c^3*d^3*e*f^4 - 2*a^3
*b^5*e^4*f*g^3 - 2*b^5*c^3*d^4*f^3*g + 16*a*b^3*c^4*d^3*e*f^4 - 2*a*b^5*c^2*d*e^3*f^4 - 32*a^2*b*c^5*d^3*e*f^4
- 32*a^3*b*c^4*d*e^3*f^4 - 2*a^2*b^5*c*d^3*e*g^4 - 32*a^4*b*c^3*d^3*e*g^4 + 16*a^4*b^3*c*d*e^3*g^4 - 32*a^5*b
*c^2*d*e^3*g^4 + 16*a*b^3*c^4*d^4*f^3*g - 2*a*b^5*c^2*d^4*f*g^3 - 32*a^2*b*c^5*d^4*f^3*g - 32*a^3*b*c^4*d^4*f*
g^3 - 2*a^2*b^5*c*e^4*f^3*g - 32*a^4*b*c^3*e^4*f^3*g + 16*a^4*b^3*c*e^4*f*g^3 - 32*a^5*b*c^2*e^4*f*g^3 - 2*a*b
^7*d*e^3*f^2*g^2 - 2*a*b^7*d^2*e^2*f*g^3 + 4*a^2*b^6*d*e^3*f*g^3 + 4*b^6*c^2*d^3*e*f^3*g - 2*b^7*c*d^2*e^2*f^3
*g - 2*b^7*c*d^3*e*f^2*g^2 - 6*a*b^4*c^3*d^2*e^2*f^4 + 16*a^2*b^3*c^3*d*e^3*f^4 + 16*a^3*b^3*c^2*d^3*e*g^4 - 6
*a^3*b^4*c*d^2*e^2*g^4 - 6*a*b^4*c^3*d^4*f^2*g^2 + 16*a^2*b^3*c^3*d^4*f*g^3 + 16*a^3*b^3*c^2*e^4*f^3*g - 6*a^3
*b^4*c*e^4*f^2*g^2 + 64*a^4*c^4*d^2*e^2*f^2*g^2 + 4*a*b^6*c*d*e^3*f^3*g + 4*a*b^6*c*d^3*e*f*g^3 - 32*a*b^4*c^3
*d^3*e*f^3*g - 32*a^3*b^4*c*d*e^3*f*g^3 - 12*a^2*b^4*c^2*d^2*e^2*f^2*g^2 + 32*a^3*b^2*c^3*d^2*e^2*f^2*g^2 + 12
*a*b^5*c^2*d^2*e^2*f^3*g + 12*a*b^5*c^2*d^3*e*f^2*g^2 - 4*a*b^6*c*d^2*e^2*f^2*g^2 + 64*a^2*b^2*c^4*d^3*e*f^3*g
- 32*a^2*b^4*c^2*d*e^3*f^3*g - 32*a^2*b^4*c^2*d^3*e*f*g^3 + 12*a^2*b^5*c*d*e^3*f^2*g^2 + 12*a^2*b^5*c*d^2*e^2
*f*g^3 - 64*a^3*b*c^4*d^2*e^2*f^3*g - 64*a^3*b*c^4*d^3*e*f^2*g^2 + 64*a^3*b^2*c^3*d*e^3*f^3*g + 64*a^3*b^2*c^3
*d^3*e*f*g^3 - 64*a^4*b*c^3*d*e^3*f^2*g^2 - 64*a^4*b*c^3*d^2*e^2*f*g^3 + 64*a^4*b^2*c^2*d*e^3*f*g^3))*root(112
0*a^6*b^2*c^6*d^9*e*f*g^9*z^4 + 1120*a^6*b^2*c^6*d*e^9*f^9*g*z^4 - 792*a^5*b^4*c^5*d^9*e*f*g^9*z^4 - 792*a^5*b
^4*c^5*d*e^9*f^9*g*z^4 + 512*a^9*b*c^4*d^4*e^6*f*g^9*z^4 + 512*a^9*b*c^4*d*e^9*f^4*g^6*z^4 - 512*a^7*b*c^6*d^8
*e^2*f*g^9*z^4 - 512*a^7*b*c^6*d*e^9*f^8*g^2*z^4 - 512*a^6*b*c^7*d^9*e*f^2*g^8*z^4 - 512*a^6*b*c^7*d^2*e^8*f^9
*g*z^4 + 512*a^4*b*c^9*d^9*e*f^6*g^4*z^4 + 512*a^4*b*c^9*d^6*e^4*f^9*g*z^4 + 256*a^10*b*c^3*d^2*e^8*f*g^9*z^4
+ 256*a^10*b*c^3*d*e^9*f^2*g^8*z^4 + 256*a^3*b*c^10*d^9*e*f^8*g^2*z^4 + 256*a^3*b*c^10*d^8*e^2*f^9*g*z^4 - 200
*a^6*b^7*c*d^4*e^6*f*g^9*z^4 - 200*a^6*b^7*c*d*e^9*f^4*g^6*z^4 - 200*a*b^7*c^6*d^9*e*f^6*g^4*z^4 - 200*a*b^7*c
^6*d^6*e^4*f^9*g*z^4 + 194*a^4*b^6*c^4*d^9*e*f*g^9*z^4 + 194*a^4*b^6*c^4*d*e^9*f^9*g*z^4 + 144*a^5*b^8*c*d^5*e
^5*f*g^9*z^4 + 144*a^5*b^8*c*d*e^9*f^5*g^5*z^4 + 144*a*b^8*c^5*d^9*e*f^5*g^5*z^4 + 144*a*b^8*c^5*d^5*e^5*f^9*g
*z^4 + 96*a^10*b^2*c^2*d*e^9*f*g^9*z^4 + 96*a^2*b^2*c^10*d^9*e*f^9*g*z^4 + 56*a^7*b^6*c*d^3*e^7*f*g^9*z^4 + 56
*a^7*b^6*c*d*e^9*f^3*g^7*z^4 + 56*a*b^6*c^7*d^9*e*f^7*g^3*z^4 + 56*a*b^6*c^7*d^7*e^3*f^9*g*z^4 + 48*a^8*b^5*c*
d^2*e^8*f*g^9*z^4 + 48*a^8*b^5*c*d*e^9*f^2*g^8*z^4 + 48*a*b^5*c^8*d^9*e*f^8*g^2*z^4 + 48*a*b^5*c^8*d^8*e^2*f^9
*g*z^4 + 20*a*b^12*c*d^6*e^4*f^4*g^6*z^4 + 20*a*b^12*c*d^4*e^6*f^6*g^4*z^4 - 16*a^3*b^10*c*d^7*e^3*f*g^9*z^4 -
16*a^3*b^10*c*d*e^9*f^7*g^3*z^4 - 16*a^3*b^8*c^3*d^9*e*f*g^9*z^4 - 16*a^3*b^8*c^3*d*e^9*f^9*g*z^4 - 16*a*b^12
*c*d^7*e^3*f^3*g^7*z^4 - 16*a*b^12*c*d^3*e^7*f^7*g^3*z^4 - 16*a*b^10*c^3*d^9*e*f^3*g^7*z^4 - 16*a*b^10*c^3*d^3
*e^7*f^9*g*z^4 - 8*a^4*b^9*c*d^6*e^4*f*g^9*z^4 - 8*a^4*b^9*c*d*e^9*f^6*g^4*z^4 - 8*a*b^12*c*d^5*e^5*f^5*g^5*z^
4 - 8*a*b^9*c^4*d^9*e*f^4*g^6*z^4 - 8*a*b^9*c^4*d^4*e^6*f^9*g*z^4 - 9984*a^7*b^2*c^5*d^4*e^6*f^4*g^6*z^4 - 998
4*a^5*b^2*c^7*d^6*e^4*f^6*g^4*z^4 - 8640*a^6*b^2*c^6*d^6*e^4*f^4*g^6*z^4 - 8640*a^6*b^2*c^6*d^4*e^6*f^6*g^4*z^
4 - 8544*a^5*b^4*c^5*d^5*e^5*f^5*g^5*z^4 + 5632*a^6*b^2*c^6*d^7*e^3*f^3*g^7*z^4 + 5632*a^6*b^2*c^6*d^3*e^7*f^7
*g^3*z^4 + 5232*a^5*b^4*c^5*d^6*e^4*f^4*g^6*z^4 + 5232*a^5*b^4*c^5*d^4*e^6*f^6*g^4*z^4 + 4808*a^4*b^6*c^4*d^5*
e^5*f^5*g^5*z^4 - 4288*a^6*b^4*c^4*d^5*e^5*f^3*g^7*z^4 - 4288*a^6*b^4*c^4*d^3*e^7*f^5*g^5*z^4 - 4288*a^4*b^4*c
^6*d^7*e^3*f^5*g^5*z^4 - 4288*a^4*b^4*c^6*d^5*e^5*f^7*g^3*z^4 + 3968*a^6*b^3*c^5*d^5*e^5*f^4*g^6*z^4 + 3968*a^
6*b^3*c^5*d^4*e^6*f^5*g^5*z^4 + 3968*a^5*b^3*c^6*d^6*e^4*f^5*g^5*z^4 + 3968*a^5*b^3*c^6*d^5*e^5*f^6*g^4*z^4 +
3840*a^7*b^2*c^5*d^5*e^5*f^3*g^7*z^4 + 3840*a^7*b^2*c^5*d^3*e^7*f^5*g^5*z^4 + 3840*a^5*b^2*c^7*d^7*e^3*f^5*g^5
*z^4 + 3840*a^5*b^2*c^7*d^5*e^5*f^7*g^3*z^4 + 3776*a^6*b^4*c^4*d^4*e^6*f^4*g^6*z^4 + 3776*a^4*b^4*c^6*d^6*e^4*
f^6*g^4*z^4 + 3456*a^6*b^2*c^6*d^5*e^5*f^5*g^5*z^4 + 3440*a^6*b^4*c^4*d^6*e^4*f^2*g^8*z^4 + 3440*a^6*b^4*c^4*d
^2*e^8*f^6*g^4*z^4 + 3440*a^4*b^4*c^6*d^8*e^2*f^4*g^6*z^4 + 3440*a^4*b^4*c^6*d^4*e^6*f^8*g^2*z^4 - 3360*a^8*b^
2*c^4*d^4*e^6*f^2*g^8*z^4 - 3360*a^8*b^2*c^4*d^2*e^8*f^4*g^6*z^4 - 3360*a^4*b^2*c^8*d^8*e^2*f^6*g^4*z^4 - 3360
*a^4*b^2*c^8*d^6*e^4*f^8*g^2*z^4 - 2944*a^7*b^4*c^3*d^3*e^7*f^3*g^7*z^4 - 2944*a^3*b^4*c^7*d^7*e^3*f^7*g^3*z^4
+ 2512*a^5*b^6*c^3*d^5*e^5*f^3*g^7*z^4 + 2512*a^5*b^6*c^3*d^3*e^7*f^5*g^5*z^4 + 2512*a^3*b^6*c^5*d^7*e^3*f^5*
g^5*z^4 + 2512*a^3*b^6*c^5*d^5*e^5*f^7*g^3*z^4 + 2312*a^7*b^4*c^3*d^4*e^6*f^2*g^8*z^4 + 2312*a^7*b^4*c^3*d^2*e
^8*f^4*g^6*z^4 + 2312*a^3*b^4*c^7*d^8*e^2*f^6*g^4*z^4 + 2312*a^3*b^4*c^7*d^6*e^4*f^8*g^2*z^4 + 1952*a^6*b^6*c^
2*d^3*e^7*f^3*g^7*z^4 + 1952*a^2*b^6*c^6*d^7*e^3*f^7*g^3*z^4 - 1920*a^5*b^4*c^5*d^7*e^3*f^3*g^7*z^4 - 1920*a^5
*b^4*c^5*d^3*e^7*f^7*g^3*z^4 - 1828*a^5*b^6*c^3*d^6*e^4*f^2*g^8*z^4 - 1828*a^5*b^6*c^3*d^2*e^8*f^6*g^4*z^4 - 1
828*a^3*b^6*c^5*d^8*e^2*f^4*g^6*z^4 - 1828*a^3*b^6*c^5*d^4*e^6*f^8*g^2*z^4 + 1740*a^5*b^4*c^5*d^8*e^2*f^2*g^8*
z^4 + 1740*a^5*b^4*c^5*d^2*e^8*f^8*g^2*z^4 - 1728*a^7*b^2*c^5*d^6*e^4*f^2*g^8*z^4 - 1728*a^7*b^2*c^5*d^2*e^8*f
^6*g^4*z^4 - 1728*a^5*b^2*c^7*d^8*e^2*f^4*g^6*z^4 - 1728*a^5*b^2*c^7*d^4*e^6*f^8*g^2*z^4 - 1716*a^4*b^6*c^4*d^
6*e^4*f^4*g^6*z^4 - 1716*a^4*b^6*c^4*d^4*e^6*f^6*g^4*z^4 - 1664*a^9*b^2*c^3*d^2*e^8*f^2*g^8*z^4 - 1664*a^3*b^2
*c^9*d^8*e^2*f^8*g^2*z^4 - 1600*a^6*b^3*c^5*d^7*e^3*f^2*g^8*z^4 - 1600*a^6*b^3*c^5*d^2*e^8*f^7*g^3*z^4 - 1600*
a^5*b^3*c^6*d^8*e^2*f^3*g^7*z^4 - 1600*a^5*b^3*c^6*d^3*e^7*f^8*g^2*z^4 - 1553*a^4*b^6*c^4*d^8*e^2*f^2*g^8*z^4
- 1553*a^4*b^6*c^4*d^2*e^8*f^8*g^2*z^4 + 1536*a^8*b^2*c^4*d^3*e^7*f^3*g^7*z^4 + 1536*a^4*b^2*c^8*d^7*e^3*f^7*g
^3*z^4 + 1408*a^7*b^3*c^4*d^4*e^6*f^3*g^7*z^4 + 1408*a^7*b^3*c^4*d^3*e^7*f^4*g^6*z^4 - 1408*a^6*b^3*c^5*d^6*e^
4*f^3*g^7*z^4 - 1408*a^6*b^3*c^5*d^3*e^7*f^6*g^4*z^4 - 1408*a^5*b^3*c^6*d^7*e^3*f^4*g^6*z^4 - 1408*a^5*b^3*c^6
*d^4*e^6*f^7*g^3*z^4 + 1408*a^4*b^3*c^7*d^7*e^3*f^6*g^4*z^4 + 1408*a^4*b^3*c^7*d^6*e^4*f^7*g^3*z^4 - 1360*a^6*
b^5*c^3*d^5*e^5*f^2*g^8*z^4 - 1360*a^6*b^5*c^3*d^2*e^8*f^5*g^5*z^4 - 1360*a^3*b^5*c^6*d^8*e^2*f^5*g^5*z^4 - 13
60*a^3*b^5*c^6*d^5*e^5*f^8*g^2*z^4 - 1248*a^5*b^5*c^4*d^5*e^5*f^4*g^6*z^4 - 1248*a^5*b^5*c^4*d^4*e^6*f^5*g^5*z
^4 - 1248*a^4*b^5*c^5*d^6*e^4*f^5*g^5*z^4 - 1248*a^4*b^5*c^5*d^5*e^5*f^6*g^4*z^4 + 1088*a^8*b^3*c^3*d^3*e^7*f^
2*g^8*z^4 + 1088*a^8*b^3*c^3*d^2*e^8*f^3*g^7*z^4 + 1088*a^3*b^3*c^8*d^8*e^2*f^7*g^3*z^4 + 1088*a^3*b^3*c^8*d^7
*e^3*f^8*g^2*z^4 + 1056*a^8*b^4*c^2*d^2*e^8*f^2*g^8*z^4 + 1056*a^2*b^4*c^8*d^8*e^2*f^8*g^2*z^4 - 912*a^7*b^5*c
^2*d^3*e^7*f^2*g^8*z^4 - 912*a^7*b^5*c^2*d^2*e^8*f^3*g^7*z^4 - 912*a^2*b^5*c^7*d^8*e^2*f^7*g^3*z^4 - 912*a^2*b
^5*c^7*d^7*e^3*f^8*g^2*z^4 - 848*a^5*b^6*c^3*d^4*e^6*f^4*g^6*z^4 - 848*a^3*b^6*c^5*d^6*e^4*f^6*g^4*z^4 + 832*a
^7*b^3*c^4*d^5*e^5*f^2*g^8*z^4 + 832*a^7*b^3*c^4*d^2*e^8*f^5*g^5*z^4 + 832*a^4*b^3*c^7*d^8*e^2*f^5*g^5*z^4 + 8
32*a^4*b^3*c^7*d^5*e^5*f^8*g^2*z^4 + 828*a^5*b^7*c^2*d^5*e^5*f^2*g^8*z^4 + 828*a^5*b^7*c^2*d^2*e^8*f^5*g^5*z^4
+ 828*a^2*b^7*c^5*d^8*e^2*f^5*g^5*z^4 + 828*a^2*b^7*c^5*d^5*e^5*f^8*g^2*z^4 - 800*a^3*b^8*c^3*d^5*e^5*f^5*g^5
*z^4 - 696*a^4*b^8*c^2*d^5*e^5*f^3*g^7*z^4 - 696*a^4*b^8*c^2*d^3*e^7*f^5*g^5*z^4 - 696*a^2*b^8*c^4*d^7*e^3*f^5
*g^5*z^4 - 696*a^2*b^8*c^4*d^5*e^5*f^7*g^3*z^4 - 694*a^6*b^6*c^2*d^4*e^6*f^2*g^8*z^4 - 694*a^6*b^6*c^2*d^2*e^8
*f^4*g^6*z^4 - 694*a^2*b^6*c^6*d^8*e^2*f^6*g^4*z^4 - 694*a^2*b^6*c^6*d^6*e^4*f^8*g^2*z^4 + 692*a^4*b^7*c^3*d^7
*e^3*f^2*g^8*z^4 + 692*a^4*b^7*c^3*d^2*e^8*f^7*g^3*z^4 + 692*a^3*b^7*c^4*d^8*e^2*f^3*g^7*z^4 + 692*a^3*b^7*c^4
*d^3*e^7*f^8*g^2*z^4 + 672*a^4*b^6*c^4*d^7*e^3*f^3*g^7*z^4 + 672*a^4*b^6*c^4*d^3*e^7*f^7*g^3*z^4 + 600*a^4*b^8
*c^2*d^4*e^6*f^4*g^6*z^4 + 600*a^2*b^8*c^4*d^6*e^4*f^6*g^4*z^4 - 544*a^3*b^8*c^3*d^7*e^3*f^3*g^7*z^4 + 544*a^3
*b^8*c^3*d^6*e^4*f^4*g^6*z^4 + 544*a^3*b^8*c^3*d^4*e^6*f^6*g^4*z^4 - 544*a^3*b^8*c^3*d^3*e^7*f^7*g^3*z^4 - 536
*a^4*b^7*c^3*d^5*e^5*f^4*g^6*z^4 - 536*a^4*b^7*c^3*d^4*e^6*f^5*g^5*z^4 - 536*a^3*b^7*c^4*d^6*e^4*f^5*g^5*z^4 -
536*a^3*b^7*c^4*d^5*e^5*f^6*g^4*z^4 - 504*a^5*b^7*c^2*d^4*e^6*f^3*g^7*z^4 - 504*a^5*b^7*c^2*d^3*e^7*f^4*g^6*z
^4 - 504*a^2*b^7*c^5*d^7*e^3*f^6*g^4*z^4 - 504*a^2*b^7*c^5*d^6*e^4*f^7*g^3*z^4 + 416*a^3*b^8*c^3*d^8*e^2*f^2*g
^8*z^4 + 416*a^3*b^8*c^3*d^2*e^8*f^8*g^2*z^4 - 352*a^6*b^5*c^3*d^4*e^6*f^3*g^7*z^4 - 352*a^6*b^5*c^3*d^3*e^7*f
^4*g^6*z^4 - 352*a^3*b^5*c^6*d^7*e^3*f^6*g^4*z^4 - 352*a^3*b^5*c^6*d^6*e^4*f^7*g^3*z^4 - 248*a^3*b^9*c^2*d^7*e
^3*f^2*g^8*z^4 - 248*a^3*b^9*c^2*d^2*e^8*f^7*g^3*z^4 - 248*a^2*b^9*c^3*d^8*e^2*f^3*g^7*z^4 - 248*a^2*b^9*c^3*d
^3*e^7*f^8*g^2*z^4 + 246*a^4*b^8*c^2*d^6*e^4*f^2*g^8*z^4 + 246*a^4*b^8*c^2*d^2*e^8*f^6*g^4*z^4 + 246*a^2*b^8*c
^4*d^8*e^2*f^4*g^6*z^4 + 246*a^2*b^8*c^4*d^4*e^6*f^8*g^2*z^4 + 208*a^6*b^2*c^6*d^8*e^2*f^2*g^8*z^4 + 208*a^6*b
^2*c^6*d^2*e^8*f^8*g^2*z^4 + 168*a^2*b^10*c^2*d^7*e^3*f^3*g^7*z^4 + 168*a^2*b^10*c^2*d^3*e^7*f^7*g^3*z^4 + 160
*a^3*b^9*c^2*d^5*e^5*f^4*g^6*z^4 + 160*a^3*b^9*c^2*d^4*e^6*f^5*g^5*z^4 + 160*a^2*b^9*c^3*d^6*e^4*f^5*g^5*z^4 +
160*a^2*b^9*c^3*d^5*e^5*f^6*g^4*z^4 + 144*a^5*b^5*c^4*d^7*e^3*f^2*g^8*z^4 + 144*a^5*b^5*c^4*d^2*e^8*f^7*g^3*z
^4 + 144*a^4*b^5*c^5*d^8*e^2*f^3*g^7*z^4 + 144*a^4*b^5*c^5*d^3*e^7*f^8*g^2*z^4 - 144*a^2*b^10*c^2*d^6*e^4*f^4*
g^6*z^4 - 144*a^2*b^10*c^2*d^4*e^6*f^6*g^4*z^4 + 120*a^4*b^7*c^3*d^6*e^4*f^3*g^7*z^4 + 120*a^4*b^7*c^3*d^3*e^7
*f^6*g^4*z^4 + 120*a^3*b^7*c^4*d^7*e^3*f^4*g^6*z^4 + 120*a^3*b^7*c^4*d^4*e^6*f^7*g^3*z^4 + 96*a^5*b^5*c^4*d^6*
e^4*f^3*g^7*z^4 + 96*a^5*b^5*c^4*d^3*e^7*f^6*g^4*z^4 + 96*a^4*b^5*c^5*d^7*e^3*f^4*g^6*z^4 + 96*a^4*b^5*c^5*d^4
*e^6*f^7*g^3*z^4 + 64*a^3*b^9*c^2*d^6*e^4*f^3*g^7*z^4 + 64*a^3*b^9*c^2*d^3*e^7*f^6*g^4*z^4 + 64*a^2*b^9*c^3*d^
7*e^3*f^4*g^6*z^4 + 64*a^2*b^9*c^3*d^4*e^6*f^7*g^3*z^4 - 36*a^2*b^10*c^2*d^8*e^2*f^2*g^8*z^4 - 36*a^2*b^10*c^2
*d^2*e^8*f^8*g^2*z^4 + 24*a^2*b^10*c^2*d^5*e^5*f^5*g^5*z^4 - 24*a^9*b^4*c*d*e^9*f*g^9*z^4 - 24*a*b^4*c^9*d^9*e
*f^9*g*z^4 + 2688*a^7*b^2*c^5*d^7*e^3*f*g^9*z^4 + 2688*a^7*b^2*c^5*d*e^9*f^7*g^3*z^4 + 2688*a^5*b^2*c^7*d^9*e*
f^3*g^7*z^4 + 2688*a^5*b^2*c^7*d^3*e^7*f^9*g*z^4 - 2560*a^7*b^3*c^4*d^6*e^4*f*g^9*z^4 - 2560*a^7*b^3*c^4*d*e^9
*f^6*g^4*z^4 - 2560*a^4*b^3*c^7*d^9*e*f^4*g^6*z^4 - 2560*a^4*b^3*c^7*d^4*e^6*f^9*g*z^4 + 2112*a^8*b^2*c^4*d^5*
e^5*f*g^9*z^4 + 2112*a^8*b^2*c^4*d*e^9*f^5*g^5*z^4 + 2112*a^4*b^2*c^8*d^9*e*f^5*g^5*z^4 + 2112*a^4*b^2*c^8*d^5
*e^5*f^9*g*z^4 + 1664*a^6*b^5*c^3*d^6*e^4*f*g^9*z^4 + 1664*a^6*b^5*c^3*d*e^9*f^6*g^4*z^4 + 1664*a^3*b^5*c^6*d^
9*e*f^4*g^6*z^4 + 1664*a^3*b^5*c^6*d^4*e^6*f^9*g*z^4 + 1536*a^8*b*c^5*d^4*e^6*f^3*g^7*z^4 + 1536*a^8*b*c^5*d^3
*e^7*f^4*g^6*z^4 + 1536*a^7*b*c^6*d^5*e^5*f^4*g^6*z^4 + 1536*a^7*b*c^6*d^4*e^6*f^5*g^5*z^4 + 1536*a^6*b*c^7*d^
6*e^4*f^5*g^5*z^4 + 1536*a^6*b*c^7*d^5*e^5*f^6*g^4*z^4 + 1536*a^5*b*c^8*d^7*e^3*f^6*g^4*z^4 + 1536*a^5*b*c^8*d
^6*e^4*f^7*g^3*z^4 - 1408*a^8*b^3*c^3*d^4*e^6*f*g^9*z^4 - 1408*a^8*b^3*c^3*d*e^9*f^4*g^6*z^4 - 1408*a^3*b^3*c^
8*d^9*e*f^6*g^4*z^4 - 1408*a^3*b^3*c^8*d^6*e^4*f^9*g*z^4 - 1280*a^7*b*c^6*d^7*e^3*f^2*g^8*z^4 - 1280*a^7*b*c^6
*d^2*e^8*f^7*g^3*z^4 - 1280*a^6*b*c^7*d^8*e^2*f^3*g^7*z^4 - 1280*a^6*b*c^7*d^3*e^7*f^8*g^2*z^4 - 1152*a^6*b^3*
c^5*d^8*e^2*f*g^9*z^4 - 1152*a^6*b^3*c^5*d*e^9*f^8*g^2*z^4 - 1152*a^5*b^3*c^6*d^9*e*f^2*g^8*z^4 - 1152*a^5*b^3
*c^6*d^2*e^8*f^9*g*z^4 + 1056*a^5*b^5*c^4*d^8*e^2*f*g^9*z^4 + 1056*a^5*b^5*c^4*d*e^9*f^8*g^2*z^4 + 1056*a^4*b^
5*c^5*d^9*e*f^2*g^8*z^4 + 1056*a^4*b^5*c^5*d^2*e^8*f^9*g*z^4 + 864*a^7*b^5*c^2*d^4*e^6*f*g^9*z^4 + 864*a^7*b^5
*c^2*d*e^9*f^4*g^6*z^4 + 864*a^2*b^5*c^7*d^9*e*f^6*g^4*z^4 + 864*a^2*b^5*c^7*d^6*e^4*f^9*g*z^4 - 800*a^6*b^4*c
^4*d^7*e^3*f*g^9*z^4 - 800*a^6*b^4*c^4*d*e^9*f^7*g^3*z^4 - 800*a^4*b^4*c^6*d^9*e*f^3*g^7*z^4 - 800*a^4*b^4*c^6
*d^3*e^7*f^9*g*z^4 - 768*a^8*b*c^5*d^5*e^5*f^2*g^8*z^4 - 768*a^8*b*c^5*d^2*e^8*f^5*g^5*z^4 - 768*a^5*b*c^8*d^8
*e^2*f^5*g^5*z^4 - 768*a^5*b*c^8*d^5*e^5*f^8*g^2*z^4 + 640*a^9*b^2*c^3*d^3*e^7*f*g^9*z^4 + 640*a^9*b^2*c^3*d*e
^9*f^3*g^7*z^4 + 640*a^3*b^2*c^9*d^9*e*f^7*g^3*z^4 + 640*a^3*b^2*c^9*d^7*e^3*f^9*g*z^4 + 512*a^7*b*c^6*d^6*e^4
*f^3*g^7*z^4 + 512*a^7*b*c^6*d^3*e^7*f^6*g^4*z^4 + 512*a^6*b*c^7*d^7*e^3*f^4*g^6*z^4 + 512*a^6*b*c^7*d^4*e^6*f
^7*g^3*z^4 - 480*a^5*b^8*c*d^3*e^7*f^3*g^7*z^4 - 480*a*b^8*c^5*d^7*e^3*f^7*g^3*z^4 - 400*a^7*b^4*c^3*d^5*e^5*f
*g^9*z^4 - 400*a^7*b^4*c^3*d*e^9*f^5*g^5*z^4 - 400*a^3*b^4*c^7*d^9*e*f^5*g^5*z^4 - 400*a^3*b^4*c^7*d^5*e^5*f^9
*g*z^4 - 372*a^6*b^6*c^2*d^5*e^5*f*g^9*z^4 - 372*a^6*b^6*c^2*d*e^9*f^5*g^5*z^4 - 372*a^2*b^6*c^6*d^9*e*f^5*g^5
*z^4 - 372*a^2*b^6*c^6*d^5*e^5*f^9*g*z^4 - 328*a^5*b^6*c^3*d^7*e^3*f*g^9*z^4 - 328*a^5*b^6*c^3*d*e^9*f^7*g^3*z
^4 - 328*a^3*b^6*c^5*d^9*e*f^3*g^7*z^4 - 328*a^3*b^6*c^5*d^3*e^7*f^9*g*z^4 - 288*a^8*b^4*c^2*d^3*e^7*f*g^9*z^4
- 288*a^8*b^4*c^2*d*e^9*f^3*g^7*z^4 - 288*a^5*b^7*c^2*d^6*e^4*f*g^9*z^4 - 288*a^5*b^7*c^2*d*e^9*f^6*g^4*z^4 -
288*a^2*b^7*c^5*d^9*e*f^4*g^6*z^4 - 288*a^2*b^7*c^5*d^4*e^6*f^9*g*z^4 - 288*a^2*b^4*c^8*d^9*e*f^7*g^3*z^4 - 2
88*a^2*b^4*c^8*d^7*e^3*f^9*g*z^4 - 280*a^4*b^7*c^3*d^8*e^2*f*g^9*z^4 - 280*a^4*b^7*c^3*d*e^9*f^8*g^2*z^4 - 280
*a^3*b^7*c^4*d^9*e*f^2*g^8*z^4 - 280*a^3*b^7*c^4*d^2*e^8*f^9*g*z^4 + 256*a^9*b*c^4*d^3*e^7*f^2*g^8*z^4 + 256*a
^9*b*c^4*d^2*e^8*f^3*g^7*z^4 + 256*a^4*b*c^9*d^8*e^2*f^7*g^3*z^4 + 256*a^4*b*c^9*d^7*e^3*f^8*g^2*z^4 - 248*a^7
*b^6*c*d^2*e^8*f^2*g^8*z^4 - 248*a*b^6*c^7*d^8*e^2*f^8*g^2*z^4 + 236*a^6*b^7*c*d^3*e^7*f^2*g^8*z^4 + 236*a^6*b
^7*c*d^2*e^8*f^3*g^7*z^4 + 236*a*b^7*c^6*d^8*e^2*f^7*g^3*z^4 + 236*a*b^7*c^6*d^7*e^3*f^8*g^2*z^4 + 200*a^4*b^9
*c*d^4*e^6*f^3*g^7*z^4 + 200*a^4*b^9*c*d^3*e^7*f^4*g^6*z^4 - 200*a^3*b^10*c*d^4*e^6*f^4*g^6*z^4 - 200*a*b^10*c
^3*d^6*e^4*f^6*g^4*z^4 + 200*a*b^9*c^4*d^7*e^3*f^6*g^4*z^4 + 200*a*b^9*c^4*d^6*e^4*f^7*g^3*z^4 - 196*a^4*b^9*c
*d^5*e^5*f^2*g^8*z^4 - 196*a^4*b^9*c*d^2*e^8*f^5*g^5*z^4 - 196*a*b^9*c^4*d^8*e^2*f^5*g^5*z^4 - 196*a*b^9*c^4*d
^5*e^5*f^8*g^2*z^4 - 192*a^9*b^3*c^2*d^2*e^8*f*g^9*z^4 - 192*a^9*b^3*c^2*d*e^9*f^2*g^8*z^4 - 192*a^2*b^3*c^9*d
^9*e*f^8*g^2*z^4 - 192*a^2*b^3*c^9*d^8*e^2*f^9*g*z^4 + 156*a^4*b^8*c^2*d^7*e^3*f*g^9*z^4 + 156*a^4*b^8*c^2*d*e
^9*f^7*g^3*z^4 + 156*a^2*b^8*c^4*d^9*e*f^3*g^7*z^4 + 156*a^2*b^8*c^4*d^3*e^7*f^9*g*z^4 + 96*a^5*b^8*c*d^4*e^6*
f^2*g^8*z^4 + 96*a^5*b^8*c*d^2*e^8*f^4*g^6*z^4 + 96*a*b^8*c^5*d^8*e^2*f^6*g^4*z^4 + 96*a*b^8*c^5*d^6*e^4*f^8*g
^2*z^4 + 88*a^3*b^10*c*d^5*e^5*f^3*g^7*z^4 + 88*a^3*b^10*c*d^3*e^7*f^5*g^5*z^4 + 88*a*b^10*c^3*d^7*e^3*f^5*g^5
*z^4 + 88*a*b^10*c^3*d^5*e^5*f^7*g^3*z^4 - 36*a^2*b^11*c*d^6*e^4*f^3*g^7*z^4 - 36*a^2*b^11*c*d^3*e^7*f^6*g^4*z
^4 - 36*a*b^11*c^2*d^7*e^3*f^4*g^6*z^4 - 36*a*b^11*c^2*d^4*e^6*f^7*g^3*z^4 + 28*a^3*b^10*c*d^6*e^4*f^2*g^8*z^4
+ 28*a^3*b^10*c*d^2*e^8*f^6*g^4*z^4 + 28*a*b^10*c^3*d^8*e^2*f^4*g^6*z^4 + 28*a*b^10*c^3*d^4*e^6*f^8*g^2*z^4 +
24*a^3*b^9*c^2*d^8*e^2*f*g^9*z^4 + 24*a^3*b^9*c^2*d*e^9*f^8*g^2*z^4 + 24*a^2*b^11*c*d^7*e^3*f^2*g^8*z^4 + 24*
a^2*b^11*c*d^2*e^8*f^7*g^3*z^4 + 24*a^2*b^9*c^3*d^9*e*f^2*g^8*z^4 + 24*a^2*b^9*c^3*d^2*e^8*f^9*g*z^4 + 24*a*b^
11*c^2*d^8*e^2*f^3*g^7*z^4 + 24*a*b^11*c^2*d^3*e^7*f^8*g^2*z^4 + 12*a^2*b^11*c*d^5*e^5*f^4*g^6*z^4 + 12*a^2*b^
11*c*d^4*e^6*f^5*g^5*z^4 + 12*a*b^11*c^2*d^6*e^4*f^5*g^5*z^4 + 12*a*b^11*c^2*d^5*e^5*f^6*g^4*z^4 + 40*b^10*c^4
*d^7*e^3*f^7*g^3*z^4 + 20*b^12*c^2*d^6*e^4*f^6*g^4*z^4 - 20*b^11*c^3*d^7*e^3*f^6*g^4*z^4 - 20*b^11*c^3*d^6*e^4
*f^7*g^3*z^4 - 20*b^9*c^5*d^8*e^2*f^7*g^3*z^4 - 20*b^9*c^5*d^7*e^3*f^8*g^2*z^4 + 20*b^8*c^6*d^8*e^2*f^8*g^2*z^
4 + 16*b^11*c^3*d^8*e^2*f^5*g^5*z^4 + 16*b^11*c^3*d^5*e^5*f^8*g^2*z^4 - 6*b^12*c^2*d^8*e^2*f^4*g^6*z^4 - 6*b^1
2*c^2*d^4*e^6*f^8*g^2*z^4 - 5*b^10*c^4*d^8*e^2*f^6*g^4*z^4 - 5*b^10*c^4*d^6*e^4*f^8*g^2*z^4 - 4*b^12*c^2*d^7*e
^3*f^5*g^5*z^4 - 4*b^12*c^2*d^5*e^5*f^7*g^3*z^4 - 4608*a^7*c^7*d^5*e^5*f^5*g^5*z^4 + 3328*a^7*c^7*d^6*e^4*f^4*
g^6*z^4 + 3328*a^7*c^7*d^4*e^6*f^6*g^4*z^4 - 3072*a^8*c^6*d^5*e^5*f^3*g^7*z^4 + 3072*a^8*c^6*d^4*e^6*f^4*g^6*z
^4 - 3072*a^8*c^6*d^3*e^7*f^5*g^5*z^4 - 3072*a^6*c^8*d^7*e^3*f^5*g^5*z^4 + 3072*a^6*c^8*d^6*e^4*f^6*g^4*z^4 -
3072*a^6*c^8*d^5*e^5*f^7*g^3*z^4 - 2048*a^9*c^5*d^3*e^7*f^3*g^7*z^4 - 2048*a^7*c^7*d^7*e^3*f^3*g^7*z^4 - 2048*
a^7*c^7*d^3*e^7*f^7*g^3*z^4 - 2048*a^5*c^9*d^7*e^3*f^7*g^3*z^4 + 1792*a^8*c^6*d^6*e^4*f^2*g^8*z^4 + 1792*a^8*c
^6*d^2*e^8*f^6*g^4*z^4 + 1792*a^6*c^8*d^8*e^2*f^4*g^6*z^4 + 1792*a^6*c^8*d^4*e^6*f^8*g^2*z^4 + 1408*a^9*c^5*d^
4*e^6*f^2*g^8*z^4 + 1408*a^9*c^5*d^2*e^8*f^4*g^6*z^4 + 1408*a^5*c^9*d^8*e^2*f^6*g^4*z^4 + 1408*a^5*c^9*d^6*e^4
*f^8*g^2*z^4 + 1088*a^7*c^7*d^8*e^2*f^2*g^8*z^4 + 1088*a^7*c^7*d^2*e^8*f^8*g^2*z^4 + 512*a^10*c^4*d^2*e^8*f^2*
g^8*z^4 + 512*a^4*c^10*d^8*e^2*f^8*g^2*z^4 + 40*a^4*b^10*d^3*e^7*f^3*g^7*z^4 + 20*a^6*b^8*d^2*e^8*f^2*g^8*z^4
- 20*a^5*b^9*d^3*e^7*f^2*g^8*z^4 - 20*a^5*b^9*d^2*e^8*f^3*g^7*z^4 - 20*a^3*b^11*d^4*e^6*f^3*g^7*z^4 - 20*a^3*b
^11*d^3*e^7*f^4*g^6*z^4 + 20*a^2*b^12*d^4*e^6*f^4*g^6*z^4 + 16*a^3*b^11*d^5*e^5*f^2*g^8*z^4 + 16*a^3*b^11*d^2*
e^8*f^5*g^5*z^4 - 6*a^2*b^12*d^6*e^4*f^2*g^8*z^4 - 6*a^2*b^12*d^2*e^8*f^6*g^4*z^4 - 5*a^4*b^10*d^4*e^6*f^2*g^8
*z^4 - 5*a^4*b^10*d^2*e^8*f^4*g^6*z^4 - 4*a^2*b^12*d^5*e^5*f^3*g^7*z^4 - 4*a^2*b^12*d^3*e^7*f^5*g^5*z^4 + 480*
a^8*b^2*c^4*e^10*f^6*g^4*z^4 - 440*a^7*b^4*c^3*e^10*f^6*g^4*z^4 + 320*a^8*b^3*c^3*e^10*f^5*g^5*z^4 + 320*a^7*b
^3*c^4*e^10*f^7*g^3*z^4 - 240*a^8*b^4*c^2*e^10*f^4*g^6*z^4 - 240*a^6*b^4*c^4*e^10*f^8*g^2*z^4 + 192*a^9*b^3*c^
2*e^10*f^3*g^7*z^4 + 192*a^9*b^2*c^3*e^10*f^4*g^6*z^4 + 192*a^7*b^2*c^5*e^10*f^8*g^2*z^4 + 90*a^6*b^6*c^2*e^10
*f^6*g^4*z^4 + 68*a^5*b^6*c^3*e^10*f^8*g^2*z^4 - 48*a^10*b^2*c^2*e^10*f^2*g^8*z^4 + 48*a^7*b^5*c^2*e^10*f^5*g^
5*z^4 + 48*a^6*b^5*c^3*e^10*f^7*g^3*z^4 - 36*a^5*b^7*c^2*e^10*f^7*g^3*z^4 - 6*a^4*b^8*c^2*e^10*f^8*g^2*z^4 + 4
80*a^4*b^2*c^8*d^10*f^4*g^6*z^4 - 440*a^3*b^4*c^7*d^10*f^4*g^6*z^4 + 320*a^4*b^3*c^7*d^10*f^3*g^7*z^4 + 320*a^
3*b^3*c^8*d^10*f^5*g^5*z^4 - 240*a^4*b^4*c^6*d^10*f^2*g^8*z^4 - 240*a^2*b^4*c^8*d^10*f^6*g^4*z^4 + 192*a^5*b^2
*c^7*d^10*f^2*g^8*z^4 + 192*a^3*b^2*c^9*d^10*f^6*g^4*z^4 + 192*a^2*b^3*c^9*d^10*f^7*g^3*z^4 + 90*a^2*b^6*c^6*d
^10*f^4*g^6*z^4 + 68*a^3*b^6*c^5*d^10*f^2*g^8*z^4 + 48*a^3*b^5*c^6*d^10*f^3*g^7*z^4 + 48*a^2*b^5*c^7*d^10*f^5*
g^5*z^4 - 48*a^2*b^2*c^10*d^10*f^8*g^2*z^4 - 36*a^2*b^7*c^5*d^10*f^3*g^7*z^4 - 6*a^2*b^8*c^4*d^10*f^2*g^8*z^4
+ 480*a^8*b^2*c^4*d^6*e^4*g^10*z^4 - 440*a^7*b^4*c^3*d^6*e^4*g^10*z^4 + 320*a^8*b^3*c^3*d^5*e^5*g^10*z^4 + 320
*a^7*b^3*c^4*d^7*e^3*g^10*z^4 - 240*a^8*b^4*c^2*d^4*e^6*g^10*z^4 - 240*a^6*b^4*c^4*d^8*e^2*g^10*z^4 + 192*a^9*
b^3*c^2*d^3*e^7*g^10*z^4 + 192*a^9*b^2*c^3*d^4*e^6*g^10*z^4 + 192*a^7*b^2*c^5*d^8*e^2*g^10*z^4 + 90*a^6*b^6*c^
2*d^6*e^4*g^10*z^4 + 68*a^5*b^6*c^3*d^8*e^2*g^10*z^4 - 48*a^10*b^2*c^2*d^2*e^8*g^10*z^4 + 48*a^7*b^5*c^2*d^5*e
^5*g^10*z^4 + 48*a^6*b^5*c^3*d^7*e^3*g^10*z^4 - 36*a^5*b^7*c^2*d^7*e^3*g^10*z^4 - 6*a^4*b^8*c^2*d^8*e^2*g^10*z
^4 + 480*a^4*b^2*c^8*d^4*e^6*f^10*z^4 - 440*a^3*b^4*c^7*d^4*e^6*f^10*z^4 + 320*a^4*b^3*c^7*d^3*e^7*f^10*z^4 +
320*a^3*b^3*c^8*d^5*e^5*f^10*z^4 - 240*a^4*b^4*c^6*d^2*e^8*f^10*z^4 - 240*a^2*b^4*c^8*d^6*e^4*f^10*z^4 + 192*a
^5*b^2*c^7*d^2*e^8*f^10*z^4 + 192*a^3*b^2*c^9*d^6*e^4*f^10*z^4 + 192*a^2*b^3*c^9*d^7*e^3*f^10*z^4 + 90*a^2*b^6
*c^6*d^4*e^6*f^10*z^4 + 68*a^3*b^6*c^5*d^2*e^8*f^10*z^4 + 48*a^3*b^5*c^6*d^3*e^7*f^10*z^4 + 48*a^2*b^5*c^7*d^5
*e^5*f^10*z^4 - 48*a^2*b^2*c^10*d^8*e^2*f^10*z^4 - 36*a^2*b^7*c^5*d^3*e^7*f^10*z^4 - 6*a^2*b^8*c^4*d^2*e^8*f^1
0*z^4 + 16*b^9*c^5*d^9*e*f^6*g^4*z^4 + 16*b^9*c^5*d^6*e^4*f^9*g*z^4 - 14*b^10*c^4*d^9*e*f^5*g^5*z^4 - 14*b^10*
c^4*d^5*e^5*f^9*g*z^4 + 4*b^13*c*d^7*e^3*f^4*g^6*z^4 - 4*b^13*c*d^6*e^4*f^5*g^5*z^4 - 4*b^13*c*d^5*e^5*f^6*g^4
*z^4 + 4*b^13*c*d^4*e^6*f^7*g^3*z^4 + 4*b^11*c^3*d^9*e*f^4*g^6*z^4 + 4*b^11*c^3*d^4*e^6*f^9*g*z^4 - 4*b^8*c^6*
d^9*e*f^7*g^3*z^4 - 4*b^8*c^6*d^7*e^3*f^9*g*z^4 - 4*b^7*c^7*d^9*e*f^8*g^2*z^4 - 4*b^7*c^7*d^8*e^2*f^9*g*z^4 -
768*a^9*c^5*d^5*e^5*f*g^9*z^4 - 768*a^9*c^5*d*e^9*f^5*g^5*z^4 - 768*a^5*c^9*d^9*e*f^5*g^5*z^4 - 768*a^5*c^9*d^
5*e^5*f^9*g*z^4 - 512*a^10*c^4*d^3*e^7*f*g^9*z^4 - 512*a^10*c^4*d*e^9*f^3*g^7*z^4 - 512*a^8*c^6*d^7*e^3*f*g^9*
z^4 - 512*a^8*c^6*d*e^9*f^7*g^3*z^4 - 512*a^6*c^8*d^9*e*f^3*g^7*z^4 - 512*a^6*c^8*d^3*e^7*f^9*g*z^4 - 512*a^4*
c^10*d^9*e*f^7*g^3*z^4 - 512*a^4*c^10*d^7*e^3*f^9*g*z^4 + 16*a^5*b^9*d^4*e^6*f*g^9*z^4 + 16*a^5*b^9*d*e^9*f^4*
g^6*z^4 - 14*a^4*b^10*d^5*e^5*f*g^9*z^4 - 14*a^4*b^10*d*e^9*f^5*g^5*z^4 - 4*a^7*b^7*d^2*e^8*f*g^9*z^4 - 4*a^7*
b^7*d*e^9*f^2*g^8*z^4 - 4*a^6*b^8*d^3*e^7*f*g^9*z^4 - 4*a^6*b^8*d*e^9*f^3*g^7*z^4 + 4*a^3*b^11*d^6*e^4*f*g^9*z
^4 + 4*a^3*b^11*d*e^9*f^6*g^4*z^4 + 4*a*b^13*d^6*e^4*f^3*g^7*z^4 - 4*a*b^13*d^5*e^5*f^4*g^6*z^4 - 4*a*b^13*d^4
*e^6*f^5*g^5*z^4 + 4*a*b^13*d^3*e^7*f^6*g^4*z^4 - 768*a^9*b*c^4*e^10*f^5*g^5*z^4 - 768*a^8*b*c^5*e^10*f^7*g^3*
z^4 - 256*a^10*b*c^3*e^10*f^3*g^7*z^4 + 192*a^6*b^3*c^5*e^10*f^9*g*z^4 + 68*a^7*b^6*c*e^10*f^4*g^6*z^4 - 48*a^
8*b^5*c*e^10*f^3*g^7*z^4 - 48*a^5*b^5*c^4*e^10*f^9*g*z^4 - 36*a^6*b^7*c*e^10*f^5*g^5*z^4 + 12*a^9*b^4*c*e^10*f
^2*g^8*z^4 + 4*a^4*b^9*c*e^10*f^7*g^3*z^4 + 4*a^4*b^7*c^3*e^10*f^9*g*z^4 - 768*a^5*b*c^8*d^10*f^3*g^7*z^4 - 76
8*a^4*b*c^9*d^10*f^5*g^5*z^4 - 256*a^3*b*c^10*d^10*f^7*g^3*z^4 + 192*a^5*b^3*c^6*d^10*f*g^9*z^4 + 68*a*b^6*c^7
*d^10*f^6*g^4*z^4 - 48*a^4*b^5*c^5*d^10*f*g^9*z^4 - 48*a*b^5*c^8*d^10*f^7*g^3*z^4 - 36*a*b^7*c^6*d^10*f^5*g^5*
z^4 + 12*a*b^4*c^9*d^10*f^8*g^2*z^4 + 4*a^3*b^7*c^4*d^10*f*g^9*z^4 + 4*a*b^9*c^4*d^10*f^3*g^7*z^4 - 768*a^9*b*
c^4*d^5*e^5*g^10*z^4 - 768*a^8*b*c^5*d^7*e^3*g^10*z^4 - 256*a^10*b*c^3*d^3*e^7*g^10*z^4 + 192*a^6*b^3*c^5*d^9*
e*g^10*z^4 + 68*a^7*b^6*c*d^4*e^6*g^10*z^4 - 48*a^8*b^5*c*d^3*e^7*g^10*z^4 - 48*a^5*b^5*c^4*d^9*e*g^10*z^4 - 3
6*a^6*b^7*c*d^5*e^5*g^10*z^4 + 12*a^9*b^4*c*d^2*e^8*g^10*z^4 + 4*a^4*b^9*c*d^7*e^3*g^10*z^4 + 4*a^4*b^7*c^3*d^
9*e*g^10*z^4 - 768*a^5*b*c^8*d^3*e^7*f^10*z^4 - 768*a^4*b*c^9*d^5*e^5*f^10*z^4 - 256*a^3*b*c^10*d^7*e^3*f^10*z
^4 + 192*a^5*b^3*c^6*d*e^9*f^10*z^4 + 68*a*b^6*c^7*d^6*e^4*f^10*z^4 - 48*a^4*b^5*c^5*d*e^9*f^10*z^4 - 48*a*b^5
*c^8*d^7*e^3*f^10*z^4 - 36*a*b^7*c^6*d^5*e^5*f^10*z^4 + 12*a*b^4*c^9*d^8*e^2*f^10*z^4 + 4*a^3*b^7*c^4*d*e^9*f^
10*z^4 + 4*a*b^9*c^4*d^3*e^7*f^10*z^4 + 2*b^6*c^8*d^9*e*f^9*g*z^4 - 128*a^11*c^3*d*e^9*f*g^9*z^4 - 128*a^7*c^7
*d^9*e*f*g^9*z^4 - 128*a^7*c^7*d*e^9*f^9*g*z^4 - 128*a^3*c^11*d^9*e*f^9*g*z^4 + 2*a^8*b^6*d*e^9*f*g^9*z^4 - 25
6*a^7*b*c^6*e^10*f^9*g*z^4 - 256*a^6*b*c^7*d^10*f*g^9*z^4 - 256*a^7*b*c^6*d^9*e*g^10*z^4 - 256*a^6*b*c^7*d*e^9
*f^10*z^4 + 2*b^14*d^5*e^5*f^5*g^5*z^4 + 384*a^9*c^5*e^10*f^6*g^4*z^4 + 256*a^10*c^4*e^10*f^4*g^6*z^4 + 256*a^
8*c^6*e^10*f^8*g^2*z^4 + 64*a^11*c^3*e^10*f^2*g^8*z^4 - 6*b^8*c^6*d^10*f^6*g^4*z^4 + 4*b^9*c^5*d^10*f^5*g^5*z^
4 + 4*b^7*c^7*d^10*f^7*g^3*z^4 + 384*a^5*c^9*d^10*f^4*g^6*z^4 + 256*a^6*c^8*d^10*f^2*g^8*z^4 + 256*a^4*c^10*d^
10*f^6*g^4*z^4 + 64*a^3*c^11*d^10*f^8*g^2*z^4 - 6*a^6*b^8*e^10*f^4*g^6*z^4 + 4*a^7*b^7*e^10*f^3*g^7*z^4 + 4*a^
5*b^9*e^10*f^5*g^5*z^4 + 384*a^9*c^5*d^6*e^4*g^10*z^4 + 256*a^10*c^4*d^4*e^6*g^10*z^4 + 256*a^8*c^6*d^8*e^2*g^
10*z^4 + 64*a^11*c^3*d^2*e^8*g^10*z^4 - 6*b^8*c^6*d^6*e^4*f^10*z^4 + 4*b^9*c^5*d^5*e^5*f^10*z^4 + 4*b^7*c^7*d^
7*e^3*f^10*z^4 + 384*a^5*c^9*d^4*e^6*f^10*z^4 + 256*a^6*c^8*d^2*e^8*f^10*z^4 + 256*a^4*c^10*d^6*e^4*f^10*z^4 +
64*a^3*c^11*d^8*e^2*f^10*z^4 - 6*a^6*b^8*d^4*e^6*g^10*z^4 + 4*a^7*b^7*d^3*e^7*g^10*z^4 + 4*a^5*b^9*d^5*e^5*g^
10*z^4 - 48*a^6*b^2*c^6*e^10*f^10*z^4 - 48*a^6*b^2*c^6*d^10*g^10*z^4 + 12*a^5*b^4*c^5*e^10*f^10*z^4 + 12*a^5*b
^4*c^5*d^10*g^10*z^4 + 64*a^7*c^7*e^10*f^10*z^4 + 64*a^7*c^7*d^10*g^10*z^4 - b^14*d^6*e^4*f^4*g^6*z^4 - b^14*d
^4*e^6*f^6*g^4*z^4 - b^10*c^4*d^10*f^4*g^6*z^4 - b^6*c^8*d^10*f^8*g^2*z^4 - a^8*b^6*e^10*f^2*g^8*z^4 - a^4*b^1
0*e^10*f^6*g^4*z^4 - b^10*c^4*d^4*e^6*f^10*z^4 - b^6*c^8*d^8*e^2*f^10*z^4 - a^8*b^6*d^2*e^8*g^10*z^4 - a^4*b^1
0*d^6*e^4*g^10*z^4 - a^4*b^6*c^4*e^10*f^10*z^4 - a^4*b^6*c^4*d^10*g^10*z^4 + 272*a^5*b^2*c^3*d*e^7*f*g^7*z^2 -
192*a^4*b^4*c^2*d*e^7*f*g^7*z^2 - 164*a^5*b*c^4*d^2*e^6*f*g^7*z^2 - 164*a^5*b*c^4*d*e^7*f^2*g^6*z^2 + 120*a^2
*b^2*c^6*d^7*e*f*g^7*z^2 + 120*a^2*b^2*c^6*d*e^7*f^7*g*z^2 + 120*a*b^2*c^7*d^7*e*f^3*g^5*z^2 + 120*a*b^2*c^7*d
^3*e^5*f^7*g*z^2 - 76*a^4*b*c^5*d^4*e^4*f*g^7*z^2 - 76*a^4*b*c^5*d*e^7*f^4*g^4*z^2 - 76*a^3*b*c^6*d^6*e^2*f*g^
7*z^2 - 76*a^3*b*c^6*d*e^7*f^6*g^2*z^2 - 64*a*b^3*c^6*d^7*e*f^2*g^6*z^2 - 64*a*b^3*c^6*d^2*e^6*f^7*g*z^2 - 60*
a^2*b*c^7*d^7*e*f^2*g^6*z^2 - 60*a^2*b*c^7*d^2*e^6*f^7*g*z^2 + 44*a*b*c^8*d^6*e^2*f^5*g^3*z^2 + 44*a*b*c^8*d^5
*e^3*f^6*g^2*z^2 + 22*a*b^5*c^4*d^6*e^2*f*g^7*z^2 + 22*a*b^5*c^4*d*e^7*f^6*g^2*z^2 - 20*a^2*b^7*c*d^2*e^6*f*g^
7*z^2 - 20*a^2*b^7*c*d*e^7*f^2*g^6*z^2 + 8*a*b^8*c*d^2*e^6*f^2*g^6*z^2 - 8*a*b^6*c^3*d^5*e^3*f*g^7*z^2 - 8*a*b
^6*c^3*d*e^7*f^5*g^3*z^2 + 2*a*b^7*c^2*d^4*e^4*f*g^7*z^2 + 2*a*b^7*c^2*d*e^7*f^4*g^4*z^2 - 590*a^2*b^2*c^6*d^4
*e^4*f^4*g^4*z^2 - 352*a^2*b^4*c^4*d^3*e^5*f^3*g^5*z^2 - 346*a^3*b^2*c^5*d^4*e^4*f^2*g^6*z^2 - 346*a^3*b^2*c^5
*d^2*e^6*f^4*g^4*z^2 - 274*a^4*b^2*c^4*d^2*e^6*f^2*g^6*z^2 + 272*a^3*b^2*c^5*d^3*e^5*f^3*g^5*z^2 + 250*a^2*b^3
*c^5*d^4*e^4*f^3*g^5*z^2 + 250*a^2*b^3*c^5*d^3*e^5*f^4*g^4*z^2 + 204*a^3*b^3*c^4*d^3*e^5*f^2*g^6*z^2 + 204*a^3
*b^3*c^4*d^2*e^6*f^3*g^5*z^2 + 136*a^2*b^2*c^6*d^5*e^3*f^3*g^5*z^2 + 136*a^2*b^2*c^6*d^3*e^5*f^5*g^3*z^2 + 71*
a^2*b^4*c^4*d^4*e^4*f^2*g^6*z^2 + 71*a^2*b^4*c^4*d^2*e^6*f^4*g^4*z^2 - 56*a^2*b^3*c^5*d^5*e^3*f^2*g^6*z^2 - 56
*a^2*b^3*c^5*d^2*e^6*f^5*g^3*z^2 + 18*a^2*b^2*c^6*d^6*e^2*f^2*g^6*z^2 + 18*a^2*b^2*c^6*d^2*e^6*f^6*g^2*z^2 - 1
6*a^3*b^4*c^3*d^2*e^6*f^2*g^6*z^2 + 16*a^2*b^5*c^3*d^3*e^5*f^2*g^6*z^2 + 16*a^2*b^5*c^3*d^2*e^6*f^3*g^5*z^2 -
4*a^2*b^6*c^2*d^2*e^6*f^2*g^6*z^2 + 48*a^3*b^6*c*d*e^7*f*g^7*z^2 - 20*a*b^4*c^5*d^7*e*f*g^7*z^2 - 20*a*b^4*c^5
*d*e^7*f^7*g*z^2 - 4*a*b^8*c*d^3*e^5*f*g^7*z^2 - 4*a*b^8*c*d*e^7*f^3*g^5*z^2 + 4*a*b*c^8*d^7*e*f^4*g^4*z^2 + 4
*a*b*c^8*d^4*e^4*f^7*g*z^2 + 368*a^4*b^2*c^4*d^3*e^5*f*g^7*z^2 + 368*a^4*b^2*c^4*d*e^7*f^3*g^5*z^2 + 264*a^3*b
^2*c^5*d^5*e^3*f*g^7*z^2 + 264*a^3*b^2*c^5*d*e^7*f^5*g^3*z^2 - 208*a^3*b^4*c^3*d^3*e^5*f*g^7*z^2 - 208*a^3*b^4
*c^3*d*e^7*f^3*g^5*z^2 - 164*a^4*b*c^5*d^3*e^5*f^2*g^6*z^2 - 164*a^4*b*c^5*d^2*e^6*f^3*g^5*z^2 + 140*a^2*b*c^7
*d^5*e^3*f^4*g^4*z^2 + 140*a^2*b*c^7*d^4*e^4*f^5*g^3*z^2 - 122*a*b^2*c^7*d^6*e^2*f^4*g^4*z^2 - 122*a*b^2*c^7*d
^4*e^4*f^6*g^2*z^2 - 108*a^2*b^3*c^5*d^6*e^2*f*g^7*z^2 - 108*a^2*b^3*c^5*d*e^7*f^6*g^2*z^2 + 102*a*b^3*c^6*d^5
*e^3*f^4*g^4*z^2 + 102*a*b^3*c^6*d^4*e^4*f^5*g^3*z^2 + 80*a*b^6*c^3*d^3*e^5*f^3*g^5*z^2 + 68*a*b^4*c^5*d^6*e^2
*f^2*g^6*z^2 + 68*a*b^4*c^5*d^2*e^6*f^6*g^2*z^2 - 60*a^3*b*c^6*d^5*e^3*f^2*g^6*z^2 + 60*a^3*b*c^6*d^4*e^4*f^3*
g^5*z^2 + 60*a^3*b*c^6*d^3*e^5*f^4*g^4*z^2 - 60*a^3*b*c^6*d^2*e^6*f^5*g^3*z^2 - 54*a^3*b^3*c^4*d^4*e^4*f*g^7*z
^2 - 54*a^3*b^3*c^4*d*e^7*f^4*g^4*z^2 - 52*a*b^4*c^5*d^5*e^3*f^3*g^5*z^2 - 52*a*b^4*c^5*d^3*e^5*f^5*g^3*z^2 +
48*a^3*b^5*c^2*d^2*e^6*f*g^7*z^2 + 48*a^3*b^5*c^2*d*e^7*f^2*g^6*z^2 + 48*a^2*b^6*c^2*d^3*e^5*f*g^7*z^2 + 48*a^
2*b^6*c^2*d*e^7*f^3*g^5*z^2 + 44*a^4*b^3*c^3*d^2*e^6*f*g^7*z^2 + 44*a^4*b^3*c^3*d*e^7*f^2*g^6*z^2 - 44*a^2*b*c
^7*d^6*e^2*f^3*g^5*z^2 - 44*a^2*b*c^7*d^3*e^5*f^6*g^2*z^2 - 44*a*b^3*c^6*d^6*e^2*f^3*g^5*z^2 - 44*a*b^3*c^6*d^
3*e^5*f^6*g^2*z^2 - 32*a*b^5*c^4*d^4*e^4*f^3*g^5*z^2 - 32*a*b^5*c^4*d^3*e^5*f^4*g^4*z^2 - 32*a*b^2*c^7*d^5*e^3
*f^5*g^3*z^2 - 20*a*b^7*c^2*d^3*e^5*f^2*g^6*z^2 - 20*a*b^7*c^2*d^2*e^6*f^3*g^5*z^2 + 20*a*b^4*c^5*d^4*e^4*f^4*
g^4*z^2 - 14*a*b^5*c^4*d^5*e^3*f^2*g^6*z^2 - 14*a*b^5*c^4*d^2*e^6*f^5*g^3*z^2 + 4*a^2*b^5*c^3*d^4*e^4*f*g^7*z^
2 + 4*a^2*b^5*c^3*d*e^7*f^4*g^4*z^2 - 4*a^2*b^4*c^4*d^5*e^3*f*g^7*z^2 - 4*a^2*b^4*c^4*d*e^7*f^5*g^3*z^2 + 2*a*
b^6*c^3*d^4*e^4*f^2*g^6*z^2 + 2*a*b^6*c^3*d^2*e^6*f^4*g^4*z^2 - 50*b^2*c^8*d^6*e^2*f^6*g^2*z^2 - 32*b^4*c^6*d^
5*e^3*f^5*g^3*z^2 + 24*b^3*c^7*d^6*e^2*f^5*g^3*z^2 + 24*b^3*c^7*d^5*e^3*f^6*g^2*z^2 + 23*b^4*c^6*d^6*e^2*f^4*g
^4*z^2 + 23*b^4*c^6*d^4*e^4*f^6*g^2*z^2 - 11*b^6*c^4*d^6*e^2*f^2*g^6*z^2 - 11*b^6*c^4*d^2*e^6*f^6*g^2*z^2 + 8*
b^6*c^4*d^5*e^3*f^3*g^5*z^2 + 8*b^6*c^4*d^3*e^5*f^5*g^3*z^2 - 8*b^5*c^5*d^5*e^3*f^4*g^4*z^2 - 8*b^5*c^5*d^4*e^
4*f^5*g^3*z^2 + 5*b^6*c^4*d^4*e^4*f^4*g^4*z^2 - 4*b^8*c^2*d^3*e^5*f^3*g^5*z^2 + 4*b^7*c^3*d^5*e^3*f^2*g^6*z^2
+ 4*b^7*c^3*d^2*e^6*f^5*g^3*z^2 - 2*b^7*c^3*d^4*e^4*f^3*g^5*z^2 - 2*b^7*c^3*d^3*e^5*f^4*g^4*z^2 - 2*b^5*c^5*d^
6*e^2*f^3*g^5*z^2 - 2*b^5*c^5*d^3*e^5*f^6*g^2*z^2 + 416*a^5*c^5*d^2*e^6*f^2*g^6*z^2 - 392*a^4*c^6*d^3*e^5*f^3*
g^5*z^2 + 376*a^4*c^6*d^4*e^4*f^2*g^6*z^2 + 376*a^4*c^6*d^2*e^6*f^4*g^4*z^2 + 320*a^3*c^7*d^4*e^4*f^4*g^4*z^2
- 280*a^3*c^7*d^5*e^3*f^3*g^5*z^2 - 280*a^3*c^7*d^3*e^5*f^5*g^3*z^2 - 200*a^2*c^8*d^5*e^3*f^5*g^3*z^2 + 160*a^
3*c^7*d^6*e^2*f^2*g^6*z^2 + 160*a^3*c^7*d^2*e^6*f^6*g^2*z^2 + 120*a^2*c^8*d^6*e^2*f^4*g^4*z^2 + 120*a^2*c^8*d^
4*e^4*f^6*g^2*z^2 - 471*a^4*b^2*c^4*e^8*f^4*g^4*z^2 + 436*a^3*b^4*c^3*e^8*f^4*g^4*z^2 - 310*a^3*b^3*c^4*e^8*f^
5*g^3*z^2 - 232*a^5*b^2*c^3*e^8*f^2*g^6*z^2 + 229*a^2*b^4*c^4*e^8*f^6*g^2*z^2 + 216*a^4*b^4*c^2*e^8*f^2*g^6*z^
2 - 204*a^4*b^3*c^3*e^8*f^3*g^5*z^2 - 150*a^3*b^2*c^5*e^8*f^6*g^2*z^2 - 91*a^2*b^6*c^2*e^8*f^4*g^4*z^2 - 72*a^
3*b^5*c^2*e^8*f^3*g^5*z^2 - 44*a^2*b^5*c^3*e^8*f^5*g^3*z^2 - 471*a^4*b^2*c^4*d^4*e^4*g^8*z^2 + 436*a^3*b^4*c^3
*d^4*e^4*g^8*z^2 - 310*a^3*b^3*c^4*d^5*e^3*g^8*z^2 - 232*a^5*b^2*c^3*d^2*e^6*g^8*z^2 + 229*a^2*b^4*c^4*d^6*e^2
*g^8*z^2 + 216*a^4*b^4*c^2*d^2*e^6*g^8*z^2 - 204*a^4*b^3*c^3*d^3*e^5*g^8*z^2 - 150*a^3*b^2*c^5*d^6*e^2*g^8*z^2
- 91*a^2*b^6*c^2*d^4*e^4*g^8*z^2 - 72*a^3*b^5*c^2*d^3*e^5*g^8*z^2 - 44*a^2*b^5*c^3*d^5*e^3*g^8*z^2 - 26*b^3*c
^7*d^7*e*f^4*g^4*z^2 - 26*b^3*c^7*d^4*e^4*f^7*g*z^2 + 16*b^2*c^8*d^7*e*f^5*g^3*z^2 + 16*b^2*c^8*d^5*e^3*f^7*g*
z^2 + 10*b^5*c^5*d^7*e*f^2*g^6*z^2 + 10*b^5*c^5*d^2*e^6*f^7*g*z^2 - 4*b^4*c^6*d^7*e*f^3*g^5*z^2 - 4*b^4*c^6*d^
3*e^5*f^7*g*z^2 + 2*b^9*c*d^3*e^5*f^2*g^6*z^2 + 2*b^9*c*d^2*e^6*f^3*g^5*z^2 - 168*a^5*c^5*d^3*e^5*f*g^7*z^2 -
168*a^5*c^5*d*e^7*f^3*g^5*z^2 - 120*a^4*c^6*d^5*e^3*f*g^7*z^2 - 120*a^4*c^6*d*e^7*f^5*g^3*z^2 - 56*a^2*c^8*d^7
*e*f^3*g^5*z^2 - 56*a^2*c^8*d^3*e^5*f^7*g*z^2 + 32*a*c^9*d^6*e^2*f^6*g^2*z^2 + 624*a^4*b*c^5*e^8*f^5*g^3*z^2 +
548*a^5*b*c^4*e^8*f^3*g^5*z^2 - 182*a^2*b^3*c^5*e^8*f^7*g*z^2 - 96*a^5*b^3*c^2*e^8*f*g^7*z^2 - 68*a*b^6*c^3*e
^8*f^6*g^2*z^2 - 58*a^3*b^6*c*e^8*f^2*g^6*z^2 + 38*a^2*b^7*c*e^8*f^3*g^5*z^2 + 36*a*b^7*c^2*e^8*f^5*g^3*z^2 +
18*a*b^2*c^7*d^8*f^2*g^6*z^2 + 624*a^4*b*c^5*d^5*e^3*g^8*z^2 + 548*a^5*b*c^4*d^3*e^5*g^8*z^2 - 182*a^2*b^3*c^5
*d^7*e*g^8*z^2 - 96*a^5*b^3*c^2*d*e^7*g^8*z^2 - 68*a*b^6*c^3*d^6*e^2*g^8*z^2 - 58*a^3*b^6*c*d^2*e^6*g^8*z^2 +
38*a^2*b^7*c*d^3*e^5*g^8*z^2 + 36*a*b^7*c^2*d^5*e^3*g^8*z^2 + 18*a*b^2*c^7*d^2*e^6*f^8*z^2 + 12*b*c^9*d^7*e*f^
6*g^2*z^2 + 12*b*c^9*d^6*e^2*f^7*g*z^2 - 72*a^6*c^4*d*e^7*f*g^7*z^2 - 40*a*c^9*d^7*e*f^5*g^3*z^2 - 40*a*c^9*d^
5*e^3*f^7*g*z^2 - 24*a^3*c^7*d^7*e*f*g^7*z^2 - 24*a^3*c^7*d*e^7*f^7*g*z^2 - 4*a^2*b^8*d*e^7*f*g^7*z^2 + 2*a*b^
9*d^2*e^6*f*g^7*z^2 + 2*a*b^9*d*e^7*f^2*g^6*z^2 + 204*a^3*b*c^6*e^8*f^7*g*z^2 + 128*a^6*b*c^3*e^8*f*g^7*z^2 +
48*a*b^5*c^4*e^8*f^7*g*z^2 + 24*a^4*b^5*c*e^8*f*g^7*z^2 - 48*a*b*c^8*d^8*f^3*g^5*z^2 - 36*a^2*b*c^7*d^8*f*g^7*
z^2 + 6*a*b^3*c^6*d^8*f*g^7*z^2 + 204*a^3*b*c^6*d^7*e*g^8*z^2 + 128*a^6*b*c^3*d*e^7*g^8*z^2 + 48*a*b^5*c^4*d^7
*e*g^8*z^2 + 24*a^4*b^5*c*d*e^7*g^8*z^2 - 48*a*b*c^8*d^3*e^5*f^8*z^2 - 36*a^2*b*c^7*d*e^7*f^8*z^2 + 6*a*b^3*c^
6*d*e^7*f^8*z^2 - b^8*c^2*d^4*e^4*f^2*g^6*z^2 - b^8*c^2*d^2*e^6*f^4*g^4*z^2 - 4*b^9*c*e^8*f^5*g^3*z^2 - 4*b^7*
c^3*e^8*f^7*g*z^2 - 12*b*c^9*d^8*f^5*g^3*z^2 + 24*a*c^9*d^8*f^4*g^4*z^2 - 4*b^9*c*d^5*e^3*g^8*z^2 - 4*b^7*c^3*
d^7*e*g^8*z^2 - 4*a*b^9*e^8*f^3*g^5*z^2 - 2*a^3*b^7*e^8*f*g^7*z^2 - 12*b*c^9*d^5*e^3*f^8*z^2 + 24*a*c^9*d^4*e^
4*f^8*z^2 - 4*a*b^9*d^3*e^5*g^8*z^2 - 2*a^3*b^7*d*e^7*g^8*z^2 - 12*a^5*b^4*c*e^8*g^8*z^2 - 12*a*b^4*c^5*e^8*f^
8*z^2 - 12*a*b^4*c^5*d^8*g^8*z^2 - 8*c^10*d^7*e*f^7*g*z^2 + 6*b^8*c^2*e^8*f^6*g^2*z^2 - 232*a^5*c^5*e^8*f^4*g^
4*z^2 - 188*a^4*c^6*e^8*f^6*g^2*z^2 - 92*a^6*c^4*e^8*f^2*g^6*z^2 + 9*b^2*c^8*d^8*f^4*g^4*z^2 - 3*b^4*c^6*d^8*f
^2*g^6*z^2 + 2*b^3*c^7*d^8*f^3*g^5*z^2 + 36*a^2*c^8*d^8*f^2*g^6*z^2 + 6*b^8*c^2*d^6*e^2*g^8*z^2 + 5*a^2*b^8*e^
8*f^2*g^6*z^2 - 232*a^5*c^5*d^4*e^4*g^8*z^2 - 188*a^4*c^6*d^6*e^2*g^8*z^2 - 92*a^6*c^4*d^2*e^6*g^8*z^2 + 9*b^2
*c^8*d^4*e^4*f^8*z^2 - 3*b^4*c^6*d^2*e^6*f^8*z^2 + 2*b^3*c^7*d^3*e^5*f^8*z^2 + 36*a^2*c^8*d^2*e^6*f^8*z^2 + 5*
a^2*b^8*d^2*e^6*g^8*z^2 + 48*a^6*b^2*c^2*e^8*g^8*z^2 + 45*a^2*b^2*c^6*e^8*f^8*z^2 + 45*a^2*b^2*c^6*d^8*g^8*z^2
+ 4*c^10*d^8*f^6*g^2*z^2 + b^10*e^8*f^4*g^4*z^2 + 4*c^10*d^6*e^2*f^8*z^2 + b^10*d^4*e^4*g^8*z^2 - 64*a^7*c^3*
e^8*g^8*z^2 + b^6*c^4*e^8*f^8*z^2 + b^6*c^4*d^8*g^8*z^2 - 48*a^3*c^7*e^8*f^8*z^2 - 48*a^3*c^7*d^8*g^8*z^2 + a^
4*b^6*e^8*g^8*z^2 - b^10*d^2*e^6*f^2*g^6*z^2 + 108*a^2*b^2*c^4*d^2*e^5*f*g^6*z + 108*a^2*b^2*c^4*d*e^6*f^2*g^5
*z + 60*a*b^2*c^5*d^3*e^4*f^2*g^5*z + 60*a*b^2*c^5*d^2*e^5*f^3*g^4*z - 48*a^2*b*c^5*d^2*e^5*f^2*g^5*z - 44*a*b
^3*c^4*d^2*e^5*f^2*g^5*z - 120*a^2*b*c^5*d^3*e^4*f*g^6*z - 120*a^2*b*c^5*d*e^6*f^3*g^4*z - 96*a*b*c^6*d^3*e^4*
f^3*g^4*z - 64*a^2*b^3*c^3*d*e^6*f*g^6*z + 32*a*b^3*c^4*d^3*e^4*f*g^6*z + 32*a*b^3*c^4*d*e^6*f^3*g^4*z - 28*a*
b^4*c^3*d^2*e^5*f*g^6*z - 28*a*b^4*c^3*d*e^6*f^2*g^5*z - 18*a*b^2*c^5*d^4*e^3*f*g^6*z - 18*a*b^2*c^5*d*e^6*f^4
*g^3*z + 4*a*b*c^6*d^4*e^3*f^2*g^5*z + 4*a*b*c^6*d^2*e^5*f^4*g^3*z + 24*a*b^5*c^2*d*e^6*f*g^6*z - 16*a^3*b*c^4
*d*e^6*f*g^6*z - 8*a*b*c^6*d^5*e^2*f*g^6*z - 8*a*b*c^6*d*e^6*f^5*g^2*z - 13*b^2*c^6*d^6*e*f*g^6*z - 13*b^2*c^6
*d*e^6*f^6*g*z + 8*b*c^7*d^6*e*f^2*g^5*z + 8*b*c^7*d^2*e^5*f^6*g*z + 9*b^2*c^6*d^4*e^3*f^3*g^4*z + 9*b^2*c^6*d
^3*e^4*f^4*g^3*z + 8*b^5*c^3*d^2*e^5*f^2*g^5*z - 6*b^4*c^4*d^3*e^4*f^2*g^5*z - 6*b^4*c^4*d^2*e^5*f^3*g^4*z - 6
*b^3*c^5*d^4*e^3*f^2*g^5*z - 6*b^3*c^5*d^2*e^5*f^4*g^3*z + 4*b^3*c^5*d^3*e^4*f^3*g^4*z + b^2*c^6*d^5*e^2*f^2*g
^5*z + b^2*c^6*d^2*e^5*f^5*g^2*z + 16*a^2*c^6*d^3*e^4*f^2*g^5*z + 16*a^2*c^6*d^2*e^5*f^3*g^4*z - 112*a^2*b^3*c
^3*e^7*f^2*g^5*z - 12*a^2*b^2*c^4*e^7*f^3*g^4*z - 112*a^2*b^3*c^3*d^2*e^5*g^7*z - 12*a^2*b^2*c^4*d^3*e^4*g^7*z
- 2*b^7*c*d*e^6*f*g^6*z + 8*a*c^7*d^6*e*f*g^6*z + 8*a*c^7*d*e^6*f^6*g*z + 52*a*b*c^6*e^7*f^6*g*z - 10*a*b^6*c
*e^7*f*g^6*z + 52*a*b*c^6*d^6*e*g^7*z - 10*a*b^6*c*d*e^6*g^7*z + 14*b^3*c^5*d^5*e^2*f*g^6*z + 14*b^3*c^5*d*e^6
*f^5*g^2*z - 12*b*c^7*d^5*e^2*f^3*g^4*z - 12*b*c^7*d^3*e^4*f^5*g^2*z - 5*b^4*c^4*d^4*e^3*f*g^6*z - 5*b^4*c^4*d
*e^6*f^4*g^3*z + b^6*c^2*d^2*e^5*f*g^6*z + b^6*c^2*d*e^6*f^2*g^5*z + 52*a^2*c^6*d^4*e^3*f*g^6*z + 52*a^2*c^6*d
*e^6*f^4*g^3*z + 24*a*c^7*d^4*e^3*f^3*g^4*z + 24*a*c^7*d^3*e^4*f^4*g^3*z - 16*a*c^7*d^5*e^2*f^2*g^5*z - 16*a*c
^7*d^2*e^5*f^5*g^2*z + 8*a^3*c^5*d^2*e^5*f*g^6*z + 8*a^3*c^5*d*e^6*f^2*g^5*z + 200*a^3*b*c^4*e^7*f^2*g^5*z + 1
44*a^2*b*c^5*e^7*f^4*g^3*z - 42*a*b^2*c^5*e^7*f^5*g^2*z + 32*a^3*b^2*c^3*e^7*f*g^6*z + 24*a^2*b^4*c^2*e^7*f*g^
6*z + 24*a*b^5*c^2*e^7*f^2*g^5*z - 10*a*b^3*c^4*e^7*f^4*g^3*z + 4*a*b^4*c^3*e^7*f^3*g^4*z + 200*a^3*b*c^4*d^2*
e^5*g^7*z + 144*a^2*b*c^5*d^4*e^3*g^7*z - 42*a*b^2*c^5*d^5*e^2*g^7*z + 32*a^3*b^2*c^3*d*e^6*g^7*z + 24*a^2*b^4
*c^2*d*e^6*g^7*z + 24*a*b^5*c^2*d^2*e^5*g^7*z - 10*a*b^3*c^4*d^4*e^3*g^7*z + 4*a*b^4*c^3*d^3*e^4*g^7*z + 4*b*c
^7*d^7*f*g^6*z + 4*b*c^7*d*e^6*f^7*z + 11*b^4*c^4*e^7*f^5*g^2*z - 4*b^5*c^3*e^7*f^4*g^3*z + b^6*c^2*e^7*f^3*g^
4*z - 136*a^3*c^5*e^7*f^3*g^4*z - 68*a^2*c^6*e^7*f^5*g^2*z + 11*b^4*c^4*d^5*e^2*g^7*z - 4*b^5*c^3*d^4*e^3*g^7*
z + b^6*c^2*d^3*e^4*g^7*z - 136*a^3*c^5*d^3*e^4*g^7*z - 68*a^2*c^6*d^5*e^2*g^7*z - 96*a^3*b^3*c^2*e^7*g^7*z +
4*c^8*d^6*e*f^3*g^4*z + 4*c^8*d^3*e^4*f^6*g*z - 10*b^3*c^5*e^7*f^6*g*z - 2*b^7*c*e^7*f^2*g^5*z - 128*a^4*c^4*e
^7*f*g^6*z - 10*b^3*c^5*d^6*e*g^7*z - 2*b^7*c*d^2*e^5*g^7*z - 128*a^4*c^4*d*e^6*g^7*z + 128*a^4*b*c^3*e^7*g^7*
z + 24*a^2*b^5*c*e^7*g^7*z - 4*c^8*d^7*f^2*g^5*z - 4*c^8*d^2*e^5*f^7*z + 3*b^2*c^6*e^7*f^7*z + 3*b^2*c^6*d^7*g
^7*z + b^8*e^7*f*g^6*z + b^8*d*e^6*g^7*z - 16*a*c^7*e^7*f^7*z - 16*a*c^7*d^7*g^7*z - 2*a*b^7*e^7*g^7*z - 8*a*c
^5*d*e^5*f*g^5 + 20*a*b*c^4*e^6*f*g^5 + 20*a*b*c^4*d*e^5*g^6 + 4*b*c^5*d^2*e^4*f*g^5 + 4*b*c^5*d*e^5*f^2*g^4 -
2*b^2*c^4*d*e^5*f*g^5 - 4*b^3*c^3*e^6*f*g^5 - 16*a*c^5*e^6*f^2*g^4 - 4*b^3*c^3*d*e^5*g^6 - 16*a*c^5*d^2*e^4*g
^6 + 8*a*b^2*c^3*e^6*g^6 - 4*c^6*d^2*e^4*f^2*g^4 + 3*b^2*c^4*e^6*f^2*g^4 + 3*b^2*c^4*d^2*e^4*g^6 - 36*a^2*c^4*
e^6*g^6, z, k), k, 1, 4)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(e*x+d)/(g*x+f)/(c*x**2+b*x+a)**2,x)

[Out]

Timed out

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