3.1.41 \(\int \frac {d+e x+f x^2+g x^3+h x^4+j x^5+k x^6+l x^7+m x^8}{(a+b x^2+c x^4)^2} \, dx\)

Optimal. Leaf size=770 \[ -\frac {x \left (-\left (b^2 \left (a^2 m+c^2 d\right )\right )+x^2 \left (-b c \left (-3 a^2 m+a c h+c^2 d\right )-a b^3 m+a b^2 c k+2 a c^2 (c f-a k)\right )+2 a c \left (a^2 m-a c h+c^2 d\right )+a b c (a k+c f)\right )}{2 a c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) \left (-\frac {-b^2 c \left (-19 a^2 m-a c h+c^2 d\right )+4 a c^2 \left (-5 a^2 m+a c h+3 c^2 d\right )-3 a b^4 m+a b^3 c k-4 a b c^2 (2 a k+c f)}{\sqrt {b^2-4 a c}}+b c \left (13 a^2 m+a c h+c^2 d\right )-3 a b^3 m+a b^2 c k-2 a c^2 (3 a k+c f)\right )}{2 \sqrt {2} a c^{5/2} \left (b^2-4 a c\right ) \sqrt {b-\sqrt {b^2-4 a c}}}+\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right ) \left (\frac {-b^2 c \left (-19 a^2 m-a c h+c^2 d\right )+4 a c^2 \left (-5 a^2 m+a c h+3 c^2 d\right )-3 a b^4 m+a b^3 c k-4 a b c^2 (2 a k+c f)}{\sqrt {b^2-4 a c}}+b c \left (13 a^2 m+a c h+c^2 d\right )-3 a b^3 m+a b^2 c k-2 a c^2 (3 a k+c f)\right )}{2 \sqrt {2} a c^{5/2} \left (b^2-4 a c\right ) \sqrt {\sqrt {b^2-4 a c}+b}}+\frac {\tanh ^{-1}\left (\frac {b+2 c x^2}{\sqrt {b^2-4 a c}}\right ) \left (-c^2 (2 b g-4 a j)-6 a b c l+b^3 l+4 c^3 e\right )}{2 c^2 \left (b^2-4 a c\right )^{3/2}}-\frac {x^2 \left (-c^2 (2 a j+b g)+b c (3 a l+b j)+b^3 (-l)+2 c^3 e\right )-a b^2 l+b c (a j+c e)-2 a c (c g-a l)}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {l \log \left (a+b x^2+c x^4\right )}{4 c^2}+\frac {m x}{c^2} \]

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Rubi [A]  time = 7.83, antiderivative size = 770, normalized size of antiderivative = 1.00, number of steps used = 13, number of rules used = 11, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {1673, 1678, 1676, 1166, 205, 1663, 1660, 634, 618, 206, 628} \begin {gather*} -\frac {x \left (x^2 \left (-b c \left (-3 a^2 m+a c h+c^2 d\right )+a b^2 c k-a b^3 m+2 a c^2 (c f-a k)\right )+b^2 \left (-\left (a^2 m+c^2 d\right )\right )+2 a c \left (a^2 m-a c h+c^2 d\right )+a b c (a k+c f)\right )}{2 a c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right ) \left (-\frac {-b^2 c \left (-19 a^2 m-a c h+c^2 d\right )+4 a c^2 \left (-5 a^2 m+a c h+3 c^2 d\right )+a b^3 c k-3 a b^4 m-4 a b c^2 (2 a k+c f)}{\sqrt {b^2-4 a c}}+b c \left (13 a^2 m+a c h+c^2 d\right )+a b^2 c k-3 a b^3 m-2 a c^2 (3 a k+c f)\right )}{2 \sqrt {2} a c^{5/2} \left (b^2-4 a c\right ) \sqrt {b-\sqrt {b^2-4 a c}}}+\frac {\tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {\sqrt {b^2-4 a c}+b}}\right ) \left (\frac {-b^2 c \left (-19 a^2 m-a c h+c^2 d\right )+4 a c^2 \left (-5 a^2 m+a c h+3 c^2 d\right )+a b^3 c k-3 a b^4 m-4 a b c^2 (2 a k+c f)}{\sqrt {b^2-4 a c}}+b c \left (13 a^2 m+a c h+c^2 d\right )+a b^2 c k-3 a b^3 m-2 a c^2 (3 a k+c f)\right )}{2 \sqrt {2} a c^{5/2} \left (b^2-4 a c\right ) \sqrt {\sqrt {b^2-4 a c}+b}}-\frac {x^2 \left (-c^2 (2 a j+b g)+b c (3 a l+b j)+b^3 (-l)+2 c^3 e\right )-a b^2 l+b c (a j+c e)-2 a c (c g-a l)}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {\tanh ^{-1}\left (\frac {b+2 c x^2}{\sqrt {b^2-4 a c}}\right ) \left (-c^2 (2 b g-4 a j)-6 a b c l+b^3 l+4 c^3 e\right )}{2 c^2 \left (b^2-4 a c\right )^{3/2}}+\frac {l \log \left (a+b x^2+c x^4\right )}{4 c^2}+\frac {m x}{c^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(d + e*x + f*x^2 + g*x^3 + h*x^4 + j*x^5 + k*x^6 + l*x^7 + m*x^8)/(a + b*x^2 + c*x^4)^2,x]

[Out]

(m*x)/c^2 - (b*c*(c*e + a*j) - a*b^2*l - 2*a*c*(c*g - a*l) + (2*c^3*e - c^2*(b*g + 2*a*j) - b^3*l + b*c*(b*j +
3*a*l))*x^2)/(2*c^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) - (x*(a*b*c*(c*f + a*k) - b^2*(c^2*d + a^2*m) + 2*a*c*
(c^2*d - a*c*h + a^2*m) + (a*b^2*c*k + 2*a*c^2*(c*f - a*k) - a*b^3*m - b*c*(c^2*d + a*c*h - 3*a^2*m))*x^2))/(2
*a*c^2*(b^2 - 4*a*c)*(a + b*x^2 + c*x^4)) + ((a*b^2*c*k - 2*a*c^2*(c*f + 3*a*k) - 3*a*b^3*m + b*c*(c^2*d + a*c
*h + 13*a^2*m) - (a*b^3*c*k - 4*a*b*c^2*(c*f + 2*a*k) - 3*a*b^4*m - b^2*c*(c^2*d - a*c*h - 19*a^2*m) + 4*a*c^2
*(3*c^2*d + a*c*h - 5*a^2*m))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(2*S
qrt[2]*a*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((a*b^2*c*k - 2*a*c^2*(c*f + 3*a*k) - 3*a*b^3*m
+ b*c*(c^2*d + a*c*h + 13*a^2*m) + (a*b^3*c*k - 4*a*b*c^2*(c*f + 2*a*k) - 3*a*b^4*m - b^2*c*(c^2*d - a*c*h - 1
9*a^2*m) + 4*a*c^2*(3*c^2*d + a*c*h - 5*a^2*m))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b + Sqrt[b^
2 - 4*a*c]]])/(2*Sqrt[2]*a*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + ((4*c^3*e - c^2*(2*b*g - 4*a*j
) + b^3*l - 6*a*b*c*l)*ArcTanh[(b + 2*c*x^2)/Sqrt[b^2 - 4*a*c]])/(2*c^2*(b^2 - 4*a*c)^(3/2)) + (l*Log[a + b*x^
2 + c*x^4])/(4*c^2)

Rule 205

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[a/b, 2]*ArcTan[x/Rt[a/b, 2]])/a, x] /; FreeQ[{a, b}, x]
&& PosQ[a/b]

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 1166

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

Rule 1660

Int[(Pq_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> With[{Q = PolynomialQuotient[Pq, a + b*x + c*
x^2, x], f = Coeff[PolynomialRemainder[Pq, a + b*x + c*x^2, x], x, 0], g = Coeff[PolynomialRemainder[Pq, a + b
*x + c*x^2, x], x, 1]}, Simp[((b*f - 2*a*g + (2*c*f - b*g)*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c
)), x] + Dist[1/((p + 1)*(b^2 - 4*a*c)), Int[(a + b*x + c*x^2)^(p + 1)*ExpandToSum[(p + 1)*(b^2 - 4*a*c)*Q - (
2*p + 3)*(2*c*f - b*g), x], x], x]] /; FreeQ[{a, b, c}, x] && PolyQ[Pq, x] && NeQ[b^2 - 4*a*c, 0] && LtQ[p, -1
]

Rule 1663

Int[(Pq_)*(x_)^(m_.)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_), x_Symbol] :> Dist[1/2, Subst[Int[x^((m - 1)/2)
*SubstFor[x^2, Pq, x]*(a + b*x + c*x^2)^p, x], x, x^2], x] /; FreeQ[{a, b, c, p}, x] && PolyQ[Pq, x^2] && Inte
gerQ[(m - 1)/2]

Rule 1673

Int[(Pq_)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_), x_Symbol] :> Module[{q = Expon[Pq, x], k}, Int[Sum[Coeff[
Pq, x, 2*k]*x^(2*k), {k, 0, q/2}]*(a + b*x^2 + c*x^4)^p, x] + Int[x*Sum[Coeff[Pq, x, 2*k + 1]*x^(2*k), {k, 0,
(q - 1)/2}]*(a + b*x^2 + c*x^4)^p, x]] /; FreeQ[{a, b, c, p}, x] && PolyQ[Pq, x] &&  !PolyQ[Pq, x^2]

Rule 1676

Int[(Pq_)/((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4), x_Symbol] :> Int[ExpandIntegrand[Pq/(a + b*x^2 + c*x^4), x], x
] /; FreeQ[{a, b, c}, x] && PolyQ[Pq, x^2] && Expon[Pq, x^2] > 1

Rule 1678

Int[(Pq_)*((a_) + (b_.)*(x_)^2 + (c_.)*(x_)^4)^(p_), x_Symbol] :> With[{d = Coeff[PolynomialRemainder[Pq, a +
b*x^2 + c*x^4, x], x, 0], e = Coeff[PolynomialRemainder[Pq, a + b*x^2 + c*x^4, x], x, 2]}, Simp[(x*(a + b*x^2
+ c*x^4)^(p + 1)*(a*b*e - d*(b^2 - 2*a*c) - c*(b*d - 2*a*e)*x^2))/(2*a*(p + 1)*(b^2 - 4*a*c)), x] + Dist[1/(2*
a*(p + 1)*(b^2 - 4*a*c)), Int[(a + b*x^2 + c*x^4)^(p + 1)*ExpandToSum[2*a*(p + 1)*(b^2 - 4*a*c)*PolynomialQuot
ient[Pq, a + b*x^2 + c*x^4, x] + b^2*d*(2*p + 3) - 2*a*c*d*(4*p + 5) - a*b*e + c*(4*p + 7)*(b*d - 2*a*e)*x^2,
x], x], x]] /; FreeQ[{a, b, c}, x] && PolyQ[Pq, x^2] && Expon[Pq, x^2] > 1 && NeQ[b^2 - 4*a*c, 0] && LtQ[p, -1
]

Rubi steps

\begin {align*} \int \frac {d+e x+f x^2+g x^3+h x^4+j x^5+k x^6+l x^7+m x^8}{\left (a+b x^2+c x^4\right )^2} \, dx &=\int \frac {x \left (e+g x^2+j x^4+l x^6\right )}{\left (a+b x^2+c x^4\right )^2} \, dx+\int \frac {d+f x^2+h x^4+k x^6+m x^8}{\left (a+b x^2+c x^4\right )^2} \, dx\\ &=-\frac {x \left (a b c (c f+a k)-b^2 \left (c^2 d+a^2 m\right )+2 a c \left (c^2 d-a c h+a^2 m\right )+\left (a b^2 c k+2 a c^2 (c f-a k)-a b^3 m-b c \left (c^2 d+a c h-3 a^2 m\right )\right ) x^2\right )}{2 a c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {1}{2} \operatorname {Subst}\left (\int \frac {e+g x+j x^2+l x^3}{\left (a+b x+c x^2\right )^2} \, dx,x,x^2\right )-\frac {\int \frac {-\frac {a b c (c f+a k)+b^2 \left (c^2 d-a^2 m\right )-2 a c \left (3 c^2 d+a c h-a^2 m\right )}{c^2}-\frac {\left (a b^2 c k-2 a c^2 (c f+3 a k)-a b^3 m+b c \left (c^2 d+a c h+5 a^2 m\right )\right ) x^2}{c^2}+2 a \left (4 a-\frac {b^2}{c}\right ) m x^4}{a+b x^2+c x^4} \, dx}{2 a \left (b^2-4 a c\right )}\\ &=-\frac {b c (c e+a j)-a b^2 l-2 a c (c g-a l)+\left (2 c^3 e-c^2 (b g+2 a j)-b^3 l+b c (b j+3 a l)\right ) x^2}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {x \left (a b c (c f+a k)-b^2 \left (c^2 d+a^2 m\right )+2 a c \left (c^2 d-a c h+a^2 m\right )+\left (a b^2 c k+2 a c^2 (c f-a k)-a b^3 m-b c \left (c^2 d+a c h-3 a^2 m\right )\right ) x^2\right )}{2 a c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {\operatorname {Subst}\left (\int \frac {2 c e-b g+2 a j-\frac {a b l}{c}+\left (4 a-\frac {b^2}{c}\right ) l x}{a+b x+c x^2} \, dx,x,x^2\right )}{2 \left (b^2-4 a c\right )}-\frac {\int \left (-\frac {2 a \left (b^2-4 a c\right ) m}{c^2}-\frac {a b c (c f+a k)-2 a c \left (3 c^2 d+a c h-5 a^2 m\right )+b^2 \left (c^2 d-3 a^2 m\right )+\left (a b^2 c k-2 a c^2 (c f+3 a k)-3 a b^3 m+b c \left (c^2 d+a c h+13 a^2 m\right )\right ) x^2}{c^2 \left (a+b x^2+c x^4\right )}\right ) \, dx}{2 a \left (b^2-4 a c\right )}\\ &=\frac {m x}{c^2}-\frac {b c (c e+a j)-a b^2 l-2 a c (c g-a l)+\left (2 c^3 e-c^2 (b g+2 a j)-b^3 l+b c (b j+3 a l)\right ) x^2}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {x \left (a b c (c f+a k)-b^2 \left (c^2 d+a^2 m\right )+2 a c \left (c^2 d-a c h+a^2 m\right )+\left (a b^2 c k+2 a c^2 (c f-a k)-a b^3 m-b c \left (c^2 d+a c h-3 a^2 m\right )\right ) x^2\right )}{2 a c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {\int \frac {a b c (c f+a k)-2 a c \left (3 c^2 d+a c h-5 a^2 m\right )+b^2 \left (c^2 d-3 a^2 m\right )+\left (a b^2 c k-2 a c^2 (c f+3 a k)-3 a b^3 m+b c \left (c^2 d+a c h+13 a^2 m\right )\right ) x^2}{a+b x^2+c x^4} \, dx}{2 a c^2 \left (b^2-4 a c\right )}+\frac {l \operatorname {Subst}\left (\int \frac {b+2 c x}{a+b x+c x^2} \, dx,x,x^2\right )}{4 c^2}-\frac {\left (4 c^3 e-c^2 (2 b g-4 a j)+b^3 l-6 a b c l\right ) \operatorname {Subst}\left (\int \frac {1}{a+b x+c x^2} \, dx,x,x^2\right )}{4 c^2 \left (b^2-4 a c\right )}\\ &=\frac {m x}{c^2}-\frac {b c (c e+a j)-a b^2 l-2 a c (c g-a l)+\left (2 c^3 e-c^2 (b g+2 a j)-b^3 l+b c (b j+3 a l)\right ) x^2}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {x \left (a b c (c f+a k)-b^2 \left (c^2 d+a^2 m\right )+2 a c \left (c^2 d-a c h+a^2 m\right )+\left (a b^2 c k+2 a c^2 (c f-a k)-a b^3 m-b c \left (c^2 d+a c h-3 a^2 m\right )\right ) x^2\right )}{2 a c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {l \log \left (a+b x^2+c x^4\right )}{4 c^2}+\frac {\left (4 c^3 e-c^2 (2 b g-4 a j)+b^3 l-6 a b c l\right ) \operatorname {Subst}\left (\int \frac {1}{b^2-4 a c-x^2} \, dx,x,b+2 c x^2\right )}{2 c^2 \left (b^2-4 a c\right )}+\frac {\left (a b^2 c k-2 a c^2 (c f+3 a k)-3 a b^3 m+b c \left (c^2 d+a c h+13 a^2 m\right )-\frac {a b^3 c k-4 a b c^2 (c f+2 a k)-3 a b^4 m-b^2 c \left (c^2 d-a c h-19 a^2 m\right )+4 a c^2 \left (3 c^2 d+a c h-5 a^2 m\right )}{\sqrt {b^2-4 a c}}\right ) \int \frac {1}{\frac {b}{2}-\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{4 a c^2 \left (b^2-4 a c\right )}+\frac {\left (a b^2 c k-2 a c^2 (c f+3 a k)-3 a b^3 m+b c \left (c^2 d+a c h+13 a^2 m\right )+\frac {a b^3 c k-4 a b c^2 (c f+2 a k)-3 a b^4 m-b^2 c \left (c^2 d-a c h-19 a^2 m\right )+4 a c^2 \left (3 c^2 d+a c h-5 a^2 m\right )}{\sqrt {b^2-4 a c}}\right ) \int \frac {1}{\frac {b}{2}+\frac {1}{2} \sqrt {b^2-4 a c}+c x^2} \, dx}{4 a c^2 \left (b^2-4 a c\right )}\\ &=\frac {m x}{c^2}-\frac {b c (c e+a j)-a b^2 l-2 a c (c g-a l)+\left (2 c^3 e-c^2 (b g+2 a j)-b^3 l+b c (b j+3 a l)\right ) x^2}{2 c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}-\frac {x \left (a b c (c f+a k)-b^2 \left (c^2 d+a^2 m\right )+2 a c \left (c^2 d-a c h+a^2 m\right )+\left (a b^2 c k+2 a c^2 (c f-a k)-a b^3 m-b c \left (c^2 d+a c h-3 a^2 m\right )\right ) x^2\right )}{2 a c^2 \left (b^2-4 a c\right ) \left (a+b x^2+c x^4\right )}+\frac {\left (a b^2 c k-2 a c^2 (c f+3 a k)-3 a b^3 m+b c \left (c^2 d+a c h+13 a^2 m\right )-\frac {a b^3 c k-4 a b c^2 (c f+2 a k)-3 a b^4 m-b^2 c \left (c^2 d-a c h-19 a^2 m\right )+4 a c^2 \left (3 c^2 d+a c h-5 a^2 m\right )}{\sqrt {b^2-4 a c}}\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{2 \sqrt {2} a c^{5/2} \left (b^2-4 a c\right ) \sqrt {b-\sqrt {b^2-4 a c}}}+\frac {\left (a b^2 c k-2 a c^2 (c f+3 a k)-3 a b^3 m+b c \left (c^2 d+a c h+13 a^2 m\right )+\frac {a b^3 c k-4 a b c^2 (c f+2 a k)-3 a b^4 m-b^2 c \left (c^2 d-a c h-19 a^2 m\right )+4 a c^2 \left (3 c^2 d+a c h-5 a^2 m\right )}{\sqrt {b^2-4 a c}}\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{2 \sqrt {2} a c^{5/2} \left (b^2-4 a c\right ) \sqrt {b+\sqrt {b^2-4 a c}}}+\frac {\left (4 c^3 e-c^2 (2 b g-4 a j)+b^3 l-6 a b c l\right ) \tanh ^{-1}\left (\frac {b+2 c x^2}{\sqrt {b^2-4 a c}}\right )}{2 c^2 \left (b^2-4 a c\right )^{3/2}}+\frac {l \log \left (a+b x^2+c x^4\right )}{4 c^2}\\ \end {align*}

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Mathematica [A]  time = 5.70, size = 935, normalized size = 1.21 \begin {gather*} \frac {4 \sqrt {c} m x+\frac {2 \sqrt {c} \left (2 c (l+m x) a^3-\left ((l+m x) b^2-c (j+x (k+3 x (l+m x))) b+2 c^2 (g+x (h+x (j+k x)))\right ) a^2+\left (-x^2 (l+m x) b^3+c x^2 (j+k x) b^2+c^2 (e+x (f-x (g+h x))) b+2 c^3 x (d+x (e+f x))\right ) a-b c^2 d x \left (c x^2+b\right )\right )}{a \left (4 a c-b^2\right ) \left (c x^4+b x^2+a\right )}-\frac {\sqrt {2} \left (-3 a m b^4+a \left (c k+3 \sqrt {b^2-4 a c} m\right ) b^3+c \left (-d c^2+a h c+a \left (19 a m-\sqrt {b^2-4 a c} k\right )\right ) b^2-c \left (13 \sqrt {b^2-4 a c} m a^2+c \left (\sqrt {b^2-4 a c} h+8 a k\right ) a+c^2 \left (\sqrt {b^2-4 a c} d+4 a f\right )\right ) b+2 a c^2 \left (-10 m a^2+2 c h a+3 \sqrt {b^2-4 a c} k a+6 c^2 d+c \sqrt {b^2-4 a c} f\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b-\sqrt {b^2-4 a c}}}\right )}{a \left (b^2-4 a c\right )^{3/2} \sqrt {b-\sqrt {b^2-4 a c}}}-\frac {\sqrt {2} \left (3 a m b^4+a \left (3 \sqrt {b^2-4 a c} m-c k\right ) b^3+c \left (d c^2-a h c-a \left (\sqrt {b^2-4 a c} k+19 a m\right )\right ) b^2-c \left (13 \sqrt {b^2-4 a c} m a^2+c \left (\sqrt {b^2-4 a c} h-8 a k\right ) a+c^2 \left (\sqrt {b^2-4 a c} d-4 a f\right )\right ) b+2 a c^2 \left (10 m a^2-2 c h a+3 \sqrt {b^2-4 a c} k a-6 c^2 d+c \sqrt {b^2-4 a c} f\right )\right ) \tan ^{-1}\left (\frac {\sqrt {2} \sqrt {c} x}{\sqrt {b+\sqrt {b^2-4 a c}}}\right )}{a \left (b^2-4 a c\right )^{3/2} \sqrt {b+\sqrt {b^2-4 a c}}}+\frac {\sqrt {c} \left (-4 e c^3+2 (b g-2 a j) c^2+a \left (6 b l-4 \sqrt {b^2-4 a c} l\right ) c+b^2 \left (\sqrt {b^2-4 a c}-b\right ) l\right ) \log \left (-2 c x^2-b+\sqrt {b^2-4 a c}\right )}{\left (b^2-4 a c\right )^{3/2}}+\frac {\sqrt {c} \left (4 e c^3+(4 a j-2 b g) c^2-2 a \left (3 b+2 \sqrt {b^2-4 a c}\right ) l c+b^2 \left (b+\sqrt {b^2-4 a c}\right ) l\right ) \log \left (2 c x^2+b+\sqrt {b^2-4 a c}\right )}{\left (b^2-4 a c\right )^{3/2}}}{4 c^{5/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(d + e*x + f*x^2 + g*x^3 + h*x^4 + j*x^5 + k*x^6 + l*x^7 + m*x^8)/(a + b*x^2 + c*x^4)^2,x]

[Out]

(4*Sqrt[c]*m*x + (2*Sqrt[c]*(2*a^3*c*(l + m*x) - b*c^2*d*x*(b + c*x^2) + a*(b^2*c*x^2*(j + k*x) - b^3*x^2*(l +
m*x) + 2*c^3*x*(d + x*(e + f*x)) + b*c^2*(e + x*(f - x*(g + h*x)))) - a^2*(b^2*(l + m*x) + 2*c^2*(g + x*(h +
x*(j + k*x))) - b*c*(j + x*(k + 3*x*(l + m*x))))))/(a*(-b^2 + 4*a*c)*(a + b*x^2 + c*x^4)) - (Sqrt[2]*(-3*a*b^4
*m + 2*a*c^2*(6*c^2*d + c*Sqrt[b^2 - 4*a*c]*f + 2*a*c*h + 3*a*Sqrt[b^2 - 4*a*c]*k - 10*a^2*m) + a*b^3*(c*k + 3
*Sqrt[b^2 - 4*a*c]*m) - b*c*(c^2*(Sqrt[b^2 - 4*a*c]*d + 4*a*f) + a*c*(Sqrt[b^2 - 4*a*c]*h + 8*a*k) + 13*a^2*Sq
rt[b^2 - 4*a*c]*m) + b^2*c*(-(c^2*d) + a*c*h + a*(-(Sqrt[b^2 - 4*a*c]*k) + 19*a*m)))*ArcTan[(Sqrt[2]*Sqrt[c]*x
)/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(a*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*(3*a*b^4*m + 2*
a*c^2*(-6*c^2*d + c*Sqrt[b^2 - 4*a*c]*f - 2*a*c*h + 3*a*Sqrt[b^2 - 4*a*c]*k + 10*a^2*m) + a*b^3*(-(c*k) + 3*Sq
rt[b^2 - 4*a*c]*m) - b*c*(c^2*(Sqrt[b^2 - 4*a*c]*d - 4*a*f) + a*c*(Sqrt[b^2 - 4*a*c]*h - 8*a*k) + 13*a^2*Sqrt[
b^2 - 4*a*c]*m) + b^2*c*(c^2*d - a*c*h - a*(Sqrt[b^2 - 4*a*c]*k + 19*a*m)))*ArcTan[(Sqrt[2]*Sqrt[c]*x)/Sqrt[b
+ Sqrt[b^2 - 4*a*c]]])/(a*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(-4*c^3*e + 2*c^2*(b*g -
2*a*j) + b^2*(-b + Sqrt[b^2 - 4*a*c])*l + a*c*(6*b*l - 4*Sqrt[b^2 - 4*a*c]*l))*Log[-b + Sqrt[b^2 - 4*a*c] - 2
*c*x^2])/(b^2 - 4*a*c)^(3/2) + (Sqrt[c]*(4*c^3*e + c^2*(-2*b*g + 4*a*j) + b^2*(b + Sqrt[b^2 - 4*a*c])*l - 2*a*
c*(3*b + 2*Sqrt[b^2 - 4*a*c])*l)*Log[b + Sqrt[b^2 - 4*a*c] + 2*c*x^2])/(b^2 - 4*a*c)^(3/2))/(4*c^(5/2))

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IntegrateAlgebraic [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {d+e x+f x^2+g x^3+h x^4+j x^5+k x^6+l x^7+m x^8}{\left (a+b x^2+c x^4\right )^2} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[(d + e*x + f*x^2 + g*x^3 + h*x^4 + j*x^5 + k*x^6 + l*x^7 + m*x^8)/(a + b*x^2 + c*x^4)^2,x]

[Out]

IntegrateAlgebraic[(d + e*x + f*x^2 + g*x^3 + h*x^4 + j*x^5 + k*x^6 + l*x^7 + m*x^8)/(a + b*x^2 + c*x^4)^2, x]

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((m*x^8+l*x^7+k*x^6+j*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^2,x, algorithm="fricas")

[Out]

Timed out

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((m*x^8+l*x^7+k*x^6+j*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^2,x, algorithm="giac")

[Out]

Timed out

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maple [B]  time = 0.10, size = 4570, normalized size = 5.94 \begin {gather*} \text {output too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((m*x^8+l*x^7+k*x^6+j*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^2,x)

[Out]

-3/4/c^2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2
)*c*x)*b^5*m+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*b^2*h*arctan(2^(1/2
)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^
(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*b^2*h+4*a^2/(4*a*c-b^2)^2*ln(2*c*x^2+b+(-4*a*c
+b^2)^(1/2))*l-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*g+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b*e+4*a^2/(4*a*c-b^2)^2*ln(-2
*c*x^2-b+(-4*a*c+b^2)^(1/2))*l-1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)/a
*b^2*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/4*c/(4*a*c-b^2)^2/a*2^(1/2)/((-b+(-4*a*c+b^2)^
(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*b^2*d+m*x/c^2-c/(4*a
*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4
*a*c+b^2)^(1/2)*b*f-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*b*c*f*arctan(2
^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-2*c^2/(4*a*c-b^2)^2*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a
rctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f+1/2*c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c
)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f+2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^
(1/2))*c)^(1/2)*a*c^2*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4
*a*c+b^2)^(1/2))*c)^(1/2)*b^2*c*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/4*c/(4*a*c-b^2)^2/a*2
^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d+a/(4*a*c
-b^2)^2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*h
+1/2/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)*b*g*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))+1/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)
*c*e*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))-1/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)*c*e*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))
+c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*d+1/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a^2*l-1/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x^3*k
-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a*j-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*b*g-1/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)
*x*h-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b*h+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b*f+1/4/c^2/(4*a*c-b^2)^2*ln(-2
*c*x^2-b+(-4*a*c+b^2)^(1/2))*b^4*l-a/(4*a*c-b^2)^2*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*(-4*a*c+b^2)^(1/2)*j+a/(4
*a*c-b^2)^2*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*(-4*a*c+b^2)^(1/2)*j+1/4/c^2/(4*a*c-b^2)^2*ln(2*c*x^2+b+(-4*a*c+b
^2)^(1/2))*b^4*l+3/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*c^2*d*arctan(2^(1
/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b*c^2*d*arc
tan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+3*c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2
)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*d+c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(
-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+1/4/(4*a*c-b^2)^2*2^(1/
2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*b^3*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+3/2/c/(c*x^
4+b*x^2+a)*a/(4*a*c-b^2)*x^3*b*m-1/2*c/(c*x^4+b*x^2+a)/a/(4*a*c-b^2)*x^3*b*d+3/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)
*x^2*a*b*l+1/2/c/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b*k-1/2/c^2/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b^2*m-5*a^2/(4*a*
c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*
a*c+b^2)^(1/2)*m+13*a^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b
^2)^(1/2))*c)^(1/2)*c*x)*b*m+5/2*a/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-
b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*k-13*a^2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan
(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*m-5/2*a/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2
)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*k-5*a^2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2
))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*m+3/2/c*a/(4*a*c-b^2)^2*ln
(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b*l-6*c*a^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*
c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*k-3/2/c*a/(4*a*c-b^2)^2*ln(2*c*x^2+b+(-4*a*c+b
^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b*l+6*c*a^2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2
)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*k+3/4/c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arct
anh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5*m-1/4/c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*
c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*k+1/4/c/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+
b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*k-1/4/(4*a*c-b^2)^2*2^(1/2)/((-b
+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*h-1/2/(4*a*c-b^2)^2*(
-4*a*c+b^2)^(1/2)*b*g*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))+19/4/c*a/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))
*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*b^2*m+19/4/c*a/(4*a*c-b^2)
^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^
(1/2)*b^2*m+1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*a*c*h*arctan(2^(1/2)/(
(b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*b*c*h*arctan(2
^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+a/(4*a*c-b^2)^2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arcta
nh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*h+c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*e+c/(
c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*f+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b^3*h*arctan(2^(1/
2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-25/4/c*a/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arct
anh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*m+25/4/c*a/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2)
)*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*m-3/4/c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a
*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*b^4*m-3/4/c^
2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*
(-4*a*c+b^2)^(1/2)*b^4*m+1/4/c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-
4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*b^3*k-2*a/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)
^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*b*k-2*a/(4*a*c-b^2)^2*2^(1/2)
/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*b*k+
1/4/c/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c
*x)*(-4*a*c+b^2)^(1/2)*b^3*k-1/2/(c*x^4+b*x^2+a)/a/(4*a*c-b^2)*x*b^2*d-1/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2
*b^3*l-1/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^3*m-1/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*b^2*l+1/2/c/(c*x^4+
b*x^2+a)/(4*a*c-b^2)*x^2*b^2*j+1/c/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*x*m+1/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*b*j
+1/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^2*k-1/4/c^2/(4*a*c-b^2)^2*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*(-4*a*c+b
^2)^(1/2)*b^3*l+1/4/c^2/(4*a*c-b^2)^2*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b^3*l-2/c*a/(4*a*c-b
^2)^2*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*b^2*l-2/c*a/(4*a*c-b^2)^2*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*b^2*l

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} -\frac {a b c^{2} e - 2 \, a^{2} c^{2} g + a^{2} b c j - {\left (b c^{3} d - 2 \, a c^{3} f + a b c^{2} h - {\left (a b^{2} c - 2 \, a^{2} c^{2}\right )} k + {\left (a b^{3} - 3 \, a^{2} b c\right )} m\right )} x^{3} + {\left (2 \, a c^{3} e - a b c^{2} g + {\left (a b^{2} c - 2 \, a^{2} c^{2}\right )} j - {\left (a b^{3} - 3 \, a^{2} b c\right )} l\right )} x^{2} - {\left (a^{2} b^{2} - 2 \, a^{3} c\right )} l + {\left (a b c^{2} f - 2 \, a^{2} c^{2} h + a^{2} b c k - {\left (b^{2} c^{2} - 2 \, a c^{3}\right )} d - {\left (a^{2} b^{2} - 2 \, a^{3} c\right )} m\right )} x}{2 \, {\left (a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3} + {\left (a b^{2} c^{3} - 4 \, a^{2} c^{4}\right )} x^{4} + {\left (a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right )} x^{2}\right )}} + \frac {m x}{c^{2}} - \frac {-\int \frac {a b c^{2} f - 2 \, a^{2} c^{2} h + a^{2} b c k + 2 \, {\left (a b^{2} c - 4 \, a^{2} c^{2}\right )} l x^{3} + {\left (b c^{3} d - 2 \, a c^{3} f + a b c^{2} h + {\left (a b^{2} c - 6 \, a^{2} c^{2}\right )} k - {\left (3 \, a b^{3} - 13 \, a^{2} b c\right )} m\right )} x^{2} + {\left (b^{2} c^{2} - 6 \, a c^{3}\right )} d - {\left (3 \, a^{2} b^{2} - 10 \, a^{3} c\right )} m - 2 \, {\left (2 \, a c^{3} e - a b c^{2} g + 2 \, a^{2} c^{2} j - a^{2} b c l\right )} x}{c x^{4} + b x^{2} + a}\,{d x}}{2 \, {\left (a b^{2} c^{2} - 4 \, a^{2} c^{3}\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((m*x^8+l*x^7+k*x^6+j*x^5+h*x^4+g*x^3+f*x^2+e*x+d)/(c*x^4+b*x^2+a)^2,x, algorithm="maxima")

[Out]

-1/2*(a*b*c^2*e - 2*a^2*c^2*g + a^2*b*c*j - (b*c^3*d - 2*a*c^3*f + a*b*c^2*h - (a*b^2*c - 2*a^2*c^2)*k + (a*b^
3 - 3*a^2*b*c)*m)*x^3 + (2*a*c^3*e - a*b*c^2*g + (a*b^2*c - 2*a^2*c^2)*j - (a*b^3 - 3*a^2*b*c)*l)*x^2 - (a^2*b
^2 - 2*a^3*c)*l + (a*b*c^2*f - 2*a^2*c^2*h + a^2*b*c*k - (b^2*c^2 - 2*a*c^3)*d - (a^2*b^2 - 2*a^3*c)*m)*x)/(a^
2*b^2*c^2 - 4*a^3*c^3 + (a*b^2*c^3 - 4*a^2*c^4)*x^4 + (a*b^3*c^2 - 4*a^2*b*c^3)*x^2) + m*x/c^2 - 1/2*integrate
(-(a*b*c^2*f - 2*a^2*c^2*h + a^2*b*c*k + 2*(a*b^2*c - 4*a^2*c^2)*l*x^3 + (b*c^3*d - 2*a*c^3*f + a*b*c^2*h + (a
*b^2*c - 6*a^2*c^2)*k - (3*a*b^3 - 13*a^2*b*c)*m)*x^2 + (b^2*c^2 - 6*a*c^3)*d - (3*a^2*b^2 - 10*a^3*c)*m - 2*(
2*a*c^3*e - a*b*c^2*g + 2*a^2*c^2*j - a^2*b*c*l)*x)/(c*x^4 + b*x^2 + a), x)/(a*b^2*c^2 - 4*a^2*c^3)

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mupad [B]  time = 13.91, size = 82785, normalized size = 107.51

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d + e*x + f*x^2 + g*x^3 + h*x^4 + j*x^5 + k*x^6 + l*x^7 + m*x^8)/(a + b*x^2 + c*x^4)^2,x)

[Out]

symsum(log(root(1572864*a^8*b^2*c^10*z^4 - 983040*a^7*b^4*c^9*z^4 + 327680*a^6*b^6*c^8*z^4 - 61440*a^5*b^8*c^7
*z^4 + 6144*a^4*b^10*c^6*z^4 - 256*a^3*b^12*c^5*z^4 - 1048576*a^9*c^11*z^4 - 1572864*a^8*b^2*c^8*l*z^3 + 98304
0*a^7*b^4*c^7*l*z^3 - 327680*a^6*b^6*c^6*l*z^3 + 61440*a^5*b^8*c^5*l*z^3 - 6144*a^4*b^10*c^4*l*z^3 + 256*a^3*b
^12*c^3*l*z^3 + 1048576*a^9*c^9*l*z^3 + 96*a^3*b^12*c*k*m*z^2 + 98304*a^8*b*c^7*j*l*z^2 + 24576*a^8*b*c^7*h*m*
z^2 + 155648*a^7*b*c^8*d*m*z^2 + 98304*a^7*b*c^8*e*l*z^2 + 57344*a^7*b*c^8*f*k*z^2 + 32768*a^7*b*c^8*g*j*z^2 +
57344*a^6*b*c^9*d*h*z^2 + 32768*a^6*b*c^9*e*g*z^2 - 32*a*b^10*c^5*d*f*z^2 - 491520*a^8*b^2*c^6*k*m*z^2 + 3584
00*a^7*b^4*c^5*k*m*z^2 - 129024*a^6*b^6*c^4*k*m*z^2 + 24768*a^5*b^8*c^3*k*m*z^2 - 2432*a^4*b^10*c^2*k*m*z^2 -
90112*a^7*b^3*c^6*j*l*z^2 + 30720*a^6*b^5*c^5*j*l*z^2 - 4608*a^5*b^7*c^4*j*l*z^2 + 256*a^4*b^9*c^3*j*l*z^2 - 2
1504*a^6*b^5*c^5*h*m*z^2 + 9216*a^5*b^7*c^4*h*m*z^2 + 8192*a^7*b^3*c^6*h*m*z^2 - 1568*a^4*b^9*c^3*h*m*z^2 + 96
*a^3*b^11*c^2*h*m*z^2 - 172032*a^7*b^2*c^7*f*m*z^2 + 116736*a^6*b^4*c^6*f*m*z^2 - 49152*a^7*b^2*c^7*g*l*z^2 +
45056*a^6*b^4*c^6*g*l*z^2 - 35840*a^5*b^6*c^5*f*m*z^2 + 24576*a^7*b^2*c^7*h*k*z^2 - 15360*a^5*b^6*c^5*g*l*z^2
+ 5184*a^4*b^8*c^4*f*m*z^2 - 3072*a^5*b^6*c^5*h*k*z^2 + 2304*a^4*b^8*c^4*g*l*z^2 + 2048*a^6*b^4*c^6*h*k*z^2 +
576*a^4*b^8*c^4*h*k*z^2 - 288*a^3*b^10*c^3*f*m*z^2 - 128*a^3*b^10*c^3*g*l*z^2 - 32*a^3*b^10*c^3*h*k*z^2 - 1474
56*a^6*b^3*c^7*d*m*z^2 - 90112*a^6*b^3*c^7*e*l*z^2 + 52224*a^5*b^5*c^6*d*m*z^2 - 49152*a^6*b^3*c^7*f*k*z^2 + 3
0720*a^5*b^5*c^6*e*l*z^2 - 24576*a^6*b^3*c^7*g*j*z^2 + 15360*a^5*b^5*c^6*f*k*z^2 - 8192*a^4*b^7*c^5*d*m*z^2 +
6144*a^5*b^5*c^6*g*j*z^2 - 4608*a^4*b^7*c^5*e*l*z^2 - 2048*a^4*b^7*c^5*f*k*z^2 - 512*a^4*b^7*c^5*g*j*z^2 + 480
*a^3*b^9*c^4*d*m*z^2 + 256*a^3*b^9*c^4*e*l*z^2 + 96*a^3*b^9*c^4*f*k*z^2 + 131072*a^6*b^2*c^8*d*k*z^2 + 49152*a
^6*b^2*c^8*e*j*z^2 - 43008*a^5*b^4*c^7*d*k*z^2 - 12288*a^5*b^4*c^7*e*j*z^2 + 6144*a^4*b^6*c^6*d*k*z^2 + 1024*a
^4*b^6*c^6*e*j*z^2 - 320*a^3*b^8*c^5*d*k*z^2 + 6144*a^5*b^4*c^7*f*h*z^2 - 2048*a^4*b^6*c^6*f*h*z^2 + 192*a^3*b
^8*c^5*f*h*z^2 - 49152*a^5*b^3*c^8*d*h*z^2 - 24576*a^5*b^3*c^8*e*g*z^2 + 15360*a^4*b^5*c^7*d*h*z^2 + 6144*a^4*
b^5*c^7*e*g*z^2 - 2048*a^3*b^7*c^6*d*h*z^2 - 512*a^3*b^7*c^6*e*g*z^2 + 96*a^2*b^9*c^5*d*h*z^2 + 24576*a^5*b^2*
c^9*d*f*z^2 - 3072*a^3*b^6*c^7*d*f*z^2 + 2048*a^4*b^4*c^8*d*f*z^2 + 576*a^2*b^8*c^6*d*f*z^2 - 430080*a^9*b*c^6
*m^2*z^2 + 3408*a^4*b^11*c*m^2*z^2 - 64*a^3*b^12*c*l^2*z^2 + 61440*a^8*b*c^7*k^2*z^2 + 12288*a^7*b*c^8*h^2*z^2
+ 12288*a^6*b*c^9*f^2*z^2 + 61440*a^5*b*c^10*d^2*z^2 + 432*a*b^9*c^6*d^2*z^2 + 245760*a^9*c^7*k*m*z^2 + 81920
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z^2 - 49152*a^6*c^10*d*f*z^2 + 716800*a^8*b^3*c^5*m^2*z^2 - 483840*a^7*b^5*c^4*m^2*z^2 + 170496*a^6*b^7*c^3*m^
2*z^2 - 33232*a^5*b^9*c^2*m^2*z^2 + 516096*a^8*b^2*c^6*l^2*z^2 - 288768*a^7*b^4*c^5*l^2*z^2 + 88576*a^6*b^6*c^
4*l^2*z^2 - 15744*a^5*b^8*c^3*l^2*z^2 + 1536*a^4*b^10*c^2*l^2*z^2 - 61440*a^7*b^3*c^6*k^2*z^2 + 24064*a^6*b^5*
c^5*k^2*z^2 - 4608*a^5*b^7*c^4*k^2*z^2 + 432*a^4*b^9*c^3*k^2*z^2 - 16*a^3*b^11*c^2*k^2*z^2 + 24576*a^7*b^2*c^7
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2*z^2 - 16*a^3*b^9*c^4*h^2*z^2 - 8192*a^6*b^2*c^8*g^2*z^2 + 6144*a^5*b^4*c^7*g^2*z^2 - 1536*a^4*b^6*c^6*g^2*z^
2 + 128*a^3*b^8*c^5*g^2*z^2 - 8192*a^5*b^3*c^8*f^2*z^2 + 1536*a^4*b^5*c^7*f^2*z^2 - 16*a^2*b^9*c^5*f^2*z^2 + 2
4576*a^5*b^2*c^9*e^2*z^2 - 6144*a^4*b^4*c^8*e^2*z^2 + 512*a^3*b^6*c^7*e^2*z^2 - 61440*a^4*b^3*c^9*d^2*z^2 + 24
064*a^3*b^5*c^8*d^2*z^2 - 4608*a^2*b^7*c^7*d^2*z^2 - 393216*a^9*c^7*l^2*z^2 - 144*a^3*b^13*m^2*z^2 - 32768*a^8
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0*a^7*b*c^6*f*k*l*z + 4096*a^7*b*c^6*h*j*k*z + 10240*a^7*b*c^6*g*h*m*z - 47104*a^6*b*c^7*d*h*l*z + 36864*a^6*b
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6*c^2*k*l*m*z - 79872*a^7*b^3*c^4*j*k*m*z + 26112*a^6*b^5*c^3*j*k*m*z - 3712*a^5*b^7*c^2*j*k*m*z - 13824*a^7*b
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4*c^4*g*k*m*z + 30720*a^7*b^2*c^5*f*l*m*z - 18432*a^7*b^2*c^5*h*k*l*z - 13056*a^5*b^6*c^3*g*k*m*z - 7680*a^6*b
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h*j*m*z - 79872*a^6*b^3*c^5*e*k*m*z - 27648*a^6*b^3*c^5*f*j*m*z + 26112*a^5*b^5*c^4*e*k*m*z + 12288*a^6*b^3*c^
5*g*j*l*z - 10752*a^6*b^3*c^5*d*l*m*z + 7680*a^6*b^3*c^5*f*k*l*z + 6912*a^5*b^5*c^4*f*j*m*z - 3712*a^4*b^7*c^3
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6*a^6*b^3*c^5*g*h*m*z + 992*a^4*b^7*c^3*g*h*m*z - 96*a^3*b^9*c^2*g*h*m*z - 65536*a^6*b^2*c^6*d*k*l*z + 46080*a
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5*g*h*k*z + 1024*a^4*b^6*c^4*f*h*l*z - 384*a^4*b^6*c^4*g*h*k*z + 288*a^3*b^8*c^3*f*g*m*z + 192*a^3*b^8*c^3*e*h
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z + 5760*a^4*b^5*c^5*d*g*m*z - 4608*a^5*b^3*c^6*f*g*k*z - 3072*a^5*b^3*c^6*e*h*k*z - 3072*a^4*b^5*c^5*e*g*l*z
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0*a^3*b^7*c^4*d*g*m*z + 256*a^3*b^7*c^4*e*g*l*z - 96*a^3*b^7*c^4*f*g*k*z - 96*a^2*b^9*c^3*d*h*l*z - 64*a^3*b^7
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1024*a^6*b*c^7*g*h^2*z + 32*a*b^8*c^5*d^2*j*z + 1024*a^5*b*c^8*f^2*g*z - 9216*a^4*b*c^9*d^2*g*z + 336*a*b^7*c
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20480*a^8*c^6*h*j*m*z + 73728*a^7*c^7*d*k*l*z - 61440*a^7*c^7*d*j*m*z + 32768*a^7*c^7*e*j*l*z - 12288*a^7*c^7*
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15872*a^4*b^2*c^8*d^2*j*z + 4992*a^3*b^4*c^7*d^2*j*z - 672*a^2*b^6*c^6*d^2*j*z - 1536*a^5*b^2*c^7*e*h^2*z - 7
68*a^4*b^3*c^7*f^2*g*z + 384*a^4*b^4*c^6*e*h^2*z + 192*a^3*b^5*c^6*f^2*g*z - 32*a^3*b^6*c^5*e*h^2*z - 16*a^2*b
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4*l^3*z + 21504*a^7*b^4*c^3*l^3*z - 3328*a^6*b^6*c^2*l^3*z + 432*a^5*b^9*l*m^2*z + 51200*a^9*c^5*j*m^2*z + 163
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*f^2*j*z + 18432*a^5*c^9*d^2*j*z + 192*a^5*b^8*c*l^3*z + 2048*a^6*c^8*e*h^2*z - 16*b^9*c^5*d^2*g*z - 2048*a^5*
c^9*e*f^2*z + 32*b^8*c^6*d^2*e*z + 18432*a^4*c^10*d^2*e*z + 65536*a^9*c^5*l^3*z - 11008*a^8*b*c^3*j*k*l*m - 28
8*a^6*b^5*c*j*k*l*m + 144*a^5*b^6*c*g*k*l*m - 11008*a^7*b*c^4*e*k*l*m - 5376*a^7*b*c^4*f*j*l*m + 3840*a^7*b*c^
4*g*j*k*m - 3328*a^7*b*c^4*h*j*k*l - 96*a^4*b^7*c*g*j*k*m - 2560*a^7*b*c^4*g*h*l*m - 36*a^3*b^8*c*f*h*k*m - 69
12*a^6*b*c^5*d*j*k*l - 7872*a^6*b*c^5*d*h*k*m - 7680*a^6*b*c^5*d*g*l*m - 5376*a^6*b*c^5*e*f*l*m + 3840*a^6*b*c
^5*e*g*k*m - 3328*a^6*b*c^5*e*h*k*l - 1536*a^6*b*c^5*f*g*k*l + 1280*a^6*b*c^5*f*g*j*m - 768*a^6*b*c^5*g*h*j*k
- 768*a^6*b*c^5*f*h*j*l - 768*a^6*b*c^5*e*h*j*m - 36*a^2*b^9*c*d*h*k*m - 6912*a^5*b*c^6*d*e*k*l - 4864*a^5*b*c
^6*d*e*j*m - 2304*a^5*b*c^6*d*g*j*k - 1792*a^5*b*c^6*e*f*j*k - 1280*a^5*b*c^6*d*f*j*l - 4544*a^5*b*c^6*d*f*h*m
+ 1536*a^5*b*c^6*d*g*h*l + 1280*a^5*b*c^6*e*f*g*m - 768*a^5*b*c^6*e*g*h*k - 768*a^5*b*c^6*e*f*h*l - 256*a^5*b
*c^6*f*g*h*j + 12*a*b^9*c^2*d*f*h*m + 16*a*b^8*c^3*d*f*g*l - 4*a*b^8*c^3*d*f*h*k - 2304*a^4*b*c^7*d*e*g*k - 17
92*a^4*b*c^7*d*e*h*j - 1280*a^4*b*c^7*d*e*f*l - 768*a^4*b*c^7*d*f*g*j - 32*a*b^7*c^4*d*e*f*l - 256*a^4*b*c^7*e
*f*g*h - 768*a^3*b*c^8*d*e*f*g + 32*a*b^5*c^6*d*e*f*g + 12*a*b^10*c*d*f*k*m + 3648*a^7*b^3*c^2*j*k*l*m + 5504*
a^7*b^2*c^3*g*k*l*m - 1824*a^6*b^4*c^2*g*k*l*m + 384*a^7*b^2*c^3*h*j*l*m - 288*a^6*b^4*c^2*h*j*l*m - 4800*a^6*
b^3*c^3*g*j*k*m + 3648*a^6*b^3*c^3*e*k*l*m + 1280*a^5*b^5*c^2*g*j*k*m + 1088*a^6*b^3*c^3*f*j*l*m + 576*a^6*b^3
*c^3*h*j*k*l - 288*a^5*b^5*c^2*e*k*l*m - 192*a^6*b^3*c^3*g*h*l*m + 144*a^5*b^5*c^2*g*h*l*m + 9600*a^6*b^2*c^4*
e*j*k*m - 4224*a^6*b^2*c^4*d*j*l*m - 2560*a^5*b^4*c^3*e*j*k*m + 384*a^6*b^2*c^4*f*j*k*l + 224*a^5*b^4*c^3*d*j*
l*m + 192*a^4*b^6*c^2*e*j*k*m - 160*a^5*b^4*c^3*f*j*k*l - 4608*a^6*b^2*c^4*f*h*k*m + 2688*a^6*b^2*c^4*f*g*l*m
+ 1664*a^6*b^2*c^4*g*h*k*l - 744*a^5*b^4*c^3*f*h*k*m - 544*a^5*b^4*c^3*f*g*l*m + 492*a^4*b^6*c^2*f*h*k*m + 416
*a^5*b^4*c^3*g*h*j*m + 384*a^6*b^2*c^4*g*h*j*m + 384*a^6*b^2*c^4*e*h*l*m - 288*a^5*b^4*c^3*g*h*k*l - 288*a^5*b
^4*c^3*e*h*l*m - 96*a^4*b^6*c^2*g*h*j*m + 2112*a^5*b^3*c^4*d*j*k*l - 160*a^4*b^5*c^3*d*j*k*l + 16992*a^5*b^3*c
^4*d*h*k*m - 6252*a^4*b^5*c^3*d*h*k*m - 4800*a^5*b^3*c^4*e*g*k*m + 2112*a^5*b^3*c^4*d*g*l*m - 1728*a^5*b^3*c^4
*f*g*j*m + 1280*a^4*b^5*c^3*e*g*k*m + 1088*a^5*b^3*c^4*e*f*l*m - 832*a^5*b^3*c^4*e*h*j*m + 816*a^3*b^7*c^2*d*h
*k*m + 576*a^5*b^3*c^4*e*h*k*l - 448*a^5*b^3*c^4*f*h*j*l + 288*a^4*b^5*c^3*f*g*j*m - 192*a^5*b^3*c^4*g*h*j*k -
192*a^5*b^3*c^4*f*g*k*l + 192*a^4*b^5*c^3*e*h*j*m - 112*a^4*b^5*c^3*d*g*l*m + 96*a^4*b^5*c^3*f*h*j*l - 96*a^3
*b^7*c^2*e*g*k*m + 80*a^4*b^5*c^3*f*g*k*l + 32*a^4*b^5*c^3*g*h*j*k - 11456*a^5*b^2*c^5*d*f*k*m + 4992*a^5*b^2*
c^5*d*h*j*l - 4608*a^5*b^2*c^5*e*g*j*l - 4224*a^5*b^2*c^5*d*e*l*m + 3456*a^5*b^2*c^5*e*f*j*m + 3456*a^5*b^2*c^
5*d*g*k*l + 2432*a^5*b^2*c^5*d*g*j*m - 1312*a^4*b^4*c^4*d*h*j*l + 1272*a^3*b^6*c^3*d*f*k*m - 1056*a^4*b^4*c^4*
d*g*k*l + 896*a^5*b^2*c^5*f*g*j*k + 768*a^4*b^4*c^4*e*g*j*l - 576*a^4*b^4*c^4*e*f*j*m - 480*a^4*b^4*c^4*d*g*j*
m + 384*a^5*b^2*c^5*e*h*j*k + 384*a^5*b^2*c^5*e*f*k*l - 232*a^2*b^8*c^2*d*f*k*m + 224*a^4*b^4*c^4*d*e*l*m - 16
0*a^4*b^4*c^4*e*f*k*l - 96*a^4*b^4*c^4*f*g*j*k + 96*a^3*b^6*c^3*d*h*j*l + 80*a^3*b^6*c^3*d*g*k*l - 64*a^4*b^4*
c^4*e*h*j*k - 24*a^4*b^4*c^4*d*f*k*m + 416*a^4*b^4*c^4*e*g*h*m + 384*a^5*b^2*c^5*f*g*h*l + 384*a^5*b^2*c^5*e*g
*h*m + 224*a^4*b^4*c^4*f*g*h*l - 96*a^3*b^6*c^3*e*g*h*m - 48*a^3*b^6*c^3*f*g*h*l + 2112*a^4*b^3*c^5*d*e*k*l -
960*a^4*b^3*c^5*d*f*j*l + 960*a^4*b^3*c^5*d*e*j*m + 384*a^3*b^5*c^4*d*f*j*l + 320*a^4*b^3*c^5*d*g*j*k + 192*a^
4*b^3*c^5*e*f*j*k - 160*a^3*b^5*c^4*d*e*k*l - 32*a^2*b^7*c^3*d*f*j*l + 7392*a^4*b^3*c^5*d*f*h*m - 2496*a^4*b^3
*c^5*d*g*h*l - 1728*a^4*b^3*c^5*e*f*g*m - 1500*a^3*b^5*c^4*d*f*h*m + 656*a^3*b^5*c^4*d*g*h*l - 448*a^4*b^3*c^5
*e*f*h*l + 288*a^3*b^5*c^4*e*f*g*m - 192*a^4*b^3*c^5*f*g*h*j - 192*a^4*b^3*c^5*e*g*h*k + 96*a^3*b^5*c^4*e*f*h*
l - 48*a^2*b^7*c^3*d*g*h*l + 32*a^3*b^5*c^4*e*g*h*k - 16*a^2*b^7*c^3*d*f*h*m - 640*a^4*b^2*c^6*d*e*j*k + 4992*
a^4*b^2*c^6*d*e*h*l - 3584*a^4*b^2*c^6*d*f*h*k + 2432*a^4*b^2*c^6*d*e*g*m - 1312*a^3*b^4*c^5*d*e*h*l + 896*a^4
*b^2*c^6*e*f*g*k + 896*a^4*b^2*c^6*d*g*h*j + 640*a^4*b^2*c^6*d*f*g*l + 600*a^3*b^4*c^5*d*f*h*k + 480*a^3*b^4*c
^5*d*f*g*l - 480*a^3*b^4*c^5*d*e*g*m + 384*a^4*b^2*c^6*e*f*h*j - 192*a^2*b^6*c^4*d*f*g*l - 96*a^3*b^4*c^5*e*f*
g*k - 96*a^3*b^4*c^5*d*g*h*j + 96*a^2*b^6*c^4*d*e*h*l + 12*a^2*b^6*c^4*d*f*h*k - 960*a^3*b^3*c^6*d*e*f*l + 384
*a^2*b^5*c^5*d*e*f*l + 320*a^3*b^3*c^6*d*e*g*k - 192*a^3*b^3*c^6*d*f*g*j + 192*a^3*b^3*c^6*d*e*h*j + 32*a^2*b^
5*c^5*d*f*g*j - 192*a^3*b^3*c^6*e*f*g*h + 384*a^3*b^2*c^7*d*e*f*j - 64*a^2*b^4*c^6*d*e*f*j + 896*a^3*b^2*c^7*d
*e*g*h - 96*a^2*b^4*c^6*d*e*g*h - 192*a^2*b^3*c^7*d*e*f*g + 496*a^7*b^4*c*k*l^2*m - 4752*a^7*b^4*c*j*l*m^2 + 9
6*a^5*b^6*c*j^2*k*m - 6144*a^8*b*c^3*h*l^2*m - 168*a^6*b^5*c*h*l^2*m + 6400*a^8*b*c^3*g*l*m^2 - 2862*a^6*b^5*c
*h*k*m^2 + 2376*a^6*b^5*c*g*l*m^2 - 1632*a^7*b*c^4*h^2*k*m - 480*a^8*b*c^3*h*k*m^2 - 180*a^5*b^6*c*h*k^2*m + 5
4*a^4*b^7*c*h^2*k*m - 384*a^7*b*c^4*h*j^2*m + 120*a^5*b^6*c*h*k*l^2 + 56*a^5*b^6*c*f*l^2*m + 24*a^3*b^8*c*g^2*
k*m + 4512*a^7*b*c^4*f*k^2*m - 2304*a^7*b*c^4*g*k^2*l - 1680*a^5*b^6*c*g*j*m^2 + 1184*a^6*b*c^5*f^2*k*m + 804*
a^5*b^6*c*f*k*m^2 + 432*a^5*b^6*c*e*l*m^2 + 60*a^4*b^7*c*f*k^2*m + 6*a^2*b^9*c*f^2*k*m - 13312*a^7*b*c^4*d*l^2
*m + 2048*a^7*b*c^4*g*j*l^2 - 1024*a^7*b*c^4*f*k*l^2 + 64*a^4*b^7*c*g*j*l^2 + 56*a^4*b^7*c*d*l^2*m - 40*a^4*b^
7*c*f*k*l^2 + 13440*a^7*b*c^4*e*j*m^2 - 8928*a^5*b*c^6*d^2*k*m - 6240*a^7*b*c^4*d*k*m^2 + 1614*a^4*b^7*c*d*k*m
^2 - 288*a^4*b^7*c*e*j*m^2 - 170*a*b^9*c^2*d^2*k*m + 60*a^3*b^8*c*d*k^2*m + 4608*a^6*b*c^5*e*j^2*l + 4608*a^5*
b*c^6*e^2*j*l - 2432*a^6*b*c^5*d*j^2*m + 1440*a^7*b*c^4*f*h*m^2 - 896*a^6*b*c^5*f*j^2*k - 864*a^6*b*c^5*f*h^2*
m - 558*a^4*b^7*c*f*h*m^2 + 256*a^6*b*c^5*g*h^2*l - 40*a^3*b^8*c*d*k*l^2 - 1920*a^6*b*c^5*e*j*k^2 - 384*a^5*b*
c^6*e^2*h*m + 24*a^3*b^8*c*f*h*l^2 - 16*a*b^8*c^3*d^2*j*l + 2208*a^6*b*c^5*f*h*k^2 - 1044*a^3*b^8*c*d*h*m^2 +
800*a^5*b*c^6*f^2*h*k - 256*a^5*b*c^6*f^2*g*l + 144*a^3*b^8*c*e*g*m^2 - 116*a*b^8*c^3*d^2*h*m + 8192*a^6*b*c^5
*d*h*l^2 + 2048*a^6*b*c^5*e*g*l^2 + 24*a^2*b^9*c*d*h*l^2 - 5856*a^4*b*c^7*d^2*f*m + 4896*a^4*b*c^7*d^2*h*k + 2
720*a^6*b*c^5*d*f*m^2 + 2304*a^4*b*c^7*d^2*g*l + 1824*a^5*b*c^6*d*h^2*k + 438*a*b^7*c^4*d^2*f*m - 384*a^5*b*c^
6*e*h^2*j + 318*a^2*b^9*c*d*f*m^2 - 168*a*b^7*c^4*d^2*g*l + 42*a*b^7*c^4*d^2*h*k - 36*a*b^8*c^3*d*f^2*m - 2432
*a^4*b*c^7*d*e^2*m + 1536*a^5*b*c^6*e*g*j^2 + 1536*a^4*b*c^7*e^2*g*j - 896*a^5*b*c^6*d*h*j^2 - 896*a^4*b*c^7*e
^2*f*k + 4896*a^5*b*c^6*d*f*k^2 + 1824*a^4*b*c^7*d*f^2*k - 384*a^4*b*c^7*e*f^2*j + 336*a*b^6*c^5*d^2*e*l - 156
*a*b^6*c^5*d^2*f*k + 16*a*b^6*c^5*d^2*g*j + 12*a*b^7*c^4*d*f^2*k - 2*a*b^9*c^2*d*f*k^2 - 1920*a^3*b*c^8*d^2*e*
j - 32*a*b^5*c^6*d^2*e*j + 2208*a^3*b*c^8*d^2*f*h + 800*a^4*b*c^7*d*f*h^2 - 102*a*b^5*c^6*d^2*f*h + 12*a*b^6*c
^5*d*f^2*h - 2*a*b^7*c^4*d*f*h^2 - 896*a^3*b*c^8*d*e^2*h - 8*a*b^6*c^5*d*f*g^2 - 240*a*b^4*c^7*d^2*e*g - 32*a*
b^4*c^7*d*e^2*f + 5120*a^8*c^4*h*j*l*m + 15360*a^7*c^5*d*j*l*m - 7680*a^7*c^5*e*j*k*m + 3072*a^7*c^5*f*j*k*l +
5120*a^7*c^5*e*h*l*m + 1920*a^7*c^5*f*h*k*m + 15360*a^6*c^6*d*e*l*m + 5760*a^6*c^6*d*f*k*m + 3072*a^6*c^6*e*f
*k*l - 3072*a^6*c^6*d*h*j*l - 2560*a^6*c^6*e*f*j*m + 1536*a^6*c^6*e*h*j*k + 4608*a^5*c^7*d*e*j*k - 3072*a^5*c^
7*d*e*h*l - 1152*a^5*c^7*d*f*h*k + 512*a^5*c^7*e*f*h*j + 1536*a^4*c^8*d*e*f*j - 8*a*b^10*c*d*f*l^2 - 5568*a^8*
b^2*c^2*k*l^2*m + 15552*a^8*b^2*c^2*j*l*m^2 + 4800*a^7*b^2*c^3*j^2*k*m - 1280*a^6*b^4*c^2*j^2*k*m + 2080*a^7*b
^3*c^2*h*l^2*m - 1088*a^7*b^2*c^3*j*k^2*l + 48*a^6*b^4*c^2*j*k^2*l - 8544*a^7*b^2*c^3*h*k^2*m - 7776*a^7*b^3*c
^2*g*l*m^2 + 7632*a^7*b^3*c^2*h*k*m^2 + 3600*a^6*b^3*c^3*h^2*k*m + 2484*a^6*b^4*c^2*h*k^2*m - 918*a^5*b^5*c^2*
h^2*k*m + 4800*a^7*b^2*c^3*h*k*l^2 - 1424*a^6*b^4*c^2*h*k*l^2 + 1200*a^5*b^4*c^3*g^2*k*m - 960*a^6*b^2*c^4*g^2
*k*m - 528*a^6*b^4*c^2*f*l^2*m - 416*a^6*b^3*c^3*h*j^2*m - 320*a^4*b^6*c^2*g^2*k*m + 192*a^7*b^2*c^3*f*l^2*m +
96*a^5*b^5*c^2*h*j^2*m + 15552*a^7*b^2*c^3*e*l*m^2 - 6720*a^7*b^2*c^3*g*j*m^2 + 6160*a^6*b^4*c^2*g*j*m^2 - 47
52*a^6*b^4*c^2*e*l*m^2 - 2016*a^7*b^2*c^3*f*k*m^2 - 1164*a^6*b^4*c^2*f*k*m^2 + 1104*a^5*b^3*c^4*f^2*k*m + 1008
*a^6*b^3*c^3*f*k^2*m + 960*a^6*b^2*c^4*h^2*j*l - 678*a^5*b^5*c^2*f*k^2*m + 544*a^6*b^3*c^3*g*k^2*l - 144*a^5*b
^4*c^3*h^2*j*l - 102*a^4*b^5*c^3*f^2*k*m - 62*a^3*b^7*c^2*f^2*k*m - 24*a^5*b^5*c^2*g*k^2*l + 6432*a^6*b^3*c^3*
d*l^2*m + 4800*a^5*b^2*c^5*e^2*k*m - 2304*a^6*b^2*c^4*g*j^2*l + 1920*a^6*b^3*c^3*g*j*l^2 + 1728*a^6*b^2*c^4*f*
j^2*m - 1280*a^4*b^4*c^4*e^2*k*m + 1152*a^5*b^3*c^4*g^2*j*l - 1032*a^5*b^5*c^2*d*l^2*m - 864*a^6*b^3*c^3*f*k*l
^2 - 768*a^5*b^5*c^2*g*j*l^2 + 408*a^5*b^5*c^2*f*k*l^2 + 384*a^5*b^4*c^3*g*j^2*l - 288*a^5*b^4*c^3*f*j^2*m + 1
92*a^6*b^2*c^4*h*j^2*k - 192*a^4*b^5*c^3*g^2*j*l + 96*a^3*b^6*c^3*e^2*k*m - 32*a^5*b^4*c^3*h*j^2*k - 21120*a^6
*b^2*c^4*d*k^2*m + 20880*a^6*b^3*c^3*d*k*m^2 + 19760*a^4*b^3*c^5*d^2*k*m - 12320*a^6*b^3*c^3*e*j*m^2 - 9750*a^
5*b^5*c^2*d*k*m^2 - 9390*a^3*b^5*c^4*d^2*k*m + 8460*a^5*b^4*c^3*d*k^2*m + 3360*a^5*b^5*c^2*e*j*m^2 + 1860*a^2*
b^7*c^3*d^2*k*m - 1218*a^4*b^6*c^2*d*k^2*m - 1088*a^6*b^2*c^4*e*k^2*l + 960*a^6*b^2*c^4*g*j*k^2 - 240*a^5*b^4*
c^3*g*j*k^2 + 192*a^5*b^2*c^5*f^2*j*l - 104*a^4*b^5*c^3*g^2*h*m - 96*a^5*b^3*c^4*g^2*h*m + 48*a^5*b^4*c^3*e*k^
2*l + 48*a^4*b^4*c^4*f^2*j*l + 24*a^3*b^7*c^2*g^2*h*m + 16*a^4*b^6*c^2*g*j*k^2 - 16*a^3*b^6*c^3*f^2*j*l + 1337
6*a^6*b^2*c^4*d*k*l^2 - 5136*a^5*b^4*c^3*d*k*l^2 - 3840*a^6*b^2*c^4*e*j*l^2 + 1536*a^5*b^4*c^3*e*j*l^2 + 1392*
a^5*b^3*c^4*f*h^2*m + 1386*a^5*b^5*c^2*f*h*m^2 - 768*a^5*b^3*c^4*e*j^2*l + 768*a^4*b^6*c^2*d*k*l^2 - 768*a^4*b
^3*c^5*e^2*j*l - 588*a^4*b^4*c^4*f^2*h*m - 480*a^5*b^3*c^4*g*h^2*l + 480*a^5*b^3*c^4*d*j^2*m - 480*a^5*b^2*c^5
*f^2*h*m - 128*a^4*b^6*c^2*e*j*l^2 + 100*a^3*b^6*c^3*f^2*h*m + 96*a^5*b^3*c^4*f*j^2*k + 72*a^4*b^5*c^3*g*h^2*l
- 54*a^4*b^5*c^3*f*h^2*m - 48*a^6*b^3*c^3*f*h*m^2 - 36*a^3*b^7*c^2*f*h^2*m + 6*a^2*b^8*c^2*f^2*h*m + 6848*a^4
*b^2*c^6*d^2*j*l - 2448*a^3*b^4*c^5*d^2*j*l + 624*a^5*b^4*c^3*f*h*l^2 + 576*a^6*b^2*c^4*f*h*l^2 + 480*a^5*b^3*
c^4*e*j*k^2 + 432*a^4*b^4*c^4*f*g^2*m - 416*a^4*b^3*c^5*e^2*h*m + 336*a^2*b^6*c^4*d^2*j*l - 320*a^5*b^2*c^5*f*
g^2*m - 256*a^4*b^6*c^2*f*h*l^2 + 192*a^5*b^2*c^5*g^2*h*k + 96*a^3*b^5*c^4*e^2*h*m - 72*a^3*b^6*c^3*f*g^2*m +
48*a^4*b^4*c^4*g^2*h*k - 32*a^4*b^5*c^3*e*j*k^2 - 8*a^3*b^6*c^3*g^2*h*k + 24768*a^6*b^2*c^4*d*h*m^2 - 21108*a^
5*b^4*c^3*d*h*m^2 - 10048*a^4*b^2*c^6*d^2*h*m + 7218*a^4*b^6*c^2*d*h*m^2 - 6720*a^6*b^2*c^4*e*g*m^2 + 6160*a^5
*b^4*c^3*e*g*m^2 - 2592*a^5*b^2*c^5*d*h^2*m - 1680*a^4*b^6*c^2*e*g*m^2 + 1068*a^3*b^4*c^5*d^2*h*m + 960*a^5*b^
2*c^5*e*h^2*l - 876*a^4*b^4*c^4*d*h^2*m - 864*a^5*b^2*c^5*f*h^2*k + 546*a^2*b^6*c^4*d^2*h*m + 432*a^3*b^6*c^3*
d*h^2*m + 336*a^4*b^3*c^5*f^2*h*k - 320*a^5*b^2*c^5*d*j^2*k + 192*a^5*b^2*c^5*g*h^2*j + 144*a^5*b^3*c^4*f*h*k^
2 - 144*a^4*b^4*c^4*e*h^2*l - 102*a^4*b^5*c^3*f*h*k^2 - 96*a^4*b^3*c^5*f^2*g*l - 36*a^2*b^8*c^2*d*h^2*m - 30*a
^3*b^5*c^4*f^2*h*k - 24*a^3*b^5*c^4*f^2*g*l + 16*a^4*b^4*c^4*g*h^2*j - 12*a^4*b^4*c^4*f*h^2*k + 12*a^3*b^6*c^3
*f*h^2*k + 8*a^2*b^7*c^3*f^2*g*l + 6*a^3*b^7*c^2*f*h*k^2 - 2*a^2*b^7*c^3*f^2*h*k - 9312*a^5*b^3*c^4*d*h*l^2 +
3288*a^4*b^5*c^3*d*h*l^2 - 2304*a^4*b^2*c^6*e^2*g*l + 1920*a^5*b^3*c^4*e*g*l^2 + 1728*a^4*b^2*c^6*e^2*f*m + 11
52*a^4*b^3*c^5*e*g^2*l - 768*a^4*b^5*c^3*e*g*l^2 - 608*a^4*b^3*c^5*d*g^2*m - 472*a^3*b^7*c^2*d*h*l^2 + 384*a^3
*b^4*c^5*e^2*g*l - 288*a^3*b^4*c^5*e^2*f*m - 224*a^4*b^3*c^5*f*g^2*k + 192*a^5*b^2*c^5*f*h*j^2 + 192*a^4*b^2*c
^6*e^2*h*k - 192*a^3*b^5*c^4*e*g^2*l + 120*a^3*b^5*c^4*d*g^2*m + 64*a^3*b^7*c^2*e*g*l^2 - 32*a^3*b^4*c^5*e^2*h
*k + 24*a^3*b^5*c^4*f*g^2*k + 9936*a^3*b^3*c^6*d^2*f*m + 3786*a^4*b^5*c^3*d*f*m^2 - 3552*a^5*b^2*c^5*d*h*k^2 -
3486*a^2*b^5*c^5*d^2*f*m - 3424*a^3*b^3*c^6*d^2*g*l - 1868*a^3*b^7*c^2*d*f*m^2 + 1332*a^4*b^4*c^4*d*h*k^2 - 1
296*a^5*b^3*c^4*d*f*m^2 - 1236*a^3*b^4*c^5*d*f^2*m + 1224*a^2*b^5*c^5*d^2*g*l - 1152*a^4*b^2*c^6*d*f^2*m + 960
*a^5*b^2*c^5*e*g*k^2 - 496*a^3*b^3*c^6*d^2*h*k + 462*a^2*b^6*c^4*d*f^2*m + 432*a^4*b^3*c^5*d*h^2*k - 240*a^4*b
^4*c^4*e*g*k^2 - 222*a^2*b^5*c^5*d^2*h*k + 192*a^4*b^2*c^6*f^2*g*j + 192*a^4*b^2*c^6*e*f^2*l - 174*a^3*b^5*c^4
*d*h^2*k - 156*a^3*b^6*c^3*d*h*k^2 + 48*a^3*b^4*c^5*e*f^2*l - 32*a^4*b^3*c^5*e*h^2*j + 16*a^3*b^6*c^3*e*g*k^2
+ 16*a^3*b^4*c^5*f^2*g*j - 16*a^2*b^6*c^4*e*f^2*l + 12*a^2*b^7*c^3*d*h^2*k + 6*a^2*b^8*c^2*d*h*k^2 + 1728*a^5*
b^2*c^5*d*f*l^2 + 1392*a^4*b^4*c^4*d*f*l^2 - 840*a^3*b^6*c^3*d*f*l^2 - 768*a^4*b^2*c^6*e*g^2*j + 576*a^4*b^2*c
^6*d*g^2*k + 480*a^3*b^3*c^6*d*e^2*m + 144*a^2*b^8*c^2*d*f*l^2 + 96*a^4*b^3*c^5*d*h*j^2 + 96*a^3*b^3*c^6*e^2*f
*k - 80*a^3*b^4*c^5*d*g^2*k + 6848*a^3*b^2*c^7*d^2*e*l - 3552*a^3*b^2*c^7*d^2*f*k - 2448*a^2*b^4*c^6*d^2*e*l +
1332*a^2*b^4*c^6*d^2*f*k + 960*a^3*b^2*c^7*d^2*g*j - 496*a^4*b^3*c^5*d*f*k^2 + 432*a^3*b^3*c^6*d*f^2*k - 240*
a^2*b^4*c^6*d^2*g*j - 222*a^3*b^5*c^4*d*f*k^2 - 174*a^2*b^5*c^5*d*f^2*k + 64*a^4*b^2*c^6*f*g^2*h + 48*a^3*b^4*
c^5*f*g^2*h + 42*a^2*b^7*c^3*d*f*k^2 - 32*a^3*b^3*c^6*e*f^2*j - 320*a^3*b^2*c^7*d*e^2*k + 192*a^4*b^2*c^6*e*g*
h^2 + 192*a^4*b^2*c^6*d*f*j^2 - 32*a^3*b^4*c^5*d*f*j^2 + 16*a^3*b^4*c^5*e*g*h^2 + 480*a^2*b^3*c^7*d^2*e*j - 22
4*a^3*b^3*c^6*d*g^2*h + 192*a^3*b^2*c^7*e^2*f*h + 24*a^2*b^5*c^5*d*g^2*h - 864*a^3*b^2*c^7*d*f^2*h + 336*a^3*b
^3*c^6*d*f*h^2 + 192*a^3*b^2*c^7*e*f^2*g + 144*a^2*b^3*c^7*d^2*f*h - 30*a^2*b^5*c^5*d*f*h^2 + 16*a^2*b^4*c^6*e
*f^2*g - 12*a^2*b^4*c^6*d*f^2*h + 192*a^3*b^2*c^7*d*f*g^2 + 96*a^2*b^3*c^7*d*e^2*h + 48*a^2*b^4*c^6*d*f*g^2 +
960*a^2*b^2*c^8*d^2*e*g + 192*a^2*b^2*c^8*d*e^2*f - 7680*a^9*b*c^2*l^2*m^2 + 3152*a^8*b^3*c*l^2*m^2 + 2070*a^7
*b^4*c*k^2*m^2 - 1840*a^7*b^3*c^2*k^3*m + 6720*a^8*b*c^3*j^2*m^2 - 3072*a^8*b*c^3*k^2*l^2 + 1680*a^6*b^5*c*j^2
*m^2 - 100*a^6*b^5*c*k^2*l^2 - 2176*a^7*b^3*c^2*j*l^3 - 256*a^6*b^3*c^3*j^3*l - 64*a^5*b^6*c*j^2*l^2 - 12480*a
^8*b^2*c^2*h*m^3 + 972*a^5*b^6*c*h^2*m^2 - 960*a^7*b*c^4*j^2*k^2 - 252*a^5*b^4*c^3*h^3*m - 192*a^6*b^2*c^4*h^3
*m + 54*a^4*b^6*c^2*h^3*m + 1536*a^7*b*c^4*h^2*l^2 + 420*a^4*b^7*c*g^2*m^2 - 36*a^4*b^7*c*h^2*l^2 - 3072*a^7*b
^2*c^3*g*l^3 + 2096*a^7*b^3*c^2*f*m^3 + 1088*a^6*b^4*c^2*g*l^3 - 496*a^6*b^3*c^3*h*k^3 - 192*a^4*b^4*c^4*g^3*l
+ 176*a^4*b^3*c^5*f^3*m + 144*a^5*b^3*c^4*h^3*k + 78*a^3*b^8*c*f^2*m^2 + 54*a^3*b^5*c^4*f^3*m + 32*a^3*b^6*c^
3*g^3*l + 30*a^5*b^5*c^2*h*k^3 - 18*a^4*b^5*c^3*h^3*k - 18*a^2*b^7*c^3*f^3*m - 16*a^3*b^8*c*g^2*l^2 + 6720*a^6
*b*c^5*e^2*m^2 - 192*a^6*b*c^5*h^2*j^2 - 4*a^2*b^9*c*f^2*l^2 - 35040*a^7*b^2*c^3*d*m^3 + 14300*a^6*b^4*c^2*d*m
^3 - 12000*a^3*b^2*c^7*d^3*m + 4380*a^2*b^4*c^6*d^3*m - 2176*a^6*b^3*c^3*e*l^3 - 256*a^3*b^3*c^6*e^3*l - 192*a
^6*b^2*c^4*f*k^3 + 192*a^5*b^5*c^2*e*l^3 - 192*a^4*b^2*c^6*f^3*k + 132*a^5*b^4*c^3*f*k^3 + 128*a^4*b^3*c^5*g^3
*j - 28*a^3*b^4*c^5*f^3*k - 10*a^4*b^6*c^2*f*k^3 + 6*a^2*b^6*c^4*f^3*k + 10752*a^5*b*c^6*d^2*l^2 - 960*a^5*b*c
^6*e^2*k^2 - 192*a^5*b*c^6*f^2*j^2 + 108*a*b^9*c^2*d^2*l^2 - 1680*a^5*b^3*c^4*d*k^3 - 1680*a^2*b^3*c^7*d^3*k +
222*a^4*b^5*c^3*d*k^3 + 30*a*b^8*c^3*d^2*k^2 - 10*a^3*b^7*c^2*d*k^3 - 960*a^4*b*c^7*d^2*j^2 + 80*a^4*b^3*c^5*
f*h^3 + 80*a^3*b^3*c^6*f^3*h + 6*a^3*b^5*c^4*f*h^3 + 6*a^2*b^5*c^5*f^3*h - 192*a^4*b*c^7*e^2*h^2 - 192*a^4*b^2
*c^6*d*h^3 - 192*a^2*b^2*c^8*d^3*h + 128*a^3*b^3*c^6*e*g^3 - 28*a^3*b^4*c^5*d*h^3 + 12*a*b^6*c^5*d^2*h^2 + 6*a
^2*b^6*c^4*d*h^3 - 192*a^3*b*c^8*e^2*f^2 + 60*a*b^5*c^6*d^2*g^2 + 198*a*b^4*c^7*d^2*f^2 + 144*a^2*b^3*c^7*d*f^
3 - 960*a^2*b*c^9*d^2*e^2 + 240*a*b^3*c^8*d^2*e^2 + 15360*a^9*c^3*k*l^2*m - 12800*a^9*c^3*j*l*m^2 - 3840*a^8*c
^4*j^2*k*m + 432*a^6*b^6*j*l*m^2 + 4608*a^8*c^4*j*k^2*l + 2880*a^8*c^4*h*k^2*m + 5120*a^8*c^4*f*l^2*m - 3072*a
^8*c^4*h*k*l^2 + 270*a^5*b^7*h*k*m^2 - 216*a^5*b^7*g*l*m^2 - 12800*a^8*c^4*e*l*m^2 - 4800*a^8*c^4*f*k*m^2 - 51
2*a^7*c^5*h^2*j*l - 3840*a^6*c^6*e^2*k*m - 1280*a^7*c^5*f*j^2*m + 768*a^7*c^5*h*j^2*k + 144*a^4*b^8*g*j*m^2 -
90*a^4*b^8*f*k*m^2 + 8640*a^7*c^5*d*k^2*m + 4608*a^7*c^5*e*k^2*l + 512*a^6*c^6*f^2*j*l - 9216*a^7*c^5*d*k*l^2
- 4096*a^7*c^5*e*j*l^2 + 320*a^6*c^6*f^2*h*m - 90*a^3*b^9*d*k*m^2 + 15200*a^9*b*c^2*k*m^3 - 6192*a^8*b^3*c*k*m
^3 + 5472*a^8*b*c^3*k^3*m - 4608*a^5*c^7*d^2*j*l - 1024*a^7*c^5*f*h*l^2 + 150*a^6*b^5*c*k^3*m + 54*a^3*b^9*f*h
*m^2 + 6*b^10*c^2*d^2*h*m - 14400*a^7*c^5*d*h*m^2 + 8640*a^5*c^7*d^2*h*m + 2880*a^6*c^6*d*h^2*m + 2304*a^6*c^6
*d*j^2*k - 512*a^6*c^6*e*h^2*l - 192*a^6*c^6*f*h^2*k + 6144*a^8*b*c^3*j*l^3 + 1536*a^7*b*c^4*j^3*l - 1280*a^5*
c^7*e^2*f*m + 768*a^5*c^7*e^2*h*k + 256*a^6*c^6*f*h*j^2 + 192*a^6*b^5*c*j*l^3 + 54*a^2*b^10*d*h*m^2 - 18*b^9*c
^3*d^2*f*m + 8*b^9*c^3*d^2*g*l - 2*b^9*c^3*d^2*h*k + 4068*a^7*b^4*c*h*m^3 - 1728*a^6*c^6*d*h*k^2 + 960*a^5*c^7
*d*f^2*m + 512*a^5*c^7*e*f^2*l - 3072*a^6*c^6*d*f*l^2 - 16*b^8*c^4*d^2*e*l + 6*b^8*c^4*d^2*f*k - 4608*a^4*c^8*
d^2*e*l + 2400*a^8*b*c^3*f*m^3 + 2016*a^7*b*c^4*h*k^3 - 1728*a^4*c^8*d^2*f*k - 1146*a^6*b^5*c*f*m^3 + 224*a^6*
b*c^5*h^3*k - 96*a^5*b^6*c*g*l^3 + 96*a^5*b*c^6*f^3*m + 2304*a^4*c^8*d*e^2*k + 768*a^5*c^7*d*f*j^2 + 6144*a^7*
b*c^4*e*l^3 - 2280*a^5*b^6*c*d*m^3 + 1536*a^4*b*c^7*e^3*l - 616*a*b^6*c^5*d^3*m + 512*a^6*b*c^5*g*j^3 + 256*a^
4*c^8*e^2*f*h + 240*a*b^10*c*d^2*m^2 + 6*b^7*c^5*d^2*f*h - 192*a^4*c^8*d*f^2*h + 4320*a^6*b*c^5*d*k^3 + 4320*a
^3*b*c^8*d^3*k + 222*a*b^5*c^6*d^3*k + 16*b^6*c^6*d^2*e*g + 96*a^5*b*c^6*f*h^3 + 96*a^4*b*c^7*f^3*h + 768*a^3*
c^9*d*e^2*f + 512*a^3*b*c^8*e^3*g + 132*a*b^4*c^7*d^3*h + 2016*a^2*b*c^9*d^3*f - 496*a*b^3*c^8*d^3*f + 224*a^3
*b*c^8*d*f^3 - 18*a*b^5*c^6*d*f^3 - 3264*a^8*b^2*c^2*k^2*m^2 - 6160*a^7*b^3*c^2*j^2*m^2 + 1104*a^7*b^3*c^2*k^2
*l^2 - 1920*a^7*b^2*c^3*j^2*l^2 + 768*a^6*b^4*c^2*j^2*l^2 + 3888*a^7*b^2*c^3*h^2*m^2 - 3510*a^6*b^4*c^2*h^2*m^
2 + 240*a^6*b^3*c^3*j^2*k^2 - 16*a^5*b^5*c^2*j^2*k^2 + 1680*a^6*b^3*c^3*g^2*m^2 - 1648*a^6*b^3*c^3*h^2*l^2 - 1
540*a^5*b^5*c^2*g^2*m^2 + 444*a^5*b^5*c^2*h^2*l^2 - 960*a^6*b^2*c^4*h^2*k^2 - 576*a^6*b^2*c^4*f^2*m^2 - 512*a^
6*b^2*c^4*g^2*l^2 - 480*a^5*b^4*c^3*g^2*l^2 + 198*a^5*b^4*c^3*h^2*k^2 + 192*a^4*b^6*c^2*g^2*l^2 - 186*a^5*b^4*
c^3*f^2*m^2 - 97*a^4*b^6*c^2*f^2*m^2 - 9*a^4*b^6*c^2*h^2*k^2 - 6160*a^5*b^3*c^4*e^2*m^2 + 1680*a^4*b^5*c^3*e^2
*m^2 - 240*a^5*b^3*c^4*g^2*k^2 - 240*a^5*b^3*c^4*f^2*l^2 - 144*a^3*b^7*c^2*e^2*m^2 + 60*a^4*b^5*c^3*g^2*k^2 -
36*a^4*b^5*c^3*f^2*l^2 + 36*a^3*b^7*c^2*f^2*l^2 - 16*a^5*b^3*c^4*h^2*j^2 - 4*a^3*b^7*c^2*g^2*k^2 + 38512*a^5*b
^2*c^5*d^2*m^2 - 32310*a^4*b^4*c^4*d^2*m^2 + 12720*a^3*b^6*c^3*d^2*m^2 - 2500*a^2*b^8*c^2*d^2*m^2 - 1920*a^5*b
^2*c^5*e^2*l^2 + 768*a^4*b^4*c^4*e^2*l^2 - 464*a^5*b^2*c^5*f^2*k^2 - 384*a^5*b^2*c^5*g^2*j^2 - 64*a^3*b^6*c^3*
e^2*l^2 + 42*a^4*b^4*c^4*f^2*k^2 + 12*a^3*b^6*c^3*f^2*k^2 - 13104*a^4*b^3*c^5*d^2*l^2 + 5628*a^3*b^5*c^4*d^2*l
^2 - 1128*a^2*b^7*c^3*d^2*l^2 + 240*a^4*b^3*c^5*e^2*k^2 - 16*a^4*b^3*c^5*f^2*j^2 - 16*a^3*b^5*c^4*e^2*k^2 - 28
80*a^4*b^2*c^6*d^2*k^2 + 1750*a^3*b^4*c^5*d^2*k^2 - 345*a^2*b^6*c^4*d^2*k^2 - 48*a^4*b^3*c^5*g^2*h^2 - 4*a^3*b
^5*c^4*g^2*h^2 + 240*a^3*b^3*c^6*d^2*j^2 - 192*a^4*b^2*c^6*f^2*h^2 - 42*a^3*b^4*c^5*f^2*h^2 - 16*a^2*b^5*c^5*d
^2*j^2 - 48*a^3*b^3*c^6*f^2*g^2 - 16*a^3*b^3*c^6*e^2*h^2 - 4*a^2*b^5*c^5*f^2*g^2 - 464*a^3*b^2*c^7*d^2*h^2 - 3
84*a^3*b^2*c^7*e^2*g^2 + 42*a^2*b^4*c^6*d^2*h^2 - 240*a^2*b^3*c^7*d^2*g^2 - 16*a^2*b^3*c^7*e^2*f^2 - 960*a^2*b
^2*c^8*d^2*f^2 + 6*b^11*c*d^2*k*m - 18*a*b^11*d*f*m^2 - 7200*a^9*c^3*k^2*m^2 - 324*a^7*b^5*l^2*m^2 - 225*a^6*b
^6*k^2*m^2 - 2048*a^8*c^4*j^2*l^2 - 144*a^5*b^7*j^2*m^2 - 2400*a^8*c^4*h^2*m^2 - 81*a^4*b^8*h^2*m^2 - 800*a^7*
c^5*f^2*m^2 - 288*a^7*c^5*h^2*k^2 - 36*a^3*b^9*g^2*m^2 - 9*a^2*b^10*f^2*m^2 - 21600*a^6*c^6*d^2*m^2 - 2048*a^6
*c^6*e^2*l^2 - 864*a^6*c^6*f^2*k^2 - 2592*a^5*c^7*d^2*k^2 - 1536*a^5*c^7*e^2*j^2 + 1536*a^8*b^2*c^2*l^4 - 32*a
^5*c^7*f^2*h^2 + 360*a^7*b^2*c^3*k^4 - 25*a^6*b^4*c^2*k^4 - 864*a^4*c^8*d^2*h^2 - 4*b^7*c^5*d^2*g^2 - 9*b^6*c^
6*d^2*f^2 - 288*a^3*c^9*d^2*f^2 - 24*a^5*b^2*c^5*h^4 - 16*b^5*c^7*d^2*e^2 - 9*a^4*b^4*c^4*h^4 - 16*a^3*b^4*c^5
*g^4 - 24*a^3*b^2*c^7*f^4 - 9*a^2*b^4*c^6*f^4 - a^2*b^8*c^2*f^2*k^2 - a^2*b^6*c^4*f^2*h^2 + 630*a^7*b^5*k*m^3
+ 8000*a^9*c^3*h*m^3 + 320*a^7*c^5*h^3*m - 378*a^6*b^6*h*m^3 + 126*a^5*b^7*f*m^3 + 30*b^8*c^4*d^3*m + 24000*a^
8*c^4*d*m^3 + 8640*a^4*c^8*d^3*m - 1728*a^7*c^5*f*k^3 - 192*a^5*c^7*f^3*k - 4*b^11*c*d^2*l^2 + 126*a^4*b^8*d*m
^3 - 10*b^7*c^5*d^3*k + 4200*a^9*b^2*c*m^4 - 1024*a^6*c^6*e*j^3 - 1024*a^4*c^8*e^3*j - 144*a^7*b^4*c*l^4 - 10*
b^6*c^6*d^3*h - 1728*a^3*c^9*d^3*h - 192*a^5*c^7*d*h^3 + 30*b^5*c^7*d^3*f + 360*a*b^2*c^9*d^4 - 9*b^12*d^2*m^2
- 10000*a^10*c^2*m^4 - 4096*a^9*c^3*l^4 - 441*a^8*b^4*m^4 - 1296*a^8*c^4*k^4 - 256*a^7*c^5*j^4 - 16*a^6*c^6*h
^4 - 16*a^4*c^8*f^4 - 256*a^3*c^9*e^4 - 25*b^4*c^8*d^4 - 1296*a^2*c^10*d^4 - b^10*c^2*d^2*k^2 - b^8*c^4*d^2*h^
2, z, k1)*((3072*a^5*c^7*d*l - 512*a^4*c^8*e*f - 1536*a^5*c^7*e*k - 512*a^5*c^7*f*j + 1024*a^6*c^6*h*l - 1536*
a^6*c^6*j*k - 5120*a^7*c^5*l*m + 32*a*b^5*c^6*d*e + 1024*a^3*b*c^8*d*e - 16*a*b^6*c^5*d*g + 512*a^4*b*c^7*e*h
+ 256*a^4*b*c^7*f*g + 1024*a^4*b*c^7*d*j + 16*a*b^8*c^3*d*l + 2048*a^5*b*c^6*e*m + 256*a^5*b*c^6*f*l + 768*a^5
*b*c^6*g*k + 512*a^5*b*c^6*h*j + 2048*a^6*b*c^5*j*m + 1792*a^6*b*c^5*k*l - 384*a^2*b^3*c^7*d*e + 192*a^2*b^4*c
^6*d*g + 32*a^2*b^4*c^6*e*f - 512*a^3*b^2*c^7*d*g - 16*a^2*b^5*c^5*f*g - 128*a^3*b^3*c^6*e*h + 32*a^2*b^5*c^5*
d*j - 384*a^3*b^3*c^6*d*j + 64*a^3*b^4*c^5*g*h - 256*a^4*b^2*c^6*g*h - 288*a^2*b^6*c^4*d*l + 1792*a^3*b^4*c^5*
d*l - 32*a^3*b^4*c^5*e*k + 32*a^3*b^4*c^5*f*j - 4352*a^4*b^2*c^6*d*l + 512*a^4*b^2*c^6*e*k + 16*a^2*b^7*c^3*f*
l + 96*a^3*b^5*c^4*e*m - 144*a^3*b^5*c^4*f*l + 16*a^3*b^5*c^4*g*k - 896*a^4*b^3*c^5*e*m + 256*a^4*b^3*c^5*f*l
- 256*a^4*b^3*c^5*g*k - 128*a^4*b^3*c^5*h*j - 48*a^3*b^6*c^3*g*m - 48*a^3*b^6*c^3*h*l + 448*a^4*b^4*c^4*g*m +
512*a^4*b^4*c^4*h*l - 1024*a^5*b^2*c^5*g*m - 1536*a^5*b^2*c^5*h*l - 32*a^4*b^4*c^4*j*k + 512*a^5*b^2*c^5*j*k +
96*a^4*b^5*c^3*j*m + 80*a^4*b^5*c^3*k*l - 896*a^5*b^3*c^4*j*m - 768*a^5*b^3*c^4*k*l - 256*a^5*b^4*c^3*l*m + 2
304*a^6*b^2*c^4*l*m)/(8*(64*a^5*c^6 - a^2*b^6*c^3 + 12*a^3*b^4*c^4 - 48*a^4*b^2*c^5)) - root(1572864*a^8*b^2*c
^10*z^4 - 983040*a^7*b^4*c^9*z^4 + 327680*a^6*b^6*c^8*z^4 - 61440*a^5*b^8*c^7*z^4 + 6144*a^4*b^10*c^6*z^4 - 25
6*a^3*b^12*c^5*z^4 - 1048576*a^9*c^11*z^4 - 1572864*a^8*b^2*c^8*l*z^3 + 983040*a^7*b^4*c^7*l*z^3 - 327680*a^6*
b^6*c^6*l*z^3 + 61440*a^5*b^8*c^5*l*z^3 - 6144*a^4*b^10*c^4*l*z^3 + 256*a^3*b^12*c^3*l*z^3 + 1048576*a^9*c^9*l
*z^3 + 96*a^3*b^12*c*k*m*z^2 + 98304*a^8*b*c^7*j*l*z^2 + 24576*a^8*b*c^7*h*m*z^2 + 155648*a^7*b*c^8*d*m*z^2 +
98304*a^7*b*c^8*e*l*z^2 + 57344*a^7*b*c^8*f*k*z^2 + 32768*a^7*b*c^8*g*j*z^2 + 57344*a^6*b*c^9*d*h*z^2 + 32768*
a^6*b*c^9*e*g*z^2 - 32*a*b^10*c^5*d*f*z^2 - 491520*a^8*b^2*c^6*k*m*z^2 + 358400*a^7*b^4*c^5*k*m*z^2 - 129024*a
^6*b^6*c^4*k*m*z^2 + 24768*a^5*b^8*c^3*k*m*z^2 - 2432*a^4*b^10*c^2*k*m*z^2 - 90112*a^7*b^3*c^6*j*l*z^2 + 30720
*a^6*b^5*c^5*j*l*z^2 - 4608*a^5*b^7*c^4*j*l*z^2 + 256*a^4*b^9*c^3*j*l*z^2 - 21504*a^6*b^5*c^5*h*m*z^2 + 9216*a
^5*b^7*c^4*h*m*z^2 + 8192*a^7*b^3*c^6*h*m*z^2 - 1568*a^4*b^9*c^3*h*m*z^2 + 96*a^3*b^11*c^2*h*m*z^2 - 172032*a^
7*b^2*c^7*f*m*z^2 + 116736*a^6*b^4*c^6*f*m*z^2 - 49152*a^7*b^2*c^7*g*l*z^2 + 45056*a^6*b^4*c^6*g*l*z^2 - 35840
*a^5*b^6*c^5*f*m*z^2 + 24576*a^7*b^2*c^7*h*k*z^2 - 15360*a^5*b^6*c^5*g*l*z^2 + 5184*a^4*b^8*c^4*f*m*z^2 - 3072
*a^5*b^6*c^5*h*k*z^2 + 2304*a^4*b^8*c^4*g*l*z^2 + 2048*a^6*b^4*c^6*h*k*z^2 + 576*a^4*b^8*c^4*h*k*z^2 - 288*a^3
*b^10*c^3*f*m*z^2 - 128*a^3*b^10*c^3*g*l*z^2 - 32*a^3*b^10*c^3*h*k*z^2 - 147456*a^6*b^3*c^7*d*m*z^2 - 90112*a^
6*b^3*c^7*e*l*z^2 + 52224*a^5*b^5*c^6*d*m*z^2 - 49152*a^6*b^3*c^7*f*k*z^2 + 30720*a^5*b^5*c^6*e*l*z^2 - 24576*
a^6*b^3*c^7*g*j*z^2 + 15360*a^5*b^5*c^6*f*k*z^2 - 8192*a^4*b^7*c^5*d*m*z^2 + 6144*a^5*b^5*c^6*g*j*z^2 - 4608*a
^4*b^7*c^5*e*l*z^2 - 2048*a^4*b^7*c^5*f*k*z^2 - 512*a^4*b^7*c^5*g*j*z^2 + 480*a^3*b^9*c^4*d*m*z^2 + 256*a^3*b^
9*c^4*e*l*z^2 + 96*a^3*b^9*c^4*f*k*z^2 + 131072*a^6*b^2*c^8*d*k*z^2 + 49152*a^6*b^2*c^8*e*j*z^2 - 43008*a^5*b^
4*c^7*d*k*z^2 - 12288*a^5*b^4*c^7*e*j*z^2 + 6144*a^4*b^6*c^6*d*k*z^2 + 1024*a^4*b^6*c^6*e*j*z^2 - 320*a^3*b^8*
c^5*d*k*z^2 + 6144*a^5*b^4*c^7*f*h*z^2 - 2048*a^4*b^6*c^6*f*h*z^2 + 192*a^3*b^8*c^5*f*h*z^2 - 49152*a^5*b^3*c^
8*d*h*z^2 - 24576*a^5*b^3*c^8*e*g*z^2 + 15360*a^4*b^5*c^7*d*h*z^2 + 6144*a^4*b^5*c^7*e*g*z^2 - 2048*a^3*b^7*c^
6*d*h*z^2 - 512*a^3*b^7*c^6*e*g*z^2 + 96*a^2*b^9*c^5*d*h*z^2 + 24576*a^5*b^2*c^9*d*f*z^2 - 3072*a^3*b^6*c^7*d*
f*z^2 + 2048*a^4*b^4*c^8*d*f*z^2 + 576*a^2*b^8*c^6*d*f*z^2 - 430080*a^9*b*c^6*m^2*z^2 + 3408*a^4*b^11*c*m^2*z^
2 - 64*a^3*b^12*c*l^2*z^2 + 61440*a^8*b*c^7*k^2*z^2 + 12288*a^7*b*c^8*h^2*z^2 + 12288*a^6*b*c^9*f^2*z^2 + 6144
0*a^5*b*c^10*d^2*z^2 + 432*a*b^9*c^6*d^2*z^2 + 245760*a^9*c^7*k*m*z^2 + 81920*a^8*c^8*f*m*z^2 - 49152*a^8*c^8*
h*k*z^2 - 147456*a^7*c^9*d*k*z^2 - 65536*a^7*c^9*e*j*z^2 - 16384*a^7*c^9*f*h*z^2 - 49152*a^6*c^10*d*f*z^2 + 71
6800*a^8*b^3*c^5*m^2*z^2 - 483840*a^7*b^5*c^4*m^2*z^2 + 170496*a^6*b^7*c^3*m^2*z^2 - 33232*a^5*b^9*c^2*m^2*z^2
+ 516096*a^8*b^2*c^6*l^2*z^2 - 288768*a^7*b^4*c^5*l^2*z^2 + 88576*a^6*b^6*c^4*l^2*z^2 - 15744*a^5*b^8*c^3*l^2
*z^2 + 1536*a^4*b^10*c^2*l^2*z^2 - 61440*a^7*b^3*c^6*k^2*z^2 + 24064*a^6*b^5*c^5*k^2*z^2 - 4608*a^5*b^7*c^4*k^
2*z^2 + 432*a^4*b^9*c^3*k^2*z^2 - 16*a^3*b^11*c^2*k^2*z^2 + 24576*a^7*b^2*c^7*j^2*z^2 - 6144*a^6*b^4*c^6*j^2*z
^2 + 512*a^5*b^6*c^5*j^2*z^2 - 8192*a^6*b^3*c^7*h^2*z^2 + 1536*a^5*b^5*c^6*h^2*z^2 - 16*a^3*b^9*c^4*h^2*z^2 -
8192*a^6*b^2*c^8*g^2*z^2 + 6144*a^5*b^4*c^7*g^2*z^2 - 1536*a^4*b^6*c^6*g^2*z^2 + 128*a^3*b^8*c^5*g^2*z^2 - 819
2*a^5*b^3*c^8*f^2*z^2 + 1536*a^4*b^5*c^7*f^2*z^2 - 16*a^2*b^9*c^5*f^2*z^2 + 24576*a^5*b^2*c^9*e^2*z^2 - 6144*a
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2*b^7*c^7*d^2*z^2 - 393216*a^9*c^7*l^2*z^2 - 144*a^3*b^13*m^2*z^2 - 32768*a^8*c^8*j^2*z^2 - 32768*a^6*c^10*e^2
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440*a^4*b^5*c^5*d*h*l*z + 12288*a^5*b^3*c^6*e*g*l*z + 6912*a^4*b^5*c^5*e*f*m*z + 5760*a^4*b^5*c^5*d*g*m*z - 46
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*k - 1792*a^5*b*c^6*e*f*j*k - 1280*a^5*b*c^6*d*f*j*l - 4544*a^5*b*c^6*d*f*h*m + 1536*a^5*b*c^6*d*g*h*l + 1280*
a^5*b*c^6*e*f*g*m - 768*a^5*b*c^6*e*g*h*k - 768*a^5*b*c^6*e*f*h*l - 256*a^5*b*c^6*f*g*h*j + 12*a*b^9*c^2*d*f*h
*m + 16*a*b^8*c^3*d*f*g*l - 4*a*b^8*c^3*d*f*h*k - 2304*a^4*b*c^7*d*e*g*k - 1792*a^4*b*c^7*d*e*h*j - 1280*a^4*b
*c^7*d*e*f*l - 768*a^4*b*c^7*d*f*g*j - 32*a*b^7*c^4*d*e*f*l - 256*a^4*b*c^7*e*f*g*h - 768*a^3*b*c^8*d*e*f*g +
32*a*b^5*c^6*d*e*f*g + 12*a*b^10*c*d*f*k*m + 3648*a^7*b^3*c^2*j*k*l*m + 5504*a^7*b^2*c^3*g*k*l*m - 1824*a^6*b^
4*c^2*g*k*l*m + 384*a^7*b^2*c^3*h*j*l*m - 288*a^6*b^4*c^2*h*j*l*m - 4800*a^6*b^3*c^3*g*j*k*m + 3648*a^6*b^3*c^
3*e*k*l*m + 1280*a^5*b^5*c^2*g*j*k*m + 1088*a^6*b^3*c^3*f*j*l*m + 576*a^6*b^3*c^3*h*j*k*l - 288*a^5*b^5*c^2*e*
k*l*m - 192*a^6*b^3*c^3*g*h*l*m + 144*a^5*b^5*c^2*g*h*l*m + 9600*a^6*b^2*c^4*e*j*k*m - 4224*a^6*b^2*c^4*d*j*l*
m - 2560*a^5*b^4*c^3*e*j*k*m + 384*a^6*b^2*c^4*f*j*k*l + 224*a^5*b^4*c^3*d*j*l*m + 192*a^4*b^6*c^2*e*j*k*m - 1
60*a^5*b^4*c^3*f*j*k*l - 4608*a^6*b^2*c^4*f*h*k*m + 2688*a^6*b^2*c^4*f*g*l*m + 1664*a^6*b^2*c^4*g*h*k*l - 744*
a^5*b^4*c^3*f*h*k*m - 544*a^5*b^4*c^3*f*g*l*m + 492*a^4*b^6*c^2*f*h*k*m + 416*a^5*b^4*c^3*g*h*j*m + 384*a^6*b^
2*c^4*g*h*j*m + 384*a^6*b^2*c^4*e*h*l*m - 288*a^5*b^4*c^3*g*h*k*l - 288*a^5*b^4*c^3*e*h*l*m - 96*a^4*b^6*c^2*g
*h*j*m + 2112*a^5*b^3*c^4*d*j*k*l - 160*a^4*b^5*c^3*d*j*k*l + 16992*a^5*b^3*c^4*d*h*k*m - 6252*a^4*b^5*c^3*d*h
*k*m - 4800*a^5*b^3*c^4*e*g*k*m + 2112*a^5*b^3*c^4*d*g*l*m - 1728*a^5*b^3*c^4*f*g*j*m + 1280*a^4*b^5*c^3*e*g*k
*m + 1088*a^5*b^3*c^4*e*f*l*m - 832*a^5*b^3*c^4*e*h*j*m + 816*a^3*b^7*c^2*d*h*k*m + 576*a^5*b^3*c^4*e*h*k*l -
448*a^5*b^3*c^4*f*h*j*l + 288*a^4*b^5*c^3*f*g*j*m - 192*a^5*b^3*c^4*g*h*j*k - 192*a^5*b^3*c^4*f*g*k*l + 192*a^
4*b^5*c^3*e*h*j*m - 112*a^4*b^5*c^3*d*g*l*m + 96*a^4*b^5*c^3*f*h*j*l - 96*a^3*b^7*c^2*e*g*k*m + 80*a^4*b^5*c^3
*f*g*k*l + 32*a^4*b^5*c^3*g*h*j*k - 11456*a^5*b^2*c^5*d*f*k*m + 4992*a^5*b^2*c^5*d*h*j*l - 4608*a^5*b^2*c^5*e*
g*j*l - 4224*a^5*b^2*c^5*d*e*l*m + 3456*a^5*b^2*c^5*e*f*j*m + 3456*a^5*b^2*c^5*d*g*k*l + 2432*a^5*b^2*c^5*d*g*
j*m - 1312*a^4*b^4*c^4*d*h*j*l + 1272*a^3*b^6*c^3*d*f*k*m - 1056*a^4*b^4*c^4*d*g*k*l + 896*a^5*b^2*c^5*f*g*j*k
+ 768*a^4*b^4*c^4*e*g*j*l - 576*a^4*b^4*c^4*e*f*j*m - 480*a^4*b^4*c^4*d*g*j*m + 384*a^5*b^2*c^5*e*h*j*k + 384
*a^5*b^2*c^5*e*f*k*l - 232*a^2*b^8*c^2*d*f*k*m + 224*a^4*b^4*c^4*d*e*l*m - 160*a^4*b^4*c^4*e*f*k*l - 96*a^4*b^
4*c^4*f*g*j*k + 96*a^3*b^6*c^3*d*h*j*l + 80*a^3*b^6*c^3*d*g*k*l - 64*a^4*b^4*c^4*e*h*j*k - 24*a^4*b^4*c^4*d*f*
k*m + 416*a^4*b^4*c^4*e*g*h*m + 384*a^5*b^2*c^5*f*g*h*l + 384*a^5*b^2*c^5*e*g*h*m + 224*a^4*b^4*c^4*f*g*h*l -
96*a^3*b^6*c^3*e*g*h*m - 48*a^3*b^6*c^3*f*g*h*l + 2112*a^4*b^3*c^5*d*e*k*l - 960*a^4*b^3*c^5*d*f*j*l + 960*a^4
*b^3*c^5*d*e*j*m + 384*a^3*b^5*c^4*d*f*j*l + 320*a^4*b^3*c^5*d*g*j*k + 192*a^4*b^3*c^5*e*f*j*k - 160*a^3*b^5*c
^4*d*e*k*l - 32*a^2*b^7*c^3*d*f*j*l + 7392*a^4*b^3*c^5*d*f*h*m - 2496*a^4*b^3*c^5*d*g*h*l - 1728*a^4*b^3*c^5*e
*f*g*m - 1500*a^3*b^5*c^4*d*f*h*m + 656*a^3*b^5*c^4*d*g*h*l - 448*a^4*b^3*c^5*e*f*h*l + 288*a^3*b^5*c^4*e*f*g*
m - 192*a^4*b^3*c^5*f*g*h*j - 192*a^4*b^3*c^5*e*g*h*k + 96*a^3*b^5*c^4*e*f*h*l - 48*a^2*b^7*c^3*d*g*h*l + 32*a
^3*b^5*c^4*e*g*h*k - 16*a^2*b^7*c^3*d*f*h*m - 640*a^4*b^2*c^6*d*e*j*k + 4992*a^4*b^2*c^6*d*e*h*l - 3584*a^4*b^
2*c^6*d*f*h*k + 2432*a^4*b^2*c^6*d*e*g*m - 1312*a^3*b^4*c^5*d*e*h*l + 896*a^4*b^2*c^6*e*f*g*k + 896*a^4*b^2*c^
6*d*g*h*j + 640*a^4*b^2*c^6*d*f*g*l + 600*a^3*b^4*c^5*d*f*h*k + 480*a^3*b^4*c^5*d*f*g*l - 480*a^3*b^4*c^5*d*e*
g*m + 384*a^4*b^2*c^6*e*f*h*j - 192*a^2*b^6*c^4*d*f*g*l - 96*a^3*b^4*c^5*e*f*g*k - 96*a^3*b^4*c^5*d*g*h*j + 96
*a^2*b^6*c^4*d*e*h*l + 12*a^2*b^6*c^4*d*f*h*k - 960*a^3*b^3*c^6*d*e*f*l + 384*a^2*b^5*c^5*d*e*f*l + 320*a^3*b^
3*c^6*d*e*g*k - 192*a^3*b^3*c^6*d*f*g*j + 192*a^3*b^3*c^6*d*e*h*j + 32*a^2*b^5*c^5*d*f*g*j - 192*a^3*b^3*c^6*e
*f*g*h + 384*a^3*b^2*c^7*d*e*f*j - 64*a^2*b^4*c^6*d*e*f*j + 896*a^3*b^2*c^7*d*e*g*h - 96*a^2*b^4*c^6*d*e*g*h -
192*a^2*b^3*c^7*d*e*f*g + 496*a^7*b^4*c*k*l^2*m - 4752*a^7*b^4*c*j*l*m^2 + 96*a^5*b^6*c*j^2*k*m - 6144*a^8*b*
c^3*h*l^2*m - 168*a^6*b^5*c*h*l^2*m + 6400*a^8*b*c^3*g*l*m^2 - 2862*a^6*b^5*c*h*k*m^2 + 2376*a^6*b^5*c*g*l*m^2
- 1632*a^7*b*c^4*h^2*k*m - 480*a^8*b*c^3*h*k*m^2 - 180*a^5*b^6*c*h*k^2*m + 54*a^4*b^7*c*h^2*k*m - 384*a^7*b*c
^4*h*j^2*m + 120*a^5*b^6*c*h*k*l^2 + 56*a^5*b^6*c*f*l^2*m + 24*a^3*b^8*c*g^2*k*m + 4512*a^7*b*c^4*f*k^2*m - 23
04*a^7*b*c^4*g*k^2*l - 1680*a^5*b^6*c*g*j*m^2 + 1184*a^6*b*c^5*f^2*k*m + 804*a^5*b^6*c*f*k*m^2 + 432*a^5*b^6*c
*e*l*m^2 + 60*a^4*b^7*c*f*k^2*m + 6*a^2*b^9*c*f^2*k*m - 13312*a^7*b*c^4*d*l^2*m + 2048*a^7*b*c^4*g*j*l^2 - 102
4*a^7*b*c^4*f*k*l^2 + 64*a^4*b^7*c*g*j*l^2 + 56*a^4*b^7*c*d*l^2*m - 40*a^4*b^7*c*f*k*l^2 + 13440*a^7*b*c^4*e*j
*m^2 - 8928*a^5*b*c^6*d^2*k*m - 6240*a^7*b*c^4*d*k*m^2 + 1614*a^4*b^7*c*d*k*m^2 - 288*a^4*b^7*c*e*j*m^2 - 170*
a*b^9*c^2*d^2*k*m + 60*a^3*b^8*c*d*k^2*m + 4608*a^6*b*c^5*e*j^2*l + 4608*a^5*b*c^6*e^2*j*l - 2432*a^6*b*c^5*d*
j^2*m + 1440*a^7*b*c^4*f*h*m^2 - 896*a^6*b*c^5*f*j^2*k - 864*a^6*b*c^5*f*h^2*m - 558*a^4*b^7*c*f*h*m^2 + 256*a
^6*b*c^5*g*h^2*l - 40*a^3*b^8*c*d*k*l^2 - 1920*a^6*b*c^5*e*j*k^2 - 384*a^5*b*c^6*e^2*h*m + 24*a^3*b^8*c*f*h*l^
2 - 16*a*b^8*c^3*d^2*j*l + 2208*a^6*b*c^5*f*h*k^2 - 1044*a^3*b^8*c*d*h*m^2 + 800*a^5*b*c^6*f^2*h*k - 256*a^5*b
*c^6*f^2*g*l + 144*a^3*b^8*c*e*g*m^2 - 116*a*b^8*c^3*d^2*h*m + 8192*a^6*b*c^5*d*h*l^2 + 2048*a^6*b*c^5*e*g*l^2
+ 24*a^2*b^9*c*d*h*l^2 - 5856*a^4*b*c^7*d^2*f*m + 4896*a^4*b*c^7*d^2*h*k + 2720*a^6*b*c^5*d*f*m^2 + 2304*a^4*
b*c^7*d^2*g*l + 1824*a^5*b*c^6*d*h^2*k + 438*a*b^7*c^4*d^2*f*m - 384*a^5*b*c^6*e*h^2*j + 318*a^2*b^9*c*d*f*m^2
- 168*a*b^7*c^4*d^2*g*l + 42*a*b^7*c^4*d^2*h*k - 36*a*b^8*c^3*d*f^2*m - 2432*a^4*b*c^7*d*e^2*m + 1536*a^5*b*c
^6*e*g*j^2 + 1536*a^4*b*c^7*e^2*g*j - 896*a^5*b*c^6*d*h*j^2 - 896*a^4*b*c^7*e^2*f*k + 4896*a^5*b*c^6*d*f*k^2 +
1824*a^4*b*c^7*d*f^2*k - 384*a^4*b*c^7*e*f^2*j + 336*a*b^6*c^5*d^2*e*l - 156*a*b^6*c^5*d^2*f*k + 16*a*b^6*c^5
*d^2*g*j + 12*a*b^7*c^4*d*f^2*k - 2*a*b^9*c^2*d*f*k^2 - 1920*a^3*b*c^8*d^2*e*j - 32*a*b^5*c^6*d^2*e*j + 2208*a
^3*b*c^8*d^2*f*h + 800*a^4*b*c^7*d*f*h^2 - 102*a*b^5*c^6*d^2*f*h + 12*a*b^6*c^5*d*f^2*h - 2*a*b^7*c^4*d*f*h^2
- 896*a^3*b*c^8*d*e^2*h - 8*a*b^6*c^5*d*f*g^2 - 240*a*b^4*c^7*d^2*e*g - 32*a*b^4*c^7*d*e^2*f + 5120*a^8*c^4*h*
j*l*m + 15360*a^7*c^5*d*j*l*m - 7680*a^7*c^5*e*j*k*m + 3072*a^7*c^5*f*j*k*l + 5120*a^7*c^5*e*h*l*m + 1920*a^7*
c^5*f*h*k*m + 15360*a^6*c^6*d*e*l*m + 5760*a^6*c^6*d*f*k*m + 3072*a^6*c^6*e*f*k*l - 3072*a^6*c^6*d*h*j*l - 256
0*a^6*c^6*e*f*j*m + 1536*a^6*c^6*e*h*j*k + 4608*a^5*c^7*d*e*j*k - 3072*a^5*c^7*d*e*h*l - 1152*a^5*c^7*d*f*h*k
+ 512*a^5*c^7*e*f*h*j + 1536*a^4*c^8*d*e*f*j - 8*a*b^10*c*d*f*l^2 - 5568*a^8*b^2*c^2*k*l^2*m + 15552*a^8*b^2*c
^2*j*l*m^2 + 4800*a^7*b^2*c^3*j^2*k*m - 1280*a^6*b^4*c^2*j^2*k*m + 2080*a^7*b^3*c^2*h*l^2*m - 1088*a^7*b^2*c^3
*j*k^2*l + 48*a^6*b^4*c^2*j*k^2*l - 8544*a^7*b^2*c^3*h*k^2*m - 7776*a^7*b^3*c^2*g*l*m^2 + 7632*a^7*b^3*c^2*h*k
*m^2 + 3600*a^6*b^3*c^3*h^2*k*m + 2484*a^6*b^4*c^2*h*k^2*m - 918*a^5*b^5*c^2*h^2*k*m + 4800*a^7*b^2*c^3*h*k*l^
2 - 1424*a^6*b^4*c^2*h*k*l^2 + 1200*a^5*b^4*c^3*g^2*k*m - 960*a^6*b^2*c^4*g^2*k*m - 528*a^6*b^4*c^2*f*l^2*m -
416*a^6*b^3*c^3*h*j^2*m - 320*a^4*b^6*c^2*g^2*k*m + 192*a^7*b^2*c^3*f*l^2*m + 96*a^5*b^5*c^2*h*j^2*m + 15552*a
^7*b^2*c^3*e*l*m^2 - 6720*a^7*b^2*c^3*g*j*m^2 + 6160*a^6*b^4*c^2*g*j*m^2 - 4752*a^6*b^4*c^2*e*l*m^2 - 2016*a^7
*b^2*c^3*f*k*m^2 - 1164*a^6*b^4*c^2*f*k*m^2 + 1104*a^5*b^3*c^4*f^2*k*m + 1008*a^6*b^3*c^3*f*k^2*m + 960*a^6*b^
2*c^4*h^2*j*l - 678*a^5*b^5*c^2*f*k^2*m + 544*a^6*b^3*c^3*g*k^2*l - 144*a^5*b^4*c^3*h^2*j*l - 102*a^4*b^5*c^3*
f^2*k*m - 62*a^3*b^7*c^2*f^2*k*m - 24*a^5*b^5*c^2*g*k^2*l + 6432*a^6*b^3*c^3*d*l^2*m + 4800*a^5*b^2*c^5*e^2*k*
m - 2304*a^6*b^2*c^4*g*j^2*l + 1920*a^6*b^3*c^3*g*j*l^2 + 1728*a^6*b^2*c^4*f*j^2*m - 1280*a^4*b^4*c^4*e^2*k*m
+ 1152*a^5*b^3*c^4*g^2*j*l - 1032*a^5*b^5*c^2*d*l^2*m - 864*a^6*b^3*c^3*f*k*l^2 - 768*a^5*b^5*c^2*g*j*l^2 + 40
8*a^5*b^5*c^2*f*k*l^2 + 384*a^5*b^4*c^3*g*j^2*l - 288*a^5*b^4*c^3*f*j^2*m + 192*a^6*b^2*c^4*h*j^2*k - 192*a^4*
b^5*c^3*g^2*j*l + 96*a^3*b^6*c^3*e^2*k*m - 32*a^5*b^4*c^3*h*j^2*k - 21120*a^6*b^2*c^4*d*k^2*m + 20880*a^6*b^3*
c^3*d*k*m^2 + 19760*a^4*b^3*c^5*d^2*k*m - 12320*a^6*b^3*c^3*e*j*m^2 - 9750*a^5*b^5*c^2*d*k*m^2 - 9390*a^3*b^5*
c^4*d^2*k*m + 8460*a^5*b^4*c^3*d*k^2*m + 3360*a^5*b^5*c^2*e*j*m^2 + 1860*a^2*b^7*c^3*d^2*k*m - 1218*a^4*b^6*c^
2*d*k^2*m - 1088*a^6*b^2*c^4*e*k^2*l + 960*a^6*b^2*c^4*g*j*k^2 - 240*a^5*b^4*c^3*g*j*k^2 + 192*a^5*b^2*c^5*f^2
*j*l - 104*a^4*b^5*c^3*g^2*h*m - 96*a^5*b^3*c^4*g^2*h*m + 48*a^5*b^4*c^3*e*k^2*l + 48*a^4*b^4*c^4*f^2*j*l + 24
*a^3*b^7*c^2*g^2*h*m + 16*a^4*b^6*c^2*g*j*k^2 - 16*a^3*b^6*c^3*f^2*j*l + 13376*a^6*b^2*c^4*d*k*l^2 - 5136*a^5*
b^4*c^3*d*k*l^2 - 3840*a^6*b^2*c^4*e*j*l^2 + 1536*a^5*b^4*c^3*e*j*l^2 + 1392*a^5*b^3*c^4*f*h^2*m + 1386*a^5*b^
5*c^2*f*h*m^2 - 768*a^5*b^3*c^4*e*j^2*l + 768*a^4*b^6*c^2*d*k*l^2 - 768*a^4*b^3*c^5*e^2*j*l - 588*a^4*b^4*c^4*
f^2*h*m - 480*a^5*b^3*c^4*g*h^2*l + 480*a^5*b^3*c^4*d*j^2*m - 480*a^5*b^2*c^5*f^2*h*m - 128*a^4*b^6*c^2*e*j*l^
2 + 100*a^3*b^6*c^3*f^2*h*m + 96*a^5*b^3*c^4*f*j^2*k + 72*a^4*b^5*c^3*g*h^2*l - 54*a^4*b^5*c^3*f*h^2*m - 48*a^
6*b^3*c^3*f*h*m^2 - 36*a^3*b^7*c^2*f*h^2*m + 6*a^2*b^8*c^2*f^2*h*m + 6848*a^4*b^2*c^6*d^2*j*l - 2448*a^3*b^4*c
^5*d^2*j*l + 624*a^5*b^4*c^3*f*h*l^2 + 576*a^6*b^2*c^4*f*h*l^2 + 480*a^5*b^3*c^4*e*j*k^2 + 432*a^4*b^4*c^4*f*g
^2*m - 416*a^4*b^3*c^5*e^2*h*m + 336*a^2*b^6*c^4*d^2*j*l - 320*a^5*b^2*c^5*f*g^2*m - 256*a^4*b^6*c^2*f*h*l^2 +
192*a^5*b^2*c^5*g^2*h*k + 96*a^3*b^5*c^4*e^2*h*m - 72*a^3*b^6*c^3*f*g^2*m + 48*a^4*b^4*c^4*g^2*h*k - 32*a^4*b
^5*c^3*e*j*k^2 - 8*a^3*b^6*c^3*g^2*h*k + 24768*a^6*b^2*c^4*d*h*m^2 - 21108*a^5*b^4*c^3*d*h*m^2 - 10048*a^4*b^2
*c^6*d^2*h*m + 7218*a^4*b^6*c^2*d*h*m^2 - 6720*a^6*b^2*c^4*e*g*m^2 + 6160*a^5*b^4*c^3*e*g*m^2 - 2592*a^5*b^2*c
^5*d*h^2*m - 1680*a^4*b^6*c^2*e*g*m^2 + 1068*a^3*b^4*c^5*d^2*h*m + 960*a^5*b^2*c^5*e*h^2*l - 876*a^4*b^4*c^4*d
*h^2*m - 864*a^5*b^2*c^5*f*h^2*k + 546*a^2*b^6*c^4*d^2*h*m + 432*a^3*b^6*c^3*d*h^2*m + 336*a^4*b^3*c^5*f^2*h*k
- 320*a^5*b^2*c^5*d*j^2*k + 192*a^5*b^2*c^5*g*h^2*j + 144*a^5*b^3*c^4*f*h*k^2 - 144*a^4*b^4*c^4*e*h^2*l - 102
*a^4*b^5*c^3*f*h*k^2 - 96*a^4*b^3*c^5*f^2*g*l - 36*a^2*b^8*c^2*d*h^2*m - 30*a^3*b^5*c^4*f^2*h*k - 24*a^3*b^5*c
^4*f^2*g*l + 16*a^4*b^4*c^4*g*h^2*j - 12*a^4*b^4*c^4*f*h^2*k + 12*a^3*b^6*c^3*f*h^2*k + 8*a^2*b^7*c^3*f^2*g*l
+ 6*a^3*b^7*c^2*f*h*k^2 - 2*a^2*b^7*c^3*f^2*h*k - 9312*a^5*b^3*c^4*d*h*l^2 + 3288*a^4*b^5*c^3*d*h*l^2 - 2304*a
^4*b^2*c^6*e^2*g*l + 1920*a^5*b^3*c^4*e*g*l^2 + 1728*a^4*b^2*c^6*e^2*f*m + 1152*a^4*b^3*c^5*e*g^2*l - 768*a^4*
b^5*c^3*e*g*l^2 - 608*a^4*b^3*c^5*d*g^2*m - 472*a^3*b^7*c^2*d*h*l^2 + 384*a^3*b^4*c^5*e^2*g*l - 288*a^3*b^4*c^
5*e^2*f*m - 224*a^4*b^3*c^5*f*g^2*k + 192*a^5*b^2*c^5*f*h*j^2 + 192*a^4*b^2*c^6*e^2*h*k - 192*a^3*b^5*c^4*e*g^
2*l + 120*a^3*b^5*c^4*d*g^2*m + 64*a^3*b^7*c^2*e*g*l^2 - 32*a^3*b^4*c^5*e^2*h*k + 24*a^3*b^5*c^4*f*g^2*k + 993
6*a^3*b^3*c^6*d^2*f*m + 3786*a^4*b^5*c^3*d*f*m^2 - 3552*a^5*b^2*c^5*d*h*k^2 - 3486*a^2*b^5*c^5*d^2*f*m - 3424*
a^3*b^3*c^6*d^2*g*l - 1868*a^3*b^7*c^2*d*f*m^2 + 1332*a^4*b^4*c^4*d*h*k^2 - 1296*a^5*b^3*c^4*d*f*m^2 - 1236*a^
3*b^4*c^5*d*f^2*m + 1224*a^2*b^5*c^5*d^2*g*l - 1152*a^4*b^2*c^6*d*f^2*m + 960*a^5*b^2*c^5*e*g*k^2 - 496*a^3*b^
3*c^6*d^2*h*k + 462*a^2*b^6*c^4*d*f^2*m + 432*a^4*b^3*c^5*d*h^2*k - 240*a^4*b^4*c^4*e*g*k^2 - 222*a^2*b^5*c^5*
d^2*h*k + 192*a^4*b^2*c^6*f^2*g*j + 192*a^4*b^2*c^6*e*f^2*l - 174*a^3*b^5*c^4*d*h^2*k - 156*a^3*b^6*c^3*d*h*k^
2 + 48*a^3*b^4*c^5*e*f^2*l - 32*a^4*b^3*c^5*e*h^2*j + 16*a^3*b^6*c^3*e*g*k^2 + 16*a^3*b^4*c^5*f^2*g*j - 16*a^2
*b^6*c^4*e*f^2*l + 12*a^2*b^7*c^3*d*h^2*k + 6*a^2*b^8*c^2*d*h*k^2 + 1728*a^5*b^2*c^5*d*f*l^2 + 1392*a^4*b^4*c^
4*d*f*l^2 - 840*a^3*b^6*c^3*d*f*l^2 - 768*a^4*b^2*c^6*e*g^2*j + 576*a^4*b^2*c^6*d*g^2*k + 480*a^3*b^3*c^6*d*e^
2*m + 144*a^2*b^8*c^2*d*f*l^2 + 96*a^4*b^3*c^5*d*h*j^2 + 96*a^3*b^3*c^6*e^2*f*k - 80*a^3*b^4*c^5*d*g^2*k + 684
8*a^3*b^2*c^7*d^2*e*l - 3552*a^3*b^2*c^7*d^2*f*k - 2448*a^2*b^4*c^6*d^2*e*l + 1332*a^2*b^4*c^6*d^2*f*k + 960*a
^3*b^2*c^7*d^2*g*j - 496*a^4*b^3*c^5*d*f*k^2 + 432*a^3*b^3*c^6*d*f^2*k - 240*a^2*b^4*c^6*d^2*g*j - 222*a^3*b^5
*c^4*d*f*k^2 - 174*a^2*b^5*c^5*d*f^2*k + 64*a^4*b^2*c^6*f*g^2*h + 48*a^3*b^4*c^5*f*g^2*h + 42*a^2*b^7*c^3*d*f*
k^2 - 32*a^3*b^3*c^6*e*f^2*j - 320*a^3*b^2*c^7*d*e^2*k + 192*a^4*b^2*c^6*e*g*h^2 + 192*a^4*b^2*c^6*d*f*j^2 - 3
2*a^3*b^4*c^5*d*f*j^2 + 16*a^3*b^4*c^5*e*g*h^2 + 480*a^2*b^3*c^7*d^2*e*j - 224*a^3*b^3*c^6*d*g^2*h + 192*a^3*b
^2*c^7*e^2*f*h + 24*a^2*b^5*c^5*d*g^2*h - 864*a^3*b^2*c^7*d*f^2*h + 336*a^3*b^3*c^6*d*f*h^2 + 192*a^3*b^2*c^7*
e*f^2*g + 144*a^2*b^3*c^7*d^2*f*h - 30*a^2*b^5*c^5*d*f*h^2 + 16*a^2*b^4*c^6*e*f^2*g - 12*a^2*b^4*c^6*d*f^2*h +
192*a^3*b^2*c^7*d*f*g^2 + 96*a^2*b^3*c^7*d*e^2*h + 48*a^2*b^4*c^6*d*f*g^2 + 960*a^2*b^2*c^8*d^2*e*g + 192*a^2
*b^2*c^8*d*e^2*f - 7680*a^9*b*c^2*l^2*m^2 + 3152*a^8*b^3*c*l^2*m^2 + 2070*a^7*b^4*c*k^2*m^2 - 1840*a^7*b^3*c^2
*k^3*m + 6720*a^8*b*c^3*j^2*m^2 - 3072*a^8*b*c^3*k^2*l^2 + 1680*a^6*b^5*c*j^2*m^2 - 100*a^6*b^5*c*k^2*l^2 - 21
76*a^7*b^3*c^2*j*l^3 - 256*a^6*b^3*c^3*j^3*l - 64*a^5*b^6*c*j^2*l^2 - 12480*a^8*b^2*c^2*h*m^3 + 972*a^5*b^6*c*
h^2*m^2 - 960*a^7*b*c^4*j^2*k^2 - 252*a^5*b^4*c^3*h^3*m - 192*a^6*b^2*c^4*h^3*m + 54*a^4*b^6*c^2*h^3*m + 1536*
a^7*b*c^4*h^2*l^2 + 420*a^4*b^7*c*g^2*m^2 - 36*a^4*b^7*c*h^2*l^2 - 3072*a^7*b^2*c^3*g*l^3 + 2096*a^7*b^3*c^2*f
*m^3 + 1088*a^6*b^4*c^2*g*l^3 - 496*a^6*b^3*c^3*h*k^3 - 192*a^4*b^4*c^4*g^3*l + 176*a^4*b^3*c^5*f^3*m + 144*a^
5*b^3*c^4*h^3*k + 78*a^3*b^8*c*f^2*m^2 + 54*a^3*b^5*c^4*f^3*m + 32*a^3*b^6*c^3*g^3*l + 30*a^5*b^5*c^2*h*k^3 -
18*a^4*b^5*c^3*h^3*k - 18*a^2*b^7*c^3*f^3*m - 16*a^3*b^8*c*g^2*l^2 + 6720*a^6*b*c^5*e^2*m^2 - 192*a^6*b*c^5*h^
2*j^2 - 4*a^2*b^9*c*f^2*l^2 - 35040*a^7*b^2*c^3*d*m^3 + 14300*a^6*b^4*c^2*d*m^3 - 12000*a^3*b^2*c^7*d^3*m + 43
80*a^2*b^4*c^6*d^3*m - 2176*a^6*b^3*c^3*e*l^3 - 256*a^3*b^3*c^6*e^3*l - 192*a^6*b^2*c^4*f*k^3 + 192*a^5*b^5*c^
2*e*l^3 - 192*a^4*b^2*c^6*f^3*k + 132*a^5*b^4*c^3*f*k^3 + 128*a^4*b^3*c^5*g^3*j - 28*a^3*b^4*c^5*f^3*k - 10*a^
4*b^6*c^2*f*k^3 + 6*a^2*b^6*c^4*f^3*k + 10752*a^5*b*c^6*d^2*l^2 - 960*a^5*b*c^6*e^2*k^2 - 192*a^5*b*c^6*f^2*j^
2 + 108*a*b^9*c^2*d^2*l^2 - 1680*a^5*b^3*c^4*d*k^3 - 1680*a^2*b^3*c^7*d^3*k + 222*a^4*b^5*c^3*d*k^3 + 30*a*b^8
*c^3*d^2*k^2 - 10*a^3*b^7*c^2*d*k^3 - 960*a^4*b*c^7*d^2*j^2 + 80*a^4*b^3*c^5*f*h^3 + 80*a^3*b^3*c^6*f^3*h + 6*
a^3*b^5*c^4*f*h^3 + 6*a^2*b^5*c^5*f^3*h - 192*a^4*b*c^7*e^2*h^2 - 192*a^4*b^2*c^6*d*h^3 - 192*a^2*b^2*c^8*d^3*
h + 128*a^3*b^3*c^6*e*g^3 - 28*a^3*b^4*c^5*d*h^3 + 12*a*b^6*c^5*d^2*h^2 + 6*a^2*b^6*c^4*d*h^3 - 192*a^3*b*c^8*
e^2*f^2 + 60*a*b^5*c^6*d^2*g^2 + 198*a*b^4*c^7*d^2*f^2 + 144*a^2*b^3*c^7*d*f^3 - 960*a^2*b*c^9*d^2*e^2 + 240*a
*b^3*c^8*d^2*e^2 + 15360*a^9*c^3*k*l^2*m - 12800*a^9*c^3*j*l*m^2 - 3840*a^8*c^4*j^2*k*m + 432*a^6*b^6*j*l*m^2
+ 4608*a^8*c^4*j*k^2*l + 2880*a^8*c^4*h*k^2*m + 5120*a^8*c^4*f*l^2*m - 3072*a^8*c^4*h*k*l^2 + 270*a^5*b^7*h*k*
m^2 - 216*a^5*b^7*g*l*m^2 - 12800*a^8*c^4*e*l*m^2 - 4800*a^8*c^4*f*k*m^2 - 512*a^7*c^5*h^2*j*l - 3840*a^6*c^6*
e^2*k*m - 1280*a^7*c^5*f*j^2*m + 768*a^7*c^5*h*j^2*k + 144*a^4*b^8*g*j*m^2 - 90*a^4*b^8*f*k*m^2 + 8640*a^7*c^5
*d*k^2*m + 4608*a^7*c^5*e*k^2*l + 512*a^6*c^6*f^2*j*l - 9216*a^7*c^5*d*k*l^2 - 4096*a^7*c^5*e*j*l^2 + 320*a^6*
c^6*f^2*h*m - 90*a^3*b^9*d*k*m^2 + 15200*a^9*b*c^2*k*m^3 - 6192*a^8*b^3*c*k*m^3 + 5472*a^8*b*c^3*k^3*m - 4608*
a^5*c^7*d^2*j*l - 1024*a^7*c^5*f*h*l^2 + 150*a^6*b^5*c*k^3*m + 54*a^3*b^9*f*h*m^2 + 6*b^10*c^2*d^2*h*m - 14400
*a^7*c^5*d*h*m^2 + 8640*a^5*c^7*d^2*h*m + 2880*a^6*c^6*d*h^2*m + 2304*a^6*c^6*d*j^2*k - 512*a^6*c^6*e*h^2*l -
192*a^6*c^6*f*h^2*k + 6144*a^8*b*c^3*j*l^3 + 1536*a^7*b*c^4*j^3*l - 1280*a^5*c^7*e^2*f*m + 768*a^5*c^7*e^2*h*k
+ 256*a^6*c^6*f*h*j^2 + 192*a^6*b^5*c*j*l^3 + 54*a^2*b^10*d*h*m^2 - 18*b^9*c^3*d^2*f*m + 8*b^9*c^3*d^2*g*l -
2*b^9*c^3*d^2*h*k + 4068*a^7*b^4*c*h*m^3 - 1728*a^6*c^6*d*h*k^2 + 960*a^5*c^7*d*f^2*m + 512*a^5*c^7*e*f^2*l -
3072*a^6*c^6*d*f*l^2 - 16*b^8*c^4*d^2*e*l + 6*b^8*c^4*d^2*f*k - 4608*a^4*c^8*d^2*e*l + 2400*a^8*b*c^3*f*m^3 +
2016*a^7*b*c^4*h*k^3 - 1728*a^4*c^8*d^2*f*k - 1146*a^6*b^5*c*f*m^3 + 224*a^6*b*c^5*h^3*k - 96*a^5*b^6*c*g*l^3
+ 96*a^5*b*c^6*f^3*m + 2304*a^4*c^8*d*e^2*k + 768*a^5*c^7*d*f*j^2 + 6144*a^7*b*c^4*e*l^3 - 2280*a^5*b^6*c*d*m^
3 + 1536*a^4*b*c^7*e^3*l - 616*a*b^6*c^5*d^3*m + 512*a^6*b*c^5*g*j^3 + 256*a^4*c^8*e^2*f*h + 240*a*b^10*c*d^2*
m^2 + 6*b^7*c^5*d^2*f*h - 192*a^4*c^8*d*f^2*h + 4320*a^6*b*c^5*d*k^3 + 4320*a^3*b*c^8*d^3*k + 222*a*b^5*c^6*d^
3*k + 16*b^6*c^6*d^2*e*g + 96*a^5*b*c^6*f*h^3 + 96*a^4*b*c^7*f^3*h + 768*a^3*c^9*d*e^2*f + 512*a^3*b*c^8*e^3*g
+ 132*a*b^4*c^7*d^3*h + 2016*a^2*b*c^9*d^3*f - 496*a*b^3*c^8*d^3*f + 224*a^3*b*c^8*d*f^3 - 18*a*b^5*c^6*d*f^3
- 3264*a^8*b^2*c^2*k^2*m^2 - 6160*a^7*b^3*c^2*j^2*m^2 + 1104*a^7*b^3*c^2*k^2*l^2 - 1920*a^7*b^2*c^3*j^2*l^2 +
768*a^6*b^4*c^2*j^2*l^2 + 3888*a^7*b^2*c^3*h^2*m^2 - 3510*a^6*b^4*c^2*h^2*m^2 + 240*a^6*b^3*c^3*j^2*k^2 - 16*
a^5*b^5*c^2*j^2*k^2 + 1680*a^6*b^3*c^3*g^2*m^2 - 1648*a^6*b^3*c^3*h^2*l^2 - 1540*a^5*b^5*c^2*g^2*m^2 + 444*a^5
*b^5*c^2*h^2*l^2 - 960*a^6*b^2*c^4*h^2*k^2 - 576*a^6*b^2*c^4*f^2*m^2 - 512*a^6*b^2*c^4*g^2*l^2 - 480*a^5*b^4*c
^3*g^2*l^2 + 198*a^5*b^4*c^3*h^2*k^2 + 192*a^4*b^6*c^2*g^2*l^2 - 186*a^5*b^4*c^3*f^2*m^2 - 97*a^4*b^6*c^2*f^2*
m^2 - 9*a^4*b^6*c^2*h^2*k^2 - 6160*a^5*b^3*c^4*e^2*m^2 + 1680*a^4*b^5*c^3*e^2*m^2 - 240*a^5*b^3*c^4*g^2*k^2 -
240*a^5*b^3*c^4*f^2*l^2 - 144*a^3*b^7*c^2*e^2*m^2 + 60*a^4*b^5*c^3*g^2*k^2 - 36*a^4*b^5*c^3*f^2*l^2 + 36*a^3*b
^7*c^2*f^2*l^2 - 16*a^5*b^3*c^4*h^2*j^2 - 4*a^3*b^7*c^2*g^2*k^2 + 38512*a^5*b^2*c^5*d^2*m^2 - 32310*a^4*b^4*c^
4*d^2*m^2 + 12720*a^3*b^6*c^3*d^2*m^2 - 2500*a^2*b^8*c^2*d^2*m^2 - 1920*a^5*b^2*c^5*e^2*l^2 + 768*a^4*b^4*c^4*
e^2*l^2 - 464*a^5*b^2*c^5*f^2*k^2 - 384*a^5*b^2*c^5*g^2*j^2 - 64*a^3*b^6*c^3*e^2*l^2 + 42*a^4*b^4*c^4*f^2*k^2
+ 12*a^3*b^6*c^3*f^2*k^2 - 13104*a^4*b^3*c^5*d^2*l^2 + 5628*a^3*b^5*c^4*d^2*l^2 - 1128*a^2*b^7*c^3*d^2*l^2 + 2
40*a^4*b^3*c^5*e^2*k^2 - 16*a^4*b^3*c^5*f^2*j^2 - 16*a^3*b^5*c^4*e^2*k^2 - 2880*a^4*b^2*c^6*d^2*k^2 + 1750*a^3
*b^4*c^5*d^2*k^2 - 345*a^2*b^6*c^4*d^2*k^2 - 48*a^4*b^3*c^5*g^2*h^2 - 4*a^3*b^5*c^4*g^2*h^2 + 240*a^3*b^3*c^6*
d^2*j^2 - 192*a^4*b^2*c^6*f^2*h^2 - 42*a^3*b^4*c^5*f^2*h^2 - 16*a^2*b^5*c^5*d^2*j^2 - 48*a^3*b^3*c^6*f^2*g^2 -
16*a^3*b^3*c^6*e^2*h^2 - 4*a^2*b^5*c^5*f^2*g^2 - 464*a^3*b^2*c^7*d^2*h^2 - 384*a^3*b^2*c^7*e^2*g^2 + 42*a^2*b
^4*c^6*d^2*h^2 - 240*a^2*b^3*c^7*d^2*g^2 - 16*a^2*b^3*c^7*e^2*f^2 - 960*a^2*b^2*c^8*d^2*f^2 + 6*b^11*c*d^2*k*m
- 18*a*b^11*d*f*m^2 - 7200*a^9*c^3*k^2*m^2 - 324*a^7*b^5*l^2*m^2 - 225*a^6*b^6*k^2*m^2 - 2048*a^8*c^4*j^2*l^2
- 144*a^5*b^7*j^2*m^2 - 2400*a^8*c^4*h^2*m^2 - 81*a^4*b^8*h^2*m^2 - 800*a^7*c^5*f^2*m^2 - 288*a^7*c^5*h^2*k^2
- 36*a^3*b^9*g^2*m^2 - 9*a^2*b^10*f^2*m^2 - 21600*a^6*c^6*d^2*m^2 - 2048*a^6*c^6*e^2*l^2 - 864*a^6*c^6*f^2*k^
2 - 2592*a^5*c^7*d^2*k^2 - 1536*a^5*c^7*e^2*j^2 + 1536*a^8*b^2*c^2*l^4 - 32*a^5*c^7*f^2*h^2 + 360*a^7*b^2*c^3*
k^4 - 25*a^6*b^4*c^2*k^4 - 864*a^4*c^8*d^2*h^2 - 4*b^7*c^5*d^2*g^2 - 9*b^6*c^6*d^2*f^2 - 288*a^3*c^9*d^2*f^2 -
24*a^5*b^2*c^5*h^4 - 16*b^5*c^7*d^2*e^2 - 9*a^4*b^4*c^4*h^4 - 16*a^3*b^4*c^5*g^4 - 24*a^3*b^2*c^7*f^4 - 9*a^2
*b^4*c^6*f^4 - a^2*b^8*c^2*f^2*k^2 - a^2*b^6*c^4*f^2*h^2 + 630*a^7*b^5*k*m^3 + 8000*a^9*c^3*h*m^3 + 320*a^7*c^
5*h^3*m - 378*a^6*b^6*h*m^3 + 126*a^5*b^7*f*m^3 + 30*b^8*c^4*d^3*m + 24000*a^8*c^4*d*m^3 + 8640*a^4*c^8*d^3*m
- 1728*a^7*c^5*f*k^3 - 192*a^5*c^7*f^3*k - 4*b^11*c*d^2*l^2 + 126*a^4*b^8*d*m^3 - 10*b^7*c^5*d^3*k + 4200*a^9*
b^2*c*m^4 - 1024*a^6*c^6*e*j^3 - 1024*a^4*c^8*e^3*j - 144*a^7*b^4*c*l^4 - 10*b^6*c^6*d^3*h - 1728*a^3*c^9*d^3*
h - 192*a^5*c^7*d*h^3 + 30*b^5*c^7*d^3*f + 360*a*b^2*c^9*d^4 - 9*b^12*d^2*m^2 - 10000*a^10*c^2*m^4 - 4096*a^9*
c^3*l^4 - 441*a^8*b^4*m^4 - 1296*a^8*c^4*k^4 - 256*a^7*c^5*j^4 - 16*a^6*c^6*h^4 - 16*a^4*c^8*f^4 - 256*a^3*c^9
*e^4 - 25*b^4*c^8*d^4 - 1296*a^2*c^10*d^4 - b^10*c^2*d^2*k^2 - b^8*c^4*d^2*h^2, z, k1)*((6144*a^5*c^9*d + 2048
*a^6*c^8*h - 10240*a^7*c^7*m - 288*a^2*b^6*c^6*d + 1920*a^3*b^4*c^7*d - 5632*a^4*b^2*c^8*d + 16*a^2*b^7*c^5*f
- 192*a^3*b^5*c^6*f + 768*a^4*b^3*c^7*f - 32*a^3*b^6*c^5*h + 384*a^4*b^4*c^6*h - 1536*a^5*b^2*c^7*h + 16*a^3*b
^7*c^4*k - 192*a^4*b^5*c^5*k + 768*a^5*b^3*c^6*k - 48*a^3*b^8*c^3*m + 736*a^4*b^6*c^4*m - 4224*a^5*b^4*c^5*m +
10752*a^6*b^2*c^6*m + 16*a*b^8*c^5*d - 1024*a^5*b*c^8*f - 1024*a^6*b*c^7*k)/(8*(64*a^5*c^6 - a^2*b^6*c^3 + 12
*a^3*b^4*c^4 - 48*a^4*b^2*c^5)) + (x*(32*a^2*b^6*c^6*e - 2048*a^6*c^8*j - 2048*a^5*c^9*e - 384*a^3*b^4*c^7*e +
1536*a^4*b^2*c^8*e - 16*a^2*b^7*c^5*g + 192*a^3*b^5*c^6*g - 768*a^4*b^3*c^7*g + 32*a^3*b^6*c^5*j - 384*a^4*b^
4*c^6*j + 1536*a^5*b^2*c^7*j + 32*a^2*b^9*c^3*l - 528*a^3*b^7*c^4*l + 3264*a^4*b^5*c^5*l - 8960*a^5*b^3*c^6*l
+ 1024*a^5*b*c^8*g + 9216*a^6*b*c^7*l))/(4*(64*a^5*c^6 - a^2*b^6*c^3 + 12*a^3*b^4*c^4 - 48*a^4*b^2*c^5)) - (ro
ot(1572864*a^8*b^2*c^10*z^4 - 983040*a^7*b^4*c^9*z^4 + 327680*a^6*b^6*c^8*z^4 - 61440*a^5*b^8*c^7*z^4 + 6144*a
^4*b^10*c^6*z^4 - 256*a^3*b^12*c^5*z^4 - 1048576*a^9*c^11*z^4 - 1572864*a^8*b^2*c^8*l*z^3 + 983040*a^7*b^4*c^7
*l*z^3 - 327680*a^6*b^6*c^6*l*z^3 + 61440*a^5*b^8*c^5*l*z^3 - 6144*a^4*b^10*c^4*l*z^3 + 256*a^3*b^12*c^3*l*z^3
+ 1048576*a^9*c^9*l*z^3 + 96*a^3*b^12*c*k*m*z^2 + 98304*a^8*b*c^7*j*l*z^2 + 24576*a^8*b*c^7*h*m*z^2 + 155648*
a^7*b*c^8*d*m*z^2 + 98304*a^7*b*c^8*e*l*z^2 + 57344*a^7*b*c^8*f*k*z^2 + 32768*a^7*b*c^8*g*j*z^2 + 57344*a^6*b*
c^9*d*h*z^2 + 32768*a^6*b*c^9*e*g*z^2 - 32*a*b^10*c^5*d*f*z^2 - 491520*a^8*b^2*c^6*k*m*z^2 + 358400*a^7*b^4*c^
5*k*m*z^2 - 129024*a^6*b^6*c^4*k*m*z^2 + 24768*a^5*b^8*c^3*k*m*z^2 - 2432*a^4*b^10*c^2*k*m*z^2 - 90112*a^7*b^3
*c^6*j*l*z^2 + 30720*a^6*b^5*c^5*j*l*z^2 - 4608*a^5*b^7*c^4*j*l*z^2 + 256*a^4*b^9*c^3*j*l*z^2 - 21504*a^6*b^5*
c^5*h*m*z^2 + 9216*a^5*b^7*c^4*h*m*z^2 + 8192*a^7*b^3*c^6*h*m*z^2 - 1568*a^4*b^9*c^3*h*m*z^2 + 96*a^3*b^11*c^2
*h*m*z^2 - 172032*a^7*b^2*c^7*f*m*z^2 + 116736*a^6*b^4*c^6*f*m*z^2 - 49152*a^7*b^2*c^7*g*l*z^2 + 45056*a^6*b^4
*c^6*g*l*z^2 - 35840*a^5*b^6*c^5*f*m*z^2 + 24576*a^7*b^2*c^7*h*k*z^2 - 15360*a^5*b^6*c^5*g*l*z^2 + 5184*a^4*b^
8*c^4*f*m*z^2 - 3072*a^5*b^6*c^5*h*k*z^2 + 2304*a^4*b^8*c^4*g*l*z^2 + 2048*a^6*b^4*c^6*h*k*z^2 + 576*a^4*b^8*c
^4*h*k*z^2 - 288*a^3*b^10*c^3*f*m*z^2 - 128*a^3*b^10*c^3*g*l*z^2 - 32*a^3*b^10*c^3*h*k*z^2 - 147456*a^6*b^3*c^
7*d*m*z^2 - 90112*a^6*b^3*c^7*e*l*z^2 + 52224*a^5*b^5*c^6*d*m*z^2 - 49152*a^6*b^3*c^7*f*k*z^2 + 30720*a^5*b^5*
c^6*e*l*z^2 - 24576*a^6*b^3*c^7*g*j*z^2 + 15360*a^5*b^5*c^6*f*k*z^2 - 8192*a^4*b^7*c^5*d*m*z^2 + 6144*a^5*b^5*
c^6*g*j*z^2 - 4608*a^4*b^7*c^5*e*l*z^2 - 2048*a^4*b^7*c^5*f*k*z^2 - 512*a^4*b^7*c^5*g*j*z^2 + 480*a^3*b^9*c^4*
d*m*z^2 + 256*a^3*b^9*c^4*e*l*z^2 + 96*a^3*b^9*c^4*f*k*z^2 + 131072*a^6*b^2*c^8*d*k*z^2 + 49152*a^6*b^2*c^8*e*
j*z^2 - 43008*a^5*b^4*c^7*d*k*z^2 - 12288*a^5*b^4*c^7*e*j*z^2 + 6144*a^4*b^6*c^6*d*k*z^2 + 1024*a^4*b^6*c^6*e*
j*z^2 - 320*a^3*b^8*c^5*d*k*z^2 + 6144*a^5*b^4*c^7*f*h*z^2 - 2048*a^4*b^6*c^6*f*h*z^2 + 192*a^3*b^8*c^5*f*h*z^
2 - 49152*a^5*b^3*c^8*d*h*z^2 - 24576*a^5*b^3*c^8*e*g*z^2 + 15360*a^4*b^5*c^7*d*h*z^2 + 6144*a^4*b^5*c^7*e*g*z
^2 - 2048*a^3*b^7*c^6*d*h*z^2 - 512*a^3*b^7*c^6*e*g*z^2 + 96*a^2*b^9*c^5*d*h*z^2 + 24576*a^5*b^2*c^9*d*f*z^2 -
3072*a^3*b^6*c^7*d*f*z^2 + 2048*a^4*b^4*c^8*d*f*z^2 + 576*a^2*b^8*c^6*d*f*z^2 - 430080*a^9*b*c^6*m^2*z^2 + 34
08*a^4*b^11*c*m^2*z^2 - 64*a^3*b^12*c*l^2*z^2 + 61440*a^8*b*c^7*k^2*z^2 + 12288*a^7*b*c^8*h^2*z^2 + 12288*a^6*
b*c^9*f^2*z^2 + 61440*a^5*b*c^10*d^2*z^2 + 432*a*b^9*c^6*d^2*z^2 + 245760*a^9*c^7*k*m*z^2 + 81920*a^8*c^8*f*m*
z^2 - 49152*a^8*c^8*h*k*z^2 - 147456*a^7*c^9*d*k*z^2 - 65536*a^7*c^9*e*j*z^2 - 16384*a^7*c^9*f*h*z^2 - 49152*a
^6*c^10*d*f*z^2 + 716800*a^8*b^3*c^5*m^2*z^2 - 483840*a^7*b^5*c^4*m^2*z^2 + 170496*a^6*b^7*c^3*m^2*z^2 - 33232
*a^5*b^9*c^2*m^2*z^2 + 516096*a^8*b^2*c^6*l^2*z^2 - 288768*a^7*b^4*c^5*l^2*z^2 + 88576*a^6*b^6*c^4*l^2*z^2 - 1
5744*a^5*b^8*c^3*l^2*z^2 + 1536*a^4*b^10*c^2*l^2*z^2 - 61440*a^7*b^3*c^6*k^2*z^2 + 24064*a^6*b^5*c^5*k^2*z^2 -
4608*a^5*b^7*c^4*k^2*z^2 + 432*a^4*b^9*c^3*k^2*z^2 - 16*a^3*b^11*c^2*k^2*z^2 + 24576*a^7*b^2*c^7*j^2*z^2 - 61
44*a^6*b^4*c^6*j^2*z^2 + 512*a^5*b^6*c^5*j^2*z^2 - 8192*a^6*b^3*c^7*h^2*z^2 + 1536*a^5*b^5*c^6*h^2*z^2 - 16*a^
3*b^9*c^4*h^2*z^2 - 8192*a^6*b^2*c^8*g^2*z^2 + 6144*a^5*b^4*c^7*g^2*z^2 - 1536*a^4*b^6*c^6*g^2*z^2 + 128*a^3*b
^8*c^5*g^2*z^2 - 8192*a^5*b^3*c^8*f^2*z^2 + 1536*a^4*b^5*c^7*f^2*z^2 - 16*a^2*b^9*c^5*f^2*z^2 + 24576*a^5*b^2*
c^9*e^2*z^2 - 6144*a^4*b^4*c^8*e^2*z^2 + 512*a^3*b^6*c^7*e^2*z^2 - 61440*a^4*b^3*c^9*d^2*z^2 + 24064*a^3*b^5*c
^8*d^2*z^2 - 4608*a^2*b^7*c^7*d^2*z^2 - 393216*a^9*c^7*l^2*z^2 - 144*a^3*b^13*m^2*z^2 - 32768*a^8*c^8*j^2*z^2
- 32768*a^6*c^10*e^2*z^2 - 16*b^11*c^5*d^2*z^2 + 18432*a^8*b*c^5*h*l*m*z - 96*a^3*b^10*c*g*k*m*z + 90112*a^7*b
*c^6*e*k*m*z + 36864*a^7*b*c^6*f*j*m*z - 16384*a^7*b*c^6*g*j*l*z + 14336*a^7*b*c^6*d*l*m*z - 10240*a^7*b*c^6*f
*k*l*z + 4096*a^7*b*c^6*h*j*k*z + 10240*a^7*b*c^6*g*h*m*z - 47104*a^6*b*c^7*d*h*l*z + 36864*a^6*b*c^7*e*f*m*z
+ 30720*a^6*b*c^7*d*g*m*z - 16384*a^6*b*c^7*e*g*l*z + 6144*a^6*b*c^7*f*g*k*z + 4096*a^6*b*c^7*e*h*k*z + 32*a*b
^10*c^3*d*f*l*z - 4096*a^5*b*c^8*d*f*j*z - 6144*a^5*b*c^8*d*g*h*z - 32*a*b^8*c^5*d*f*g*z - 4096*a^4*b*c^9*d*e*
f*z + 64*a*b^7*c^6*d*e*f*z + 110592*a^8*b^2*c^4*k*l*m*z - 36864*a^7*b^4*c^3*k*l*m*z + 5376*a^6*b^6*c^2*k*l*m*z
- 79872*a^7*b^3*c^4*j*k*m*z + 26112*a^6*b^5*c^3*j*k*m*z - 3712*a^5*b^7*c^2*j*k*m*z - 13824*a^7*b^3*c^4*h*l*m*
z + 3456*a^6*b^5*c^3*h*l*m*z - 288*a^5*b^7*c^2*h*l*m*z - 45056*a^7*b^2*c^5*g*k*m*z + 39936*a^6*b^4*c^4*g*k*m*z
+ 30720*a^7*b^2*c^5*f*l*m*z - 18432*a^7*b^2*c^5*h*k*l*z - 13056*a^5*b^6*c^3*g*k*m*z - 7680*a^6*b^4*c^4*f*l*m*
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2*c^4*g*h*k*l - 744*a^5*b^4*c^3*f*h*k*m - 544*a^5*b^4*c^3*f*g*l*m + 492*a^4*b^6*c^2*f*h*k*m + 416*a^5*b^4*c^3*
g*h*j*m + 384*a^6*b^2*c^4*g*h*j*m + 384*a^6*b^2*c^4*e*h*l*m - 288*a^5*b^4*c^3*g*h*k*l - 288*a^5*b^4*c^3*e*h*l*
m - 96*a^4*b^6*c^2*g*h*j*m + 2112*a^5*b^3*c^4*d*j*k*l - 160*a^4*b^5*c^3*d*j*k*l + 16992*a^5*b^3*c^4*d*h*k*m -
6252*a^4*b^5*c^3*d*h*k*m - 4800*a^5*b^3*c^4*e*g*k*m + 2112*a^5*b^3*c^4*d*g*l*m - 1728*a^5*b^3*c^4*f*g*j*m + 12
80*a^4*b^5*c^3*e*g*k*m + 1088*a^5*b^3*c^4*e*f*l*m - 832*a^5*b^3*c^4*e*h*j*m + 816*a^3*b^7*c^2*d*h*k*m + 576*a^
5*b^3*c^4*e*h*k*l - 448*a^5*b^3*c^4*f*h*j*l + 288*a^4*b^5*c^3*f*g*j*m - 192*a^5*b^3*c^4*g*h*j*k - 192*a^5*b^3*
c^4*f*g*k*l + 192*a^4*b^5*c^3*e*h*j*m - 112*a^4*b^5*c^3*d*g*l*m + 96*a^4*b^5*c^3*f*h*j*l - 96*a^3*b^7*c^2*e*g*
k*m + 80*a^4*b^5*c^3*f*g*k*l + 32*a^4*b^5*c^3*g*h*j*k - 11456*a^5*b^2*c^5*d*f*k*m + 4992*a^5*b^2*c^5*d*h*j*l -
4608*a^5*b^2*c^5*e*g*j*l - 4224*a^5*b^2*c^5*d*e*l*m + 3456*a^5*b^2*c^5*e*f*j*m + 3456*a^5*b^2*c^5*d*g*k*l + 2
432*a^5*b^2*c^5*d*g*j*m - 1312*a^4*b^4*c^4*d*h*j*l + 1272*a^3*b^6*c^3*d*f*k*m - 1056*a^4*b^4*c^4*d*g*k*l + 896
*a^5*b^2*c^5*f*g*j*k + 768*a^4*b^4*c^4*e*g*j*l - 576*a^4*b^4*c^4*e*f*j*m - 480*a^4*b^4*c^4*d*g*j*m + 384*a^5*b
^2*c^5*e*h*j*k + 384*a^5*b^2*c^5*e*f*k*l - 232*a^2*b^8*c^2*d*f*k*m + 224*a^4*b^4*c^4*d*e*l*m - 160*a^4*b^4*c^4
*e*f*k*l - 96*a^4*b^4*c^4*f*g*j*k + 96*a^3*b^6*c^3*d*h*j*l + 80*a^3*b^6*c^3*d*g*k*l - 64*a^4*b^4*c^4*e*h*j*k -
24*a^4*b^4*c^4*d*f*k*m + 416*a^4*b^4*c^4*e*g*h*m + 384*a^5*b^2*c^5*f*g*h*l + 384*a^5*b^2*c^5*e*g*h*m + 224*a^
4*b^4*c^4*f*g*h*l - 96*a^3*b^6*c^3*e*g*h*m - 48*a^3*b^6*c^3*f*g*h*l + 2112*a^4*b^3*c^5*d*e*k*l - 960*a^4*b^3*c
^5*d*f*j*l + 960*a^4*b^3*c^5*d*e*j*m + 384*a^3*b^5*c^4*d*f*j*l + 320*a^4*b^3*c^5*d*g*j*k + 192*a^4*b^3*c^5*e*f
*j*k - 160*a^3*b^5*c^4*d*e*k*l - 32*a^2*b^7*c^3*d*f*j*l + 7392*a^4*b^3*c^5*d*f*h*m - 2496*a^4*b^3*c^5*d*g*h*l
- 1728*a^4*b^3*c^5*e*f*g*m - 1500*a^3*b^5*c^4*d*f*h*m + 656*a^3*b^5*c^4*d*g*h*l - 448*a^4*b^3*c^5*e*f*h*l + 28
8*a^3*b^5*c^4*e*f*g*m - 192*a^4*b^3*c^5*f*g*h*j - 192*a^4*b^3*c^5*e*g*h*k + 96*a^3*b^5*c^4*e*f*h*l - 48*a^2*b^
7*c^3*d*g*h*l + 32*a^3*b^5*c^4*e*g*h*k - 16*a^2*b^7*c^3*d*f*h*m - 640*a^4*b^2*c^6*d*e*j*k + 4992*a^4*b^2*c^6*d
*e*h*l - 3584*a^4*b^2*c^6*d*f*h*k + 2432*a^4*b^2*c^6*d*e*g*m - 1312*a^3*b^4*c^5*d*e*h*l + 896*a^4*b^2*c^6*e*f*
g*k + 896*a^4*b^2*c^6*d*g*h*j + 640*a^4*b^2*c^6*d*f*g*l + 600*a^3*b^4*c^5*d*f*h*k + 480*a^3*b^4*c^5*d*f*g*l -
480*a^3*b^4*c^5*d*e*g*m + 384*a^4*b^2*c^6*e*f*h*j - 192*a^2*b^6*c^4*d*f*g*l - 96*a^3*b^4*c^5*e*f*g*k - 96*a^3*
b^4*c^5*d*g*h*j + 96*a^2*b^6*c^4*d*e*h*l + 12*a^2*b^6*c^4*d*f*h*k - 960*a^3*b^3*c^6*d*e*f*l + 384*a^2*b^5*c^5*
d*e*f*l + 320*a^3*b^3*c^6*d*e*g*k - 192*a^3*b^3*c^6*d*f*g*j + 192*a^3*b^3*c^6*d*e*h*j + 32*a^2*b^5*c^5*d*f*g*j
- 192*a^3*b^3*c^6*e*f*g*h + 384*a^3*b^2*c^7*d*e*f*j - 64*a^2*b^4*c^6*d*e*f*j + 896*a^3*b^2*c^7*d*e*g*h - 96*a
^2*b^4*c^6*d*e*g*h - 192*a^2*b^3*c^7*d*e*f*g + 496*a^7*b^4*c*k*l^2*m - 4752*a^7*b^4*c*j*l*m^2 + 96*a^5*b^6*c*j
^2*k*m - 6144*a^8*b*c^3*h*l^2*m - 168*a^6*b^5*c*h*l^2*m + 6400*a^8*b*c^3*g*l*m^2 - 2862*a^6*b^5*c*h*k*m^2 + 23
76*a^6*b^5*c*g*l*m^2 - 1632*a^7*b*c^4*h^2*k*m - 480*a^8*b*c^3*h*k*m^2 - 180*a^5*b^6*c*h*k^2*m + 54*a^4*b^7*c*h
^2*k*m - 384*a^7*b*c^4*h*j^2*m + 120*a^5*b^6*c*h*k*l^2 + 56*a^5*b^6*c*f*l^2*m + 24*a^3*b^8*c*g^2*k*m + 4512*a^
7*b*c^4*f*k^2*m - 2304*a^7*b*c^4*g*k^2*l - 1680*a^5*b^6*c*g*j*m^2 + 1184*a^6*b*c^5*f^2*k*m + 804*a^5*b^6*c*f*k
*m^2 + 432*a^5*b^6*c*e*l*m^2 + 60*a^4*b^7*c*f*k^2*m + 6*a^2*b^9*c*f^2*k*m - 13312*a^7*b*c^4*d*l^2*m + 2048*a^7
*b*c^4*g*j*l^2 - 1024*a^7*b*c^4*f*k*l^2 + 64*a^4*b^7*c*g*j*l^2 + 56*a^4*b^7*c*d*l^2*m - 40*a^4*b^7*c*f*k*l^2 +
13440*a^7*b*c^4*e*j*m^2 - 8928*a^5*b*c^6*d^2*k*m - 6240*a^7*b*c^4*d*k*m^2 + 1614*a^4*b^7*c*d*k*m^2 - 288*a^4*
b^7*c*e*j*m^2 - 170*a*b^9*c^2*d^2*k*m + 60*a^3*b^8*c*d*k^2*m + 4608*a^6*b*c^5*e*j^2*l + 4608*a^5*b*c^6*e^2*j*l
- 2432*a^6*b*c^5*d*j^2*m + 1440*a^7*b*c^4*f*h*m^2 - 896*a^6*b*c^5*f*j^2*k - 864*a^6*b*c^5*f*h^2*m - 558*a^4*b
^7*c*f*h*m^2 + 256*a^6*b*c^5*g*h^2*l - 40*a^3*b^8*c*d*k*l^2 - 1920*a^6*b*c^5*e*j*k^2 - 384*a^5*b*c^6*e^2*h*m +
24*a^3*b^8*c*f*h*l^2 - 16*a*b^8*c^3*d^2*j*l + 2208*a^6*b*c^5*f*h*k^2 - 1044*a^3*b^8*c*d*h*m^2 + 800*a^5*b*c^6
*f^2*h*k - 256*a^5*b*c^6*f^2*g*l + 144*a^3*b^8*c*e*g*m^2 - 116*a*b^8*c^3*d^2*h*m + 8192*a^6*b*c^5*d*h*l^2 + 20
48*a^6*b*c^5*e*g*l^2 + 24*a^2*b^9*c*d*h*l^2 - 5856*a^4*b*c^7*d^2*f*m + 4896*a^4*b*c^7*d^2*h*k + 2720*a^6*b*c^5
*d*f*m^2 + 2304*a^4*b*c^7*d^2*g*l + 1824*a^5*b*c^6*d*h^2*k + 438*a*b^7*c^4*d^2*f*m - 384*a^5*b*c^6*e*h^2*j + 3
18*a^2*b^9*c*d*f*m^2 - 168*a*b^7*c^4*d^2*g*l + 42*a*b^7*c^4*d^2*h*k - 36*a*b^8*c^3*d*f^2*m - 2432*a^4*b*c^7*d*
e^2*m + 1536*a^5*b*c^6*e*g*j^2 + 1536*a^4*b*c^7*e^2*g*j - 896*a^5*b*c^6*d*h*j^2 - 896*a^4*b*c^7*e^2*f*k + 4896
*a^5*b*c^6*d*f*k^2 + 1824*a^4*b*c^7*d*f^2*k - 384*a^4*b*c^7*e*f^2*j + 336*a*b^6*c^5*d^2*e*l - 156*a*b^6*c^5*d^
2*f*k + 16*a*b^6*c^5*d^2*g*j + 12*a*b^7*c^4*d*f^2*k - 2*a*b^9*c^2*d*f*k^2 - 1920*a^3*b*c^8*d^2*e*j - 32*a*b^5*
c^6*d^2*e*j + 2208*a^3*b*c^8*d^2*f*h + 800*a^4*b*c^7*d*f*h^2 - 102*a*b^5*c^6*d^2*f*h + 12*a*b^6*c^5*d*f^2*h -
2*a*b^7*c^4*d*f*h^2 - 896*a^3*b*c^8*d*e^2*h - 8*a*b^6*c^5*d*f*g^2 - 240*a*b^4*c^7*d^2*e*g - 32*a*b^4*c^7*d*e^2
*f + 5120*a^8*c^4*h*j*l*m + 15360*a^7*c^5*d*j*l*m - 7680*a^7*c^5*e*j*k*m + 3072*a^7*c^5*f*j*k*l + 5120*a^7*c^5
*e*h*l*m + 1920*a^7*c^5*f*h*k*m + 15360*a^6*c^6*d*e*l*m + 5760*a^6*c^6*d*f*k*m + 3072*a^6*c^6*e*f*k*l - 3072*a
^6*c^6*d*h*j*l - 2560*a^6*c^6*e*f*j*m + 1536*a^6*c^6*e*h*j*k + 4608*a^5*c^7*d*e*j*k - 3072*a^5*c^7*d*e*h*l - 1
152*a^5*c^7*d*f*h*k + 512*a^5*c^7*e*f*h*j + 1536*a^4*c^8*d*e*f*j - 8*a*b^10*c*d*f*l^2 - 5568*a^8*b^2*c^2*k*l^2
*m + 15552*a^8*b^2*c^2*j*l*m^2 + 4800*a^7*b^2*c^3*j^2*k*m - 1280*a^6*b^4*c^2*j^2*k*m + 2080*a^7*b^3*c^2*h*l^2*
m - 1088*a^7*b^2*c^3*j*k^2*l + 48*a^6*b^4*c^2*j*k^2*l - 8544*a^7*b^2*c^3*h*k^2*m - 7776*a^7*b^3*c^2*g*l*m^2 +
7632*a^7*b^3*c^2*h*k*m^2 + 3600*a^6*b^3*c^3*h^2*k*m + 2484*a^6*b^4*c^2*h*k^2*m - 918*a^5*b^5*c^2*h^2*k*m + 480
0*a^7*b^2*c^3*h*k*l^2 - 1424*a^6*b^4*c^2*h*k*l^2 + 1200*a^5*b^4*c^3*g^2*k*m - 960*a^6*b^2*c^4*g^2*k*m - 528*a^
6*b^4*c^2*f*l^2*m - 416*a^6*b^3*c^3*h*j^2*m - 320*a^4*b^6*c^2*g^2*k*m + 192*a^7*b^2*c^3*f*l^2*m + 96*a^5*b^5*c
^2*h*j^2*m + 15552*a^7*b^2*c^3*e*l*m^2 - 6720*a^7*b^2*c^3*g*j*m^2 + 6160*a^6*b^4*c^2*g*j*m^2 - 4752*a^6*b^4*c^
2*e*l*m^2 - 2016*a^7*b^2*c^3*f*k*m^2 - 1164*a^6*b^4*c^2*f*k*m^2 + 1104*a^5*b^3*c^4*f^2*k*m + 1008*a^6*b^3*c^3*
f*k^2*m + 960*a^6*b^2*c^4*h^2*j*l - 678*a^5*b^5*c^2*f*k^2*m + 544*a^6*b^3*c^3*g*k^2*l - 144*a^5*b^4*c^3*h^2*j*
l - 102*a^4*b^5*c^3*f^2*k*m - 62*a^3*b^7*c^2*f^2*k*m - 24*a^5*b^5*c^2*g*k^2*l + 6432*a^6*b^3*c^3*d*l^2*m + 480
0*a^5*b^2*c^5*e^2*k*m - 2304*a^6*b^2*c^4*g*j^2*l + 1920*a^6*b^3*c^3*g*j*l^2 + 1728*a^6*b^2*c^4*f*j^2*m - 1280*
a^4*b^4*c^4*e^2*k*m + 1152*a^5*b^3*c^4*g^2*j*l - 1032*a^5*b^5*c^2*d*l^2*m - 864*a^6*b^3*c^3*f*k*l^2 - 768*a^5*
b^5*c^2*g*j*l^2 + 408*a^5*b^5*c^2*f*k*l^2 + 384*a^5*b^4*c^3*g*j^2*l - 288*a^5*b^4*c^3*f*j^2*m + 192*a^6*b^2*c^
4*h*j^2*k - 192*a^4*b^5*c^3*g^2*j*l + 96*a^3*b^6*c^3*e^2*k*m - 32*a^5*b^4*c^3*h*j^2*k - 21120*a^6*b^2*c^4*d*k^
2*m + 20880*a^6*b^3*c^3*d*k*m^2 + 19760*a^4*b^3*c^5*d^2*k*m - 12320*a^6*b^3*c^3*e*j*m^2 - 9750*a^5*b^5*c^2*d*k
*m^2 - 9390*a^3*b^5*c^4*d^2*k*m + 8460*a^5*b^4*c^3*d*k^2*m + 3360*a^5*b^5*c^2*e*j*m^2 + 1860*a^2*b^7*c^3*d^2*k
*m - 1218*a^4*b^6*c^2*d*k^2*m - 1088*a^6*b^2*c^4*e*k^2*l + 960*a^6*b^2*c^4*g*j*k^2 - 240*a^5*b^4*c^3*g*j*k^2 +
192*a^5*b^2*c^5*f^2*j*l - 104*a^4*b^5*c^3*g^2*h*m - 96*a^5*b^3*c^4*g^2*h*m + 48*a^5*b^4*c^3*e*k^2*l + 48*a^4*
b^4*c^4*f^2*j*l + 24*a^3*b^7*c^2*g^2*h*m + 16*a^4*b^6*c^2*g*j*k^2 - 16*a^3*b^6*c^3*f^2*j*l + 13376*a^6*b^2*c^4
*d*k*l^2 - 5136*a^5*b^4*c^3*d*k*l^2 - 3840*a^6*b^2*c^4*e*j*l^2 + 1536*a^5*b^4*c^3*e*j*l^2 + 1392*a^5*b^3*c^4*f
*h^2*m + 1386*a^5*b^5*c^2*f*h*m^2 - 768*a^5*b^3*c^4*e*j^2*l + 768*a^4*b^6*c^2*d*k*l^2 - 768*a^4*b^3*c^5*e^2*j*
l - 588*a^4*b^4*c^4*f^2*h*m - 480*a^5*b^3*c^4*g*h^2*l + 480*a^5*b^3*c^4*d*j^2*m - 480*a^5*b^2*c^5*f^2*h*m - 12
8*a^4*b^6*c^2*e*j*l^2 + 100*a^3*b^6*c^3*f^2*h*m + 96*a^5*b^3*c^4*f*j^2*k + 72*a^4*b^5*c^3*g*h^2*l - 54*a^4*b^5
*c^3*f*h^2*m - 48*a^6*b^3*c^3*f*h*m^2 - 36*a^3*b^7*c^2*f*h^2*m + 6*a^2*b^8*c^2*f^2*h*m + 6848*a^4*b^2*c^6*d^2*
j*l - 2448*a^3*b^4*c^5*d^2*j*l + 624*a^5*b^4*c^3*f*h*l^2 + 576*a^6*b^2*c^4*f*h*l^2 + 480*a^5*b^3*c^4*e*j*k^2 +
432*a^4*b^4*c^4*f*g^2*m - 416*a^4*b^3*c^5*e^2*h*m + 336*a^2*b^6*c^4*d^2*j*l - 320*a^5*b^2*c^5*f*g^2*m - 256*a
^4*b^6*c^2*f*h*l^2 + 192*a^5*b^2*c^5*g^2*h*k + 96*a^3*b^5*c^4*e^2*h*m - 72*a^3*b^6*c^3*f*g^2*m + 48*a^4*b^4*c^
4*g^2*h*k - 32*a^4*b^5*c^3*e*j*k^2 - 8*a^3*b^6*c^3*g^2*h*k + 24768*a^6*b^2*c^4*d*h*m^2 - 21108*a^5*b^4*c^3*d*h
*m^2 - 10048*a^4*b^2*c^6*d^2*h*m + 7218*a^4*b^6*c^2*d*h*m^2 - 6720*a^6*b^2*c^4*e*g*m^2 + 6160*a^5*b^4*c^3*e*g*
m^2 - 2592*a^5*b^2*c^5*d*h^2*m - 1680*a^4*b^6*c^2*e*g*m^2 + 1068*a^3*b^4*c^5*d^2*h*m + 960*a^5*b^2*c^5*e*h^2*l
- 876*a^4*b^4*c^4*d*h^2*m - 864*a^5*b^2*c^5*f*h^2*k + 546*a^2*b^6*c^4*d^2*h*m + 432*a^3*b^6*c^3*d*h^2*m + 336
*a^4*b^3*c^5*f^2*h*k - 320*a^5*b^2*c^5*d*j^2*k + 192*a^5*b^2*c^5*g*h^2*j + 144*a^5*b^3*c^4*f*h*k^2 - 144*a^4*b
^4*c^4*e*h^2*l - 102*a^4*b^5*c^3*f*h*k^2 - 96*a^4*b^3*c^5*f^2*g*l - 36*a^2*b^8*c^2*d*h^2*m - 30*a^3*b^5*c^4*f^
2*h*k - 24*a^3*b^5*c^4*f^2*g*l + 16*a^4*b^4*c^4*g*h^2*j - 12*a^4*b^4*c^4*f*h^2*k + 12*a^3*b^6*c^3*f*h^2*k + 8*
a^2*b^7*c^3*f^2*g*l + 6*a^3*b^7*c^2*f*h*k^2 - 2*a^2*b^7*c^3*f^2*h*k - 9312*a^5*b^3*c^4*d*h*l^2 + 3288*a^4*b^5*
c^3*d*h*l^2 - 2304*a^4*b^2*c^6*e^2*g*l + 1920*a^5*b^3*c^4*e*g*l^2 + 1728*a^4*b^2*c^6*e^2*f*m + 1152*a^4*b^3*c^
5*e*g^2*l - 768*a^4*b^5*c^3*e*g*l^2 - 608*a^4*b^3*c^5*d*g^2*m - 472*a^3*b^7*c^2*d*h*l^2 + 384*a^3*b^4*c^5*e^2*
g*l - 288*a^3*b^4*c^5*e^2*f*m - 224*a^4*b^3*c^5*f*g^2*k + 192*a^5*b^2*c^5*f*h*j^2 + 192*a^4*b^2*c^6*e^2*h*k -
192*a^3*b^5*c^4*e*g^2*l + 120*a^3*b^5*c^4*d*g^2*m + 64*a^3*b^7*c^2*e*g*l^2 - 32*a^3*b^4*c^5*e^2*h*k + 24*a^3*b
^5*c^4*f*g^2*k + 9936*a^3*b^3*c^6*d^2*f*m + 3786*a^4*b^5*c^3*d*f*m^2 - 3552*a^5*b^2*c^5*d*h*k^2 - 3486*a^2*b^5
*c^5*d^2*f*m - 3424*a^3*b^3*c^6*d^2*g*l - 1868*a^3*b^7*c^2*d*f*m^2 + 1332*a^4*b^4*c^4*d*h*k^2 - 1296*a^5*b^3*c
^4*d*f*m^2 - 1236*a^3*b^4*c^5*d*f^2*m + 1224*a^2*b^5*c^5*d^2*g*l - 1152*a^4*b^2*c^6*d*f^2*m + 960*a^5*b^2*c^5*
e*g*k^2 - 496*a^3*b^3*c^6*d^2*h*k + 462*a^2*b^6*c^4*d*f^2*m + 432*a^4*b^3*c^5*d*h^2*k - 240*a^4*b^4*c^4*e*g*k^
2 - 222*a^2*b^5*c^5*d^2*h*k + 192*a^4*b^2*c^6*f^2*g*j + 192*a^4*b^2*c^6*e*f^2*l - 174*a^3*b^5*c^4*d*h^2*k - 15
6*a^3*b^6*c^3*d*h*k^2 + 48*a^3*b^4*c^5*e*f^2*l - 32*a^4*b^3*c^5*e*h^2*j + 16*a^3*b^6*c^3*e*g*k^2 + 16*a^3*b^4*
c^5*f^2*g*j - 16*a^2*b^6*c^4*e*f^2*l + 12*a^2*b^7*c^3*d*h^2*k + 6*a^2*b^8*c^2*d*h*k^2 + 1728*a^5*b^2*c^5*d*f*l
^2 + 1392*a^4*b^4*c^4*d*f*l^2 - 840*a^3*b^6*c^3*d*f*l^2 - 768*a^4*b^2*c^6*e*g^2*j + 576*a^4*b^2*c^6*d*g^2*k +
480*a^3*b^3*c^6*d*e^2*m + 144*a^2*b^8*c^2*d*f*l^2 + 96*a^4*b^3*c^5*d*h*j^2 + 96*a^3*b^3*c^6*e^2*f*k - 80*a^3*b
^4*c^5*d*g^2*k + 6848*a^3*b^2*c^7*d^2*e*l - 3552*a^3*b^2*c^7*d^2*f*k - 2448*a^2*b^4*c^6*d^2*e*l + 1332*a^2*b^4
*c^6*d^2*f*k + 960*a^3*b^2*c^7*d^2*g*j - 496*a^4*b^3*c^5*d*f*k^2 + 432*a^3*b^3*c^6*d*f^2*k - 240*a^2*b^4*c^6*d
^2*g*j - 222*a^3*b^5*c^4*d*f*k^2 - 174*a^2*b^5*c^5*d*f^2*k + 64*a^4*b^2*c^6*f*g^2*h + 48*a^3*b^4*c^5*f*g^2*h +
42*a^2*b^7*c^3*d*f*k^2 - 32*a^3*b^3*c^6*e*f^2*j - 320*a^3*b^2*c^7*d*e^2*k + 192*a^4*b^2*c^6*e*g*h^2 + 192*a^4
*b^2*c^6*d*f*j^2 - 32*a^3*b^4*c^5*d*f*j^2 + 16*a^3*b^4*c^5*e*g*h^2 + 480*a^2*b^3*c^7*d^2*e*j - 224*a^3*b^3*c^6
*d*g^2*h + 192*a^3*b^2*c^7*e^2*f*h + 24*a^2*b^5*c^5*d*g^2*h - 864*a^3*b^2*c^7*d*f^2*h + 336*a^3*b^3*c^6*d*f*h^
2 + 192*a^3*b^2*c^7*e*f^2*g + 144*a^2*b^3*c^7*d^2*f*h - 30*a^2*b^5*c^5*d*f*h^2 + 16*a^2*b^4*c^6*e*f^2*g - 12*a
^2*b^4*c^6*d*f^2*h + 192*a^3*b^2*c^7*d*f*g^2 + 96*a^2*b^3*c^7*d*e^2*h + 48*a^2*b^4*c^6*d*f*g^2 + 960*a^2*b^2*c
^8*d^2*e*g + 192*a^2*b^2*c^8*d*e^2*f - 7680*a^9*b*c^2*l^2*m^2 + 3152*a^8*b^3*c*l^2*m^2 + 2070*a^7*b^4*c*k^2*m^
2 - 1840*a^7*b^3*c^2*k^3*m + 6720*a^8*b*c^3*j^2*m^2 - 3072*a^8*b*c^3*k^2*l^2 + 1680*a^6*b^5*c*j^2*m^2 - 100*a^
6*b^5*c*k^2*l^2 - 2176*a^7*b^3*c^2*j*l^3 - 256*a^6*b^3*c^3*j^3*l - 64*a^5*b^6*c*j^2*l^2 - 12480*a^8*b^2*c^2*h*
m^3 + 972*a^5*b^6*c*h^2*m^2 - 960*a^7*b*c^4*j^2*k^2 - 252*a^5*b^4*c^3*h^3*m - 192*a^6*b^2*c^4*h^3*m + 54*a^4*b
^6*c^2*h^3*m + 1536*a^7*b*c^4*h^2*l^2 + 420*a^4*b^7*c*g^2*m^2 - 36*a^4*b^7*c*h^2*l^2 - 3072*a^7*b^2*c^3*g*l^3
+ 2096*a^7*b^3*c^2*f*m^3 + 1088*a^6*b^4*c^2*g*l^3 - 496*a^6*b^3*c^3*h*k^3 - 192*a^4*b^4*c^4*g^3*l + 176*a^4*b^
3*c^5*f^3*m + 144*a^5*b^3*c^4*h^3*k + 78*a^3*b^8*c*f^2*m^2 + 54*a^3*b^5*c^4*f^3*m + 32*a^3*b^6*c^3*g^3*l + 30*
a^5*b^5*c^2*h*k^3 - 18*a^4*b^5*c^3*h^3*k - 18*a^2*b^7*c^3*f^3*m - 16*a^3*b^8*c*g^2*l^2 + 6720*a^6*b*c^5*e^2*m^
2 - 192*a^6*b*c^5*h^2*j^2 - 4*a^2*b^9*c*f^2*l^2 - 35040*a^7*b^2*c^3*d*m^3 + 14300*a^6*b^4*c^2*d*m^3 - 12000*a^
3*b^2*c^7*d^3*m + 4380*a^2*b^4*c^6*d^3*m - 2176*a^6*b^3*c^3*e*l^3 - 256*a^3*b^3*c^6*e^3*l - 192*a^6*b^2*c^4*f*
k^3 + 192*a^5*b^5*c^2*e*l^3 - 192*a^4*b^2*c^6*f^3*k + 132*a^5*b^4*c^3*f*k^3 + 128*a^4*b^3*c^5*g^3*j - 28*a^3*b
^4*c^5*f^3*k - 10*a^4*b^6*c^2*f*k^3 + 6*a^2*b^6*c^4*f^3*k + 10752*a^5*b*c^6*d^2*l^2 - 960*a^5*b*c^6*e^2*k^2 -
192*a^5*b*c^6*f^2*j^2 + 108*a*b^9*c^2*d^2*l^2 - 1680*a^5*b^3*c^4*d*k^3 - 1680*a^2*b^3*c^7*d^3*k + 222*a^4*b^5*
c^3*d*k^3 + 30*a*b^8*c^3*d^2*k^2 - 10*a^3*b^7*c^2*d*k^3 - 960*a^4*b*c^7*d^2*j^2 + 80*a^4*b^3*c^5*f*h^3 + 80*a^
3*b^3*c^6*f^3*h + 6*a^3*b^5*c^4*f*h^3 + 6*a^2*b^5*c^5*f^3*h - 192*a^4*b*c^7*e^2*h^2 - 192*a^4*b^2*c^6*d*h^3 -
192*a^2*b^2*c^8*d^3*h + 128*a^3*b^3*c^6*e*g^3 - 28*a^3*b^4*c^5*d*h^3 + 12*a*b^6*c^5*d^2*h^2 + 6*a^2*b^6*c^4*d*
h^3 - 192*a^3*b*c^8*e^2*f^2 + 60*a*b^5*c^6*d^2*g^2 + 198*a*b^4*c^7*d^2*f^2 + 144*a^2*b^3*c^7*d*f^3 - 960*a^2*b
*c^9*d^2*e^2 + 240*a*b^3*c^8*d^2*e^2 + 15360*a^9*c^3*k*l^2*m - 12800*a^9*c^3*j*l*m^2 - 3840*a^8*c^4*j^2*k*m +
432*a^6*b^6*j*l*m^2 + 4608*a^8*c^4*j*k^2*l + 2880*a^8*c^4*h*k^2*m + 5120*a^8*c^4*f*l^2*m - 3072*a^8*c^4*h*k*l^
2 + 270*a^5*b^7*h*k*m^2 - 216*a^5*b^7*g*l*m^2 - 12800*a^8*c^4*e*l*m^2 - 4800*a^8*c^4*f*k*m^2 - 512*a^7*c^5*h^2
*j*l - 3840*a^6*c^6*e^2*k*m - 1280*a^7*c^5*f*j^2*m + 768*a^7*c^5*h*j^2*k + 144*a^4*b^8*g*j*m^2 - 90*a^4*b^8*f*
k*m^2 + 8640*a^7*c^5*d*k^2*m + 4608*a^7*c^5*e*k^2*l + 512*a^6*c^6*f^2*j*l - 9216*a^7*c^5*d*k*l^2 - 4096*a^7*c^
5*e*j*l^2 + 320*a^6*c^6*f^2*h*m - 90*a^3*b^9*d*k*m^2 + 15200*a^9*b*c^2*k*m^3 - 6192*a^8*b^3*c*k*m^3 + 5472*a^8
*b*c^3*k^3*m - 4608*a^5*c^7*d^2*j*l - 1024*a^7*c^5*f*h*l^2 + 150*a^6*b^5*c*k^3*m + 54*a^3*b^9*f*h*m^2 + 6*b^10
*c^2*d^2*h*m - 14400*a^7*c^5*d*h*m^2 + 8640*a^5*c^7*d^2*h*m + 2880*a^6*c^6*d*h^2*m + 2304*a^6*c^6*d*j^2*k - 51
2*a^6*c^6*e*h^2*l - 192*a^6*c^6*f*h^2*k + 6144*a^8*b*c^3*j*l^3 + 1536*a^7*b*c^4*j^3*l - 1280*a^5*c^7*e^2*f*m +
768*a^5*c^7*e^2*h*k + 256*a^6*c^6*f*h*j^2 + 192*a^6*b^5*c*j*l^3 + 54*a^2*b^10*d*h*m^2 - 18*b^9*c^3*d^2*f*m +
8*b^9*c^3*d^2*g*l - 2*b^9*c^3*d^2*h*k + 4068*a^7*b^4*c*h*m^3 - 1728*a^6*c^6*d*h*k^2 + 960*a^5*c^7*d*f^2*m + 51
2*a^5*c^7*e*f^2*l - 3072*a^6*c^6*d*f*l^2 - 16*b^8*c^4*d^2*e*l + 6*b^8*c^4*d^2*f*k - 4608*a^4*c^8*d^2*e*l + 240
0*a^8*b*c^3*f*m^3 + 2016*a^7*b*c^4*h*k^3 - 1728*a^4*c^8*d^2*f*k - 1146*a^6*b^5*c*f*m^3 + 224*a^6*b*c^5*h^3*k -
96*a^5*b^6*c*g*l^3 + 96*a^5*b*c^6*f^3*m + 2304*a^4*c^8*d*e^2*k + 768*a^5*c^7*d*f*j^2 + 6144*a^7*b*c^4*e*l^3 -
2280*a^5*b^6*c*d*m^3 + 1536*a^4*b*c^7*e^3*l - 616*a*b^6*c^5*d^3*m + 512*a^6*b*c^5*g*j^3 + 256*a^4*c^8*e^2*f*h
+ 240*a*b^10*c*d^2*m^2 + 6*b^7*c^5*d^2*f*h - 192*a^4*c^8*d*f^2*h + 4320*a^6*b*c^5*d*k^3 + 4320*a^3*b*c^8*d^3*
k + 222*a*b^5*c^6*d^3*k + 16*b^6*c^6*d^2*e*g + 96*a^5*b*c^6*f*h^3 + 96*a^4*b*c^7*f^3*h + 768*a^3*c^9*d*e^2*f +
512*a^3*b*c^8*e^3*g + 132*a*b^4*c^7*d^3*h + 2016*a^2*b*c^9*d^3*f - 496*a*b^3*c^8*d^3*f + 224*a^3*b*c^8*d*f^3
- 18*a*b^5*c^6*d*f^3 - 3264*a^8*b^2*c^2*k^2*m^2 - 6160*a^7*b^3*c^2*j^2*m^2 + 1104*a^7*b^3*c^2*k^2*l^2 - 1920*a
^7*b^2*c^3*j^2*l^2 + 768*a^6*b^4*c^2*j^2*l^2 + 3888*a^7*b^2*c^3*h^2*m^2 - 3510*a^6*b^4*c^2*h^2*m^2 + 240*a^6*b
^3*c^3*j^2*k^2 - 16*a^5*b^5*c^2*j^2*k^2 + 1680*a^6*b^3*c^3*g^2*m^2 - 1648*a^6*b^3*c^3*h^2*l^2 - 1540*a^5*b^5*c
^2*g^2*m^2 + 444*a^5*b^5*c^2*h^2*l^2 - 960*a^6*b^2*c^4*h^2*k^2 - 576*a^6*b^2*c^4*f^2*m^2 - 512*a^6*b^2*c^4*g^2
*l^2 - 480*a^5*b^4*c^3*g^2*l^2 + 198*a^5*b^4*c^3*h^2*k^2 + 192*a^4*b^6*c^2*g^2*l^2 - 186*a^5*b^4*c^3*f^2*m^2 -
97*a^4*b^6*c^2*f^2*m^2 - 9*a^4*b^6*c^2*h^2*k^2 - 6160*a^5*b^3*c^4*e^2*m^2 + 1680*a^4*b^5*c^3*e^2*m^2 - 240*a^
5*b^3*c^4*g^2*k^2 - 240*a^5*b^3*c^4*f^2*l^2 - 144*a^3*b^7*c^2*e^2*m^2 + 60*a^4*b^5*c^3*g^2*k^2 - 36*a^4*b^5*c^
3*f^2*l^2 + 36*a^3*b^7*c^2*f^2*l^2 - 16*a^5*b^3*c^4*h^2*j^2 - 4*a^3*b^7*c^2*g^2*k^2 + 38512*a^5*b^2*c^5*d^2*m^
2 - 32310*a^4*b^4*c^4*d^2*m^2 + 12720*a^3*b^6*c^3*d^2*m^2 - 2500*a^2*b^8*c^2*d^2*m^2 - 1920*a^5*b^2*c^5*e^2*l^
2 + 768*a^4*b^4*c^4*e^2*l^2 - 464*a^5*b^2*c^5*f^2*k^2 - 384*a^5*b^2*c^5*g^2*j^2 - 64*a^3*b^6*c^3*e^2*l^2 + 42*
a^4*b^4*c^4*f^2*k^2 + 12*a^3*b^6*c^3*f^2*k^2 - 13104*a^4*b^3*c^5*d^2*l^2 + 5628*a^3*b^5*c^4*d^2*l^2 - 1128*a^2
*b^7*c^3*d^2*l^2 + 240*a^4*b^3*c^5*e^2*k^2 - 16*a^4*b^3*c^5*f^2*j^2 - 16*a^3*b^5*c^4*e^2*k^2 - 2880*a^4*b^2*c^
6*d^2*k^2 + 1750*a^3*b^4*c^5*d^2*k^2 - 345*a^2*b^6*c^4*d^2*k^2 - 48*a^4*b^3*c^5*g^2*h^2 - 4*a^3*b^5*c^4*g^2*h^
2 + 240*a^3*b^3*c^6*d^2*j^2 - 192*a^4*b^2*c^6*f^2*h^2 - 42*a^3*b^4*c^5*f^2*h^2 - 16*a^2*b^5*c^5*d^2*j^2 - 48*a
^3*b^3*c^6*f^2*g^2 - 16*a^3*b^3*c^6*e^2*h^2 - 4*a^2*b^5*c^5*f^2*g^2 - 464*a^3*b^2*c^7*d^2*h^2 - 384*a^3*b^2*c^
7*e^2*g^2 + 42*a^2*b^4*c^6*d^2*h^2 - 240*a^2*b^3*c^7*d^2*g^2 - 16*a^2*b^3*c^7*e^2*f^2 - 960*a^2*b^2*c^8*d^2*f^
2 + 6*b^11*c*d^2*k*m - 18*a*b^11*d*f*m^2 - 7200*a^9*c^3*k^2*m^2 - 324*a^7*b^5*l^2*m^2 - 225*a^6*b^6*k^2*m^2 -
2048*a^8*c^4*j^2*l^2 - 144*a^5*b^7*j^2*m^2 - 2400*a^8*c^4*h^2*m^2 - 81*a^4*b^8*h^2*m^2 - 800*a^7*c^5*f^2*m^2 -
288*a^7*c^5*h^2*k^2 - 36*a^3*b^9*g^2*m^2 - 9*a^2*b^10*f^2*m^2 - 21600*a^6*c^6*d^2*m^2 - 2048*a^6*c^6*e^2*l^2
- 864*a^6*c^6*f^2*k^2 - 2592*a^5*c^7*d^2*k^2 - 1536*a^5*c^7*e^2*j^2 + 1536*a^8*b^2*c^2*l^4 - 32*a^5*c^7*f^2*h^
2 + 360*a^7*b^2*c^3*k^4 - 25*a^6*b^4*c^2*k^4 - 864*a^4*c^8*d^2*h^2 - 4*b^7*c^5*d^2*g^2 - 9*b^6*c^6*d^2*f^2 - 2
88*a^3*c^9*d^2*f^2 - 24*a^5*b^2*c^5*h^4 - 16*b^5*c^7*d^2*e^2 - 9*a^4*b^4*c^4*h^4 - 16*a^3*b^4*c^5*g^4 - 24*a^3
*b^2*c^7*f^4 - 9*a^2*b^4*c^6*f^4 - a^2*b^8*c^2*f^2*k^2 - a^2*b^6*c^4*f^2*h^2 + 630*a^7*b^5*k*m^3 + 8000*a^9*c^
3*h*m^3 + 320*a^7*c^5*h^3*m - 378*a^6*b^6*h*m^3 + 126*a^5*b^7*f*m^3 + 30*b^8*c^4*d^3*m + 24000*a^8*c^4*d*m^3 +
8640*a^4*c^8*d^3*m - 1728*a^7*c^5*f*k^3 - 192*a^5*c^7*f^3*k - 4*b^11*c*d^2*l^2 + 126*a^4*b^8*d*m^3 - 10*b^7*c
^5*d^3*k + 4200*a^9*b^2*c*m^4 - 1024*a^6*c^6*e*j^3 - 1024*a^4*c^8*e^3*j - 144*a^7*b^4*c*l^4 - 10*b^6*c^6*d^3*h
- 1728*a^3*c^9*d^3*h - 192*a^5*c^7*d*h^3 + 30*b^5*c^7*d^3*f + 360*a*b^2*c^9*d^4 - 9*b^12*d^2*m^2 - 10000*a^10
*c^2*m^4 - 4096*a^9*c^3*l^4 - 441*a^8*b^4*m^4 - 1296*a^8*c^4*k^4 - 256*a^7*c^5*j^4 - 16*a^6*c^6*h^4 - 16*a^4*c
^8*f^4 - 256*a^3*c^9*e^4 - 25*b^4*c^8*d^4 - 1296*a^2*c^10*d^4 - b^10*c^2*d^2*k^2 - b^8*c^4*d^2*h^2, z, k1)*x*(
8192*a^6*b*c^9 + 32*a^2*b^9*c^5 - 512*a^3*b^7*c^6 + 3072*a^4*b^5*c^7 - 8192*a^5*b^3*c^8))/(4*(64*a^5*c^6 - a^2
*b^6*c^3 + 12*a^3*b^4*c^4 - 48*a^4*b^2*c^5))) + (x*(2*b^6*c^6*d^2 - 576*a^3*c^9*d^2 + 64*a^4*c^8*f^2 - 64*a^5*
c^7*h^2 + 576*a^6*c^6*k^2 + 18*a^2*b^10*m^2 - 1600*a^7*c^5*m^2 - 36*a*b^4*c^7*d^2 + 128*a^3*b*c^8*e^2 + 128*a^
5*b*c^6*j^2 + 8*a^2*b^9*c*l^2 + 3072*a^6*b*c^5*l^2 - 300*a^3*b^8*c*m^2 + 256*a^2*b^2*c^8*d^2 - 32*a^2*b^3*c^7*
e^2 + 20*a^2*b^4*c^6*f^2 - 96*a^3*b^2*c^7*f^2 - 8*a^2*b^5*c^5*g^2 + 32*a^3*b^3*c^6*g^2 + 2*a^2*b^6*c^4*h^2 - 4
*a^3*b^4*c^5*h^2 - 32*a^4*b^3*c^5*j^2 + 2*a^2*b^8*c^2*k^2 - 40*a^3*b^6*c^3*k^2 + 276*a^4*b^4*c^4*k^2 - 736*a^5
*b^2*c^5*k^2 - 136*a^3*b^7*c^2*l^2 + 888*a^4*b^5*c^3*l^2 - 2656*a^5*b^3*c^4*l^2 + 1874*a^4*b^6*c^2*m^2 - 5284*
a^5*b^4*c^3*m^2 + 6144*a^6*b^2*c^4*m^2 - 384*a^4*c^8*d*h + 1920*a^5*c^7*d*m - 1024*a^5*c^7*e*l + 384*a^5*c^7*f
*k + 640*a^6*c^6*h*m - 1024*a^6*c^6*j*l + 4*a*b^5*c^6*d*f + 320*a^3*b*c^8*d*f + 64*a^4*b*c^7*f*h + 576*a^4*b*c
^7*d*k + 256*a^4*b*c^7*e*j - 1472*a^5*b*c^6*f*m + 512*a^5*b*c^6*g*l + 64*a^5*b*c^6*h*k - 12*a^2*b^9*c*k*m - 37
76*a^6*b*c^5*k*m - 96*a^2*b^3*c^7*d*f + 8*a^2*b^4*c^6*d*h + 32*a^2*b^4*c^6*e*g + 64*a^3*b^2*c^7*d*h - 128*a^3*
b^2*c^7*e*g - 12*a^2*b^5*c^5*f*h + 32*a^3*b^3*c^6*f*h + 20*a^2*b^5*c^5*d*k - 224*a^3*b^3*c^6*d*k - 64*a^3*b^3*
c^6*e*j - 60*a^2*b^6*c^4*d*m - 12*a^2*b^6*c^4*f*k + 632*a^3*b^4*c^5*d*m - 32*a^3*b^4*c^5*e*l + 152*a^3*b^4*c^5
*f*k + 32*a^3*b^4*c^5*g*j - 2048*a^4*b^2*c^6*d*m + 384*a^4*b^2*c^6*e*l - 512*a^4*b^2*c^6*f*k - 128*a^4*b^2*c^6
*g*j + 36*a^2*b^7*c^3*f*m + 4*a^2*b^7*c^3*h*k - 396*a^3*b^5*c^4*f*m + 16*a^3*b^5*c^4*g*l - 44*a^3*b^5*c^4*h*k
+ 1376*a^4*b^3*c^5*f*m - 192*a^4*b^3*c^5*g*l + 96*a^4*b^3*c^5*h*k - 12*a^2*b^8*c^2*h*m + 112*a^3*b^6*c^3*h*m -
248*a^4*b^4*c^4*h*m - 192*a^5*b^2*c^5*h*m - 32*a^4*b^4*c^4*j*l + 384*a^5*b^2*c^5*j*l + 220*a^3*b^7*c^2*k*m -
1436*a^4*b^5*c^3*k*m + 3936*a^5*b^3*c^4*k*m))/(4*(64*a^5*c^6 - a^2*b^6*c^3 + 12*a^3*b^4*c^4 - 48*a^4*b^2*c^5))
) - (5*b^3*c^7*d^3 + 8*a^3*c^7*f^3 + 216*a^6*c^4*k^3 - 63*a^5*b^5*m^3 - 96*a^2*c^8*d*e^2 + 72*a^2*c^8*d^2*f -
4*a^4*b*c^5*h^3 - 3*b^4*c^6*d^2*f - 32*a^3*c^7*e^2*h + b^5*c^5*d^2*h - 96*a^4*c^6*d*j^2 + 8*a^4*c^6*f*h^2 + 21
6*a^3*c^7*d^2*k + 573*a^6*b^3*c*m^3 - 1300*a^7*b*c^2*m^3 + 384*a^5*c^5*d*l^2 + b^6*c^4*d^2*k + 72*a^4*c^6*f^2*
k + 216*a^5*c^5*f*k^2 + 9*a^2*b^8*f*m^2 + 160*a^4*c^6*e^2*m - 32*a^5*c^5*h*j^2 - 3*b^7*c^3*d^2*m + 24*a^5*c^5*
h^2*k + 200*a^6*c^4*f*m^2 - 27*a^3*b^7*h*m^2 + 128*a^6*c^4*h*l^2 + 45*a^4*b^6*k*m^2 + 160*a^6*c^4*j^2*m + 600*
a^7*c^3*k*m^2 - 640*a^7*c^3*l^2*m + 6*a^2*b^2*c^6*f^3 - 3*a^3*b^3*c^4*h^3 + 5*a^4*b^4*c^2*k^3 - 66*a^5*b^2*c^3
*k^3 - 36*a*b*c^8*d^3 + 9*a*b^9*d*m^2 + 4*a*b^8*c*d*l^2 + 48*a^3*c^7*d*f*h - 192*a^3*c^7*d*e*j - 240*a^4*c^6*d
*f*m + 144*a^4*c^6*d*h*k - 128*a^4*c^6*e*f*l - 64*a^4*c^6*e*h*j - 80*a^5*c^5*f*h*m - 720*a^5*c^5*d*k*m + 320*a
^5*c^5*e*j*m - 384*a^5*c^5*e*k*l - 128*a^5*c^5*f*j*l - 240*a^6*c^4*h*k*m - 384*a^6*c^4*j*k*l + 16*a*b^2*c^7*d*
e^2 + 18*a*b^2*c^7*d^2*f + 3*a*b^3*c^6*d*f^2 - 60*a^2*b*c^7*d*f^2 + 4*a*b^4*c^5*d*g^2 + 16*a^2*b*c^7*e^2*f - a
*b^3*c^6*d^2*h + a*b^5*c^4*d*h^2 - 60*a^2*b*c^7*d^2*h - 28*a^3*b*c^6*d*h^2 - 28*a^3*b*c^6*f^2*h - 10*a*b^4*c^5
*d^2*k + a*b^7*c^2*d*k^2 - 396*a^4*b*c^5*d*k^2 + 16*a^3*b*c^6*e^2*k + 16*a^4*b*c^5*f*j^2 + 25*a*b^5*c^4*d^2*m
- 159*a^2*b^7*c*d*m^2 - 348*a^3*b*c^6*d^2*m + 1460*a^5*b*c^4*d*m^2 + 4*a^2*b^7*c*f*l^2 + 128*a^5*b*c^4*f*l^2 -
78*a^3*b^6*c*f*m^2 - 76*a^4*b*c^5*f^2*m - 204*a^5*b*c^4*h*k^2 - 12*a^3*b^6*c*h*l^2 + 279*a^4*b^5*c*h*m^2 - 12
*a^5*b*c^4*h^2*m + 16*a^5*b*c^4*j^2*k + 420*a^6*b*c^3*h*m^2 + 20*a^4*b^5*c*k*l^2 + 512*a^6*b*c^3*k*l^2 - 30*a^
4*b^5*c*k^2*m - 402*a^5*b^4*c*k*m^2 - 924*a^6*b*c^3*k^2*m - 28*a^5*b^4*c*l^2*m - 24*a^2*b^2*c^6*d*g^2 - 9*a^2*
b^3*c^5*d*h^2 + 4*a^2*b^3*c^5*f*g^2 - 5*a^2*b^3*c^5*f^2*h + a^2*b^4*c^4*f*h^2 + 16*a^3*b^2*c^5*d*j^2 + 18*a^3*
b^2*c^5*f*h^2 - 6*a^2*b^2*c^6*d^2*k - 21*a^2*b^5*c^3*d*k^2 - 8*a^3*b^2*c^5*g^2*h + 155*a^3*b^3*c^4*d*k^2 - 72*
a^2*b^6*c^2*d*l^2 + 436*a^3*b^4*c^3*d*l^2 - 952*a^4*b^2*c^4*d*l^2 + 23*a^2*b^3*c^5*d^2*m - 5*a^2*b^4*c^4*f^2*k
+ a^2*b^6*c^2*f*k^2 + 26*a^3*b^2*c^5*f^2*k - 12*a^3*b^4*c^3*f*k^2 + 970*a^3*b^5*c^2*d*m^2 + 2*a^4*b^2*c^4*f*k
^2 - 2289*a^4*b^3*c^3*d*m^2 - 48*a^3*b^2*c^5*e^2*m + 4*a^3*b^3*c^4*g^2*k - 36*a^3*b^5*c^2*f*l^2 + 52*a^4*b^3*c
^3*f*l^2 + 15*a^2*b^5*c^3*f^2*m - 53*a^3*b^3*c^4*f^2*m - 6*a^3*b^4*c^3*h^2*k - 3*a^3*b^5*c^2*h*k^2 + 42*a^4*b^
2*c^4*h^2*k + 51*a^4*b^3*c^3*h*k^2 + 133*a^4*b^4*c^2*f*m^2 + 114*a^5*b^2*c^3*f*m^2 - 12*a^3*b^4*c^3*g^2*m + 40
*a^4*b^2*c^4*g^2*m + 128*a^4*b^4*c^2*h*l^2 - 360*a^5*b^2*c^3*h*l^2 + 18*a^3*b^5*c^2*h^2*m - 81*a^4*b^3*c^3*h^2
*m - 801*a^5*b^3*c^2*h*m^2 - 48*a^5*b^2*c^3*j^2*m - 204*a^5*b^3*c^2*k*l^2 + 339*a^5*b^3*c^2*k^2*m + 762*a^6*b^
2*c^2*k*m^2 + 264*a^6*b^2*c^2*l^2*m - 6*a*b^8*c*d*k*m - 16*a*b^3*c^6*d*e*g + 96*a^2*b*c^7*d*e*g - 4*a*b^4*c^5*
d*f*h + 32*a^3*b*c^6*e*g*h + 16*a*b^5*c^4*d*e*l - 4*a*b^5*c^4*d*f*k + 544*a^3*b*c^6*d*e*l - 312*a^3*b*c^6*d*f*
k + 96*a^3*b*c^6*d*g*j + 32*a^3*b*c^6*e*f*j + 12*a*b^6*c^3*d*f*m - 8*a*b^6*c^3*d*g*l + 2*a*b^6*c^3*d*h*k - 6*a
*b^7*c^2*d*h*m - 152*a^4*b*c^5*d*h*m - 160*a^4*b*c^5*e*g*m + 224*a^4*b*c^5*e*h*l + 64*a^4*b*c^5*f*g*l - 152*a^
4*b*c^5*f*h*k + 32*a^4*b*c^5*g*h*j + 544*a^4*b*c^5*d*j*l + 32*a^4*b*c^5*e*j*k - 6*a^2*b^7*c*f*k*m + 32*a^5*b*c
^4*e*l*m - 536*a^5*b*c^4*f*k*m - 160*a^5*b*c^4*g*j*m + 192*a^5*b*c^4*g*k*l + 224*a^5*b*c^4*h*j*l + 18*a^3*b^6*
c*h*k*m + 32*a^6*b*c^3*j*l*m + 52*a^2*b^2*c^6*d*f*h - 16*a^2*b^2*c^6*e*f*g + 32*a^2*b^2*c^6*d*e*j - 192*a^2*b^
3*c^5*d*e*l + 70*a^2*b^3*c^5*d*f*k - 16*a^2*b^3*c^5*d*g*j - 190*a^2*b^4*c^4*d*f*m + 96*a^2*b^4*c^4*d*g*l - 30*
a^2*b^4*c^4*d*h*k + 16*a^2*b^4*c^4*e*f*l + 676*a^3*b^2*c^5*d*f*m - 272*a^3*b^2*c^5*d*g*l + 100*a^3*b^2*c^5*d*h
*k - 48*a^3*b^2*c^5*e*f*l - 16*a^3*b^2*c^5*e*g*k - 16*a^3*b^2*c^5*f*g*j + 80*a^2*b^5*c^3*d*h*m - 8*a^2*b^5*c^3
*f*g*l + 2*a^2*b^5*c^3*f*h*k - 210*a^3*b^3*c^4*d*h*m + 48*a^3*b^3*c^4*e*g*m - 48*a^3*b^3*c^4*e*h*l + 24*a^3*b^
3*c^4*f*g*l + 6*a^3*b^3*c^4*f*h*k + 16*a^2*b^5*c^3*d*j*l - 192*a^3*b^3*c^4*d*j*l - 6*a^2*b^6*c^2*f*h*m - 28*a^
3*b^4*c^3*f*h*m + 24*a^3*b^4*c^3*g*h*l + 276*a^4*b^2*c^4*f*h*m - 112*a^4*b^2*c^4*g*h*l + 116*a^2*b^6*c^2*d*k*m
- 780*a^3*b^4*c^3*d*k*m + 16*a^3*b^4*c^3*f*j*l + 1876*a^4*b^2*c^4*d*k*m - 96*a^4*b^2*c^4*e*j*m + 80*a^4*b^2*c
^4*e*k*l - 48*a^4*b^2*c^4*f*j*l - 16*a^4*b^2*c^4*g*j*k + 62*a^3*b^5*c^2*f*k*m - 42*a^4*b^3*c^3*f*k*m + 48*a^4*
b^3*c^3*g*j*m - 40*a^4*b^3*c^3*g*k*l - 48*a^4*b^3*c^3*h*j*l - 246*a^4*b^4*c^2*h*k*m - 16*a^5*b^2*c^3*g*l*m + 8
04*a^5*b^2*c^3*h*k*m + 80*a^5*b^2*c^3*j*k*l)/(8*(64*a^5*c^6 - a^2*b^6*c^3 + 12*a^3*b^4*c^4 - 48*a^4*b^2*c^5))
+ (x*(32*a^2*c^8*e^3 + 32*a^5*c^5*j^3 - 2*b^3*c^7*d^2*e + b^4*c^6*d^2*g - 12*a^4*b^5*c*l^3 - 320*a^6*b*c^3*l^3
+ 96*a^3*c^7*e^2*j + 96*a^4*c^6*e*j^2 + 144*a^3*c^7*d^2*l + 128*a^5*c^5*e*l^2 - b^6*c^4*d^2*l - 16*a^4*c^6*f^
2*l - 9*a^2*b^8*g*m^2 + 16*a^5*c^5*h^2*l + 18*a^3*b^7*j*m^2 + 128*a^6*c^4*j*l^2 - 144*a^6*c^4*k^2*l - 27*a^4*b
^6*l*m^2 + 400*a^7*c^3*l*m^2 - 4*a^2*b^3*c^5*g^3 + 124*a^5*b^3*c^2*l^3 + 24*a*b*c^8*d^2*e - 48*a^2*c^8*d*e*f -
16*a^3*c^7*e*f*h - 144*a^3*c^7*d*e*k - 48*a^3*c^7*d*f*j + 96*a^4*c^6*d*h*l + 80*a^4*c^6*e*f*m - 48*a^4*c^6*e*
h*k - 16*a^4*c^6*f*h*j - 144*a^4*c^6*d*j*k - 480*a^5*c^5*d*l*m + 240*a^5*c^5*e*k*m + 80*a^5*c^5*f*j*m - 96*a^5
*c^5*f*k*l - 48*a^5*c^5*h*j*k - 160*a^6*c^4*h*l*m + 240*a^6*c^4*j*k*m - 12*a*b^2*c^7*d^2*g + 16*a^2*b*c^7*e*f^
2 - 48*a^2*b*c^7*e^2*g + 8*a^3*b*c^6*e*h^2 - 2*a*b^3*c^6*d^2*j + 24*a^2*b*c^7*d^2*j + 18*a*b^4*c^5*d^2*l + 16*
a^3*b*c^6*f^2*j + 96*a^4*b*c^5*e*k^2 - 176*a^3*b*c^6*e^2*l - 48*a^4*b*c^5*g*j^2 + 18*a^2*b^7*c*e*m^2 + 8*a^4*b
*c^5*h^2*j - 520*a^5*b*c^4*e*m^2 - 4*a^2*b^7*c*g*l^2 - 64*a^5*b*c^4*g*l^2 + 96*a^3*b^6*c*g*m^2 + 96*a^5*b*c^4*
j*k^2 + 8*a^3*b^6*c*j*l^2 - 176*a^5*b*c^4*j^2*l - 192*a^4*b^5*c*j*m^2 - 520*a^6*b*c^3*j*m^2 + 270*a^5*b^4*c*l*
m^2 + 24*a^2*b^2*c^6*e*g^2 - 8*a^2*b^2*c^6*f^2*g + 2*a^2*b^3*c^5*e*h^2 - a^2*b^4*c^4*g*h^2 - 4*a^3*b^2*c^5*g*h
^2 - 100*a^2*b^2*c^6*d^2*l + 2*a^2*b^5*c^3*e*k^2 - 28*a^3*b^3*c^4*e*k^2 + 32*a^2*b^3*c^5*e^2*l + 8*a^2*b^6*c^2
*e*l^2 + 24*a^3*b^2*c^5*g^2*j - 88*a^3*b^4*c^3*e*l^2 + 216*a^4*b^2*c^4*e*l^2 - a^2*b^4*c^4*f^2*l - a^2*b^6*c^2
*g*k^2 + 2*a^3*b^3*c^4*h^2*j + 14*a^3*b^4*c^3*g*k^2 - 192*a^3*b^5*c^2*e*m^2 - 48*a^4*b^2*c^4*g*k^2 + 614*a^4*b
^3*c^3*e*m^2 + 8*a^2*b^5*c^3*g^2*l - 44*a^3*b^3*c^4*g^2*l + 44*a^3*b^5*c^2*g*l^2 - 108*a^4*b^3*c^3*g*l^2 - 12*
a^4*b^2*c^4*h^2*l - 307*a^4*b^4*c^2*g*m^2 + 260*a^5*b^2*c^3*g*m^2 + 2*a^3*b^5*c^2*j*k^2 - 28*a^4*b^3*c^3*j*k^2
+ 32*a^4*b^3*c^3*j^2*l - 88*a^4*b^4*c^2*j*l^2 + 216*a^5*b^2*c^3*j*l^2 - 3*a^4*b^4*c^2*k^2*l + 40*a^5*b^2*c^3*
k^2*l + 614*a^5*b^3*c^2*j*m^2 - 756*a^6*b^2*c^2*l*m^2 - 4*a*b^2*c^7*d*e*f + 2*a*b^3*c^6*d*f*g + 32*a^2*b*c^7*d
*e*h + 24*a^2*b*c^7*d*f*g + 8*a^3*b*c^6*f*g*h - 2*a*b^5*c^4*d*f*l + 272*a^3*b*c^6*d*e*m - 8*a^3*b*c^6*d*f*l +
72*a^3*b*c^6*d*g*k + 32*a^3*b*c^6*d*h*j + 80*a^3*b*c^6*e*f*k - 96*a^3*b*c^6*e*g*j + 64*a^4*b*c^5*e*h*m - 40*a^
4*b*c^5*f*g*m + 8*a^4*b*c^5*f*h*l + 24*a^4*b*c^5*g*h*k + 272*a^4*b*c^5*d*j*m + 72*a^4*b*c^5*d*k*l - 352*a^4*b*
c^5*e*j*l + 80*a^4*b*c^5*f*j*k + 6*a^2*b^7*c*g*k*m + 248*a^5*b*c^4*f*l*m - 120*a^5*b*c^4*g*k*m + 64*a^5*b*c^4*
h*j*m + 56*a^5*b*c^4*h*k*l - 12*a^3*b^6*c*j*k*m + 18*a^4*b^5*c*k*l*m + 584*a^6*b*c^3*k*l*m - 16*a^2*b^2*c^6*d*
g*h - 12*a^2*b^2*c^6*e*f*h + 20*a^2*b^2*c^6*d*e*k - 4*a^2*b^2*c^6*d*f*j + 6*a^2*b^3*c^5*f*g*h - 60*a^2*b^3*c^5
*d*e*m + 18*a^2*b^3*c^5*d*f*l - 10*a^2*b^3*c^5*d*g*k - 12*a^2*b^3*c^5*e*f*k + 30*a^2*b^4*c^4*d*g*m + 6*a^2*b^4
*c^4*d*h*l + 36*a^2*b^4*c^4*e*f*m - 32*a^2*b^4*c^4*e*g*l + 4*a^2*b^4*c^4*e*h*k + 6*a^2*b^4*c^4*f*g*k - 136*a^3
*b^2*c^5*d*g*m - 64*a^3*b^2*c^5*d*h*l - 180*a^3*b^2*c^5*e*f*m + 176*a^3*b^2*c^5*e*g*l - 20*a^3*b^2*c^5*e*h*k -
40*a^3*b^2*c^5*f*g*k - 12*a^3*b^2*c^5*f*h*j + 20*a^3*b^2*c^5*d*j*k - 12*a^2*b^5*c^3*e*h*m - 18*a^2*b^5*c^3*f*
g*m - 2*a^2*b^5*c^3*g*h*k + 40*a^3*b^3*c^4*e*h*m + 90*a^3*b^3*c^4*f*g*m + 6*a^3*b^3*c^4*f*h*l + 10*a^3*b^3*c^4
*g*h*k - 60*a^3*b^3*c^4*d*j*m - 10*a^3*b^3*c^4*d*k*l + 64*a^3*b^3*c^4*e*j*l - 12*a^3*b^3*c^4*f*j*k + 6*a^2*b^6
*c^2*g*h*m - 20*a^3*b^4*c^3*g*h*m - 32*a^4*b^2*c^4*g*h*m - 12*a^2*b^6*c^2*e*k*m + 148*a^3*b^4*c^3*e*k*m + 36*a
^3*b^4*c^3*f*j*m - 32*a^3*b^4*c^3*g*j*l + 4*a^3*b^4*c^3*h*j*k + 104*a^4*b^2*c^4*d*l*m - 476*a^4*b^2*c^4*e*k*m
- 180*a^4*b^2*c^4*f*j*m + 8*a^4*b^2*c^4*f*k*l + 176*a^4*b^2*c^4*g*j*l - 20*a^4*b^2*c^4*h*j*k - 74*a^3*b^5*c^2*
g*k*m - 12*a^3*b^5*c^2*h*j*m - 54*a^4*b^3*c^3*f*l*m + 238*a^4*b^3*c^3*g*k*m + 40*a^4*b^3*c^3*h*j*m - 6*a^4*b^3
*c^3*h*k*l + 18*a^4*b^4*c^2*h*l*m - 48*a^5*b^2*c^3*h*l*m + 148*a^4*b^4*c^2*j*k*m - 476*a^5*b^2*c^3*j*k*m - 210
*a^5*b^3*c^2*k*l*m))/(4*(64*a^5*c^6 - a^2*b^6*c^3 + 12*a^3*b^4*c^4 - 48*a^4*b^2*c^5)))*root(1572864*a^8*b^2*c^
10*z^4 - 983040*a^7*b^4*c^9*z^4 + 327680*a^6*b^6*c^8*z^4 - 61440*a^5*b^8*c^7*z^4 + 6144*a^4*b^10*c^6*z^4 - 256
*a^3*b^12*c^5*z^4 - 1048576*a^9*c^11*z^4 - 1572864*a^8*b^2*c^8*l*z^3 + 983040*a^7*b^4*c^7*l*z^3 - 327680*a^6*b
^6*c^6*l*z^3 + 61440*a^5*b^8*c^5*l*z^3 - 6144*a^4*b^10*c^4*l*z^3 + 256*a^3*b^12*c^3*l*z^3 + 1048576*a^9*c^9*l*
z^3 + 96*a^3*b^12*c*k*m*z^2 + 98304*a^8*b*c^7*j*l*z^2 + 24576*a^8*b*c^7*h*m*z^2 + 155648*a^7*b*c^8*d*m*z^2 + 9
8304*a^7*b*c^8*e*l*z^2 + 57344*a^7*b*c^8*f*k*z^2 + 32768*a^7*b*c^8*g*j*z^2 + 57344*a^6*b*c^9*d*h*z^2 + 32768*a
^6*b*c^9*e*g*z^2 - 32*a*b^10*c^5*d*f*z^2 - 491520*a^8*b^2*c^6*k*m*z^2 + 358400*a^7*b^4*c^5*k*m*z^2 - 129024*a^
6*b^6*c^4*k*m*z^2 + 24768*a^5*b^8*c^3*k*m*z^2 - 2432*a^4*b^10*c^2*k*m*z^2 - 90112*a^7*b^3*c^6*j*l*z^2 + 30720*
a^6*b^5*c^5*j*l*z^2 - 4608*a^5*b^7*c^4*j*l*z^2 + 256*a^4*b^9*c^3*j*l*z^2 - 21504*a^6*b^5*c^5*h*m*z^2 + 9216*a^
5*b^7*c^4*h*m*z^2 + 8192*a^7*b^3*c^6*h*m*z^2 - 1568*a^4*b^9*c^3*h*m*z^2 + 96*a^3*b^11*c^2*h*m*z^2 - 172032*a^7
*b^2*c^7*f*m*z^2 + 116736*a^6*b^4*c^6*f*m*z^2 - 49152*a^7*b^2*c^7*g*l*z^2 + 45056*a^6*b^4*c^6*g*l*z^2 - 35840*
a^5*b^6*c^5*f*m*z^2 + 24576*a^7*b^2*c^7*h*k*z^2 - 15360*a^5*b^6*c^5*g*l*z^2 + 5184*a^4*b^8*c^4*f*m*z^2 - 3072*
a^5*b^6*c^5*h*k*z^2 + 2304*a^4*b^8*c^4*g*l*z^2 + 2048*a^6*b^4*c^6*h*k*z^2 + 576*a^4*b^8*c^4*h*k*z^2 - 288*a^3*
b^10*c^3*f*m*z^2 - 128*a^3*b^10*c^3*g*l*z^2 - 32*a^3*b^10*c^3*h*k*z^2 - 147456*a^6*b^3*c^7*d*m*z^2 - 90112*a^6
*b^3*c^7*e*l*z^2 + 52224*a^5*b^5*c^6*d*m*z^2 - 49152*a^6*b^3*c^7*f*k*z^2 + 30720*a^5*b^5*c^6*e*l*z^2 - 24576*a
^6*b^3*c^7*g*j*z^2 + 15360*a^5*b^5*c^6*f*k*z^2 - 8192*a^4*b^7*c^5*d*m*z^2 + 6144*a^5*b^5*c^6*g*j*z^2 - 4608*a^
4*b^7*c^5*e*l*z^2 - 2048*a^4*b^7*c^5*f*k*z^2 - 512*a^4*b^7*c^5*g*j*z^2 + 480*a^3*b^9*c^4*d*m*z^2 + 256*a^3*b^9
*c^4*e*l*z^2 + 96*a^3*b^9*c^4*f*k*z^2 + 131072*a^6*b^2*c^8*d*k*z^2 + 49152*a^6*b^2*c^8*e*j*z^2 - 43008*a^5*b^4
*c^7*d*k*z^2 - 12288*a^5*b^4*c^7*e*j*z^2 + 6144*a^4*b^6*c^6*d*k*z^2 + 1024*a^4*b^6*c^6*e*j*z^2 - 320*a^3*b^8*c
^5*d*k*z^2 + 6144*a^5*b^4*c^7*f*h*z^2 - 2048*a^4*b^6*c^6*f*h*z^2 + 192*a^3*b^8*c^5*f*h*z^2 - 49152*a^5*b^3*c^8
*d*h*z^2 - 24576*a^5*b^3*c^8*e*g*z^2 + 15360*a^4*b^5*c^7*d*h*z^2 + 6144*a^4*b^5*c^7*e*g*z^2 - 2048*a^3*b^7*c^6
*d*h*z^2 - 512*a^3*b^7*c^6*e*g*z^2 + 96*a^2*b^9*c^5*d*h*z^2 + 24576*a^5*b^2*c^9*d*f*z^2 - 3072*a^3*b^6*c^7*d*f
*z^2 + 2048*a^4*b^4*c^8*d*f*z^2 + 576*a^2*b^8*c^6*d*f*z^2 - 430080*a^9*b*c^6*m^2*z^2 + 3408*a^4*b^11*c*m^2*z^2
- 64*a^3*b^12*c*l^2*z^2 + 61440*a^8*b*c^7*k^2*z^2 + 12288*a^7*b*c^8*h^2*z^2 + 12288*a^6*b*c^9*f^2*z^2 + 61440
*a^5*b*c^10*d^2*z^2 + 432*a*b^9*c^6*d^2*z^2 + 245760*a^9*c^7*k*m*z^2 + 81920*a^8*c^8*f*m*z^2 - 49152*a^8*c^8*h
*k*z^2 - 147456*a^7*c^9*d*k*z^2 - 65536*a^7*c^9*e*j*z^2 - 16384*a^7*c^9*f*h*z^2 - 49152*a^6*c^10*d*f*z^2 + 716
800*a^8*b^3*c^5*m^2*z^2 - 483840*a^7*b^5*c^4*m^2*z^2 + 170496*a^6*b^7*c^3*m^2*z^2 - 33232*a^5*b^9*c^2*m^2*z^2
+ 516096*a^8*b^2*c^6*l^2*z^2 - 288768*a^7*b^4*c^5*l^2*z^2 + 88576*a^6*b^6*c^4*l^2*z^2 - 15744*a^5*b^8*c^3*l^2*
z^2 + 1536*a^4*b^10*c^2*l^2*z^2 - 61440*a^7*b^3*c^6*k^2*z^2 + 24064*a^6*b^5*c^5*k^2*z^2 - 4608*a^5*b^7*c^4*k^2
*z^2 + 432*a^4*b^9*c^3*k^2*z^2 - 16*a^3*b^11*c^2*k^2*z^2 + 24576*a^7*b^2*c^7*j^2*z^2 - 6144*a^6*b^4*c^6*j^2*z^
2 + 512*a^5*b^6*c^5*j^2*z^2 - 8192*a^6*b^3*c^7*h^2*z^2 + 1536*a^5*b^5*c^6*h^2*z^2 - 16*a^3*b^9*c^4*h^2*z^2 - 8
192*a^6*b^2*c^8*g^2*z^2 + 6144*a^5*b^4*c^7*g^2*z^2 - 1536*a^4*b^6*c^6*g^2*z^2 + 128*a^3*b^8*c^5*g^2*z^2 - 8192
*a^5*b^3*c^8*f^2*z^2 + 1536*a^4*b^5*c^7*f^2*z^2 - 16*a^2*b^9*c^5*f^2*z^2 + 24576*a^5*b^2*c^9*e^2*z^2 - 6144*a^
4*b^4*c^8*e^2*z^2 + 512*a^3*b^6*c^7*e^2*z^2 - 61440*a^4*b^3*c^9*d^2*z^2 + 24064*a^3*b^5*c^8*d^2*z^2 - 4608*a^2
*b^7*c^7*d^2*z^2 - 393216*a^9*c^7*l^2*z^2 - 144*a^3*b^13*m^2*z^2 - 32768*a^8*c^8*j^2*z^2 - 32768*a^6*c^10*e^2*
z^2 - 16*b^11*c^5*d^2*z^2 + 18432*a^8*b*c^5*h*l*m*z - 96*a^3*b^10*c*g*k*m*z + 90112*a^7*b*c^6*e*k*m*z + 36864*
a^7*b*c^6*f*j*m*z - 16384*a^7*b*c^6*g*j*l*z + 14336*a^7*b*c^6*d*l*m*z - 10240*a^7*b*c^6*f*k*l*z + 4096*a^7*b*c
^6*h*j*k*z + 10240*a^7*b*c^6*g*h*m*z - 47104*a^6*b*c^7*d*h*l*z + 36864*a^6*b*c^7*e*f*m*z + 30720*a^6*b*c^7*d*g
*m*z - 16384*a^6*b*c^7*e*g*l*z + 6144*a^6*b*c^7*f*g*k*z + 4096*a^6*b*c^7*e*h*k*z + 32*a*b^10*c^3*d*f*l*z - 409
6*a^5*b*c^8*d*f*j*z - 6144*a^5*b*c^8*d*g*h*z - 32*a*b^8*c^5*d*f*g*z - 4096*a^4*b*c^9*d*e*f*z + 64*a*b^7*c^6*d*
e*f*z + 110592*a^8*b^2*c^4*k*l*m*z - 36864*a^7*b^4*c^3*k*l*m*z + 5376*a^6*b^6*c^2*k*l*m*z - 79872*a^7*b^3*c^4*
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*l*m - 192*a^6*b^3*c^3*g*h*l*m + 144*a^5*b^5*c^2*g*h*l*m + 9600*a^6*b^2*c^4*e*j*k*m - 4224*a^6*b^2*c^4*d*j*l*m
- 2560*a^5*b^4*c^3*e*j*k*m + 384*a^6*b^2*c^4*f*j*k*l + 224*a^5*b^4*c^3*d*j*l*m + 192*a^4*b^6*c^2*e*j*k*m - 16
0*a^5*b^4*c^3*f*j*k*l - 4608*a^6*b^2*c^4*f*h*k*m + 2688*a^6*b^2*c^4*f*g*l*m + 1664*a^6*b^2*c^4*g*h*k*l - 744*a
^5*b^4*c^3*f*h*k*m - 544*a^5*b^4*c^3*f*g*l*m + 492*a^4*b^6*c^2*f*h*k*m + 416*a^5*b^4*c^3*g*h*j*m + 384*a^6*b^2
*c^4*g*h*j*m + 384*a^6*b^2*c^4*e*h*l*m - 288*a^5*b^4*c^3*g*h*k*l - 288*a^5*b^4*c^3*e*h*l*m - 96*a^4*b^6*c^2*g*
h*j*m + 2112*a^5*b^3*c^4*d*j*k*l - 160*a^4*b^5*c^3*d*j*k*l + 16992*a^5*b^3*c^4*d*h*k*m - 6252*a^4*b^5*c^3*d*h*
k*m - 4800*a^5*b^3*c^4*e*g*k*m + 2112*a^5*b^3*c^4*d*g*l*m - 1728*a^5*b^3*c^4*f*g*j*m + 1280*a^4*b^5*c^3*e*g*k*
m + 1088*a^5*b^3*c^4*e*f*l*m - 832*a^5*b^3*c^4*e*h*j*m + 816*a^3*b^7*c^2*d*h*k*m + 576*a^5*b^3*c^4*e*h*k*l - 4
48*a^5*b^3*c^4*f*h*j*l + 288*a^4*b^5*c^3*f*g*j*m - 192*a^5*b^3*c^4*g*h*j*k - 192*a^5*b^3*c^4*f*g*k*l + 192*a^4
*b^5*c^3*e*h*j*m - 112*a^4*b^5*c^3*d*g*l*m + 96*a^4*b^5*c^3*f*h*j*l - 96*a^3*b^7*c^2*e*g*k*m + 80*a^4*b^5*c^3*
f*g*k*l + 32*a^4*b^5*c^3*g*h*j*k - 11456*a^5*b^2*c^5*d*f*k*m + 4992*a^5*b^2*c^5*d*h*j*l - 4608*a^5*b^2*c^5*e*g
*j*l - 4224*a^5*b^2*c^5*d*e*l*m + 3456*a^5*b^2*c^5*e*f*j*m + 3456*a^5*b^2*c^5*d*g*k*l + 2432*a^5*b^2*c^5*d*g*j
*m - 1312*a^4*b^4*c^4*d*h*j*l + 1272*a^3*b^6*c^3*d*f*k*m - 1056*a^4*b^4*c^4*d*g*k*l + 896*a^5*b^2*c^5*f*g*j*k
+ 768*a^4*b^4*c^4*e*g*j*l - 576*a^4*b^4*c^4*e*f*j*m - 480*a^4*b^4*c^4*d*g*j*m + 384*a^5*b^2*c^5*e*h*j*k + 384*
a^5*b^2*c^5*e*f*k*l - 232*a^2*b^8*c^2*d*f*k*m + 224*a^4*b^4*c^4*d*e*l*m - 160*a^4*b^4*c^4*e*f*k*l - 96*a^4*b^4
*c^4*f*g*j*k + 96*a^3*b^6*c^3*d*h*j*l + 80*a^3*b^6*c^3*d*g*k*l - 64*a^4*b^4*c^4*e*h*j*k - 24*a^4*b^4*c^4*d*f*k
*m + 416*a^4*b^4*c^4*e*g*h*m + 384*a^5*b^2*c^5*f*g*h*l + 384*a^5*b^2*c^5*e*g*h*m + 224*a^4*b^4*c^4*f*g*h*l - 9
6*a^3*b^6*c^3*e*g*h*m - 48*a^3*b^6*c^3*f*g*h*l + 2112*a^4*b^3*c^5*d*e*k*l - 960*a^4*b^3*c^5*d*f*j*l + 960*a^4*
b^3*c^5*d*e*j*m + 384*a^3*b^5*c^4*d*f*j*l + 320*a^4*b^3*c^5*d*g*j*k + 192*a^4*b^3*c^5*e*f*j*k - 160*a^3*b^5*c^
4*d*e*k*l - 32*a^2*b^7*c^3*d*f*j*l + 7392*a^4*b^3*c^5*d*f*h*m - 2496*a^4*b^3*c^5*d*g*h*l - 1728*a^4*b^3*c^5*e*
f*g*m - 1500*a^3*b^5*c^4*d*f*h*m + 656*a^3*b^5*c^4*d*g*h*l - 448*a^4*b^3*c^5*e*f*h*l + 288*a^3*b^5*c^4*e*f*g*m
- 192*a^4*b^3*c^5*f*g*h*j - 192*a^4*b^3*c^5*e*g*h*k + 96*a^3*b^5*c^4*e*f*h*l - 48*a^2*b^7*c^3*d*g*h*l + 32*a^
3*b^5*c^4*e*g*h*k - 16*a^2*b^7*c^3*d*f*h*m - 640*a^4*b^2*c^6*d*e*j*k + 4992*a^4*b^2*c^6*d*e*h*l - 3584*a^4*b^2
*c^6*d*f*h*k + 2432*a^4*b^2*c^6*d*e*g*m - 1312*a^3*b^4*c^5*d*e*h*l + 896*a^4*b^2*c^6*e*f*g*k + 896*a^4*b^2*c^6
*d*g*h*j + 640*a^4*b^2*c^6*d*f*g*l + 600*a^3*b^4*c^5*d*f*h*k + 480*a^3*b^4*c^5*d*f*g*l - 480*a^3*b^4*c^5*d*e*g
*m + 384*a^4*b^2*c^6*e*f*h*j - 192*a^2*b^6*c^4*d*f*g*l - 96*a^3*b^4*c^5*e*f*g*k - 96*a^3*b^4*c^5*d*g*h*j + 96*
a^2*b^6*c^4*d*e*h*l + 12*a^2*b^6*c^4*d*f*h*k - 960*a^3*b^3*c^6*d*e*f*l + 384*a^2*b^5*c^5*d*e*f*l + 320*a^3*b^3
*c^6*d*e*g*k - 192*a^3*b^3*c^6*d*f*g*j + 192*a^3*b^3*c^6*d*e*h*j + 32*a^2*b^5*c^5*d*f*g*j - 192*a^3*b^3*c^6*e*
f*g*h + 384*a^3*b^2*c^7*d*e*f*j - 64*a^2*b^4*c^6*d*e*f*j + 896*a^3*b^2*c^7*d*e*g*h - 96*a^2*b^4*c^6*d*e*g*h -
192*a^2*b^3*c^7*d*e*f*g + 496*a^7*b^4*c*k*l^2*m - 4752*a^7*b^4*c*j*l*m^2 + 96*a^5*b^6*c*j^2*k*m - 6144*a^8*b*c
^3*h*l^2*m - 168*a^6*b^5*c*h*l^2*m + 6400*a^8*b*c^3*g*l*m^2 - 2862*a^6*b^5*c*h*k*m^2 + 2376*a^6*b^5*c*g*l*m^2
- 1632*a^7*b*c^4*h^2*k*m - 480*a^8*b*c^3*h*k*m^2 - 180*a^5*b^6*c*h*k^2*m + 54*a^4*b^7*c*h^2*k*m - 384*a^7*b*c^
4*h*j^2*m + 120*a^5*b^6*c*h*k*l^2 + 56*a^5*b^6*c*f*l^2*m + 24*a^3*b^8*c*g^2*k*m + 4512*a^7*b*c^4*f*k^2*m - 230
4*a^7*b*c^4*g*k^2*l - 1680*a^5*b^6*c*g*j*m^2 + 1184*a^6*b*c^5*f^2*k*m + 804*a^5*b^6*c*f*k*m^2 + 432*a^5*b^6*c*
e*l*m^2 + 60*a^4*b^7*c*f*k^2*m + 6*a^2*b^9*c*f^2*k*m - 13312*a^7*b*c^4*d*l^2*m + 2048*a^7*b*c^4*g*j*l^2 - 1024
*a^7*b*c^4*f*k*l^2 + 64*a^4*b^7*c*g*j*l^2 + 56*a^4*b^7*c*d*l^2*m - 40*a^4*b^7*c*f*k*l^2 + 13440*a^7*b*c^4*e*j*
m^2 - 8928*a^5*b*c^6*d^2*k*m - 6240*a^7*b*c^4*d*k*m^2 + 1614*a^4*b^7*c*d*k*m^2 - 288*a^4*b^7*c*e*j*m^2 - 170*a
*b^9*c^2*d^2*k*m + 60*a^3*b^8*c*d*k^2*m + 4608*a^6*b*c^5*e*j^2*l + 4608*a^5*b*c^6*e^2*j*l - 2432*a^6*b*c^5*d*j
^2*m + 1440*a^7*b*c^4*f*h*m^2 - 896*a^6*b*c^5*f*j^2*k - 864*a^6*b*c^5*f*h^2*m - 558*a^4*b^7*c*f*h*m^2 + 256*a^
6*b*c^5*g*h^2*l - 40*a^3*b^8*c*d*k*l^2 - 1920*a^6*b*c^5*e*j*k^2 - 384*a^5*b*c^6*e^2*h*m + 24*a^3*b^8*c*f*h*l^2
- 16*a*b^8*c^3*d^2*j*l + 2208*a^6*b*c^5*f*h*k^2 - 1044*a^3*b^8*c*d*h*m^2 + 800*a^5*b*c^6*f^2*h*k - 256*a^5*b*
c^6*f^2*g*l + 144*a^3*b^8*c*e*g*m^2 - 116*a*b^8*c^3*d^2*h*m + 8192*a^6*b*c^5*d*h*l^2 + 2048*a^6*b*c^5*e*g*l^2
+ 24*a^2*b^9*c*d*h*l^2 - 5856*a^4*b*c^7*d^2*f*m + 4896*a^4*b*c^7*d^2*h*k + 2720*a^6*b*c^5*d*f*m^2 + 2304*a^4*b
*c^7*d^2*g*l + 1824*a^5*b*c^6*d*h^2*k + 438*a*b^7*c^4*d^2*f*m - 384*a^5*b*c^6*e*h^2*j + 318*a^2*b^9*c*d*f*m^2
- 168*a*b^7*c^4*d^2*g*l + 42*a*b^7*c^4*d^2*h*k - 36*a*b^8*c^3*d*f^2*m - 2432*a^4*b*c^7*d*e^2*m + 1536*a^5*b*c^
6*e*g*j^2 + 1536*a^4*b*c^7*e^2*g*j - 896*a^5*b*c^6*d*h*j^2 - 896*a^4*b*c^7*e^2*f*k + 4896*a^5*b*c^6*d*f*k^2 +
1824*a^4*b*c^7*d*f^2*k - 384*a^4*b*c^7*e*f^2*j + 336*a*b^6*c^5*d^2*e*l - 156*a*b^6*c^5*d^2*f*k + 16*a*b^6*c^5*
d^2*g*j + 12*a*b^7*c^4*d*f^2*k - 2*a*b^9*c^2*d*f*k^2 - 1920*a^3*b*c^8*d^2*e*j - 32*a*b^5*c^6*d^2*e*j + 2208*a^
3*b*c^8*d^2*f*h + 800*a^4*b*c^7*d*f*h^2 - 102*a*b^5*c^6*d^2*f*h + 12*a*b^6*c^5*d*f^2*h - 2*a*b^7*c^4*d*f*h^2 -
896*a^3*b*c^8*d*e^2*h - 8*a*b^6*c^5*d*f*g^2 - 240*a*b^4*c^7*d^2*e*g - 32*a*b^4*c^7*d*e^2*f + 5120*a^8*c^4*h*j
*l*m + 15360*a^7*c^5*d*j*l*m - 7680*a^7*c^5*e*j*k*m + 3072*a^7*c^5*f*j*k*l + 5120*a^7*c^5*e*h*l*m + 1920*a^7*c
^5*f*h*k*m + 15360*a^6*c^6*d*e*l*m + 5760*a^6*c^6*d*f*k*m + 3072*a^6*c^6*e*f*k*l - 3072*a^6*c^6*d*h*j*l - 2560
*a^6*c^6*e*f*j*m + 1536*a^6*c^6*e*h*j*k + 4608*a^5*c^7*d*e*j*k - 3072*a^5*c^7*d*e*h*l - 1152*a^5*c^7*d*f*h*k +
512*a^5*c^7*e*f*h*j + 1536*a^4*c^8*d*e*f*j - 8*a*b^10*c*d*f*l^2 - 5568*a^8*b^2*c^2*k*l^2*m + 15552*a^8*b^2*c^
2*j*l*m^2 + 4800*a^7*b^2*c^3*j^2*k*m - 1280*a^6*b^4*c^2*j^2*k*m + 2080*a^7*b^3*c^2*h*l^2*m - 1088*a^7*b^2*c^3*
j*k^2*l + 48*a^6*b^4*c^2*j*k^2*l - 8544*a^7*b^2*c^3*h*k^2*m - 7776*a^7*b^3*c^2*g*l*m^2 + 7632*a^7*b^3*c^2*h*k*
m^2 + 3600*a^6*b^3*c^3*h^2*k*m + 2484*a^6*b^4*c^2*h*k^2*m - 918*a^5*b^5*c^2*h^2*k*m + 4800*a^7*b^2*c^3*h*k*l^2
- 1424*a^6*b^4*c^2*h*k*l^2 + 1200*a^5*b^4*c^3*g^2*k*m - 960*a^6*b^2*c^4*g^2*k*m - 528*a^6*b^4*c^2*f*l^2*m - 4
16*a^6*b^3*c^3*h*j^2*m - 320*a^4*b^6*c^2*g^2*k*m + 192*a^7*b^2*c^3*f*l^2*m + 96*a^5*b^5*c^2*h*j^2*m + 15552*a^
7*b^2*c^3*e*l*m^2 - 6720*a^7*b^2*c^3*g*j*m^2 + 6160*a^6*b^4*c^2*g*j*m^2 - 4752*a^6*b^4*c^2*e*l*m^2 - 2016*a^7*
b^2*c^3*f*k*m^2 - 1164*a^6*b^4*c^2*f*k*m^2 + 1104*a^5*b^3*c^4*f^2*k*m + 1008*a^6*b^3*c^3*f*k^2*m + 960*a^6*b^2
*c^4*h^2*j*l - 678*a^5*b^5*c^2*f*k^2*m + 544*a^6*b^3*c^3*g*k^2*l - 144*a^5*b^4*c^3*h^2*j*l - 102*a^4*b^5*c^3*f
^2*k*m - 62*a^3*b^7*c^2*f^2*k*m - 24*a^5*b^5*c^2*g*k^2*l + 6432*a^6*b^3*c^3*d*l^2*m + 4800*a^5*b^2*c^5*e^2*k*m
- 2304*a^6*b^2*c^4*g*j^2*l + 1920*a^6*b^3*c^3*g*j*l^2 + 1728*a^6*b^2*c^4*f*j^2*m - 1280*a^4*b^4*c^4*e^2*k*m +
1152*a^5*b^3*c^4*g^2*j*l - 1032*a^5*b^5*c^2*d*l^2*m - 864*a^6*b^3*c^3*f*k*l^2 - 768*a^5*b^5*c^2*g*j*l^2 + 408
*a^5*b^5*c^2*f*k*l^2 + 384*a^5*b^4*c^3*g*j^2*l - 288*a^5*b^4*c^3*f*j^2*m + 192*a^6*b^2*c^4*h*j^2*k - 192*a^4*b
^5*c^3*g^2*j*l + 96*a^3*b^6*c^3*e^2*k*m - 32*a^5*b^4*c^3*h*j^2*k - 21120*a^6*b^2*c^4*d*k^2*m + 20880*a^6*b^3*c
^3*d*k*m^2 + 19760*a^4*b^3*c^5*d^2*k*m - 12320*a^6*b^3*c^3*e*j*m^2 - 9750*a^5*b^5*c^2*d*k*m^2 - 9390*a^3*b^5*c
^4*d^2*k*m + 8460*a^5*b^4*c^3*d*k^2*m + 3360*a^5*b^5*c^2*e*j*m^2 + 1860*a^2*b^7*c^3*d^2*k*m - 1218*a^4*b^6*c^2
*d*k^2*m - 1088*a^6*b^2*c^4*e*k^2*l + 960*a^6*b^2*c^4*g*j*k^2 - 240*a^5*b^4*c^3*g*j*k^2 + 192*a^5*b^2*c^5*f^2*
j*l - 104*a^4*b^5*c^3*g^2*h*m - 96*a^5*b^3*c^4*g^2*h*m + 48*a^5*b^4*c^3*e*k^2*l + 48*a^4*b^4*c^4*f^2*j*l + 24*
a^3*b^7*c^2*g^2*h*m + 16*a^4*b^6*c^2*g*j*k^2 - 16*a^3*b^6*c^3*f^2*j*l + 13376*a^6*b^2*c^4*d*k*l^2 - 5136*a^5*b
^4*c^3*d*k*l^2 - 3840*a^6*b^2*c^4*e*j*l^2 + 1536*a^5*b^4*c^3*e*j*l^2 + 1392*a^5*b^3*c^4*f*h^2*m + 1386*a^5*b^5
*c^2*f*h*m^2 - 768*a^5*b^3*c^4*e*j^2*l + 768*a^4*b^6*c^2*d*k*l^2 - 768*a^4*b^3*c^5*e^2*j*l - 588*a^4*b^4*c^4*f
^2*h*m - 480*a^5*b^3*c^4*g*h^2*l + 480*a^5*b^3*c^4*d*j^2*m - 480*a^5*b^2*c^5*f^2*h*m - 128*a^4*b^6*c^2*e*j*l^2
+ 100*a^3*b^6*c^3*f^2*h*m + 96*a^5*b^3*c^4*f*j^2*k + 72*a^4*b^5*c^3*g*h^2*l - 54*a^4*b^5*c^3*f*h^2*m - 48*a^6
*b^3*c^3*f*h*m^2 - 36*a^3*b^7*c^2*f*h^2*m + 6*a^2*b^8*c^2*f^2*h*m + 6848*a^4*b^2*c^6*d^2*j*l - 2448*a^3*b^4*c^
5*d^2*j*l + 624*a^5*b^4*c^3*f*h*l^2 + 576*a^6*b^2*c^4*f*h*l^2 + 480*a^5*b^3*c^4*e*j*k^2 + 432*a^4*b^4*c^4*f*g^
2*m - 416*a^4*b^3*c^5*e^2*h*m + 336*a^2*b^6*c^4*d^2*j*l - 320*a^5*b^2*c^5*f*g^2*m - 256*a^4*b^6*c^2*f*h*l^2 +
192*a^5*b^2*c^5*g^2*h*k + 96*a^3*b^5*c^4*e^2*h*m - 72*a^3*b^6*c^3*f*g^2*m + 48*a^4*b^4*c^4*g^2*h*k - 32*a^4*b^
5*c^3*e*j*k^2 - 8*a^3*b^6*c^3*g^2*h*k + 24768*a^6*b^2*c^4*d*h*m^2 - 21108*a^5*b^4*c^3*d*h*m^2 - 10048*a^4*b^2*
c^6*d^2*h*m + 7218*a^4*b^6*c^2*d*h*m^2 - 6720*a^6*b^2*c^4*e*g*m^2 + 6160*a^5*b^4*c^3*e*g*m^2 - 2592*a^5*b^2*c^
5*d*h^2*m - 1680*a^4*b^6*c^2*e*g*m^2 + 1068*a^3*b^4*c^5*d^2*h*m + 960*a^5*b^2*c^5*e*h^2*l - 876*a^4*b^4*c^4*d*
h^2*m - 864*a^5*b^2*c^5*f*h^2*k + 546*a^2*b^6*c^4*d^2*h*m + 432*a^3*b^6*c^3*d*h^2*m + 336*a^4*b^3*c^5*f^2*h*k
- 320*a^5*b^2*c^5*d*j^2*k + 192*a^5*b^2*c^5*g*h^2*j + 144*a^5*b^3*c^4*f*h*k^2 - 144*a^4*b^4*c^4*e*h^2*l - 102*
a^4*b^5*c^3*f*h*k^2 - 96*a^4*b^3*c^5*f^2*g*l - 36*a^2*b^8*c^2*d*h^2*m - 30*a^3*b^5*c^4*f^2*h*k - 24*a^3*b^5*c^
4*f^2*g*l + 16*a^4*b^4*c^4*g*h^2*j - 12*a^4*b^4*c^4*f*h^2*k + 12*a^3*b^6*c^3*f*h^2*k + 8*a^2*b^7*c^3*f^2*g*l +
6*a^3*b^7*c^2*f*h*k^2 - 2*a^2*b^7*c^3*f^2*h*k - 9312*a^5*b^3*c^4*d*h*l^2 + 3288*a^4*b^5*c^3*d*h*l^2 - 2304*a^
4*b^2*c^6*e^2*g*l + 1920*a^5*b^3*c^4*e*g*l^2 + 1728*a^4*b^2*c^6*e^2*f*m + 1152*a^4*b^3*c^5*e*g^2*l - 768*a^4*b
^5*c^3*e*g*l^2 - 608*a^4*b^3*c^5*d*g^2*m - 472*a^3*b^7*c^2*d*h*l^2 + 384*a^3*b^4*c^5*e^2*g*l - 288*a^3*b^4*c^5
*e^2*f*m - 224*a^4*b^3*c^5*f*g^2*k + 192*a^5*b^2*c^5*f*h*j^2 + 192*a^4*b^2*c^6*e^2*h*k - 192*a^3*b^5*c^4*e*g^2
*l + 120*a^3*b^5*c^4*d*g^2*m + 64*a^3*b^7*c^2*e*g*l^2 - 32*a^3*b^4*c^5*e^2*h*k + 24*a^3*b^5*c^4*f*g^2*k + 9936
*a^3*b^3*c^6*d^2*f*m + 3786*a^4*b^5*c^3*d*f*m^2 - 3552*a^5*b^2*c^5*d*h*k^2 - 3486*a^2*b^5*c^5*d^2*f*m - 3424*a
^3*b^3*c^6*d^2*g*l - 1868*a^3*b^7*c^2*d*f*m^2 + 1332*a^4*b^4*c^4*d*h*k^2 - 1296*a^5*b^3*c^4*d*f*m^2 - 1236*a^3
*b^4*c^5*d*f^2*m + 1224*a^2*b^5*c^5*d^2*g*l - 1152*a^4*b^2*c^6*d*f^2*m + 960*a^5*b^2*c^5*e*g*k^2 - 496*a^3*b^3
*c^6*d^2*h*k + 462*a^2*b^6*c^4*d*f^2*m + 432*a^4*b^3*c^5*d*h^2*k - 240*a^4*b^4*c^4*e*g*k^2 - 222*a^2*b^5*c^5*d
^2*h*k + 192*a^4*b^2*c^6*f^2*g*j + 192*a^4*b^2*c^6*e*f^2*l - 174*a^3*b^5*c^4*d*h^2*k - 156*a^3*b^6*c^3*d*h*k^2
+ 48*a^3*b^4*c^5*e*f^2*l - 32*a^4*b^3*c^5*e*h^2*j + 16*a^3*b^6*c^3*e*g*k^2 + 16*a^3*b^4*c^5*f^2*g*j - 16*a^2*
b^6*c^4*e*f^2*l + 12*a^2*b^7*c^3*d*h^2*k + 6*a^2*b^8*c^2*d*h*k^2 + 1728*a^5*b^2*c^5*d*f*l^2 + 1392*a^4*b^4*c^4
*d*f*l^2 - 840*a^3*b^6*c^3*d*f*l^2 - 768*a^4*b^2*c^6*e*g^2*j + 576*a^4*b^2*c^6*d*g^2*k + 480*a^3*b^3*c^6*d*e^2
*m + 144*a^2*b^8*c^2*d*f*l^2 + 96*a^4*b^3*c^5*d*h*j^2 + 96*a^3*b^3*c^6*e^2*f*k - 80*a^3*b^4*c^5*d*g^2*k + 6848
*a^3*b^2*c^7*d^2*e*l - 3552*a^3*b^2*c^7*d^2*f*k - 2448*a^2*b^4*c^6*d^2*e*l + 1332*a^2*b^4*c^6*d^2*f*k + 960*a^
3*b^2*c^7*d^2*g*j - 496*a^4*b^3*c^5*d*f*k^2 + 432*a^3*b^3*c^6*d*f^2*k - 240*a^2*b^4*c^6*d^2*g*j - 222*a^3*b^5*
c^4*d*f*k^2 - 174*a^2*b^5*c^5*d*f^2*k + 64*a^4*b^2*c^6*f*g^2*h + 48*a^3*b^4*c^5*f*g^2*h + 42*a^2*b^7*c^3*d*f*k
^2 - 32*a^3*b^3*c^6*e*f^2*j - 320*a^3*b^2*c^7*d*e^2*k + 192*a^4*b^2*c^6*e*g*h^2 + 192*a^4*b^2*c^6*d*f*j^2 - 32
*a^3*b^4*c^5*d*f*j^2 + 16*a^3*b^4*c^5*e*g*h^2 + 480*a^2*b^3*c^7*d^2*e*j - 224*a^3*b^3*c^6*d*g^2*h + 192*a^3*b^
2*c^7*e^2*f*h + 24*a^2*b^5*c^5*d*g^2*h - 864*a^3*b^2*c^7*d*f^2*h + 336*a^3*b^3*c^6*d*f*h^2 + 192*a^3*b^2*c^7*e
*f^2*g + 144*a^2*b^3*c^7*d^2*f*h - 30*a^2*b^5*c^5*d*f*h^2 + 16*a^2*b^4*c^6*e*f^2*g - 12*a^2*b^4*c^6*d*f^2*h +
192*a^3*b^2*c^7*d*f*g^2 + 96*a^2*b^3*c^7*d*e^2*h + 48*a^2*b^4*c^6*d*f*g^2 + 960*a^2*b^2*c^8*d^2*e*g + 192*a^2*
b^2*c^8*d*e^2*f - 7680*a^9*b*c^2*l^2*m^2 + 3152*a^8*b^3*c*l^2*m^2 + 2070*a^7*b^4*c*k^2*m^2 - 1840*a^7*b^3*c^2*
k^3*m + 6720*a^8*b*c^3*j^2*m^2 - 3072*a^8*b*c^3*k^2*l^2 + 1680*a^6*b^5*c*j^2*m^2 - 100*a^6*b^5*c*k^2*l^2 - 217
6*a^7*b^3*c^2*j*l^3 - 256*a^6*b^3*c^3*j^3*l - 64*a^5*b^6*c*j^2*l^2 - 12480*a^8*b^2*c^2*h*m^3 + 972*a^5*b^6*c*h
^2*m^2 - 960*a^7*b*c^4*j^2*k^2 - 252*a^5*b^4*c^3*h^3*m - 192*a^6*b^2*c^4*h^3*m + 54*a^4*b^6*c^2*h^3*m + 1536*a
^7*b*c^4*h^2*l^2 + 420*a^4*b^7*c*g^2*m^2 - 36*a^4*b^7*c*h^2*l^2 - 3072*a^7*b^2*c^3*g*l^3 + 2096*a^7*b^3*c^2*f*
m^3 + 1088*a^6*b^4*c^2*g*l^3 - 496*a^6*b^3*c^3*h*k^3 - 192*a^4*b^4*c^4*g^3*l + 176*a^4*b^3*c^5*f^3*m + 144*a^5
*b^3*c^4*h^3*k + 78*a^3*b^8*c*f^2*m^2 + 54*a^3*b^5*c^4*f^3*m + 32*a^3*b^6*c^3*g^3*l + 30*a^5*b^5*c^2*h*k^3 - 1
8*a^4*b^5*c^3*h^3*k - 18*a^2*b^7*c^3*f^3*m - 16*a^3*b^8*c*g^2*l^2 + 6720*a^6*b*c^5*e^2*m^2 - 192*a^6*b*c^5*h^2
*j^2 - 4*a^2*b^9*c*f^2*l^2 - 35040*a^7*b^2*c^3*d*m^3 + 14300*a^6*b^4*c^2*d*m^3 - 12000*a^3*b^2*c^7*d^3*m + 438
0*a^2*b^4*c^6*d^3*m - 2176*a^6*b^3*c^3*e*l^3 - 256*a^3*b^3*c^6*e^3*l - 192*a^6*b^2*c^4*f*k^3 + 192*a^5*b^5*c^2
*e*l^3 - 192*a^4*b^2*c^6*f^3*k + 132*a^5*b^4*c^3*f*k^3 + 128*a^4*b^3*c^5*g^3*j - 28*a^3*b^4*c^5*f^3*k - 10*a^4
*b^6*c^2*f*k^3 + 6*a^2*b^6*c^4*f^3*k + 10752*a^5*b*c^6*d^2*l^2 - 960*a^5*b*c^6*e^2*k^2 - 192*a^5*b*c^6*f^2*j^2
+ 108*a*b^9*c^2*d^2*l^2 - 1680*a^5*b^3*c^4*d*k^3 - 1680*a^2*b^3*c^7*d^3*k + 222*a^4*b^5*c^3*d*k^3 + 30*a*b^8*
c^3*d^2*k^2 - 10*a^3*b^7*c^2*d*k^3 - 960*a^4*b*c^7*d^2*j^2 + 80*a^4*b^3*c^5*f*h^3 + 80*a^3*b^3*c^6*f^3*h + 6*a
^3*b^5*c^4*f*h^3 + 6*a^2*b^5*c^5*f^3*h - 192*a^4*b*c^7*e^2*h^2 - 192*a^4*b^2*c^6*d*h^3 - 192*a^2*b^2*c^8*d^3*h
+ 128*a^3*b^3*c^6*e*g^3 - 28*a^3*b^4*c^5*d*h^3 + 12*a*b^6*c^5*d^2*h^2 + 6*a^2*b^6*c^4*d*h^3 - 192*a^3*b*c^8*e
^2*f^2 + 60*a*b^5*c^6*d^2*g^2 + 198*a*b^4*c^7*d^2*f^2 + 144*a^2*b^3*c^7*d*f^3 - 960*a^2*b*c^9*d^2*e^2 + 240*a*
b^3*c^8*d^2*e^2 + 15360*a^9*c^3*k*l^2*m - 12800*a^9*c^3*j*l*m^2 - 3840*a^8*c^4*j^2*k*m + 432*a^6*b^6*j*l*m^2 +
4608*a^8*c^4*j*k^2*l + 2880*a^8*c^4*h*k^2*m + 5120*a^8*c^4*f*l^2*m - 3072*a^8*c^4*h*k*l^2 + 270*a^5*b^7*h*k*m
^2 - 216*a^5*b^7*g*l*m^2 - 12800*a^8*c^4*e*l*m^2 - 4800*a^8*c^4*f*k*m^2 - 512*a^7*c^5*h^2*j*l - 3840*a^6*c^6*e
^2*k*m - 1280*a^7*c^5*f*j^2*m + 768*a^7*c^5*h*j^2*k + 144*a^4*b^8*g*j*m^2 - 90*a^4*b^8*f*k*m^2 + 8640*a^7*c^5*
d*k^2*m + 4608*a^7*c^5*e*k^2*l + 512*a^6*c^6*f^2*j*l - 9216*a^7*c^5*d*k*l^2 - 4096*a^7*c^5*e*j*l^2 + 320*a^6*c
^6*f^2*h*m - 90*a^3*b^9*d*k*m^2 + 15200*a^9*b*c^2*k*m^3 - 6192*a^8*b^3*c*k*m^3 + 5472*a^8*b*c^3*k^3*m - 4608*a
^5*c^7*d^2*j*l - 1024*a^7*c^5*f*h*l^2 + 150*a^6*b^5*c*k^3*m + 54*a^3*b^9*f*h*m^2 + 6*b^10*c^2*d^2*h*m - 14400*
a^7*c^5*d*h*m^2 + 8640*a^5*c^7*d^2*h*m + 2880*a^6*c^6*d*h^2*m + 2304*a^6*c^6*d*j^2*k - 512*a^6*c^6*e*h^2*l - 1
92*a^6*c^6*f*h^2*k + 6144*a^8*b*c^3*j*l^3 + 1536*a^7*b*c^4*j^3*l - 1280*a^5*c^7*e^2*f*m + 768*a^5*c^7*e^2*h*k
+ 256*a^6*c^6*f*h*j^2 + 192*a^6*b^5*c*j*l^3 + 54*a^2*b^10*d*h*m^2 - 18*b^9*c^3*d^2*f*m + 8*b^9*c^3*d^2*g*l - 2
*b^9*c^3*d^2*h*k + 4068*a^7*b^4*c*h*m^3 - 1728*a^6*c^6*d*h*k^2 + 960*a^5*c^7*d*f^2*m + 512*a^5*c^7*e*f^2*l - 3
072*a^6*c^6*d*f*l^2 - 16*b^8*c^4*d^2*e*l + 6*b^8*c^4*d^2*f*k - 4608*a^4*c^8*d^2*e*l + 2400*a^8*b*c^3*f*m^3 + 2
016*a^7*b*c^4*h*k^3 - 1728*a^4*c^8*d^2*f*k - 1146*a^6*b^5*c*f*m^3 + 224*a^6*b*c^5*h^3*k - 96*a^5*b^6*c*g*l^3 +
96*a^5*b*c^6*f^3*m + 2304*a^4*c^8*d*e^2*k + 768*a^5*c^7*d*f*j^2 + 6144*a^7*b*c^4*e*l^3 - 2280*a^5*b^6*c*d*m^3
+ 1536*a^4*b*c^7*e^3*l - 616*a*b^6*c^5*d^3*m + 512*a^6*b*c^5*g*j^3 + 256*a^4*c^8*e^2*f*h + 240*a*b^10*c*d^2*m
^2 + 6*b^7*c^5*d^2*f*h - 192*a^4*c^8*d*f^2*h + 4320*a^6*b*c^5*d*k^3 + 4320*a^3*b*c^8*d^3*k + 222*a*b^5*c^6*d^3
*k + 16*b^6*c^6*d^2*e*g + 96*a^5*b*c^6*f*h^3 + 96*a^4*b*c^7*f^3*h + 768*a^3*c^9*d*e^2*f + 512*a^3*b*c^8*e^3*g
+ 132*a*b^4*c^7*d^3*h + 2016*a^2*b*c^9*d^3*f - 496*a*b^3*c^8*d^3*f + 224*a^3*b*c^8*d*f^3 - 18*a*b^5*c^6*d*f^3
- 3264*a^8*b^2*c^2*k^2*m^2 - 6160*a^7*b^3*c^2*j^2*m^2 + 1104*a^7*b^3*c^2*k^2*l^2 - 1920*a^7*b^2*c^3*j^2*l^2 +
768*a^6*b^4*c^2*j^2*l^2 + 3888*a^7*b^2*c^3*h^2*m^2 - 3510*a^6*b^4*c^2*h^2*m^2 + 240*a^6*b^3*c^3*j^2*k^2 - 16*a
^5*b^5*c^2*j^2*k^2 + 1680*a^6*b^3*c^3*g^2*m^2 - 1648*a^6*b^3*c^3*h^2*l^2 - 1540*a^5*b^5*c^2*g^2*m^2 + 444*a^5*
b^5*c^2*h^2*l^2 - 960*a^6*b^2*c^4*h^2*k^2 - 576*a^6*b^2*c^4*f^2*m^2 - 512*a^6*b^2*c^4*g^2*l^2 - 480*a^5*b^4*c^
3*g^2*l^2 + 198*a^5*b^4*c^3*h^2*k^2 + 192*a^4*b^6*c^2*g^2*l^2 - 186*a^5*b^4*c^3*f^2*m^2 - 97*a^4*b^6*c^2*f^2*m
^2 - 9*a^4*b^6*c^2*h^2*k^2 - 6160*a^5*b^3*c^4*e^2*m^2 + 1680*a^4*b^5*c^3*e^2*m^2 - 240*a^5*b^3*c^4*g^2*k^2 - 2
40*a^5*b^3*c^4*f^2*l^2 - 144*a^3*b^7*c^2*e^2*m^2 + 60*a^4*b^5*c^3*g^2*k^2 - 36*a^4*b^5*c^3*f^2*l^2 + 36*a^3*b^
7*c^2*f^2*l^2 - 16*a^5*b^3*c^4*h^2*j^2 - 4*a^3*b^7*c^2*g^2*k^2 + 38512*a^5*b^2*c^5*d^2*m^2 - 32310*a^4*b^4*c^4
*d^2*m^2 + 12720*a^3*b^6*c^3*d^2*m^2 - 2500*a^2*b^8*c^2*d^2*m^2 - 1920*a^5*b^2*c^5*e^2*l^2 + 768*a^4*b^4*c^4*e
^2*l^2 - 464*a^5*b^2*c^5*f^2*k^2 - 384*a^5*b^2*c^5*g^2*j^2 - 64*a^3*b^6*c^3*e^2*l^2 + 42*a^4*b^4*c^4*f^2*k^2 +
12*a^3*b^6*c^3*f^2*k^2 - 13104*a^4*b^3*c^5*d^2*l^2 + 5628*a^3*b^5*c^4*d^2*l^2 - 1128*a^2*b^7*c^3*d^2*l^2 + 24
0*a^4*b^3*c^5*e^2*k^2 - 16*a^4*b^3*c^5*f^2*j^2 - 16*a^3*b^5*c^4*e^2*k^2 - 2880*a^4*b^2*c^6*d^2*k^2 + 1750*a^3*
b^4*c^5*d^2*k^2 - 345*a^2*b^6*c^4*d^2*k^2 - 48*a^4*b^3*c^5*g^2*h^2 - 4*a^3*b^5*c^4*g^2*h^2 + 240*a^3*b^3*c^6*d
^2*j^2 - 192*a^4*b^2*c^6*f^2*h^2 - 42*a^3*b^4*c^5*f^2*h^2 - 16*a^2*b^5*c^5*d^2*j^2 - 48*a^3*b^3*c^6*f^2*g^2 -
16*a^3*b^3*c^6*e^2*h^2 - 4*a^2*b^5*c^5*f^2*g^2 - 464*a^3*b^2*c^7*d^2*h^2 - 384*a^3*b^2*c^7*e^2*g^2 + 42*a^2*b^
4*c^6*d^2*h^2 - 240*a^2*b^3*c^7*d^2*g^2 - 16*a^2*b^3*c^7*e^2*f^2 - 960*a^2*b^2*c^8*d^2*f^2 + 6*b^11*c*d^2*k*m
- 18*a*b^11*d*f*m^2 - 7200*a^9*c^3*k^2*m^2 - 324*a^7*b^5*l^2*m^2 - 225*a^6*b^6*k^2*m^2 - 2048*a^8*c^4*j^2*l^2
- 144*a^5*b^7*j^2*m^2 - 2400*a^8*c^4*h^2*m^2 - 81*a^4*b^8*h^2*m^2 - 800*a^7*c^5*f^2*m^2 - 288*a^7*c^5*h^2*k^2
- 36*a^3*b^9*g^2*m^2 - 9*a^2*b^10*f^2*m^2 - 21600*a^6*c^6*d^2*m^2 - 2048*a^6*c^6*e^2*l^2 - 864*a^6*c^6*f^2*k^2
- 2592*a^5*c^7*d^2*k^2 - 1536*a^5*c^7*e^2*j^2 + 1536*a^8*b^2*c^2*l^4 - 32*a^5*c^7*f^2*h^2 + 360*a^7*b^2*c^3*k
^4 - 25*a^6*b^4*c^2*k^4 - 864*a^4*c^8*d^2*h^2 - 4*b^7*c^5*d^2*g^2 - 9*b^6*c^6*d^2*f^2 - 288*a^3*c^9*d^2*f^2 -
24*a^5*b^2*c^5*h^4 - 16*b^5*c^7*d^2*e^2 - 9*a^4*b^4*c^4*h^4 - 16*a^3*b^4*c^5*g^4 - 24*a^3*b^2*c^7*f^4 - 9*a^2*
b^4*c^6*f^4 - a^2*b^8*c^2*f^2*k^2 - a^2*b^6*c^4*f^2*h^2 + 630*a^7*b^5*k*m^3 + 8000*a^9*c^3*h*m^3 + 320*a^7*c^5
*h^3*m - 378*a^6*b^6*h*m^3 + 126*a^5*b^7*f*m^3 + 30*b^8*c^4*d^3*m + 24000*a^8*c^4*d*m^3 + 8640*a^4*c^8*d^3*m -
1728*a^7*c^5*f*k^3 - 192*a^5*c^7*f^3*k - 4*b^11*c*d^2*l^2 + 126*a^4*b^8*d*m^3 - 10*b^7*c^5*d^3*k + 4200*a^9*b
^2*c*m^4 - 1024*a^6*c^6*e*j^3 - 1024*a^4*c^8*e^3*j - 144*a^7*b^4*c*l^4 - 10*b^6*c^6*d^3*h - 1728*a^3*c^9*d^3*h
- 192*a^5*c^7*d*h^3 + 30*b^5*c^7*d^3*f + 360*a*b^2*c^9*d^4 - 9*b^12*d^2*m^2 - 10000*a^10*c^2*m^4 - 4096*a^9*c
^3*l^4 - 441*a^8*b^4*m^4 - 1296*a^8*c^4*k^4 - 256*a^7*c^5*j^4 - 16*a^6*c^6*h^4 - 16*a^4*c^8*f^4 - 256*a^3*c^9*
e^4 - 25*b^4*c^8*d^4 - 1296*a^2*c^10*d^4 - b^10*c^2*d^2*k^2 - b^8*c^4*d^2*h^2, z, k1), k1, 1, 4) + ((b*c^2*e -
2*a*c^2*g - a*b^2*l + 2*a^2*c*l + a*b*c*j)/(2*(4*a*c - b^2)) + (x^2*(2*c^3*e - b^3*l - b*c^2*g - 2*a*c^2*j +
b^2*c*j + 3*a*b*c*l))/(2*(4*a*c - b^2)) + (x*(2*a*c^3*d - 2*a^2*c^2*h - a^2*b^2*m - b^2*c^2*d + 2*a^3*c*m + a*
b*c^2*f + a^2*b*c*k))/(2*a*(4*a*c - b^2)) - (x^3*(2*a^2*c^2*k + b*c^3*d - 2*a*c^3*f + a*b^3*m + a*b*c^2*h - a*
b^2*c*k - 3*a^2*b*c*m))/(2*a*(4*a*c - b^2)))/(a*c^2 + c^3*x^4 + b*c^2*x^2) + (m*x)/c^2

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((m*x**8+l*x**7+k*x**6+j*x**5+h*x**4+g*x**3+f*x**2+e*x+d)/(c*x**4+b*x**2+a)**2,x)

[Out]

Timed out

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