3.20 \(\int \frac {1}{(a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3)^3} \, dx\)

Optimal. Leaf size=495 \[ \frac {3 f^5 \log (e+f x) \left (2 a^2 d^2 f^2-a b d f (7 d e-3 c f)+b^2 \left (2 c^2 f^2-7 c d e f+7 d^2 e^2\right )\right )}{(b e-a f)^5 (d e-c f)^5}-\frac {3 d^5 \log (c+d x) \left (2 a^2 d^2 f^2+a b d f (3 d e-7 c f)+b^2 \left (7 c^2 f^2-7 c d e f+2 d^2 e^2\right )\right )}{(b c-a d)^5 (d e-c f)^5}+\frac {3 b^5 \log (a+b x) \left (7 a^2 d^2 f^2-7 a b d f (c f+d e)+b^2 \left (2 c^2 f^2+3 c d e f+2 d^2 e^2\right )\right )}{(b c-a d)^5 (b e-a f)^5}+\frac {3 b^5 (-2 a d f+b c f+b d e)}{(a+b x) (b c-a d)^4 (b e-a f)^4}-\frac {b^5}{2 (a+b x)^2 (b c-a d)^3 (b e-a f)^3}+\frac {3 d^5 (a d f-2 b c f+b d e)}{(c+d x) (b c-a d)^4 (d e-c f)^4}+\frac {d^5}{2 (c+d x)^2 (b c-a d)^3 (d e-c f)^3}-\frac {3 f^5 (-a d f-b c f+2 b d e)}{(e+f x) (b e-a f)^4 (d e-c f)^4}-\frac {f^5}{2 (e+f x)^2 (b e-a f)^3 (d e-c f)^3} \]

[Out]

-1/2*b^5/(-a*d+b*c)^3/(-a*f+b*e)^3/(b*x+a)^2+3*b^5*(-2*a*d*f+b*c*f+b*d*e)/(-a*d+b*c)^4/(-a*f+b*e)^4/(b*x+a)+1/
2*d^5/(-a*d+b*c)^3/(-c*f+d*e)^3/(d*x+c)^2+3*d^5*(a*d*f-2*b*c*f+b*d*e)/(-a*d+b*c)^4/(-c*f+d*e)^4/(d*x+c)-1/2*f^
5/(-a*f+b*e)^3/(-c*f+d*e)^3/(f*x+e)^2-3*f^5*(-a*d*f-b*c*f+2*b*d*e)/(-a*f+b*e)^4/(-c*f+d*e)^4/(f*x+e)+3*b^5*(7*
a^2*d^2*f^2-7*a*b*d*f*(c*f+d*e)+b^2*(2*c^2*f^2+3*c*d*e*f+2*d^2*e^2))*ln(b*x+a)/(-a*d+b*c)^5/(-a*f+b*e)^5-3*d^5
*(2*a^2*d^2*f^2+a*b*d*f*(-7*c*f+3*d*e)+b^2*(7*c^2*f^2-7*c*d*e*f+2*d^2*e^2))*ln(d*x+c)/(-a*d+b*c)^5/(-c*f+d*e)^
5+3*f^5*(2*a^2*d^2*f^2-a*b*d*f*(-3*c*f+7*d*e)+b^2*(2*c^2*f^2-7*c*d*e*f+7*d^2*e^2))*ln(f*x+e)/(-a*f+b*e)^5/(-c*
f+d*e)^5

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Rubi [A]  time = 1.46, antiderivative size = 495, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {2058} \[ \frac {3 b^5 \log (a+b x) \left (7 a^2 d^2 f^2-7 a b d f (c f+d e)+b^2 \left (2 c^2 f^2+3 c d e f+2 d^2 e^2\right )\right )}{(b c-a d)^5 (b e-a f)^5}-\frac {3 d^5 \log (c+d x) \left (2 a^2 d^2 f^2+a b d f (3 d e-7 c f)+b^2 \left (7 c^2 f^2-7 c d e f+2 d^2 e^2\right )\right )}{(b c-a d)^5 (d e-c f)^5}+\frac {3 f^5 \log (e+f x) \left (2 a^2 d^2 f^2-a b d f (7 d e-3 c f)+b^2 \left (2 c^2 f^2-7 c d e f+7 d^2 e^2\right )\right )}{(b e-a f)^5 (d e-c f)^5}+\frac {3 b^5 (-2 a d f+b c f+b d e)}{(a+b x) (b c-a d)^4 (b e-a f)^4}-\frac {b^5}{2 (a+b x)^2 (b c-a d)^3 (b e-a f)^3}+\frac {3 d^5 (a d f-2 b c f+b d e)}{(c+d x) (b c-a d)^4 (d e-c f)^4}+\frac {d^5}{2 (c+d x)^2 (b c-a d)^3 (d e-c f)^3}-\frac {3 f^5 (-a d f-b c f+2 b d e)}{(e+f x) (b e-a f)^4 (d e-c f)^4}-\frac {f^5}{2 (e+f x)^2 (b e-a f)^3 (d e-c f)^3} \]

Antiderivative was successfully verified.

[In]

Int[(a*c*e + (b*c*e + a*d*e + a*c*f)*x + (b*d*e + b*c*f + a*d*f)*x^2 + b*d*f*x^3)^(-3),x]

[Out]

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

Rule 2058

Int[(P_)^(p_), x_Symbol] :> With[{u = Factor[P]}, Int[ExpandIntegrand[u^p, x], x] /;  !SumQ[NonfreeFactors[u,
x]]] /; PolyQ[P, x] && ILtQ[p, 0]

Rubi steps

\begin {align*} \int \frac {1}{\left (a c e+(b c e+a d e+a c f) x+(b d e+b c f+a d f) x^2+b d f x^3\right )^3} \, dx &=\int \left (\frac {b^6}{(b c-a d)^3 (b e-a f)^3 (a+b x)^3}-\frac {3 b^6 (b d e+b c f-2 a d f)}{(b c-a d)^4 (b e-a f)^4 (a+b x)^2}+\frac {3 b^6 \left (7 a^2 d^2 f^2-7 a b d f (d e+c f)+b^2 \left (2 d^2 e^2+3 c d e f+2 c^2 f^2\right )\right )}{(b c-a d)^5 (b e-a f)^5 (a+b x)}+\frac {d^6}{(b c-a d)^3 (-d e+c f)^3 (c+d x)^3}-\frac {3 d^6 (b d e-2 b c f+a d f)}{(b c-a d)^4 (-d e+c f)^4 (c+d x)^2}+\frac {3 d^6 \left (-2 a^2 d^2 f^2-a b d f (3 d e-7 c f)-b^2 \left (2 d^2 e^2-7 c d e f+7 c^2 f^2\right )\right )}{(b c-a d)^5 (d e-c f)^5 (c+d x)}+\frac {f^6}{(b e-a f)^3 (d e-c f)^3 (e+f x)^3}-\frac {3 f^6 (-2 b d e+b c f+a d f)}{(b e-a f)^4 (d e-c f)^4 (e+f x)^2}+\frac {3 f^6 \left (2 a^2 d^2 f^2-a b d f (7 d e-3 c f)+b^2 \left (7 d^2 e^2-7 c d e f+2 c^2 f^2\right )\right )}{(b e-a f)^5 (d e-c f)^5 (e+f x)}\right ) \, dx\\ &=-\frac {b^5}{2 (b c-a d)^3 (b e-a f)^3 (a+b x)^2}+\frac {3 b^5 (b d e+b c f-2 a d f)}{(b c-a d)^4 (b e-a f)^4 (a+b x)}+\frac {d^5}{2 (b c-a d)^3 (d e-c f)^3 (c+d x)^2}+\frac {3 d^5 (b d e-2 b c f+a d f)}{(b c-a d)^4 (d e-c f)^4 (c+d x)}-\frac {f^5}{2 (b e-a f)^3 (d e-c f)^3 (e+f x)^2}-\frac {3 f^5 (2 b d e-b c f-a d f)}{(b e-a f)^4 (d e-c f)^4 (e+f x)}+\frac {3 b^5 \left (7 a^2 d^2 f^2-7 a b d f (d e+c f)+b^2 \left (2 d^2 e^2+3 c d e f+2 c^2 f^2\right )\right ) \log (a+b x)}{(b c-a d)^5 (b e-a f)^5}-\frac {3 d^5 \left (2 a^2 d^2 f^2+a b d f (3 d e-7 c f)+b^2 \left (2 d^2 e^2-7 c d e f+7 c^2 f^2\right )\right ) \log (c+d x)}{(b c-a d)^5 (d e-c f)^5}+\frac {3 f^5 \left (2 a^2 d^2 f^2-a b d f (7 d e-3 c f)+b^2 \left (7 d^2 e^2-7 c d e f+2 c^2 f^2\right )\right ) \log (e+f x)}{(b e-a f)^5 (d e-c f)^5}\\ \end {align*}

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Mathematica [A]  time = 1.19, size = 490, normalized size = 0.99 \[ \frac {1}{2} \left (\frac {6 f^5 \log (e+f x) \left (2 a^2 d^2 f^2+a b d f (3 c f-7 d e)+b^2 \left (2 c^2 f^2-7 c d e f+7 d^2 e^2\right )\right )}{(b e-a f)^5 (d e-c f)^5}+\frac {6 d^5 \log (c+d x) \left (2 a^2 d^2 f^2+a b d f (3 d e-7 c f)+b^2 \left (7 c^2 f^2-7 c d e f+2 d^2 e^2\right )\right )}{(b c-a d)^5 (c f-d e)^5}+\frac {6 b^5 \log (a+b x) \left (7 a^2 d^2 f^2-7 a b d f (c f+d e)+b^2 \left (2 c^2 f^2+3 c d e f+2 d^2 e^2\right )\right )}{(b c-a d)^5 (b e-a f)^5}+\frac {6 b^5 (-2 a d f+b c f+b d e)}{(a+b x) (b c-a d)^4 (b e-a f)^4}-\frac {b^5}{(a+b x)^2 (b c-a d)^3 (b e-a f)^3}+\frac {6 d^5 (a d f-2 b c f+b d e)}{(c+d x) (b c-a d)^4 (d e-c f)^4}-\frac {d^5}{(c+d x)^2 (b c-a d)^3 (c f-d e)^3}+\frac {6 f^5 (a d f+b c f-2 b d e)}{(e+f x) (b e-a f)^4 (d e-c f)^4}-\frac {f^5}{(e+f x)^2 (b e-a f)^3 (d e-c f)^3}\right ) \]

Antiderivative was successfully verified.

[In]

Integrate[(a*c*e + (b*c*e + a*d*e + a*c*f)*x + (b*d*e + b*c*f + a*d*f)*x^2 + b*d*f*x^3)^(-3),x]

[Out]

(-(b^5/((b*c - a*d)^3*(b*e - a*f)^3*(a + b*x)^2)) + (6*b^5*(b*d*e + b*c*f - 2*a*d*f))/((b*c - a*d)^4*(b*e - a*
f)^4*(a + b*x)) - d^5/((b*c - a*d)^3*(-(d*e) + c*f)^3*(c + d*x)^2) + (6*d^5*(b*d*e - 2*b*c*f + a*d*f))/((b*c -
a*d)^4*(d*e - c*f)^4*(c + d*x)) - f^5/((b*e - a*f)^3*(d*e - c*f)^3*(e + f*x)^2) + (6*f^5*(-2*b*d*e + b*c*f +
a*d*f))/((b*e - a*f)^4*(d*e - c*f)^4*(e + f*x)) + (6*b^5*(7*a^2*d^2*f^2 - 7*a*b*d*f*(d*e + c*f) + b^2*(2*d^2*e
^2 + 3*c*d*e*f + 2*c^2*f^2))*Log[a + b*x])/((b*c - a*d)^5*(b*e - a*f)^5) + (6*d^5*(2*a^2*d^2*f^2 + a*b*d*f*(3*
d*e - 7*c*f) + b^2*(2*d^2*e^2 - 7*c*d*e*f + 7*c^2*f^2))*Log[c + d*x])/((b*c - a*d)^5*(-(d*e) + c*f)^5) + (6*f^
5*(2*a^2*d^2*f^2 + a*b*d*f*(-7*d*e + 3*c*f) + b^2*(7*d^2*e^2 - 7*c*d*e*f + 2*c^2*f^2))*Log[e + f*x])/((b*e - a
*f)^5*(d*e - c*f)^5))/2

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^3,x, algorithm="fricas")

[Out]

Timed out

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giac [B]  time = 1.10, size = 6908, normalized size = 13.96 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^3,x, algorithm="giac")

[Out]

-3*(2*b^8*c^2*f^2 - 7*a*b^7*c*d*f^2 + 7*a^2*b^6*d^2*f^2 + 3*b^8*c*d*f*e - 7*a*b^7*d^2*f*e + 2*b^8*d^2*e^2)*log
(abs(b*x + a))/(a^5*b^6*c^5*f^5 - 5*a^6*b^5*c^4*d*f^5 + 10*a^7*b^4*c^3*d^2*f^5 - 10*a^8*b^3*c^2*d^3*f^5 + 5*a^
9*b^2*c*d^4*f^5 - a^10*b*d^5*f^5 - 5*a^4*b^7*c^5*f^4*e + 25*a^5*b^6*c^4*d*f^4*e - 50*a^6*b^5*c^3*d^2*f^4*e + 5
0*a^7*b^4*c^2*d^3*f^4*e - 25*a^8*b^3*c*d^4*f^4*e + 5*a^9*b^2*d^5*f^4*e + 10*a^3*b^8*c^5*f^3*e^2 - 50*a^4*b^7*c
^4*d*f^3*e^2 + 100*a^5*b^6*c^3*d^2*f^3*e^2 - 100*a^6*b^5*c^2*d^3*f^3*e^2 + 50*a^7*b^4*c*d^4*f^3*e^2 - 10*a^8*b
^3*d^5*f^3*e^2 - 10*a^2*b^9*c^5*f^2*e^3 + 50*a^3*b^8*c^4*d*f^2*e^3 - 100*a^4*b^7*c^3*d^2*f^2*e^3 + 100*a^5*b^6
*c^2*d^3*f^2*e^3 - 50*a^6*b^5*c*d^4*f^2*e^3 + 10*a^7*b^4*d^5*f^2*e^3 + 5*a*b^10*c^5*f*e^4 - 25*a^2*b^9*c^4*d*f
*e^4 + 50*a^3*b^8*c^3*d^2*f*e^4 - 50*a^4*b^7*c^2*d^3*f*e^4 + 25*a^5*b^6*c*d^4*f*e^4 - 5*a^6*b^5*d^5*f*e^4 - b^
11*c^5*e^5 + 5*a*b^10*c^4*d*e^5 - 10*a^2*b^9*c^3*d^2*e^5 + 10*a^3*b^8*c^2*d^3*e^5 - 5*a^4*b^7*c*d^4*e^5 + a^5*
b^6*d^5*e^5) + 3*(7*b^2*c^2*d^6*f^2 - 7*a*b*c*d^7*f^2 + 2*a^2*d^8*f^2 - 7*b^2*c*d^7*f*e + 3*a*b*d^8*f*e + 2*b^
2*d^8*e^2)*log(abs(d*x + c))/(b^5*c^10*d*f^5 - 5*a*b^4*c^9*d^2*f^5 + 10*a^2*b^3*c^8*d^3*f^5 - 10*a^3*b^2*c^7*d
^4*f^5 + 5*a^4*b*c^6*d^5*f^5 - a^5*c^5*d^6*f^5 - 5*b^5*c^9*d^2*f^4*e + 25*a*b^4*c^8*d^3*f^4*e - 50*a^2*b^3*c^7
*d^4*f^4*e + 50*a^3*b^2*c^6*d^5*f^4*e - 25*a^4*b*c^5*d^6*f^4*e + 5*a^5*c^4*d^7*f^4*e + 10*b^5*c^8*d^3*f^3*e^2
- 50*a*b^4*c^7*d^4*f^3*e^2 + 100*a^2*b^3*c^6*d^5*f^3*e^2 - 100*a^3*b^2*c^5*d^6*f^3*e^2 + 50*a^4*b*c^4*d^7*f^3*
e^2 - 10*a^5*c^3*d^8*f^3*e^2 - 10*b^5*c^7*d^4*f^2*e^3 + 50*a*b^4*c^6*d^5*f^2*e^3 - 100*a^2*b^3*c^5*d^6*f^2*e^3
+ 100*a^3*b^2*c^4*d^7*f^2*e^3 - 50*a^4*b*c^3*d^8*f^2*e^3 + 10*a^5*c^2*d^9*f^2*e^3 + 5*b^5*c^6*d^5*f*e^4 - 25*
a*b^4*c^5*d^6*f*e^4 + 50*a^2*b^3*c^4*d^7*f*e^4 - 50*a^3*b^2*c^3*d^8*f*e^4 + 25*a^4*b*c^2*d^9*f*e^4 - 5*a^5*c*d
^10*f*e^4 - b^5*c^5*d^6*e^5 + 5*a*b^4*c^4*d^7*e^5 - 10*a^2*b^3*c^3*d^8*e^5 + 10*a^3*b^2*c^2*d^9*e^5 - 5*a^4*b*
c*d^10*e^5 + a^5*d^11*e^5) + 3*(2*b^2*c^2*f^8 + 3*a*b*c*d*f^8 + 2*a^2*d^2*f^8 - 7*b^2*c*d*f^7*e - 7*a*b*d^2*f^
7*e + 7*b^2*d^2*f^6*e^2)*log(abs(f*x + e))/(a^5*c^5*f^11 - 5*a^4*b*c^5*f^10*e - 5*a^5*c^4*d*f^10*e + 10*a^3*b^
2*c^5*f^9*e^2 + 25*a^4*b*c^4*d*f^9*e^2 + 10*a^5*c^3*d^2*f^9*e^2 - 10*a^2*b^3*c^5*f^8*e^3 - 50*a^3*b^2*c^4*d*f^
8*e^3 - 50*a^4*b*c^3*d^2*f^8*e^3 - 10*a^5*c^2*d^3*f^8*e^3 + 5*a*b^4*c^5*f^7*e^4 + 50*a^2*b^3*c^4*d*f^7*e^4 + 1
00*a^3*b^2*c^3*d^2*f^7*e^4 + 50*a^4*b*c^2*d^3*f^7*e^4 + 5*a^5*c*d^4*f^7*e^4 - b^5*c^5*f^6*e^5 - 25*a*b^4*c^4*d
*f^6*e^5 - 100*a^2*b^3*c^3*d^2*f^6*e^5 - 100*a^3*b^2*c^2*d^3*f^6*e^5 - 25*a^4*b*c*d^4*f^6*e^5 - a^5*d^5*f^6*e^
5 + 5*b^5*c^4*d*f^5*e^6 + 50*a*b^4*c^3*d^2*f^5*e^6 + 100*a^2*b^3*c^2*d^3*f^5*e^6 + 50*a^3*b^2*c*d^4*f^5*e^6 +
5*a^4*b*d^5*f^5*e^6 - 10*b^5*c^3*d^2*f^4*e^7 - 50*a*b^4*c^2*d^3*f^4*e^7 - 50*a^2*b^3*c*d^4*f^4*e^7 - 10*a^3*b^
2*d^5*f^4*e^7 + 10*b^5*c^2*d^3*f^3*e^8 + 25*a*b^4*c*d^4*f^3*e^8 + 10*a^2*b^3*d^5*f^3*e^8 - 5*b^5*c*d^4*f^2*e^9
- 5*a*b^4*d^5*f^2*e^9 + b^5*d^5*f*e^10) + 1/2*(12*b^7*c^5*d^2*f^7*x^5 - 30*a*b^6*c^4*d^3*f^7*x^5 + 12*a^2*b^5
*c^3*d^4*f^7*x^5 + 12*a^3*b^4*c^2*d^5*f^7*x^5 - 30*a^4*b^3*c*d^6*f^7*x^5 + 12*a^5*b^2*d^7*f^7*x^5 - 30*b^7*c^4
*d^3*f^6*x^5*e + 96*a*b^6*c^3*d^4*f^6*x^5*e - 72*a^2*b^5*c^2*d^5*f^6*x^5*e + 96*a^3*b^4*c*d^6*f^6*x^5*e - 30*a
^4*b^3*d^7*f^6*x^5*e + 24*b^7*c^6*d*f^7*x^4 - 42*a*b^6*c^5*d^2*f^7*x^4 - 21*a^2*b^5*c^4*d^3*f^7*x^4 + 42*a^3*b
^4*c^3*d^4*f^7*x^4 - 21*a^4*b^3*c^2*d^5*f^7*x^4 - 42*a^5*b^2*c*d^6*f^7*x^4 + 24*a^6*b*d^7*f^7*x^4 + 12*b^7*c^3
*d^4*f^5*x^5*e^2 - 72*a*b^6*c^2*d^5*f^5*x^5*e^2 - 72*a^2*b^5*c*d^6*f^5*x^5*e^2 + 12*a^3*b^4*d^7*f^5*x^5*e^2 -
42*b^7*c^5*d^2*f^6*x^4*e + 102*a*b^6*c^4*d^3*f^6*x^4*e + 18*a^2*b^5*c^3*d^4*f^6*x^4*e + 18*a^3*b^4*c^2*d^5*f^6
*x^4*e + 102*a^4*b^3*c*d^6*f^6*x^4*e - 42*a^5*b^2*d^7*f^6*x^4*e + 12*b^7*c^7*f^7*x^3 + 6*a*b^6*c^6*d*f^7*x^3 -
74*a^2*b^5*c^5*d^2*f^7*x^3 + 38*a^3*b^4*c^4*d^3*f^7*x^3 + 38*a^4*b^3*c^3*d^4*f^7*x^3 - 74*a^5*b^2*c^2*d^5*f^7
*x^3 + 6*a^6*b*c*d^6*f^7*x^3 + 12*a^7*d^7*f^7*x^3 + 12*b^7*c^2*d^5*f^4*x^5*e^3 + 96*a*b^6*c*d^6*f^4*x^5*e^3 +
12*a^2*b^5*d^7*f^4*x^5*e^3 - 21*b^7*c^4*d^3*f^5*x^4*e^2 + 18*a*b^6*c^3*d^4*f^5*x^4*e^2 - 234*a^2*b^5*c^2*d^5*f
^5*x^4*e^2 + 18*a^3*b^4*c*d^6*f^5*x^4*e^2 - 21*a^4*b^3*d^7*f^5*x^4*e^2 + 6*b^7*c^6*d*f^6*x^3*e - 56*a*b^6*c^5*
d^2*f^6*x^3*e + 172*a^2*b^5*c^4*d^3*f^6*x^3*e - 136*a^3*b^4*c^3*d^4*f^6*x^3*e + 172*a^4*b^3*c^2*d^5*f^6*x^3*e
- 56*a^5*b^2*c*d^6*f^6*x^3*e + 6*a^6*b*d^7*f^6*x^3*e + 18*a*b^6*c^7*f^7*x^2 - 37*a^2*b^5*c^6*d*f^7*x^2 - 3*a^3
*b^4*c^5*d^2*f^7*x^2 + 32*a^4*b^3*c^4*d^3*f^7*x^2 - 3*a^5*b^2*c^3*d^4*f^7*x^2 - 37*a^6*b*c^2*d^5*f^7*x^2 + 18*
a^7*c*d^6*f^7*x^2 - 30*b^7*c*d^6*f^3*x^5*e^4 - 30*a*b^6*d^7*f^3*x^5*e^4 + 42*b^7*c^3*d^4*f^4*x^4*e^3 + 18*a*b^
6*c^2*d^5*f^4*x^4*e^3 + 18*a^2*b^5*c*d^6*f^4*x^4*e^3 + 42*a^3*b^4*d^7*f^4*x^4*e^3 - 74*b^7*c^5*d^2*f^5*x^3*e^2
+ 172*a*b^6*c^4*d^3*f^5*x^3*e^2 - 104*a^2*b^5*c^3*d^4*f^5*x^3*e^2 - 104*a^3*b^4*c^2*d^5*f^5*x^3*e^2 + 172*a^4
*b^3*c*d^6*f^5*x^3*e^2 - 74*a^5*b^2*d^7*f^5*x^3*e^2 + 18*b^7*c^7*f^6*x^2*e - 34*a*b^6*c^6*d*f^6*x^2*e + 9*a^2*
b^5*c^5*d^2*f^6*x^2*e + a^3*b^4*c^4*d^3*f^6*x^2*e + a^4*b^3*c^3*d^4*f^6*x^2*e + 9*a^5*b^2*c^2*d^5*f^6*x^2*e -
34*a^6*b*c*d^6*f^6*x^2*e + 18*a^7*d^7*f^6*x^2*e + 4*a^2*b^5*c^7*f^7*x - 12*a^3*b^4*c^6*d*f^7*x + 8*a^4*b^3*c^5
*d^2*f^7*x + 8*a^5*b^2*c^4*d^3*f^7*x - 12*a^6*b*c^3*d^4*f^7*x + 4*a^7*c^2*d^5*f^7*x + 12*b^7*d^7*f^2*x^5*e^5 -
21*b^7*c^2*d^5*f^3*x^4*e^4 + 102*a*b^6*c*d^6*f^3*x^4*e^4 - 21*a^2*b^5*d^7*f^3*x^4*e^4 + 38*b^7*c^4*d^3*f^4*x^
3*e^3 - 136*a*b^6*c^3*d^4*f^4*x^3*e^3 - 104*a^2*b^5*c^2*d^5*f^4*x^3*e^3 - 136*a^3*b^4*c*d^6*f^4*x^3*e^3 + 38*a
^4*b^3*d^7*f^4*x^3*e^3 - 37*b^7*c^6*d*f^5*x^2*e^2 + 9*a*b^6*c^5*d^2*f^5*x^2*e^2 + 234*a^2*b^5*c^4*d^3*f^5*x^2*
e^2 - 208*a^3*b^4*c^3*d^4*f^5*x^2*e^2 + 234*a^4*b^3*c^2*d^5*f^5*x^2*e^2 + 9*a^5*b^2*c*d^6*f^5*x^2*e^2 - 37*a^6
*b*d^7*f^5*x^2*e^2 + 28*a*b^6*c^7*f^6*x*e - 66*a^2*b^5*c^6*d*f^6*x*e + 34*a^3*b^4*c^5*d^2*f^6*x*e - 16*a^4*b^3
*c^4*d^3*f^6*x*e + 34*a^5*b^2*c^3*d^4*f^6*x*e - 66*a^6*b*c^2*d^5*f^6*x*e + 28*a^7*c*d^6*f^6*x*e - a^3*b^4*c^7*
f^7 + 4*a^4*b^3*c^6*d*f^7 - 6*a^5*b^2*c^5*d^2*f^7 + 4*a^6*b*c^4*d^3*f^7 - a^7*c^3*d^4*f^7 - 42*b^7*c*d^6*f^2*x
^4*e^5 - 42*a*b^6*d^7*f^2*x^4*e^5 + 38*b^7*c^3*d^4*f^3*x^3*e^4 + 172*a*b^6*c^2*d^5*f^3*x^3*e^4 + 172*a^2*b^5*c
*d^6*f^3*x^3*e^4 + 38*a^3*b^4*d^7*f^3*x^3*e^4 - 3*b^7*c^5*d^2*f^4*x^2*e^3 + a*b^6*c^4*d^3*f^4*x^2*e^3 - 208*a^
2*b^5*c^3*d^4*f^4*x^2*e^3 - 208*a^3*b^4*c^2*d^5*f^4*x^2*e^3 + a^4*b^3*c*d^6*f^4*x^2*e^3 - 3*a^5*b^2*d^7*f^4*x^
2*e^3 + 4*b^7*c^7*f^5*x*e^2 - 66*a*b^6*c^6*d*f^5*x*e^2 + 156*a^2*b^5*c^5*d^2*f^5*x*e^2 - 52*a^3*b^4*c^4*d^3*f^
5*x*e^2 - 52*a^4*b^3*c^3*d^4*f^5*x*e^2 + 156*a^5*b^2*c^2*d^5*f^5*x*e^2 - 66*a^6*b*c*d^6*f^5*x*e^2 + 4*a^7*d^7*
f^5*x*e^2 + 7*a^2*b^5*c^7*f^6*e - 21*a^3*b^4*c^6*d*f^6*e + 14*a^4*b^3*c^5*d^2*f^6*e + 14*a^5*b^2*c^4*d^3*f^6*e
- 21*a^6*b*c^3*d^4*f^6*e + 7*a^7*c^2*d^5*f^6*e + 24*b^7*d^7*f*x^4*e^6 - 74*b^7*c^2*d^5*f^2*x^3*e^5 - 56*a*b^6
*c*d^6*f^2*x^3*e^5 - 74*a^2*b^5*d^7*f^2*x^3*e^5 + 32*b^7*c^4*d^3*f^3*x^2*e^4 + a*b^6*c^3*d^4*f^3*x^2*e^4 + 234
*a^2*b^5*c^2*d^5*f^3*x^2*e^4 + a^3*b^4*c*d^6*f^3*x^2*e^4 + 32*a^4*b^3*d^7*f^3*x^2*e^4 - 12*b^7*c^6*d*f^4*x*e^3
+ 34*a*b^6*c^5*d^2*f^4*x*e^3 - 52*a^2*b^5*c^4*d^3*f^4*x*e^3 - 52*a^4*b^3*c^2*d^5*f^4*x*e^3 + 34*a^5*b^2*c*d^6
*f^4*x*e^3 - 12*a^6*b*d^7*f^4*x*e^3 + 7*a*b^6*c^7*f^5*e^2 - 26*a^2*b^5*c^6*d*f^5*e^2 + 52*a^3*b^4*c^5*d^2*f^5*
e^2 - 78*a^4*b^3*c^4*d^3*f^5*e^2 + 52*a^5*b^2*c^3*d^4*f^5*e^2 - 26*a^6*b*c^2*d^5*f^5*e^2 + 7*a^7*c*d^6*f^5*e^2
+ 6*b^7*c*d^6*f*x^3*e^6 + 6*a*b^6*d^7*f*x^3*e^6 - 3*b^7*c^3*d^4*f^2*x^2*e^5 + 9*a*b^6*c^2*d^5*f^2*x^2*e^5 + 9
*a^2*b^5*c*d^6*f^2*x^2*e^5 - 3*a^3*b^4*d^7*f^2*x^2*e^5 + 8*b^7*c^5*d^2*f^3*x*e^4 - 16*a*b^6*c^4*d^3*f^3*x*e^4
- 52*a^2*b^5*c^3*d^4*f^3*x*e^4 - 52*a^3*b^4*c^2*d^5*f^3*x*e^4 - 16*a^4*b^3*c*d^6*f^3*x*e^4 + 8*a^5*b^2*d^7*f^3
*x*e^4 - b^7*c^7*f^4*e^3 - 21*a*b^6*c^6*d*f^4*e^3 + 52*a^2*b^5*c^5*d^2*f^4*e^3 + 52*a^5*b^2*c^2*d^5*f^4*e^3 -
21*a^6*b*c*d^6*f^4*e^3 - a^7*d^7*f^4*e^3 + 12*b^7*d^7*x^3*e^7 - 37*b^7*c^2*d^5*f*x^2*e^6 - 34*a*b^6*c*d^6*f*x^
2*e^6 - 37*a^2*b^5*d^7*f*x^2*e^6 + 8*b^7*c^4*d^3*f^2*x*e^5 + 34*a*b^6*c^3*d^4*f^2*x*e^5 + 156*a^2*b^5*c^2*d^5*
f^2*x*e^5 + 34*a^3*b^4*c*d^6*f^2*x*e^5 + 8*a^4*b^3*d^7*f^2*x*e^5 + 4*b^7*c^6*d*f^3*e^4 + 14*a*b^6*c^5*d^2*f^3*
e^4 - 78*a^2*b^5*c^4*d^3*f^3*e^4 - 78*a^4*b^3*c^2*d^5*f^3*e^4 + 14*a^5*b^2*c*d^6*f^3*e^4 + 4*a^6*b*d^7*f^3*e^4
+ 18*b^7*c*d^6*x^2*e^7 + 18*a*b^6*d^7*x^2*e^7 - 12*b^7*c^3*d^4*f*x*e^6 - 66*a*b^6*c^2*d^5*f*x*e^6 - 66*a^2*b^
5*c*d^6*f*x*e^6 - 12*a^3*b^4*d^7*f*x*e^6 - 6*b^7*c^5*d^2*f^2*e^5 + 14*a*b^6*c^4*d^3*f^2*e^5 + 52*a^2*b^5*c^3*d
^4*f^2*e^5 + 52*a^3*b^4*c^2*d^5*f^2*e^5 + 14*a^4*b^3*c*d^6*f^2*e^5 - 6*a^5*b^2*d^7*f^2*e^5 + 4*b^7*c^2*d^5*x*e
^7 + 28*a*b^6*c*d^6*x*e^7 + 4*a^2*b^5*d^7*x*e^7 + 4*b^7*c^4*d^3*f*e^6 - 21*a*b^6*c^3*d^4*f*e^6 - 26*a^2*b^5*c^
2*d^5*f*e^6 - 21*a^3*b^4*c*d^6*f*e^6 + 4*a^4*b^3*d^7*f*e^6 - b^7*c^3*d^4*e^7 + 7*a*b^6*c^2*d^5*e^7 + 7*a^2*b^5
*c*d^6*e^7 - a^3*b^4*d^7*e^7)/((a^4*b^4*c^8*f^8 - 4*a^5*b^3*c^7*d*f^8 + 6*a^6*b^2*c^6*d^2*f^8 - 4*a^7*b*c^5*d^
3*f^8 + a^8*c^4*d^4*f^8 - 4*a^3*b^5*c^8*f^7*e + 12*a^4*b^4*c^7*d*f^7*e - 8*a^5*b^3*c^6*d^2*f^7*e - 8*a^6*b^2*c
^5*d^3*f^7*e + 12*a^7*b*c^4*d^4*f^7*e - 4*a^8*c^3*d^5*f^7*e + 6*a^2*b^6*c^8*f^6*e^2 - 8*a^3*b^5*c^7*d*f^6*e^2
- 22*a^4*b^4*c^6*d^2*f^6*e^2 + 48*a^5*b^3*c^5*d^3*f^6*e^2 - 22*a^6*b^2*c^4*d^4*f^6*e^2 - 8*a^7*b*c^3*d^5*f^6*e
^2 + 6*a^8*c^2*d^6*f^6*e^2 - 4*a*b^7*c^8*f^5*e^3 - 8*a^2*b^6*c^7*d*f^5*e^3 + 48*a^3*b^5*c^6*d^2*f^5*e^3 - 36*a
^4*b^4*c^5*d^3*f^5*e^3 - 36*a^5*b^3*c^4*d^4*f^5*e^3 + 48*a^6*b^2*c^3*d^5*f^5*e^3 - 8*a^7*b*c^2*d^6*f^5*e^3 - 4
*a^8*c*d^7*f^5*e^3 + b^8*c^8*f^4*e^4 + 12*a*b^7*c^7*d*f^4*e^4 - 22*a^2*b^6*c^6*d^2*f^4*e^4 - 36*a^3*b^5*c^5*d^
3*f^4*e^4 + 90*a^4*b^4*c^4*d^4*f^4*e^4 - 36*a^5*b^3*c^3*d^5*f^4*e^4 - 22*a^6*b^2*c^2*d^6*f^4*e^4 + 12*a^7*b*c*
d^7*f^4*e^4 + a^8*d^8*f^4*e^4 - 4*b^8*c^7*d*f^3*e^5 - 8*a*b^7*c^6*d^2*f^3*e^5 + 48*a^2*b^6*c^5*d^3*f^3*e^5 - 3
6*a^3*b^5*c^4*d^4*f^3*e^5 - 36*a^4*b^4*c^3*d^5*f^3*e^5 + 48*a^5*b^3*c^2*d^6*f^3*e^5 - 8*a^6*b^2*c*d^7*f^3*e^5
- 4*a^7*b*d^8*f^3*e^5 + 6*b^8*c^6*d^2*f^2*e^6 - 8*a*b^7*c^5*d^3*f^2*e^6 - 22*a^2*b^6*c^4*d^4*f^2*e^6 + 48*a^3*
b^5*c^3*d^5*f^2*e^6 - 22*a^4*b^4*c^2*d^6*f^2*e^6 - 8*a^5*b^3*c*d^7*f^2*e^6 + 6*a^6*b^2*d^8*f^2*e^6 - 4*b^8*c^5
*d^3*f*e^7 + 12*a*b^7*c^4*d^4*f*e^7 - 8*a^2*b^6*c^3*d^5*f*e^7 - 8*a^3*b^5*c^2*d^6*f*e^7 + 12*a^4*b^4*c*d^7*f*e
^7 - 4*a^5*b^3*d^8*f*e^7 + b^8*c^4*d^4*e^8 - 4*a*b^7*c^3*d^5*e^8 + 6*a^2*b^6*c^2*d^6*e^8 - 4*a^3*b^5*c*d^7*e^8
+ a^4*b^4*d^8*e^8)*(b*d*f*x^3 + b*c*f*x^2 + a*d*f*x^2 + b*d*x^2*e + a*c*f*x + b*c*x*e + a*d*x*e + a*c*e)^2)

________________________________________________________________________________________

maple [B]  time = 0.03, size = 1076, normalized size = 2.17 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^3,x)

[Out]

21*d^6/(c*f-d*e)^5/(a*d-b*c)^5*ln(d*x+c)*b^2*c*e*f-21*b^6/(a*f-b*e)^5/(a*d-b*c)^5*ln(b*x+a)*a*c*d*f^2-21*b^6/(
a*f-b*e)^5/(a*d-b*c)^5*ln(b*x+a)*a*d^2*e*f+9*b^7/(a*f-b*e)^5/(a*d-b*c)^5*ln(b*x+a)*c*d*e*f+9*f^7/(c*f-d*e)^5/(
a*f-b*e)^5*ln(f*x+e)*a*b*c*d-21*f^6/(c*f-d*e)^5/(a*f-b*e)^5*ln(f*x+e)*a*b*d^2*e-21*f^6/(c*f-d*e)^5/(a*f-b*e)^5
*ln(f*x+e)*b^2*c*d*e+21*d^6/(c*f-d*e)^5/(a*d-b*c)^5*ln(d*x+c)*a*b*c*f^2-9*d^7/(c*f-d*e)^5/(a*d-b*c)^5*ln(d*x+c
)*a*b*e*f-6*d^7/(c*f-d*e)^5/(a*d-b*c)^5*ln(d*x+c)*e^2*b^2+3*b^6/(a*f-b*e)^4/(a*d-b*c)^4/(b*x+a)*c*f+3*b^6/(a*f
-b*e)^4/(a*d-b*c)^4/(b*x+a)*d*e+6*b^7/(a*f-b*e)^5/(a*d-b*c)^5*ln(b*x+a)*c^2*f^2+6*b^7/(a*f-b*e)^5/(a*d-b*c)^5*
ln(b*x+a)*d^2*e^2+3*f^6/(c*f-d*e)^4/(a*f-b*e)^4/(f*x+e)*b*c+6*f^7/(c*f-d*e)^5/(a*f-b*e)^5*ln(f*x+e)*a^2*d^2+6*
f^7/(c*f-d*e)^5/(a*f-b*e)^5*ln(f*x+e)*b^2*c^2+3*d^6/(c*f-d*e)^4/(a*d-b*c)^4/(d*x+c)*a*f+3*d^6/(c*f-d*e)^4/(a*d
-b*c)^4/(d*x+c)*b*e-6*d^7/(c*f-d*e)^5/(a*d-b*c)^5*ln(d*x+c)*a^2*f^2+3*f^6/(c*f-d*e)^4/(a*f-b*e)^4/(f*x+e)*a*d-
1/2*b^5/(a*f-b*e)^3/(a*d-b*c)^3/(b*x+a)^2+1/2*d^5/(c*f-d*e)^3/(a*d-b*c)^3/(d*x+c)^2-1/2*f^5/(c*f-d*e)^3/(a*f-b
*e)^3/(f*x+e)^2-6*f^5/(c*f-d*e)^4/(a*f-b*e)^4/(f*x+e)*b*d*e+21*f^5/(c*f-d*e)^5/(a*f-b*e)^5*ln(f*x+e)*d^2*e^2*b
^2-6*d^5/(c*f-d*e)^4/(a*d-b*c)^4/(d*x+c)*b*c*f-21*d^5/(c*f-d*e)^5/(a*d-b*c)^5*ln(d*x+c)*b^2*c^2*f^2-6*b^5/(a*f
-b*e)^4/(a*d-b*c)^4/(b*x+a)*a*d*f+21*b^5/(a*f-b*e)^5/(a*d-b*c)^5*ln(b*x+a)*a^2*d^2*f^2

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maxima [B]  time = 5.72, size = 11005, normalized size = 22.23 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x^2+b*d*f*x^3)^3,x, algorithm="maxima")

[Out]

3*(2*b^7*d^2*e^2 + (3*b^7*c*d - 7*a*b^6*d^2)*e*f + (2*b^7*c^2 - 7*a*b^6*c*d + 7*a^2*b^5*d^2)*f^2)*log(b*x + a)
/((b^10*c^5 - 5*a*b^9*c^4*d + 10*a^2*b^8*c^3*d^2 - 10*a^3*b^7*c^2*d^3 + 5*a^4*b^6*c*d^4 - a^5*b^5*d^5)*e^5 - 5
*(a*b^9*c^5 - 5*a^2*b^8*c^4*d + 10*a^3*b^7*c^3*d^2 - 10*a^4*b^6*c^2*d^3 + 5*a^5*b^5*c*d^4 - a^6*b^4*d^5)*e^4*f
+ 10*(a^2*b^8*c^5 - 5*a^3*b^7*c^4*d + 10*a^4*b^6*c^3*d^2 - 10*a^5*b^5*c^2*d^3 + 5*a^6*b^4*c*d^4 - a^7*b^3*d^5
)*e^3*f^2 - 10*(a^3*b^7*c^5 - 5*a^4*b^6*c^4*d + 10*a^5*b^5*c^3*d^2 - 10*a^6*b^4*c^2*d^3 + 5*a^7*b^3*c*d^4 - a^
8*b^2*d^5)*e^2*f^3 + 5*(a^4*b^6*c^5 - 5*a^5*b^5*c^4*d + 10*a^6*b^4*c^3*d^2 - 10*a^7*b^3*c^2*d^3 + 5*a^8*b^2*c*
d^4 - a^9*b*d^5)*e*f^4 - (a^5*b^5*c^5 - 5*a^6*b^4*c^4*d + 10*a^7*b^3*c^3*d^2 - 10*a^8*b^2*c^2*d^3 + 5*a^9*b*c*
d^4 - a^10*d^5)*f^5) - 3*(2*b^2*d^7*e^2 - (7*b^2*c*d^6 - 3*a*b*d^7)*e*f + (7*b^2*c^2*d^5 - 7*a*b*c*d^6 + 2*a^2
*d^7)*f^2)*log(d*x + c)/((b^5*c^5*d^5 - 5*a*b^4*c^4*d^6 + 10*a^2*b^3*c^3*d^7 - 10*a^3*b^2*c^2*d^8 + 5*a^4*b*c*
d^9 - a^5*d^10)*e^5 - 5*(b^5*c^6*d^4 - 5*a*b^4*c^5*d^5 + 10*a^2*b^3*c^4*d^6 - 10*a^3*b^2*c^3*d^7 + 5*a^4*b*c^2
*d^8 - a^5*c*d^9)*e^4*f + 10*(b^5*c^7*d^3 - 5*a*b^4*c^6*d^4 + 10*a^2*b^3*c^5*d^5 - 10*a^3*b^2*c^4*d^6 + 5*a^4*
b*c^3*d^7 - a^5*c^2*d^8)*e^3*f^2 - 10*(b^5*c^8*d^2 - 5*a*b^4*c^7*d^3 + 10*a^2*b^3*c^6*d^4 - 10*a^3*b^2*c^5*d^5
+ 5*a^4*b*c^4*d^6 - a^5*c^3*d^7)*e^2*f^3 + 5*(b^5*c^9*d - 5*a*b^4*c^8*d^2 + 10*a^2*b^3*c^7*d^3 - 10*a^3*b^2*c
^6*d^4 + 5*a^4*b*c^5*d^5 - a^5*c^4*d^6)*e*f^4 - (b^5*c^10 - 5*a*b^4*c^9*d + 10*a^2*b^3*c^8*d^2 - 10*a^3*b^2*c^
7*d^3 + 5*a^4*b*c^6*d^4 - a^5*c^5*d^5)*f^5) + 3*(7*b^2*d^2*e^2*f^5 - 7*(b^2*c*d + a*b*d^2)*e*f^6 + (2*b^2*c^2
+ 3*a*b*c*d + 2*a^2*d^2)*f^7)*log(f*x + e)/(b^5*d^5*e^10 + a^5*c^5*f^10 - 5*(b^5*c*d^4 + a*b^4*d^5)*e^9*f + 5*
(2*b^5*c^2*d^3 + 5*a*b^4*c*d^4 + 2*a^2*b^3*d^5)*e^8*f^2 - 10*(b^5*c^3*d^2 + 5*a*b^4*c^2*d^3 + 5*a^2*b^3*c*d^4
+ a^3*b^2*d^5)*e^7*f^3 + 5*(b^5*c^4*d + 10*a*b^4*c^3*d^2 + 20*a^2*b^3*c^2*d^3 + 10*a^3*b^2*c*d^4 + a^4*b*d^5)*
e^6*f^4 - (b^5*c^5 + 25*a*b^4*c^4*d + 100*a^2*b^3*c^3*d^2 + 100*a^3*b^2*c^2*d^3 + 25*a^4*b*c*d^4 + a^5*d^5)*e^
5*f^5 + 5*(a*b^4*c^5 + 10*a^2*b^3*c^4*d + 20*a^3*b^2*c^3*d^2 + 10*a^4*b*c^2*d^3 + a^5*c*d^4)*e^4*f^6 - 10*(a^2
*b^3*c^5 + 5*a^3*b^2*c^4*d + 5*a^4*b*c^3*d^2 + a^5*c^2*d^3)*e^3*f^7 + 5*(2*a^3*b^2*c^5 + 5*a^4*b*c^4*d + 2*a^5
*c^3*d^2)*e^2*f^8 - 5*(a^4*b*c^5 + a^5*c^4*d)*e*f^9) - 1/2*((b^7*c^3*d^4 - 7*a*b^6*c^2*d^5 - 7*a^2*b^5*c*d^6 +
a^3*b^4*d^7)*e^7 - (4*b^7*c^4*d^3 - 21*a*b^6*c^3*d^4 - 26*a^2*b^5*c^2*d^5 - 21*a^3*b^4*c*d^6 + 4*a^4*b^3*d^7)
*e^6*f + 2*(3*b^7*c^5*d^2 - 7*a*b^6*c^4*d^3 - 26*a^2*b^5*c^3*d^4 - 26*a^3*b^4*c^2*d^5 - 7*a^4*b^3*c*d^6 + 3*a^
5*b^2*d^7)*e^5*f^2 - 2*(2*b^7*c^6*d + 7*a*b^6*c^5*d^2 - 39*a^2*b^5*c^4*d^3 - 39*a^4*b^3*c^2*d^5 + 7*a^5*b^2*c*
d^6 + 2*a^6*b*d^7)*e^4*f^3 + (b^7*c^7 + 21*a*b^6*c^6*d - 52*a^2*b^5*c^5*d^2 - 52*a^5*b^2*c^2*d^5 + 21*a^6*b*c*
d^6 + a^7*d^7)*e^3*f^4 - (7*a*b^6*c^7 - 26*a^2*b^5*c^6*d + 52*a^3*b^4*c^5*d^2 - 78*a^4*b^3*c^4*d^3 + 52*a^5*b^
2*c^3*d^4 - 26*a^6*b*c^2*d^5 + 7*a^7*c*d^6)*e^2*f^5 - 7*(a^2*b^5*c^7 - 3*a^3*b^4*c^6*d + 2*a^4*b^3*c^5*d^2 + 2
*a^5*b^2*c^4*d^3 - 3*a^6*b*c^3*d^4 + a^7*c^2*d^5)*e*f^6 + (a^3*b^4*c^7 - 4*a^4*b^3*c^6*d + 6*a^5*b^2*c^5*d^2 -
4*a^6*b*c^4*d^3 + a^7*c^3*d^4)*f^7 - 6*(2*b^7*d^7*e^5*f^2 - 5*(b^7*c*d^6 + a*b^6*d^7)*e^4*f^3 + 2*(b^7*c^2*d^
5 + 8*a*b^6*c*d^6 + a^2*b^5*d^7)*e^3*f^4 + 2*(b^7*c^3*d^4 - 6*a*b^6*c^2*d^5 - 6*a^2*b^5*c*d^6 + a^3*b^4*d^7)*e
^2*f^5 - (5*b^7*c^4*d^3 - 16*a*b^6*c^3*d^4 + 12*a^2*b^5*c^2*d^5 - 16*a^3*b^4*c*d^6 + 5*a^4*b^3*d^7)*e*f^6 + (2
*b^7*c^5*d^2 - 5*a*b^6*c^4*d^3 + 2*a^2*b^5*c^3*d^4 + 2*a^3*b^4*c^2*d^5 - 5*a^4*b^3*c*d^6 + 2*a^5*b^2*d^7)*f^7)
*x^5 - 3*(8*b^7*d^7*e^6*f - 14*(b^7*c*d^6 + a*b^6*d^7)*e^5*f^2 - (7*b^7*c^2*d^5 - 34*a*b^6*c*d^6 + 7*a^2*b^5*d
^7)*e^4*f^3 + 2*(7*b^7*c^3*d^4 + 3*a*b^6*c^2*d^5 + 3*a^2*b^5*c*d^6 + 7*a^3*b^4*d^7)*e^3*f^4 - (7*b^7*c^4*d^3 -
6*a*b^6*c^3*d^4 + 78*a^2*b^5*c^2*d^5 - 6*a^3*b^4*c*d^6 + 7*a^4*b^3*d^7)*e^2*f^5 - 2*(7*b^7*c^5*d^2 - 17*a*b^6
*c^4*d^3 - 3*a^2*b^5*c^3*d^4 - 3*a^3*b^4*c^2*d^5 - 17*a^4*b^3*c*d^6 + 7*a^5*b^2*d^7)*e*f^6 + (8*b^7*c^6*d - 14
*a*b^6*c^5*d^2 - 7*a^2*b^5*c^4*d^3 + 14*a^3*b^4*c^3*d^4 - 7*a^4*b^3*c^2*d^5 - 14*a^5*b^2*c*d^6 + 8*a^6*b*d^7)*
f^7)*x^4 - 2*(6*b^7*d^7*e^7 + 3*(b^7*c*d^6 + a*b^6*d^7)*e^6*f - (37*b^7*c^2*d^5 + 28*a*b^6*c*d^6 + 37*a^2*b^5*
d^7)*e^5*f^2 + (19*b^7*c^3*d^4 + 86*a*b^6*c^2*d^5 + 86*a^2*b^5*c*d^6 + 19*a^3*b^4*d^7)*e^4*f^3 + (19*b^7*c^4*d
^3 - 68*a*b^6*c^3*d^4 - 52*a^2*b^5*c^2*d^5 - 68*a^3*b^4*c*d^6 + 19*a^4*b^3*d^7)*e^3*f^4 - (37*b^7*c^5*d^2 - 86
*a*b^6*c^4*d^3 + 52*a^2*b^5*c^3*d^4 + 52*a^3*b^4*c^2*d^5 - 86*a^4*b^3*c*d^6 + 37*a^5*b^2*d^7)*e^2*f^5 + (3*b^7
*c^6*d - 28*a*b^6*c^5*d^2 + 86*a^2*b^5*c^4*d^3 - 68*a^3*b^4*c^3*d^4 + 86*a^4*b^3*c^2*d^5 - 28*a^5*b^2*c*d^6 +
3*a^6*b*d^7)*e*f^6 + (6*b^7*c^7 + 3*a*b^6*c^6*d - 37*a^2*b^5*c^5*d^2 + 19*a^3*b^4*c^4*d^3 + 19*a^4*b^3*c^3*d^4
- 37*a^5*b^2*c^2*d^5 + 3*a^6*b*c*d^6 + 6*a^7*d^7)*f^7)*x^3 - (18*(b^7*c*d^6 + a*b^6*d^7)*e^7 - (37*b^7*c^2*d^
5 + 34*a*b^6*c*d^6 + 37*a^2*b^5*d^7)*e^6*f - 3*(b^7*c^3*d^4 - 3*a*b^6*c^2*d^5 - 3*a^2*b^5*c*d^6 + a^3*b^4*d^7)
*e^5*f^2 + (32*b^7*c^4*d^3 + a*b^6*c^3*d^4 + 234*a^2*b^5*c^2*d^5 + a^3*b^4*c*d^6 + 32*a^4*b^3*d^7)*e^4*f^3 - (
3*b^7*c^5*d^2 - a*b^6*c^4*d^3 + 208*a^2*b^5*c^3*d^4 + 208*a^3*b^4*c^2*d^5 - a^4*b^3*c*d^6 + 3*a^5*b^2*d^7)*e^3
*f^4 - (37*b^7*c^6*d - 9*a*b^6*c^5*d^2 - 234*a^2*b^5*c^4*d^3 + 208*a^3*b^4*c^3*d^4 - 234*a^4*b^3*c^2*d^5 - 9*a
^5*b^2*c*d^6 + 37*a^6*b*d^7)*e^2*f^5 + (18*b^7*c^7 - 34*a*b^6*c^6*d + 9*a^2*b^5*c^5*d^2 + a^3*b^4*c^4*d^3 + a^
4*b^3*c^3*d^4 + 9*a^5*b^2*c^2*d^5 - 34*a^6*b*c*d^6 + 18*a^7*d^7)*e*f^6 + (18*a*b^6*c^7 - 37*a^2*b^5*c^6*d - 3*
a^3*b^4*c^5*d^2 + 32*a^4*b^3*c^4*d^3 - 3*a^5*b^2*c^3*d^4 - 37*a^6*b*c^2*d^5 + 18*a^7*c*d^6)*f^7)*x^2 - 2*(2*(b
^7*c^2*d^5 + 7*a*b^6*c*d^6 + a^2*b^5*d^7)*e^7 - 3*(2*b^7*c^3*d^4 + 11*a*b^6*c^2*d^5 + 11*a^2*b^5*c*d^6 + 2*a^3
*b^4*d^7)*e^6*f + (4*b^7*c^4*d^3 + 17*a*b^6*c^3*d^4 + 78*a^2*b^5*c^2*d^5 + 17*a^3*b^4*c*d^6 + 4*a^4*b^3*d^7)*e
^5*f^2 + 2*(2*b^7*c^5*d^2 - 4*a*b^6*c^4*d^3 - 13*a^2*b^5*c^3*d^4 - 13*a^3*b^4*c^2*d^5 - 4*a^4*b^3*c*d^6 + 2*a^
5*b^2*d^7)*e^4*f^3 - (6*b^7*c^6*d - 17*a*b^6*c^5*d^2 + 26*a^2*b^5*c^4*d^3 + 26*a^4*b^3*c^2*d^5 - 17*a^5*b^2*c*
d^6 + 6*a^6*b*d^7)*e^3*f^4 + (2*b^7*c^7 - 33*a*b^6*c^6*d + 78*a^2*b^5*c^5*d^2 - 26*a^3*b^4*c^4*d^3 - 26*a^4*b^
3*c^3*d^4 + 78*a^5*b^2*c^2*d^5 - 33*a^6*b*c*d^6 + 2*a^7*d^7)*e^2*f^5 + (14*a*b^6*c^7 - 33*a^2*b^5*c^6*d + 17*a
^3*b^4*c^5*d^2 - 8*a^4*b^3*c^4*d^3 + 17*a^5*b^2*c^3*d^4 - 33*a^6*b*c^2*d^5 + 14*a^7*c*d^6)*e*f^6 + 2*(a^2*b^5*
c^7 - 3*a^3*b^4*c^6*d + 2*a^4*b^3*c^5*d^2 + 2*a^5*b^2*c^4*d^3 - 3*a^6*b*c^3*d^4 + a^7*c^2*d^5)*f^7)*x)/((a^2*b
^8*c^6*d^4 - 4*a^3*b^7*c^5*d^5 + 6*a^4*b^6*c^4*d^6 - 4*a^5*b^5*c^3*d^7 + a^6*b^4*c^2*d^8)*e^10 - 4*(a^2*b^8*c^
7*d^3 - 3*a^3*b^7*c^6*d^4 + 2*a^4*b^6*c^5*d^5 + 2*a^5*b^5*c^4*d^6 - 3*a^6*b^4*c^3*d^7 + a^7*b^3*c^2*d^8)*e^9*f
+ 2*(3*a^2*b^8*c^8*d^2 - 4*a^3*b^7*c^7*d^3 - 11*a^4*b^6*c^6*d^4 + 24*a^5*b^5*c^5*d^5 - 11*a^6*b^4*c^4*d^6 - 4
*a^7*b^3*c^3*d^7 + 3*a^8*b^2*c^2*d^8)*e^8*f^2 - 4*(a^2*b^8*c^9*d + 2*a^3*b^7*c^8*d^2 - 12*a^4*b^6*c^7*d^3 + 9*
a^5*b^5*c^6*d^4 + 9*a^6*b^4*c^5*d^5 - 12*a^7*b^3*c^4*d^6 + 2*a^8*b^2*c^3*d^7 + a^9*b*c^2*d^8)*e^7*f^3 + (a^2*b
^8*c^10 + 12*a^3*b^7*c^9*d - 22*a^4*b^6*c^8*d^2 - 36*a^5*b^5*c^7*d^3 + 90*a^6*b^4*c^6*d^4 - 36*a^7*b^3*c^5*d^5
- 22*a^8*b^2*c^4*d^6 + 12*a^9*b*c^3*d^7 + a^10*c^2*d^8)*e^6*f^4 - 4*(a^3*b^7*c^10 + 2*a^4*b^6*c^9*d - 12*a^5*
b^5*c^8*d^2 + 9*a^6*b^4*c^7*d^3 + 9*a^7*b^3*c^6*d^4 - 12*a^8*b^2*c^5*d^5 + 2*a^9*b*c^4*d^6 + a^10*c^3*d^7)*e^5
*f^5 + 2*(3*a^4*b^6*c^10 - 4*a^5*b^5*c^9*d - 11*a^6*b^4*c^8*d^2 + 24*a^7*b^3*c^7*d^3 - 11*a^8*b^2*c^6*d^4 - 4*
a^9*b*c^5*d^5 + 3*a^10*c^4*d^6)*e^4*f^6 - 4*(a^5*b^5*c^10 - 3*a^6*b^4*c^9*d + 2*a^7*b^3*c^8*d^2 + 2*a^8*b^2*c^
7*d^3 - 3*a^9*b*c^6*d^4 + a^10*c^5*d^5)*e^3*f^7 + (a^6*b^4*c^10 - 4*a^7*b^3*c^9*d + 6*a^8*b^2*c^8*d^2 - 4*a^9*
b*c^7*d^3 + a^10*c^6*d^4)*e^2*f^8 + ((b^10*c^4*d^6 - 4*a*b^9*c^3*d^7 + 6*a^2*b^8*c^2*d^8 - 4*a^3*b^7*c*d^9 + a
^4*b^6*d^10)*e^8*f^2 - 4*(b^10*c^5*d^5 - 3*a*b^9*c^4*d^6 + 2*a^2*b^8*c^3*d^7 + 2*a^3*b^7*c^2*d^8 - 3*a^4*b^6*c
*d^9 + a^5*b^5*d^10)*e^7*f^3 + 2*(3*b^10*c^6*d^4 - 4*a*b^9*c^5*d^5 - 11*a^2*b^8*c^4*d^6 + 24*a^3*b^7*c^3*d^7 -
11*a^4*b^6*c^2*d^8 - 4*a^5*b^5*c*d^9 + 3*a^6*b^4*d^10)*e^6*f^4 - 4*(b^10*c^7*d^3 + 2*a*b^9*c^6*d^4 - 12*a^2*b
^8*c^5*d^5 + 9*a^3*b^7*c^4*d^6 + 9*a^4*b^6*c^3*d^7 - 12*a^5*b^5*c^2*d^8 + 2*a^6*b^4*c*d^9 + a^7*b^3*d^10)*e^5*
f^5 + (b^10*c^8*d^2 + 12*a*b^9*c^7*d^3 - 22*a^2*b^8*c^6*d^4 - 36*a^3*b^7*c^5*d^5 + 90*a^4*b^6*c^4*d^6 - 36*a^5
*b^5*c^3*d^7 - 22*a^6*b^4*c^2*d^8 + 12*a^7*b^3*c*d^9 + a^8*b^2*d^10)*e^4*f^6 - 4*(a*b^9*c^8*d^2 + 2*a^2*b^8*c^
7*d^3 - 12*a^3*b^7*c^6*d^4 + 9*a^4*b^6*c^5*d^5 + 9*a^5*b^5*c^4*d^6 - 12*a^6*b^4*c^3*d^7 + 2*a^7*b^3*c^2*d^8 +
a^8*b^2*c*d^9)*e^3*f^7 + 2*(3*a^2*b^8*c^8*d^2 - 4*a^3*b^7*c^7*d^3 - 11*a^4*b^6*c^6*d^4 + 24*a^5*b^5*c^5*d^5 -
11*a^6*b^4*c^4*d^6 - 4*a^7*b^3*c^3*d^7 + 3*a^8*b^2*c^2*d^8)*e^2*f^8 - 4*(a^3*b^7*c^8*d^2 - 3*a^4*b^6*c^7*d^3 +
2*a^5*b^5*c^6*d^4 + 2*a^6*b^4*c^5*d^5 - 3*a^7*b^3*c^4*d^6 + a^8*b^2*c^3*d^7)*e*f^9 + (a^4*b^6*c^8*d^2 - 4*a^5
*b^5*c^7*d^3 + 6*a^6*b^4*c^6*d^4 - 4*a^7*b^3*c^5*d^5 + a^8*b^2*c^4*d^6)*f^10)*x^6 + 2*((b^10*c^4*d^6 - 4*a*b^9
*c^3*d^7 + 6*a^2*b^8*c^2*d^8 - 4*a^3*b^7*c*d^9 + a^4*b^6*d^10)*e^9*f - 3*(b^10*c^5*d^5 - 3*a*b^9*c^4*d^6 + 2*a
^2*b^8*c^3*d^7 + 2*a^3*b^7*c^2*d^8 - 3*a^4*b^6*c*d^9 + a^5*b^5*d^10)*e^8*f^2 + 2*(b^10*c^6*d^4 - 9*a^2*b^8*c^4
*d^6 + 16*a^3*b^7*c^3*d^7 - 9*a^4*b^6*c^2*d^8 + a^6*b^4*d^10)*e^7*f^3 + 2*(b^10*c^7*d^3 - 5*a*b^9*c^6*d^4 + 9*
a^2*b^8*c^5*d^5 - 5*a^3*b^7*c^4*d^6 - 5*a^4*b^6*c^3*d^7 + 9*a^5*b^5*c^2*d^8 - 5*a^6*b^4*c*d^9 + a^7*b^3*d^10)*
e^6*f^4 - 3*(b^10*c^8*d^2 - 6*a^2*b^8*c^6*d^4 + 8*a^3*b^7*c^5*d^5 - 6*a^4*b^6*c^4*d^6 + 8*a^5*b^5*c^3*d^7 - 6*
a^6*b^4*c^2*d^8 + a^8*b^2*d^10)*e^5*f^5 + (b^10*c^9*d + 9*a*b^9*c^8*d^2 - 18*a^2*b^8*c^7*d^3 - 10*a^3*b^7*c^6*
d^4 + 18*a^4*b^6*c^5*d^5 + 18*a^5*b^5*c^4*d^6 - 10*a^6*b^4*c^3*d^7 - 18*a^7*b^3*c^2*d^8 + 9*a^8*b^2*c*d^9 + a^
9*b*d^10)*e^4*f^6 - 2*(2*a*b^9*c^9*d + 3*a^2*b^8*c^8*d^2 - 16*a^3*b^7*c^7*d^3 + 5*a^4*b^6*c^6*d^4 + 12*a^5*b^5
*c^5*d^5 + 5*a^6*b^4*c^4*d^6 - 16*a^7*b^3*c^3*d^7 + 3*a^8*b^2*c^2*d^8 + 2*a^9*b*c*d^9)*e^3*f^7 + 6*(a^2*b^8*c^
9*d - a^3*b^7*c^8*d^2 - 3*a^4*b^6*c^7*d^3 + 3*a^5*b^5*c^6*d^4 + 3*a^6*b^4*c^5*d^5 - 3*a^7*b^3*c^4*d^6 - a^8*b^
2*c^3*d^7 + a^9*b*c^2*d^8)*e^2*f^8 - (4*a^3*b^7*c^9*d - 9*a^4*b^6*c^8*d^2 + 10*a^6*b^4*c^6*d^4 - 9*a^8*b^2*c^4
*d^6 + 4*a^9*b*c^3*d^7)*e*f^9 + (a^4*b^6*c^9*d - 3*a^5*b^5*c^8*d^2 + 2*a^6*b^4*c^7*d^3 + 2*a^7*b^3*c^6*d^4 - 3
*a^8*b^2*c^5*d^5 + a^9*b*c^4*d^6)*f^10)*x^5 + ((b^10*c^4*d^6 - 4*a*b^9*c^3*d^7 + 6*a^2*b^8*c^2*d^8 - 4*a^3*b^7
*c*d^9 + a^4*b^6*d^10)*e^10 - 3*(3*b^10*c^6*d^4 - 8*a*b^9*c^5*d^5 + 5*a^2*b^8*c^4*d^6 + 5*a^4*b^6*c^2*d^8 - 8*
a^5*b^5*c*d^9 + 3*a^6*b^4*d^10)*e^8*f^2 + 4*(4*b^10*c^7*d^3 - 5*a*b^9*c^6*d^4 - 9*a^2*b^8*c^5*d^5 + 10*a^3*b^7
*c^4*d^6 + 10*a^4*b^6*c^3*d^7 - 9*a^5*b^5*c^2*d^8 - 5*a^6*b^4*c*d^9 + 4*a^7*b^3*d^10)*e^7*f^3 - (9*b^10*c^8*d^
2 + 20*a*b^9*c^7*d^3 - 90*a^2*b^8*c^6*d^4 + 36*a^3*b^7*c^5*d^5 + 50*a^4*b^6*c^4*d^6 + 36*a^5*b^5*c^3*d^7 - 90*
a^6*b^4*c^2*d^8 + 20*a^7*b^3*c*d^9 + 9*a^8*b^2*d^10)*e^6*f^4 + 12*(2*a*b^9*c^8*d^2 - 3*a^2*b^8*c^7*d^3 - 3*a^3
*b^7*c^6*d^4 + 4*a^4*b^6*c^5*d^5 + 4*a^5*b^5*c^4*d^6 - 3*a^6*b^4*c^3*d^7 - 3*a^7*b^3*c^2*d^8 + 2*a^8*b^2*c*d^9
)*e^5*f^5 + (b^10*c^10 - 15*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 - 50*a^4*b^6*c^6*d^4 + 48*a^5*b^5*c^5*d^5 - 5
0*a^6*b^4*c^4*d^6 + 40*a^7*b^3*c^3*d^7 - 15*a^8*b^2*c^2*d^8 + a^10*d^10)*e^4*f^6 - 4*(a*b^9*c^10 - 10*a^4*b^6*
c^7*d^3 + 9*a^5*b^5*c^6*d^4 + 9*a^6*b^4*c^5*d^5 - 10*a^7*b^3*c^4*d^6 + a^10*c*d^9)*e^3*f^7 + 3*(2*a^2*b^8*c^10
- 5*a^4*b^6*c^8*d^2 - 12*a^5*b^5*c^7*d^3 + 30*a^6*b^4*c^6*d^4 - 12*a^7*b^3*c^5*d^5 - 5*a^8*b^2*c^4*d^6 + 2*a^
10*c^2*d^8)*e^2*f^8 - 4*(a^3*b^7*c^10 - 6*a^5*b^5*c^8*d^2 + 5*a^6*b^4*c^7*d^3 + 5*a^7*b^3*c^6*d^4 - 6*a^8*b^2*
c^5*d^5 + a^10*c^3*d^7)*e*f^9 + (a^4*b^6*c^10 - 9*a^6*b^4*c^8*d^2 + 16*a^7*b^3*c^7*d^3 - 9*a^8*b^2*c^6*d^4 + a
^10*c^4*d^6)*f^10)*x^4 + 2*((b^10*c^5*d^5 - 3*a*b^9*c^4*d^6 + 2*a^2*b^8*c^3*d^7 + 2*a^3*b^7*c^2*d^8 - 3*a^4*b^
6*c*d^9 + a^5*b^5*d^10)*e^10 - (3*b^10*c^6*d^4 - 8*a*b^9*c^5*d^5 + 5*a^2*b^8*c^4*d^6 + 5*a^4*b^6*c^2*d^8 - 8*a
^5*b^5*c*d^9 + 3*a^6*b^4*d^10)*e^9*f + (2*b^10*c^7*d^3 - 5*a*b^9*c^6*d^4 + 3*a^2*b^8*c^5*d^5 + 3*a^5*b^5*c^2*d
^8 - 5*a^6*b^4*c*d^9 + 2*a^7*b^3*d^10)*e^8*f^2 + 2*(b^10*c^8*d^2 - 16*a^3*b^7*c^5*d^5 + 30*a^4*b^6*c^4*d^6 - 1
6*a^5*b^5*c^3*d^7 + a^8*b^2*d^10)*e^7*f^3 - (3*b^10*c^9*d + 5*a*b^9*c^8*d^2 - 60*a^3*b^7*c^6*d^4 + 52*a^4*b^6*
c^5*d^5 + 52*a^5*b^5*c^4*d^6 - 60*a^6*b^4*c^3*d^7 + 5*a^8*b^2*c*d^9 + 3*a^9*b*d^10)*e^6*f^4 + (b^10*c^10 + 8*a
*b^9*c^9*d + 3*a^2*b^8*c^8*d^2 - 32*a^3*b^7*c^7*d^3 - 52*a^4*b^6*c^6*d^4 + 144*a^5*b^5*c^5*d^5 - 52*a^6*b^4*c^
4*d^6 - 32*a^7*b^3*c^3*d^7 + 3*a^8*b^2*c^2*d^8 + 8*a^9*b*c*d^9 + a^10*d^10)*e^5*f^5 - (3*a*b^9*c^10 + 5*a^2*b^
8*c^9*d - 60*a^4*b^6*c^7*d^3 + 52*a^5*b^5*c^6*d^4 + 52*a^6*b^4*c^5*d^5 - 60*a^7*b^3*c^4*d^6 + 5*a^9*b*c^2*d^8
+ 3*a^10*c*d^9)*e^4*f^6 + 2*(a^2*b^8*c^10 - 16*a^5*b^5*c^7*d^3 + 30*a^6*b^4*c^6*d^4 - 16*a^7*b^3*c^5*d^5 + a^1
0*c^2*d^8)*e^3*f^7 + (2*a^3*b^7*c^10 - 5*a^4*b^6*c^9*d + 3*a^5*b^5*c^8*d^2 + 3*a^8*b^2*c^5*d^5 - 5*a^9*b*c^4*d
^6 + 2*a^10*c^3*d^7)*e^2*f^8 - (3*a^4*b^6*c^10 - 8*a^5*b^5*c^9*d + 5*a^6*b^4*c^8*d^2 + 5*a^8*b^2*c^6*d^4 - 8*a
^9*b*c^5*d^5 + 3*a^10*c^4*d^6)*e*f^9 + (a^5*b^5*c^10 - 3*a^6*b^4*c^9*d + 2*a^7*b^3*c^8*d^2 + 2*a^8*b^2*c^7*d^3
- 3*a^9*b*c^6*d^4 + a^10*c^5*d^5)*f^10)*x^3 + ((b^10*c^6*d^4 - 9*a^2*b^8*c^4*d^6 + 16*a^3*b^7*c^3*d^7 - 9*a^4
*b^6*c^2*d^8 + a^6*b^4*d^10)*e^10 - 4*(b^10*c^7*d^3 - 6*a^2*b^8*c^5*d^5 + 5*a^3*b^7*c^4*d^6 + 5*a^4*b^6*c^3*d^
7 - 6*a^5*b^5*c^2*d^8 + a^7*b^3*d^10)*e^9*f + 3*(2*b^10*c^8*d^2 - 5*a^2*b^8*c^6*d^4 - 12*a^3*b^7*c^5*d^5 + 30*
a^4*b^6*c^4*d^6 - 12*a^5*b^5*c^3*d^7 - 5*a^6*b^4*c^2*d^8 + 2*a^8*b^2*d^10)*e^8*f^2 - 4*(b^10*c^9*d - 10*a^3*b^
7*c^6*d^4 + 9*a^4*b^6*c^5*d^5 + 9*a^5*b^5*c^4*d^6 - 10*a^6*b^4*c^3*d^7 + a^9*b*d^10)*e^7*f^3 + (b^10*c^10 - 15
*a^2*b^8*c^8*d^2 + 40*a^3*b^7*c^7*d^3 - 50*a^4*b^6*c^6*d^4 + 48*a^5*b^5*c^5*d^5 - 50*a^6*b^4*c^4*d^6 + 40*a^7*
b^3*c^3*d^7 - 15*a^8*b^2*c^2*d^8 + a^10*d^10)*e^6*f^4 + 12*(2*a^2*b^8*c^9*d - 3*a^3*b^7*c^8*d^2 - 3*a^4*b^6*c^
7*d^3 + 4*a^5*b^5*c^6*d^4 + 4*a^6*b^4*c^5*d^5 - 3*a^7*b^3*c^4*d^6 - 3*a^8*b^2*c^3*d^7 + 2*a^9*b*c^2*d^8)*e^5*f
^5 - (9*a^2*b^8*c^10 + 20*a^3*b^7*c^9*d - 90*a^4*b^6*c^8*d^2 + 36*a^5*b^5*c^7*d^3 + 50*a^6*b^4*c^6*d^4 + 36*a^
7*b^3*c^5*d^5 - 90*a^8*b^2*c^4*d^6 + 20*a^9*b*c^3*d^7 + 9*a^10*c^2*d^8)*e^4*f^6 + 4*(4*a^3*b^7*c^10 - 5*a^4*b^
6*c^9*d - 9*a^5*b^5*c^8*d^2 + 10*a^6*b^4*c^7*d^3 + 10*a^7*b^3*c^6*d^4 - 9*a^8*b^2*c^5*d^5 - 5*a^9*b*c^4*d^6 +
4*a^10*c^3*d^7)*e^3*f^7 - 3*(3*a^4*b^6*c^10 - 8*a^5*b^5*c^9*d + 5*a^6*b^4*c^8*d^2 + 5*a^8*b^2*c^6*d^4 - 8*a^9*
b*c^5*d^5 + 3*a^10*c^4*d^6)*e^2*f^8 + (a^6*b^4*c^10 - 4*a^7*b^3*c^9*d + 6*a^8*b^2*c^8*d^2 - 4*a^9*b*c^7*d^3 +
a^10*c^6*d^4)*f^10)*x^2 + 2*((a*b^9*c^6*d^4 - 3*a^2*b^8*c^5*d^5 + 2*a^3*b^7*c^4*d^6 + 2*a^4*b^6*c^3*d^7 - 3*a^
5*b^5*c^2*d^8 + a^6*b^4*c*d^9)*e^10 - (4*a*b^9*c^7*d^3 - 9*a^2*b^8*c^6*d^4 + 10*a^4*b^6*c^4*d^6 - 9*a^6*b^4*c^
2*d^8 + 4*a^7*b^3*c*d^9)*e^9*f + 6*(a*b^9*c^8*d^2 - a^2*b^8*c^7*d^3 - 3*a^3*b^7*c^6*d^4 + 3*a^4*b^6*c^5*d^5 +
3*a^5*b^5*c^4*d^6 - 3*a^6*b^4*c^3*d^7 - a^7*b^3*c^2*d^8 + a^8*b^2*c*d^9)*e^8*f^2 - 2*(2*a*b^9*c^9*d + 3*a^2*b^
8*c^8*d^2 - 16*a^3*b^7*c^7*d^3 + 5*a^4*b^6*c^6*d^4 + 12*a^5*b^5*c^5*d^5 + 5*a^6*b^4*c^4*d^6 - 16*a^7*b^3*c^3*d
^7 + 3*a^8*b^2*c^2*d^8 + 2*a^9*b*c*d^9)*e^7*f^3 + (a*b^9*c^10 + 9*a^2*b^8*c^9*d - 18*a^3*b^7*c^8*d^2 - 10*a^4*
b^6*c^7*d^3 + 18*a^5*b^5*c^6*d^4 + 18*a^6*b^4*c^5*d^5 - 10*a^7*b^3*c^4*d^6 - 18*a^8*b^2*c^3*d^7 + 9*a^9*b*c^2*
d^8 + a^10*c*d^9)*e^6*f^4 - 3*(a^2*b^8*c^10 - 6*a^4*b^6*c^8*d^2 + 8*a^5*b^5*c^7*d^3 - 6*a^6*b^4*c^6*d^4 + 8*a^
7*b^3*c^5*d^5 - 6*a^8*b^2*c^4*d^6 + a^10*c^2*d^8)*e^5*f^5 + 2*(a^3*b^7*c^10 - 5*a^4*b^6*c^9*d + 9*a^5*b^5*c^8*
d^2 - 5*a^6*b^4*c^7*d^3 - 5*a^7*b^3*c^6*d^4 + 9*a^8*b^2*c^5*d^5 - 5*a^9*b*c^4*d^6 + a^10*c^3*d^7)*e^4*f^6 + 2*
(a^4*b^6*c^10 - 9*a^6*b^4*c^8*d^2 + 16*a^7*b^3*c^7*d^3 - 9*a^8*b^2*c^6*d^4 + a^10*c^4*d^6)*e^3*f^7 - 3*(a^5*b^
5*c^10 - 3*a^6*b^4*c^9*d + 2*a^7*b^3*c^8*d^2 + 2*a^8*b^2*c^7*d^3 - 3*a^9*b*c^6*d^4 + a^10*c^5*d^5)*e^2*f^8 + (
a^6*b^4*c^10 - 4*a^7*b^3*c^9*d + 6*a^8*b^2*c^8*d^2 - 4*a^9*b*c^7*d^3 + a^10*c^6*d^4)*e*f^9)*x)

________________________________________________________________________________________

mupad [B]  time = 20.46, size = 82532, normalized size = 166.73 \[ \text {result too large to display} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(x^2*(a*d*f + b*c*f + b*d*e) + x*(a*c*f + a*d*e + b*c*e) + a*c*e + b*d*f*x^3)^3,x)

[Out]

symsum(log(root(756756*a^10*b^10*c^10*d^10*e^10*f^10*z^3 + 573300*a^12*b^8*c^9*d^11*e^9*f^11*z^3 + 573300*a^11
*b^9*c^11*d^9*e^8*f^12*z^3 + 573300*a^11*b^9*c^8*d^12*e^11*f^9*z^3 + 573300*a^9*b^11*c^12*d^8*e^9*f^11*z^3 + 5
73300*a^9*b^11*c^9*d^11*e^12*f^8*z^3 + 573300*a^8*b^12*c^11*d^9*e^11*f^9*z^3 - 343980*a^11*b^9*c^10*d^10*e^9*f
^11*z^3 - 343980*a^11*b^9*c^9*d^11*e^10*f^10*z^3 - 343980*a^10*b^10*c^11*d^9*e^9*f^11*z^3 - 343980*a^10*b^10*c
^9*d^11*e^11*f^9*z^3 - 343980*a^9*b^11*c^11*d^9*e^10*f^10*z^3 - 343980*a^9*b^11*c^10*d^10*e^11*f^9*z^3 + 32634
0*a^13*b^7*c^10*d^10*e^7*f^13*z^3 + 326340*a^13*b^7*c^7*d^13*e^10*f^10*z^3 + 326340*a^10*b^10*c^13*d^7*e^7*f^1
3*z^3 + 326340*a^10*b^10*c^7*d^13*e^13*f^7*z^3 + 326340*a^7*b^13*c^13*d^7*e^10*f^10*z^3 + 326340*a^7*b^13*c^10
*d^10*e^13*f^7*z^3 - 267540*a^12*b^8*c^10*d^10*e^8*f^12*z^3 - 267540*a^12*b^8*c^8*d^12*e^10*f^10*z^3 - 267540*
a^10*b^10*c^12*d^8*e^8*f^12*z^3 - 267540*a^10*b^10*c^8*d^12*e^12*f^8*z^3 - 267540*a^8*b^12*c^12*d^8*e^10*f^10*
z^3 - 267540*a^8*b^12*c^10*d^10*e^12*f^8*z^3 + 245700*a^14*b^6*c^8*d^12*e^8*f^12*z^3 + 245700*a^12*b^8*c^12*d^
8*e^6*f^14*z^3 + 245700*a^12*b^8*c^6*d^14*e^12*f^8*z^3 + 245700*a^8*b^12*c^14*d^6*e^8*f^12*z^3 + 245700*a^8*b^
12*c^8*d^12*e^14*f^6*z^3 + 245700*a^6*b^14*c^12*d^8*e^12*f^8*z^3 - 191100*a^13*b^7*c^9*d^11*e^8*f^12*z^3 - 191
100*a^13*b^7*c^8*d^12*e^9*f^11*z^3 - 191100*a^12*b^8*c^11*d^9*e^7*f^13*z^3 - 191100*a^12*b^8*c^7*d^13*e^11*f^9
*z^3 - 191100*a^11*b^9*c^12*d^8*e^7*f^13*z^3 - 191100*a^11*b^9*c^7*d^13*e^12*f^8*z^3 - 191100*a^9*b^11*c^13*d^
7*e^8*f^12*z^3 - 191100*a^9*b^11*c^8*d^12*e^13*f^7*z^3 - 191100*a^8*b^12*c^13*d^7*e^9*f^11*z^3 - 191100*a^8*b^
12*c^9*d^11*e^13*f^7*z^3 - 191100*a^7*b^13*c^12*d^8*e^11*f^9*z^3 - 191100*a^7*b^13*c^11*d^9*e^12*f^8*z^3 - 123
900*a^14*b^6*c^9*d^11*e^7*f^13*z^3 - 123900*a^14*b^6*c^7*d^13*e^9*f^11*z^3 - 123900*a^13*b^7*c^11*d^9*e^6*f^14
*z^3 - 123900*a^13*b^7*c^6*d^14*e^11*f^9*z^3 - 123900*a^11*b^9*c^13*d^7*e^6*f^14*z^3 - 123900*a^11*b^9*c^6*d^1
4*e^13*f^7*z^3 - 123900*a^9*b^11*c^14*d^6*e^7*f^13*z^3 - 123900*a^9*b^11*c^7*d^13*e^14*f^6*z^3 - 123900*a^7*b^
13*c^14*d^6*e^9*f^11*z^3 - 123900*a^7*b^13*c^9*d^11*e^14*f^6*z^3 - 123900*a^6*b^14*c^13*d^7*e^11*f^9*z^3 - 123
900*a^6*b^14*c^11*d^9*e^13*f^7*z^3 + 101700*a^15*b^5*c^9*d^11*e^6*f^14*z^3 + 101700*a^15*b^5*c^6*d^14*e^9*f^11
*z^3 + 101700*a^14*b^6*c^11*d^9*e^5*f^15*z^3 + 101700*a^14*b^6*c^5*d^15*e^11*f^9*z^3 + 101700*a^11*b^9*c^14*d^
6*e^5*f^15*z^3 + 101700*a^11*b^9*c^5*d^15*e^14*f^6*z^3 + 101700*a^9*b^11*c^15*d^5*e^6*f^14*z^3 + 101700*a^9*b^
11*c^6*d^14*e^15*f^5*z^3 + 101700*a^6*b^14*c^15*d^5*e^9*f^11*z^3 + 101700*a^6*b^14*c^9*d^11*e^15*f^5*z^3 + 101
700*a^5*b^15*c^14*d^6*e^11*f^9*z^3 + 101700*a^5*b^15*c^11*d^9*e^14*f^6*z^3 - 65820*a^14*b^6*c^10*d^10*e^6*f^14
*z^3 - 65820*a^14*b^6*c^6*d^14*e^10*f^10*z^3 - 65820*a^10*b^10*c^14*d^6*e^6*f^14*z^3 - 65820*a^10*b^10*c^6*d^1
4*e^14*f^6*z^3 - 65820*a^6*b^14*c^14*d^6*e^10*f^10*z^3 - 65820*a^6*b^14*c^10*d^10*e^14*f^6*z^3 + 56700*a^16*b^
4*c^7*d^13*e^7*f^13*z^3 - 56700*a^15*b^5*c^8*d^12*e^7*f^13*z^3 - 56700*a^15*b^5*c^7*d^13*e^8*f^12*z^3 + 56700*
a^13*b^7*c^13*d^7*e^4*f^16*z^3 - 56700*a^13*b^7*c^12*d^8*e^5*f^15*z^3 - 56700*a^13*b^7*c^5*d^15*e^12*f^8*z^3 +
56700*a^13*b^7*c^4*d^16*e^13*f^7*z^3 - 56700*a^12*b^8*c^13*d^7*e^5*f^15*z^3 - 56700*a^12*b^8*c^5*d^15*e^13*f^
7*z^3 - 56700*a^8*b^12*c^15*d^5*e^7*f^13*z^3 - 56700*a^8*b^12*c^7*d^13*e^15*f^5*z^3 + 56700*a^7*b^13*c^16*d^4*
e^7*f^13*z^3 - 56700*a^7*b^13*c^15*d^5*e^8*f^12*z^3 - 56700*a^7*b^13*c^8*d^12*e^15*f^5*z^3 + 56700*a^7*b^13*c^
7*d^13*e^16*f^4*z^3 - 56700*a^5*b^15*c^13*d^7*e^12*f^8*z^3 - 56700*a^5*b^15*c^12*d^8*e^13*f^7*z^3 + 56700*a^4*
b^16*c^13*d^7*e^13*f^7*z^3 - 48252*a^15*b^5*c^10*d^10*e^5*f^15*z^3 - 48252*a^15*b^5*c^5*d^15*e^10*f^10*z^3 - 4
8252*a^10*b^10*c^15*d^5*e^5*f^15*z^3 - 48252*a^10*b^10*c^5*d^15*e^15*f^5*z^3 - 48252*a^5*b^15*c^15*d^5*e^10*f^
10*z^3 - 48252*a^5*b^15*c^10*d^10*e^15*f^5*z^3 - 32400*a^16*b^4*c^8*d^12*e^6*f^14*z^3 - 32400*a^16*b^4*c^6*d^1
4*e^8*f^12*z^3 - 32400*a^14*b^6*c^12*d^8*e^4*f^16*z^3 - 32400*a^14*b^6*c^4*d^16*e^12*f^8*z^3 - 32400*a^12*b^8*
c^14*d^6*e^4*f^16*z^3 - 32400*a^12*b^8*c^4*d^16*e^14*f^6*z^3 - 32400*a^8*b^12*c^16*d^4*e^6*f^14*z^3 - 32400*a^
8*b^12*c^6*d^14*e^16*f^4*z^3 - 32400*a^6*b^14*c^16*d^4*e^8*f^12*z^3 - 32400*a^6*b^14*c^8*d^12*e^16*f^4*z^3 - 3
2400*a^4*b^16*c^14*d^6*e^12*f^8*z^3 - 32400*a^4*b^16*c^12*d^8*e^14*f^6*z^3 + 20565*a^16*b^4*c^10*d^10*e^4*f^16
*z^3 + 20565*a^16*b^4*c^4*d^16*e^10*f^10*z^3 + 20565*a^10*b^10*c^16*d^4*e^4*f^16*z^3 + 20565*a^10*b^10*c^4*d^1
6*e^16*f^4*z^3 + 20565*a^4*b^16*c^16*d^4*e^10*f^10*z^3 + 20565*a^4*b^16*c^10*d^10*e^16*f^4*z^3 + 15660*a^17*b^
3*c^8*d^12*e^5*f^15*z^3 + 15660*a^17*b^3*c^5*d^15*e^8*f^12*z^3 + 15660*a^15*b^5*c^12*d^8*e^3*f^17*z^3 + 15660*
a^15*b^5*c^3*d^17*e^12*f^8*z^3 + 15660*a^12*b^8*c^15*d^5*e^3*f^17*z^3 + 15660*a^12*b^8*c^3*d^17*e^15*f^5*z^3 +
15660*a^8*b^12*c^17*d^3*e^5*f^15*z^3 + 15660*a^8*b^12*c^5*d^15*e^17*f^3*z^3 + 15660*a^5*b^15*c^17*d^3*e^8*f^1
2*z^3 + 15660*a^5*b^15*c^8*d^12*e^17*f^3*z^3 + 15660*a^3*b^17*c^15*d^5*e^12*f^8*z^3 + 15660*a^3*b^17*c^12*d^8*
e^15*f^5*z^3 - 9750*a^17*b^3*c^9*d^11*e^4*f^16*z^3 - 9750*a^17*b^3*c^4*d^16*e^9*f^11*z^3 - 9750*a^16*b^4*c^11*
d^9*e^3*f^17*z^3 - 9750*a^16*b^4*c^3*d^17*e^11*f^9*z^3 - 9750*a^11*b^9*c^16*d^4*e^3*f^17*z^3 - 9750*a^11*b^9*c
^3*d^17*e^16*f^4*z^3 - 9750*a^9*b^11*c^17*d^3*e^4*f^16*z^3 - 9750*a^9*b^11*c^4*d^16*e^17*f^3*z^3 - 9750*a^4*b^
16*c^17*d^3*e^9*f^11*z^3 - 9750*a^4*b^16*c^9*d^11*e^17*f^3*z^3 - 9750*a^3*b^17*c^16*d^4*e^11*f^9*z^3 - 9750*a^
3*b^17*c^11*d^9*e^16*f^4*z^3 - 8100*a^17*b^3*c^7*d^13*e^6*f^14*z^3 - 8100*a^17*b^3*c^6*d^14*e^7*f^13*z^3 - 810
0*a^14*b^6*c^13*d^7*e^3*f^17*z^3 - 8100*a^14*b^6*c^3*d^17*e^13*f^7*z^3 - 8100*a^13*b^7*c^14*d^6*e^3*f^17*z^3 -
8100*a^13*b^7*c^3*d^17*e^14*f^6*z^3 - 8100*a^7*b^13*c^17*d^3*e^6*f^14*z^3 - 8100*a^7*b^13*c^6*d^14*e^17*f^3*z
^3 - 8100*a^6*b^14*c^17*d^3*e^7*f^13*z^3 - 8100*a^6*b^14*c^7*d^13*e^17*f^3*z^3 - 8100*a^3*b^17*c^14*d^6*e^13*f
^7*z^3 - 8100*a^3*b^17*c^13*d^7*e^14*f^6*z^3 - 7980*a^16*b^4*c^9*d^11*e^5*f^15*z^3 - 7980*a^16*b^4*c^5*d^15*e^
9*f^11*z^3 - 7980*a^15*b^5*c^11*d^9*e^4*f^16*z^3 - 7980*a^15*b^5*c^4*d^16*e^11*f^9*z^3 - 7980*a^11*b^9*c^15*d^
5*e^4*f^16*z^3 - 7980*a^11*b^9*c^4*d^16*e^15*f^5*z^3 - 7980*a^9*b^11*c^16*d^4*e^5*f^15*z^3 - 7980*a^9*b^11*c^5
*d^15*e^16*f^4*z^3 - 7980*a^5*b^15*c^16*d^4*e^9*f^11*z^3 - 7980*a^5*b^15*c^9*d^11*e^16*f^4*z^3 - 7980*a^4*b^16
*c^15*d^5*e^11*f^9*z^3 - 7980*a^4*b^16*c^11*d^9*e^15*f^5*z^3 + 6300*a^18*b^2*c^6*d^14*e^6*f^14*z^3 + 6300*a^14
*b^6*c^14*d^6*e^2*f^18*z^3 + 6300*a^14*b^6*c^2*d^18*e^14*f^6*z^3 + 6300*a^6*b^14*c^18*d^2*e^6*f^14*z^3 + 6300*
a^6*b^14*c^6*d^14*e^18*f^2*z^3 + 6300*a^2*b^18*c^14*d^6*e^14*f^6*z^3 - 4260*a^18*b^2*c^7*d^13*e^5*f^15*z^3 - 4
260*a^18*b^2*c^5*d^15*e^7*f^13*z^3 - 4260*a^15*b^5*c^13*d^7*e^2*f^18*z^3 - 4260*a^15*b^5*c^2*d^18*e^13*f^7*z^3
- 4260*a^13*b^7*c^15*d^5*e^2*f^18*z^3 - 4260*a^13*b^7*c^2*d^18*e^15*f^5*z^3 - 4260*a^7*b^13*c^18*d^2*e^5*f^15
*z^3 - 4260*a^7*b^13*c^5*d^15*e^18*f^2*z^3 - 4260*a^5*b^15*c^18*d^2*e^7*f^13*z^3 - 4260*a^5*b^15*c^7*d^13*e^18
*f^2*z^3 - 4260*a^2*b^18*c^15*d^5*e^13*f^7*z^3 - 4260*a^2*b^18*c^13*d^7*e^15*f^5*z^3 + 1470*a^17*b^3*c^10*d^10
*e^3*f^17*z^3 + 1470*a^17*b^3*c^3*d^17*e^10*f^10*z^3 + 1470*a^10*b^10*c^17*d^3*e^3*f^17*z^3 + 1470*a^10*b^10*c
^3*d^17*e^17*f^3*z^3 + 1470*a^3*b^17*c^17*d^3*e^10*f^10*z^3 + 1470*a^3*b^17*c^10*d^10*e^17*f^3*z^3 + 1350*a^18
*b^2*c^9*d^11*e^3*f^17*z^3 + 1350*a^18*b^2*c^3*d^17*e^9*f^11*z^3 + 1350*a^17*b^3*c^11*d^9*e^2*f^18*z^3 + 1350*
a^17*b^3*c^2*d^18*e^11*f^9*z^3 + 1350*a^11*b^9*c^17*d^3*e^2*f^18*z^3 + 1350*a^11*b^9*c^2*d^18*e^17*f^3*z^3 + 1
350*a^9*b^11*c^18*d^2*e^3*f^17*z^3 + 1350*a^9*b^11*c^3*d^17*e^18*f^2*z^3 + 1350*a^3*b^17*c^18*d^2*e^9*f^11*z^3
+ 1350*a^3*b^17*c^9*d^11*e^18*f^2*z^3 + 1350*a^2*b^18*c^17*d^3*e^11*f^9*z^3 + 1350*a^2*b^18*c^11*d^9*e^17*f^3
*z^3 - 1070*a^18*b^2*c^10*d^10*e^2*f^18*z^3 - 1070*a^18*b^2*c^2*d^18*e^10*f^10*z^3 - 1070*a^10*b^10*c^18*d^2*e
^2*f^18*z^3 - 1070*a^10*b^10*c^2*d^18*e^18*f^2*z^3 - 1070*a^2*b^18*c^18*d^2*e^10*f^10*z^3 - 1070*a^2*b^18*c^10
*d^10*e^18*f^2*z^3 + 525*a^18*b^2*c^8*d^12*e^4*f^16*z^3 + 525*a^18*b^2*c^4*d^16*e^8*f^12*z^3 + 525*a^16*b^4*c^
12*d^8*e^2*f^18*z^3 + 525*a^16*b^4*c^2*d^18*e^12*f^8*z^3 + 525*a^12*b^8*c^16*d^4*e^2*f^18*z^3 + 525*a^12*b^8*c
^2*d^18*e^16*f^4*z^3 + 525*a^8*b^12*c^18*d^2*e^4*f^16*z^3 + 525*a^8*b^12*c^4*d^16*e^18*f^2*z^3 + 525*a^4*b^16*
c^18*d^2*e^8*f^12*z^3 + 525*a^4*b^16*c^8*d^12*e^18*f^2*z^3 + 525*a^2*b^18*c^16*d^4*e^12*f^8*z^3 + 525*a^2*b^18
*c^12*d^8*e^16*f^4*z^3 + 900*a^19*b*c^7*d^13*e^4*f^16*z^3 + 900*a^19*b*c^4*d^16*e^7*f^13*z^3 + 900*a^16*b^4*c^
13*d^7*e*f^19*z^3 + 900*a^16*b^4*c*d^19*e^13*f^7*z^3 + 900*a^13*b^7*c^16*d^4*e*f^19*z^3 + 900*a^13*b^7*c*d^19*
e^16*f^4*z^3 + 900*a^7*b^13*c^19*d*e^4*f^16*z^3 + 900*a^7*b^13*c^4*d^16*e^19*f*z^3 + 900*a^4*b^16*c^19*d*e^7*f
^13*z^3 + 900*a^4*b^16*c^7*d^13*e^19*f*z^3 + 900*a*b^19*c^16*d^4*e^13*f^7*z^3 + 900*a*b^19*c^13*d^7*e^16*f^4*z
^3 - 750*a^19*b*c^8*d^12*e^3*f^17*z^3 - 750*a^19*b*c^3*d^17*e^8*f^12*z^3 - 750*a^17*b^3*c^12*d^8*e*f^19*z^3 -
750*a^17*b^3*c*d^19*e^12*f^8*z^3 - 750*a^12*b^8*c^17*d^3*e*f^19*z^3 - 750*a^12*b^8*c*d^19*e^17*f^3*z^3 - 750*a
^8*b^12*c^19*d*e^3*f^17*z^3 - 750*a^8*b^12*c^3*d^17*e^19*f*z^3 - 750*a^3*b^17*c^19*d*e^8*f^12*z^3 - 750*a^3*b^
17*c^8*d^12*e^19*f*z^3 - 750*a*b^19*c^17*d^3*e^12*f^8*z^3 - 750*a*b^19*c^12*d^8*e^17*f^3*z^3 - 420*a^19*b*c^6*
d^14*e^5*f^15*z^3 - 420*a^19*b*c^5*d^15*e^6*f^14*z^3 - 420*a^15*b^5*c^14*d^6*e*f^19*z^3 - 420*a^15*b^5*c*d^19*
e^14*f^6*z^3 - 420*a^14*b^6*c^15*d^5*e*f^19*z^3 - 420*a^14*b^6*c*d^19*e^15*f^5*z^3 - 420*a^6*b^14*c^19*d*e^5*f
^15*z^3 - 420*a^6*b^14*c^5*d^15*e^19*f*z^3 - 420*a^5*b^15*c^19*d*e^6*f^14*z^3 - 420*a^5*b^15*c^6*d^14*e^19*f*z
^3 - 420*a*b^19*c^15*d^5*e^14*f^6*z^3 - 420*a*b^19*c^14*d^6*e^15*f^5*z^3 + 350*a^19*b*c^9*d^11*e^2*f^18*z^3 +
350*a^19*b*c^2*d^18*e^9*f^11*z^3 + 350*a^18*b^2*c^11*d^9*e*f^19*z^3 + 350*a^18*b^2*c*d^19*e^11*f^9*z^3 + 350*a
^11*b^9*c^18*d^2*e*f^19*z^3 + 350*a^11*b^9*c*d^19*e^18*f^2*z^3 + 350*a^9*b^11*c^19*d*e^2*f^18*z^3 + 350*a^9*b^
11*c^2*d^18*e^19*f*z^3 + 350*a^2*b^18*c^19*d*e^9*f^11*z^3 + 350*a^2*b^18*c^9*d^11*e^19*f*z^3 + 350*a*b^19*c^18
*d^2*e^11*f^9*z^3 + 350*a*b^19*c^11*d^9*e^18*f^2*z^3 - 90*a^19*b*c^10*d^10*e*f^19*z^3 - 90*a^19*b*c*d^19*e^10*
f^10*z^3 - 90*a^10*b^10*c^19*d*e*f^19*z^3 - 90*a^10*b^10*c*d^19*e^19*f*z^3 - 90*a*b^19*c^19*d*e^10*f^10*z^3 -
90*a*b^19*c^10*d^10*e^19*f*z^3 + 10*b^20*c^19*d*e^11*f^9*z^3 + 10*b^20*c^11*d^9*e^19*f*z^3 + 10*a^20*c^9*d^11*
e*f^19*z^3 + 10*a^20*c*d^19*e^9*f^11*z^3 + 10*a^19*b*d^20*e^11*f^9*z^3 + 10*a^11*b^9*d^20*e^19*f*z^3 + 10*a^9*
b^11*c^20*e*f^19*z^3 + 10*a*b^19*c^20*e^9*f^11*z^3 + 10*a^19*b*c^11*d^9*f^20*z^3 + 10*a^11*b^9*c^19*d*f^20*z^3
+ 10*a^9*b^11*c*d^19*e^20*z^3 + 10*a*b^19*c^9*d^11*e^20*z^3 + 252*b^20*c^15*d^5*e^15*f^5*z^3 - 210*b^20*c^16*
d^4*e^14*f^6*z^3 - 210*b^20*c^14*d^6*e^16*f^4*z^3 + 120*b^20*c^17*d^3*e^13*f^7*z^3 + 120*b^20*c^13*d^7*e^17*f^
3*z^3 - 45*b^20*c^18*d^2*e^12*f^8*z^3 - 45*b^20*c^12*d^8*e^18*f^2*z^3 + 252*a^20*c^5*d^15*e^5*f^15*z^3 - 210*a
^20*c^6*d^14*e^4*f^16*z^3 - 210*a^20*c^4*d^16*e^6*f^14*z^3 + 120*a^20*c^7*d^13*e^3*f^17*z^3 + 120*a^20*c^3*d^1
7*e^7*f^13*z^3 - 45*a^20*c^8*d^12*e^2*f^18*z^3 - 45*a^20*c^2*d^18*e^8*f^12*z^3 + 252*a^15*b^5*d^20*e^15*f^5*z^
3 - 210*a^16*b^4*d^20*e^14*f^6*z^3 - 210*a^14*b^6*d^20*e^16*f^4*z^3 + 120*a^17*b^3*d^20*e^13*f^7*z^3 + 120*a^1
3*b^7*d^20*e^17*f^3*z^3 - 45*a^18*b^2*d^20*e^12*f^8*z^3 - 45*a^12*b^8*d^20*e^18*f^2*z^3 + 252*a^5*b^15*c^20*e^
5*f^15*z^3 - 210*a^6*b^14*c^20*e^4*f^16*z^3 - 210*a^4*b^16*c^20*e^6*f^14*z^3 + 120*a^7*b^13*c^20*e^3*f^17*z^3
+ 120*a^3*b^17*c^20*e^7*f^13*z^3 - 45*a^8*b^12*c^20*e^2*f^18*z^3 - 45*a^2*b^18*c^20*e^8*f^12*z^3 + 252*a^15*b^
5*c^15*d^5*f^20*z^3 - 210*a^16*b^4*c^14*d^6*f^20*z^3 - 210*a^14*b^6*c^16*d^4*f^20*z^3 + 120*a^17*b^3*c^13*d^7*
f^20*z^3 + 120*a^13*b^7*c^17*d^3*f^20*z^3 - 45*a^18*b^2*c^12*d^8*f^20*z^3 - 45*a^12*b^8*c^18*d^2*f^20*z^3 + 25
2*a^5*b^15*c^5*d^15*e^20*z^3 - 210*a^6*b^14*c^4*d^16*e^20*z^3 - 210*a^4*b^16*c^6*d^14*e^20*z^3 + 120*a^7*b^13*
c^3*d^17*e^20*z^3 + 120*a^3*b^17*c^7*d^13*e^20*z^3 - 45*a^8*b^12*c^2*d^18*e^20*z^3 - 45*a^2*b^18*c^8*d^12*e^20
*z^3 - b^20*c^20*e^10*f^10*z^3 - a^20*d^20*e^10*f^10*z^3 - b^20*c^10*d^10*e^20*z^3 - a^20*c^10*d^10*f^20*z^3 -
a^10*b^10*d^20*e^20*z^3 - a^10*b^10*c^20*f^20*z^3 + 1890*a^12*b^2*c*d^13*e*f^13*z + 1890*a*b^13*c^12*d^2*e*f^
13*z + 1890*a*b^13*c*d^13*e^12*f^2*z + 92610*a^6*b^8*c^4*d^10*e^4*f^10*z + 92610*a^4*b^10*c^6*d^8*e^4*f^10*z +
92610*a^4*b^10*c^4*d^10*e^6*f^8*z + 66150*a^8*b^6*c^3*d^11*e^3*f^11*z - 66150*a^7*b^7*c^4*d^10*e^3*f^11*z - 6
6150*a^7*b^7*c^3*d^11*e^4*f^10*z - 66150*a^4*b^10*c^7*d^7*e^3*f^11*z - 66150*a^4*b^10*c^3*d^11*e^7*f^7*z + 661
50*a^3*b^11*c^8*d^6*e^3*f^11*z - 66150*a^3*b^11*c^7*d^7*e^4*f^10*z - 66150*a^3*b^11*c^4*d^10*e^7*f^7*z + 66150
*a^3*b^11*c^3*d^11*e^8*f^6*z - 55566*a^5*b^9*c^5*d^9*e^4*f^10*z - 55566*a^5*b^9*c^4*d^10*e^5*f^9*z - 55566*a^4
*b^10*c^5*d^9*e^5*f^9*z - 32130*a^9*b^5*c^3*d^11*e^2*f^12*z - 32130*a^9*b^5*c^2*d^12*e^3*f^11*z - 32130*a^3*b^
11*c^9*d^5*e^2*f^12*z - 32130*a^3*b^11*c^2*d^12*e^9*f^5*z - 32130*a^2*b^12*c^9*d^5*e^3*f^11*z - 32130*a^2*b^12
*c^3*d^11*e^9*f^5*z + 22680*a^8*b^6*c^4*d^10*e^2*f^12*z + 22680*a^8*b^6*c^2*d^12*e^4*f^10*z + 22680*a^4*b^10*c
^8*d^6*e^2*f^12*z + 22680*a^4*b^10*c^2*d^12*e^8*f^6*z + 22680*a^2*b^12*c^8*d^6*e^4*f^10*z + 22680*a^2*b^12*c^4
*d^10*e^8*f^6*z + 19278*a^10*b^4*c^2*d^12*e^2*f^12*z + 19278*a^2*b^12*c^10*d^4*e^2*f^12*z + 19278*a^2*b^12*c^2
*d^12*e^10*f^4*z + 18522*a^6*b^8*c^5*d^9*e^3*f^11*z + 18522*a^6*b^8*c^3*d^11*e^5*f^9*z + 18522*a^5*b^9*c^6*d^8
*e^3*f^11*z + 18522*a^5*b^9*c^3*d^11*e^6*f^8*z + 18522*a^3*b^11*c^6*d^8*e^5*f^9*z + 18522*a^3*b^11*c^5*d^9*e^6
*f^8*z - 13230*a^6*b^8*c^6*d^8*e^2*f^12*z - 13230*a^6*b^8*c^2*d^12*e^6*f^8*z - 13230*a^2*b^12*c^6*d^8*e^6*f^8*
z + 3402*a^7*b^7*c^5*d^9*e^2*f^12*z + 3402*a^7*b^7*c^2*d^12*e^5*f^9*z + 3402*a^5*b^9*c^7*d^7*e^2*f^12*z + 3402
*a^5*b^9*c^2*d^12*e^7*f^7*z + 3402*a^2*b^12*c^7*d^7*e^5*f^9*z + 3402*a^2*b^12*c^5*d^9*e^7*f^7*z + 7938*a^10*b^
4*c^3*d^11*e*f^13*z + 7938*a^10*b^4*c*d^13*e^3*f^11*z + 7938*a^3*b^11*c^10*d^4*e*f^13*z + 7938*a^3*b^11*c*d^13
*e^10*f^4*z + 7938*a*b^13*c^10*d^4*e^3*f^11*z + 7938*a*b^13*c^3*d^11*e^10*f^4*z - 5670*a^11*b^3*c^2*d^12*e*f^1
3*z - 5670*a^11*b^3*c*d^13*e^2*f^12*z - 5670*a^2*b^12*c^11*d^3*e*f^13*z - 5670*a^2*b^12*c*d^13*e^11*f^3*z - 56
70*a*b^13*c^11*d^3*e^2*f^12*z - 5670*a*b^13*c^2*d^12*e^11*f^3*z - 3780*a^9*b^5*c^4*d^10*e*f^13*z - 3780*a^9*b^
5*c*d^13*e^4*f^10*z - 3780*a^4*b^10*c^9*d^5*e*f^13*z - 3780*a^4*b^10*c*d^13*e^9*f^5*z - 3780*a*b^13*c^9*d^5*e^
4*f^10*z - 3780*a*b^13*c^4*d^10*e^9*f^5*z - 2268*a^8*b^6*c^5*d^9*e*f^13*z - 2268*a^8*b^6*c*d^13*e^5*f^9*z - 22
68*a^5*b^9*c^8*d^6*e*f^13*z - 2268*a^5*b^9*c*d^13*e^8*f^6*z - 2268*a*b^13*c^8*d^6*e^5*f^9*z - 2268*a*b^13*c^5*
d^9*e^8*f^6*z + 1890*a^7*b^7*c^6*d^8*e*f^13*z + 1890*a^7*b^7*c*d^13*e^6*f^8*z + 1890*a^6*b^8*c^7*d^7*e*f^13*z
+ 1890*a^6*b^8*c*d^13*e^7*f^7*z + 1890*a*b^13*c^7*d^7*e^6*f^8*z + 1890*a*b^13*c^6*d^8*e^7*f^7*z - 252*b^14*c^1
3*d*e*f^13*z - 252*b^14*c*d^13*e^13*f*z - 252*a^13*b*d^14*e*f^13*z - 252*a*b^13*d^14*e^13*f*z - 252*a^13*b*c*d
^13*f^14*z - 252*a*b^13*c^13*d*f^14*z - 918*b^14*c^7*d^7*e^7*f^7*z - 882*b^14*c^11*d^3*e^3*f^11*z - 882*b^14*c
^3*d^11*e^11*f^3*z + 693*b^14*c^12*d^2*e^2*f^12*z + 693*b^14*c^2*d^12*e^12*f^2*z + 567*b^14*c^8*d^6*e^6*f^8*z
+ 567*b^14*c^6*d^8*e^8*f^6*z + 441*b^14*c^10*d^4*e^4*f^10*z + 441*b^14*c^4*d^10*e^10*f^4*z - 126*b^14*c^9*d^5*
e^5*f^9*z - 126*b^14*c^5*d^9*e^9*f^5*z - 918*a^7*b^7*d^14*e^7*f^7*z - 882*a^11*b^3*d^14*e^3*f^11*z - 882*a^3*b
^11*d^14*e^11*f^3*z + 693*a^12*b^2*d^14*e^2*f^12*z + 693*a^2*b^12*d^14*e^12*f^2*z + 567*a^8*b^6*d^14*e^6*f^8*z
+ 567*a^6*b^8*d^14*e^8*f^6*z + 441*a^10*b^4*d^14*e^4*f^10*z + 441*a^4*b^10*d^14*e^10*f^4*z - 126*a^9*b^5*d^14
*e^5*f^9*z - 126*a^5*b^9*d^14*e^9*f^5*z - 918*a^7*b^7*c^7*d^7*f^14*z - 882*a^11*b^3*c^3*d^11*f^14*z - 882*a^3*
b^11*c^11*d^3*f^14*z + 693*a^12*b^2*c^2*d^12*f^14*z + 693*a^2*b^12*c^12*d^2*f^14*z + 567*a^8*b^6*c^6*d^8*f^14*
z + 567*a^6*b^8*c^8*d^6*f^14*z + 441*a^10*b^4*c^4*d^10*f^14*z + 441*a^4*b^10*c^10*d^4*f^14*z - 126*a^9*b^5*c^5
*d^9*f^14*z - 126*a^5*b^9*c^9*d^5*f^14*z + 36*b^14*d^14*e^14*z + 36*b^14*c^14*f^14*z + 36*a^14*d^14*f^14*z - 2
7054*a^2*b^9*c^2*d^9*e^2*f^9 + 9018*a^3*b^8*c^2*d^9*e*f^10 + 9018*a^3*b^8*c*d^10*e^2*f^9 + 9018*a^2*b^9*c^3*d^
8*e*f^10 + 9018*a^2*b^9*c*d^10*e^3*f^8 + 9018*a*b^10*c^3*d^8*e^2*f^9 + 9018*a*b^10*c^2*d^9*e^3*f^8 - 9018*a^4*
b^7*c*d^10*e*f^10 - 9018*a*b^10*c^4*d^7*e*f^10 - 9018*a*b^10*c*d^10*e^4*f^7 + 2268*b^11*c^5*d^6*e*f^10 + 2268*
b^11*c*d^10*e^5*f^6 + 2268*a^5*b^6*d^11*e*f^10 + 2268*a*b^10*d^11*e^5*f^6 + 2268*a^5*b^6*c*d^10*f^11 + 2268*a*
b^10*c^5*d^6*f^11 - 1458*b^11*c^3*d^8*e^3*f^8 - 1161*b^11*c^4*d^7*e^2*f^9 - 1161*b^11*c^2*d^9*e^4*f^7 - 1458*a
^3*b^8*d^11*e^3*f^8 - 1161*a^4*b^7*d^11*e^2*f^9 - 1161*a^2*b^9*d^11*e^4*f^7 - 1458*a^3*b^8*c^3*d^8*f^11 - 1161
*a^4*b^7*c^2*d^9*f^11 - 1161*a^2*b^9*c^4*d^7*f^11 - 756*b^11*d^11*e^6*f^5 - 756*b^11*c^6*d^5*f^11 - 756*a^6*b^
5*d^11*f^11, z, k)*((39*a^5*b^11*c^14*d^2*f^16 - 102*a^6*b^10*c^13*d^3*f^16 + 132*a^7*b^9*c^12*d^4*f^16 - 84*a
^8*b^8*c^11*d^5*f^16 + 21*a^9*b^7*c^10*d^6*f^16 + 21*a^10*b^6*c^9*d^7*f^16 - 84*a^11*b^5*c^8*d^8*f^16 + 132*a^
12*b^4*c^7*d^9*f^16 - 102*a^13*b^3*c^6*d^10*f^16 + 39*a^14*b^2*c^5*d^11*f^16 + 39*a^5*b^11*d^16*e^14*f^2 - 102
*a^6*b^10*d^16*e^13*f^3 + 132*a^7*b^9*d^16*e^12*f^4 - 84*a^8*b^8*d^16*e^11*f^5 + 21*a^9*b^7*d^16*e^10*f^6 + 21
*a^10*b^6*d^16*e^9*f^7 - 84*a^11*b^5*d^16*e^8*f^8 + 132*a^12*b^4*d^16*e^7*f^9 - 102*a^13*b^3*d^16*e^6*f^10 + 3
9*a^14*b^2*d^16*e^5*f^11 + 39*b^16*c^5*d^11*e^14*f^2 - 102*b^16*c^6*d^10*e^13*f^3 + 132*b^16*c^7*d^9*e^12*f^4
- 84*b^16*c^8*d^8*e^11*f^5 + 21*b^16*c^9*d^7*e^10*f^6 + 21*b^16*c^10*d^6*e^9*f^7 - 84*b^16*c^11*d^5*e^8*f^8 +
132*b^16*c^12*d^4*e^7*f^9 - 102*b^16*c^13*d^3*e^6*f^10 + 39*b^16*c^14*d^2*e^5*f^11 - 6*a^4*b^12*c^15*d*f^16 -
6*a^15*b*c^4*d^12*f^16 - 6*a^4*b^12*d^16*e^15*f - 6*a^15*b*d^16*e^4*f^12 - 6*b^16*c^4*d^12*e^15*f - 6*b^16*c^1
5*d*e^4*f^12 + 24*a*b^15*c^3*d^13*e^15*f + 24*a*b^15*c^15*d*e^3*f^13 + 24*a^3*b^13*c*d^15*e^15*f + 24*a^3*b^13
*c^15*d*e*f^15 + 24*a^15*b*c*d^15*e^3*f^13 + 24*a^15*b*c^3*d^13*e*f^15 - 117*a*b^15*c^4*d^12*e^14*f^2 + 150*a*
b^15*c^5*d^11*e^13*f^3 + 159*a*b^15*c^6*d^10*e^12*f^4 - 546*a*b^15*c^7*d^9*e^11*f^5 + 414*a*b^15*c^8*d^8*e^10*
f^6 - 168*a*b^15*c^9*d^7*e^9*f^7 + 414*a*b^15*c^10*d^6*e^8*f^8 - 546*a*b^15*c^11*d^5*e^7*f^9 + 159*a*b^15*c^12
*d^4*e^6*f^10 + 150*a*b^15*c^13*d^3*e^5*f^11 - 117*a*b^15*c^14*d^2*e^4*f^12 - 36*a^2*b^14*c^2*d^14*e^15*f - 36
*a^2*b^14*c^15*d*e^2*f^14 - 117*a^4*b^12*c*d^15*e^14*f^2 - 117*a^4*b^12*c^14*d^2*e*f^15 + 150*a^5*b^11*c*d^15*
e^13*f^3 + 150*a^5*b^11*c^13*d^3*e*f^15 + 159*a^6*b^10*c*d^15*e^12*f^4 + 159*a^6*b^10*c^12*d^4*e*f^15 - 546*a^
7*b^9*c*d^15*e^11*f^5 - 546*a^7*b^9*c^11*d^5*e*f^15 + 414*a^8*b^8*c*d^15*e^10*f^6 + 414*a^8*b^8*c^10*d^6*e*f^1
5 - 168*a^9*b^7*c*d^15*e^9*f^7 - 168*a^9*b^7*c^9*d^7*e*f^15 + 414*a^10*b^6*c*d^15*e^8*f^8 + 414*a^10*b^6*c^8*d
^8*e*f^15 - 546*a^11*b^5*c*d^15*e^7*f^9 - 546*a^11*b^5*c^7*d^9*e*f^15 + 159*a^12*b^4*c*d^15*e^6*f^10 + 159*a^1
2*b^4*c^6*d^10*e*f^15 + 150*a^13*b^3*c*d^15*e^5*f^11 + 150*a^13*b^3*c^5*d^11*e*f^15 - 117*a^14*b^2*c*d^15*e^4*
f^12 - 117*a^14*b^2*c^4*d^12*e*f^15 - 36*a^15*b*c^2*d^14*e^2*f^14 + 78*a^2*b^14*c^3*d^13*e^14*f^2 + 318*a^2*b^
14*c^4*d^12*e^13*f^3 - 1269*a^2*b^14*c^5*d^11*e^12*f^4 + 1134*a^2*b^14*c^6*d^10*e^11*f^5 + 618*a^2*b^14*c^7*d^
9*e^10*f^6 - 843*a^2*b^14*c^8*d^8*e^9*f^7 - 843*a^2*b^14*c^9*d^7*e^8*f^8 + 618*a^2*b^14*c^10*d^6*e^7*f^9 + 113
4*a^2*b^14*c^11*d^5*e^6*f^10 - 1269*a^2*b^14*c^12*d^4*e^5*f^11 + 318*a^2*b^14*c^13*d^3*e^4*f^12 + 78*a^2*b^14*
c^14*d^2*e^3*f^13 + 78*a^3*b^13*c^2*d^14*e^14*f^2 - 732*a^3*b^13*c^3*d^13*e^13*f^3 + 978*a^3*b^13*c^4*d^12*e^1
2*f^4 + 1722*a^3*b^13*c^5*d^11*e^11*f^5 - 4548*a^3*b^13*c^6*d^10*e^10*f^6 + 1362*a^3*b^13*c^7*d^9*e^9*f^7 + 22
32*a^3*b^13*c^8*d^8*e^8*f^8 + 1362*a^3*b^13*c^9*d^7*e^7*f^9 - 4548*a^3*b^13*c^10*d^6*e^6*f^10 + 1722*a^3*b^13*
c^11*d^5*e^5*f^11 + 978*a^3*b^13*c^12*d^4*e^4*f^12 - 732*a^3*b^13*c^13*d^3*e^3*f^13 + 78*a^3*b^13*c^14*d^2*e^2
*f^14 + 318*a^4*b^12*c^2*d^14*e^13*f^3 + 978*a^4*b^12*c^3*d^13*e^12*f^4 - 4452*a^4*b^12*c^4*d^12*e^11*f^5 + 34
95*a^4*b^12*c^5*d^11*e^10*f^6 + 4302*a^4*b^12*c^6*d^10*e^9*f^7 - 4518*a^4*b^12*c^7*d^9*e^8*f^8 - 4518*a^4*b^12
*c^8*d^8*e^7*f^9 + 4302*a^4*b^12*c^9*d^7*e^6*f^10 + 3495*a^4*b^12*c^10*d^6*e^5*f^11 - 4452*a^4*b^12*c^11*d^5*e
^4*f^12 + 978*a^4*b^12*c^12*d^4*e^3*f^13 + 318*a^4*b^12*c^13*d^3*e^2*f^14 - 1269*a^5*b^11*c^2*d^14*e^12*f^4 +
1722*a^5*b^11*c^3*d^13*e^11*f^5 + 3495*a^5*b^11*c^4*d^12*e^10*f^6 - 9348*a^5*b^11*c^5*d^11*e^9*f^7 + 2799*a^5*
b^11*c^6*d^10*e^8*f^8 + 4824*a^5*b^11*c^7*d^9*e^7*f^9 + 2799*a^5*b^11*c^8*d^8*e^6*f^10 - 9348*a^5*b^11*c^9*d^7
*e^5*f^11 + 3495*a^5*b^11*c^10*d^6*e^4*f^12 + 1722*a^5*b^11*c^11*d^5*e^3*f^13 - 1269*a^5*b^11*c^12*d^4*e^2*f^1
4 + 1134*a^6*b^10*c^2*d^14*e^11*f^5 - 4548*a^6*b^10*c^3*d^13*e^10*f^6 + 4302*a^6*b^10*c^4*d^12*e^9*f^7 + 2799*
a^6*b^10*c^5*d^11*e^8*f^8 - 3744*a^6*b^10*c^6*d^10*e^7*f^9 - 3744*a^6*b^10*c^7*d^9*e^6*f^10 + 2799*a^6*b^10*c^
8*d^8*e^5*f^11 + 4302*a^6*b^10*c^9*d^7*e^4*f^12 - 4548*a^6*b^10*c^10*d^6*e^3*f^13 + 1134*a^6*b^10*c^11*d^5*e^2
*f^14 + 618*a^7*b^9*c^2*d^14*e^10*f^6 + 1362*a^7*b^9*c^3*d^13*e^9*f^7 - 4518*a^7*b^9*c^4*d^12*e^8*f^8 + 4824*a
^7*b^9*c^5*d^11*e^7*f^9 - 3744*a^7*b^9*c^6*d^10*e^6*f^10 + 4824*a^7*b^9*c^7*d^9*e^5*f^11 - 4518*a^7*b^9*c^8*d^
8*e^4*f^12 + 1362*a^7*b^9*c^9*d^7*e^3*f^13 + 618*a^7*b^9*c^10*d^6*e^2*f^14 - 843*a^8*b^8*c^2*d^14*e^9*f^7 + 22
32*a^8*b^8*c^3*d^13*e^8*f^8 - 4518*a^8*b^8*c^4*d^12*e^7*f^9 + 2799*a^8*b^8*c^5*d^11*e^6*f^10 + 2799*a^8*b^8*c^
6*d^10*e^5*f^11 - 4518*a^8*b^8*c^7*d^9*e^4*f^12 + 2232*a^8*b^8*c^8*d^8*e^3*f^13 - 843*a^8*b^8*c^9*d^7*e^2*f^14
- 843*a^9*b^7*c^2*d^14*e^8*f^8 + 1362*a^9*b^7*c^3*d^13*e^7*f^9 + 4302*a^9*b^7*c^4*d^12*e^6*f^10 - 9348*a^9*b^
7*c^5*d^11*e^5*f^11 + 4302*a^9*b^7*c^6*d^10*e^4*f^12 + 1362*a^9*b^7*c^7*d^9*e^3*f^13 - 843*a^9*b^7*c^8*d^8*e^2
*f^14 + 618*a^10*b^6*c^2*d^14*e^7*f^9 - 4548*a^10*b^6*c^3*d^13*e^6*f^10 + 3495*a^10*b^6*c^4*d^12*e^5*f^11 + 34
95*a^10*b^6*c^5*d^11*e^4*f^12 - 4548*a^10*b^6*c^6*d^10*e^3*f^13 + 618*a^10*b^6*c^7*d^9*e^2*f^14 + 1134*a^11*b^
5*c^2*d^14*e^6*f^10 + 1722*a^11*b^5*c^3*d^13*e^5*f^11 - 4452*a^11*b^5*c^4*d^12*e^4*f^12 + 1722*a^11*b^5*c^5*d^
11*e^3*f^13 + 1134*a^11*b^5*c^6*d^10*e^2*f^14 - 1269*a^12*b^4*c^2*d^14*e^5*f^11 + 978*a^12*b^4*c^3*d^13*e^4*f^
12 + 978*a^12*b^4*c^4*d^12*e^3*f^13 - 1269*a^12*b^4*c^5*d^11*e^2*f^14 + 318*a^13*b^3*c^2*d^14*e^4*f^12 - 732*a
^13*b^3*c^3*d^13*e^3*f^13 + 318*a^13*b^3*c^4*d^12*e^2*f^14 + 78*a^14*b^2*c^2*d^14*e^3*f^13 + 78*a^14*b^2*c^3*d
^13*e^2*f^14)/(56*a^3*b^13*c^5*d^11*e^16 - a^8*b^8*d^16*e^16 - a^16*c^8*d^8*f^16 - b^16*c^8*d^8*e^16 - a^16*d^
16*e^8*f^8 - b^16*c^16*e^8*f^8 - 28*a^2*b^14*c^6*d^10*e^16 - a^8*b^8*c^16*f^16 - 70*a^4*b^12*c^4*d^12*e^16 + 5
6*a^5*b^11*c^3*d^13*e^16 - 28*a^6*b^10*c^2*d^14*e^16 - 28*a^10*b^6*c^14*d^2*f^16 + 56*a^11*b^5*c^13*d^3*f^16 -
70*a^12*b^4*c^12*d^4*f^16 + 56*a^13*b^3*c^11*d^5*f^16 - 28*a^14*b^2*c^10*d^6*f^16 - 28*a^2*b^14*c^16*e^6*f^10
+ 56*a^3*b^13*c^16*e^5*f^11 - 70*a^4*b^12*c^16*e^4*f^12 + 56*a^5*b^11*c^16*e^3*f^13 - 28*a^6*b^10*c^16*e^2*f^
14 - 28*a^10*b^6*d^16*e^14*f^2 + 56*a^11*b^5*d^16*e^13*f^3 - 70*a^12*b^4*d^16*e^12*f^4 + 56*a^13*b^3*d^16*e^11
*f^5 - 28*a^14*b^2*d^16*e^10*f^6 - 28*a^16*c^2*d^14*e^6*f^10 + 56*a^16*c^3*d^13*e^5*f^11 - 70*a^16*c^4*d^12*e^
4*f^12 + 56*a^16*c^5*d^11*e^3*f^13 - 28*a^16*c^6*d^10*e^2*f^14 - 28*b^16*c^10*d^6*e^14*f^2 + 56*b^16*c^11*d^5*
e^13*f^3 - 70*b^16*c^12*d^4*e^12*f^4 + 56*b^16*c^13*d^3*e^11*f^5 - 28*b^16*c^14*d^2*e^10*f^6 + 8*a*b^15*c^7*d^
9*e^16 + 8*a^7*b^9*c*d^15*e^16 + 8*a^9*b^7*c^15*d*f^16 + 8*a^15*b*c^9*d^7*f^16 + 8*a*b^15*c^16*e^7*f^9 + 8*a^7
*b^9*c^16*e*f^15 + 8*a^9*b^7*d^16*e^15*f + 8*a^15*b*d^16*e^9*f^7 + 8*a^16*c*d^15*e^7*f^9 + 8*a^16*c^7*d^9*e*f^
15 + 8*b^16*c^9*d^7*e^15*f + 8*b^16*c^15*d*e^9*f^7 - 56*a*b^15*c^8*d^8*e^15*f - 56*a*b^15*c^15*d*e^8*f^8 - 56*
a^8*b^8*c*d^15*e^15*f - 56*a^8*b^8*c^15*d*e*f^15 - 56*a^15*b*c*d^15*e^8*f^8 - 56*a^15*b*c^8*d^8*e*f^15 + 160*a
*b^15*c^9*d^7*e^14*f^2 - 224*a*b^15*c^10*d^6*e^13*f^3 + 112*a*b^15*c^11*d^5*e^12*f^4 + 112*a*b^15*c^12*d^4*e^1
1*f^5 - 224*a*b^15*c^13*d^3*e^10*f^6 + 160*a*b^15*c^14*d^2*e^9*f^7 + 160*a^2*b^14*c^7*d^9*e^15*f + 160*a^2*b^1
4*c^15*d*e^7*f^9 - 224*a^3*b^13*c^6*d^10*e^15*f - 224*a^3*b^13*c^15*d*e^6*f^10 + 112*a^4*b^12*c^5*d^11*e^15*f
+ 112*a^4*b^12*c^15*d*e^5*f^11 + 112*a^5*b^11*c^4*d^12*e^15*f + 112*a^5*b^11*c^15*d*e^4*f^12 - 224*a^6*b^10*c^
3*d^13*e^15*f - 224*a^6*b^10*c^15*d*e^3*f^13 + 160*a^7*b^9*c^2*d^14*e^15*f + 160*a^7*b^9*c^15*d*e^2*f^14 + 160
*a^9*b^7*c*d^15*e^14*f^2 + 160*a^9*b^7*c^14*d^2*e*f^15 - 224*a^10*b^6*c*d^15*e^13*f^3 - 224*a^10*b^6*c^13*d^3*
e*f^15 + 112*a^11*b^5*c*d^15*e^12*f^4 + 112*a^11*b^5*c^12*d^4*e*f^15 + 112*a^12*b^4*c*d^15*e^11*f^5 + 112*a^12
*b^4*c^11*d^5*e*f^15 - 224*a^13*b^3*c*d^15*e^10*f^6 - 224*a^13*b^3*c^10*d^6*e*f^15 + 160*a^14*b^2*c*d^15*e^9*f
^7 + 160*a^14*b^2*c^9*d^7*e*f^15 + 160*a^15*b*c^2*d^14*e^7*f^9 - 224*a^15*b*c^3*d^13*e^6*f^10 + 112*a^15*b*c^4
*d^12*e^5*f^11 + 112*a^15*b*c^5*d^11*e^4*f^12 - 224*a^15*b*c^6*d^10*e^3*f^13 + 160*a^15*b*c^7*d^9*e^2*f^14 - 3
00*a^2*b^14*c^8*d^8*e^14*f^2 + 840*a^2*b^14*c^10*d^6*e^12*f^4 - 1344*a^2*b^14*c^11*d^5*e^11*f^5 + 840*a^2*b^14
*c^12*d^4*e^10*f^6 - 300*a^2*b^14*c^14*d^2*e^8*f^8 + 1400*a^3*b^13*c^8*d^8*e^13*f^3 - 2800*a^3*b^13*c^9*d^7*e^
12*f^4 + 1568*a^3*b^13*c^10*d^6*e^11*f^5 + 1568*a^3*b^13*c^11*d^5*e^10*f^6 - 2800*a^3*b^13*c^12*d^4*e^9*f^7 +
1400*a^3*b^13*c^13*d^3*e^8*f^8 + 840*a^4*b^12*c^6*d^10*e^14*f^2 - 2800*a^4*b^12*c^7*d^9*e^13*f^3 + 1750*a^4*b^
12*c^8*d^8*e^12*f^4 + 4480*a^4*b^12*c^9*d^7*e^11*f^5 - 8624*a^4*b^12*c^10*d^6*e^10*f^6 + 4480*a^4*b^12*c^11*d^
5*e^9*f^7 + 1750*a^4*b^12*c^12*d^4*e^8*f^8 - 2800*a^4*b^12*c^13*d^3*e^7*f^9 + 840*a^4*b^12*c^14*d^2*e^6*f^10 -
1344*a^5*b^11*c^5*d^11*e^14*f^2 + 1568*a^5*b^11*c^6*d^10*e^13*f^3 + 4480*a^5*b^11*c^7*d^9*e^12*f^4 - 12264*a^
5*b^11*c^8*d^8*e^11*f^5 + 7392*a^5*b^11*c^9*d^7*e^10*f^6 + 7392*a^5*b^11*c^10*d^6*e^9*f^7 - 12264*a^5*b^11*c^1
1*d^5*e^8*f^8 + 4480*a^5*b^11*c^12*d^4*e^7*f^9 + 1568*a^5*b^11*c^13*d^3*e^6*f^10 - 1344*a^5*b^11*c^14*d^2*e^5*
f^11 + 840*a^6*b^10*c^4*d^12*e^14*f^2 + 1568*a^6*b^10*c^5*d^11*e^13*f^3 - 8624*a^6*b^10*c^6*d^10*e^12*f^4 + 73
92*a^6*b^10*c^7*d^9*e^11*f^5 + 11396*a^6*b^10*c^8*d^8*e^10*f^6 - 24640*a^6*b^10*c^9*d^7*e^9*f^7 + 11396*a^6*b^
10*c^10*d^6*e^8*f^8 + 7392*a^6*b^10*c^11*d^5*e^7*f^9 - 8624*a^6*b^10*c^12*d^4*e^6*f^10 + 1568*a^6*b^10*c^13*d^
3*e^5*f^11 + 840*a^6*b^10*c^14*d^2*e^4*f^12 - 2800*a^7*b^9*c^4*d^12*e^13*f^3 + 4480*a^7*b^9*c^5*d^11*e^12*f^4
+ 7392*a^7*b^9*c^6*d^10*e^11*f^5 - 24640*a^7*b^9*c^7*d^9*e^10*f^6 + 15400*a^7*b^9*c^8*d^8*e^9*f^7 + 15400*a^7*
b^9*c^9*d^7*e^8*f^8 - 24640*a^7*b^9*c^10*d^6*e^7*f^9 + 7392*a^7*b^9*c^11*d^5*e^6*f^10 + 4480*a^7*b^9*c^12*d^4*
e^5*f^11 - 2800*a^7*b^9*c^13*d^3*e^4*f^12 - 300*a^8*b^8*c^2*d^14*e^14*f^2 + 1400*a^8*b^8*c^3*d^13*e^13*f^3 + 1
750*a^8*b^8*c^4*d^12*e^12*f^4 - 12264*a^8*b^8*c^5*d^11*e^11*f^5 + 11396*a^8*b^8*c^6*d^10*e^10*f^6 + 15400*a^8*
b^8*c^7*d^9*e^9*f^7 - 34650*a^8*b^8*c^8*d^8*e^8*f^8 + 15400*a^8*b^8*c^9*d^7*e^7*f^9 + 11396*a^8*b^8*c^10*d^6*e
^6*f^10 - 12264*a^8*b^8*c^11*d^5*e^5*f^11 + 1750*a^8*b^8*c^12*d^4*e^4*f^12 + 1400*a^8*b^8*c^13*d^3*e^3*f^13 -
300*a^8*b^8*c^14*d^2*e^2*f^14 - 2800*a^9*b^7*c^3*d^13*e^12*f^4 + 4480*a^9*b^7*c^4*d^12*e^11*f^5 + 7392*a^9*b^7
*c^5*d^11*e^10*f^6 - 24640*a^9*b^7*c^6*d^10*e^9*f^7 + 15400*a^9*b^7*c^7*d^9*e^8*f^8 + 15400*a^9*b^7*c^8*d^8*e^
7*f^9 - 24640*a^9*b^7*c^9*d^7*e^6*f^10 + 7392*a^9*b^7*c^10*d^6*e^5*f^11 + 4480*a^9*b^7*c^11*d^5*e^4*f^12 - 280
0*a^9*b^7*c^12*d^4*e^3*f^13 + 840*a^10*b^6*c^2*d^14*e^12*f^4 + 1568*a^10*b^6*c^3*d^13*e^11*f^5 - 8624*a^10*b^6
*c^4*d^12*e^10*f^6 + 7392*a^10*b^6*c^5*d^11*e^9*f^7 + 11396*a^10*b^6*c^6*d^10*e^8*f^8 - 24640*a^10*b^6*c^7*d^9
*e^7*f^9 + 11396*a^10*b^6*c^8*d^8*e^6*f^10 + 7392*a^10*b^6*c^9*d^7*e^5*f^11 - 8624*a^10*b^6*c^10*d^6*e^4*f^12
+ 1568*a^10*b^6*c^11*d^5*e^3*f^13 + 840*a^10*b^6*c^12*d^4*e^2*f^14 - 1344*a^11*b^5*c^2*d^14*e^11*f^5 + 1568*a^
11*b^5*c^3*d^13*e^10*f^6 + 4480*a^11*b^5*c^4*d^12*e^9*f^7 - 12264*a^11*b^5*c^5*d^11*e^8*f^8 + 7392*a^11*b^5*c^
6*d^10*e^7*f^9 + 7392*a^11*b^5*c^7*d^9*e^6*f^10 - 12264*a^11*b^5*c^8*d^8*e^5*f^11 + 4480*a^11*b^5*c^9*d^7*e^4*
f^12 + 1568*a^11*b^5*c^10*d^6*e^3*f^13 - 1344*a^11*b^5*c^11*d^5*e^2*f^14 + 840*a^12*b^4*c^2*d^14*e^10*f^6 - 28
00*a^12*b^4*c^3*d^13*e^9*f^7 + 1750*a^12*b^4*c^4*d^12*e^8*f^8 + 4480*a^12*b^4*c^5*d^11*e^7*f^9 - 8624*a^12*b^4
*c^6*d^10*e^6*f^10 + 4480*a^12*b^4*c^7*d^9*e^5*f^11 + 1750*a^12*b^4*c^8*d^8*e^4*f^12 - 2800*a^12*b^4*c^9*d^7*e
^3*f^13 + 840*a^12*b^4*c^10*d^6*e^2*f^14 + 1400*a^13*b^3*c^3*d^13*e^8*f^8 - 2800*a^13*b^3*c^4*d^12*e^7*f^9 + 1
568*a^13*b^3*c^5*d^11*e^6*f^10 + 1568*a^13*b^3*c^6*d^10*e^5*f^11 - 2800*a^13*b^3*c^7*d^9*e^4*f^12 + 1400*a^13*
b^3*c^8*d^8*e^3*f^13 - 300*a^14*b^2*c^2*d^14*e^8*f^8 + 840*a^14*b^2*c^4*d^12*e^6*f^10 - 1344*a^14*b^2*c^5*d^11
*e^5*f^11 + 840*a^14*b^2*c^6*d^10*e^4*f^12 - 300*a^14*b^2*c^8*d^8*e^2*f^14) + root(756756*a^10*b^10*c^10*d^10*
e^10*f^10*z^3 + 573300*a^12*b^8*c^9*d^11*e^9*f^11*z^3 + 573300*a^11*b^9*c^11*d^9*e^8*f^12*z^3 + 573300*a^11*b^
9*c^8*d^12*e^11*f^9*z^3 + 573300*a^9*b^11*c^12*d^8*e^9*f^11*z^3 + 573300*a^9*b^11*c^9*d^11*e^12*f^8*z^3 + 5733
00*a^8*b^12*c^11*d^9*e^11*f^9*z^3 - 343980*a^11*b^9*c^10*d^10*e^9*f^11*z^3 - 343980*a^11*b^9*c^9*d^11*e^10*f^1
0*z^3 - 343980*a^10*b^10*c^11*d^9*e^9*f^11*z^3 - 343980*a^10*b^10*c^9*d^11*e^11*f^9*z^3 - 343980*a^9*b^11*c^11
*d^9*e^10*f^10*z^3 - 343980*a^9*b^11*c^10*d^10*e^11*f^9*z^3 + 326340*a^13*b^7*c^10*d^10*e^7*f^13*z^3 + 326340*
a^13*b^7*c^7*d^13*e^10*f^10*z^3 + 326340*a^10*b^10*c^13*d^7*e^7*f^13*z^3 + 326340*a^10*b^10*c^7*d^13*e^13*f^7*
z^3 + 326340*a^7*b^13*c^13*d^7*e^10*f^10*z^3 + 326340*a^7*b^13*c^10*d^10*e^13*f^7*z^3 - 267540*a^12*b^8*c^10*d
^10*e^8*f^12*z^3 - 267540*a^12*b^8*c^8*d^12*e^10*f^10*z^3 - 267540*a^10*b^10*c^12*d^8*e^8*f^12*z^3 - 267540*a^
10*b^10*c^8*d^12*e^12*f^8*z^3 - 267540*a^8*b^12*c^12*d^8*e^10*f^10*z^3 - 267540*a^8*b^12*c^10*d^10*e^12*f^8*z^
3 + 245700*a^14*b^6*c^8*d^12*e^8*f^12*z^3 + 245700*a^12*b^8*c^12*d^8*e^6*f^14*z^3 + 245700*a^12*b^8*c^6*d^14*e
^12*f^8*z^3 + 245700*a^8*b^12*c^14*d^6*e^8*f^12*z^3 + 245700*a^8*b^12*c^8*d^12*e^14*f^6*z^3 + 245700*a^6*b^14*
c^12*d^8*e^12*f^8*z^3 - 191100*a^13*b^7*c^9*d^11*e^8*f^12*z^3 - 191100*a^13*b^7*c^8*d^12*e^9*f^11*z^3 - 191100
*a^12*b^8*c^11*d^9*e^7*f^13*z^3 - 191100*a^12*b^8*c^7*d^13*e^11*f^9*z^3 - 191100*a^11*b^9*c^12*d^8*e^7*f^13*z^
3 - 191100*a^11*b^9*c^7*d^13*e^12*f^8*z^3 - 191100*a^9*b^11*c^13*d^7*e^8*f^12*z^3 - 191100*a^9*b^11*c^8*d^12*e
^13*f^7*z^3 - 191100*a^8*b^12*c^13*d^7*e^9*f^11*z^3 - 191100*a^8*b^12*c^9*d^11*e^13*f^7*z^3 - 191100*a^7*b^13*
c^12*d^8*e^11*f^9*z^3 - 191100*a^7*b^13*c^11*d^9*e^12*f^8*z^3 - 123900*a^14*b^6*c^9*d^11*e^7*f^13*z^3 - 123900
*a^14*b^6*c^7*d^13*e^9*f^11*z^3 - 123900*a^13*b^7*c^11*d^9*e^6*f^14*z^3 - 123900*a^13*b^7*c^6*d^14*e^11*f^9*z^
3 - 123900*a^11*b^9*c^13*d^7*e^6*f^14*z^3 - 123900*a^11*b^9*c^6*d^14*e^13*f^7*z^3 - 123900*a^9*b^11*c^14*d^6*e
^7*f^13*z^3 - 123900*a^9*b^11*c^7*d^13*e^14*f^6*z^3 - 123900*a^7*b^13*c^14*d^6*e^9*f^11*z^3 - 123900*a^7*b^13*
c^9*d^11*e^14*f^6*z^3 - 123900*a^6*b^14*c^13*d^7*e^11*f^9*z^3 - 123900*a^6*b^14*c^11*d^9*e^13*f^7*z^3 + 101700
*a^15*b^5*c^9*d^11*e^6*f^14*z^3 + 101700*a^15*b^5*c^6*d^14*e^9*f^11*z^3 + 101700*a^14*b^6*c^11*d^9*e^5*f^15*z^
3 + 101700*a^14*b^6*c^5*d^15*e^11*f^9*z^3 + 101700*a^11*b^9*c^14*d^6*e^5*f^15*z^3 + 101700*a^11*b^9*c^5*d^15*e
^14*f^6*z^3 + 101700*a^9*b^11*c^15*d^5*e^6*f^14*z^3 + 101700*a^9*b^11*c^6*d^14*e^15*f^5*z^3 + 101700*a^6*b^14*
c^15*d^5*e^9*f^11*z^3 + 101700*a^6*b^14*c^9*d^11*e^15*f^5*z^3 + 101700*a^5*b^15*c^14*d^6*e^11*f^9*z^3 + 101700
*a^5*b^15*c^11*d^9*e^14*f^6*z^3 - 65820*a^14*b^6*c^10*d^10*e^6*f^14*z^3 - 65820*a^14*b^6*c^6*d^14*e^10*f^10*z^
3 - 65820*a^10*b^10*c^14*d^6*e^6*f^14*z^3 - 65820*a^10*b^10*c^6*d^14*e^14*f^6*z^3 - 65820*a^6*b^14*c^14*d^6*e^
10*f^10*z^3 - 65820*a^6*b^14*c^10*d^10*e^14*f^6*z^3 + 56700*a^16*b^4*c^7*d^13*e^7*f^13*z^3 - 56700*a^15*b^5*c^
8*d^12*e^7*f^13*z^3 - 56700*a^15*b^5*c^7*d^13*e^8*f^12*z^3 + 56700*a^13*b^7*c^13*d^7*e^4*f^16*z^3 - 56700*a^13
*b^7*c^12*d^8*e^5*f^15*z^3 - 56700*a^13*b^7*c^5*d^15*e^12*f^8*z^3 + 56700*a^13*b^7*c^4*d^16*e^13*f^7*z^3 - 567
00*a^12*b^8*c^13*d^7*e^5*f^15*z^3 - 56700*a^12*b^8*c^5*d^15*e^13*f^7*z^3 - 56700*a^8*b^12*c^15*d^5*e^7*f^13*z^
3 - 56700*a^8*b^12*c^7*d^13*e^15*f^5*z^3 + 56700*a^7*b^13*c^16*d^4*e^7*f^13*z^3 - 56700*a^7*b^13*c^15*d^5*e^8*
f^12*z^3 - 56700*a^7*b^13*c^8*d^12*e^15*f^5*z^3 + 56700*a^7*b^13*c^7*d^13*e^16*f^4*z^3 - 56700*a^5*b^15*c^13*d
^7*e^12*f^8*z^3 - 56700*a^5*b^15*c^12*d^8*e^13*f^7*z^3 + 56700*a^4*b^16*c^13*d^7*e^13*f^7*z^3 - 48252*a^15*b^5
*c^10*d^10*e^5*f^15*z^3 - 48252*a^15*b^5*c^5*d^15*e^10*f^10*z^3 - 48252*a^10*b^10*c^15*d^5*e^5*f^15*z^3 - 4825
2*a^10*b^10*c^5*d^15*e^15*f^5*z^3 - 48252*a^5*b^15*c^15*d^5*e^10*f^10*z^3 - 48252*a^5*b^15*c^10*d^10*e^15*f^5*
z^3 - 32400*a^16*b^4*c^8*d^12*e^6*f^14*z^3 - 32400*a^16*b^4*c^6*d^14*e^8*f^12*z^3 - 32400*a^14*b^6*c^12*d^8*e^
4*f^16*z^3 - 32400*a^14*b^6*c^4*d^16*e^12*f^8*z^3 - 32400*a^12*b^8*c^14*d^6*e^4*f^16*z^3 - 32400*a^12*b^8*c^4*
d^16*e^14*f^6*z^3 - 32400*a^8*b^12*c^16*d^4*e^6*f^14*z^3 - 32400*a^8*b^12*c^6*d^14*e^16*f^4*z^3 - 32400*a^6*b^
14*c^16*d^4*e^8*f^12*z^3 - 32400*a^6*b^14*c^8*d^12*e^16*f^4*z^3 - 32400*a^4*b^16*c^14*d^6*e^12*f^8*z^3 - 32400
*a^4*b^16*c^12*d^8*e^14*f^6*z^3 + 20565*a^16*b^4*c^10*d^10*e^4*f^16*z^3 + 20565*a^16*b^4*c^4*d^16*e^10*f^10*z^
3 + 20565*a^10*b^10*c^16*d^4*e^4*f^16*z^3 + 20565*a^10*b^10*c^4*d^16*e^16*f^4*z^3 + 20565*a^4*b^16*c^16*d^4*e^
10*f^10*z^3 + 20565*a^4*b^16*c^10*d^10*e^16*f^4*z^3 + 15660*a^17*b^3*c^8*d^12*e^5*f^15*z^3 + 15660*a^17*b^3*c^
5*d^15*e^8*f^12*z^3 + 15660*a^15*b^5*c^12*d^8*e^3*f^17*z^3 + 15660*a^15*b^5*c^3*d^17*e^12*f^8*z^3 + 15660*a^12
*b^8*c^15*d^5*e^3*f^17*z^3 + 15660*a^12*b^8*c^3*d^17*e^15*f^5*z^3 + 15660*a^8*b^12*c^17*d^3*e^5*f^15*z^3 + 156
60*a^8*b^12*c^5*d^15*e^17*f^3*z^3 + 15660*a^5*b^15*c^17*d^3*e^8*f^12*z^3 + 15660*a^5*b^15*c^8*d^12*e^17*f^3*z^
3 + 15660*a^3*b^17*c^15*d^5*e^12*f^8*z^3 + 15660*a^3*b^17*c^12*d^8*e^15*f^5*z^3 - 9750*a^17*b^3*c^9*d^11*e^4*f
^16*z^3 - 9750*a^17*b^3*c^4*d^16*e^9*f^11*z^3 - 9750*a^16*b^4*c^11*d^9*e^3*f^17*z^3 - 9750*a^16*b^4*c^3*d^17*e
^11*f^9*z^3 - 9750*a^11*b^9*c^16*d^4*e^3*f^17*z^3 - 9750*a^11*b^9*c^3*d^17*e^16*f^4*z^3 - 9750*a^9*b^11*c^17*d
^3*e^4*f^16*z^3 - 9750*a^9*b^11*c^4*d^16*e^17*f^3*z^3 - 9750*a^4*b^16*c^17*d^3*e^9*f^11*z^3 - 9750*a^4*b^16*c^
9*d^11*e^17*f^3*z^3 - 9750*a^3*b^17*c^16*d^4*e^11*f^9*z^3 - 9750*a^3*b^17*c^11*d^9*e^16*f^4*z^3 - 8100*a^17*b^
3*c^7*d^13*e^6*f^14*z^3 - 8100*a^17*b^3*c^6*d^14*e^7*f^13*z^3 - 8100*a^14*b^6*c^13*d^7*e^3*f^17*z^3 - 8100*a^1
4*b^6*c^3*d^17*e^13*f^7*z^3 - 8100*a^13*b^7*c^14*d^6*e^3*f^17*z^3 - 8100*a^13*b^7*c^3*d^17*e^14*f^6*z^3 - 8100
*a^7*b^13*c^17*d^3*e^6*f^14*z^3 - 8100*a^7*b^13*c^6*d^14*e^17*f^3*z^3 - 8100*a^6*b^14*c^17*d^3*e^7*f^13*z^3 -
8100*a^6*b^14*c^7*d^13*e^17*f^3*z^3 - 8100*a^3*b^17*c^14*d^6*e^13*f^7*z^3 - 8100*a^3*b^17*c^13*d^7*e^14*f^6*z^
3 - 7980*a^16*b^4*c^9*d^11*e^5*f^15*z^3 - 7980*a^16*b^4*c^5*d^15*e^9*f^11*z^3 - 7980*a^15*b^5*c^11*d^9*e^4*f^1
6*z^3 - 7980*a^15*b^5*c^4*d^16*e^11*f^9*z^3 - 7980*a^11*b^9*c^15*d^5*e^4*f^16*z^3 - 7980*a^11*b^9*c^4*d^16*e^1
5*f^5*z^3 - 7980*a^9*b^11*c^16*d^4*e^5*f^15*z^3 - 7980*a^9*b^11*c^5*d^15*e^16*f^4*z^3 - 7980*a^5*b^15*c^16*d^4
*e^9*f^11*z^3 - 7980*a^5*b^15*c^9*d^11*e^16*f^4*z^3 - 7980*a^4*b^16*c^15*d^5*e^11*f^9*z^3 - 7980*a^4*b^16*c^11
*d^9*e^15*f^5*z^3 + 6300*a^18*b^2*c^6*d^14*e^6*f^14*z^3 + 6300*a^14*b^6*c^14*d^6*e^2*f^18*z^3 + 6300*a^14*b^6*
c^2*d^18*e^14*f^6*z^3 + 6300*a^6*b^14*c^18*d^2*e^6*f^14*z^3 + 6300*a^6*b^14*c^6*d^14*e^18*f^2*z^3 + 6300*a^2*b
^18*c^14*d^6*e^14*f^6*z^3 - 4260*a^18*b^2*c^7*d^13*e^5*f^15*z^3 - 4260*a^18*b^2*c^5*d^15*e^7*f^13*z^3 - 4260*a
^15*b^5*c^13*d^7*e^2*f^18*z^3 - 4260*a^15*b^5*c^2*d^18*e^13*f^7*z^3 - 4260*a^13*b^7*c^15*d^5*e^2*f^18*z^3 - 42
60*a^13*b^7*c^2*d^18*e^15*f^5*z^3 - 4260*a^7*b^13*c^18*d^2*e^5*f^15*z^3 - 4260*a^7*b^13*c^5*d^15*e^18*f^2*z^3
- 4260*a^5*b^15*c^18*d^2*e^7*f^13*z^3 - 4260*a^5*b^15*c^7*d^13*e^18*f^2*z^3 - 4260*a^2*b^18*c^15*d^5*e^13*f^7*
z^3 - 4260*a^2*b^18*c^13*d^7*e^15*f^5*z^3 + 1470*a^17*b^3*c^10*d^10*e^3*f^17*z^3 + 1470*a^17*b^3*c^3*d^17*e^10
*f^10*z^3 + 1470*a^10*b^10*c^17*d^3*e^3*f^17*z^3 + 1470*a^10*b^10*c^3*d^17*e^17*f^3*z^3 + 1470*a^3*b^17*c^17*d
^3*e^10*f^10*z^3 + 1470*a^3*b^17*c^10*d^10*e^17*f^3*z^3 + 1350*a^18*b^2*c^9*d^11*e^3*f^17*z^3 + 1350*a^18*b^2*
c^3*d^17*e^9*f^11*z^3 + 1350*a^17*b^3*c^11*d^9*e^2*f^18*z^3 + 1350*a^17*b^3*c^2*d^18*e^11*f^9*z^3 + 1350*a^11*
b^9*c^17*d^3*e^2*f^18*z^3 + 1350*a^11*b^9*c^2*d^18*e^17*f^3*z^3 + 1350*a^9*b^11*c^18*d^2*e^3*f^17*z^3 + 1350*a
^9*b^11*c^3*d^17*e^18*f^2*z^3 + 1350*a^3*b^17*c^18*d^2*e^9*f^11*z^3 + 1350*a^3*b^17*c^9*d^11*e^18*f^2*z^3 + 13
50*a^2*b^18*c^17*d^3*e^11*f^9*z^3 + 1350*a^2*b^18*c^11*d^9*e^17*f^3*z^3 - 1070*a^18*b^2*c^10*d^10*e^2*f^18*z^3
- 1070*a^18*b^2*c^2*d^18*e^10*f^10*z^3 - 1070*a^10*b^10*c^18*d^2*e^2*f^18*z^3 - 1070*a^10*b^10*c^2*d^18*e^18*
f^2*z^3 - 1070*a^2*b^18*c^18*d^2*e^10*f^10*z^3 - 1070*a^2*b^18*c^10*d^10*e^18*f^2*z^3 + 525*a^18*b^2*c^8*d^12*
e^4*f^16*z^3 + 525*a^18*b^2*c^4*d^16*e^8*f^12*z^3 + 525*a^16*b^4*c^12*d^8*e^2*f^18*z^3 + 525*a^16*b^4*c^2*d^18
*e^12*f^8*z^3 + 525*a^12*b^8*c^16*d^4*e^2*f^18*z^3 + 525*a^12*b^8*c^2*d^18*e^16*f^4*z^3 + 525*a^8*b^12*c^18*d^
2*e^4*f^16*z^3 + 525*a^8*b^12*c^4*d^16*e^18*f^2*z^3 + 525*a^4*b^16*c^18*d^2*e^8*f^12*z^3 + 525*a^4*b^16*c^8*d^
12*e^18*f^2*z^3 + 525*a^2*b^18*c^16*d^4*e^12*f^8*z^3 + 525*a^2*b^18*c^12*d^8*e^16*f^4*z^3 + 900*a^19*b*c^7*d^1
3*e^4*f^16*z^3 + 900*a^19*b*c^4*d^16*e^7*f^13*z^3 + 900*a^16*b^4*c^13*d^7*e*f^19*z^3 + 900*a^16*b^4*c*d^19*e^1
3*f^7*z^3 + 900*a^13*b^7*c^16*d^4*e*f^19*z^3 + 900*a^13*b^7*c*d^19*e^16*f^4*z^3 + 900*a^7*b^13*c^19*d*e^4*f^16
*z^3 + 900*a^7*b^13*c^4*d^16*e^19*f*z^3 + 900*a^4*b^16*c^19*d*e^7*f^13*z^3 + 900*a^4*b^16*c^7*d^13*e^19*f*z^3
+ 900*a*b^19*c^16*d^4*e^13*f^7*z^3 + 900*a*b^19*c^13*d^7*e^16*f^4*z^3 - 750*a^19*b*c^8*d^12*e^3*f^17*z^3 - 750
*a^19*b*c^3*d^17*e^8*f^12*z^3 - 750*a^17*b^3*c^12*d^8*e*f^19*z^3 - 750*a^17*b^3*c*d^19*e^12*f^8*z^3 - 750*a^12
*b^8*c^17*d^3*e*f^19*z^3 - 750*a^12*b^8*c*d^19*e^17*f^3*z^3 - 750*a^8*b^12*c^19*d*e^3*f^17*z^3 - 750*a^8*b^12*
c^3*d^17*e^19*f*z^3 - 750*a^3*b^17*c^19*d*e^8*f^12*z^3 - 750*a^3*b^17*c^8*d^12*e^19*f*z^3 - 750*a*b^19*c^17*d^
3*e^12*f^8*z^3 - 750*a*b^19*c^12*d^8*e^17*f^3*z^3 - 420*a^19*b*c^6*d^14*e^5*f^15*z^3 - 420*a^19*b*c^5*d^15*e^6
*f^14*z^3 - 420*a^15*b^5*c^14*d^6*e*f^19*z^3 - 420*a^15*b^5*c*d^19*e^14*f^6*z^3 - 420*a^14*b^6*c^15*d^5*e*f^19
*z^3 - 420*a^14*b^6*c*d^19*e^15*f^5*z^3 - 420*a^6*b^14*c^19*d*e^5*f^15*z^3 - 420*a^6*b^14*c^5*d^15*e^19*f*z^3
- 420*a^5*b^15*c^19*d*e^6*f^14*z^3 - 420*a^5*b^15*c^6*d^14*e^19*f*z^3 - 420*a*b^19*c^15*d^5*e^14*f^6*z^3 - 420
*a*b^19*c^14*d^6*e^15*f^5*z^3 + 350*a^19*b*c^9*d^11*e^2*f^18*z^3 + 350*a^19*b*c^2*d^18*e^9*f^11*z^3 + 350*a^18
*b^2*c^11*d^9*e*f^19*z^3 + 350*a^18*b^2*c*d^19*e^11*f^9*z^3 + 350*a^11*b^9*c^18*d^2*e*f^19*z^3 + 350*a^11*b^9*
c*d^19*e^18*f^2*z^3 + 350*a^9*b^11*c^19*d*e^2*f^18*z^3 + 350*a^9*b^11*c^2*d^18*e^19*f*z^3 + 350*a^2*b^18*c^19*
d*e^9*f^11*z^3 + 350*a^2*b^18*c^9*d^11*e^19*f*z^3 + 350*a*b^19*c^18*d^2*e^11*f^9*z^3 + 350*a*b^19*c^11*d^9*e^1
8*f^2*z^3 - 90*a^19*b*c^10*d^10*e*f^19*z^3 - 90*a^19*b*c*d^19*e^10*f^10*z^3 - 90*a^10*b^10*c^19*d*e*f^19*z^3 -
90*a^10*b^10*c*d^19*e^19*f*z^3 - 90*a*b^19*c^19*d*e^10*f^10*z^3 - 90*a*b^19*c^10*d^10*e^19*f*z^3 + 10*b^20*c^
19*d*e^11*f^9*z^3 + 10*b^20*c^11*d^9*e^19*f*z^3 + 10*a^20*c^9*d^11*e*f^19*z^3 + 10*a^20*c*d^19*e^9*f^11*z^3 +
10*a^19*b*d^20*e^11*f^9*z^3 + 10*a^11*b^9*d^20*e^19*f*z^3 + 10*a^9*b^11*c^20*e*f^19*z^3 + 10*a*b^19*c^20*e^9*f
^11*z^3 + 10*a^19*b*c^11*d^9*f^20*z^3 + 10*a^11*b^9*c^19*d*f^20*z^3 + 10*a^9*b^11*c*d^19*e^20*z^3 + 10*a*b^19*
c^9*d^11*e^20*z^3 + 252*b^20*c^15*d^5*e^15*f^5*z^3 - 210*b^20*c^16*d^4*e^14*f^6*z^3 - 210*b^20*c^14*d^6*e^16*f
^4*z^3 + 120*b^20*c^17*d^3*e^13*f^7*z^3 + 120*b^20*c^13*d^7*e^17*f^3*z^3 - 45*b^20*c^18*d^2*e^12*f^8*z^3 - 45*
b^20*c^12*d^8*e^18*f^2*z^3 + 252*a^20*c^5*d^15*e^5*f^15*z^3 - 210*a^20*c^6*d^14*e^4*f^16*z^3 - 210*a^20*c^4*d^
16*e^6*f^14*z^3 + 120*a^20*c^7*d^13*e^3*f^17*z^3 + 120*a^20*c^3*d^17*e^7*f^13*z^3 - 45*a^20*c^8*d^12*e^2*f^18*
z^3 - 45*a^20*c^2*d^18*e^8*f^12*z^3 + 252*a^15*b^5*d^20*e^15*f^5*z^3 - 210*a^16*b^4*d^20*e^14*f^6*z^3 - 210*a^
14*b^6*d^20*e^16*f^4*z^3 + 120*a^17*b^3*d^20*e^13*f^7*z^3 + 120*a^13*b^7*d^20*e^17*f^3*z^3 - 45*a^18*b^2*d^20*
e^12*f^8*z^3 - 45*a^12*b^8*d^20*e^18*f^2*z^3 + 252*a^5*b^15*c^20*e^5*f^15*z^3 - 210*a^6*b^14*c^20*e^4*f^16*z^3
- 210*a^4*b^16*c^20*e^6*f^14*z^3 + 120*a^7*b^13*c^20*e^3*f^17*z^3 + 120*a^3*b^17*c^20*e^7*f^13*z^3 - 45*a^8*b
^12*c^20*e^2*f^18*z^3 - 45*a^2*b^18*c^20*e^8*f^12*z^3 + 252*a^15*b^5*c^15*d^5*f^20*z^3 - 210*a^16*b^4*c^14*d^6
*f^20*z^3 - 210*a^14*b^6*c^16*d^4*f^20*z^3 + 120*a^17*b^3*c^13*d^7*f^20*z^3 + 120*a^13*b^7*c^17*d^3*f^20*z^3 -
45*a^18*b^2*c^12*d^8*f^20*z^3 - 45*a^12*b^8*c^18*d^2*f^20*z^3 + 252*a^5*b^15*c^5*d^15*e^20*z^3 - 210*a^6*b^14
*c^4*d^16*e^20*z^3 - 210*a^4*b^16*c^6*d^14*e^20*z^3 + 120*a^7*b^13*c^3*d^17*e^20*z^3 + 120*a^3*b^17*c^7*d^13*e
^20*z^3 - 45*a^8*b^12*c^2*d^18*e^20*z^3 - 45*a^2*b^18*c^8*d^12*e^20*z^3 - b^20*c^20*e^10*f^10*z^3 - a^20*d^20*
e^10*f^10*z^3 - b^20*c^10*d^10*e^20*z^3 - a^20*c^10*d^10*f^20*z^3 - a^10*b^10*d^20*e^20*z^3 - a^10*b^10*c^20*f
^20*z^3 + 1890*a^12*b^2*c*d^13*e*f^13*z + 1890*a*b^13*c^12*d^2*e*f^13*z + 1890*a*b^13*c*d^13*e^12*f^2*z + 9261
0*a^6*b^8*c^4*d^10*e^4*f^10*z + 92610*a^4*b^10*c^6*d^8*e^4*f^10*z + 92610*a^4*b^10*c^4*d^10*e^6*f^8*z + 66150*
a^8*b^6*c^3*d^11*e^3*f^11*z - 66150*a^7*b^7*c^4*d^10*e^3*f^11*z - 66150*a^7*b^7*c^3*d^11*e^4*f^10*z - 66150*a^
4*b^10*c^7*d^7*e^3*f^11*z - 66150*a^4*b^10*c^3*d^11*e^7*f^7*z + 66150*a^3*b^11*c^8*d^6*e^3*f^11*z - 66150*a^3*
b^11*c^7*d^7*e^4*f^10*z - 66150*a^3*b^11*c^4*d^10*e^7*f^7*z + 66150*a^3*b^11*c^3*d^11*e^8*f^6*z - 55566*a^5*b^
9*c^5*d^9*e^4*f^10*z - 55566*a^5*b^9*c^4*d^10*e^5*f^9*z - 55566*a^4*b^10*c^5*d^9*e^5*f^9*z - 32130*a^9*b^5*c^3
*d^11*e^2*f^12*z - 32130*a^9*b^5*c^2*d^12*e^3*f^11*z - 32130*a^3*b^11*c^9*d^5*e^2*f^12*z - 32130*a^3*b^11*c^2*
d^12*e^9*f^5*z - 32130*a^2*b^12*c^9*d^5*e^3*f^11*z - 32130*a^2*b^12*c^3*d^11*e^9*f^5*z + 22680*a^8*b^6*c^4*d^1
0*e^2*f^12*z + 22680*a^8*b^6*c^2*d^12*e^4*f^10*z + 22680*a^4*b^10*c^8*d^6*e^2*f^12*z + 22680*a^4*b^10*c^2*d^12
*e^8*f^6*z + 22680*a^2*b^12*c^8*d^6*e^4*f^10*z + 22680*a^2*b^12*c^4*d^10*e^8*f^6*z + 19278*a^10*b^4*c^2*d^12*e
^2*f^12*z + 19278*a^2*b^12*c^10*d^4*e^2*f^12*z + 19278*a^2*b^12*c^2*d^12*e^10*f^4*z + 18522*a^6*b^8*c^5*d^9*e^
3*f^11*z + 18522*a^6*b^8*c^3*d^11*e^5*f^9*z + 18522*a^5*b^9*c^6*d^8*e^3*f^11*z + 18522*a^5*b^9*c^3*d^11*e^6*f^
8*z + 18522*a^3*b^11*c^6*d^8*e^5*f^9*z + 18522*a^3*b^11*c^5*d^9*e^6*f^8*z - 13230*a^6*b^8*c^6*d^8*e^2*f^12*z -
13230*a^6*b^8*c^2*d^12*e^6*f^8*z - 13230*a^2*b^12*c^6*d^8*e^6*f^8*z + 3402*a^7*b^7*c^5*d^9*e^2*f^12*z + 3402*
a^7*b^7*c^2*d^12*e^5*f^9*z + 3402*a^5*b^9*c^7*d^7*e^2*f^12*z + 3402*a^5*b^9*c^2*d^12*e^7*f^7*z + 3402*a^2*b^12
*c^7*d^7*e^5*f^9*z + 3402*a^2*b^12*c^5*d^9*e^7*f^7*z + 7938*a^10*b^4*c^3*d^11*e*f^13*z + 7938*a^10*b^4*c*d^13*
e^3*f^11*z + 7938*a^3*b^11*c^10*d^4*e*f^13*z + 7938*a^3*b^11*c*d^13*e^10*f^4*z + 7938*a*b^13*c^10*d^4*e^3*f^11
*z + 7938*a*b^13*c^3*d^11*e^10*f^4*z - 5670*a^11*b^3*c^2*d^12*e*f^13*z - 5670*a^11*b^3*c*d^13*e^2*f^12*z - 567
0*a^2*b^12*c^11*d^3*e*f^13*z - 5670*a^2*b^12*c*d^13*e^11*f^3*z - 5670*a*b^13*c^11*d^3*e^2*f^12*z - 5670*a*b^13
*c^2*d^12*e^11*f^3*z - 3780*a^9*b^5*c^4*d^10*e*f^13*z - 3780*a^9*b^5*c*d^13*e^4*f^10*z - 3780*a^4*b^10*c^9*d^5
*e*f^13*z - 3780*a^4*b^10*c*d^13*e^9*f^5*z - 3780*a*b^13*c^9*d^5*e^4*f^10*z - 3780*a*b^13*c^4*d^10*e^9*f^5*z -
2268*a^8*b^6*c^5*d^9*e*f^13*z - 2268*a^8*b^6*c*d^13*e^5*f^9*z - 2268*a^5*b^9*c^8*d^6*e*f^13*z - 2268*a^5*b^9*
c*d^13*e^8*f^6*z - 2268*a*b^13*c^8*d^6*e^5*f^9*z - 2268*a*b^13*c^5*d^9*e^8*f^6*z + 1890*a^7*b^7*c^6*d^8*e*f^13
*z + 1890*a^7*b^7*c*d^13*e^6*f^8*z + 1890*a^6*b^8*c^7*d^7*e*f^13*z + 1890*a^6*b^8*c*d^13*e^7*f^7*z + 1890*a*b^
13*c^7*d^7*e^6*f^8*z + 1890*a*b^13*c^6*d^8*e^7*f^7*z - 252*b^14*c^13*d*e*f^13*z - 252*b^14*c*d^13*e^13*f*z - 2
52*a^13*b*d^14*e*f^13*z - 252*a*b^13*d^14*e^13*f*z - 252*a^13*b*c*d^13*f^14*z - 252*a*b^13*c^13*d*f^14*z - 918
*b^14*c^7*d^7*e^7*f^7*z - 882*b^14*c^11*d^3*e^3*f^11*z - 882*b^14*c^3*d^11*e^11*f^3*z + 693*b^14*c^12*d^2*e^2*
f^12*z + 693*b^14*c^2*d^12*e^12*f^2*z + 567*b^14*c^8*d^6*e^6*f^8*z + 567*b^14*c^6*d^8*e^8*f^6*z + 441*b^14*c^1
0*d^4*e^4*f^10*z + 441*b^14*c^4*d^10*e^10*f^4*z - 126*b^14*c^9*d^5*e^5*f^9*z - 126*b^14*c^5*d^9*e^9*f^5*z - 91
8*a^7*b^7*d^14*e^7*f^7*z - 882*a^11*b^3*d^14*e^3*f^11*z - 882*a^3*b^11*d^14*e^11*f^3*z + 693*a^12*b^2*d^14*e^2
*f^12*z + 693*a^2*b^12*d^14*e^12*f^2*z + 567*a^8*b^6*d^14*e^6*f^8*z + 567*a^6*b^8*d^14*e^8*f^6*z + 441*a^10*b^
4*d^14*e^4*f^10*z + 441*a^4*b^10*d^14*e^10*f^4*z - 126*a^9*b^5*d^14*e^5*f^9*z - 126*a^5*b^9*d^14*e^9*f^5*z - 9
18*a^7*b^7*c^7*d^7*f^14*z - 882*a^11*b^3*c^3*d^11*f^14*z - 882*a^3*b^11*c^11*d^3*f^14*z + 693*a^12*b^2*c^2*d^1
2*f^14*z + 693*a^2*b^12*c^12*d^2*f^14*z + 567*a^8*b^6*c^6*d^8*f^14*z + 567*a^6*b^8*c^8*d^6*f^14*z + 441*a^10*b
^4*c^4*d^10*f^14*z + 441*a^4*b^10*c^10*d^4*f^14*z - 126*a^9*b^5*c^5*d^9*f^14*z - 126*a^5*b^9*c^9*d^5*f^14*z +
36*b^14*d^14*e^14*z + 36*b^14*c^14*f^14*z + 36*a^14*d^14*f^14*z - 27054*a^2*b^9*c^2*d^9*e^2*f^9 + 9018*a^3*b^8
*c^2*d^9*e*f^10 + 9018*a^3*b^8*c*d^10*e^2*f^9 + 9018*a^2*b^9*c^3*d^8*e*f^10 + 9018*a^2*b^9*c*d^10*e^3*f^8 + 90
18*a*b^10*c^3*d^8*e^2*f^9 + 9018*a*b^10*c^2*d^9*e^3*f^8 - 9018*a^4*b^7*c*d^10*e*f^10 - 9018*a*b^10*c^4*d^7*e*f
^10 - 9018*a*b^10*c*d^10*e^4*f^7 + 2268*b^11*c^5*d^6*e*f^10 + 2268*b^11*c*d^10*e^5*f^6 + 2268*a^5*b^6*d^11*e*f
^10 + 2268*a*b^10*d^11*e^5*f^6 + 2268*a^5*b^6*c*d^10*f^11 + 2268*a*b^10*c^5*d^6*f^11 - 1458*b^11*c^3*d^8*e^3*f
^8 - 1161*b^11*c^4*d^7*e^2*f^9 - 1161*b^11*c^2*d^9*e^4*f^7 - 1458*a^3*b^8*d^11*e^3*f^8 - 1161*a^4*b^7*d^11*e^2
*f^9 - 1161*a^2*b^9*d^11*e^4*f^7 - 1458*a^3*b^8*c^3*d^8*f^11 - 1161*a^4*b^7*c^2*d^9*f^11 - 1161*a^2*b^9*c^4*d^
7*f^11 - 756*b^11*d^11*e^6*f^5 - 756*b^11*c^6*d^5*f^11 - 756*a^6*b^5*d^11*f^11, z, k)*((20*a^11*b^8*c^16*d^3*f
^19 - 7*a^10*b^9*c^17*d^2*f^19 - 28*a^12*b^7*c^15*d^4*f^19 + 14*a^13*b^6*c^14*d^5*f^19 + 14*a^14*b^5*c^13*d^6*
f^19 - 28*a^15*b^4*c^12*d^7*f^19 + 20*a^16*b^3*c^11*d^8*f^19 - 7*a^17*b^2*c^10*d^9*f^19 - 7*a^10*b^9*d^19*e^17
*f^2 + 20*a^11*b^8*d^19*e^16*f^3 - 28*a^12*b^7*d^19*e^15*f^4 + 14*a^13*b^6*d^19*e^14*f^5 + 14*a^14*b^5*d^19*e^
13*f^6 - 28*a^15*b^4*d^19*e^12*f^7 + 20*a^16*b^3*d^19*e^11*f^8 - 7*a^17*b^2*d^19*e^10*f^9 - 7*b^19*c^10*d^9*e^
17*f^2 + 20*b^19*c^11*d^8*e^16*f^3 - 28*b^19*c^12*d^7*e^15*f^4 + 14*b^19*c^13*d^6*e^14*f^5 + 14*b^19*c^14*d^5*
e^13*f^6 - 28*b^19*c^15*d^4*e^12*f^7 + 20*b^19*c^16*d^3*e^11*f^8 - 7*b^19*c^17*d^2*e^10*f^9 + a^9*b^10*c^18*d*
f^19 + a^18*b*c^9*d^10*f^19 + a^9*b^10*d^19*e^18*f + a^18*b*d^19*e^9*f^10 + b^19*c^9*d^10*e^18*f + b^19*c^18*d
*e^9*f^10 - 7*a*b^18*c^8*d^11*e^18*f - 7*a*b^18*c^18*d*e^8*f^11 - 7*a^8*b^11*c*d^18*e^18*f - 7*a^8*b^11*c^18*d
*e*f^18 - 7*a^18*b*c*d^18*e^8*f^11 - 7*a^18*b*c^8*d^11*e*f^18 + 34*a*b^18*c^9*d^10*e^17*f^2 - 27*a*b^18*c^10*d
^9*e^16*f^3 - 168*a*b^18*c^11*d^8*e^15*f^4 + 546*a*b^18*c^12*d^7*e^14*f^5 - 756*a*b^18*c^13*d^6*e^13*f^6 + 546
*a*b^18*c^14*d^5*e^12*f^7 - 168*a*b^18*c^15*d^4*e^11*f^8 - 27*a*b^18*c^16*d^3*e^10*f^9 + 34*a*b^18*c^17*d^2*e^
9*f^10 + 20*a^2*b^17*c^7*d^12*e^18*f + 20*a^2*b^17*c^18*d*e^7*f^12 - 28*a^3*b^16*c^6*d^13*e^18*f - 28*a^3*b^16
*c^18*d*e^6*f^13 + 14*a^4*b^15*c^5*d^14*e^18*f + 14*a^4*b^15*c^18*d*e^5*f^14 + 14*a^5*b^14*c^4*d^15*e^18*f + 1
4*a^5*b^14*c^18*d*e^4*f^15 - 28*a^6*b^13*c^3*d^16*e^18*f - 28*a^6*b^13*c^18*d*e^3*f^16 + 20*a^7*b^12*c^2*d^17*
e^18*f + 20*a^7*b^12*c^18*d*e^2*f^17 + 34*a^9*b^10*c*d^18*e^17*f^2 + 34*a^9*b^10*c^17*d^2*e*f^18 - 27*a^10*b^9
*c*d^18*e^16*f^3 - 27*a^10*b^9*c^16*d^3*e*f^18 - 168*a^11*b^8*c*d^18*e^15*f^4 - 168*a^11*b^8*c^15*d^4*e*f^18 +
546*a^12*b^7*c*d^18*e^14*f^5 + 546*a^12*b^7*c^14*d^5*e*f^18 - 756*a^13*b^6*c*d^18*e^13*f^6 - 756*a^13*b^6*c^1
3*d^6*e*f^18 + 546*a^14*b^5*c*d^18*e^12*f^7 + 546*a^14*b^5*c^12*d^7*e*f^18 - 168*a^15*b^4*c*d^18*e^11*f^8 - 16
8*a^15*b^4*c^11*d^8*e*f^18 - 27*a^16*b^3*c*d^18*e^10*f^9 - 27*a^16*b^3*c^10*d^9*e*f^18 + 34*a^17*b^2*c*d^18*e^
9*f^10 + 34*a^17*b^2*c^9*d^10*e*f^18 + 20*a^18*b*c^2*d^17*e^7*f^12 - 28*a^18*b*c^3*d^16*e^6*f^13 + 14*a^18*b*c
^4*d^15*e^5*f^14 + 14*a^18*b*c^5*d^14*e^4*f^15 - 28*a^18*b*c^6*d^13*e^3*f^16 + 20*a^18*b*c^7*d^12*e^2*f^17 - 2
7*a^2*b^17*c^8*d^11*e^17*f^2 - 371*a^2*b^17*c^9*d^10*e^16*f^3 + 1560*a^2*b^17*c^10*d^9*e^15*f^4 - 2484*a^2*b^1
7*c^11*d^8*e^14*f^5 + 1302*a^2*b^17*c^12*d^7*e^13*f^6 + 1302*a^2*b^17*c^13*d^6*e^12*f^7 - 2484*a^2*b^17*c^14*d
^5*e^11*f^8 + 1560*a^2*b^17*c^15*d^4*e^10*f^9 - 371*a^2*b^17*c^16*d^3*e^9*f^10 - 27*a^2*b^17*c^17*d^2*e^8*f^11
- 168*a^3*b^16*c^7*d^12*e^17*f^2 + 1560*a^3*b^16*c^8*d^11*e^16*f^3 - 3464*a^3*b^16*c^9*d^10*e^15*f^4 + 924*a^
3*b^16*c^10*d^9*e^14*f^5 + 7728*a^3*b^16*c^11*d^8*e^13*f^6 - 13104*a^3*b^16*c^12*d^7*e^12*f^7 + 7728*a^3*b^16*
c^13*d^6*e^11*f^8 + 924*a^3*b^16*c^14*d^5*e^10*f^9 - 3464*a^3*b^16*c^15*d^4*e^9*f^10 + 1560*a^3*b^16*c^16*d^3*
e^8*f^11 - 168*a^3*b^16*c^17*d^2*e^7*f^12 + 546*a^4*b^15*c^6*d^13*e^17*f^2 - 2484*a^4*b^15*c^7*d^12*e^16*f^3 +
924*a^4*b^15*c^8*d^11*e^15*f^4 + 12550*a^4*b^15*c^9*d^10*e^14*f^5 - 26838*a^4*b^15*c^10*d^9*e^13*f^6 + 15288*
a^4*b^15*c^11*d^8*e^12*f^7 + 15288*a^4*b^15*c^12*d^7*e^11*f^8 - 26838*a^4*b^15*c^13*d^6*e^10*f^9 + 12550*a^4*b
^15*c^14*d^5*e^9*f^10 + 924*a^4*b^15*c^15*d^4*e^8*f^11 - 2484*a^4*b^15*c^16*d^3*e^7*f^12 + 546*a^4*b^15*c^17*d
^2*e^6*f^13 - 756*a^5*b^14*c^5*d^14*e^17*f^2 + 1302*a^5*b^14*c^6*d^13*e^16*f^3 + 7728*a^5*b^14*c^7*d^12*e^15*f
^4 - 26838*a^5*b^14*c^8*d^11*e^14*f^5 + 18004*a^5*b^14*c^9*d^10*e^13*f^6 + 39858*a^5*b^14*c^10*d^9*e^12*f^7 -
78624*a^5*b^14*c^11*d^8*e^11*f^8 + 39858*a^5*b^14*c^12*d^7*e^10*f^9 + 18004*a^5*b^14*c^13*d^6*e^9*f^10 - 26838
*a^5*b^14*c^14*d^5*e^8*f^11 + 7728*a^5*b^14*c^15*d^4*e^7*f^12 + 1302*a^5*b^14*c^16*d^3*e^6*f^13 - 756*a^5*b^14
*c^17*d^2*e^5*f^14 + 546*a^6*b^13*c^4*d^15*e^17*f^2 + 1302*a^6*b^13*c^5*d^14*e^16*f^3 - 13104*a^6*b^13*c^6*d^1
3*e^15*f^4 + 15288*a^6*b^13*c^7*d^12*e^14*f^5 + 39858*a^6*b^13*c^8*d^11*e^13*f^6 - 110474*a^6*b^13*c^9*d^10*e^
12*f^7 + 66612*a^6*b^13*c^10*d^9*e^11*f^8 + 66612*a^6*b^13*c^11*d^8*e^10*f^9 - 110474*a^6*b^13*c^12*d^7*e^9*f^
10 + 39858*a^6*b^13*c^13*d^6*e^8*f^11 + 15288*a^6*b^13*c^14*d^5*e^7*f^12 - 13104*a^6*b^13*c^15*d^4*e^6*f^13 +
1302*a^6*b^13*c^16*d^3*e^5*f^14 + 546*a^6*b^13*c^17*d^2*e^4*f^15 - 168*a^7*b^12*c^3*d^16*e^17*f^2 - 2484*a^7*b
^12*c^4*d^15*e^16*f^3 + 7728*a^7*b^12*c^5*d^14*e^15*f^4 + 15288*a^7*b^12*c^6*d^13*e^14*f^5 - 78624*a^7*b^12*c^
7*d^12*e^13*f^6 + 66612*a^7*b^12*c^8*d^11*e^12*f^7 + 99736*a^7*b^12*c^9*d^10*e^11*f^8 - 216216*a^7*b^12*c^10*d
^9*e^10*f^9 + 99736*a^7*b^12*c^11*d^8*e^9*f^10 + 66612*a^7*b^12*c^12*d^7*e^8*f^11 - 78624*a^7*b^12*c^13*d^6*e^
7*f^12 + 15288*a^7*b^12*c^14*d^5*e^6*f^13 + 7728*a^7*b^12*c^15*d^4*e^5*f^14 - 2484*a^7*b^12*c^16*d^3*e^4*f^15
- 168*a^7*b^12*c^17*d^2*e^3*f^16 - 27*a^8*b^11*c^2*d^17*e^17*f^2 + 1560*a^8*b^11*c^3*d^16*e^16*f^3 + 924*a^8*b
^11*c^4*d^15*e^15*f^4 - 26838*a^8*b^11*c^5*d^14*e^14*f^5 + 39858*a^8*b^11*c^6*d^13*e^13*f^6 + 66612*a^8*b^11*c
^7*d^12*e^12*f^7 - 216216*a^8*b^11*c^8*d^11*e^11*f^8 + 134134*a^8*b^11*c^9*d^10*e^10*f^9 + 134134*a^8*b^11*c^1
0*d^9*e^9*f^10 - 216216*a^8*b^11*c^11*d^8*e^8*f^11 + 66612*a^8*b^11*c^12*d^7*e^7*f^12 + 39858*a^8*b^11*c^13*d^
6*e^6*f^13 - 26838*a^8*b^11*c^14*d^5*e^5*f^14 + 924*a^8*b^11*c^15*d^4*e^4*f^15 + 1560*a^8*b^11*c^16*d^3*e^3*f^
16 - 27*a^8*b^11*c^17*d^2*e^2*f^17 - 371*a^9*b^10*c^2*d^17*e^16*f^3 - 3464*a^9*b^10*c^3*d^16*e^15*f^4 + 12550*
a^9*b^10*c^4*d^15*e^14*f^5 + 18004*a^9*b^10*c^5*d^14*e^13*f^6 - 110474*a^9*b^10*c^6*d^13*e^12*f^7 + 99736*a^9*
b^10*c^7*d^12*e^11*f^8 + 134134*a^9*b^10*c^8*d^11*e^10*f^9 - 300300*a^9*b^10*c^9*d^10*e^9*f^10 + 134134*a^9*b^
10*c^10*d^9*e^8*f^11 + 99736*a^9*b^10*c^11*d^8*e^7*f^12 - 110474*a^9*b^10*c^12*d^7*e^6*f^13 + 18004*a^9*b^10*c
^13*d^6*e^5*f^14 + 12550*a^9*b^10*c^14*d^5*e^4*f^15 - 3464*a^9*b^10*c^15*d^4*e^3*f^16 - 371*a^9*b^10*c^16*d^3*
e^2*f^17 + 1560*a^10*b^9*c^2*d^17*e^15*f^4 + 924*a^10*b^9*c^3*d^16*e^14*f^5 - 26838*a^10*b^9*c^4*d^15*e^13*f^6
+ 39858*a^10*b^9*c^5*d^14*e^12*f^7 + 66612*a^10*b^9*c^6*d^13*e^11*f^8 - 216216*a^10*b^9*c^7*d^12*e^10*f^9 + 1
34134*a^10*b^9*c^8*d^11*e^9*f^10 + 134134*a^10*b^9*c^9*d^10*e^8*f^11 - 216216*a^10*b^9*c^10*d^9*e^7*f^12 + 666
12*a^10*b^9*c^11*d^8*e^6*f^13 + 39858*a^10*b^9*c^12*d^7*e^5*f^14 - 26838*a^10*b^9*c^13*d^6*e^4*f^15 + 924*a^10
*b^9*c^14*d^5*e^3*f^16 + 1560*a^10*b^9*c^15*d^4*e^2*f^17 - 2484*a^11*b^8*c^2*d^17*e^14*f^5 + 7728*a^11*b^8*c^3
*d^16*e^13*f^6 + 15288*a^11*b^8*c^4*d^15*e^12*f^7 - 78624*a^11*b^8*c^5*d^14*e^11*f^8 + 66612*a^11*b^8*c^6*d^13
*e^10*f^9 + 99736*a^11*b^8*c^7*d^12*e^9*f^10 - 216216*a^11*b^8*c^8*d^11*e^8*f^11 + 99736*a^11*b^8*c^9*d^10*e^7
*f^12 + 66612*a^11*b^8*c^10*d^9*e^6*f^13 - 78624*a^11*b^8*c^11*d^8*e^5*f^14 + 15288*a^11*b^8*c^12*d^7*e^4*f^15
+ 7728*a^11*b^8*c^13*d^6*e^3*f^16 - 2484*a^11*b^8*c^14*d^5*e^2*f^17 + 1302*a^12*b^7*c^2*d^17*e^13*f^6 - 13104
*a^12*b^7*c^3*d^16*e^12*f^7 + 15288*a^12*b^7*c^4*d^15*e^11*f^8 + 39858*a^12*b^7*c^5*d^14*e^10*f^9 - 110474*a^1
2*b^7*c^6*d^13*e^9*f^10 + 66612*a^12*b^7*c^7*d^12*e^8*f^11 + 66612*a^12*b^7*c^8*d^11*e^7*f^12 - 110474*a^12*b^
7*c^9*d^10*e^6*f^13 + 39858*a^12*b^7*c^10*d^9*e^5*f^14 + 15288*a^12*b^7*c^11*d^8*e^4*f^15 - 13104*a^12*b^7*c^1
2*d^7*e^3*f^16 + 1302*a^12*b^7*c^13*d^6*e^2*f^17 + 1302*a^13*b^6*c^2*d^17*e^12*f^7 + 7728*a^13*b^6*c^3*d^16*e^
11*f^8 - 26838*a^13*b^6*c^4*d^15*e^10*f^9 + 18004*a^13*b^6*c^5*d^14*e^9*f^10 + 39858*a^13*b^6*c^6*d^13*e^8*f^1
1 - 78624*a^13*b^6*c^7*d^12*e^7*f^12 + 39858*a^13*b^6*c^8*d^11*e^6*f^13 + 18004*a^13*b^6*c^9*d^10*e^5*f^14 - 2
6838*a^13*b^6*c^10*d^9*e^4*f^15 + 7728*a^13*b^6*c^11*d^8*e^3*f^16 + 1302*a^13*b^6*c^12*d^7*e^2*f^17 - 2484*a^1
4*b^5*c^2*d^17*e^11*f^8 + 924*a^14*b^5*c^3*d^16*e^10*f^9 + 12550*a^14*b^5*c^4*d^15*e^9*f^10 - 26838*a^14*b^5*c
^5*d^14*e^8*f^11 + 15288*a^14*b^5*c^6*d^13*e^7*f^12 + 15288*a^14*b^5*c^7*d^12*e^6*f^13 - 26838*a^14*b^5*c^8*d^
11*e^5*f^14 + 12550*a^14*b^5*c^9*d^10*e^4*f^15 + 924*a^14*b^5*c^10*d^9*e^3*f^16 - 2484*a^14*b^5*c^11*d^8*e^2*f
^17 + 1560*a^15*b^4*c^2*d^17*e^10*f^9 - 3464*a^15*b^4*c^3*d^16*e^9*f^10 + 924*a^15*b^4*c^4*d^15*e^8*f^11 + 772
8*a^15*b^4*c^5*d^14*e^7*f^12 - 13104*a^15*b^4*c^6*d^13*e^6*f^13 + 7728*a^15*b^4*c^7*d^12*e^5*f^14 + 924*a^15*b
^4*c^8*d^11*e^4*f^15 - 3464*a^15*b^4*c^9*d^10*e^3*f^16 + 1560*a^15*b^4*c^10*d^9*e^2*f^17 - 371*a^16*b^3*c^2*d^
17*e^9*f^10 + 1560*a^16*b^3*c^3*d^16*e^8*f^11 - 2484*a^16*b^3*c^4*d^15*e^7*f^12 + 1302*a^16*b^3*c^5*d^14*e^6*f
^13 + 1302*a^16*b^3*c^6*d^13*e^5*f^14 - 2484*a^16*b^3*c^7*d^12*e^4*f^15 + 1560*a^16*b^3*c^8*d^11*e^3*f^16 - 37
1*a^16*b^3*c^9*d^10*e^2*f^17 - 27*a^17*b^2*c^2*d^17*e^8*f^11 - 168*a^17*b^2*c^3*d^16*e^7*f^12 + 546*a^17*b^2*c
^4*d^15*e^6*f^13 - 756*a^17*b^2*c^5*d^14*e^5*f^14 + 546*a^17*b^2*c^6*d^13*e^4*f^15 - 168*a^17*b^2*c^7*d^12*e^3
*f^16 - 27*a^17*b^2*c^8*d^11*e^2*f^17)/(56*a^3*b^13*c^5*d^11*e^16 - a^8*b^8*d^16*e^16 - a^16*c^8*d^8*f^16 - b^
16*c^8*d^8*e^16 - a^16*d^16*e^8*f^8 - b^16*c^16*e^8*f^8 - 28*a^2*b^14*c^6*d^10*e^16 - a^8*b^8*c^16*f^16 - 70*a
^4*b^12*c^4*d^12*e^16 + 56*a^5*b^11*c^3*d^13*e^16 - 28*a^6*b^10*c^2*d^14*e^16 - 28*a^10*b^6*c^14*d^2*f^16 + 56
*a^11*b^5*c^13*d^3*f^16 - 70*a^12*b^4*c^12*d^4*f^16 + 56*a^13*b^3*c^11*d^5*f^16 - 28*a^14*b^2*c^10*d^6*f^16 -
28*a^2*b^14*c^16*e^6*f^10 + 56*a^3*b^13*c^16*e^5*f^11 - 70*a^4*b^12*c^16*e^4*f^12 + 56*a^5*b^11*c^16*e^3*f^13
- 28*a^6*b^10*c^16*e^2*f^14 - 28*a^10*b^6*d^16*e^14*f^2 + 56*a^11*b^5*d^16*e^13*f^3 - 70*a^12*b^4*d^16*e^12*f^
4 + 56*a^13*b^3*d^16*e^11*f^5 - 28*a^14*b^2*d^16*e^10*f^6 - 28*a^16*c^2*d^14*e^6*f^10 + 56*a^16*c^3*d^13*e^5*f
^11 - 70*a^16*c^4*d^12*e^4*f^12 + 56*a^16*c^5*d^11*e^3*f^13 - 28*a^16*c^6*d^10*e^2*f^14 - 28*b^16*c^10*d^6*e^1
4*f^2 + 56*b^16*c^11*d^5*e^13*f^3 - 70*b^16*c^12*d^4*e^12*f^4 + 56*b^16*c^13*d^3*e^11*f^5 - 28*b^16*c^14*d^2*e
^10*f^6 + 8*a*b^15*c^7*d^9*e^16 + 8*a^7*b^9*c*d^15*e^16 + 8*a^9*b^7*c^15*d*f^16 + 8*a^15*b*c^9*d^7*f^16 + 8*a*
b^15*c^16*e^7*f^9 + 8*a^7*b^9*c^16*e*f^15 + 8*a^9*b^7*d^16*e^15*f + 8*a^15*b*d^16*e^9*f^7 + 8*a^16*c*d^15*e^7*
f^9 + 8*a^16*c^7*d^9*e*f^15 + 8*b^16*c^9*d^7*e^15*f + 8*b^16*c^15*d*e^9*f^7 - 56*a*b^15*c^8*d^8*e^15*f - 56*a*
b^15*c^15*d*e^8*f^8 - 56*a^8*b^8*c*d^15*e^15*f - 56*a^8*b^8*c^15*d*e*f^15 - 56*a^15*b*c*d^15*e^8*f^8 - 56*a^15
*b*c^8*d^8*e*f^15 + 160*a*b^15*c^9*d^7*e^14*f^2 - 224*a*b^15*c^10*d^6*e^13*f^3 + 112*a*b^15*c^11*d^5*e^12*f^4
+ 112*a*b^15*c^12*d^4*e^11*f^5 - 224*a*b^15*c^13*d^3*e^10*f^6 + 160*a*b^15*c^14*d^2*e^9*f^7 + 160*a^2*b^14*c^7
*d^9*e^15*f + 160*a^2*b^14*c^15*d*e^7*f^9 - 224*a^3*b^13*c^6*d^10*e^15*f - 224*a^3*b^13*c^15*d*e^6*f^10 + 112*
a^4*b^12*c^5*d^11*e^15*f + 112*a^4*b^12*c^15*d*e^5*f^11 + 112*a^5*b^11*c^4*d^12*e^15*f + 112*a^5*b^11*c^15*d*e
^4*f^12 - 224*a^6*b^10*c^3*d^13*e^15*f - 224*a^6*b^10*c^15*d*e^3*f^13 + 160*a^7*b^9*c^2*d^14*e^15*f + 160*a^7*
b^9*c^15*d*e^2*f^14 + 160*a^9*b^7*c*d^15*e^14*f^2 + 160*a^9*b^7*c^14*d^2*e*f^15 - 224*a^10*b^6*c*d^15*e^13*f^3
- 224*a^10*b^6*c^13*d^3*e*f^15 + 112*a^11*b^5*c*d^15*e^12*f^4 + 112*a^11*b^5*c^12*d^4*e*f^15 + 112*a^12*b^4*c
*d^15*e^11*f^5 + 112*a^12*b^4*c^11*d^5*e*f^15 - 224*a^13*b^3*c*d^15*e^10*f^6 - 224*a^13*b^3*c^10*d^6*e*f^15 +
160*a^14*b^2*c*d^15*e^9*f^7 + 160*a^14*b^2*c^9*d^7*e*f^15 + 160*a^15*b*c^2*d^14*e^7*f^9 - 224*a^15*b*c^3*d^13*
e^6*f^10 + 112*a^15*b*c^4*d^12*e^5*f^11 + 112*a^15*b*c^5*d^11*e^4*f^12 - 224*a^15*b*c^6*d^10*e^3*f^13 + 160*a^
15*b*c^7*d^9*e^2*f^14 - 300*a^2*b^14*c^8*d^8*e^14*f^2 + 840*a^2*b^14*c^10*d^6*e^12*f^4 - 1344*a^2*b^14*c^11*d^
5*e^11*f^5 + 840*a^2*b^14*c^12*d^4*e^10*f^6 - 300*a^2*b^14*c^14*d^2*e^8*f^8 + 1400*a^3*b^13*c^8*d^8*e^13*f^3 -
2800*a^3*b^13*c^9*d^7*e^12*f^4 + 1568*a^3*b^13*c^10*d^6*e^11*f^5 + 1568*a^3*b^13*c^11*d^5*e^10*f^6 - 2800*a^3
*b^13*c^12*d^4*e^9*f^7 + 1400*a^3*b^13*c^13*d^3*e^8*f^8 + 840*a^4*b^12*c^6*d^10*e^14*f^2 - 2800*a^4*b^12*c^7*d
^9*e^13*f^3 + 1750*a^4*b^12*c^8*d^8*e^12*f^4 + 4480*a^4*b^12*c^9*d^7*e^11*f^5 - 8624*a^4*b^12*c^10*d^6*e^10*f^
6 + 4480*a^4*b^12*c^11*d^5*e^9*f^7 + 1750*a^4*b^12*c^12*d^4*e^8*f^8 - 2800*a^4*b^12*c^13*d^3*e^7*f^9 + 840*a^4
*b^12*c^14*d^2*e^6*f^10 - 1344*a^5*b^11*c^5*d^11*e^14*f^2 + 1568*a^5*b^11*c^6*d^10*e^13*f^3 + 4480*a^5*b^11*c^
7*d^9*e^12*f^4 - 12264*a^5*b^11*c^8*d^8*e^11*f^5 + 7392*a^5*b^11*c^9*d^7*e^10*f^6 + 7392*a^5*b^11*c^10*d^6*e^9
*f^7 - 12264*a^5*b^11*c^11*d^5*e^8*f^8 + 4480*a^5*b^11*c^12*d^4*e^7*f^9 + 1568*a^5*b^11*c^13*d^3*e^6*f^10 - 13
44*a^5*b^11*c^14*d^2*e^5*f^11 + 840*a^6*b^10*c^4*d^12*e^14*f^2 + 1568*a^6*b^10*c^5*d^11*e^13*f^3 - 8624*a^6*b^
10*c^6*d^10*e^12*f^4 + 7392*a^6*b^10*c^7*d^9*e^11*f^5 + 11396*a^6*b^10*c^8*d^8*e^10*f^6 - 24640*a^6*b^10*c^9*d
^7*e^9*f^7 + 11396*a^6*b^10*c^10*d^6*e^8*f^8 + 7392*a^6*b^10*c^11*d^5*e^7*f^9 - 8624*a^6*b^10*c^12*d^4*e^6*f^1
0 + 1568*a^6*b^10*c^13*d^3*e^5*f^11 + 840*a^6*b^10*c^14*d^2*e^4*f^12 - 2800*a^7*b^9*c^4*d^12*e^13*f^3 + 4480*a
^7*b^9*c^5*d^11*e^12*f^4 + 7392*a^7*b^9*c^6*d^10*e^11*f^5 - 24640*a^7*b^9*c^7*d^9*e^10*f^6 + 15400*a^7*b^9*c^8
*d^8*e^9*f^7 + 15400*a^7*b^9*c^9*d^7*e^8*f^8 - 24640*a^7*b^9*c^10*d^6*e^7*f^9 + 7392*a^7*b^9*c^11*d^5*e^6*f^10
+ 4480*a^7*b^9*c^12*d^4*e^5*f^11 - 2800*a^7*b^9*c^13*d^3*e^4*f^12 - 300*a^8*b^8*c^2*d^14*e^14*f^2 + 1400*a^8*
b^8*c^3*d^13*e^13*f^3 + 1750*a^8*b^8*c^4*d^12*e^12*f^4 - 12264*a^8*b^8*c^5*d^11*e^11*f^5 + 11396*a^8*b^8*c^6*d
^10*e^10*f^6 + 15400*a^8*b^8*c^7*d^9*e^9*f^7 - 34650*a^8*b^8*c^8*d^8*e^8*f^8 + 15400*a^8*b^8*c^9*d^7*e^7*f^9 +
11396*a^8*b^8*c^10*d^6*e^6*f^10 - 12264*a^8*b^8*c^11*d^5*e^5*f^11 + 1750*a^8*b^8*c^12*d^4*e^4*f^12 + 1400*a^8
*b^8*c^13*d^3*e^3*f^13 - 300*a^8*b^8*c^14*d^2*e^2*f^14 - 2800*a^9*b^7*c^3*d^13*e^12*f^4 + 4480*a^9*b^7*c^4*d^1
2*e^11*f^5 + 7392*a^9*b^7*c^5*d^11*e^10*f^6 - 24640*a^9*b^7*c^6*d^10*e^9*f^7 + 15400*a^9*b^7*c^7*d^9*e^8*f^8 +
15400*a^9*b^7*c^8*d^8*e^7*f^9 - 24640*a^9*b^7*c^9*d^7*e^6*f^10 + 7392*a^9*b^7*c^10*d^6*e^5*f^11 + 4480*a^9*b^
7*c^11*d^5*e^4*f^12 - 2800*a^9*b^7*c^12*d^4*e^3*f^13 + 840*a^10*b^6*c^2*d^14*e^12*f^4 + 1568*a^10*b^6*c^3*d^13
*e^11*f^5 - 8624*a^10*b^6*c^4*d^12*e^10*f^6 + 7392*a^10*b^6*c^5*d^11*e^9*f^7 + 11396*a^10*b^6*c^6*d^10*e^8*f^8
- 24640*a^10*b^6*c^7*d^9*e^7*f^9 + 11396*a^10*b^6*c^8*d^8*e^6*f^10 + 7392*a^10*b^6*c^9*d^7*e^5*f^11 - 8624*a^
10*b^6*c^10*d^6*e^4*f^12 + 1568*a^10*b^6*c^11*d^5*e^3*f^13 + 840*a^10*b^6*c^12*d^4*e^2*f^14 - 1344*a^11*b^5*c^
2*d^14*e^11*f^5 + 1568*a^11*b^5*c^3*d^13*e^10*f^6 + 4480*a^11*b^5*c^4*d^12*e^9*f^7 - 12264*a^11*b^5*c^5*d^11*e
^8*f^8 + 7392*a^11*b^5*c^6*d^10*e^7*f^9 + 7392*a^11*b^5*c^7*d^9*e^6*f^10 - 12264*a^11*b^5*c^8*d^8*e^5*f^11 + 4
480*a^11*b^5*c^9*d^7*e^4*f^12 + 1568*a^11*b^5*c^10*d^6*e^3*f^13 - 1344*a^11*b^5*c^11*d^5*e^2*f^14 + 840*a^12*b
^4*c^2*d^14*e^10*f^6 - 2800*a^12*b^4*c^3*d^13*e^9*f^7 + 1750*a^12*b^4*c^4*d^12*e^8*f^8 + 4480*a^12*b^4*c^5*d^1
1*e^7*f^9 - 8624*a^12*b^4*c^6*d^10*e^6*f^10 + 4480*a^12*b^4*c^7*d^9*e^5*f^11 + 1750*a^12*b^4*c^8*d^8*e^4*f^12
- 2800*a^12*b^4*c^9*d^7*e^3*f^13 + 840*a^12*b^4*c^10*d^6*e^2*f^14 + 1400*a^13*b^3*c^3*d^13*e^8*f^8 - 2800*a^13
*b^3*c^4*d^12*e^7*f^9 + 1568*a^13*b^3*c^5*d^11*e^6*f^10 + 1568*a^13*b^3*c^6*d^10*e^5*f^11 - 2800*a^13*b^3*c^7*
d^9*e^4*f^12 + 1400*a^13*b^3*c^8*d^8*e^3*f^13 - 300*a^14*b^2*c^2*d^14*e^8*f^8 + 840*a^14*b^2*c^4*d^12*e^6*f^10
- 1344*a^14*b^2*c^5*d^11*e^5*f^11 + 840*a^14*b^2*c^6*d^10*e^4*f^12 - 300*a^14*b^2*c^8*d^8*e^2*f^14) - (x*(18*
a^9*b^10*c^17*d^2*f^19 - 74*a^10*b^9*c^16*d^3*f^19 + 184*a^11*b^8*c^15*d^4*f^19 - 308*a^12*b^7*c^14*d^5*f^19 +
364*a^13*b^6*c^13*d^6*f^19 - 308*a^14*b^5*c^12*d^7*f^19 + 184*a^15*b^4*c^11*d^8*f^19 - 74*a^16*b^3*c^10*d^9*f
^19 + 18*a^17*b^2*c^9*d^10*f^19 + 18*a^9*b^10*d^19*e^17*f^2 - 74*a^10*b^9*d^19*e^16*f^3 + 184*a^11*b^8*d^19*e^
15*f^4 - 308*a^12*b^7*d^19*e^14*f^5 + 364*a^13*b^6*d^19*e^13*f^6 - 308*a^14*b^5*d^19*e^12*f^7 + 184*a^15*b^4*d
^19*e^11*f^8 - 74*a^16*b^3*d^19*e^10*f^9 + 18*a^17*b^2*d^19*e^9*f^10 + 18*b^19*c^9*d^10*e^17*f^2 - 74*b^19*c^1
0*d^9*e^16*f^3 + 184*b^19*c^11*d^8*e^15*f^4 - 308*b^19*c^12*d^7*e^14*f^5 + 364*b^19*c^13*d^6*e^13*f^6 - 308*b^
19*c^14*d^5*e^12*f^7 + 184*b^19*c^15*d^4*e^11*f^8 - 74*b^19*c^16*d^3*e^10*f^9 + 18*b^19*c^17*d^2*e^9*f^10 - 2*
a^8*b^11*c^18*d*f^19 - 2*a^18*b*c^8*d^11*f^19 - 2*a^8*b^11*d^19*e^18*f - 2*a^18*b*d^19*e^8*f^11 - 2*b^19*c^8*d
^11*e^18*f - 2*b^19*c^18*d*e^8*f^11 + 16*a*b^18*c^7*d^12*e^18*f + 16*a*b^18*c^18*d*e^7*f^12 + 16*a^7*b^12*c*d^
18*e^18*f + 16*a^7*b^12*c^18*d*e*f^18 + 16*a^18*b*c*d^18*e^7*f^12 + 16*a^18*b*c^7*d^12*e*f^18 - 126*a*b^18*c^8
*d^11*e^17*f^2 + 434*a*b^18*c^9*d^10*e^16*f^3 - 840*a*b^18*c^10*d^9*e^15*f^4 + 936*a*b^18*c^11*d^8*e^14*f^5 -
420*a*b^18*c^12*d^7*e^13*f^6 - 420*a*b^18*c^13*d^6*e^12*f^7 + 936*a*b^18*c^14*d^5*e^11*f^8 - 840*a*b^18*c^15*d
^4*e^10*f^9 + 434*a*b^18*c^16*d^3*e^9*f^10 - 126*a*b^18*c^17*d^2*e^8*f^11 - 56*a^2*b^17*c^6*d^13*e^18*f - 56*a
^2*b^17*c^18*d*e^6*f^13 + 112*a^3*b^16*c^5*d^14*e^18*f + 112*a^3*b^16*c^18*d*e^5*f^14 - 140*a^4*b^15*c^4*d^15*
e^18*f - 140*a^4*b^15*c^18*d*e^4*f^15 + 112*a^5*b^14*c^3*d^16*e^18*f + 112*a^5*b^14*c^18*d*e^3*f^16 - 56*a^6*b
^13*c^2*d^17*e^18*f - 56*a^6*b^13*c^18*d*e^2*f^17 - 126*a^8*b^11*c*d^18*e^17*f^2 - 126*a^8*b^11*c^17*d^2*e*f^1
8 + 434*a^9*b^10*c*d^18*e^16*f^3 + 434*a^9*b^10*c^16*d^3*e*f^18 - 840*a^10*b^9*c*d^18*e^15*f^4 - 840*a^10*b^9*
c^15*d^4*e*f^18 + 936*a^11*b^8*c*d^18*e^14*f^5 + 936*a^11*b^8*c^14*d^5*e*f^18 - 420*a^12*b^7*c*d^18*e^13*f^6 -
420*a^12*b^7*c^13*d^6*e*f^18 - 420*a^13*b^6*c*d^18*e^12*f^7 - 420*a^13*b^6*c^12*d^7*e*f^18 + 936*a^14*b^5*c*d
^18*e^11*f^8 + 936*a^14*b^5*c^11*d^8*e*f^18 - 840*a^15*b^4*c*d^18*e^10*f^9 - 840*a^15*b^4*c^10*d^9*e*f^18 + 43
4*a^16*b^3*c*d^18*e^9*f^10 + 434*a^16*b^3*c^9*d^10*e*f^18 - 126*a^17*b^2*c*d^18*e^8*f^11 - 126*a^17*b^2*c^8*d^
11*e*f^18 - 56*a^18*b*c^2*d^17*e^6*f^13 + 112*a^18*b*c^3*d^16*e^5*f^14 - 140*a^18*b*c^4*d^15*e^4*f^15 + 112*a^
18*b*c^5*d^14*e^3*f^16 - 56*a^18*b*c^6*d^13*e^2*f^17 + 360*a^2*b^17*c^7*d^12*e^17*f^2 - 882*a^2*b^17*c^8*d^11*
e^16*f^3 + 728*a^2*b^17*c^9*d^10*e^15*f^4 + 1152*a^2*b^17*c^10*d^9*e^14*f^5 - 4032*a^2*b^17*c^11*d^8*e^13*f^6
+ 5460*a^2*b^17*c^12*d^7*e^12*f^7 - 4032*a^2*b^17*c^13*d^6*e^11*f^8 + 1152*a^2*b^17*c^14*d^5*e^10*f^9 + 728*a^
2*b^17*c^15*d^4*e^9*f^10 - 882*a^2*b^17*c^16*d^3*e^8*f^11 + 360*a^2*b^17*c^17*d^2*e^7*f^12 - 504*a^3*b^16*c^6*
d^13*e^17*f^2 + 312*a^3*b^16*c^7*d^12*e^16*f^3 + 2520*a^3*b^16*c^8*d^11*e^15*f^4 - 7480*a^3*b^16*c^9*d^10*e^14
*f^5 + 9408*a^3*b^16*c^10*d^9*e^13*f^6 - 4368*a^3*b^16*c^11*d^8*e^12*f^7 - 4368*a^3*b^16*c^12*d^7*e^11*f^8 + 9
408*a^3*b^16*c^13*d^6*e^10*f^9 - 7480*a^3*b^16*c^14*d^5*e^9*f^10 + 2520*a^3*b^16*c^15*d^4*e^8*f^11 + 312*a^3*b
^16*c^16*d^3*e^7*f^12 - 504*a^3*b^16*c^17*d^2*e^6*f^13 + 252*a^4*b^15*c^5*d^14*e^17*f^2 + 1596*a^4*b^15*c^6*d^
13*e^16*f^3 - 6288*a^4*b^15*c^7*d^12*e^15*f^4 + 7380*a^4*b^15*c^8*d^11*e^14*f^5 + 2660*a^4*b^15*c^9*d^10*e^13*
f^6 - 18564*a^4*b^15*c^10*d^9*e^12*f^7 + 26208*a^4*b^15*c^11*d^8*e^11*f^8 - 18564*a^4*b^15*c^12*d^7*e^10*f^9 +
2660*a^4*b^15*c^13*d^6*e^9*f^10 + 7380*a^4*b^15*c^14*d^5*e^8*f^11 - 6288*a^4*b^15*c^15*d^4*e^7*f^12 + 1596*a^
4*b^15*c^16*d^3*e^6*f^13 + 252*a^4*b^15*c^17*d^2*e^5*f^14 + 252*a^5*b^14*c^4*d^15*e^17*f^2 - 2772*a^5*b^14*c^5
*d^14*e^16*f^3 + 3696*a^5*b^14*c^6*d^13*e^15*f^4 + 7056*a^5*b^14*c^7*d^12*e^14*f^5 - 25452*a^5*b^14*c^8*d^11*e
^13*f^6 + 30212*a^5*b^14*c^9*d^10*e^12*f^7 - 13104*a^5*b^14*c^10*d^9*e^11*f^8 - 13104*a^5*b^14*c^11*d^8*e^10*f
^9 + 30212*a^5*b^14*c^12*d^7*e^9*f^10 - 25452*a^5*b^14*c^13*d^6*e^8*f^11 + 7056*a^5*b^14*c^14*d^5*e^7*f^12 + 3
696*a^5*b^14*c^15*d^4*e^6*f^13 - 2772*a^5*b^14*c^16*d^3*e^5*f^14 + 252*a^5*b^14*c^17*d^2*e^4*f^15 - 504*a^6*b^
13*c^3*d^16*e^17*f^2 + 1596*a^6*b^13*c^4*d^15*e^16*f^3 + 3696*a^6*b^13*c^5*d^14*e^15*f^4 - 17472*a^6*b^13*c^6*
d^13*e^14*f^5 + 17472*a^6*b^13*c^7*d^12*e^13*f^6 + 9828*a^6*b^13*c^8*d^11*e^12*f^7 - 38584*a^6*b^13*c^9*d^10*e
^11*f^8 + 48048*a^6*b^13*c^10*d^9*e^10*f^9 - 38584*a^6*b^13*c^11*d^8*e^9*f^10 + 9828*a^6*b^13*c^12*d^7*e^8*f^1
1 + 17472*a^6*b^13*c^13*d^6*e^7*f^12 - 17472*a^6*b^13*c^14*d^5*e^6*f^13 + 3696*a^6*b^13*c^15*d^4*e^5*f^14 + 15
96*a^6*b^13*c^16*d^3*e^4*f^15 - 504*a^6*b^13*c^17*d^2*e^3*f^16 + 360*a^7*b^12*c^2*d^17*e^17*f^2 + 312*a^7*b^12
*c^3*d^16*e^16*f^3 - 6288*a^7*b^12*c^4*d^15*e^15*f^4 + 7056*a^7*b^12*c^5*d^14*e^14*f^5 + 17472*a^7*b^12*c^6*d^
13*e^13*f^6 - 43680*a^7*b^12*c^7*d^12*e^12*f^7 + 32760*a^7*b^12*c^8*d^11*e^11*f^8 - 8008*a^7*b^12*c^9*d^10*e^1
0*f^9 - 8008*a^7*b^12*c^10*d^9*e^9*f^10 + 32760*a^7*b^12*c^11*d^8*e^8*f^11 - 43680*a^7*b^12*c^12*d^7*e^7*f^12
+ 17472*a^7*b^12*c^13*d^6*e^6*f^13 + 7056*a^7*b^12*c^14*d^5*e^5*f^14 - 6288*a^7*b^12*c^15*d^4*e^4*f^15 + 312*a
^7*b^12*c^16*d^3*e^3*f^16 + 360*a^7*b^12*c^17*d^2*e^2*f^17 - 882*a^8*b^11*c^2*d^17*e^16*f^3 + 2520*a^8*b^11*c^
3*d^16*e^15*f^4 + 7380*a^8*b^11*c^4*d^15*e^14*f^5 - 25452*a^8*b^11*c^5*d^14*e^13*f^6 + 9828*a^8*b^11*c^6*d^13*
e^12*f^7 + 32760*a^8*b^11*c^7*d^12*e^11*f^8 - 36036*a^8*b^11*c^8*d^11*e^10*f^9 + 20020*a^8*b^11*c^9*d^10*e^9*f
^10 - 36036*a^8*b^11*c^10*d^9*e^8*f^11 + 32760*a^8*b^11*c^11*d^8*e^7*f^12 + 9828*a^8*b^11*c^12*d^7*e^6*f^13 -
25452*a^8*b^11*c^13*d^6*e^5*f^14 + 7380*a^8*b^11*c^14*d^5*e^4*f^15 + 2520*a^8*b^11*c^15*d^4*e^3*f^16 - 882*a^8
*b^11*c^16*d^3*e^2*f^17 + 728*a^9*b^10*c^2*d^17*e^15*f^4 - 7480*a^9*b^10*c^3*d^16*e^14*f^5 + 2660*a^9*b^10*c^4
*d^15*e^13*f^6 + 30212*a^9*b^10*c^5*d^14*e^12*f^7 - 38584*a^9*b^10*c^6*d^13*e^11*f^8 - 8008*a^9*b^10*c^7*d^12*
e^10*f^9 + 20020*a^9*b^10*c^8*d^11*e^9*f^10 + 20020*a^9*b^10*c^9*d^10*e^8*f^11 - 8008*a^9*b^10*c^10*d^9*e^7*f^
12 - 38584*a^9*b^10*c^11*d^8*e^6*f^13 + 30212*a^9*b^10*c^12*d^7*e^5*f^14 + 2660*a^9*b^10*c^13*d^6*e^4*f^15 - 7
480*a^9*b^10*c^14*d^5*e^3*f^16 + 728*a^9*b^10*c^15*d^4*e^2*f^17 + 1152*a^10*b^9*c^2*d^17*e^14*f^5 + 9408*a^10*
b^9*c^3*d^16*e^13*f^6 - 18564*a^10*b^9*c^4*d^15*e^12*f^7 - 13104*a^10*b^9*c^5*d^14*e^11*f^8 + 48048*a^10*b^9*c
^6*d^13*e^10*f^9 - 8008*a^10*b^9*c^7*d^12*e^9*f^10 - 36036*a^10*b^9*c^8*d^11*e^8*f^11 - 8008*a^10*b^9*c^9*d^10
*e^7*f^12 + 48048*a^10*b^9*c^10*d^9*e^6*f^13 - 13104*a^10*b^9*c^11*d^8*e^5*f^14 - 18564*a^10*b^9*c^12*d^7*e^4*
f^15 + 9408*a^10*b^9*c^13*d^6*e^3*f^16 + 1152*a^10*b^9*c^14*d^5*e^2*f^17 - 4032*a^11*b^8*c^2*d^17*e^13*f^6 - 4
368*a^11*b^8*c^3*d^16*e^12*f^7 + 26208*a^11*b^8*c^4*d^15*e^11*f^8 - 13104*a^11*b^8*c^5*d^14*e^10*f^9 - 38584*a
^11*b^8*c^6*d^13*e^9*f^10 + 32760*a^11*b^8*c^7*d^12*e^8*f^11 + 32760*a^11*b^8*c^8*d^11*e^7*f^12 - 38584*a^11*b
^8*c^9*d^10*e^6*f^13 - 13104*a^11*b^8*c^10*d^9*e^5*f^14 + 26208*a^11*b^8*c^11*d^8*e^4*f^15 - 4368*a^11*b^8*c^1
2*d^7*e^3*f^16 - 4032*a^11*b^8*c^13*d^6*e^2*f^17 + 5460*a^12*b^7*c^2*d^17*e^12*f^7 - 4368*a^12*b^7*c^3*d^16*e^
11*f^8 - 18564*a^12*b^7*c^4*d^15*e^10*f^9 + 30212*a^12*b^7*c^5*d^14*e^9*f^10 + 9828*a^12*b^7*c^6*d^13*e^8*f^11
- 43680*a^12*b^7*c^7*d^12*e^7*f^12 + 9828*a^12*b^7*c^8*d^11*e^6*f^13 + 30212*a^12*b^7*c^9*d^10*e^5*f^14 - 185
64*a^12*b^7*c^10*d^9*e^4*f^15 - 4368*a^12*b^7*c^11*d^8*e^3*f^16 + 5460*a^12*b^7*c^12*d^7*e^2*f^17 - 4032*a^13*
b^6*c^2*d^17*e^11*f^8 + 9408*a^13*b^6*c^3*d^16*e^10*f^9 + 2660*a^13*b^6*c^4*d^15*e^9*f^10 - 25452*a^13*b^6*c^5
*d^14*e^8*f^11 + 17472*a^13*b^6*c^6*d^13*e^7*f^12 + 17472*a^13*b^6*c^7*d^12*e^6*f^13 - 25452*a^13*b^6*c^8*d^11
*e^5*f^14 + 2660*a^13*b^6*c^9*d^10*e^4*f^15 + 9408*a^13*b^6*c^10*d^9*e^3*f^16 - 4032*a^13*b^6*c^11*d^8*e^2*f^1
7 + 1152*a^14*b^5*c^2*d^17*e^10*f^9 - 7480*a^14*b^5*c^3*d^16*e^9*f^10 + 7380*a^14*b^5*c^4*d^15*e^8*f^11 + 7056
*a^14*b^5*c^5*d^14*e^7*f^12 - 17472*a^14*b^5*c^6*d^13*e^6*f^13 + 7056*a^14*b^5*c^7*d^12*e^5*f^14 + 7380*a^14*b
^5*c^8*d^11*e^4*f^15 - 7480*a^14*b^5*c^9*d^10*e^3*f^16 + 1152*a^14*b^5*c^10*d^9*e^2*f^17 + 728*a^15*b^4*c^2*d^
17*e^9*f^10 + 2520*a^15*b^4*c^3*d^16*e^8*f^11 - 6288*a^15*b^4*c^4*d^15*e^7*f^12 + 3696*a^15*b^4*c^5*d^14*e^6*f
^13 + 3696*a^15*b^4*c^6*d^13*e^5*f^14 - 6288*a^15*b^4*c^7*d^12*e^4*f^15 + 2520*a^15*b^4*c^8*d^11*e^3*f^16 + 72
8*a^15*b^4*c^9*d^10*e^2*f^17 - 882*a^16*b^3*c^2*d^17*e^8*f^11 + 312*a^16*b^3*c^3*d^16*e^7*f^12 + 1596*a^16*b^3
*c^4*d^15*e^6*f^13 - 2772*a^16*b^3*c^5*d^14*e^5*f^14 + 1596*a^16*b^3*c^6*d^13*e^4*f^15 + 312*a^16*b^3*c^7*d^12
*e^3*f^16 - 882*a^16*b^3*c^8*d^11*e^2*f^17 + 360*a^17*b^2*c^2*d^17*e^7*f^12 - 504*a^17*b^2*c^3*d^16*e^6*f^13 +
252*a^17*b^2*c^4*d^15*e^5*f^14 + 252*a^17*b^2*c^5*d^14*e^4*f^15 - 504*a^17*b^2*c^6*d^13*e^3*f^16 + 360*a^17*b
^2*c^7*d^12*e^2*f^17))/(56*a^3*b^13*c^5*d^11*e^16 - a^8*b^8*d^16*e^16 - a^16*c^8*d^8*f^16 - b^16*c^8*d^8*e^16
- a^16*d^16*e^8*f^8 - b^16*c^16*e^8*f^8 - 28*a^2*b^14*c^6*d^10*e^16 - a^8*b^8*c^16*f^16 - 70*a^4*b^12*c^4*d^12
*e^16 + 56*a^5*b^11*c^3*d^13*e^16 - 28*a^6*b^10*c^2*d^14*e^16 - 28*a^10*b^6*c^14*d^2*f^16 + 56*a^11*b^5*c^13*d
^3*f^16 - 70*a^12*b^4*c^12*d^4*f^16 + 56*a^13*b^3*c^11*d^5*f^16 - 28*a^14*b^2*c^10*d^6*f^16 - 28*a^2*b^14*c^16
*e^6*f^10 + 56*a^3*b^13*c^16*e^5*f^11 - 70*a^4*b^12*c^16*e^4*f^12 + 56*a^5*b^11*c^16*e^3*f^13 - 28*a^6*b^10*c^
16*e^2*f^14 - 28*a^10*b^6*d^16*e^14*f^2 + 56*a^11*b^5*d^16*e^13*f^3 - 70*a^12*b^4*d^16*e^12*f^4 + 56*a^13*b^3*
d^16*e^11*f^5 - 28*a^14*b^2*d^16*e^10*f^6 - 28*a^16*c^2*d^14*e^6*f^10 + 56*a^16*c^3*d^13*e^5*f^11 - 70*a^16*c^
4*d^12*e^4*f^12 + 56*a^16*c^5*d^11*e^3*f^13 - 28*a^16*c^6*d^10*e^2*f^14 - 28*b^16*c^10*d^6*e^14*f^2 + 56*b^16*
c^11*d^5*e^13*f^3 - 70*b^16*c^12*d^4*e^12*f^4 + 56*b^16*c^13*d^3*e^11*f^5 - 28*b^16*c^14*d^2*e^10*f^6 + 8*a*b^
15*c^7*d^9*e^16 + 8*a^7*b^9*c*d^15*e^16 + 8*a^9*b^7*c^15*d*f^16 + 8*a^15*b*c^9*d^7*f^16 + 8*a*b^15*c^16*e^7*f^
9 + 8*a^7*b^9*c^16*e*f^15 + 8*a^9*b^7*d^16*e^15*f + 8*a^15*b*d^16*e^9*f^7 + 8*a^16*c*d^15*e^7*f^9 + 8*a^16*c^7
*d^9*e*f^15 + 8*b^16*c^9*d^7*e^15*f + 8*b^16*c^15*d*e^9*f^7 - 56*a*b^15*c^8*d^8*e^15*f - 56*a*b^15*c^15*d*e^8*
f^8 - 56*a^8*b^8*c*d^15*e^15*f - 56*a^8*b^8*c^15*d*e*f^15 - 56*a^15*b*c*d^15*e^8*f^8 - 56*a^15*b*c^8*d^8*e*f^1
5 + 160*a*b^15*c^9*d^7*e^14*f^2 - 224*a*b^15*c^10*d^6*e^13*f^3 + 112*a*b^15*c^11*d^5*e^12*f^4 + 112*a*b^15*c^1
2*d^4*e^11*f^5 - 224*a*b^15*c^13*d^3*e^10*f^6 + 160*a*b^15*c^14*d^2*e^9*f^7 + 160*a^2*b^14*c^7*d^9*e^15*f + 16
0*a^2*b^14*c^15*d*e^7*f^9 - 224*a^3*b^13*c^6*d^10*e^15*f - 224*a^3*b^13*c^15*d*e^6*f^10 + 112*a^4*b^12*c^5*d^1
1*e^15*f + 112*a^4*b^12*c^15*d*e^5*f^11 + 112*a^5*b^11*c^4*d^12*e^15*f + 112*a^5*b^11*c^15*d*e^4*f^12 - 224*a^
6*b^10*c^3*d^13*e^15*f - 224*a^6*b^10*c^15*d*e^3*f^13 + 160*a^7*b^9*c^2*d^14*e^15*f + 160*a^7*b^9*c^15*d*e^2*f
^14 + 160*a^9*b^7*c*d^15*e^14*f^2 + 160*a^9*b^7*c^14*d^2*e*f^15 - 224*a^10*b^6*c*d^15*e^13*f^3 - 224*a^10*b^6*
c^13*d^3*e*f^15 + 112*a^11*b^5*c*d^15*e^12*f^4 + 112*a^11*b^5*c^12*d^4*e*f^15 + 112*a^12*b^4*c*d^15*e^11*f^5 +
112*a^12*b^4*c^11*d^5*e*f^15 - 224*a^13*b^3*c*d^15*e^10*f^6 - 224*a^13*b^3*c^10*d^6*e*f^15 + 160*a^14*b^2*c*d
^15*e^9*f^7 + 160*a^14*b^2*c^9*d^7*e*f^15 + 160*a^15*b*c^2*d^14*e^7*f^9 - 224*a^15*b*c^3*d^13*e^6*f^10 + 112*a
^15*b*c^4*d^12*e^5*f^11 + 112*a^15*b*c^5*d^11*e^4*f^12 - 224*a^15*b*c^6*d^10*e^3*f^13 + 160*a^15*b*c^7*d^9*e^2
*f^14 - 300*a^2*b^14*c^8*d^8*e^14*f^2 + 840*a^2*b^14*c^10*d^6*e^12*f^4 - 1344*a^2*b^14*c^11*d^5*e^11*f^5 + 840
*a^2*b^14*c^12*d^4*e^10*f^6 - 300*a^2*b^14*c^14*d^2*e^8*f^8 + 1400*a^3*b^13*c^8*d^8*e^13*f^3 - 2800*a^3*b^13*c
^9*d^7*e^12*f^4 + 1568*a^3*b^13*c^10*d^6*e^11*f^5 + 1568*a^3*b^13*c^11*d^5*e^10*f^6 - 2800*a^3*b^13*c^12*d^4*e
^9*f^7 + 1400*a^3*b^13*c^13*d^3*e^8*f^8 + 840*a^4*b^12*c^6*d^10*e^14*f^2 - 2800*a^4*b^12*c^7*d^9*e^13*f^3 + 17
50*a^4*b^12*c^8*d^8*e^12*f^4 + 4480*a^4*b^12*c^9*d^7*e^11*f^5 - 8624*a^4*b^12*c^10*d^6*e^10*f^6 + 4480*a^4*b^1
2*c^11*d^5*e^9*f^7 + 1750*a^4*b^12*c^12*d^4*e^8*f^8 - 2800*a^4*b^12*c^13*d^3*e^7*f^9 + 840*a^4*b^12*c^14*d^2*e
^6*f^10 - 1344*a^5*b^11*c^5*d^11*e^14*f^2 + 1568*a^5*b^11*c^6*d^10*e^13*f^3 + 4480*a^5*b^11*c^7*d^9*e^12*f^4 -
12264*a^5*b^11*c^8*d^8*e^11*f^5 + 7392*a^5*b^11*c^9*d^7*e^10*f^6 + 7392*a^5*b^11*c^10*d^6*e^9*f^7 - 12264*a^5
*b^11*c^11*d^5*e^8*f^8 + 4480*a^5*b^11*c^12*d^4*e^7*f^9 + 1568*a^5*b^11*c^13*d^3*e^6*f^10 - 1344*a^5*b^11*c^14
*d^2*e^5*f^11 + 840*a^6*b^10*c^4*d^12*e^14*f^2 + 1568*a^6*b^10*c^5*d^11*e^13*f^3 - 8624*a^6*b^10*c^6*d^10*e^12
*f^4 + 7392*a^6*b^10*c^7*d^9*e^11*f^5 + 11396*a^6*b^10*c^8*d^8*e^10*f^6 - 24640*a^6*b^10*c^9*d^7*e^9*f^7 + 113
96*a^6*b^10*c^10*d^6*e^8*f^8 + 7392*a^6*b^10*c^11*d^5*e^7*f^9 - 8624*a^6*b^10*c^12*d^4*e^6*f^10 + 1568*a^6*b^1
0*c^13*d^3*e^5*f^11 + 840*a^6*b^10*c^14*d^2*e^4*f^12 - 2800*a^7*b^9*c^4*d^12*e^13*f^3 + 4480*a^7*b^9*c^5*d^11*
e^12*f^4 + 7392*a^7*b^9*c^6*d^10*e^11*f^5 - 24640*a^7*b^9*c^7*d^9*e^10*f^6 + 15400*a^7*b^9*c^8*d^8*e^9*f^7 + 1
5400*a^7*b^9*c^9*d^7*e^8*f^8 - 24640*a^7*b^9*c^10*d^6*e^7*f^9 + 7392*a^7*b^9*c^11*d^5*e^6*f^10 + 4480*a^7*b^9*
c^12*d^4*e^5*f^11 - 2800*a^7*b^9*c^13*d^3*e^4*f^12 - 300*a^8*b^8*c^2*d^14*e^14*f^2 + 1400*a^8*b^8*c^3*d^13*e^1
3*f^3 + 1750*a^8*b^8*c^4*d^12*e^12*f^4 - 12264*a^8*b^8*c^5*d^11*e^11*f^5 + 11396*a^8*b^8*c^6*d^10*e^10*f^6 + 1
5400*a^8*b^8*c^7*d^9*e^9*f^7 - 34650*a^8*b^8*c^8*d^8*e^8*f^8 + 15400*a^8*b^8*c^9*d^7*e^7*f^9 + 11396*a^8*b^8*c
^10*d^6*e^6*f^10 - 12264*a^8*b^8*c^11*d^5*e^5*f^11 + 1750*a^8*b^8*c^12*d^4*e^4*f^12 + 1400*a^8*b^8*c^13*d^3*e^
3*f^13 - 300*a^8*b^8*c^14*d^2*e^2*f^14 - 2800*a^9*b^7*c^3*d^13*e^12*f^4 + 4480*a^9*b^7*c^4*d^12*e^11*f^5 + 739
2*a^9*b^7*c^5*d^11*e^10*f^6 - 24640*a^9*b^7*c^6*d^10*e^9*f^7 + 15400*a^9*b^7*c^7*d^9*e^8*f^8 + 15400*a^9*b^7*c
^8*d^8*e^7*f^9 - 24640*a^9*b^7*c^9*d^7*e^6*f^10 + 7392*a^9*b^7*c^10*d^6*e^5*f^11 + 4480*a^9*b^7*c^11*d^5*e^4*f
^12 - 2800*a^9*b^7*c^12*d^4*e^3*f^13 + 840*a^10*b^6*c^2*d^14*e^12*f^4 + 1568*a^10*b^6*c^3*d^13*e^11*f^5 - 8624
*a^10*b^6*c^4*d^12*e^10*f^6 + 7392*a^10*b^6*c^5*d^11*e^9*f^7 + 11396*a^10*b^6*c^6*d^10*e^8*f^8 - 24640*a^10*b^
6*c^7*d^9*e^7*f^9 + 11396*a^10*b^6*c^8*d^8*e^6*f^10 + 7392*a^10*b^6*c^9*d^7*e^5*f^11 - 8624*a^10*b^6*c^10*d^6*
e^4*f^12 + 1568*a^10*b^6*c^11*d^5*e^3*f^13 + 840*a^10*b^6*c^12*d^4*e^2*f^14 - 1344*a^11*b^5*c^2*d^14*e^11*f^5
+ 1568*a^11*b^5*c^3*d^13*e^10*f^6 + 4480*a^11*b^5*c^4*d^12*e^9*f^7 - 12264*a^11*b^5*c^5*d^11*e^8*f^8 + 7392*a^
11*b^5*c^6*d^10*e^7*f^9 + 7392*a^11*b^5*c^7*d^9*e^6*f^10 - 12264*a^11*b^5*c^8*d^8*e^5*f^11 + 4480*a^11*b^5*c^9
*d^7*e^4*f^12 + 1568*a^11*b^5*c^10*d^6*e^3*f^13 - 1344*a^11*b^5*c^11*d^5*e^2*f^14 + 840*a^12*b^4*c^2*d^14*e^10
*f^6 - 2800*a^12*b^4*c^3*d^13*e^9*f^7 + 1750*a^12*b^4*c^4*d^12*e^8*f^8 + 4480*a^12*b^4*c^5*d^11*e^7*f^9 - 8624
*a^12*b^4*c^6*d^10*e^6*f^10 + 4480*a^12*b^4*c^7*d^9*e^5*f^11 + 1750*a^12*b^4*c^8*d^8*e^4*f^12 - 2800*a^12*b^4*
c^9*d^7*e^3*f^13 + 840*a^12*b^4*c^10*d^6*e^2*f^14 + 1400*a^13*b^3*c^3*d^13*e^8*f^8 - 2800*a^13*b^3*c^4*d^12*e^
7*f^9 + 1568*a^13*b^3*c^5*d^11*e^6*f^10 + 1568*a^13*b^3*c^6*d^10*e^5*f^11 - 2800*a^13*b^3*c^7*d^9*e^4*f^12 + 1
400*a^13*b^3*c^8*d^8*e^3*f^13 - 300*a^14*b^2*c^2*d^14*e^8*f^8 + 840*a^14*b^2*c^4*d^12*e^6*f^10 - 1344*a^14*b^2
*c^5*d^11*e^5*f^11 + 840*a^14*b^2*c^6*d^10*e^4*f^12 - 300*a^14*b^2*c^8*d^8*e^2*f^14)) + (x*(84*a^5*b^11*c^13*d
^3*f^16 - 12*a^4*b^12*c^14*d^2*f^16 - 243*a^6*b^10*c^12*d^4*f^16 + 366*a^7*b^9*c^11*d^5*f^16 - 321*a^8*b^8*c^1
0*d^6*f^16 + 252*a^9*b^7*c^9*d^7*f^16 - 321*a^10*b^6*c^8*d^8*f^16 + 366*a^11*b^5*c^7*d^9*f^16 - 243*a^12*b^4*c
^6*d^10*f^16 + 84*a^13*b^3*c^5*d^11*f^16 - 12*a^14*b^2*c^4*d^12*f^16 - 12*a^4*b^12*d^16*e^14*f^2 + 84*a^5*b^11
*d^16*e^13*f^3 - 243*a^6*b^10*d^16*e^12*f^4 + 366*a^7*b^9*d^16*e^11*f^5 - 321*a^8*b^8*d^16*e^10*f^6 + 252*a^9*
b^7*d^16*e^9*f^7 - 321*a^10*b^6*d^16*e^8*f^8 + 366*a^11*b^5*d^16*e^7*f^9 - 243*a^12*b^4*d^16*e^6*f^10 + 84*a^1
3*b^3*d^16*e^5*f^11 - 12*a^14*b^2*d^16*e^4*f^12 - 12*b^16*c^4*d^12*e^14*f^2 + 84*b^16*c^5*d^11*e^13*f^3 - 243*
b^16*c^6*d^10*e^12*f^4 + 366*b^16*c^7*d^9*e^11*f^5 - 321*b^16*c^8*d^8*e^10*f^6 + 252*b^16*c^9*d^7*e^9*f^7 - 32
1*b^16*c^10*d^6*e^8*f^8 + 366*b^16*c^11*d^5*e^7*f^9 - 243*b^16*c^12*d^4*e^6*f^10 + 84*b^16*c^13*d^3*e^5*f^11 -
12*b^16*c^14*d^2*e^4*f^12 + 48*a*b^15*c^3*d^13*e^14*f^2 - 252*a*b^15*c^4*d^12*e^13*f^3 + 366*a*b^15*c^5*d^11*
e^12*f^4 + 354*a*b^15*c^6*d^10*e^11*f^5 - 1458*a*b^15*c^7*d^9*e^10*f^6 + 942*a*b^15*c^8*d^8*e^9*f^7 + 942*a*b^
15*c^9*d^7*e^8*f^8 - 1458*a*b^15*c^10*d^6*e^7*f^9 + 354*a*b^15*c^11*d^5*e^6*f^10 + 366*a*b^15*c^12*d^4*e^5*f^1
1 - 252*a*b^15*c^13*d^3*e^4*f^12 + 48*a*b^15*c^14*d^2*e^3*f^13 + 48*a^3*b^13*c*d^15*e^14*f^2 + 48*a^3*b^13*c^1
4*d^2*e*f^15 - 252*a^4*b^12*c*d^15*e^13*f^3 - 252*a^4*b^12*c^13*d^3*e*f^15 + 366*a^5*b^11*c*d^15*e^12*f^4 + 36
6*a^5*b^11*c^12*d^4*e*f^15 + 354*a^6*b^10*c*d^15*e^11*f^5 + 354*a^6*b^10*c^11*d^5*e*f^15 - 1458*a^7*b^9*c*d^15
*e^10*f^6 - 1458*a^7*b^9*c^10*d^6*e*f^15 + 942*a^8*b^8*c*d^15*e^9*f^7 + 942*a^8*b^8*c^9*d^7*e*f^15 + 942*a^9*b
^7*c*d^15*e^8*f^8 + 942*a^9*b^7*c^8*d^8*e*f^15 - 1458*a^10*b^6*c*d^15*e^7*f^9 - 1458*a^10*b^6*c^7*d^9*e*f^15 +
354*a^11*b^5*c*d^15*e^6*f^10 + 354*a^11*b^5*c^6*d^10*e*f^15 + 366*a^12*b^4*c*d^15*e^5*f^11 + 366*a^12*b^4*c^5
*d^11*e*f^15 - 252*a^13*b^3*c*d^15*e^4*f^12 - 252*a^13*b^3*c^4*d^12*e*f^15 + 48*a^14*b^2*c*d^15*e^3*f^13 + 48*
a^14*b^2*c^3*d^13*e*f^15 - 72*a^2*b^14*c^2*d^14*e^14*f^2 + 168*a^2*b^14*c^3*d^13*e^13*f^3 + 723*a^2*b^14*c^4*d
^12*e^12*f^4 - 3258*a^2*b^14*c^5*d^11*e^11*f^5 + 3156*a^2*b^14*c^6*d^10*e^10*f^6 + 3522*a^2*b^14*c^7*d^9*e^9*f
^7 - 8478*a^2*b^14*c^8*d^8*e^8*f^8 + 3522*a^2*b^14*c^9*d^7*e^7*f^9 + 3156*a^2*b^14*c^10*d^6*e^6*f^10 - 3258*a^
2*b^14*c^11*d^5*e^5*f^11 + 723*a^2*b^14*c^12*d^4*e^4*f^12 + 168*a^2*b^14*c^13*d^3*e^3*f^13 - 72*a^2*b^14*c^14*
d^2*e^2*f^14 + 168*a^3*b^13*c^2*d^14*e^13*f^3 - 1692*a^3*b^13*c^3*d^13*e^12*f^4 + 2538*a^3*b^13*c^4*d^12*e^11*
f^5 + 5634*a^3*b^13*c^5*d^11*e^10*f^6 - 18738*a^3*b^13*c^6*d^10*e^9*f^7 + 12042*a^3*b^13*c^7*d^9*e^8*f^8 + 120
42*a^3*b^13*c^8*d^8*e^7*f^9 - 18738*a^3*b^13*c^9*d^7*e^6*f^10 + 5634*a^3*b^13*c^10*d^6*e^5*f^11 + 2538*a^3*b^1
3*c^11*d^5*e^4*f^12 - 1692*a^3*b^13*c^12*d^4*e^3*f^13 + 168*a^3*b^13*c^13*d^3*e^2*f^14 + 723*a^4*b^12*c^2*d^14
*e^12*f^4 + 2538*a^4*b^12*c^3*d^13*e^11*f^5 - 14022*a^4*b^12*c^4*d^12*e^10*f^6 + 14022*a^4*b^12*c^5*d^11*e^9*f
^7 + 21087*a^4*b^12*c^6*d^10*e^8*f^8 - 48168*a^4*b^12*c^7*d^9*e^7*f^9 + 21087*a^4*b^12*c^8*d^8*e^6*f^10 + 1402
2*a^4*b^12*c^9*d^7*e^5*f^11 - 14022*a^4*b^12*c^10*d^6*e^4*f^12 + 2538*a^4*b^12*c^11*d^5*e^3*f^13 + 723*a^4*b^1
2*c^12*d^4*e^2*f^14 - 3258*a^5*b^11*c^2*d^14*e^11*f^5 + 5634*a^5*b^11*c^3*d^13*e^10*f^6 + 14022*a^5*b^11*c^4*d
^12*e^9*f^7 - 50544*a^5*b^11*c^5*d^11*e^8*f^8 + 33696*a^5*b^11*c^6*d^10*e^7*f^9 + 33696*a^5*b^11*c^7*d^9*e^6*f
^10 - 50544*a^5*b^11*c^8*d^8*e^5*f^11 + 14022*a^5*b^11*c^9*d^7*e^4*f^12 + 5634*a^5*b^11*c^10*d^6*e^3*f^13 - 32
58*a^5*b^11*c^11*d^5*e^2*f^14 + 3156*a^6*b^10*c^2*d^14*e^10*f^6 - 18738*a^6*b^10*c^3*d^13*e^9*f^7 + 21087*a^6*
b^10*c^4*d^12*e^8*f^8 + 33696*a^6*b^10*c^5*d^11*e^7*f^9 - 78624*a^6*b^10*c^6*d^10*e^6*f^10 + 33696*a^6*b^10*c^
7*d^9*e^5*f^11 + 21087*a^6*b^10*c^8*d^8*e^4*f^12 - 18738*a^6*b^10*c^9*d^7*e^3*f^13 + 3156*a^6*b^10*c^10*d^6*e^
2*f^14 + 3522*a^7*b^9*c^2*d^14*e^9*f^7 + 12042*a^7*b^9*c^3*d^13*e^8*f^8 - 48168*a^7*b^9*c^4*d^12*e^7*f^9 + 336
96*a^7*b^9*c^5*d^11*e^6*f^10 + 33696*a^7*b^9*c^6*d^10*e^5*f^11 - 48168*a^7*b^9*c^7*d^9*e^4*f^12 + 12042*a^7*b^
9*c^8*d^8*e^3*f^13 + 3522*a^7*b^9*c^9*d^7*e^2*f^14 - 8478*a^8*b^8*c^2*d^14*e^8*f^8 + 12042*a^8*b^8*c^3*d^13*e^
7*f^9 + 21087*a^8*b^8*c^4*d^12*e^6*f^10 - 50544*a^8*b^8*c^5*d^11*e^5*f^11 + 21087*a^8*b^8*c^6*d^10*e^4*f^12 +
12042*a^8*b^8*c^7*d^9*e^3*f^13 - 8478*a^8*b^8*c^8*d^8*e^2*f^14 + 3522*a^9*b^7*c^2*d^14*e^7*f^9 - 18738*a^9*b^7
*c^3*d^13*e^6*f^10 + 14022*a^9*b^7*c^4*d^12*e^5*f^11 + 14022*a^9*b^7*c^5*d^11*e^4*f^12 - 18738*a^9*b^7*c^6*d^1
0*e^3*f^13 + 3522*a^9*b^7*c^7*d^9*e^2*f^14 + 3156*a^10*b^6*c^2*d^14*e^6*f^10 + 5634*a^10*b^6*c^3*d^13*e^5*f^11
- 14022*a^10*b^6*c^4*d^12*e^4*f^12 + 5634*a^10*b^6*c^5*d^11*e^3*f^13 + 3156*a^10*b^6*c^6*d^10*e^2*f^14 - 3258
*a^11*b^5*c^2*d^14*e^5*f^11 + 2538*a^11*b^5*c^3*d^13*e^4*f^12 + 2538*a^11*b^5*c^4*d^12*e^3*f^13 - 3258*a^11*b^
5*c^5*d^11*e^2*f^14 + 723*a^12*b^4*c^2*d^14*e^4*f^12 - 1692*a^12*b^4*c^3*d^13*e^3*f^13 + 723*a^12*b^4*c^4*d^12
*e^2*f^14 + 168*a^13*b^3*c^2*d^14*e^3*f^13 + 168*a^13*b^3*c^3*d^13*e^2*f^14 - 72*a^14*b^2*c^2*d^14*e^2*f^14))/
(56*a^3*b^13*c^5*d^11*e^16 - a^8*b^8*d^16*e^16 - a^16*c^8*d^8*f^16 - b^16*c^8*d^8*e^16 - a^16*d^16*e^8*f^8 - b
^16*c^16*e^8*f^8 - 28*a^2*b^14*c^6*d^10*e^16 - a^8*b^8*c^16*f^16 - 70*a^4*b^12*c^4*d^12*e^16 + 56*a^5*b^11*c^3
*d^13*e^16 - 28*a^6*b^10*c^2*d^14*e^16 - 28*a^10*b^6*c^14*d^2*f^16 + 56*a^11*b^5*c^13*d^3*f^16 - 70*a^12*b^4*c
^12*d^4*f^16 + 56*a^13*b^3*c^11*d^5*f^16 - 28*a^14*b^2*c^10*d^6*f^16 - 28*a^2*b^14*c^16*e^6*f^10 + 56*a^3*b^13
*c^16*e^5*f^11 - 70*a^4*b^12*c^16*e^4*f^12 + 56*a^5*b^11*c^16*e^3*f^13 - 28*a^6*b^10*c^16*e^2*f^14 - 28*a^10*b
^6*d^16*e^14*f^2 + 56*a^11*b^5*d^16*e^13*f^3 - 70*a^12*b^4*d^16*e^12*f^4 + 56*a^13*b^3*d^16*e^11*f^5 - 28*a^14
*b^2*d^16*e^10*f^6 - 28*a^16*c^2*d^14*e^6*f^10 + 56*a^16*c^3*d^13*e^5*f^11 - 70*a^16*c^4*d^12*e^4*f^12 + 56*a^
16*c^5*d^11*e^3*f^13 - 28*a^16*c^6*d^10*e^2*f^14 - 28*b^16*c^10*d^6*e^14*f^2 + 56*b^16*c^11*d^5*e^13*f^3 - 70*
b^16*c^12*d^4*e^12*f^4 + 56*b^16*c^13*d^3*e^11*f^5 - 28*b^16*c^14*d^2*e^10*f^6 + 8*a*b^15*c^7*d^9*e^16 + 8*a^7
*b^9*c*d^15*e^16 + 8*a^9*b^7*c^15*d*f^16 + 8*a^15*b*c^9*d^7*f^16 + 8*a*b^15*c^16*e^7*f^9 + 8*a^7*b^9*c^16*e*f^
15 + 8*a^9*b^7*d^16*e^15*f + 8*a^15*b*d^16*e^9*f^7 + 8*a^16*c*d^15*e^7*f^9 + 8*a^16*c^7*d^9*e*f^15 + 8*b^16*c^
9*d^7*e^15*f + 8*b^16*c^15*d*e^9*f^7 - 56*a*b^15*c^8*d^8*e^15*f - 56*a*b^15*c^15*d*e^8*f^8 - 56*a^8*b^8*c*d^15
*e^15*f - 56*a^8*b^8*c^15*d*e*f^15 - 56*a^15*b*c*d^15*e^8*f^8 - 56*a^15*b*c^8*d^8*e*f^15 + 160*a*b^15*c^9*d^7*
e^14*f^2 - 224*a*b^15*c^10*d^6*e^13*f^3 + 112*a*b^15*c^11*d^5*e^12*f^4 + 112*a*b^15*c^12*d^4*e^11*f^5 - 224*a*
b^15*c^13*d^3*e^10*f^6 + 160*a*b^15*c^14*d^2*e^9*f^7 + 160*a^2*b^14*c^7*d^9*e^15*f + 160*a^2*b^14*c^15*d*e^7*f
^9 - 224*a^3*b^13*c^6*d^10*e^15*f - 224*a^3*b^13*c^15*d*e^6*f^10 + 112*a^4*b^12*c^5*d^11*e^15*f + 112*a^4*b^12
*c^15*d*e^5*f^11 + 112*a^5*b^11*c^4*d^12*e^15*f + 112*a^5*b^11*c^15*d*e^4*f^12 - 224*a^6*b^10*c^3*d^13*e^15*f
- 224*a^6*b^10*c^15*d*e^3*f^13 + 160*a^7*b^9*c^2*d^14*e^15*f + 160*a^7*b^9*c^15*d*e^2*f^14 + 160*a^9*b^7*c*d^1
5*e^14*f^2 + 160*a^9*b^7*c^14*d^2*e*f^15 - 224*a^10*b^6*c*d^15*e^13*f^3 - 224*a^10*b^6*c^13*d^3*e*f^15 + 112*a
^11*b^5*c*d^15*e^12*f^4 + 112*a^11*b^5*c^12*d^4*e*f^15 + 112*a^12*b^4*c*d^15*e^11*f^5 + 112*a^12*b^4*c^11*d^5*
e*f^15 - 224*a^13*b^3*c*d^15*e^10*f^6 - 224*a^13*b^3*c^10*d^6*e*f^15 + 160*a^14*b^2*c*d^15*e^9*f^7 + 160*a^14*
b^2*c^9*d^7*e*f^15 + 160*a^15*b*c^2*d^14*e^7*f^9 - 224*a^15*b*c^3*d^13*e^6*f^10 + 112*a^15*b*c^4*d^12*e^5*f^11
+ 112*a^15*b*c^5*d^11*e^4*f^12 - 224*a^15*b*c^6*d^10*e^3*f^13 + 160*a^15*b*c^7*d^9*e^2*f^14 - 300*a^2*b^14*c^
8*d^8*e^14*f^2 + 840*a^2*b^14*c^10*d^6*e^12*f^4 - 1344*a^2*b^14*c^11*d^5*e^11*f^5 + 840*a^2*b^14*c^12*d^4*e^10
*f^6 - 300*a^2*b^14*c^14*d^2*e^8*f^8 + 1400*a^3*b^13*c^8*d^8*e^13*f^3 - 2800*a^3*b^13*c^9*d^7*e^12*f^4 + 1568*
a^3*b^13*c^10*d^6*e^11*f^5 + 1568*a^3*b^13*c^11*d^5*e^10*f^6 - 2800*a^3*b^13*c^12*d^4*e^9*f^7 + 1400*a^3*b^13*
c^13*d^3*e^8*f^8 + 840*a^4*b^12*c^6*d^10*e^14*f^2 - 2800*a^4*b^12*c^7*d^9*e^13*f^3 + 1750*a^4*b^12*c^8*d^8*e^1
2*f^4 + 4480*a^4*b^12*c^9*d^7*e^11*f^5 - 8624*a^4*b^12*c^10*d^6*e^10*f^6 + 4480*a^4*b^12*c^11*d^5*e^9*f^7 + 17
50*a^4*b^12*c^12*d^4*e^8*f^8 - 2800*a^4*b^12*c^13*d^3*e^7*f^9 + 840*a^4*b^12*c^14*d^2*e^6*f^10 - 1344*a^5*b^11
*c^5*d^11*e^14*f^2 + 1568*a^5*b^11*c^6*d^10*e^13*f^3 + 4480*a^5*b^11*c^7*d^9*e^12*f^4 - 12264*a^5*b^11*c^8*d^8
*e^11*f^5 + 7392*a^5*b^11*c^9*d^7*e^10*f^6 + 7392*a^5*b^11*c^10*d^6*e^9*f^7 - 12264*a^5*b^11*c^11*d^5*e^8*f^8
+ 4480*a^5*b^11*c^12*d^4*e^7*f^9 + 1568*a^5*b^11*c^13*d^3*e^6*f^10 - 1344*a^5*b^11*c^14*d^2*e^5*f^11 + 840*a^6
*b^10*c^4*d^12*e^14*f^2 + 1568*a^6*b^10*c^5*d^11*e^13*f^3 - 8624*a^6*b^10*c^6*d^10*e^12*f^4 + 7392*a^6*b^10*c^
7*d^9*e^11*f^5 + 11396*a^6*b^10*c^8*d^8*e^10*f^6 - 24640*a^6*b^10*c^9*d^7*e^9*f^7 + 11396*a^6*b^10*c^10*d^6*e^
8*f^8 + 7392*a^6*b^10*c^11*d^5*e^7*f^9 - 8624*a^6*b^10*c^12*d^4*e^6*f^10 + 1568*a^6*b^10*c^13*d^3*e^5*f^11 + 8
40*a^6*b^10*c^14*d^2*e^4*f^12 - 2800*a^7*b^9*c^4*d^12*e^13*f^3 + 4480*a^7*b^9*c^5*d^11*e^12*f^4 + 7392*a^7*b^9
*c^6*d^10*e^11*f^5 - 24640*a^7*b^9*c^7*d^9*e^10*f^6 + 15400*a^7*b^9*c^8*d^8*e^9*f^7 + 15400*a^7*b^9*c^9*d^7*e^
8*f^8 - 24640*a^7*b^9*c^10*d^6*e^7*f^9 + 7392*a^7*b^9*c^11*d^5*e^6*f^10 + 4480*a^7*b^9*c^12*d^4*e^5*f^11 - 280
0*a^7*b^9*c^13*d^3*e^4*f^12 - 300*a^8*b^8*c^2*d^14*e^14*f^2 + 1400*a^8*b^8*c^3*d^13*e^13*f^3 + 1750*a^8*b^8*c^
4*d^12*e^12*f^4 - 12264*a^8*b^8*c^5*d^11*e^11*f^5 + 11396*a^8*b^8*c^6*d^10*e^10*f^6 + 15400*a^8*b^8*c^7*d^9*e^
9*f^7 - 34650*a^8*b^8*c^8*d^8*e^8*f^8 + 15400*a^8*b^8*c^9*d^7*e^7*f^9 + 11396*a^8*b^8*c^10*d^6*e^6*f^10 - 1226
4*a^8*b^8*c^11*d^5*e^5*f^11 + 1750*a^8*b^8*c^12*d^4*e^4*f^12 + 1400*a^8*b^8*c^13*d^3*e^3*f^13 - 300*a^8*b^8*c^
14*d^2*e^2*f^14 - 2800*a^9*b^7*c^3*d^13*e^12*f^4 + 4480*a^9*b^7*c^4*d^12*e^11*f^5 + 7392*a^9*b^7*c^5*d^11*e^10
*f^6 - 24640*a^9*b^7*c^6*d^10*e^9*f^7 + 15400*a^9*b^7*c^7*d^9*e^8*f^8 + 15400*a^9*b^7*c^8*d^8*e^7*f^9 - 24640*
a^9*b^7*c^9*d^7*e^6*f^10 + 7392*a^9*b^7*c^10*d^6*e^5*f^11 + 4480*a^9*b^7*c^11*d^5*e^4*f^12 - 2800*a^9*b^7*c^12
*d^4*e^3*f^13 + 840*a^10*b^6*c^2*d^14*e^12*f^4 + 1568*a^10*b^6*c^3*d^13*e^11*f^5 - 8624*a^10*b^6*c^4*d^12*e^10
*f^6 + 7392*a^10*b^6*c^5*d^11*e^9*f^7 + 11396*a^10*b^6*c^6*d^10*e^8*f^8 - 24640*a^10*b^6*c^7*d^9*e^7*f^9 + 113
96*a^10*b^6*c^8*d^8*e^6*f^10 + 7392*a^10*b^6*c^9*d^7*e^5*f^11 - 8624*a^10*b^6*c^10*d^6*e^4*f^12 + 1568*a^10*b^
6*c^11*d^5*e^3*f^13 + 840*a^10*b^6*c^12*d^4*e^2*f^14 - 1344*a^11*b^5*c^2*d^14*e^11*f^5 + 1568*a^11*b^5*c^3*d^1
3*e^10*f^6 + 4480*a^11*b^5*c^4*d^12*e^9*f^7 - 12264*a^11*b^5*c^5*d^11*e^8*f^8 + 7392*a^11*b^5*c^6*d^10*e^7*f^9
+ 7392*a^11*b^5*c^7*d^9*e^6*f^10 - 12264*a^11*b^5*c^8*d^8*e^5*f^11 + 4480*a^11*b^5*c^9*d^7*e^4*f^12 + 1568*a^
11*b^5*c^10*d^6*e^3*f^13 - 1344*a^11*b^5*c^11*d^5*e^2*f^14 + 840*a^12*b^4*c^2*d^14*e^10*f^6 - 2800*a^12*b^4*c^
3*d^13*e^9*f^7 + 1750*a^12*b^4*c^4*d^12*e^8*f^8 + 4480*a^12*b^4*c^5*d^11*e^7*f^9 - 8624*a^12*b^4*c^6*d^10*e^6*
f^10 + 4480*a^12*b^4*c^7*d^9*e^5*f^11 + 1750*a^12*b^4*c^8*d^8*e^4*f^12 - 2800*a^12*b^4*c^9*d^7*e^3*f^13 + 840*
a^12*b^4*c^10*d^6*e^2*f^14 + 1400*a^13*b^3*c^3*d^13*e^8*f^8 - 2800*a^13*b^3*c^4*d^12*e^7*f^9 + 1568*a^13*b^3*c
^5*d^11*e^6*f^10 + 1568*a^13*b^3*c^6*d^10*e^5*f^11 - 2800*a^13*b^3*c^7*d^9*e^4*f^12 + 1400*a^13*b^3*c^8*d^8*e^
3*f^13 - 300*a^14*b^2*c^2*d^14*e^8*f^8 + 840*a^14*b^2*c^4*d^12*e^6*f^10 - 1344*a^14*b^2*c^5*d^11*e^5*f^11 + 84
0*a^14*b^2*c^6*d^10*e^4*f^12 - 300*a^14*b^2*c^8*d^8*e^2*f^14)) - (36*a^11*b^2*d^13*f^13 + 36*b^13*c^11*d^2*f^1
3 + 36*b^13*d^13*e^11*f^2 + 297*a^2*b^11*c^9*d^4*f^13 - 108*a^3*b^10*c^8*d^5*f^13 - 198*a^4*b^9*c^7*d^6*f^13 +
153*a^5*b^8*c^6*d^7*f^13 + 153*a^6*b^7*c^5*d^8*f^13 - 198*a^7*b^6*c^4*d^9*f^13 - 108*a^8*b^5*c^3*d^10*f^13 +
297*a^9*b^4*c^2*d^11*f^13 + 297*a^2*b^11*d^13*e^9*f^4 - 108*a^3*b^10*d^13*e^8*f^5 - 198*a^4*b^9*d^13*e^7*f^6 +
153*a^5*b^8*d^13*e^6*f^7 + 153*a^6*b^7*d^13*e^5*f^8 - 198*a^7*b^6*d^13*e^4*f^9 - 108*a^8*b^5*d^13*e^3*f^10 +
297*a^9*b^4*d^13*e^2*f^11 + 297*b^13*c^2*d^11*e^9*f^4 - 108*b^13*c^3*d^10*e^8*f^5 - 198*b^13*c^4*d^9*e^7*f^6 +
153*b^13*c^5*d^8*e^6*f^7 + 153*b^13*c^6*d^7*e^5*f^8 - 198*b^13*c^7*d^6*e^4*f^9 - 108*b^13*c^8*d^5*e^3*f^10 +
297*b^13*c^9*d^4*e^2*f^11 - 180*a*b^12*c^10*d^3*f^13 - 180*a^10*b^3*c*d^12*f^13 - 180*a*b^12*d^13*e^10*f^3 - 1
80*a^10*b^3*d^13*e*f^12 - 180*b^13*c*d^12*e^10*f^3 - 180*b^13*c^10*d^3*e*f^12 + 1026*a*b^12*c*d^12*e^9*f^4 + 1
026*a*b^12*c^9*d^4*e*f^12 + 1026*a^9*b^4*c*d^12*e*f^12 - 2052*a*b^12*c^2*d^11*e^8*f^5 + 1548*a*b^12*c^3*d^10*e
^7*f^6 + 297*a*b^12*c^4*d^9*e^6*f^7 - 1242*a*b^12*c^5*d^8*e^5*f^8 + 297*a*b^12*c^6*d^7*e^4*f^9 + 1548*a*b^12*c
^7*d^6*e^3*f^10 - 2052*a*b^12*c^8*d^5*e^2*f^11 - 2052*a^2*b^11*c*d^12*e^8*f^5 - 2052*a^2*b^11*c^8*d^5*e*f^12 +
1548*a^3*b^10*c*d^12*e^7*f^6 + 1548*a^3*b^10*c^7*d^6*e*f^12 + 297*a^4*b^9*c*d^12*e^6*f^7 + 297*a^4*b^9*c^6*d^
7*e*f^12 - 1242*a^5*b^8*c*d^12*e^5*f^8 - 1242*a^5*b^8*c^5*d^8*e*f^12 + 297*a^6*b^7*c*d^12*e^4*f^9 + 297*a^6*b^
7*c^4*d^9*e*f^12 + 1548*a^7*b^6*c*d^12*e^3*f^10 + 1548*a^7*b^6*c^3*d^10*e*f^12 - 2052*a^8*b^5*c*d^12*e^2*f^11
- 2052*a^8*b^5*c^2*d^11*e*f^12 + 4860*a^2*b^11*c^2*d^11*e^7*f^6 - 4986*a^2*b^11*c^3*d^10*e^6*f^7 + 1701*a^2*b^
11*c^4*d^9*e^5*f^8 + 1701*a^2*b^11*c^5*d^8*e^4*f^9 - 4986*a^2*b^11*c^6*d^7*e^3*f^10 + 4860*a^2*b^11*c^7*d^6*e^
2*f^11 - 4986*a^3*b^10*c^2*d^11*e^6*f^7 + 6336*a^3*b^10*c^3*d^10*e^5*f^8 - 3960*a^3*b^10*c^4*d^9*e^4*f^9 + 633
6*a^3*b^10*c^5*d^8*e^3*f^10 - 4986*a^3*b^10*c^6*d^7*e^2*f^11 + 1701*a^4*b^9*c^2*d^11*e^5*f^8 - 3960*a^4*b^9*c^
3*d^10*e^4*f^9 - 3960*a^4*b^9*c^4*d^9*e^3*f^10 + 1701*a^4*b^9*c^5*d^8*e^2*f^11 + 1701*a^5*b^8*c^2*d^11*e^4*f^9
+ 6336*a^5*b^8*c^3*d^10*e^3*f^10 + 1701*a^5*b^8*c^4*d^9*e^2*f^11 - 4986*a^6*b^7*c^2*d^11*e^3*f^10 - 4986*a^6*
b^7*c^3*d^10*e^2*f^11 + 4860*a^7*b^6*c^2*d^11*e^2*f^11)/(56*a^3*b^13*c^5*d^11*e^16 - a^8*b^8*d^16*e^16 - a^16*
c^8*d^8*f^16 - b^16*c^8*d^8*e^16 - a^16*d^16*e^8*f^8 - b^16*c^16*e^8*f^8 - 28*a^2*b^14*c^6*d^10*e^16 - a^8*b^8
*c^16*f^16 - 70*a^4*b^12*c^4*d^12*e^16 + 56*a^5*b^11*c^3*d^13*e^16 - 28*a^6*b^10*c^2*d^14*e^16 - 28*a^10*b^6*c
^14*d^2*f^16 + 56*a^11*b^5*c^13*d^3*f^16 - 70*a^12*b^4*c^12*d^4*f^16 + 56*a^13*b^3*c^11*d^5*f^16 - 28*a^14*b^2
*c^10*d^6*f^16 - 28*a^2*b^14*c^16*e^6*f^10 + 56*a^3*b^13*c^16*e^5*f^11 - 70*a^4*b^12*c^16*e^4*f^12 + 56*a^5*b^
11*c^16*e^3*f^13 - 28*a^6*b^10*c^16*e^2*f^14 - 28*a^10*b^6*d^16*e^14*f^2 + 56*a^11*b^5*d^16*e^13*f^3 - 70*a^12
*b^4*d^16*e^12*f^4 + 56*a^13*b^3*d^16*e^11*f^5 - 28*a^14*b^2*d^16*e^10*f^6 - 28*a^16*c^2*d^14*e^6*f^10 + 56*a^
16*c^3*d^13*e^5*f^11 - 70*a^16*c^4*d^12*e^4*f^12 + 56*a^16*c^5*d^11*e^3*f^13 - 28*a^16*c^6*d^10*e^2*f^14 - 28*
b^16*c^10*d^6*e^14*f^2 + 56*b^16*c^11*d^5*e^13*f^3 - 70*b^16*c^12*d^4*e^12*f^4 + 56*b^16*c^13*d^3*e^11*f^5 - 2
8*b^16*c^14*d^2*e^10*f^6 + 8*a*b^15*c^7*d^9*e^16 + 8*a^7*b^9*c*d^15*e^16 + 8*a^9*b^7*c^15*d*f^16 + 8*a^15*b*c^
9*d^7*f^16 + 8*a*b^15*c^16*e^7*f^9 + 8*a^7*b^9*c^16*e*f^15 + 8*a^9*b^7*d^16*e^15*f + 8*a^15*b*d^16*e^9*f^7 + 8
*a^16*c*d^15*e^7*f^9 + 8*a^16*c^7*d^9*e*f^15 + 8*b^16*c^9*d^7*e^15*f + 8*b^16*c^15*d*e^9*f^7 - 56*a*b^15*c^8*d
^8*e^15*f - 56*a*b^15*c^15*d*e^8*f^8 - 56*a^8*b^8*c*d^15*e^15*f - 56*a^8*b^8*c^15*d*e*f^15 - 56*a^15*b*c*d^15*
e^8*f^8 - 56*a^15*b*c^8*d^8*e*f^15 + 160*a*b^15*c^9*d^7*e^14*f^2 - 224*a*b^15*c^10*d^6*e^13*f^3 + 112*a*b^15*c
^11*d^5*e^12*f^4 + 112*a*b^15*c^12*d^4*e^11*f^5 - 224*a*b^15*c^13*d^3*e^10*f^6 + 160*a*b^15*c^14*d^2*e^9*f^7 +
160*a^2*b^14*c^7*d^9*e^15*f + 160*a^2*b^14*c^15*d*e^7*f^9 - 224*a^3*b^13*c^6*d^10*e^15*f - 224*a^3*b^13*c^15*
d*e^6*f^10 + 112*a^4*b^12*c^5*d^11*e^15*f + 112*a^4*b^12*c^15*d*e^5*f^11 + 112*a^5*b^11*c^4*d^12*e^15*f + 112*
a^5*b^11*c^15*d*e^4*f^12 - 224*a^6*b^10*c^3*d^13*e^15*f - 224*a^6*b^10*c^15*d*e^3*f^13 + 160*a^7*b^9*c^2*d^14*
e^15*f + 160*a^7*b^9*c^15*d*e^2*f^14 + 160*a^9*b^7*c*d^15*e^14*f^2 + 160*a^9*b^7*c^14*d^2*e*f^15 - 224*a^10*b^
6*c*d^15*e^13*f^3 - 224*a^10*b^6*c^13*d^3*e*f^15 + 112*a^11*b^5*c*d^15*e^12*f^4 + 112*a^11*b^5*c^12*d^4*e*f^15
+ 112*a^12*b^4*c*d^15*e^11*f^5 + 112*a^12*b^4*c^11*d^5*e*f^15 - 224*a^13*b^3*c*d^15*e^10*f^6 - 224*a^13*b^3*c
^10*d^6*e*f^15 + 160*a^14*b^2*c*d^15*e^9*f^7 + 160*a^14*b^2*c^9*d^7*e*f^15 + 160*a^15*b*c^2*d^14*e^7*f^9 - 224
*a^15*b*c^3*d^13*e^6*f^10 + 112*a^15*b*c^4*d^12*e^5*f^11 + 112*a^15*b*c^5*d^11*e^4*f^12 - 224*a^15*b*c^6*d^10*
e^3*f^13 + 160*a^15*b*c^7*d^9*e^2*f^14 - 300*a^2*b^14*c^8*d^8*e^14*f^2 + 840*a^2*b^14*c^10*d^6*e^12*f^4 - 1344
*a^2*b^14*c^11*d^5*e^11*f^5 + 840*a^2*b^14*c^12*d^4*e^10*f^6 - 300*a^2*b^14*c^14*d^2*e^8*f^8 + 1400*a^3*b^13*c
^8*d^8*e^13*f^3 - 2800*a^3*b^13*c^9*d^7*e^12*f^4 + 1568*a^3*b^13*c^10*d^6*e^11*f^5 + 1568*a^3*b^13*c^11*d^5*e^
10*f^6 - 2800*a^3*b^13*c^12*d^4*e^9*f^7 + 1400*a^3*b^13*c^13*d^3*e^8*f^8 + 840*a^4*b^12*c^6*d^10*e^14*f^2 - 28
00*a^4*b^12*c^7*d^9*e^13*f^3 + 1750*a^4*b^12*c^8*d^8*e^12*f^4 + 4480*a^4*b^12*c^9*d^7*e^11*f^5 - 8624*a^4*b^12
*c^10*d^6*e^10*f^6 + 4480*a^4*b^12*c^11*d^5*e^9*f^7 + 1750*a^4*b^12*c^12*d^4*e^8*f^8 - 2800*a^4*b^12*c^13*d^3*
e^7*f^9 + 840*a^4*b^12*c^14*d^2*e^6*f^10 - 1344*a^5*b^11*c^5*d^11*e^14*f^2 + 1568*a^5*b^11*c^6*d^10*e^13*f^3 +
4480*a^5*b^11*c^7*d^9*e^12*f^4 - 12264*a^5*b^11*c^8*d^8*e^11*f^5 + 7392*a^5*b^11*c^9*d^7*e^10*f^6 + 7392*a^5*
b^11*c^10*d^6*e^9*f^7 - 12264*a^5*b^11*c^11*d^5*e^8*f^8 + 4480*a^5*b^11*c^12*d^4*e^7*f^9 + 1568*a^5*b^11*c^13*
d^3*e^6*f^10 - 1344*a^5*b^11*c^14*d^2*e^5*f^11 + 840*a^6*b^10*c^4*d^12*e^14*f^2 + 1568*a^6*b^10*c^5*d^11*e^13*
f^3 - 8624*a^6*b^10*c^6*d^10*e^12*f^4 + 7392*a^6*b^10*c^7*d^9*e^11*f^5 + 11396*a^6*b^10*c^8*d^8*e^10*f^6 - 246
40*a^6*b^10*c^9*d^7*e^9*f^7 + 11396*a^6*b^10*c^10*d^6*e^8*f^8 + 7392*a^6*b^10*c^11*d^5*e^7*f^9 - 8624*a^6*b^10
*c^12*d^4*e^6*f^10 + 1568*a^6*b^10*c^13*d^3*e^5*f^11 + 840*a^6*b^10*c^14*d^2*e^4*f^12 - 2800*a^7*b^9*c^4*d^12*
e^13*f^3 + 4480*a^7*b^9*c^5*d^11*e^12*f^4 + 7392*a^7*b^9*c^6*d^10*e^11*f^5 - 24640*a^7*b^9*c^7*d^9*e^10*f^6 +
15400*a^7*b^9*c^8*d^8*e^9*f^7 + 15400*a^7*b^9*c^9*d^7*e^8*f^8 - 24640*a^7*b^9*c^10*d^6*e^7*f^9 + 7392*a^7*b^9*
c^11*d^5*e^6*f^10 + 4480*a^7*b^9*c^12*d^4*e^5*f^11 - 2800*a^7*b^9*c^13*d^3*e^4*f^12 - 300*a^8*b^8*c^2*d^14*e^1
4*f^2 + 1400*a^8*b^8*c^3*d^13*e^13*f^3 + 1750*a^8*b^8*c^4*d^12*e^12*f^4 - 12264*a^8*b^8*c^5*d^11*e^11*f^5 + 11
396*a^8*b^8*c^6*d^10*e^10*f^6 + 15400*a^8*b^8*c^7*d^9*e^9*f^7 - 34650*a^8*b^8*c^8*d^8*e^8*f^8 + 15400*a^8*b^8*
c^9*d^7*e^7*f^9 + 11396*a^8*b^8*c^10*d^6*e^6*f^10 - 12264*a^8*b^8*c^11*d^5*e^5*f^11 + 1750*a^8*b^8*c^12*d^4*e^
4*f^12 + 1400*a^8*b^8*c^13*d^3*e^3*f^13 - 300*a^8*b^8*c^14*d^2*e^2*f^14 - 2800*a^9*b^7*c^3*d^13*e^12*f^4 + 448
0*a^9*b^7*c^4*d^12*e^11*f^5 + 7392*a^9*b^7*c^5*d^11*e^10*f^6 - 24640*a^9*b^7*c^6*d^10*e^9*f^7 + 15400*a^9*b^7*
c^7*d^9*e^8*f^8 + 15400*a^9*b^7*c^8*d^8*e^7*f^9 - 24640*a^9*b^7*c^9*d^7*e^6*f^10 + 7392*a^9*b^7*c^10*d^6*e^5*f
^11 + 4480*a^9*b^7*c^11*d^5*e^4*f^12 - 2800*a^9*b^7*c^12*d^4*e^3*f^13 + 840*a^10*b^6*c^2*d^14*e^12*f^4 + 1568*
a^10*b^6*c^3*d^13*e^11*f^5 - 8624*a^10*b^6*c^4*d^12*e^10*f^6 + 7392*a^10*b^6*c^5*d^11*e^9*f^7 + 11396*a^10*b^6
*c^6*d^10*e^8*f^8 - 24640*a^10*b^6*c^7*d^9*e^7*f^9 + 11396*a^10*b^6*c^8*d^8*e^6*f^10 + 7392*a^10*b^6*c^9*d^7*e
^5*f^11 - 8624*a^10*b^6*c^10*d^6*e^4*f^12 + 1568*a^10*b^6*c^11*d^5*e^3*f^13 + 840*a^10*b^6*c^12*d^4*e^2*f^14 -
1344*a^11*b^5*c^2*d^14*e^11*f^5 + 1568*a^11*b^5*c^3*d^13*e^10*f^6 + 4480*a^11*b^5*c^4*d^12*e^9*f^7 - 12264*a^
11*b^5*c^5*d^11*e^8*f^8 + 7392*a^11*b^5*c^6*d^10*e^7*f^9 + 7392*a^11*b^5*c^7*d^9*e^6*f^10 - 12264*a^11*b^5*c^8
*d^8*e^5*f^11 + 4480*a^11*b^5*c^9*d^7*e^4*f^12 + 1568*a^11*b^5*c^10*d^6*e^3*f^13 - 1344*a^11*b^5*c^11*d^5*e^2*
f^14 + 840*a^12*b^4*c^2*d^14*e^10*f^6 - 2800*a^12*b^4*c^3*d^13*e^9*f^7 + 1750*a^12*b^4*c^4*d^12*e^8*f^8 + 4480
*a^12*b^4*c^5*d^11*e^7*f^9 - 8624*a^12*b^4*c^6*d^10*e^6*f^10 + 4480*a^12*b^4*c^7*d^9*e^5*f^11 + 1750*a^12*b^4*
c^8*d^8*e^4*f^12 - 2800*a^12*b^4*c^9*d^7*e^3*f^13 + 840*a^12*b^4*c^10*d^6*e^2*f^14 + 1400*a^13*b^3*c^3*d^13*e^
8*f^8 - 2800*a^13*b^3*c^4*d^12*e^7*f^9 + 1568*a^13*b^3*c^5*d^11*e^6*f^10 + 1568*a^13*b^3*c^6*d^10*e^5*f^11 - 2
800*a^13*b^3*c^7*d^9*e^4*f^12 + 1400*a^13*b^3*c^8*d^8*e^3*f^13 - 300*a^14*b^2*c^2*d^14*e^8*f^8 + 840*a^14*b^2*
c^4*d^12*e^6*f^10 - 1344*a^14*b^2*c^5*d^11*e^5*f^11 + 840*a^14*b^2*c^6*d^10*e^4*f^12 - 300*a^14*b^2*c^8*d^8*e^
2*f^14) + (x*(108*a^3*b^10*c^7*d^6*f^13 - 36*b^13*c^10*d^3*f^13 - 36*b^13*d^13*e^10*f^3 - 297*a^2*b^11*c^8*d^5
*f^13 - 36*a^10*b^3*d^13*f^13 + 324*a^4*b^9*c^6*d^7*f^13 - 594*a^5*b^8*c^5*d^8*f^13 + 324*a^6*b^7*c^4*d^9*f^13
+ 108*a^7*b^6*c^3*d^10*f^13 - 297*a^8*b^5*c^2*d^11*f^13 - 297*a^2*b^11*d^13*e^8*f^5 + 108*a^3*b^10*d^13*e^7*f
^6 + 324*a^4*b^9*d^13*e^6*f^7 - 594*a^5*b^8*d^13*e^5*f^8 + 324*a^6*b^7*d^13*e^4*f^9 + 108*a^7*b^6*d^13*e^3*f^1
0 - 297*a^8*b^5*d^13*e^2*f^11 - 297*b^13*c^2*d^11*e^8*f^5 + 108*b^13*c^3*d^10*e^7*f^6 + 324*b^13*c^4*d^9*e^6*f
^7 - 594*b^13*c^5*d^8*e^5*f^8 + 324*b^13*c^6*d^7*e^4*f^9 + 108*b^13*c^7*d^6*e^3*f^10 - 297*b^13*c^8*d^5*e^2*f^
11 + 180*a*b^12*c^9*d^4*f^13 + 180*a^9*b^4*c*d^12*f^13 + 180*a*b^12*d^13*e^9*f^4 + 180*a^9*b^4*d^13*e*f^12 + 1
80*b^13*c*d^12*e^9*f^4 + 180*b^13*c^9*d^4*e*f^12 - 1026*a*b^12*c*d^12*e^8*f^5 - 1026*a*b^12*c^8*d^5*e*f^12 - 1
026*a^8*b^5*c*d^12*e*f^12 + 2052*a*b^12*c^2*d^11*e^7*f^6 - 2052*a*b^12*c^3*d^10*e^6*f^7 + 1026*a*b^12*c^4*d^9*
e^5*f^8 + 1026*a*b^12*c^5*d^8*e^4*f^9 - 2052*a*b^12*c^6*d^7*e^3*f^10 + 2052*a*b^12*c^7*d^6*e^2*f^11 + 2052*a^2
*b^11*c*d^12*e^7*f^6 + 2052*a^2*b^11*c^7*d^6*e*f^12 - 2052*a^3*b^10*c*d^12*e^6*f^7 - 2052*a^3*b^10*c^6*d^7*e*f
^12 + 1026*a^4*b^9*c*d^12*e^5*f^8 + 1026*a^4*b^9*c^5*d^8*e*f^12 + 1026*a^5*b^8*c*d^12*e^4*f^9 + 1026*a^5*b^8*c
^4*d^9*e*f^12 - 2052*a^6*b^7*c*d^12*e^3*f^10 - 2052*a^6*b^7*c^3*d^10*e*f^12 + 2052*a^7*b^6*c*d^12*e^2*f^11 + 2
052*a^7*b^6*c^2*d^11*e*f^12 - 4104*a^2*b^11*c^2*d^11*e^6*f^7 + 4104*a^2*b^11*c^3*d^10*e^5*f^8 - 5130*a^2*b^11*
c^4*d^9*e^4*f^9 + 4104*a^2*b^11*c^5*d^8*e^3*f^10 - 4104*a^2*b^11*c^6*d^7*e^2*f^11 + 4104*a^3*b^10*c^2*d^11*e^5
*f^8 + 4104*a^3*b^10*c^5*d^8*e^2*f^11 - 5130*a^4*b^9*c^2*d^11*e^4*f^9 - 5130*a^4*b^9*c^4*d^9*e^2*f^11 + 4104*a
^5*b^8*c^2*d^11*e^3*f^10 + 4104*a^5*b^8*c^3*d^10*e^2*f^11 - 4104*a^6*b^7*c^2*d^11*e^2*f^11))/(56*a^3*b^13*c^5*
d^11*e^16 - a^8*b^8*d^16*e^16 - a^16*c^8*d^8*f^16 - b^16*c^8*d^8*e^16 - a^16*d^16*e^8*f^8 - b^16*c^16*e^8*f^8
- 28*a^2*b^14*c^6*d^10*e^16 - a^8*b^8*c^16*f^16 - 70*a^4*b^12*c^4*d^12*e^16 + 56*a^5*b^11*c^3*d^13*e^16 - 28*a
^6*b^10*c^2*d^14*e^16 - 28*a^10*b^6*c^14*d^2*f^16 + 56*a^11*b^5*c^13*d^3*f^16 - 70*a^12*b^4*c^12*d^4*f^16 + 56
*a^13*b^3*c^11*d^5*f^16 - 28*a^14*b^2*c^10*d^6*f^16 - 28*a^2*b^14*c^16*e^6*f^10 + 56*a^3*b^13*c^16*e^5*f^11 -
70*a^4*b^12*c^16*e^4*f^12 + 56*a^5*b^11*c^16*e^3*f^13 - 28*a^6*b^10*c^16*e^2*f^14 - 28*a^10*b^6*d^16*e^14*f^2
+ 56*a^11*b^5*d^16*e^13*f^3 - 70*a^12*b^4*d^16*e^12*f^4 + 56*a^13*b^3*d^16*e^11*f^5 - 28*a^14*b^2*d^16*e^10*f^
6 - 28*a^16*c^2*d^14*e^6*f^10 + 56*a^16*c^3*d^13*e^5*f^11 - 70*a^16*c^4*d^12*e^4*f^12 + 56*a^16*c^5*d^11*e^3*f
^13 - 28*a^16*c^6*d^10*e^2*f^14 - 28*b^16*c^10*d^6*e^14*f^2 + 56*b^16*c^11*d^5*e^13*f^3 - 70*b^16*c^12*d^4*e^1
2*f^4 + 56*b^16*c^13*d^3*e^11*f^5 - 28*b^16*c^14*d^2*e^10*f^6 + 8*a*b^15*c^7*d^9*e^16 + 8*a^7*b^9*c*d^15*e^16
+ 8*a^9*b^7*c^15*d*f^16 + 8*a^15*b*c^9*d^7*f^16 + 8*a*b^15*c^16*e^7*f^9 + 8*a^7*b^9*c^16*e*f^15 + 8*a^9*b^7*d^
16*e^15*f + 8*a^15*b*d^16*e^9*f^7 + 8*a^16*c*d^15*e^7*f^9 + 8*a^16*c^7*d^9*e*f^15 + 8*b^16*c^9*d^7*e^15*f + 8*
b^16*c^15*d*e^9*f^7 - 56*a*b^15*c^8*d^8*e^15*f - 56*a*b^15*c^15*d*e^8*f^8 - 56*a^8*b^8*c*d^15*e^15*f - 56*a^8*
b^8*c^15*d*e*f^15 - 56*a^15*b*c*d^15*e^8*f^8 - 56*a^15*b*c^8*d^8*e*f^15 + 160*a*b^15*c^9*d^7*e^14*f^2 - 224*a*
b^15*c^10*d^6*e^13*f^3 + 112*a*b^15*c^11*d^5*e^12*f^4 + 112*a*b^15*c^12*d^4*e^11*f^5 - 224*a*b^15*c^13*d^3*e^1
0*f^6 + 160*a*b^15*c^14*d^2*e^9*f^7 + 160*a^2*b^14*c^7*d^9*e^15*f + 160*a^2*b^14*c^15*d*e^7*f^9 - 224*a^3*b^13
*c^6*d^10*e^15*f - 224*a^3*b^13*c^15*d*e^6*f^10 + 112*a^4*b^12*c^5*d^11*e^15*f + 112*a^4*b^12*c^15*d*e^5*f^11
+ 112*a^5*b^11*c^4*d^12*e^15*f + 112*a^5*b^11*c^15*d*e^4*f^12 - 224*a^6*b^10*c^3*d^13*e^15*f - 224*a^6*b^10*c^
15*d*e^3*f^13 + 160*a^7*b^9*c^2*d^14*e^15*f + 160*a^7*b^9*c^15*d*e^2*f^14 + 160*a^9*b^7*c*d^15*e^14*f^2 + 160*
a^9*b^7*c^14*d^2*e*f^15 - 224*a^10*b^6*c*d^15*e^13*f^3 - 224*a^10*b^6*c^13*d^3*e*f^15 + 112*a^11*b^5*c*d^15*e^
12*f^4 + 112*a^11*b^5*c^12*d^4*e*f^15 + 112*a^12*b^4*c*d^15*e^11*f^5 + 112*a^12*b^4*c^11*d^5*e*f^15 - 224*a^13
*b^3*c*d^15*e^10*f^6 - 224*a^13*b^3*c^10*d^6*e*f^15 + 160*a^14*b^2*c*d^15*e^9*f^7 + 160*a^14*b^2*c^9*d^7*e*f^1
5 + 160*a^15*b*c^2*d^14*e^7*f^9 - 224*a^15*b*c^3*d^13*e^6*f^10 + 112*a^15*b*c^4*d^12*e^5*f^11 + 112*a^15*b*c^5
*d^11*e^4*f^12 - 224*a^15*b*c^6*d^10*e^3*f^13 + 160*a^15*b*c^7*d^9*e^2*f^14 - 300*a^2*b^14*c^8*d^8*e^14*f^2 +
840*a^2*b^14*c^10*d^6*e^12*f^4 - 1344*a^2*b^14*c^11*d^5*e^11*f^5 + 840*a^2*b^14*c^12*d^4*e^10*f^6 - 300*a^2*b^
14*c^14*d^2*e^8*f^8 + 1400*a^3*b^13*c^8*d^8*e^13*f^3 - 2800*a^3*b^13*c^9*d^7*e^12*f^4 + 1568*a^3*b^13*c^10*d^6
*e^11*f^5 + 1568*a^3*b^13*c^11*d^5*e^10*f^6 - 2800*a^3*b^13*c^12*d^4*e^9*f^7 + 1400*a^3*b^13*c^13*d^3*e^8*f^8
+ 840*a^4*b^12*c^6*d^10*e^14*f^2 - 2800*a^4*b^12*c^7*d^9*e^13*f^3 + 1750*a^4*b^12*c^8*d^8*e^12*f^4 + 4480*a^4*
b^12*c^9*d^7*e^11*f^5 - 8624*a^4*b^12*c^10*d^6*e^10*f^6 + 4480*a^4*b^12*c^11*d^5*e^9*f^7 + 1750*a^4*b^12*c^12*
d^4*e^8*f^8 - 2800*a^4*b^12*c^13*d^3*e^7*f^9 + 840*a^4*b^12*c^14*d^2*e^6*f^10 - 1344*a^5*b^11*c^5*d^11*e^14*f^
2 + 1568*a^5*b^11*c^6*d^10*e^13*f^3 + 4480*a^5*b^11*c^7*d^9*e^12*f^4 - 12264*a^5*b^11*c^8*d^8*e^11*f^5 + 7392*
a^5*b^11*c^9*d^7*e^10*f^6 + 7392*a^5*b^11*c^10*d^6*e^9*f^7 - 12264*a^5*b^11*c^11*d^5*e^8*f^8 + 4480*a^5*b^11*c
^12*d^4*e^7*f^9 + 1568*a^5*b^11*c^13*d^3*e^6*f^10 - 1344*a^5*b^11*c^14*d^2*e^5*f^11 + 840*a^6*b^10*c^4*d^12*e^
14*f^2 + 1568*a^6*b^10*c^5*d^11*e^13*f^3 - 8624*a^6*b^10*c^6*d^10*e^12*f^4 + 7392*a^6*b^10*c^7*d^9*e^11*f^5 +
11396*a^6*b^10*c^8*d^8*e^10*f^6 - 24640*a^6*b^10*c^9*d^7*e^9*f^7 + 11396*a^6*b^10*c^10*d^6*e^8*f^8 + 7392*a^6*
b^10*c^11*d^5*e^7*f^9 - 8624*a^6*b^10*c^12*d^4*e^6*f^10 + 1568*a^6*b^10*c^13*d^3*e^5*f^11 + 840*a^6*b^10*c^14*
d^2*e^4*f^12 - 2800*a^7*b^9*c^4*d^12*e^13*f^3 + 4480*a^7*b^9*c^5*d^11*e^12*f^4 + 7392*a^7*b^9*c^6*d^10*e^11*f^
5 - 24640*a^7*b^9*c^7*d^9*e^10*f^6 + 15400*a^7*b^9*c^8*d^8*e^9*f^7 + 15400*a^7*b^9*c^9*d^7*e^8*f^8 - 24640*a^7
*b^9*c^10*d^6*e^7*f^9 + 7392*a^7*b^9*c^11*d^5*e^6*f^10 + 4480*a^7*b^9*c^12*d^4*e^5*f^11 - 2800*a^7*b^9*c^13*d^
3*e^4*f^12 - 300*a^8*b^8*c^2*d^14*e^14*f^2 + 1400*a^8*b^8*c^3*d^13*e^13*f^3 + 1750*a^8*b^8*c^4*d^12*e^12*f^4 -
12264*a^8*b^8*c^5*d^11*e^11*f^5 + 11396*a^8*b^8*c^6*d^10*e^10*f^6 + 15400*a^8*b^8*c^7*d^9*e^9*f^7 - 34650*a^8
*b^8*c^8*d^8*e^8*f^8 + 15400*a^8*b^8*c^9*d^7*e^7*f^9 + 11396*a^8*b^8*c^10*d^6*e^6*f^10 - 12264*a^8*b^8*c^11*d^
5*e^5*f^11 + 1750*a^8*b^8*c^12*d^4*e^4*f^12 + 1400*a^8*b^8*c^13*d^3*e^3*f^13 - 300*a^8*b^8*c^14*d^2*e^2*f^14 -
2800*a^9*b^7*c^3*d^13*e^12*f^4 + 4480*a^9*b^7*c^4*d^12*e^11*f^5 + 7392*a^9*b^7*c^5*d^11*e^10*f^6 - 24640*a^9*
b^7*c^6*d^10*e^9*f^7 + 15400*a^9*b^7*c^7*d^9*e^8*f^8 + 15400*a^9*b^7*c^8*d^8*e^7*f^9 - 24640*a^9*b^7*c^9*d^7*e
^6*f^10 + 7392*a^9*b^7*c^10*d^6*e^5*f^11 + 4480*a^9*b^7*c^11*d^5*e^4*f^12 - 2800*a^9*b^7*c^12*d^4*e^3*f^13 + 8
40*a^10*b^6*c^2*d^14*e^12*f^4 + 1568*a^10*b^6*c^3*d^13*e^11*f^5 - 8624*a^10*b^6*c^4*d^12*e^10*f^6 + 7392*a^10*
b^6*c^5*d^11*e^9*f^7 + 11396*a^10*b^6*c^6*d^10*e^8*f^8 - 24640*a^10*b^6*c^7*d^9*e^7*f^9 + 11396*a^10*b^6*c^8*d
^8*e^6*f^10 + 7392*a^10*b^6*c^9*d^7*e^5*f^11 - 8624*a^10*b^6*c^10*d^6*e^4*f^12 + 1568*a^10*b^6*c^11*d^5*e^3*f^
13 + 840*a^10*b^6*c^12*d^4*e^2*f^14 - 1344*a^11*b^5*c^2*d^14*e^11*f^5 + 1568*a^11*b^5*c^3*d^13*e^10*f^6 + 4480
*a^11*b^5*c^4*d^12*e^9*f^7 - 12264*a^11*b^5*c^5*d^11*e^8*f^8 + 7392*a^11*b^5*c^6*d^10*e^7*f^9 + 7392*a^11*b^5*
c^7*d^9*e^6*f^10 - 12264*a^11*b^5*c^8*d^8*e^5*f^11 + 4480*a^11*b^5*c^9*d^7*e^4*f^12 + 1568*a^11*b^5*c^10*d^6*e
^3*f^13 - 1344*a^11*b^5*c^11*d^5*e^2*f^14 + 840*a^12*b^4*c^2*d^14*e^10*f^6 - 2800*a^12*b^4*c^3*d^13*e^9*f^7 +
1750*a^12*b^4*c^4*d^12*e^8*f^8 + 4480*a^12*b^4*c^5*d^11*e^7*f^9 - 8624*a^12*b^4*c^6*d^10*e^6*f^10 + 4480*a^12*
b^4*c^7*d^9*e^5*f^11 + 1750*a^12*b^4*c^8*d^8*e^4*f^12 - 2800*a^12*b^4*c^9*d^7*e^3*f^13 + 840*a^12*b^4*c^10*d^6
*e^2*f^14 + 1400*a^13*b^3*c^3*d^13*e^8*f^8 - 2800*a^13*b^3*c^4*d^12*e^7*f^9 + 1568*a^13*b^3*c^5*d^11*e^6*f^10
+ 1568*a^13*b^3*c^6*d^10*e^5*f^11 - 2800*a^13*b^3*c^7*d^9*e^4*f^12 + 1400*a^13*b^3*c^8*d^8*e^3*f^13 - 300*a^14
*b^2*c^2*d^14*e^8*f^8 + 840*a^14*b^2*c^4*d^12*e^6*f^10 - 1344*a^14*b^2*c^5*d^11*e^5*f^11 + 840*a^14*b^2*c^6*d^
10*e^4*f^12 - 300*a^14*b^2*c^8*d^8*e^2*f^14))*root(756756*a^10*b^10*c^10*d^10*e^10*f^10*z^3 + 573300*a^12*b^8*
c^9*d^11*e^9*f^11*z^3 + 573300*a^11*b^9*c^11*d^9*e^8*f^12*z^3 + 573300*a^11*b^9*c^8*d^12*e^11*f^9*z^3 + 573300
*a^9*b^11*c^12*d^8*e^9*f^11*z^3 + 573300*a^9*b^11*c^9*d^11*e^12*f^8*z^3 + 573300*a^8*b^12*c^11*d^9*e^11*f^9*z^
3 - 343980*a^11*b^9*c^10*d^10*e^9*f^11*z^3 - 343980*a^11*b^9*c^9*d^11*e^10*f^10*z^3 - 343980*a^10*b^10*c^11*d^
9*e^9*f^11*z^3 - 343980*a^10*b^10*c^9*d^11*e^11*f^9*z^3 - 343980*a^9*b^11*c^11*d^9*e^10*f^10*z^3 - 343980*a^9*
b^11*c^10*d^10*e^11*f^9*z^3 + 326340*a^13*b^7*c^10*d^10*e^7*f^13*z^3 + 326340*a^13*b^7*c^7*d^13*e^10*f^10*z^3
+ 326340*a^10*b^10*c^13*d^7*e^7*f^13*z^3 + 326340*a^10*b^10*c^7*d^13*e^13*f^7*z^3 + 326340*a^7*b^13*c^13*d^7*e
^10*f^10*z^3 + 326340*a^7*b^13*c^10*d^10*e^13*f^7*z^3 - 267540*a^12*b^8*c^10*d^10*e^8*f^12*z^3 - 267540*a^12*b
^8*c^8*d^12*e^10*f^10*z^3 - 267540*a^10*b^10*c^12*d^8*e^8*f^12*z^3 - 267540*a^10*b^10*c^8*d^12*e^12*f^8*z^3 -
267540*a^8*b^12*c^12*d^8*e^10*f^10*z^3 - 267540*a^8*b^12*c^10*d^10*e^12*f^8*z^3 + 245700*a^14*b^6*c^8*d^12*e^8
*f^12*z^3 + 245700*a^12*b^8*c^12*d^8*e^6*f^14*z^3 + 245700*a^12*b^8*c^6*d^14*e^12*f^8*z^3 + 245700*a^8*b^12*c^
14*d^6*e^8*f^12*z^3 + 245700*a^8*b^12*c^8*d^12*e^14*f^6*z^3 + 245700*a^6*b^14*c^12*d^8*e^12*f^8*z^3 - 191100*a
^13*b^7*c^9*d^11*e^8*f^12*z^3 - 191100*a^13*b^7*c^8*d^12*e^9*f^11*z^3 - 191100*a^12*b^8*c^11*d^9*e^7*f^13*z^3
- 191100*a^12*b^8*c^7*d^13*e^11*f^9*z^3 - 191100*a^11*b^9*c^12*d^8*e^7*f^13*z^3 - 191100*a^11*b^9*c^7*d^13*e^1
2*f^8*z^3 - 191100*a^9*b^11*c^13*d^7*e^8*f^12*z^3 - 191100*a^9*b^11*c^8*d^12*e^13*f^7*z^3 - 191100*a^8*b^12*c^
13*d^7*e^9*f^11*z^3 - 191100*a^8*b^12*c^9*d^11*e^13*f^7*z^3 - 191100*a^7*b^13*c^12*d^8*e^11*f^9*z^3 - 191100*a
^7*b^13*c^11*d^9*e^12*f^8*z^3 - 123900*a^14*b^6*c^9*d^11*e^7*f^13*z^3 - 123900*a^14*b^6*c^7*d^13*e^9*f^11*z^3
- 123900*a^13*b^7*c^11*d^9*e^6*f^14*z^3 - 123900*a^13*b^7*c^6*d^14*e^11*f^9*z^3 - 123900*a^11*b^9*c^13*d^7*e^6
*f^14*z^3 - 123900*a^11*b^9*c^6*d^14*e^13*f^7*z^3 - 123900*a^9*b^11*c^14*d^6*e^7*f^13*z^3 - 123900*a^9*b^11*c^
7*d^13*e^14*f^6*z^3 - 123900*a^7*b^13*c^14*d^6*e^9*f^11*z^3 - 123900*a^7*b^13*c^9*d^11*e^14*f^6*z^3 - 123900*a
^6*b^14*c^13*d^7*e^11*f^9*z^3 - 123900*a^6*b^14*c^11*d^9*e^13*f^7*z^3 + 101700*a^15*b^5*c^9*d^11*e^6*f^14*z^3
+ 101700*a^15*b^5*c^6*d^14*e^9*f^11*z^3 + 101700*a^14*b^6*c^11*d^9*e^5*f^15*z^3 + 101700*a^14*b^6*c^5*d^15*e^1
1*f^9*z^3 + 101700*a^11*b^9*c^14*d^6*e^5*f^15*z^3 + 101700*a^11*b^9*c^5*d^15*e^14*f^6*z^3 + 101700*a^9*b^11*c^
15*d^5*e^6*f^14*z^3 + 101700*a^9*b^11*c^6*d^14*e^15*f^5*z^3 + 101700*a^6*b^14*c^15*d^5*e^9*f^11*z^3 + 101700*a
^6*b^14*c^9*d^11*e^15*f^5*z^3 + 101700*a^5*b^15*c^14*d^6*e^11*f^9*z^3 + 101700*a^5*b^15*c^11*d^9*e^14*f^6*z^3
- 65820*a^14*b^6*c^10*d^10*e^6*f^14*z^3 - 65820*a^14*b^6*c^6*d^14*e^10*f^10*z^3 - 65820*a^10*b^10*c^14*d^6*e^6
*f^14*z^3 - 65820*a^10*b^10*c^6*d^14*e^14*f^6*z^3 - 65820*a^6*b^14*c^14*d^6*e^10*f^10*z^3 - 65820*a^6*b^14*c^1
0*d^10*e^14*f^6*z^3 + 56700*a^16*b^4*c^7*d^13*e^7*f^13*z^3 - 56700*a^15*b^5*c^8*d^12*e^7*f^13*z^3 - 56700*a^15
*b^5*c^7*d^13*e^8*f^12*z^3 + 56700*a^13*b^7*c^13*d^7*e^4*f^16*z^3 - 56700*a^13*b^7*c^12*d^8*e^5*f^15*z^3 - 567
00*a^13*b^7*c^5*d^15*e^12*f^8*z^3 + 56700*a^13*b^7*c^4*d^16*e^13*f^7*z^3 - 56700*a^12*b^8*c^13*d^7*e^5*f^15*z^
3 - 56700*a^12*b^8*c^5*d^15*e^13*f^7*z^3 - 56700*a^8*b^12*c^15*d^5*e^7*f^13*z^3 - 56700*a^8*b^12*c^7*d^13*e^15
*f^5*z^3 + 56700*a^7*b^13*c^16*d^4*e^7*f^13*z^3 - 56700*a^7*b^13*c^15*d^5*e^8*f^12*z^3 - 56700*a^7*b^13*c^8*d^
12*e^15*f^5*z^3 + 56700*a^7*b^13*c^7*d^13*e^16*f^4*z^3 - 56700*a^5*b^15*c^13*d^7*e^12*f^8*z^3 - 56700*a^5*b^15
*c^12*d^8*e^13*f^7*z^3 + 56700*a^4*b^16*c^13*d^7*e^13*f^7*z^3 - 48252*a^15*b^5*c^10*d^10*e^5*f^15*z^3 - 48252*
a^15*b^5*c^5*d^15*e^10*f^10*z^3 - 48252*a^10*b^10*c^15*d^5*e^5*f^15*z^3 - 48252*a^10*b^10*c^5*d^15*e^15*f^5*z^
3 - 48252*a^5*b^15*c^15*d^5*e^10*f^10*z^3 - 48252*a^5*b^15*c^10*d^10*e^15*f^5*z^3 - 32400*a^16*b^4*c^8*d^12*e^
6*f^14*z^3 - 32400*a^16*b^4*c^6*d^14*e^8*f^12*z^3 - 32400*a^14*b^6*c^12*d^8*e^4*f^16*z^3 - 32400*a^14*b^6*c^4*
d^16*e^12*f^8*z^3 - 32400*a^12*b^8*c^14*d^6*e^4*f^16*z^3 - 32400*a^12*b^8*c^4*d^16*e^14*f^6*z^3 - 32400*a^8*b^
12*c^16*d^4*e^6*f^14*z^3 - 32400*a^8*b^12*c^6*d^14*e^16*f^4*z^3 - 32400*a^6*b^14*c^16*d^4*e^8*f^12*z^3 - 32400
*a^6*b^14*c^8*d^12*e^16*f^4*z^3 - 32400*a^4*b^16*c^14*d^6*e^12*f^8*z^3 - 32400*a^4*b^16*c^12*d^8*e^14*f^6*z^3
+ 20565*a^16*b^4*c^10*d^10*e^4*f^16*z^3 + 20565*a^16*b^4*c^4*d^16*e^10*f^10*z^3 + 20565*a^10*b^10*c^16*d^4*e^4
*f^16*z^3 + 20565*a^10*b^10*c^4*d^16*e^16*f^4*z^3 + 20565*a^4*b^16*c^16*d^4*e^10*f^10*z^3 + 20565*a^4*b^16*c^1
0*d^10*e^16*f^4*z^3 + 15660*a^17*b^3*c^8*d^12*e^5*f^15*z^3 + 15660*a^17*b^3*c^5*d^15*e^8*f^12*z^3 + 15660*a^15
*b^5*c^12*d^8*e^3*f^17*z^3 + 15660*a^15*b^5*c^3*d^17*e^12*f^8*z^3 + 15660*a^12*b^8*c^15*d^5*e^3*f^17*z^3 + 156
60*a^12*b^8*c^3*d^17*e^15*f^5*z^3 + 15660*a^8*b^12*c^17*d^3*e^5*f^15*z^3 + 15660*a^8*b^12*c^5*d^15*e^17*f^3*z^
3 + 15660*a^5*b^15*c^17*d^3*e^8*f^12*z^3 + 15660*a^5*b^15*c^8*d^12*e^17*f^3*z^3 + 15660*a^3*b^17*c^15*d^5*e^12
*f^8*z^3 + 15660*a^3*b^17*c^12*d^8*e^15*f^5*z^3 - 9750*a^17*b^3*c^9*d^11*e^4*f^16*z^3 - 9750*a^17*b^3*c^4*d^16
*e^9*f^11*z^3 - 9750*a^16*b^4*c^11*d^9*e^3*f^17*z^3 - 9750*a^16*b^4*c^3*d^17*e^11*f^9*z^3 - 9750*a^11*b^9*c^16
*d^4*e^3*f^17*z^3 - 9750*a^11*b^9*c^3*d^17*e^16*f^4*z^3 - 9750*a^9*b^11*c^17*d^3*e^4*f^16*z^3 - 9750*a^9*b^11*
c^4*d^16*e^17*f^3*z^3 - 9750*a^4*b^16*c^17*d^3*e^9*f^11*z^3 - 9750*a^4*b^16*c^9*d^11*e^17*f^3*z^3 - 9750*a^3*b
^17*c^16*d^4*e^11*f^9*z^3 - 9750*a^3*b^17*c^11*d^9*e^16*f^4*z^3 - 8100*a^17*b^3*c^7*d^13*e^6*f^14*z^3 - 8100*a
^17*b^3*c^6*d^14*e^7*f^13*z^3 - 8100*a^14*b^6*c^13*d^7*e^3*f^17*z^3 - 8100*a^14*b^6*c^3*d^17*e^13*f^7*z^3 - 81
00*a^13*b^7*c^14*d^6*e^3*f^17*z^3 - 8100*a^13*b^7*c^3*d^17*e^14*f^6*z^3 - 8100*a^7*b^13*c^17*d^3*e^6*f^14*z^3
- 8100*a^7*b^13*c^6*d^14*e^17*f^3*z^3 - 8100*a^6*b^14*c^17*d^3*e^7*f^13*z^3 - 8100*a^6*b^14*c^7*d^13*e^17*f^3*
z^3 - 8100*a^3*b^17*c^14*d^6*e^13*f^7*z^3 - 8100*a^3*b^17*c^13*d^7*e^14*f^6*z^3 - 7980*a^16*b^4*c^9*d^11*e^5*f
^15*z^3 - 7980*a^16*b^4*c^5*d^15*e^9*f^11*z^3 - 7980*a^15*b^5*c^11*d^9*e^4*f^16*z^3 - 7980*a^15*b^5*c^4*d^16*e
^11*f^9*z^3 - 7980*a^11*b^9*c^15*d^5*e^4*f^16*z^3 - 7980*a^11*b^9*c^4*d^16*e^15*f^5*z^3 - 7980*a^9*b^11*c^16*d
^4*e^5*f^15*z^3 - 7980*a^9*b^11*c^5*d^15*e^16*f^4*z^3 - 7980*a^5*b^15*c^16*d^4*e^9*f^11*z^3 - 7980*a^5*b^15*c^
9*d^11*e^16*f^4*z^3 - 7980*a^4*b^16*c^15*d^5*e^11*f^9*z^3 - 7980*a^4*b^16*c^11*d^9*e^15*f^5*z^3 + 6300*a^18*b^
2*c^6*d^14*e^6*f^14*z^3 + 6300*a^14*b^6*c^14*d^6*e^2*f^18*z^3 + 6300*a^14*b^6*c^2*d^18*e^14*f^6*z^3 + 6300*a^6
*b^14*c^18*d^2*e^6*f^14*z^3 + 6300*a^6*b^14*c^6*d^14*e^18*f^2*z^3 + 6300*a^2*b^18*c^14*d^6*e^14*f^6*z^3 - 4260
*a^18*b^2*c^7*d^13*e^5*f^15*z^3 - 4260*a^18*b^2*c^5*d^15*e^7*f^13*z^3 - 4260*a^15*b^5*c^13*d^7*e^2*f^18*z^3 -
4260*a^15*b^5*c^2*d^18*e^13*f^7*z^3 - 4260*a^13*b^7*c^15*d^5*e^2*f^18*z^3 - 4260*a^13*b^7*c^2*d^18*e^15*f^5*z^
3 - 4260*a^7*b^13*c^18*d^2*e^5*f^15*z^3 - 4260*a^7*b^13*c^5*d^15*e^18*f^2*z^3 - 4260*a^5*b^15*c^18*d^2*e^7*f^1
3*z^3 - 4260*a^5*b^15*c^7*d^13*e^18*f^2*z^3 - 4260*a^2*b^18*c^15*d^5*e^13*f^7*z^3 - 4260*a^2*b^18*c^13*d^7*e^1
5*f^5*z^3 + 1470*a^17*b^3*c^10*d^10*e^3*f^17*z^3 + 1470*a^17*b^3*c^3*d^17*e^10*f^10*z^3 + 1470*a^10*b^10*c^17*
d^3*e^3*f^17*z^3 + 1470*a^10*b^10*c^3*d^17*e^17*f^3*z^3 + 1470*a^3*b^17*c^17*d^3*e^10*f^10*z^3 + 1470*a^3*b^17
*c^10*d^10*e^17*f^3*z^3 + 1350*a^18*b^2*c^9*d^11*e^3*f^17*z^3 + 1350*a^18*b^2*c^3*d^17*e^9*f^11*z^3 + 1350*a^1
7*b^3*c^11*d^9*e^2*f^18*z^3 + 1350*a^17*b^3*c^2*d^18*e^11*f^9*z^3 + 1350*a^11*b^9*c^17*d^3*e^2*f^18*z^3 + 1350
*a^11*b^9*c^2*d^18*e^17*f^3*z^3 + 1350*a^9*b^11*c^18*d^2*e^3*f^17*z^3 + 1350*a^9*b^11*c^3*d^17*e^18*f^2*z^3 +
1350*a^3*b^17*c^18*d^2*e^9*f^11*z^3 + 1350*a^3*b^17*c^9*d^11*e^18*f^2*z^3 + 1350*a^2*b^18*c^17*d^3*e^11*f^9*z^
3 + 1350*a^2*b^18*c^11*d^9*e^17*f^3*z^3 - 1070*a^18*b^2*c^10*d^10*e^2*f^18*z^3 - 1070*a^18*b^2*c^2*d^18*e^10*f
^10*z^3 - 1070*a^10*b^10*c^18*d^2*e^2*f^18*z^3 - 1070*a^10*b^10*c^2*d^18*e^18*f^2*z^3 - 1070*a^2*b^18*c^18*d^2
*e^10*f^10*z^3 - 1070*a^2*b^18*c^10*d^10*e^18*f^2*z^3 + 525*a^18*b^2*c^8*d^12*e^4*f^16*z^3 + 525*a^18*b^2*c^4*
d^16*e^8*f^12*z^3 + 525*a^16*b^4*c^12*d^8*e^2*f^18*z^3 + 525*a^16*b^4*c^2*d^18*e^12*f^8*z^3 + 525*a^12*b^8*c^1
6*d^4*e^2*f^18*z^3 + 525*a^12*b^8*c^2*d^18*e^16*f^4*z^3 + 525*a^8*b^12*c^18*d^2*e^4*f^16*z^3 + 525*a^8*b^12*c^
4*d^16*e^18*f^2*z^3 + 525*a^4*b^16*c^18*d^2*e^8*f^12*z^3 + 525*a^4*b^16*c^8*d^12*e^18*f^2*z^3 + 525*a^2*b^18*c
^16*d^4*e^12*f^8*z^3 + 525*a^2*b^18*c^12*d^8*e^16*f^4*z^3 + 900*a^19*b*c^7*d^13*e^4*f^16*z^3 + 900*a^19*b*c^4*
d^16*e^7*f^13*z^3 + 900*a^16*b^4*c^13*d^7*e*f^19*z^3 + 900*a^16*b^4*c*d^19*e^13*f^7*z^3 + 900*a^13*b^7*c^16*d^
4*e*f^19*z^3 + 900*a^13*b^7*c*d^19*e^16*f^4*z^3 + 900*a^7*b^13*c^19*d*e^4*f^16*z^3 + 900*a^7*b^13*c^4*d^16*e^1
9*f*z^3 + 900*a^4*b^16*c^19*d*e^7*f^13*z^3 + 900*a^4*b^16*c^7*d^13*e^19*f*z^3 + 900*a*b^19*c^16*d^4*e^13*f^7*z
^3 + 900*a*b^19*c^13*d^7*e^16*f^4*z^3 - 750*a^19*b*c^8*d^12*e^3*f^17*z^3 - 750*a^19*b*c^3*d^17*e^8*f^12*z^3 -
750*a^17*b^3*c^12*d^8*e*f^19*z^3 - 750*a^17*b^3*c*d^19*e^12*f^8*z^3 - 750*a^12*b^8*c^17*d^3*e*f^19*z^3 - 750*a
^12*b^8*c*d^19*e^17*f^3*z^3 - 750*a^8*b^12*c^19*d*e^3*f^17*z^3 - 750*a^8*b^12*c^3*d^17*e^19*f*z^3 - 750*a^3*b^
17*c^19*d*e^8*f^12*z^3 - 750*a^3*b^17*c^8*d^12*e^19*f*z^3 - 750*a*b^19*c^17*d^3*e^12*f^8*z^3 - 750*a*b^19*c^12
*d^8*e^17*f^3*z^3 - 420*a^19*b*c^6*d^14*e^5*f^15*z^3 - 420*a^19*b*c^5*d^15*e^6*f^14*z^3 - 420*a^15*b^5*c^14*d^
6*e*f^19*z^3 - 420*a^15*b^5*c*d^19*e^14*f^6*z^3 - 420*a^14*b^6*c^15*d^5*e*f^19*z^3 - 420*a^14*b^6*c*d^19*e^15*
f^5*z^3 - 420*a^6*b^14*c^19*d*e^5*f^15*z^3 - 420*a^6*b^14*c^5*d^15*e^19*f*z^3 - 420*a^5*b^15*c^19*d*e^6*f^14*z
^3 - 420*a^5*b^15*c^6*d^14*e^19*f*z^3 - 420*a*b^19*c^15*d^5*e^14*f^6*z^3 - 420*a*b^19*c^14*d^6*e^15*f^5*z^3 +
350*a^19*b*c^9*d^11*e^2*f^18*z^3 + 350*a^19*b*c^2*d^18*e^9*f^11*z^3 + 350*a^18*b^2*c^11*d^9*e*f^19*z^3 + 350*a
^18*b^2*c*d^19*e^11*f^9*z^3 + 350*a^11*b^9*c^18*d^2*e*f^19*z^3 + 350*a^11*b^9*c*d^19*e^18*f^2*z^3 + 350*a^9*b^
11*c^19*d*e^2*f^18*z^3 + 350*a^9*b^11*c^2*d^18*e^19*f*z^3 + 350*a^2*b^18*c^19*d*e^9*f^11*z^3 + 350*a^2*b^18*c^
9*d^11*e^19*f*z^3 + 350*a*b^19*c^18*d^2*e^11*f^9*z^3 + 350*a*b^19*c^11*d^9*e^18*f^2*z^3 - 90*a^19*b*c^10*d^10*
e*f^19*z^3 - 90*a^19*b*c*d^19*e^10*f^10*z^3 - 90*a^10*b^10*c^19*d*e*f^19*z^3 - 90*a^10*b^10*c*d^19*e^19*f*z^3
- 90*a*b^19*c^19*d*e^10*f^10*z^3 - 90*a*b^19*c^10*d^10*e^19*f*z^3 + 10*b^20*c^19*d*e^11*f^9*z^3 + 10*b^20*c^11
*d^9*e^19*f*z^3 + 10*a^20*c^9*d^11*e*f^19*z^3 + 10*a^20*c*d^19*e^9*f^11*z^3 + 10*a^19*b*d^20*e^11*f^9*z^3 + 10
*a^11*b^9*d^20*e^19*f*z^3 + 10*a^9*b^11*c^20*e*f^19*z^3 + 10*a*b^19*c^20*e^9*f^11*z^3 + 10*a^19*b*c^11*d^9*f^2
0*z^3 + 10*a^11*b^9*c^19*d*f^20*z^3 + 10*a^9*b^11*c*d^19*e^20*z^3 + 10*a*b^19*c^9*d^11*e^20*z^3 + 252*b^20*c^1
5*d^5*e^15*f^5*z^3 - 210*b^20*c^16*d^4*e^14*f^6*z^3 - 210*b^20*c^14*d^6*e^16*f^4*z^3 + 120*b^20*c^17*d^3*e^13*
f^7*z^3 + 120*b^20*c^13*d^7*e^17*f^3*z^3 - 45*b^20*c^18*d^2*e^12*f^8*z^3 - 45*b^20*c^12*d^8*e^18*f^2*z^3 + 252
*a^20*c^5*d^15*e^5*f^15*z^3 - 210*a^20*c^6*d^14*e^4*f^16*z^3 - 210*a^20*c^4*d^16*e^6*f^14*z^3 + 120*a^20*c^7*d
^13*e^3*f^17*z^3 + 120*a^20*c^3*d^17*e^7*f^13*z^3 - 45*a^20*c^8*d^12*e^2*f^18*z^3 - 45*a^20*c^2*d^18*e^8*f^12*
z^3 + 252*a^15*b^5*d^20*e^15*f^5*z^3 - 210*a^16*b^4*d^20*e^14*f^6*z^3 - 210*a^14*b^6*d^20*e^16*f^4*z^3 + 120*a
^17*b^3*d^20*e^13*f^7*z^3 + 120*a^13*b^7*d^20*e^17*f^3*z^3 - 45*a^18*b^2*d^20*e^12*f^8*z^3 - 45*a^12*b^8*d^20*
e^18*f^2*z^3 + 252*a^5*b^15*c^20*e^5*f^15*z^3 - 210*a^6*b^14*c^20*e^4*f^16*z^3 - 210*a^4*b^16*c^20*e^6*f^14*z^
3 + 120*a^7*b^13*c^20*e^3*f^17*z^3 + 120*a^3*b^17*c^20*e^7*f^13*z^3 - 45*a^8*b^12*c^20*e^2*f^18*z^3 - 45*a^2*b
^18*c^20*e^8*f^12*z^3 + 252*a^15*b^5*c^15*d^5*f^20*z^3 - 210*a^16*b^4*c^14*d^6*f^20*z^3 - 210*a^14*b^6*c^16*d^
4*f^20*z^3 + 120*a^17*b^3*c^13*d^7*f^20*z^3 + 120*a^13*b^7*c^17*d^3*f^20*z^3 - 45*a^18*b^2*c^12*d^8*f^20*z^3 -
45*a^12*b^8*c^18*d^2*f^20*z^3 + 252*a^5*b^15*c^5*d^15*e^20*z^3 - 210*a^6*b^14*c^4*d^16*e^20*z^3 - 210*a^4*b^1
6*c^6*d^14*e^20*z^3 + 120*a^7*b^13*c^3*d^17*e^20*z^3 + 120*a^3*b^17*c^7*d^13*e^20*z^3 - 45*a^8*b^12*c^2*d^18*e
^20*z^3 - 45*a^2*b^18*c^8*d^12*e^20*z^3 - b^20*c^20*e^10*f^10*z^3 - a^20*d^20*e^10*f^10*z^3 - b^20*c^10*d^10*e
^20*z^3 - a^20*c^10*d^10*f^20*z^3 - a^10*b^10*d^20*e^20*z^3 - a^10*b^10*c^20*f^20*z^3 + 1890*a^12*b^2*c*d^13*e
*f^13*z + 1890*a*b^13*c^12*d^2*e*f^13*z + 1890*a*b^13*c*d^13*e^12*f^2*z + 92610*a^6*b^8*c^4*d^10*e^4*f^10*z +
92610*a^4*b^10*c^6*d^8*e^4*f^10*z + 92610*a^4*b^10*c^4*d^10*e^6*f^8*z + 66150*a^8*b^6*c^3*d^11*e^3*f^11*z - 66
150*a^7*b^7*c^4*d^10*e^3*f^11*z - 66150*a^7*b^7*c^3*d^11*e^4*f^10*z - 66150*a^4*b^10*c^7*d^7*e^3*f^11*z - 6615
0*a^4*b^10*c^3*d^11*e^7*f^7*z + 66150*a^3*b^11*c^8*d^6*e^3*f^11*z - 66150*a^3*b^11*c^7*d^7*e^4*f^10*z - 66150*
a^3*b^11*c^4*d^10*e^7*f^7*z + 66150*a^3*b^11*c^3*d^11*e^8*f^6*z - 55566*a^5*b^9*c^5*d^9*e^4*f^10*z - 55566*a^5
*b^9*c^4*d^10*e^5*f^9*z - 55566*a^4*b^10*c^5*d^9*e^5*f^9*z - 32130*a^9*b^5*c^3*d^11*e^2*f^12*z - 32130*a^9*b^5
*c^2*d^12*e^3*f^11*z - 32130*a^3*b^11*c^9*d^5*e^2*f^12*z - 32130*a^3*b^11*c^2*d^12*e^9*f^5*z - 32130*a^2*b^12*
c^9*d^5*e^3*f^11*z - 32130*a^2*b^12*c^3*d^11*e^9*f^5*z + 22680*a^8*b^6*c^4*d^10*e^2*f^12*z + 22680*a^8*b^6*c^2
*d^12*e^4*f^10*z + 22680*a^4*b^10*c^8*d^6*e^2*f^12*z + 22680*a^4*b^10*c^2*d^12*e^8*f^6*z + 22680*a^2*b^12*c^8*
d^6*e^4*f^10*z + 22680*a^2*b^12*c^4*d^10*e^8*f^6*z + 19278*a^10*b^4*c^2*d^12*e^2*f^12*z + 19278*a^2*b^12*c^10*
d^4*e^2*f^12*z + 19278*a^2*b^12*c^2*d^12*e^10*f^4*z + 18522*a^6*b^8*c^5*d^9*e^3*f^11*z + 18522*a^6*b^8*c^3*d^1
1*e^5*f^9*z + 18522*a^5*b^9*c^6*d^8*e^3*f^11*z + 18522*a^5*b^9*c^3*d^11*e^6*f^8*z + 18522*a^3*b^11*c^6*d^8*e^5
*f^9*z + 18522*a^3*b^11*c^5*d^9*e^6*f^8*z - 13230*a^6*b^8*c^6*d^8*e^2*f^12*z - 13230*a^6*b^8*c^2*d^12*e^6*f^8*
z - 13230*a^2*b^12*c^6*d^8*e^6*f^8*z + 3402*a^7*b^7*c^5*d^9*e^2*f^12*z + 3402*a^7*b^7*c^2*d^12*e^5*f^9*z + 340
2*a^5*b^9*c^7*d^7*e^2*f^12*z + 3402*a^5*b^9*c^2*d^12*e^7*f^7*z + 3402*a^2*b^12*c^7*d^7*e^5*f^9*z + 3402*a^2*b^
12*c^5*d^9*e^7*f^7*z + 7938*a^10*b^4*c^3*d^11*e*f^13*z + 7938*a^10*b^4*c*d^13*e^3*f^11*z + 7938*a^3*b^11*c^10*
d^4*e*f^13*z + 7938*a^3*b^11*c*d^13*e^10*f^4*z + 7938*a*b^13*c^10*d^4*e^3*f^11*z + 7938*a*b^13*c^3*d^11*e^10*f
^4*z - 5670*a^11*b^3*c^2*d^12*e*f^13*z - 5670*a^11*b^3*c*d^13*e^2*f^12*z - 5670*a^2*b^12*c^11*d^3*e*f^13*z - 5
670*a^2*b^12*c*d^13*e^11*f^3*z - 5670*a*b^13*c^11*d^3*e^2*f^12*z - 5670*a*b^13*c^2*d^12*e^11*f^3*z - 3780*a^9*
b^5*c^4*d^10*e*f^13*z - 3780*a^9*b^5*c*d^13*e^4*f^10*z - 3780*a^4*b^10*c^9*d^5*e*f^13*z - 3780*a^4*b^10*c*d^13
*e^9*f^5*z - 3780*a*b^13*c^9*d^5*e^4*f^10*z - 3780*a*b^13*c^4*d^10*e^9*f^5*z - 2268*a^8*b^6*c^5*d^9*e*f^13*z -
2268*a^8*b^6*c*d^13*e^5*f^9*z - 2268*a^5*b^9*c^8*d^6*e*f^13*z - 2268*a^5*b^9*c*d^13*e^8*f^6*z - 2268*a*b^13*c
^8*d^6*e^5*f^9*z - 2268*a*b^13*c^5*d^9*e^8*f^6*z + 1890*a^7*b^7*c^6*d^8*e*f^13*z + 1890*a^7*b^7*c*d^13*e^6*f^8
*z + 1890*a^6*b^8*c^7*d^7*e*f^13*z + 1890*a^6*b^8*c*d^13*e^7*f^7*z + 1890*a*b^13*c^7*d^7*e^6*f^8*z + 1890*a*b^
13*c^6*d^8*e^7*f^7*z - 252*b^14*c^13*d*e*f^13*z - 252*b^14*c*d^13*e^13*f*z - 252*a^13*b*d^14*e*f^13*z - 252*a*
b^13*d^14*e^13*f*z - 252*a^13*b*c*d^13*f^14*z - 252*a*b^13*c^13*d*f^14*z - 918*b^14*c^7*d^7*e^7*f^7*z - 882*b^
14*c^11*d^3*e^3*f^11*z - 882*b^14*c^3*d^11*e^11*f^3*z + 693*b^14*c^12*d^2*e^2*f^12*z + 693*b^14*c^2*d^12*e^12*
f^2*z + 567*b^14*c^8*d^6*e^6*f^8*z + 567*b^14*c^6*d^8*e^8*f^6*z + 441*b^14*c^10*d^4*e^4*f^10*z + 441*b^14*c^4*
d^10*e^10*f^4*z - 126*b^14*c^9*d^5*e^5*f^9*z - 126*b^14*c^5*d^9*e^9*f^5*z - 918*a^7*b^7*d^14*e^7*f^7*z - 882*a
^11*b^3*d^14*e^3*f^11*z - 882*a^3*b^11*d^14*e^11*f^3*z + 693*a^12*b^2*d^14*e^2*f^12*z + 693*a^2*b^12*d^14*e^12
*f^2*z + 567*a^8*b^6*d^14*e^6*f^8*z + 567*a^6*b^8*d^14*e^8*f^6*z + 441*a^10*b^4*d^14*e^4*f^10*z + 441*a^4*b^10
*d^14*e^10*f^4*z - 126*a^9*b^5*d^14*e^5*f^9*z - 126*a^5*b^9*d^14*e^9*f^5*z - 918*a^7*b^7*c^7*d^7*f^14*z - 882*
a^11*b^3*c^3*d^11*f^14*z - 882*a^3*b^11*c^11*d^3*f^14*z + 693*a^12*b^2*c^2*d^12*f^14*z + 693*a^2*b^12*c^12*d^2
*f^14*z + 567*a^8*b^6*c^6*d^8*f^14*z + 567*a^6*b^8*c^8*d^6*f^14*z + 441*a^10*b^4*c^4*d^10*f^14*z + 441*a^4*b^1
0*c^10*d^4*f^14*z - 126*a^9*b^5*c^5*d^9*f^14*z - 126*a^5*b^9*c^9*d^5*f^14*z + 36*b^14*d^14*e^14*z + 36*b^14*c^
14*f^14*z + 36*a^14*d^14*f^14*z - 27054*a^2*b^9*c^2*d^9*e^2*f^9 + 9018*a^3*b^8*c^2*d^9*e*f^10 + 9018*a^3*b^8*c
*d^10*e^2*f^9 + 9018*a^2*b^9*c^3*d^8*e*f^10 + 9018*a^2*b^9*c*d^10*e^3*f^8 + 9018*a*b^10*c^3*d^8*e^2*f^9 + 9018
*a*b^10*c^2*d^9*e^3*f^8 - 9018*a^4*b^7*c*d^10*e*f^10 - 9018*a*b^10*c^4*d^7*e*f^10 - 9018*a*b^10*c*d^10*e^4*f^7
+ 2268*b^11*c^5*d^6*e*f^10 + 2268*b^11*c*d^10*e^5*f^6 + 2268*a^5*b^6*d^11*e*f^10 + 2268*a*b^10*d^11*e^5*f^6 +
2268*a^5*b^6*c*d^10*f^11 + 2268*a*b^10*c^5*d^6*f^11 - 1458*b^11*c^3*d^8*e^3*f^8 - 1161*b^11*c^4*d^7*e^2*f^9 -
1161*b^11*c^2*d^9*e^4*f^7 - 1458*a^3*b^8*d^11*e^3*f^8 - 1161*a^4*b^7*d^11*e^2*f^9 - 1161*a^2*b^9*d^11*e^4*f^7
- 1458*a^3*b^8*c^3*d^8*f^11 - 1161*a^4*b^7*c^2*d^9*f^11 - 1161*a^2*b^9*c^4*d^7*f^11 - 756*b^11*d^11*e^6*f^5 -
756*b^11*c^6*d^5*f^11 - 756*a^6*b^5*d^11*f^11, z, k), k, 1, 3) - ((7*a*b^6*c^2*d^5*e^7 - a^3*b^4*d^7*e^7 - a^
7*c^3*d^4*f^7 - b^7*c^3*d^4*e^7 - a^7*d^7*e^3*f^4 - b^7*c^7*e^3*f^4 - 6*a^5*b^2*c^5*d^2*f^7 - 6*a^5*b^2*d^7*e^
5*f^2 - 6*b^7*c^5*d^2*e^5*f^2 - a^3*b^4*c^7*f^7 + 7*a^2*b^5*c*d^6*e^7 + 4*a^4*b^3*c^6*d*f^7 + 4*a^6*b*c^4*d^3*
f^7 + 7*a*b^6*c^7*e^2*f^5 + 7*a^2*b^5*c^7*e*f^6 + 4*a^4*b^3*d^7*e^6*f + 4*a^6*b*d^7*e^4*f^3 + 7*a^7*c*d^6*e^2*
f^5 + 7*a^7*c^2*d^5*e*f^6 + 4*b^7*c^4*d^3*e^6*f + 4*b^7*c^6*d*e^4*f^3 - 21*a*b^6*c^3*d^4*e^6*f - 21*a*b^6*c^6*
d*e^3*f^4 - 21*a^3*b^4*c*d^6*e^6*f - 21*a^3*b^4*c^6*d*e*f^6 - 21*a^6*b*c*d^6*e^3*f^4 - 21*a^6*b*c^3*d^4*e*f^6
+ 14*a*b^6*c^4*d^3*e^5*f^2 + 14*a*b^6*c^5*d^2*e^4*f^3 - 26*a^2*b^5*c^2*d^5*e^6*f - 26*a^2*b^5*c^6*d*e^2*f^5 +
14*a^4*b^3*c*d^6*e^5*f^2 + 14*a^4*b^3*c^5*d^2*e*f^6 + 14*a^5*b^2*c*d^6*e^4*f^3 + 14*a^5*b^2*c^4*d^3*e*f^6 - 26
*a^6*b*c^2*d^5*e^2*f^5 + 52*a^2*b^5*c^3*d^4*e^5*f^2 - 78*a^2*b^5*c^4*d^3*e^4*f^3 + 52*a^2*b^5*c^5*d^2*e^3*f^4
+ 52*a^3*b^4*c^2*d^5*e^5*f^2 + 52*a^3*b^4*c^5*d^2*e^2*f^5 - 78*a^4*b^3*c^2*d^5*e^4*f^3 - 78*a^4*b^3*c^4*d^3*e^
2*f^5 + 52*a^5*b^2*c^2*d^5*e^3*f^4 + 52*a^5*b^2*c^3*d^4*e^2*f^5)/(2*(4*a*b^7*c^3*d^5*e^8 - a^4*b^4*d^8*e^8 - a
^8*c^4*d^4*f^8 - b^8*c^4*d^4*e^8 - a^8*d^8*e^4*f^4 - b^8*c^8*e^4*f^4 - 6*a^2*b^6*c^2*d^6*e^8 - 6*a^6*b^2*c^6*d
^2*f^8 - 6*a^2*b^6*c^8*e^2*f^6 - 6*a^6*b^2*d^8*e^6*f^2 - 6*a^8*c^2*d^6*e^2*f^6 - 6*b^8*c^6*d^2*e^6*f^2 - a^4*b
^4*c^8*f^8 + 4*a^3*b^5*c*d^7*e^8 + 4*a^5*b^3*c^7*d*f^8 + 4*a^7*b*c^5*d^3*f^8 + 4*a*b^7*c^8*e^3*f^5 + 4*a^3*b^5
*c^8*e*f^7 + 4*a^5*b^3*d^8*e^7*f + 4*a^7*b*d^8*e^5*f^3 + 4*a^8*c*d^7*e^3*f^5 + 4*a^8*c^3*d^5*e*f^7 + 4*b^8*c^5
*d^3*e^7*f + 4*b^8*c^7*d*e^5*f^3 - 12*a*b^7*c^4*d^4*e^7*f - 12*a*b^7*c^7*d*e^4*f^4 - 12*a^4*b^4*c*d^7*e^7*f -
12*a^4*b^4*c^7*d*e*f^7 - 12*a^7*b*c*d^7*e^4*f^4 - 12*a^7*b*c^4*d^4*e*f^7 + 8*a*b^7*c^5*d^3*e^6*f^2 + 8*a*b^7*c
^6*d^2*e^5*f^3 + 8*a^2*b^6*c^3*d^5*e^7*f + 8*a^2*b^6*c^7*d*e^3*f^5 + 8*a^3*b^5*c^2*d^6*e^7*f + 8*a^3*b^5*c^7*d
*e^2*f^6 + 8*a^5*b^3*c*d^7*e^6*f^2 + 8*a^5*b^3*c^6*d^2*e*f^7 + 8*a^6*b^2*c*d^7*e^5*f^3 + 8*a^6*b^2*c^5*d^3*e*f
^7 + 8*a^7*b*c^2*d^6*e^3*f^5 + 8*a^7*b*c^3*d^5*e^2*f^6 + 22*a^2*b^6*c^4*d^4*e^6*f^2 - 48*a^2*b^6*c^5*d^3*e^5*f
^3 + 22*a^2*b^6*c^6*d^2*e^4*f^4 - 48*a^3*b^5*c^3*d^5*e^6*f^2 + 36*a^3*b^5*c^4*d^4*e^5*f^3 + 36*a^3*b^5*c^5*d^3
*e^4*f^4 - 48*a^3*b^5*c^6*d^2*e^3*f^5 + 22*a^4*b^4*c^2*d^6*e^6*f^2 + 36*a^4*b^4*c^3*d^5*e^5*f^3 - 90*a^4*b^4*c
^4*d^4*e^4*f^4 + 36*a^4*b^4*c^5*d^3*e^3*f^5 + 22*a^4*b^4*c^6*d^2*e^2*f^6 - 48*a^5*b^3*c^2*d^6*e^5*f^3 + 36*a^5
*b^3*c^3*d^5*e^4*f^4 + 36*a^5*b^3*c^4*d^4*e^3*f^5 - 48*a^5*b^3*c^5*d^3*e^2*f^6 + 22*a^6*b^2*c^2*d^6*e^4*f^4 -
48*a^6*b^2*c^3*d^5*e^3*f^5 + 22*a^6*b^2*c^4*d^4*e^2*f^6)) + (3*x^5*(2*a^5*b^2*d^7*f^7 + 2*b^7*c^5*d^2*f^7 + 2*
b^7*d^7*e^5*f^2 + 2*a^2*b^5*c^3*d^4*f^7 + 2*a^3*b^4*c^2*d^5*f^7 + 2*a^2*b^5*d^7*e^3*f^4 + 2*a^3*b^4*d^7*e^2*f^
5 + 2*b^7*c^2*d^5*e^3*f^4 + 2*b^7*c^3*d^4*e^2*f^5 - 5*a*b^6*c^4*d^3*f^7 - 5*a^4*b^3*c*d^6*f^7 - 5*a*b^6*d^7*e^
4*f^3 - 5*a^4*b^3*d^7*e*f^6 - 5*b^7*c*d^6*e^4*f^3 - 5*b^7*c^4*d^3*e*f^6 + 16*a*b^6*c*d^6*e^3*f^4 + 16*a*b^6*c^
3*d^4*e*f^6 + 16*a^3*b^4*c*d^6*e*f^6 - 12*a*b^6*c^2*d^5*e^2*f^5 - 12*a^2*b^5*c*d^6*e^2*f^5 - 12*a^2*b^5*c^2*d^
5*e*f^6))/(4*a*b^7*c^3*d^5*e^8 - a^4*b^4*d^8*e^8 - a^8*c^4*d^4*f^8 - b^8*c^4*d^4*e^8 - a^8*d^8*e^4*f^4 - b^8*c
^8*e^4*f^4 - 6*a^2*b^6*c^2*d^6*e^8 - 6*a^6*b^2*c^6*d^2*f^8 - 6*a^2*b^6*c^8*e^2*f^6 - 6*a^6*b^2*d^8*e^6*f^2 - 6
*a^8*c^2*d^6*e^2*f^6 - 6*b^8*c^6*d^2*e^6*f^2 - a^4*b^4*c^8*f^8 + 4*a^3*b^5*c*d^7*e^8 + 4*a^5*b^3*c^7*d*f^8 + 4
*a^7*b*c^5*d^3*f^8 + 4*a*b^7*c^8*e^3*f^5 + 4*a^3*b^5*c^8*e*f^7 + 4*a^5*b^3*d^8*e^7*f + 4*a^7*b*d^8*e^5*f^3 + 4
*a^8*c*d^7*e^3*f^5 + 4*a^8*c^3*d^5*e*f^7 + 4*b^8*c^5*d^3*e^7*f + 4*b^8*c^7*d*e^5*f^3 - 12*a*b^7*c^4*d^4*e^7*f
- 12*a*b^7*c^7*d*e^4*f^4 - 12*a^4*b^4*c*d^7*e^7*f - 12*a^4*b^4*c^7*d*e*f^7 - 12*a^7*b*c*d^7*e^4*f^4 - 12*a^7*b
*c^4*d^4*e*f^7 + 8*a*b^7*c^5*d^3*e^6*f^2 + 8*a*b^7*c^6*d^2*e^5*f^3 + 8*a^2*b^6*c^3*d^5*e^7*f + 8*a^2*b^6*c^7*d
*e^3*f^5 + 8*a^3*b^5*c^2*d^6*e^7*f + 8*a^3*b^5*c^7*d*e^2*f^6 + 8*a^5*b^3*c*d^7*e^6*f^2 + 8*a^5*b^3*c^6*d^2*e*f
^7 + 8*a^6*b^2*c*d^7*e^5*f^3 + 8*a^6*b^2*c^5*d^3*e*f^7 + 8*a^7*b*c^2*d^6*e^3*f^5 + 8*a^7*b*c^3*d^5*e^2*f^6 + 2
2*a^2*b^6*c^4*d^4*e^6*f^2 - 48*a^2*b^6*c^5*d^3*e^5*f^3 + 22*a^2*b^6*c^6*d^2*e^4*f^4 - 48*a^3*b^5*c^3*d^5*e^6*f
^2 + 36*a^3*b^5*c^4*d^4*e^5*f^3 + 36*a^3*b^5*c^5*d^3*e^4*f^4 - 48*a^3*b^5*c^6*d^2*e^3*f^5 + 22*a^4*b^4*c^2*d^6
*e^6*f^2 + 36*a^4*b^4*c^3*d^5*e^5*f^3 - 90*a^4*b^4*c^4*d^4*e^4*f^4 + 36*a^4*b^4*c^5*d^3*e^3*f^5 + 22*a^4*b^4*c
^6*d^2*e^2*f^6 - 48*a^5*b^3*c^2*d^6*e^5*f^3 + 36*a^5*b^3*c^3*d^5*e^4*f^4 + 36*a^5*b^3*c^4*d^4*e^3*f^5 - 48*a^5
*b^3*c^5*d^3*e^2*f^6 + 22*a^6*b^2*c^2*d^6*e^4*f^4 - 48*a^6*b^2*c^3*d^5*e^3*f^5 + 22*a^6*b^2*c^4*d^4*e^2*f^6) +
(3*x^4*(8*a^6*b*d^7*f^7 + 8*b^7*c^6*d*f^7 + 8*b^7*d^7*e^6*f - 7*a^2*b^5*c^4*d^3*f^7 + 14*a^3*b^4*c^3*d^4*f^7
- 7*a^4*b^3*c^2*d^5*f^7 - 7*a^2*b^5*d^7*e^4*f^3 + 14*a^3*b^4*d^7*e^3*f^4 - 7*a^4*b^3*d^7*e^2*f^5 - 7*b^7*c^2*d
^5*e^4*f^3 + 14*b^7*c^3*d^4*e^3*f^4 - 7*b^7*c^4*d^3*e^2*f^5 - 14*a*b^6*c^5*d^2*f^7 - 14*a^5*b^2*c*d^6*f^7 - 14
*a*b^6*d^7*e^5*f^2 - 14*a^5*b^2*d^7*e*f^6 - 14*b^7*c*d^6*e^5*f^2 - 14*b^7*c^5*d^2*e*f^6 + 34*a*b^6*c*d^6*e^4*f
^3 + 34*a*b^6*c^4*d^3*e*f^6 + 34*a^4*b^3*c*d^6*e*f^6 + 6*a*b^6*c^2*d^5*e^3*f^4 + 6*a*b^6*c^3*d^4*e^2*f^5 + 6*a
^2*b^5*c*d^6*e^3*f^4 + 6*a^2*b^5*c^3*d^4*e*f^6 + 6*a^3*b^4*c*d^6*e^2*f^5 + 6*a^3*b^4*c^2*d^5*e*f^6 - 78*a^2*b^
5*c^2*d^5*e^2*f^5))/(2*(4*a*b^7*c^3*d^5*e^8 - a^4*b^4*d^8*e^8 - a^8*c^4*d^4*f^8 - b^8*c^4*d^4*e^8 - a^8*d^8*e^
4*f^4 - b^8*c^8*e^4*f^4 - 6*a^2*b^6*c^2*d^6*e^8 - 6*a^6*b^2*c^6*d^2*f^8 - 6*a^2*b^6*c^8*e^2*f^6 - 6*a^6*b^2*d^
8*e^6*f^2 - 6*a^8*c^2*d^6*e^2*f^6 - 6*b^8*c^6*d^2*e^6*f^2 - a^4*b^4*c^8*f^8 + 4*a^3*b^5*c*d^7*e^8 + 4*a^5*b^3*
c^7*d*f^8 + 4*a^7*b*c^5*d^3*f^8 + 4*a*b^7*c^8*e^3*f^5 + 4*a^3*b^5*c^8*e*f^7 + 4*a^5*b^3*d^8*e^7*f + 4*a^7*b*d^
8*e^5*f^3 + 4*a^8*c*d^7*e^3*f^5 + 4*a^8*c^3*d^5*e*f^7 + 4*b^8*c^5*d^3*e^7*f + 4*b^8*c^7*d*e^5*f^3 - 12*a*b^7*c
^4*d^4*e^7*f - 12*a*b^7*c^7*d*e^4*f^4 - 12*a^4*b^4*c*d^7*e^7*f - 12*a^4*b^4*c^7*d*e*f^7 - 12*a^7*b*c*d^7*e^4*f
^4 - 12*a^7*b*c^4*d^4*e*f^7 + 8*a*b^7*c^5*d^3*e^6*f^2 + 8*a*b^7*c^6*d^2*e^5*f^3 + 8*a^2*b^6*c^3*d^5*e^7*f + 8*
a^2*b^6*c^7*d*e^3*f^5 + 8*a^3*b^5*c^2*d^6*e^7*f + 8*a^3*b^5*c^7*d*e^2*f^6 + 8*a^5*b^3*c*d^7*e^6*f^2 + 8*a^5*b^
3*c^6*d^2*e*f^7 + 8*a^6*b^2*c*d^7*e^5*f^3 + 8*a^6*b^2*c^5*d^3*e*f^7 + 8*a^7*b*c^2*d^6*e^3*f^5 + 8*a^7*b*c^3*d^
5*e^2*f^6 + 22*a^2*b^6*c^4*d^4*e^6*f^2 - 48*a^2*b^6*c^5*d^3*e^5*f^3 + 22*a^2*b^6*c^6*d^2*e^4*f^4 - 48*a^3*b^5*
c^3*d^5*e^6*f^2 + 36*a^3*b^5*c^4*d^4*e^5*f^3 + 36*a^3*b^5*c^5*d^3*e^4*f^4 - 48*a^3*b^5*c^6*d^2*e^3*f^5 + 22*a^
4*b^4*c^2*d^6*e^6*f^2 + 36*a^4*b^4*c^3*d^5*e^5*f^3 - 90*a^4*b^4*c^4*d^4*e^4*f^4 + 36*a^4*b^4*c^5*d^3*e^3*f^5 +
22*a^4*b^4*c^6*d^2*e^2*f^6 - 48*a^5*b^3*c^2*d^6*e^5*f^3 + 36*a^5*b^3*c^3*d^5*e^4*f^4 + 36*a^5*b^3*c^4*d^4*e^3
*f^5 - 48*a^5*b^3*c^5*d^3*e^2*f^6 + 22*a^6*b^2*c^2*d^6*e^4*f^4 - 48*a^6*b^2*c^3*d^5*e^3*f^5 + 22*a^6*b^2*c^4*d
^4*e^2*f^6)) + (x^2*(18*a*b^6*c^7*f^7 + 18*a*b^6*d^7*e^7 + 18*a^7*c*d^6*f^7 + 18*b^7*c*d^6*e^7 + 18*a^7*d^7*e*
f^6 + 18*b^7*c^7*e*f^6 - 3*a^3*b^4*c^5*d^2*f^7 + 32*a^4*b^3*c^4*d^3*f^7 - 3*a^5*b^2*c^3*d^4*f^7 - 3*a^3*b^4*d^
7*e^5*f^2 + 32*a^4*b^3*d^7*e^4*f^3 - 3*a^5*b^2*d^7*e^3*f^4 - 3*b^7*c^3*d^4*e^5*f^2 + 32*b^7*c^4*d^3*e^4*f^3 -
3*b^7*c^5*d^2*e^3*f^4 - 37*a^2*b^5*c^6*d*f^7 - 37*a^6*b*c^2*d^5*f^7 - 37*a^2*b^5*d^7*e^6*f - 37*a^6*b*d^7*e^2*
f^5 - 37*b^7*c^2*d^5*e^6*f - 37*b^7*c^6*d*e^2*f^5 + 9*a*b^6*c^2*d^5*e^5*f^2 + a*b^6*c^3*d^4*e^4*f^3 + a*b^6*c^
4*d^3*e^3*f^4 + 9*a*b^6*c^5*d^2*e^2*f^5 + 9*a^2*b^5*c*d^6*e^5*f^2 + 9*a^2*b^5*c^5*d^2*e*f^6 + a^3*b^4*c*d^6*e^
4*f^3 + a^3*b^4*c^4*d^3*e*f^6 + a^4*b^3*c*d^6*e^3*f^4 + a^4*b^3*c^3*d^4*e*f^6 + 9*a^5*b^2*c*d^6*e^2*f^5 + 9*a^
5*b^2*c^2*d^5*e*f^6 - 34*a*b^6*c*d^6*e^6*f - 34*a*b^6*c^6*d*e*f^6 - 34*a^6*b*c*d^6*e*f^6 + 234*a^2*b^5*c^2*d^5
*e^4*f^3 - 208*a^2*b^5*c^3*d^4*e^3*f^4 + 234*a^2*b^5*c^4*d^3*e^2*f^5 - 208*a^3*b^4*c^2*d^5*e^3*f^4 - 208*a^3*b
^4*c^3*d^4*e^2*f^5 + 234*a^4*b^3*c^2*d^5*e^2*f^5))/(2*(4*a*b^7*c^3*d^5*e^8 - a^4*b^4*d^8*e^8 - a^8*c^4*d^4*f^8
- b^8*c^4*d^4*e^8 - a^8*d^8*e^4*f^4 - b^8*c^8*e^4*f^4 - 6*a^2*b^6*c^2*d^6*e^8 - 6*a^6*b^2*c^6*d^2*f^8 - 6*a^2
*b^6*c^8*e^2*f^6 - 6*a^6*b^2*d^8*e^6*f^2 - 6*a^8*c^2*d^6*e^2*f^6 - 6*b^8*c^6*d^2*e^6*f^2 - a^4*b^4*c^8*f^8 + 4
*a^3*b^5*c*d^7*e^8 + 4*a^5*b^3*c^7*d*f^8 + 4*a^7*b*c^5*d^3*f^8 + 4*a*b^7*c^8*e^3*f^5 + 4*a^3*b^5*c^8*e*f^7 + 4
*a^5*b^3*d^8*e^7*f + 4*a^7*b*d^8*e^5*f^3 + 4*a^8*c*d^7*e^3*f^5 + 4*a^8*c^3*d^5*e*f^7 + 4*b^8*c^5*d^3*e^7*f + 4
*b^8*c^7*d*e^5*f^3 - 12*a*b^7*c^4*d^4*e^7*f - 12*a*b^7*c^7*d*e^4*f^4 - 12*a^4*b^4*c*d^7*e^7*f - 12*a^4*b^4*c^7
*d*e*f^7 - 12*a^7*b*c*d^7*e^4*f^4 - 12*a^7*b*c^4*d^4*e*f^7 + 8*a*b^7*c^5*d^3*e^6*f^2 + 8*a*b^7*c^6*d^2*e^5*f^3
+ 8*a^2*b^6*c^3*d^5*e^7*f + 8*a^2*b^6*c^7*d*e^3*f^5 + 8*a^3*b^5*c^2*d^6*e^7*f + 8*a^3*b^5*c^7*d*e^2*f^6 + 8*a
^5*b^3*c*d^7*e^6*f^2 + 8*a^5*b^3*c^6*d^2*e*f^7 + 8*a^6*b^2*c*d^7*e^5*f^3 + 8*a^6*b^2*c^5*d^3*e*f^7 + 8*a^7*b*c
^2*d^6*e^3*f^5 + 8*a^7*b*c^3*d^5*e^2*f^6 + 22*a^2*b^6*c^4*d^4*e^6*f^2 - 48*a^2*b^6*c^5*d^3*e^5*f^3 + 22*a^2*b^
6*c^6*d^2*e^4*f^4 - 48*a^3*b^5*c^3*d^5*e^6*f^2 + 36*a^3*b^5*c^4*d^4*e^5*f^3 + 36*a^3*b^5*c^5*d^3*e^4*f^4 - 48*
a^3*b^5*c^6*d^2*e^3*f^5 + 22*a^4*b^4*c^2*d^6*e^6*f^2 + 36*a^4*b^4*c^3*d^5*e^5*f^3 - 90*a^4*b^4*c^4*d^4*e^4*f^4
+ 36*a^4*b^4*c^5*d^3*e^3*f^5 + 22*a^4*b^4*c^6*d^2*e^2*f^6 - 48*a^5*b^3*c^2*d^6*e^5*f^3 + 36*a^5*b^3*c^3*d^5*e
^4*f^4 + 36*a^5*b^3*c^4*d^4*e^3*f^5 - 48*a^5*b^3*c^5*d^3*e^2*f^6 + 22*a^6*b^2*c^2*d^6*e^4*f^4 - 48*a^6*b^2*c^3
*d^5*e^3*f^5 + 22*a^6*b^2*c^4*d^4*e^2*f^6)) + (x*(2*a^2*b^5*c^7*f^7 + 2*a^2*b^5*d^7*e^7 + 2*a^7*c^2*d^5*f^7 +
2*b^7*c^2*d^5*e^7 + 2*a^7*d^7*e^2*f^5 + 2*b^7*c^7*e^2*f^5 + 4*a^4*b^3*c^5*d^2*f^7 + 4*a^5*b^2*c^4*d^3*f^7 + 4*
a^4*b^3*d^7*e^5*f^2 + 4*a^5*b^2*d^7*e^4*f^3 + 4*b^7*c^4*d^3*e^5*f^2 + 4*b^7*c^5*d^2*e^4*f^3 + 14*a*b^6*c*d^6*e
^7 + 14*a*b^6*c^7*e*f^6 + 14*a^7*c*d^6*e*f^6 - 6*a^3*b^4*c^6*d*f^7 - 6*a^6*b*c^3*d^4*f^7 - 6*a^3*b^4*d^7*e^6*f
- 6*a^6*b*d^7*e^3*f^4 - 6*b^7*c^3*d^4*e^6*f - 6*b^7*c^6*d*e^3*f^4 - 33*a*b^6*c^2*d^5*e^6*f - 33*a*b^6*c^6*d*e
^2*f^5 - 33*a^2*b^5*c*d^6*e^6*f - 33*a^2*b^5*c^6*d*e*f^6 - 33*a^6*b*c*d^6*e^2*f^5 - 33*a^6*b*c^2*d^5*e*f^6 + 1
7*a*b^6*c^3*d^4*e^5*f^2 - 8*a*b^6*c^4*d^3*e^4*f^3 + 17*a*b^6*c^5*d^2*e^3*f^4 + 17*a^3*b^4*c*d^6*e^5*f^2 + 17*a
^3*b^4*c^5*d^2*e*f^6 - 8*a^4*b^3*c*d^6*e^4*f^3 - 8*a^4*b^3*c^4*d^3*e*f^6 + 17*a^5*b^2*c*d^6*e^3*f^4 + 17*a^5*b
^2*c^3*d^4*e*f^6 + 78*a^2*b^5*c^2*d^5*e^5*f^2 - 26*a^2*b^5*c^3*d^4*e^4*f^3 - 26*a^2*b^5*c^4*d^3*e^3*f^4 + 78*a
^2*b^5*c^5*d^2*e^2*f^5 - 26*a^3*b^4*c^2*d^5*e^4*f^3 - 26*a^3*b^4*c^4*d^3*e^2*f^5 - 26*a^4*b^3*c^2*d^5*e^3*f^4
- 26*a^4*b^3*c^3*d^4*e^2*f^5 + 78*a^5*b^2*c^2*d^5*e^2*f^5))/(4*a*b^7*c^3*d^5*e^8 - a^4*b^4*d^8*e^8 - a^8*c^4*d
^4*f^8 - b^8*c^4*d^4*e^8 - a^8*d^8*e^4*f^4 - b^8*c^8*e^4*f^4 - 6*a^2*b^6*c^2*d^6*e^8 - 6*a^6*b^2*c^6*d^2*f^8 -
6*a^2*b^6*c^8*e^2*f^6 - 6*a^6*b^2*d^8*e^6*f^2 - 6*a^8*c^2*d^6*e^2*f^6 - 6*b^8*c^6*d^2*e^6*f^2 - a^4*b^4*c^8*f
^8 + 4*a^3*b^5*c*d^7*e^8 + 4*a^5*b^3*c^7*d*f^8 + 4*a^7*b*c^5*d^3*f^8 + 4*a*b^7*c^8*e^3*f^5 + 4*a^3*b^5*c^8*e*f
^7 + 4*a^5*b^3*d^8*e^7*f + 4*a^7*b*d^8*e^5*f^3 + 4*a^8*c*d^7*e^3*f^5 + 4*a^8*c^3*d^5*e*f^7 + 4*b^8*c^5*d^3*e^7
*f + 4*b^8*c^7*d*e^5*f^3 - 12*a*b^7*c^4*d^4*e^7*f - 12*a*b^7*c^7*d*e^4*f^4 - 12*a^4*b^4*c*d^7*e^7*f - 12*a^4*b
^4*c^7*d*e*f^7 - 12*a^7*b*c*d^7*e^4*f^4 - 12*a^7*b*c^4*d^4*e*f^7 + 8*a*b^7*c^5*d^3*e^6*f^2 + 8*a*b^7*c^6*d^2*e
^5*f^3 + 8*a^2*b^6*c^3*d^5*e^7*f + 8*a^2*b^6*c^7*d*e^3*f^5 + 8*a^3*b^5*c^2*d^6*e^7*f + 8*a^3*b^5*c^7*d*e^2*f^6
+ 8*a^5*b^3*c*d^7*e^6*f^2 + 8*a^5*b^3*c^6*d^2*e*f^7 + 8*a^6*b^2*c*d^7*e^5*f^3 + 8*a^6*b^2*c^5*d^3*e*f^7 + 8*a
^7*b*c^2*d^6*e^3*f^5 + 8*a^7*b*c^3*d^5*e^2*f^6 + 22*a^2*b^6*c^4*d^4*e^6*f^2 - 48*a^2*b^6*c^5*d^3*e^5*f^3 + 22*
a^2*b^6*c^6*d^2*e^4*f^4 - 48*a^3*b^5*c^3*d^5*e^6*f^2 + 36*a^3*b^5*c^4*d^4*e^5*f^3 + 36*a^3*b^5*c^5*d^3*e^4*f^4
- 48*a^3*b^5*c^6*d^2*e^3*f^5 + 22*a^4*b^4*c^2*d^6*e^6*f^2 + 36*a^4*b^4*c^3*d^5*e^5*f^3 - 90*a^4*b^4*c^4*d^4*e
^4*f^4 + 36*a^4*b^4*c^5*d^3*e^3*f^5 + 22*a^4*b^4*c^6*d^2*e^2*f^6 - 48*a^5*b^3*c^2*d^6*e^5*f^3 + 36*a^5*b^3*c^3
*d^5*e^4*f^4 + 36*a^5*b^3*c^4*d^4*e^3*f^5 - 48*a^5*b^3*c^5*d^3*e^2*f^6 + 22*a^6*b^2*c^2*d^6*e^4*f^4 - 48*a^6*b
^2*c^3*d^5*e^3*f^5 + 22*a^6*b^2*c^4*d^4*e^2*f^6) + (x^3*(6*a^7*d^7*f^7 + 6*b^7*c^7*f^7 + 6*b^7*d^7*e^7 - 37*a^
2*b^5*c^5*d^2*f^7 + 19*a^3*b^4*c^4*d^3*f^7 + 19*a^4*b^3*c^3*d^4*f^7 - 37*a^5*b^2*c^2*d^5*f^7 - 37*a^2*b^5*d^7*
e^5*f^2 + 19*a^3*b^4*d^7*e^4*f^3 + 19*a^4*b^3*d^7*e^3*f^4 - 37*a^5*b^2*d^7*e^2*f^5 - 37*b^7*c^2*d^5*e^5*f^2 +
19*b^7*c^3*d^4*e^4*f^3 + 19*b^7*c^4*d^3*e^3*f^4 - 37*b^7*c^5*d^2*e^2*f^5 + 3*a*b^6*c^6*d*f^7 + 3*a^6*b*c*d^6*f
^7 + 3*a*b^6*d^7*e^6*f + 3*a^6*b*d^7*e*f^6 + 3*b^7*c*d^6*e^6*f + 3*b^7*c^6*d*e*f^6 - 28*a*b^6*c*d^6*e^5*f^2 -
28*a*b^6*c^5*d^2*e*f^6 - 28*a^5*b^2*c*d^6*e*f^6 + 86*a*b^6*c^2*d^5*e^4*f^3 - 68*a*b^6*c^3*d^4*e^3*f^4 + 86*a*b
^6*c^4*d^3*e^2*f^5 + 86*a^2*b^5*c*d^6*e^4*f^3 + 86*a^2*b^5*c^4*d^3*e*f^6 - 68*a^3*b^4*c*d^6*e^3*f^4 - 68*a^3*b
^4*c^3*d^4*e*f^6 + 86*a^4*b^3*c*d^6*e^2*f^5 + 86*a^4*b^3*c^2*d^5*e*f^6 - 52*a^2*b^5*c^2*d^5*e^3*f^4 - 52*a^2*b
^5*c^3*d^4*e^2*f^5 - 52*a^3*b^4*c^2*d^5*e^2*f^5))/(4*a*b^7*c^3*d^5*e^8 - a^4*b^4*d^8*e^8 - a^8*c^4*d^4*f^8 - b
^8*c^4*d^4*e^8 - a^8*d^8*e^4*f^4 - b^8*c^8*e^4*f^4 - 6*a^2*b^6*c^2*d^6*e^8 - 6*a^6*b^2*c^6*d^2*f^8 - 6*a^2*b^6
*c^8*e^2*f^6 - 6*a^6*b^2*d^8*e^6*f^2 - 6*a^8*c^2*d^6*e^2*f^6 - 6*b^8*c^6*d^2*e^6*f^2 - a^4*b^4*c^8*f^8 + 4*a^3
*b^5*c*d^7*e^8 + 4*a^5*b^3*c^7*d*f^8 + 4*a^7*b*c^5*d^3*f^8 + 4*a*b^7*c^8*e^3*f^5 + 4*a^3*b^5*c^8*e*f^7 + 4*a^5
*b^3*d^8*e^7*f + 4*a^7*b*d^8*e^5*f^3 + 4*a^8*c*d^7*e^3*f^5 + 4*a^8*c^3*d^5*e*f^7 + 4*b^8*c^5*d^3*e^7*f + 4*b^8
*c^7*d*e^5*f^3 - 12*a*b^7*c^4*d^4*e^7*f - 12*a*b^7*c^7*d*e^4*f^4 - 12*a^4*b^4*c*d^7*e^7*f - 12*a^4*b^4*c^7*d*e
*f^7 - 12*a^7*b*c*d^7*e^4*f^4 - 12*a^7*b*c^4*d^4*e*f^7 + 8*a*b^7*c^5*d^3*e^6*f^2 + 8*a*b^7*c^6*d^2*e^5*f^3 + 8
*a^2*b^6*c^3*d^5*e^7*f + 8*a^2*b^6*c^7*d*e^3*f^5 + 8*a^3*b^5*c^2*d^6*e^7*f + 8*a^3*b^5*c^7*d*e^2*f^6 + 8*a^5*b
^3*c*d^7*e^6*f^2 + 8*a^5*b^3*c^6*d^2*e*f^7 + 8*a^6*b^2*c*d^7*e^5*f^3 + 8*a^6*b^2*c^5*d^3*e*f^7 + 8*a^7*b*c^2*d
^6*e^3*f^5 + 8*a^7*b*c^3*d^5*e^2*f^6 + 22*a^2*b^6*c^4*d^4*e^6*f^2 - 48*a^2*b^6*c^5*d^3*e^5*f^3 + 22*a^2*b^6*c^
6*d^2*e^4*f^4 - 48*a^3*b^5*c^3*d^5*e^6*f^2 + 36*a^3*b^5*c^4*d^4*e^5*f^3 + 36*a^3*b^5*c^5*d^3*e^4*f^4 - 48*a^3*
b^5*c^6*d^2*e^3*f^5 + 22*a^4*b^4*c^2*d^6*e^6*f^2 + 36*a^4*b^4*c^3*d^5*e^5*f^3 - 90*a^4*b^4*c^4*d^4*e^4*f^4 + 3
6*a^4*b^4*c^5*d^3*e^3*f^5 + 22*a^4*b^4*c^6*d^2*e^2*f^6 - 48*a^5*b^3*c^2*d^6*e^5*f^3 + 36*a^5*b^3*c^3*d^5*e^4*f
^4 + 36*a^5*b^3*c^4*d^4*e^3*f^5 - 48*a^5*b^3*c^5*d^3*e^2*f^6 + 22*a^6*b^2*c^2*d^6*e^4*f^4 - 48*a^6*b^2*c^3*d^5
*e^3*f^5 + 22*a^6*b^2*c^4*d^4*e^2*f^6))/(x*(2*a*b*c^2*e^2 + 2*a^2*c*d*e^2 + 2*a^2*c^2*e*f) + x^3*(2*a*b*c^2*f^
2 + 2*a*b*d^2*e^2 + 2*a^2*c*d*f^2 + 2*b^2*c*d*e^2 + 2*a^2*d^2*e*f + 2*b^2*c^2*e*f + 8*a*b*c*d*e*f) + x^2*(a^2*
c^2*f^2 + a^2*d^2*e^2 + b^2*c^2*e^2 + 4*a*b*c*d*e^2 + 4*a*b*c^2*e*f + 4*a^2*c*d*e*f) + x^5*(2*a*b*d^2*f^2 + 2*
b^2*c*d*f^2 + 2*b^2*d^2*e*f) + x^4*(a^2*d^2*f^2 + b^2*c^2*f^2 + b^2*d^2*e^2 + 4*a*b*c*d*f^2 + 4*a*b*d^2*e*f +
4*b^2*c*d*e*f) + a^2*c^2*e^2 + b^2*d^2*f^2*x^6)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(a*c*e+(a*c*f+a*d*e+b*c*e)*x+(a*d*f+b*c*f+b*d*e)*x**2+b*d*f*x**3)**3,x)

[Out]

Timed out

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