## Παρασκευή, 29 Νοεμβρίου 2013

### PERSPECTIVITY - LOCUS

Let ABC be a triangle, P a point and A'B'C' the cevian triangle of P.

Denote:

Ab = the other than B intersection of the circle with diameter BA' and the circumcircle.

Ac = the other than C intersection of the circle with diameter CA' and the circumcircle.

Similarly (cyclically): Bc, Ba and Ca, Cb

Which is the locus of P such that:

1. ABC, Triangle bounded by (AbAc, BcBa, CaCb) are perspective?

Answer: The entire plane. Reference.

2. ABC, Triangle bounded by (BcCb, CaAc, AbBa) are perspective? The entire plane?

Special case: BcCb, CaAc, AbBa are concurrent.

3. Triangle bounded by (AbAc, BcBa, CaCb) and Triangle bounded by (BcCb, CaAc, AbBa) are perspective?

Antreas P. Hatzipolakis, 29 Nov. 2013

______________________________________

Which is the locus of P such that:

1. ABC, Triangle bounded by (AbAc, BcBa, CaCb) are perspective?

Answer: The entire plane.

**** Perspector, if P=(u:v:w) (baricentric coordinates):

Q =( a^2 (a^2 - b^2 - c^2)/(-2 a^2 c^2 u^2 v^2 + 2 b^2 c^2 u^2 v^2 + 2 c^4 u^2 v^2 + a^4 u^2 v w - 2 a^2 b^2 u^2 v w + b^4 u^2 v w - 2 a^2 c^2 u^2 v w + 6 b^2 c^2 u^2 v w + c^4 u^2 v w - 2 a^2 b^2 u^2 w^2 + 2 b^4 u^2 w^2 + 2 b^2 c^2 u^2 w^2 + 2 a^4 v^2 w^2 - 2 a^2 b^2 v^2 w^2 - 2 a^2 c^2 v^2 w^2) : ... : ...)

Pairs of triangle centres {P, Q}: {X(69),X(64)}, {X(99),X(520)}

2. ABC, Triangle bounded by (BcCb, CaAc, AbBa) are perspective?

**** If P lies on Darboux cubic.

Special case: BcCb, CaAc, AbBa are concurrent.

**** If P lies on the sextic (No centers ETC):

-2 a^8 c^4 x^3 y^3 + 4 a^4 b^4 c^4 x^3 y^3 - 2 b^8 c^4 x^3 y^3 + 4 a^6 c^6 x^3 y^3 - 4 a^4 b^2 c^6 x^3 y^3 - 4 a^2 b^4 c^6 x^3 y^3 + 4 b^6 c^6 x^3 y^3 + 8 a^2 b^2 c^8 x^3 y^3 - 4 a^2 c^10 x^3 y^3 - 4 b^2 c^10 x^3 y^3 + 2 c^12 x^3 y^3 + a^10 c^2 x^3 y^2 z - 3 a^8 b^2 c^2 x^3 y^2 z + 2 a^6 b^4 c^2 x^3 y^2 z + 2 a^4 b^6 c^2 x^3 y^2 z - 3 a^2 b^8 c^2 x^3 y^2 z + b^10 c^2 x^3 y^2 z - 3 a^8 c^4 x^3 y^2 z + 8 a^6 b^2 c^4 x^3 y^2 z + 2 a^4 b^4 c^4 x^3 y^2 z - 7 b^8 c^4 x^3 y^2 z + 2 a^6 c^6 x^3 y^2 z - 6 a^4 b^2 c^6 x^3 y^2 z + 6 a^2 b^4 c^6 x^3 y^2 z + 14 b^6 c^6 x^3 y^2 z + 2 a^4 c^8 x^3 y^2 z - 10 b^4 c^8 x^3 y^2 z - 3 a^2 c^10 x^3 y^2 z + b^2 c^10 x^3 y^2 z + c^12 x^3 y^2 z + a^10 c^2 x^2 y^3 z - 3 a^8 b^2 c^2 x^2 y^3 z + 2 a^6 b^4 c^2 x^2 y^3 z + 2 a^4 b^6 c^2 x^2 y^3 z - 3 a^2 b^8 c^2 x^2 y^3 z + b^10 c^2 x^2 y^3 z - 7 a^8 c^4 x^2 y^3 z + 2 a^4 b^4 c^4 x^2 y^3 z + 8 a^2 b^6 c^4 x^2 y^3 z - 3 b^8 c^4 x^2 y^3 z + 14 a^6 c^6 x^2 y^3 z + 6 a^4 b^2 c^6 x^2 y^3 z - 6 a^2 b^4 c^6 x^2 y^3 z + 2 b^6 c^6 x^2 y^3 z - 10 a^4 c^8 x^2 y^3 z + 2 b^4 c^8 x^2 y^3 z + a^2 c^10 x^2 y^3 z - 3 b^2 c^10 x^2 y^3 z + c^12 x^2 y^3 z + a^10 b^2 x^3 y z^2 - 3 a^8 b^4 x^3 y z^2 + 2 a^6 b^6 x^3 y z^2 + 2 a^4 b^8 x^3 y z^2 - 3 a^2 b^10 x^3 y z^2 + b^12 x^3 y z^2 - 3 a^8 b^2 c^2 x^3 y z^2 + 8 a^6 b^4 c^2 x^3 y z^2 - 6 a^4 b^6 c^2 x^3 y z^2 + b^10 c^2 x^3 y z^2 + 2 a^6 b^2 c^4 x^3 y z^2 + 2 a^4 b^4 c^4 x^3 y z^2 + 6 a^2 b^6 c^4 x^3 y z^2 - 10 b^8 c^4 x^3 y z^2 + 2 a^4 b^2 c^6 x^3 y z^2 + 14 b^6 c^6 x^3 y z^2 - 3 a^2 b^2 c^8 x^3 y z^2 - 7 b^4 c^8 x^3 y z^2 + b^2 c^10 x^3 y z^2 + a^12 x^2 y^2 z^2 - 2 a^10 b^2 x^2 y^2 z^2 - a^8 b^4 x^2 y^2 z^2 + 4 a^6 b^6 x^2 y^2 z^2 - a^4 b^8 x^2 y^2 z^2 - 2 a^2 b^10 x^2 y^2 z^2 + b^12 x^2 y^2 z^2 - 2 a^10 c^2 x^2 y^2 z^2 + 6 a^8 b^2 c^2 x^2 y^2 z^2 - 4 a^6 b^4 c^2 x^2 y^2 z^2 - 4 a^4 b^6 c^2 x^2 y^2 z^2 + 6 a^2 b^8 c^2 x^2 y^2 z^2 - 2 b^10 c^2 x^2 y^2 z^2 - a^8 c^4 x^2 y^2 z^2 - 4 a^6 b^2 c^4 x^2 y^2 z^2 + 10 a^4 b^4 c^4 x^2 y^2 z^2 - 4 a^2 b^6 c^4 x^2 y^2 z^2 - b^8 c^4 x^2 y^2 z^2 + 4 a^6 c^6 x^2 y^2 z^2 - 4 a^4 b^2 c^6 x^2 y^2 z^2 - 4 a^2 b^4 c^6 x^2 y^2 z^2 + 4 b^6 c^6 x^2 y^2 z^2 - a^4 c^8 x^2 y^2 z^2 + 6 a^2 b^2 c^8 x^2 y^2 z^2 - b^4 c^8 x^2 y^2 z^2 - 2 a^2 c^10 x^2 y^2 z^2 - 2 b^2 c^10 x^2 y^2 z^2 + c^12 x^2 y^2 z^2 + a^12 x y^3 z^2 - 3 a^10 b^2 x y^3 z^2 + 2 a^8 b^4 x y^3 z^2 + 2 a^6 b^6 x y^3 z^2 - 3 a^4 b^8 x y^3 z^2 + a^2 b^10 x y^3 z^2 + a^10 c^2 x y^3 z^2 - 6 a^6 b^4 c^2 x y^3 z^2 + 8 a^4 b^6 c^2 x y^3 z^2 - 3 a^2 b^8 c^2 x y^3 z^2 - 10 a^8 c^4 x y^3 z^2 + 6 a^6 b^2 c^4 x y^3 z^2 + 2 a^4 b^4 c^4 x y^3 z^2 + 2 a^2 b^6 c^4 x y^3 z^2 + 14 a^6 c^6 x y^3 z^2 + 2 a^2 b^4 c^6 x y^3 z^2 - 7 a^4 c^8 x y^3 z^2 - 3 a^2 b^2 c^8 x y^3 z^2 + a^2 c^10 x y^3 z^2 - 2 a^8 b^4 x^3 z^3 + 4 a^6 b^6 x^3 z^3 - 4 a^2 b^10 x^3 z^3 + 2 b^12 x^3 z^3 - 4 a^4 b^6 c^2 x^3 z^3 + 8 a^2 b^8 c^2 x^3 z^3 - 4 b^10 c^2 x^3 z^3 + 4 a^4 b^4 c^4 x^3 z^3 - 4 a^2 b^6 c^4 x^3 z^3 + 4 b^6 c^6 x^3 z^3 - 2 b^4 c^8 x^3 z^3 + a^10 b^2 x^2 y z^3 - 7 a^8 b^4 x^2 y z^3 + 14 a^6 b^6 x^2 y z^3 - 10 a^4 b^8 x^2 y z^3 + a^2 b^10 x^2 y z^3 + b^12 x^2 y z^3 - 3 a^8 b^2 c^2 x^2 y z^3 + 6 a^4 b^6 c^2 x^2 y z^3 - 3 b^10 c^2 x^2 y z^3 + 2 a^6 b^2 c^4 x^2 y z^3 + 2 a^4 b^4 c^4 x^2 y z^3 - 6 a^2 b^6 c^4 x^2 y z^3 + 2 b^8 c^4 x^2 y z^3 + 2 a^4 b^2 c^6 x^2 y z^3 + 8 a^2 b^4 c^6 x^2 y z^3 + 2 b^6 c^6 x^2 y z^3 - 3 a^2 b^2 c^8 x^2 y z^3 - 3 b^4 c^8 x^2 y z^3 + b^2 c^10 x^2 y z^3 + a^12 x y^2 z^3 + a^10 b^2 x y^2 z^3 - 10 a^8 b^4 x y^2 z^3 + 14 a^6 b^6 x y^2 z^3 - 7 a^4 b^8 x y^2 z^3 + a^2 b^10 x y^2 z^3 - 3 a^10 c^2 x y^2 z^3 + 6 a^6 b^4 c^2 x y^2 z^3 - 3 a^2 b^8 c^2 x y^2 z^3 + 2 a^8 c^4 x y^2 z^3 - 6 a^6 b^2 c^4 x y^2 z^3 + 2 a^4 b^4 c^4 x y^2 z^3 + 2 a^2 b^6 c^4 x y^2 z^3 + 2 a^6 c^6 x y^2 z^3 + 8 a^4 b^2 c^6 x y^2 z^3 + 2 a^2 b^4 c^6 x y^2 z^3 - 3 a^4 c^8 x y^2 z^3 - 3 a^2 b^2 c^8 x y^2 z^3 + a^2 c^10 x y^2 z^3 + 2 a^12 y^3 z^3 - 4 a^10 b^2 y^3 z^3 + 4 a^6 b^6 y^3 z^3 - 2 a^4 b^8 y^3 z^3 - 4 a^10 c^2 y^3 z^3 + 8 a^8 b^2 c^2 y^3 z^3 - 4 a^6 b^4 c^2 y^3 z^3 - 4 a^6 b^2 c^4 y^3 z^3 + 4 a^4 b^4 c^4 y^3 z^3 + 4 a^6 c^6 y^3 z^3 - 2 a^4 c^8 y^3 z^3=0

3. Triangle bounded by (AbAc, BcBa, CaCb) and Triangle bounded by (BcCb, CaAc, AbBa) are perspective?

**** Always. The coordinates of perspector is very complicated.

First barycentric coordinate:

a^2 (32 a^14 b^2 c^8 u^7 v^5+96 a^12 b^4 c^8 u^7 v^5-480 a^10 b^6 c^8 u^7 v^5+352 a^8 b^8 c^8 u^7 v^5+352 a^6 b^10 c^8 u^7 v^5-480 a^4 b^12 c^8 u^7 v^5+96 a^2 b^14 c^8 u^7 v^5+32 b^16 c^8 u^7 v^5-96 a^12 b^2 c^10 u^7 v^5+64 a^10 b^4 c^10 u^7 v^5+608 a^8 b^6 c^10 u^7 v^5-1152 a^6 b^8 c^10 u^7 v^5+608 a^4 b^10 c^10 u^7 v^5+64 a^2 b^12 c^10 u^7 v^5-96 b^14 c^10 u^7 v^5+32 a^10 b^2 c^12 u^7 v^5-608 a^8 b^4 c^12 u^7 v^5+576 a^6 b^6 c^12 u^7 v^5+576 a^4 b^8 c^12 u^7 v^5-608 a^2 b^10 c^12 u^7 v^5+32 b^12 c^12 u^7 v^5+160 a^8 b^2 c^14 u^7 v^5+384 a^6 b^4 c^14 u^7 v^5-1088 a^4 b^6 c^14 u^7 v^5+384 a^2 b^8 c^14 u^7 v^5+160 b^10 c^14 u^7 v^5-160 a^6 b^2 c^16 u^7 v^5+416 a^4 b^4 c^16 u^7 v^5+416 a^2 b^6 c^16 u^7 v^5-160 b^8 c^16 u^7 v^5-32 a^4 b^2 c^18 u^7 v^5-448 a^2 b^4 c^18 u^7 v^5-32 b^6 c^18 u^7 v^5+96 a^2 b^2 c^20 u^7 v^5+96 b^4 c^20 u^7 v^5-32 b^2 c^22 u^7 v^5+64 a^14 b^2 c^8 u^6 v^6-128 a^12 b^4 c^8 u^6 v^6-64 a^10 b^6 c^8 u^6 v^6+256 a^8 b^8 c^8 u^6 v^6-64 a^6 b^10 c^8 u^6 v^6-128 a^4 b^12 c^8 u^6 v^6+64 a^2 b^14 c^8 u^6 v^6-128 a^12 b^2 c^10 u^6 v^6+384 a^10 b^4 c^10 u^6 v^6-256 a^8 b^6 c^10 u^6 v^6-256 a^6 b^8 c^10 u^6 v^6+384 a^4 b^10 c^10 u^6 v^6-128 a^2 b^12 c^10 u^6 v^6-64 a^10 b^2 c^12 u^6 v^6-256 a^8 b^4 c^12 u^6 v^6+640 a^6 b^6 c^12 u^6 v^6-256 a^4 b^8 c^12 u^6 v^6-64 a^2 b^10 c^12 u^6 v^6+256 a^8 b^2 c^14 u^6 v^6-256 a^6 b^4 c^14 u^6 v^6-256 a^4 b^6 c^14 u^6 v^6+256 a^2 b^8 c^14 u^6 v^6-64 a^6 b^2 c^16 u^6 v^6+384 a^4 b^4 c^16 u^6 v^6-64 a^2 b^6 c^16 u^6 v^6-128 a^4 b^2 c^18 u^6 v^6-128 a^2 b^4 c^18 u^6 v^6+64 a^2 b^2 c^20 u^6 v^6-32 a^16 b^2 c^6 u^7 v^4 w-32 a^14 b^4 c^6 u^7 v^4 w+480 a^12 b^6 c^6 u^7 v^4 w-800 a^10 b^8 c^6 u^7 v^4 w+160 a^8 b^10 c^6 u^7 v^4 w+672 a^6 b^12 c^6 u^7 v^4 w-608 a^4 b^14 c^6 u^7 v^4 w+160 a^2 b^16 c^6 u^7 v^4 w+128 a^14 b^2 c^8 u^7 v^4 w-96 a^12 b^4 c^8 u^7 v^4 w-1472 a^10 b^6 c^8 u^7 v^4 w+2912 a^8 b^8 c^8 u^7 v^4 w-1024 a^6 b^10 c^8 u^7 v^4 w-928 a^4 b^12 c^8 u^7 v^4 w+320 a^2 b^14 c^8 u^7 v^4 w+160 b^16 c^8 u^7 v^4 w-128 a^12 b^2 c^10 u^7 v^4 w+480 a^10 b^4 c^10 u^7 v^4 w-480 a^8 b^6 c^10 u^7 v^4 w-2112 a^6 b^8 c^10 u^7 v^4 w+3776 a^4 b^10 c^10 u^7 v^4 w-928 a^2 b^12 c^10 u^7 v^4 w-608 b^14 c^10 u^7 v^4 w-128 a^10 b^2 c^12 u^7 v^4 w-352 a^8 b^4 c^12 u^7 v^4 w+2944 a^6 b^6 c^12 u^7 v^4 w-2112 a^4 b^8 c^12 u^7 v^4 w-1024 a^2 b^10 c^12 u^7 v^4 w+672 b^12 c^12 u^7 v^4 w+320 a^8 b^2 c^14 u^7 v^4 w-352 a^6 b^4 c^14 u^7 v^4 w-480 a^4 b^6 c^14 u^7 v^4 w+2912 a^2 b^8 c^14 u^7 v^4 w+160 b^10 c^14 u^7 v^4 w-128 a^6 b^2 c^16 u^7 v^4 w+480 a^4 b^4 c^16 u^7 v^4 w-1472 a^2 b^6 c^16 u^7 v^4 w-800 b^8 c^16 u^7 v^4 w-128 a^4 b^2 c^18 u^7 v^4 w-96 a^2 b^4 c^18 u^7 v^4 w+480 b^6 c^18 u^7 v^4 w+128 a^2 b^2 c^20 u^7 v^4 w-32 b^4 c^20 u^7 v^4 w-32 b^2 c^22 u^7 v^4 w-8 a^18 c^6 u^6 v^5 w-56 a^16 b^2 c^6 u^6 v^5 w+384 a^14 b^4 c^6 u^6 v^5 w-704 a^12 b^6 c^6 u^6 v^5 w+304 a^10 b^8 c^6 u^6 v^5 w+528 a^8 b^10 c^6 u^6 v^5 w-704 a^6 b^12 c^6 u^6 v^5 w+256 a^4 b^14 c^6 u^6 v^5 w+24 a^2 b^16 c^6 u^6 v^5 w-24 b^18 c^6 u^6 v^5 w+40 a^16 c^8 u^6 v^5 w+288 a^14 b^2 c^8 u^6 v^5 w-672 a^12 b^4 c^8 u^6 v^5 w-416 a^10 b^6 c^8 u^6 v^5 w+1328 a^8 b^8 c^8 u^6 v^5 w-32 a^6 b^10 c^8 u^6 v^5 w-800 a^4 b^12 c^8 u^6 v^5 w+160 a^2 b^14 c^8 u^6 v^5 w+104 b^16 c^8 u^6 v^5 w-64 a^14 c^10 u^6 v^5 w-480 a^12 b^2 c^10 u^6 v^5 w-96 a^10 b^4 c^10 u^6 v^5 w+704 a^8 b^6 c^10 u^6 v^5 w+256 a^6 b^8 c^10 u^6 v^5 w+416 a^4 b^10 c^10 u^6 v^5 w-608 a^2 b^12 c^10 u^6 v^5 w-128 b^14 c^10 u^6 v^5 w+96 a^10 b^2 c^12 u^6 v^5 w+64 a^8 b^4 c^12 u^6 v^5 w-192 a^6 b^6 c^12 u^6 v^5 w-256 a^4 b^8 c^12 u^6 v^5 w+352 a^2 b^10 c^12 u^6 v^5 w-64 b^12 c^12 u^6 v^5 w+112 a^10 c^14 u^6 v^5 w+560 a^8 b^2 c^14 u^6 v^5 w+1216 a^6 b^4 c^14 u^6 v^5 w+1344 a^4 b^6 c^14 u^6 v^5 w+592 a^2 b^8 c^14 u^6 v^5 w+272 b^10 c^14 u^6 v^5 w-112 a^8 c^16 u^6 v^5 w-544 a^6 b^2 c^16 u^6 v^5 w-1056 a^4 b^4 c^16 u^6 v^5 w-672 a^2 b^6 c^16 u^6 v^5 w-176 b^8 c^16 u^6 v^5 w+32 a^4 b^2 c^18 u^6 v^5 w+32 a^2 b^4 c^18 u^6 v^5 w-64 b^6 c^18 u^6 v^5 w+64 a^4 c^20 u^6 v^5 w+160 a^2 b^2 c^20 u^6 v^5 w+128 b^4 c^20 u^6 v^5 w-40 a^2 c^22 u^6 v^5 w-56 b^2 c^22 u^6 v^5 w+8 c^24 u^6 v^5 w+64 a^16 b^2 c^6 u^5 v^6 w-192 a^14 b^4 c^6 u^5 v^6 w+64 a^12 b^6 c^6 u^5 v^6 w+320 a^10 b^8 c^6 u^5 v^6 w-320 a^8 b^10 c^6 u^5 v^6 w-64 a^6 b^12 c^6 u^5 v^6 w+192 a^4 b^14 c^6 u^5 v^6 w-64 a^2 b^16 c^6 u^5 v^6 w+192 a^14 b^2 c^8 u^5 v^6 w+128 a^12 b^4 c^8 u^5 v^6 w-1216 a^10 b^6 c^8 u^5 v^6 w+768 a^8 b^8 c^8 u^5 v^6 w+832 a^6 b^10 c^8 u^5 v^6 w-896 a^4 b^12 c^8 u^5 v^6 w+192 a^2 b^14 c^8 u^5 v^6 w-960 a^12 b^2 c^10 u^5 v^6 w+1216 a^10 b^4 c^10 u^5 v^6 w+1152 a^8 b^6 c^10 u^5 v^6 w-2176 a^6 b^8 c^10 u^5 v^6 w+832 a^4 b^10 c^10 u^5 v^6 w-64 a^2 b^12 c^10 u^5 v^6 w+704 a^10 b^2 c^12 u^5 v^6 w-2304 a^8 b^4 c^12 u^5 v^6 w+1152 a^6 b^6 c^12 u^5 v^6 w+768 a^4 b^8 c^12 u^5 v^6 w-320 a^2 b^10 c^12 u^5 v^6 w+704 a^8 b^2 c^14 u^5 v^6 w+1216 a^6 b^4 c^14 u^5 v^6 w-1216 a^4 b^6 c^14 u^5 v^6 w+320 a^2 b^8 c^14 u^5 v^6 w-960 a^6 b^2 c^16 u^5 v^6 w+128 a^4 b^4 c^16 u^5 v^6 w+64 a^2 b^6 c^16 u^5 v^6 w+192 a^4 b^2 c^18 u^5 v^6 w-192 a^2 b^4 c^18 u^5 v^6 w+64 a^2 b^2 c^20 u^5 v^6 w+8 a^18 b^2 c^4 u^7 v^3 w^2-24 a^16 b^4 c^4 u^7 v^3 w^2-32 a^14 b^6 c^4 u^7 v^3 w^2+224 a^12 b^8 c^4 u^7 v^3 w^2-336 a^10 b^10 c^4 u^7 v^3 w^2+112 a^8 b^12 c^4 u^7 v^3 w^2+224 a^6 b^14 c^4 u^7 v^3 w^2-288 a^4 b^16 c^4 u^7 v^3 w^2+136 a^2 b^18 c^4 u^7 v^3 w^2-24 b^20 c^4 u^7 v^3 w^2-40 a^16 b^2 c^6 u^7 v^3 w^2+96 a^14 b^4 c^6 u^7 v^3 w^2+576 a^12 b^6 c^6 u^7 v^3 w^2-1952 a^10 b^8 c^6 u^7 v^3 w^2+1584 a^8 b^10 c^6 u^7 v^3 w^2+544 a^6 b^12 c^6 u^7 v^3 w^2-1152 a^4 b^14 c^6 u^7 v^3 w^2+288 a^2 b^16 c^6 u^7 v^3 w^2+56 b^18 c^6 u^7 v^3 w^2+64 a^14 b^2 c^8 u^7 v^3 w^2-32 a^12 b^4 c^8 u^7 v^3 w^2-1088 a^10 b^6 c^8 u^7 v^3 w^2+2656 a^8 b^8 c^8 u^7 v^3 w^2-2368 a^6 b^10 c^8 u^7 v^3 w^2+1184 a^4 b^12 c^8 u^7 v^3 w^2-704 a^2 b^14 c^8 u^7 v^3 w^2+288 b^16 c^8 u^7 v^3 w^2-352 a^10 b^4 c^10 u^7 v^3 w^2+96 a^8 b^6 c^10 u^7 v^3 w^2+1088 a^6 b^8 c^10 u^7 v^3 w^2+1728 a^4 b^10 c^10 u^7 v^3 w^2-1248 a^2 b^12 c^10 u^7 v^3 w^2-1312 b^14 c^10 u^7 v^3 w^2-112 a^10 b^2 c^12 u^7 v^3 w^2+560 a^8 b^4 c^12 u^7 v^3 w^2+608 a^6 b^6 c^12 u^7 v^3 w^2-1504 a^4 b^8 c^12 u^7 v^3 w^2+2576 a^2 b^10 c^12 u^7 v^3 w^2+1968 b^12 c^12 u^7 v^3 w^2+112 a^8 b^2 c^14 u^7 v^3 w^2-96 a^6 b^4 c^14 u^7 v^3 w^2+512 a^4 b^6 c^14 u^7 v^3 w^2-416 a^2 b^8 c^14 u^7 v^3 w^2-1136 b^10 c^14 u^7 v^3 w^2-416 a^4 b^4 c^16 u^7 v^3 w^2-1024 a^2 b^6 c^16 u^7 v^3 w^2-96 b^8 c^16 u^7 v^3 w^2-64 a^4 b^2 c^18 u^7 v^3 w^2+352 a^2 b^4 c^18 u^7 v^3 w^2+352 b^6 c^18 u^7 v^3 w^2+40 a^2 b^2 c^20 u^7 v^3 w^2-88 b^4 c^20 u^7 v^3 w^2-8 b^2 c^22 u^7 v^3 w^2+4 a^20 c^4 u^6 v^4 w^2-16 a^18 b^2 c^4 u^6 v^4 w^2-132 a^16 b^4 c^4 u^6 v^4 w^2+736 a^14 b^6 c^4 u^6 v^4 w^2-1272 a^12 b^8 c^4 u^6 v^4 w^2+576 a^10 b^10 c^4 u^6 v^4 w^2+856 a^8 b^12 c^4 u^6 v^4 w^2-1248 a^6 b^14 c^4 u^6 v^4 w^2+564 a^4 b^16 c^4 u^6 v^4 w^2-48 a^2 b^18 c^4 u^6 v^4 w^2-20 b^20 c^4 u^6 v^4 w^2-24 a^18 c^6 u^6 v^4 w^2-48 a^16 b^2 c^6 u^6 v^4 w^2+544 a^14 b^4 c^6 u^6 v^4 w^2-928 a^12 b^6 c^6 u^6 v^4 w^2+112 a^10 b^8 c^6 u^6 v^4 w^2+960 a^8 b^10 c^6 u^6 v^4 w^2-736 a^6 b^12 c^6 u^6 v^4 w^2+32 a^4 b^14 c^6 u^6 v^4 w^2+104 a^2 b^16 c^6 u^6 v^4 w^2-16 b^18 c^6 u^6 v^4 w^2+52 a^16 c^8 u^6 v^4 w^2+480 a^14 b^2 c^8 u^6 v^4 w^2-848 a^12 b^4 c^8 u^6 v^4 w^2-4224 a^10 b^6 c^8 u^6 v^4 w^2+5656 a^8 b^8 c^8 u^6 v^4 w^2+3040 a^6 b^10 c^8 u^6 v^4 w^2-4752 a^4 b^12 c^8 u^6 v^4 w^2+192 a^2 b^14 c^8 u^6 v^4 w^2+404 b^16 c^8 u^6 v^4 w^2-32 a^14 c^10 u^6 v^4 w^2-992 a^12 b^2 c^10 u^6 v^4 w^2+544 a^10 b^4 c^10 u^6 v^4 w^2+4352 a^8 b^6 c^10 u^6 v^4 w^2-4960 a^6 b^8 c^10 u^6 v^4 w^2+2976 a^4 b^10 c^10 u^6 v^4 w^2-928 a^2 b^12 c^10 u^6 v^4 w^2-960 b^14 c^10 u^6 v^4 w^2-56 a^12 c^12 u^6 v^4 w^2+576 a^10 b^2 c^12 u^6 v^4 w^2-56 a^8 b^4 c^12 u^6 v^4 w^2+4832 a^6 b^6 c^12 u^6 v^4 w^2+6072 a^4 b^8 c^12 u^6 v^4 w^2+1248 a^2 b^10 c^12 u^6 v^4 w^2+696 b^12 c^12 u^6 v^4 w^2+112 a^10 c^14 u^6 v^4 w^2+576 a^8 b^2 c^14 u^6 v^4 w^2+96 a^6 b^4 c^14 u^6 v^4 w^2-5024 a^4 b^6 c^14 u^6 v^4 w^2-528 a^2 b^8 c^14 u^6 v^4 w^2+416 b^10 c^14 u^6 v^4 w^2-56 a^8 c^16 u^6 v^4 w^2-992 a^6 b^2 c^16 u^6 v^4 w^2-400 a^4 b^4 c^16 u^6 v^4 w^2-320 a^2 b^6 c^16 u^6 v^4 w^2-984 b^8 c^16 u^6 v^4 w^2-32 a^6 c^18 u^6 v^4 w^2+480 a^4 b^2 c^18 u^6 v^4 w^2+352 a^2 b^4 c^18 u^6 v^4 w^2+576 b^6 c^18 u^6 v^4 w^2+52 a^4 c^20 u^6 v^4 w^2-48 a^2 b^2 c^20 u^6 v^4 w^2-100 b^4 c^20 u^6 v^4 w^2-24 a^2 c^22 u^6 v^4 w^2-16 b^2 c^22 u^6 v^4 w^2+4 c^24 u^6 v^4 w^2+4 a^20 c^4 u^5 v^5 w^2-104 a^18 b^2 c^4 u^5 v^5 w^2+404 a^16 b^4 c^4 u^5 v^5 w^2-512 a^14 b^6 c^4 u^5 v^5 w^2-88 a^12 b^8 c^4 u^5 v^5 w^2+752 a^10 b^10 c^4 u^5 v^5 w^2-536 a^8 b^12 c^4 u^5 v^5 w^2-64 a^6 b^14 c^4 u^5 v^5 w^2+212 a^4 b^16 c^4 u^5 v^5 w^2-72 a^2 b^18 c^4 u^5 v^5 w^2+4 b^20 c^4 u^5 v^5 w^2-56 a^18 c^6 u^5 v^5 w^2+232 a^16 b^2 c^6 u^5 v^5 w^2-128 a^14 b^4 c^6 u^5 v^5 w^2-864 a^12 b^6 c^6 u^5 v^5 w^2+2064 a^10 b^8 c^6 u^5 v^5 w^2-2064 a^8 b^10 c^6 u^5 v^5 w^2+1088 a^6 b^12 c^6 u^5 v^5 w^2-352 a^4 b^14 c^6 u^5 v^5 w^2+104 a^2 b^16 c^6 u^5 v^5 w^2-24 b^18 c^6 u^5 v^5 w^2+244 a^16 c^8 u^5 v^5 w^2+352 a^14 b^2 c^8 u^5 v^5 w^2-2608 a^12 b^4 c^8 u^5 v^5 w^2-960 a^10 b^6 c^8 u^5 v^5 w^2+6712 a^8 b^8 c^8 u^5 v^5 w^2-2848 a^6 b^10 c^8 u^5 v^5 w^2-1328 a^4 b^12 c^8 u^5 v^5 w^2+384 a^2 b^14 c^8 u^5 v^5 w^2+52 b^16 c^8 u^5 v^5 w^2-480 a^14 c^10 u^5 v^5 w^2-1440 a^12 b^2 c^10 u^5 v^5 w^2+3072 a^10 b^4 c^10 u^5 v^5 w^2-1376 a^8 b^6 c^10 u^5 v^5 w^2-1376 a^6 b^8 c^10 u^5 v^5 w^2+2592 a^4 b^10 c^10 u^5 v^5 w^2-960 a^2 b^12 c^10 u^5 v^5 w^2-32 b^14 c^10 u^5 v^5 w^2+392 a^12 c^12 u^5 v^5 w^2+1104 a^10 b^2 c^12 u^5 v^5 w^2+1240 a^8 b^4 c^12 u^5 v^5 w^2+6784 a^6 b^6 c^12 u^5 v^5 w^2+344 a^4 b^8 c^12 u^5 v^5 w^2+432 a^2 b^10 c^12 u^5 v^5 w^2-56 b^12 c^12 u^5 v^5 w^2+112 a^10 c^14 u^5 v^5 w^2+624 a^8 b^2 c^14 u^5 v^5 w^2-2688 a^6 b^4 c^14 u^5 v^5 w^2-2336 a^4 b^6 c^14 u^5 v^5 w^2+592 a^2 b^8 c^14 u^5 v^5 w^2+112 b^10 c^14 u^5 v^5 w^2-504 a^8 c^16 u^5 v^5 w^2-1312 a^6 b^2 c^16 u^5 v^5 w^2+400 a^4 b^4 c^16 u^5 v^5 w^2-704 a^2 b^6 c^16 u^5 v^5 w^2-56 b^8 c^16 u^5 v^5 w^2+416 a^6 c^18 u^5 v^5 w^2+608 a^4 b^2 c^18 u^5 v^5 w^2+256 a^2 b^4 c^18 u^5 v^5 w^2-32 b^6 c^18 u^5 v^5 w^2-140 a^4 c^20 u^5 v^5 w^2-40 a^2 b^2 c^20 u^5 v^5 w^2+52 b^4 c^20 u^5 v^5 w^2+8 a^2 c^22 u^5 v^5 w^2-24 b^2 c^22 u^5 v^5 w^2+4 c^24 u^5 v^5 w^2+16 a^18 b^2 c^4 u^4 v^6 w^2-64 a^16 b^4 c^4 u^4 v^6 w^2+64 a^14 b^6 c^4 u^4 v^6 w^2+64 a^12 b^8 c^4 u^4 v^6 w^2-160 a^10 b^10 c^4 u^4 v^6 w^2+64 a^8 b^12 c^4 u^4 v^6 w^2+64 a^6 b^14 c^4 u^4 v^6 w^2-64 a^4 b^16 c^4 u^4 v^6 w^2+16 a^2 b^18 c^4 u^4 v^6 w^2+192 a^16 b^2 c^6 u^4 v^6 w^2-320 a^14 b^4 c^6 u^4 v^6 w^2-448 a^12 b^6 c^6 u^4 v^6 w^2+1088 a^10 b^8 c^6 u^4 v^6 w^2-192 a^8 b^10 c^6 u^4 v^6 w^2-704 a^6 b^12 c^6 u^4 v^6 w^2+448 a^4 b^14 c^6 u^4 v^6 w^2-64 a^2 b^16 c^6 u^4 v^6 w^2-192 a^14 b^2 c^8 u^4 v^6 w^2+1344 a^12 b^4 c^8 u^4 v^6 w^2-1344 a^10 b^6 c^8 u^4 v^6 w^2-1152 a^8 b^8 c^8 u^4 v^6 w^2+1984 a^6 b^10 c^8 u^4 v^6 w^2-704 a^4 b^12 c^8 u^4 v^6 w^2+64 a^2 b^14 c^8 u^4 v^6 w^2-1216 a^12 b^2 c^10 u^4 v^6 w^2-960 a^10 b^4 c^10 u^4 v^6 w^2+3456 a^8 b^6 c^10 u^4 v^6 w^2-1152 a^6 b^8 c^10 u^4 v^6 w^2-192 a^4 b^10 c^10 u^4 v^6 w^2+64 a^2 b^12 c^10 u^4 v^6 w^2+2400 a^10 b^2 c^12 u^4 v^6 w^2-960 a^8 b^4 c^12 u^4 v^6 w^2-1344 a^6 b^6 c^12 u^4 v^6 w^2+1088 a^4 b^8 c^12 u^4 v^6 w^2-160 a^2 b^10 c^12 u^4 v^6 w^2-1216 a^8 b^2 c^14 u^4 v^6 w^2+1344 a^6 b^4 c^14 u^4 v^6 w^2-448 a^4 b^6 c^14 u^4 v^6 w^2+64 a^2 b^8 c^14 u^4 v^6 w^2-192 a^6 b^2 c^16 u^4 v^6 w^2-320 a^4 b^4 c^16 u^4 v^6 w^2+64 a^2 b^6 c^16 u^4 v^6 w^2+192 a^4 b^2 c^18 u^4 v^6 w^2-64 a^2 b^4 c^18 u^4 v^6 w^2+16 a^2 b^2 c^20 u^4 v^6 w^2+8 a^18 b^4 c^2 u^7 v^2 w^3-40 a^16 b^6 c^2 u^7 v^2 w^3+64 a^14 b^8 c^2 u^7 v^2 w^3-112 a^10 b^12 c^2 u^7 v^2 w^3+112 a^8 b^14 c^2 u^7 v^2 w^3-64 a^4 b^18 c^2 u^7 v^2 w^3+40 a^2 b^20 c^2 u^7 v^2 w^3-8 b^22 c^2 u^7 v^2 w^3-24 a^16 b^4 c^4 u^7 v^2 w^3+96 a^14 b^6 c^4 u^7 v^2 w^3-32 a^12 b^8 c^4 u^7 v^2 w^3-352 a^10 b^10 c^4 u^7 v^2 w^3+560 a^8 b^12 c^4 u^7 v^2 w^3-96 a^6 b^14 c^4 u^7 v^2 w^3-416 a^4 b^16 c^4 u^7 v^2 w^3+352 a^2 b^18 c^4 u^7 v^2 w^3-88 b^20 c^4 u^7 v^2 w^3-32 a^14 b^4 c^6 u^7 v^2 w^3+576 a^12 b^6 c^6 u^7 v^2 w^3-1088 a^10 b^8 c^6 u^7 v^2 w^3+96 a^8 b^10 c^6 u^7 v^2 w^3+608 a^6 b^12 c^6 u^7 v^2 w^3+512 a^4 b^14 c^6 u^7 v^2 w^3-1024 a^2 b^16 c^6 u^7 v^2 w^3+352 b^18 c^6 u^7 v^2 w^3+224 a^12 b^4 c^8 u^7 v^2 w^3-1952 a^10 b^6 c^8 u^7 v^2 w^3+2656 a^8 b^8 c^8 u^7 v^2 w^3+1088 a^6 b^10 c^8 u^7 v^2 w^3-1504 a^4 b^12 c^8 u^7 v^2 w^3-416 a^2 b^14 c^8 u^7 v^2 w^3-96 b^16 c^8 u^7 v^2 w^3-336 a^10 b^4 c^10 u^7 v^2 w^3+1584 a^8 b^6 c^10 u^7 v^2 w^3-2368 a^6 b^8 c^10 u^7 v^2 w^3+1728 a^4 b^10 c^10 u^7 v^2 w^3+2576 a^2 b^12 c^10 u^7 v^2 w^3-1136 b^14 c^10 u^7 v^2 w^3+112 a^8 b^4 c^12 u^7 v^2 w^3+544 a^6 b^6 c^12 u^7 v^2 w^3+1184 a^4 b^8 c^12 u^7 v^2 w^3-1248 a^2 b^10 c^12 u^7 v^2 w^3+1968 b^12 c^12 u^7 v^2 w^3+224 a^6 b^4 c^14 u^7 v^2 w^3-1152 a^4 b^6 c^14 u^7 v^2 w^3-704 a^2 b^8 c^14 u^7 v^2 w^3-1312 b^10 c^14 u^7 v^2 w^3-288 a^4 b^4 c^16 u^7 v^2 w^3+288 a^2 b^6 c^16 u^7 v^2 w^3+288 b^8 c^16 u^7 v^2 w^3+136 a^2 b^4 c^18 u^7 v^2 w^3+56 b^6 c^18 u^7 v^2 w^3-24 b^4 c^20 u^7 v^2 w^3+12 a^20 b^2 c^2 u^6 v^3 w^3-32 a^18 b^4 c^2 u^6 v^3 w^3-76 a^16 b^6 c^2 u^6 v^3 w^3+416 a^14 b^8 c^2 u^6 v^3 w^3-616 a^12 b^10 c^2 u^6 v^3 w^3+224 a^10 b^12 c^2 u^6 v^3 w^3+392 a^8 b^14 c^2 u^6 v^3 w^3-544 a^6 b^16 c^2 u^6 v^3 w^3+284 a^4 b^18 c^2 u^6 v^3 w^3-64 a^2 b^20 c^2 u^6 v^3 w^3+4 b^22 c^2 u^6 v^3 w^3-32 a^18 b^2 c^4 u^6 v^3 w^3-8 a^16 b^4 c^4 u^6 v^3 w^3+768 a^14 b^6 c^4 u^6 v^3 w^3-2112 a^12 b^8 c^4 u^6 v^3 w^3+1664 a^10 b^10 c^4 u^6 v^3 w^3+1072 a^8 b^12 c^4 u^6 v^3 w^3-2432 a^6 b^14 c^4 u^6 v^3 w^3+1152 a^4 b^16 c^4 u^6 v^3 w^3+32 a^2 b^18 c^4 u^6 v^3 w^3-104 b^20 c^4 u^6 v^3 w^3-76 a^16 b^2 c^6 u^6 v^3 w^3+768 a^14 b^4 c^6 u^6 v^3 w^3+464 a^12 b^6 c^6 u^6 v^3 w^3-3936 a^10 b^8 c^6 u^6 v^3 w^3+1272 a^8 b^10 c^6 u^6 v^3 w^3+4928 a^6 b^12 c^6 u^6 v^3 w^3-4016 a^4 b^14 c^6 u^6 v^3 w^3+288 a^2 b^16 c^6 u^6 v^3 w^3+308 b^18 c^6 u^6 v^3 w^3+416 a^14 b^2 c^8 u^6 v^3 w^3-2112 a^12 b^4 c^8 u^6 v^3 w^3-3936 a^10 b^6 c^8 u^6 v^3 w^3+12960 a^8 b^8 c^8 u^6 v^3 w^3-1952 a^6 b^10 c^8 u^6 v^3 w^3-4992 a^4 b^12 c^8 u^6 v^3 w^3-416 a^2 b^14 c^8 u^6 v^3 w^3+32 b^16 c^8 u^6 v^3 w^3-616 a^12 b^2 c^10 u^6 v^3 w^3+1664 a^10 b^4 c^10 u^6 v^3 w^3+1272 a^8 b^6 c^10 u^6 v^3 w^3-1952 a^6 b^8 c^10 u^6 v^3 w^3+15144 a^4 b^10 c^10 u^6 v^3 w^3+160 a^2 b^12 c^10 u^6 v^3 w^3-1336 b^14 c^10 u^6 v^3 w^3+224 a^10 b^2 c^12 u^6 v^3 w^3+1072 a^8 b^4 c^12 u^6 v^3 w^3+4928 a^6 b^6 c^12 u^6 v^3 w^3-4992 a^4 b^8 c^12 u^6 v^3 w^3+160 a^2 b^10 c^12 u^6 v^3 w^3+2192 b^12 c^12 u^6 v^3 w^3+392 a^8 b^2 c^14 u^6 v^3 w^3-2432 a^6 b^4 c^14 u^6 v^3 w^3-4016 a^4 b^6 c^14 u^6 v^3 w^3-416 a^2 b^8 c^14 u^6 v^3 w^3-1336 b^10 c^14 u^6 v^3 w^3-544 a^6 b^2 c^16 u^6 v^3 w^3+1152 a^4 b^4 c^16 u^6 v^3 w^3+288 a^2 b^6 c^16 u^6 v^3 w^3+32 b^8 c^16 u^6 v^3 w^3+284 a^4 b^2 c^18 u^6 v^3 w^3+32 a^2 b^4 c^18 u^6 v^3 w^3+308 b^6 c^18 u^6 v^3 w^3-64 a^2 b^2 c^20 u^6 v^3 w^3-104 b^4 c^20 u^6 v^3 w^3+4 b^2 c^22 u^6 v^3 w^3+4 a^22 c^2 u^5 v^4 w^3+8 a^20 b^2 c^2 u^5 v^4 w^3-148 a^18 b^4 c^2 u^5 v^4 w^3+456 a^16 b^6 c^2 u^5 v^4 w^3-568 a^14 b^8 c^2 u^5 v^4 w^3+112 a^12 b^10 c^2 u^5 v^4 w^3+504 a^10 b^12 c^2 u^5 v^4 w^3-592 a^8 b^14 c^2 u^5 v^4 w^3+244 a^6 b^16 c^2 u^5 v^4 w^3+8 a^4 b^18 c^2 u^5 v^4 w^3-36 a^2 b^20 c^2 u^5 v^4 w^3+8 b^22 c^2 u^5 v^4 w^3-12 a^20 c^4 u^5 v^4 w^3-96 a^18 b^2 c^4 u^5 v^4 w^3+356 a^16 b^4 c^4 u^5 v^4 w^3+448 a^14 b^6 c^4 u^5 v^4 w^3-3192 a^12 b^8 c^4 u^5 v^4 w^3+5056 a^10 b^10 c^4 u^5 v^4 w^3-3384 a^8 b^12 c^4 u^5 v^4 w^3+704 a^6 b^14 c^4 u^5 v^4 w^3+132 a^4 b^16 c^4 u^5 v^4 w^3+32 a^2 b^18 c^4 u^5 v^4 w^3-44 b^20 c^4 u^5 v^4 w^3-28 a^18 c^6 u^5 v^4 w^3+240 a^16 b^2 c^6 u^5 v^4 w^3+1360 a^14 b^4 c^6 u^5 v^4 w^3-4736 a^12 b^6 c^6 u^5 v^4 w^3+2520 a^10 b^8 c^6 u^5 v^4 w^3+3840 a^8 b^10 c^6 u^5 v^4 w^3-4016 a^6 b^12 c^6 u^5 v^4 w^3+576 a^4 b^14 c^6 u^5 v^4 w^3+164 a^2 b^16 c^6 u^5 v^4 w^3+80 b^18 c^6 u^5 v^4 w^3+180 a^16 c^8 u^5 v^4 w^3+96 a^14 b^2 c^8 u^5 v^4 w^3-5168 a^12 b^4 c^8 u^5 v^4 w^3+2080 a^10 b^6 c^8 u^5 v^4 w^3+8248 a^8 b^8 c^8 u^5 v^4 w^3-1504 a^6 b^10 c^8 u^5 v^4 w^3-4016 a^4 b^12 c^8 u^5 v^4 w^3+96 a^2 b^14 c^8 u^5 v^4 w^3-12 b^16 c^8 u^5 v^4 w^3-312 a^14 c^10 u^5 v^4 w^3-1264 a^12 b^2 c^10 u^5 v^4 w^3+4872 a^10 b^4 c^10 u^5 v^4 w^3+5488 a^8 b^6 c^10 u^5 v^4 w^3+9400 a^6 b^8 c^10 u^5 v^4 w^3+6032 a^4 b^10 c^10 u^5 v^4 w^3-1544 a^2 b^12 c^10 u^5 v^4 w^3-144 b^14 c^10 u^5 v^4 w^3+168 a^12 c^12 u^5 v^4 w^3+2208 a^10 b^2 c^12 u^5 v^4 w^3+824 a^8 b^4 c^12 u^5 v^4 w^3-2048 a^6 b^6 c^12 u^5 v^4 w^3-1608 a^4 b^8 c^12 u^5 v^4 w^3+2848 a^2 b^10 c^12 u^5 v^4 w^3+168 b^12 c^12 u^5 v^4 w^3+168 a^10 c^14 u^5 v^4 w^3-1824 a^8 b^2 c^14 u^5 v^4 w^3-3760 a^6 b^4 c^14 u^5 v^4 w^3-2816 a^4 b^6 c^14 u^5 v^4 w^3-2392 a^2 b^8 c^14 u^5 v^4 w^3-312 a^8 c^16 u^5 v^4 w^3+800 a^6 b^2 c^16 u^5 v^4 w^3+1936 a^4 b^4 c^16 u^5 v^4 w^3+1056 a^2 b^6 c^16 u^5 v^4 w^3-120 b^8 c^16 u^5 v^4 w^3+180 a^6 c^18 u^5 v^4 w^3-216 a^4 b^2 c^18 u^5 v^4 w^3-276 a^2 b^4 c^18 u^5 v^4 w^3+72 b^6 c^18 u^5 v^4 w^3-28 a^4 c^20 u^5 v^4 w^3+64 a^2 b^2 c^20 u^5 v^4 w^3+4 b^4 c^20 u^5 v^4 w^3-12 a^2 c^22 u^5 v^4 w^3-16 b^2 c^22 u^5 v^4 w^3+4 c^24 u^5 v^4 w^3+8 a^22 c^2 u^4 v^5 w^3-56 a^20 b^2 c^2 u^4 v^5 w^3+144 a^18 b^4 c^2 u^4 v^5 w^3-128 a^16 b^6 c^2 u^4 v^5 w^3-112 a^14 b^8 c^2 u^4 v^5 w^3+336 a^12 b^10 c^2 u^4 v^5 w^3-224 a^10 b^12 c^2 u^4 v^5 w^3-64 a^8 b^14 c^2 u^4 v^5 w^3+168 a^6 b^16 c^2 u^4 v^5 w^3-88 a^4 b^18 c^2 u^4 v^5 w^3+16 a^2 b^20 c^2 u^4 v^5 w^3-32 a^20 c^4 u^4 v^5 w^3-24 a^18 b^2 c^4 u^4 v^5 w^3+448 a^16 b^4 c^4 u^4 v^5 w^3-832 a^14 b^6 c^4 u^4 v^5 w^3+576 a^12 b^8 c^4 u^4 v^5 w^3-368 a^10 b^10 c^4 u^4 v^5 w^3+704 a^8 b^12 c^4 u^4 v^5 w^3-768 a^6 b^14 c^4 u^4 v^5 w^3+352 a^4 b^16 c^4 u^4 v^5 w^3-56 a^2 b^18 c^4 u^4 v^5 w^3-24 a^18 c^6 u^4 v^5 w^3+736 a^16 b^2 c^6 u^4 v^5 w^3-2112 a^14 b^4 c^6 u^4 v^5 w^3+192 a^12 b^6 c^6 u^4 v^5 w^3+4976 a^10 b^8 c^6 u^4 v^5 w^3-5536 a^8 b^10 c^6 u^4 v^5 w^3+1728 a^6 b^12 c^6 u^4 v^5 w^3+40 a^2 b^16 c^6 u^4 v^5 w^3+384 a^16 c^8 u^4 v^5 w^3-1312 a^14 b^2 c^8 u^4 v^5 w^3-192 a^12 b^4 c^8 u^4 v^5 w^3-2176 a^10 b^6 c^8 u^4 v^5 w^3+5248 a^8 b^8 c^8 u^4 v^5 w^3-928 a^6 b^10 c^8 u^4 v^5 w^3-1088 a^4 b^12 c^8 u^4 v^5 w^3+64 a^2 b^14 c^8 u^4 v^5 w^3-1008 a^14 c^10 u^4 v^5 w^3+304 a^12 b^2 c^10 u^4 v^5 w^3+5856 a^10 b^4 c^10 u^4 v^5 w^3+5376 a^8 b^6 c^10 u^4 v^5 w^3-528 a^6 b^8 c^10 u^4 v^5 w^3+336 a^4 b^10 c^10 u^4 v^5 w^3-96 a^2 b^12 c^10 u^4 v^5 w^3+1344 a^12 c^12 u^4 v^5 w^3+1136 a^10 b^2 c^12 u^4 v^5 w^3-5056 a^8 b^4 c^12 u^4 v^5 w^3-64 a^6 b^6 c^12 u^4 v^5 w^3+2112 a^4 b^8 c^12 u^4 v^5 w^3+16 a^2 b^10 c^12 u^4 v^5 w^3-1008 a^10 c^14 u^4 v^5 w^3-1056 a^8 b^2 c^14 u^4 v^5 w^3+192 a^6 b^4 c^14 u^4 v^5 w^3-2368 a^4 b^6 c^14 u^4 v^5 w^3+16 a^2 b^8 c^14 u^4 v^5 w^3+384 a^8 c^16 u^4 v^5 w^3+224 a^6 b^2 c^16 u^4 v^5 w^3+704 a^4 b^4 c^16 u^4 v^5 w^3-24 a^6 c^18 u^4 v^5 w^3+72 a^4 b^2 c^18 u^4 v^5 w^3+16 a^2 b^4 c^18 u^4 v^5 w^3-32 a^4 c^20 u^4 v^5 w^3-24 a^2 b^2 c^20 u^4 v^5 w^3+8 a^2 c^22 u^4 v^5 w^3-32 a^16 b^6 c^2 u^7 v w^4+128 a^14 b^8 c^2 u^7 v w^4-128 a^12 b^10 c^2 u^7 v w^4-128 a^10 b^12 c^2 u^7 v w^4+320 a^8 b^14 c^2 u^7 v w^4-128 a^6 b^16 c^2 u^7 v w^4-128 a^4 b^18 c^2 u^7 v w^4+128 a^2 b^20 c^2 u^7 v w^4-32 b^22 c^2 u^7 v w^4-32 a^14 b^6 c^4 u^7 v w^4-96 a^12 b^8 c^4 u^7 v w^4+480 a^10 b^10 c^4 u^7 v w^4-352 a^8 b^12 c^4 u^7 v w^4-352 a^6 b^14 c^4 u^7 v w^4+480 a^4 b^16 c^4 u^7 v w^4-96 a^2 b^18 c^4 u^7 v w^4-32 b^20 c^4 u^7 v w^4+480 a^12 b^6 c^6 u^7 v w^4-1472 a^10 b^8 c^6 u^7 v w^4-480 a^8 b^10 c^6 u^7 v w^4+2944 a^6 b^12 c^6 u^7 v w^4-480 a^4 b^14 c^6 u^7 v w^4-1472 a^2 b^16 c^6 u^7 v w^4+480 b^18 c^6 u^7 v w^4-800 a^10 b^6 c^8 u^7 v w^4+2912 a^8 b^8 c^8 u^7 v w^4-2112 a^6 b^10 c^8 u^7 v w^4-2112 a^4 b^12 c^8 u^7 v w^4+2912 a^2 b^14 c^8 u^7 v w^4-800 b^16 c^8 u^7 v w^4+160 a^8 b^6 c^10 u^7 v w^4-1024 a^6 b^8 c^10 u^7 v w^4+3776 a^4 b^10 c^10 u^7 v w^4-1024 a^2 b^12 c^10 u^7 v w^4+160 b^14 c^10 u^7 v w^4+672 a^6 b^6 c^12 u^7 v w^4-928 a^4 b^8 c^12 u^7 v w^4-928 a^2 b^10 c^12 u^7 v w^4+672 b^12 c^12 u^7 v w^4-608 a^4 b^6 c^14 u^7 v w^4+320 a^2 b^8 c^14 u^7 v w^4-608 b^10 c^14 u^7 v w^4+160 a^2 b^6 c^16 u^7 v w^4+160 b^8 c^16 u^7 v w^4+4 a^20 b^4 u^6 v^2 w^4-24 a^18 b^6 u^6 v^2 w^4+52 a^16 b^8 u^6 v^2 w^4-32 a^14 b^10 u^6 v^2 w^4-56 a^12 b^12 u^6 v^2 w^4+112 a^10 b^14 u^6 v^2 w^4-56 a^8 b^16 u^6 v^2 w^4-32 a^6 b^18 u^6 v^2 w^4+52 a^4 b^20 u^6 v^2 w^4-24 a^2 b^22 u^6 v^2 w^4+4 b^24 u^6 v^2 w^4-16 a^18 b^4 c^2 u^6 v^2 w^4-48 a^16 b^6 c^2 u^6 v^2 w^4+480 a^14 b^8 c^2 u^6 v^2 w^4-992 a^12 b^10 c^2 u^6 v^2 w^4+576 a^10 b^12 c^2 u^6 v^2 w^4+576 a^8 b^14 c^2 u^6 v^2 w^4-992 a^6 b^16 c^2 u^6 v^2 w^4+480 a^4 b^18 c^2 u^6 v^2 w^4-48 a^2 b^20 c^2 u^6 v^2 w^4-16 b^22 c^2 u^6 v^2 w^4-132 a^16 b^4 c^4 u^6 v^2 w^4+544 a^14 b^6 c^4 u^6 v^2 w^4-848 a^12 b^8 c^4 u^6 v^2 w^4+544 a^10 b^10 c^4 u^6 v^2 w^4-56 a^8 b^12 c^4 u^6 v^2 w^4+96 a^6 b^14 c^4 u^6 v^2 w^4-400 a^4 b^16 c^4 u^6 v^2 w^4+352 a^2 b^18 c^4 u^6 v^2 w^4-100 b^20 c^4 u^6 v^2 w^4+736 a^14 b^4 c^6 u^6 v^2 w^4-928 a^12 b^6 c^6 u^6 v^2 w^4-4224 a^10 b^8 c^6 u^6 v^2 w^4+4352 a^8 b^10 c^6 u^6 v^2 w^4+4832 a^6 b^12 c^6 u^6 v^2 w^4-5024 a^4 b^14 c^6 u^6 v^2 w^4-320 a^2 b^16 c^6 u^6 v^2 w^4+576 b^18 c^6 u^6 v^2 w^4-1272 a^12 b^4 c^8 u^6 v^2 w^4+112 a^10 b^6 c^8 u^6 v^2 w^4+5656 a^8 b^8 c^8 u^6 v^2 w^4-4960 a^6 b^10 c^8 u^6 v^2 w^4+6072 a^4 b^12 c^8 u^6 v^2 w^4-528 a^2 b^14 c^8 u^6 v^2 w^4-984 b^16 c^8 u^6 v^2 w^4+576 a^10 b^4 c^10 u^6 v^2 w^4+960 a^8 b^6 c^10 u^6 v^2 w^4+3040 a^6 b^8 c^10 u^6 v^2 w^4+2976 a^4 b^10 c^10 u^6 v^2 w^4+1248 a^2 b^12 c^10 u^6 v^2 w^4+416 b^14 c^10 u^6 v^2 w^4+856 a^8 b^4 c^12 u^6 v^2 w^4-736 a^6 b^6 c^12 u^6 v^2 w^4-4752 a^4 b^8 c^12 u^6 v^2 w^4-928 a^2 b^10 c^12 u^6 v^2 w^4+696 b^12 c^12 u^6 v^2 w^4-1248 a^6 b^4 c^14 u^6 v^2 w^4+32 a^4 b^6 c^14 u^6 v^2 w^4+192 a^2 b^8 c^14 u^6 v^2 w^4-960 b^10 c^14 u^6 v^2 w^4+564 a^4 b^4 c^16 u^6 v^2 w^4+104 a^2 b^6 c^16 u^6 v^2 w^4+404 b^8 c^16 u^6 v^2 w^4-48 a^2 b^4 c^18 u^6 v^2 w^4-16 b^6 c^18 u^6 v^2 w^4-20 b^4 c^20 u^6 v^2 w^4+4 a^22 b^2 u^5 v^3 w^4-12 a^20 b^4 u^5 v^3 w^4-28 a^18 b^6 u^5 v^3 w^4+180 a^16 b^8 u^5 v^3 w^4-312 a^14 b^10 u^5 v^3 w^4+168 a^12 b^12 u^5 v^3 w^4+168 a^10 b^14 u^5 v^3 w^4-312 a^8 b^16 u^5 v^3 w^4+180 a^6 b^18 u^5 v^3 w^4-28 a^4 b^20 u^5 v^3 w^4-12 a^2 b^22 u^5 v^3 w^4+4 b^24 u^5 v^3 w^4+8 a^20 b^2 c^2 u^5 v^3 w^4-96 a^18 b^4 c^2 u^5 v^3 w^4+240 a^16 b^6 c^2 u^5 v^3 w^4+96 a^14 b^8 c^2 u^5 v^3 w^4-1264 a^12 b^10 c^2 u^5 v^3 w^4+2208 a^10 b^12 c^2 u^5 v^3 w^4-1824 a^8 b^14 c^2 u^5 v^3 w^4+800 a^6 b^16 c^2 u^5 v^3 w^4-216 a^4 b^18 c^2 u^5 v^3 w^4+64 a^2 b^20 c^2 u^5 v^3 w^4-16 b^22 c^2 u^5 v^3 w^4-148 a^18 b^2 c^4 u^5 v^3 w^4+356 a^16 b^4 c^4 u^5 v^3 w^4+1360 a^14 b^6 c^4 u^5 v^3 w^4-5168 a^12 b^8 c^4 u^5 v^3 w^4+4872 a^10 b^10 c^4 u^5 v^3 w^4+824 a^8 b^12 c^4 u^5 v^3 w^4-3760 a^6 b^14 c^4 u^5 v^3 w^4+1936 a^4 b^16 c^4 u^5 v^3 w^4-276 a^2 b^18 c^4 u^5 v^3 w^4+4 b^20 c^4 u^5 v^3 w^4+456 a^16 b^2 c^6 u^5 v^3 w^4+448 a^14 b^4 c^6 u^5 v^3 w^4-4736 a^12 b^6 c^6 u^5 v^3 w^4+2080 a^10 b^8 c^6 u^5 v^3 w^4+5488 a^8 b^10 c^6 u^5 v^3 w^4-2048 a^6 b^12 c^6 u^5 v^3 w^4-2816 a^4 b^14 c^6 u^5 v^3 w^4+1056 a^2 b^16 c^6 u^5 v^3 w^4+72 b^18 c^6 u^5 v^3 w^4-568 a^14 b^2 c^8 u^5 v^3 w^4-3192 a^12 b^4 c^8 u^5 v^3 w^4+2520 a^10 b^6 c^8 u^5 v^3 w^4+8248 a^8 b^8 c^8 u^5 v^3 w^4+9400 a^6 b^10 c^8 u^5 v^3 w^4-1608 a^4 b^12 c^8 u^5 v^3 w^4-2392 a^2 b^14 c^8 u^5 v^3 w^4-120 b^16 c^8 u^5 v^3 w^4+112 a^12 b^2 c^10 u^5 v^3 w^4+5056 a^10 b^4 c^10 u^5 v^3 w^4+3840 a^8 b^6 c^10 u^5 v^3 w^4-1504 a^6 b^8 c^10 u^5 v^3 w^4+6032 a^4 b^10 c^10 u^5 v^3 w^4+2848 a^2 b^12 c^10 u^5 v^3 w^4+504 a^10 b^2 c^12 u^5 v^3 w^4-3384 a^8 b^4 c^12 u^5 v^3 w^4-4016 a^6 b^6 c^12 u^5 v^3 w^4-4016 a^4 b^8 c^12 u^5 v^3 w^4-1544 a^2 b^10 c^12 u^5 v^3 w^4+168 b^12 c^12 u^5 v^3 w^4-592 a^8 b^2 c^14 u^5 v^3 w^4+704 a^6 b^4 c^14 u^5 v^3 w^4+576 a^4 b^6 c^14 u^5 v^3 w^4+96 a^2 b^8 c^14 u^5 v^3 w^4-144 b^10 c^14 u^5 v^3 w^4+244 a^6 b^2 c^16 u^5 v^3 w^4+132 a^4 b^4 c^16 u^5 v^3 w^4+164 a^2 b^6 c^16 u^5 v^3 w^4-12 b^8 c^16 u^5 v^3 w^4+8 a^4 b^2 c^18 u^5 v^3 w^4+32 a^2 b^4 c^18 u^5 v^3 w^4+80 b^6 c^18 u^5 v^3 w^4-36 a^2 b^2 c^20 u^5 v^3 w^4-44 b^4 c^20 u^5 v^3 w^4+8 b^2 c^22 u^5 v^3 w^4+a^24 u^4 v^4 w^4+4 a^22 b^2 u^4 v^4 w^4-46 a^20 b^4 u^4 v^4 w^4+116 a^18 b^6 u^4 v^4 w^4-81 a^16 b^8 u^4 v^4 w^4-120 a^14 b^10 u^4 v^4 w^4+252 a^12 b^12 u^4 v^4 w^4-120 a^10 b^14 u^4 v^4 w^4-81 a^8 b^16 u^4 v^4 w^4+116 a^6 b^18 u^4 v^4 w^4-46 a^4 b^20 u^4 v^4 w^4+4 a^2 b^22 u^4 v^4 w^4+b^24 u^4 v^4 w^4+4 a^22 c^2 u^4 v^4 w^4-172 a^18 b^4 c^2 u^4 v^4 w^4+792 a^16 b^6 c^2 u^4 v^4 w^4-1688 a^14 b^8 c^2 u^4 v^4 w^4+2112 a^12 b^10 c^2 u^4 v^4 w^4-1752 a^10 b^12 c^2 u^4 v^4 w^4+1072 a^8 b^14 c^2 u^4 v^4 w^4-492 a^6 b^16 c^2 u^4 v^4 w^4+128 a^4 b^18 c^2 u^4 v^4 w^4+4 a^2 b^20 c^2 u^4 v^4 w^4-8 b^22 c^2 u^4 v^4 w^4-46 a^20 c^4 u^4 v^4 w^4-172 a^18 b^2 c^4 u^4 v^4 w^4+1586 a^16 b^4 c^4 u^4 v^4 w^4-2608 a^14 b^6 c^4 u^4 v^4 w^4-540 a^12 b^8 c^4 u^4 v^4 w^4+5144 a^10 b^10 c^4 u^4 v^4 w^4-5004 a^8 b^12 c^4 u^4 v^4 w^4+1808 a^6 b^14 c^4 u^4 v^4 w^4-118 a^4 b^16 c^4 u^4 v^4 w^4-76 a^2 b^18 c^4 u^4 v^4 w^4+26 b^20 c^4 u^4 v^4 w^4+116 a^18 c^6 u^4 v^4 w^4+792 a^16 b^2 c^6 u^4 v^4 w^4-2608 a^14 b^4 c^6 u^4 v^4 w^4-1088 a^12 b^6 c^6 u^4 v^4 w^4+5944 a^10 b^8 c^6 u^4 v^4 w^4-1648 a^8 b^10 c^6 u^4 v^4 w^4-2608 a^6 b^12 c^6 u^4 v^4 w^4+960 a^4 b^14 c^6 u^4 v^4 w^4+180 a^2 b^16 c^6 u^4 v^4 w^4-40 b^18 c^6 u^4 v^4 w^4-81 a^16 c^8 u^4 v^4 w^4-1688 a^14 b^2 c^8 u^4 v^4 w^4-540 a^12 b^4 c^8 u^4 v^4 w^4+5944 a^10 b^6 c^8 u^4 v^4 w^4+11322 a^8 b^8 c^8 u^4 v^4 w^4+1176 a^6 b^10 c^8 u^4 v^4 w^4-3676 a^4 b^12 c^8 u^4 v^4 w^4-184 a^2 b^14 c^8 u^4 v^4 w^4+15 b^16 c^8 u^4 v^4 w^4-120 a^14 c^10 u^4 v^4 w^4+2112 a^12 b^2 c^10 u^4 v^4 w^4+5144 a^10 b^4 c^10 u^4 v^4 w^4-1648 a^8 b^6 c^10 u^4 v^4 w^4+1176 a^6 b^8 c^10 u^4 v^4 w^4+5504 a^4 b^10 c^10 u^4 v^4 w^4+72 a^2 b^12 c^10 u^4 v^4 w^4+48 b^14 c^10 u^4 v^4 w^4+252 a^12 c^12 u^4 v^4 w^4-1752 a^10 b^2 c^12 u^4 v^4 w^4-5004 a^8 b^4 c^12 u^4 v^4 w^4-2608 a^6 b^6 c^12 u^4 v^4 w^4-3676 a^4 b^8 c^12 u^4 v^4 w^4+72 a^2 b^10 c^12 u^4 v^4 w^4-84 b^12 c^12 u^4 v^4 w^4-120 a^10 c^14 u^4 v^4 w^4+1072 a^8 b^2 c^14 u^4 v^4 w^4+1808 a^6 b^4 c^14 u^4 v^4 w^4+960 a^4 b^6 c^14 u^4 v^4 w^4-184 a^2 b^8 c^14 u^4 v^4 w^4+48 b^10 c^14 u^4 v^4 w^4-81 a^8 c^16 u^4 v^4 w^4-492 a^6 b^2 c^16 u^4 v^4 w^4-118 a^4 b^4 c^16 u^4 v^4 w^4+180 a^2 b^6 c^16 u^4 v^4 w^4+15 b^8 c^16 u^4 v^4 w^4+116 a^6 c^18 u^4 v^4 w^4+128 a^4 b^2 c^18 u^4 v^4 w^4-76 a^2 b^4 c^18 u^4 v^4 w^4-40 b^6 c^18 u^4 v^4 w^4-46 a^4 c^20 u^4 v^4 w^4+4 a^2 b^2 c^20 u^4 v^4 w^4+26 b^4 c^20 u^4 v^4 w^4+4 a^2 c^22 u^4 v^4 w^4-8 b^2 c^22 u^4 v^4 w^4+c^24 u^4 v^4 w^4+2 a^24 u^3 v^5 w^4-10 a^22 b^2 u^3 v^5 w^4+14 a^20 b^4 u^3 v^5 w^4+10 a^18 b^6 u^3 v^5 w^4-44 a^16 b^8 u^3 v^5 w^4+28 a^14 b^10 u^3 v^5 w^4+28 a^12 b^12 u^3 v^5 w^4-44 a^10 b^14 u^3 v^5 w^4+10 a^8 b^16 u^3 v^5 w^4+14 a^6 b^18 u^3 v^5 w^4-10 a^4 b^20 u^3 v^5 w^4+2 a^2 b^22 u^3 v^5 w^4+10 a^22 c^2 u^3 v^5 w^4-76 a^20 b^2 c^2 u^3 v^5 w^4+194 a^18 b^4 c^2 u^3 v^5 w^4-176 a^16 b^6 c^2 u^3 v^5 w^4-44 a^14 b^8 c^2 u^3 v^5 w^4+152 a^12 b^10 c^2 u^3 v^5 w^4-44 a^10 b^12 c^2 u^3 v^5 w^4+16 a^8 b^14 c^2 u^3 v^5 w^4-94 a^6 b^16 c^2 u^3 v^5 w^4+84 a^4 b^18 c^2 u^3 v^5 w^4-22 a^2 b^20 c^2 u^3 v^5 w^4-98 a^20 c^4 u^3 v^5 w^4+318 a^18 b^2 c^4 u^3 v^5 w^4-616 a^16 b^4 c^4 u^3 v^5 w^4+664 a^14 b^6 c^4 u^3 v^5 w^4+548 a^12 b^8 c^4 u^3 v^5 w^4-2076 a^10 b^10 c^4 u^3 v^5 w^4+1528 a^8 b^12 c^4 u^3 v^5 w^4-8 a^6 b^14 c^4 u^3 v^5 w^4-338 a^4 b^16 c^4 u^3 v^5 w^4+78 a^2 b^18 c^4 u^3 v^5 w^4+246 a^18 c^6 u^3 v^5 w^4-240 a^16 b^2 c^6 u^3 v^5 w^4-1560 a^14 b^4 c^6 u^3 v^5 w^4+336 a^12 b^6 c^6 u^3 v^5 w^4+4708 a^10 b^8 c^6 u^3 v^5 w^4-4048 a^8 b^10 c^6 u^3 v^5 w^4+40 a^6 b^12 c^6 u^3 v^5 w^4+624 a^4 b^14 c^6 u^3 v^5 w^4-106 a^2 b^16 c^6 u^3 v^5 w^4-236 a^16 c^8 u^3 v^5 w^4-340 a^14 b^2 c^8 u^3 v^5 w^4+5124 a^12 b^4 c^8 u^3 v^5 w^4-868 a^10 b^6 c^8 u^3 v^5 w^4+828 a^8 b^8 c^8 u^3 v^5 w^4-60 a^6 b^10 c^8 u^3 v^5 w^4-340 a^4 b^12 c^8 u^3 v^5 w^4-12 a^2 b^14 c^8 u^3 v^5 w^4-28 a^14 c^10 u^3 v^5 w^4+728 a^12 b^2 c^10 u^3 v^5 w^4-2788 a^10 b^4 c^10 u^3 v^5 w^4+2928 a^8 b^6 c^10 u^3 v^5 w^4+1468 a^6 b^8 c^10 u^3 v^5 w^4-456 a^4 b^10 c^10 u^3 v^5 w^4+196 a^2 b^12 c^10 u^3 v^5 w^4+252 a^12 c^12 u^3 v^5 w^4-724 a^10 b^2 c^12 u^3 v^5 w^4-1928 a^8 b^4 c^12 u^3 v^5 w^4-2728 a^6 b^6 c^12 u^3 v^5 w^4+716 a^4 b^8 c^12 u^3 v^5 w^4-196 a^2 b^10 c^12 u^3 v^5 w^4-212 a^10 c^14 u^3 v^5 w^4+592 a^8 b^2 c^14 u^3 v^5 w^4+1672 a^6 b^4 c^14 u^3 v^5 w^4-272 a^4 b^6 c^14 u^3 v^5 w^4+12 a^2 b^8 c^14 u^3 v^5 w^4+74 a^8 c^16 u^3 v^5 w^4-290 a^6 b^2 c^16 u^3 v^5 w^4-34 a^4 b^4 c^16 u^3 v^5 w^4+106 a^2 b^6 c^16 u^3 v^5 w^4-14 a^6 c^18 u^3 v^5 w^4+20 a^4 b^2 c^18 u^3 v^5 w^4-78 a^2 b^4 c^18 u^3 v^5 w^4+6 a^4 c^20 u^3 v^5 w^4+22 a^2 b^2 c^20 u^3 v^5 w^4-2 a^2 c^22 u^3 v^5 w^4-16 a^20 b^2 c^2 u^2 v^6 w^4+64 a^18 b^4 c^2 u^2 v^6 w^4-64 a^16 b^6 c^2 u^2 v^6 w^4-64 a^14 b^8 c^2 u^2 v^6 w^4+160 a^12 b^10 c^2 u^2 v^6 w^4-64 a^10 b^12 c^2 u^2 v^6 w^4-64 a^8 b^14 c^2 u^2 v^6 w^4+64 a^6 b^16 c^2 u^2 v^6 w^4-16 a^4 b^18 c^2 u^2 v^6 w^4-192 a^18 b^2 c^4 u^2 v^6 w^4+320 a^16 b^4 c^4 u^2 v^6 w^4+448 a^14 b^6 c^4 u^2 v^6 w^4-1088 a^12 b^8 c^4 u^2 v^6 w^4+192 a^10 b^10 c^4 u^2 v^6 w^4+704 a^8 b^12 c^4 u^2 v^6 w^4-448 a^6 b^14 c^4 u^2 v^6 w^4+64 a^4 b^16 c^4 u^2 v^6 w^4+192 a^16 b^2 c^6 u^2 v^6 w^4-1344 a^14 b^4 c^6 u^2 v^6 w^4+1344 a^12 b^6 c^6 u^2 v^6 w^4+1152 a^10 b^8 c^6 u^2 v^6 w^4-1984 a^8 b^10 c^6 u^2 v^6 w^4+704 a^6 b^12 c^6 u^2 v^6 w^4-64 a^4 b^14 c^6 u^2 v^6 w^4+1216 a^14 b^2 c^8 u^2 v^6 w^4+960 a^12 b^4 c^8 u^2 v^6 w^4-3456 a^10 b^6 c^8 u^2 v^6 w^4+1152 a^8 b^8 c^8 u^2 v^6 w^4+192 a^6 b^10 c^8 u^2 v^6 w^4-64 a^4 b^12 c^8 u^2 v^6 w^4-2400 a^12 b^2 c^10 u^2 v^6 w^4+960 a^10 b^4 c^10 u^2 v^6 w^4+1344 a^8 b^6 c^10 u^2 v^6 w^4-1088 a^6 b^8 c^10 u^2 v^6 w^4+160 a^4 b^10 c^10 u^2 v^6 w^4+1216 a^10 b^2 c^12 u^2 v^6 w^4-1344 a^8 b^4 c^12 u^2 v^6 w^4+448 a^6 b^6 c^12 u^2 v^6 w^4-64 a^4 b^8 c^12 u^2 v^6 w^4+192 a^8 b^2 c^14 u^2 v^6 w^4+320 a^6 b^4 c^14 u^2 v^6 w^4-64 a^4 b^6 c^14 u^2 v^6 w^4-192 a^6 b^2 c^16 u^2 v^6 w^4+64 a^4 b^4 c^16 u^2 v^6 w^4-16 a^4 b^2 c^18 u^2 v^6 w^4+32 a^14 b^8 c^2 u^7 w^5-96 a^12 b^10 c^2 u^7 w^5+32 a^10 b^12 c^2 u^7 w^5+160 a^8 b^14 c^2 u^7 w^5-160 a^6 b^16 c^2 u^7 w^5-32 a^4 b^18 c^2 u^7 w^5+96 a^2 b^20 c^2 u^7 w^5-32 b^22 c^2 u^7 w^5+96 a^12 b^8 c^4 u^7 w^5+64 a^10 b^10 c^4 u^7 w^5-608 a^8 b^12 c^4 u^7 w^5+384 a^6 b^14 c^4 u^7 w^5+416 a^4 b^16 c^4 u^7 w^5-448 a^2 b^18 c^4 u^7 w^5+96 b^20 c^4 u^7 w^5-480 a^10 b^8 c^6 u^7 w^5+608 a^8 b^10 c^6 u^7 w^5+576 a^6 b^12 c^6 u^7 w^5-1088 a^4 b^14 c^6 u^7 w^5+416 a^2 b^16 c^6 u^7 w^5-32 b^18 c^6 u^7 w^5+352 a^8 b^8 c^8 u^7 w^5-1152 a^6 b^10 c^8 u^7 w^5+576 a^4 b^12 c^8 u^7 w^5+384 a^2 b^14 c^8 u^7 w^5-160 b^16 c^8 u^7 w^5+352 a^6 b^8 c^10 u^7 w^5+608 a^4 b^10 c^10 u^7 w^5-608 a^2 b^12 c^10 u^7 w^5+160 b^14 c^10 u^7 w^5-480 a^4 b^8 c^12 u^7 w^5+64 a^2 b^10 c^12 u^7 w^5+32 b^12 c^12 u^7 w^5+96 a^2 b^8 c^14 u^7 w^5-96 b^10 c^14 u^7 w^5+32 b^8 c^16 u^7 w^5-8 a^18 b^6 u^6 v w^5+40 a^16 b^8 u^6 v w^5-64 a^14 b^10 u^6 v w^5+112 a^10 b^14 u^6 v w^5-112 a^8 b^16 u^6 v w^5+64 a^4 b^20 u^6 v w^5-40 a^2 b^22 u^6 v w^5+8 b^24 u^6 v w^5-56 a^16 b^6 c^2 u^6 v w^5+288 a^14 b^8 c^2 u^6 v w^5-480 a^12 b^10 c^2 u^6 v w^5+96 a^10 b^12 c^2 u^6 v w^5+560 a^8 b^14 c^2 u^6 v w^5-544 a^6 b^16 c^2 u^6 v w^5+32 a^4 b^18 c^2 u^6 v w^5+160 a^2 b^20 c^2 u^6 v w^5-56 b^22 c^2 u^6 v w^5+384 a^14 b^6 c^4 u^6 v w^5-672 a^12 b^8 c^4 u^6 v w^5-96 a^10 b^10 c^4 u^6 v w^5+64 a^8 b^12 c^4 u^6 v w^5+1216 a^6 b^14 c^4 u^6 v w^5-1056 a^4 b^16 c^4 u^6 v w^5+32 a^2 b^18 c^4 u^6 v w^5+128 b^20 c^4 u^6 v w^5-704 a^12 b^6 c^6 u^6 v w^5-416 a^10 b^8 c^6 u^6 v w^5+704 a^8 b^10 c^6 u^6 v w^5-192 a^6 b^12 c^6 u^6 v w^5+1344 a^4 b^14 c^6 u^6 v w^5-672 a^2 b^16 c^6 u^6 v w^5-64 b^18 c^6 u^6 v w^5+304 a^10 b^6 c^8 u^6 v w^5+1328 a^8 b^8 c^8 u^6 v w^5+256 a^6 b^10 c^8 u^6 v w^5-256 a^4 b^12 c^8 u^6 v w^5+592 a^2 b^14 c^8 u^6 v w^5-176 b^16 c^8 u^6 v w^5+528 a^8 b^6 c^10 u^6 v w^5-32 a^6 b^8 c^10 u^6 v w^5+416 a^4 b^10 c^10 u^6 v w^5+352 a^2 b^12 c^10 u^6 v w^5+272 b^14 c^10 u^6 v w^5-704 a^6 b^6 c^12 u^6 v w^5-800 a^4 b^8 c^12 u^6 v w^5-608 a^2 b^10 c^12 u^6 v w^5-64 b^12 c^12 u^6 v w^5+256 a^4 b^6 c^14 u^6 v w^5+160 a^2 b^8 c^14 u^6 v w^5-128 b^10 c^14 u^6 v w^5+24 a^2 b^6 c^16 u^6 v w^5+104 b^8 c^16 u^6 v w^5-24 b^6 c^18 u^6 v w^5+4 a^20 b^4 u^5 v^2 w^5-56 a^18 b^6 u^5 v^2 w^5+244 a^16 b^8 u^5 v^2 w^5-480 a^14 b^10 u^5 v^2 w^5+392 a^12 b^12 u^5 v^2 w^5+112 a^10 b^14 u^5 v^2 w^5-504 a^8 b^16 u^5 v^2 w^5+416 a^6 b^18 u^5 v^2 w^5-140 a^4 b^20 u^5 v^2 w^5+8 a^2 b^22 u^5 v^2 w^5+4 b^24 u^5 v^2 w^5-104 a^18 b^4 c^2 u^5 v^2 w^5+232 a^16 b^6 c^2 u^5 v^2 w^5+352 a^14 b^8 c^2 u^5 v^2 w^5-1440 a^12 b^10 c^2 u^5 v^2 w^5+1104 a^10 b^12 c^2 u^5 v^2 w^5+624 a^8 b^14 c^2 u^5 v^2 w^5-1312 a^6 b^16 c^2 u^5 v^2 w^5+608 a^4 b^18 c^2 u^5 v^2 w^5-40 a^2 b^20 c^2 u^5 v^2 w^5-24 b^22 c^2 u^5 v^2 w^5+404 a^16 b^4 c^4 u^5 v^2 w^5-128 a^14 b^6 c^4 u^5 v^2 w^5-2608 a^12 b^8 c^4 u^5 v^2 w^5+3072 a^10 b^10 c^4 u^5 v^2 w^5+1240 a^8 b^12 c^4 u^5 v^2 w^5-2688 a^6 b^14 c^4 u^5 v^2 w^5+400 a^4 b^16 c^4 u^5 v^2 w^5+256 a^2 b^18 c^4 u^5 v^2 w^5+52 b^20 c^4 u^5 v^2 w^5-512 a^14 b^4 c^6 u^5 v^2 w^5-864 a^12 b^6 c^6 u^5 v^2 w^5-960 a^10 b^8 c^6 u^5 v^2 w^5-1376 a^8 b^10 c^6 u^5 v^2 w^5+6784 a^6 b^12 c^6 u^5 v^2 w^5-2336 a^4 b^14 c^6 u^5 v^2 w^5-704 a^2 b^16 c^6 u^5 v^2 w^5-32 b^18 c^6 u^5 v^2 w^5-88 a^12 b^4 c^8 u^5 v^2 w^5+2064 a^10 b^6 c^8 u^5 v^2 w^5+6712 a^8 b^8 c^8 u^5 v^2 w^5-1376 a^6 b^10 c^8 u^5 v^2 w^5+344 a^4 b^12 c^8 u^5 v^2 w^5+592 a^2 b^14 c^8 u^5 v^2 w^5-56 b^16 c^8 u^5 v^2 w^5+752 a^10 b^4 c^10 u^5 v^2 w^5-2064 a^8 b^6 c^10 u^5 v^2 w^5-2848 a^6 b^8 c^10 u^5 v^2 w^5+2592 a^4 b^10 c^10 u^5 v^2 w^5+432 a^2 b^12 c^10 u^5 v^2 w^5+112 b^14 c^10 u^5 v^2 w^5-536 a^8 b^4 c^12 u^5 v^2 w^5+1088 a^6 b^6 c^12 u^5 v^2 w^5-1328 a^4 b^8 c^12 u^5 v^2 w^5-960 a^2 b^10 c^12 u^5 v^2 w^5-56 b^12 c^12 u^5 v^2 w^5-64 a^6 b^4 c^14 u^5 v^2 w^5-352 a^4 b^6 c^14 u^5 v^2 w^5+384 a^2 b^8 c^14 u^5 v^2 w^5-32 b^10 c^14 u^5 v^2 w^5+212 a^4 b^4 c^16 u^5 v^2 w^5+104 a^2 b^6 c^16 u^5 v^2 w^5+52 b^8 c^16 u^5 v^2 w^5-72 a^2 b^4 c^18 u^5 v^2 w^5-24 b^6 c^18 u^5 v^2 w^5+4 b^4 c^20 u^5 v^2 w^5+8 a^22 b^2 u^4 v^3 w^5-32 a^20 b^4 u^4 v^3 w^5-24 a^18 b^6 u^4 v^3 w^5+384 a^16 b^8 u^4 v^3 w^5-1008 a^14 b^10 u^4 v^3 w^5+1344 a^12 b^12 u^4 v^3 w^5-1008 a^10 b^14 u^4 v^3 w^5+384 a^8 b^16 u^4 v^3 w^5-24 a^6 b^18 u^4 v^3 w^5-32 a^4 b^20 u^4 v^3 w^5+8 a^2 b^22 u^4 v^3 w^5-56 a^20 b^2 c^2 u^4 v^3 w^5-24 a^18 b^4 c^2 u^4 v^3 w^5+736 a^16 b^6 c^2 u^4 v^3 w^5-1312 a^14 b^8 c^2 u^4 v^3 w^5+304 a^12 b^10 c^2 u^4 v^3 w^5+1136 a^10 b^12 c^2 u^4 v^3 w^5-1056 a^8 b^14 c^2 u^4 v^3 w^5+224 a^6 b^16 c^2 u^4 v^3 w^5+72 a^4 b^18 c^2 u^4 v^3 w^5-24 a^2 b^20 c^2 u^4 v^3 w^5+144 a^18 b^2 c^4 u^4 v^3 w^5+448 a^16 b^4 c^4 u^4 v^3 w^5-2112 a^14 b^6 c^4 u^4 v^3 w^5-192 a^12 b^8 c^4 u^4 v^3 w^5+5856 a^10 b^10 c^4 u^4 v^3 w^5-5056 a^8 b^12 c^4 u^4 v^3 w^5+192 a^6 b^14 c^4 u^4 v^3 w^5+704 a^4 b^16 c^4 u^4 v^3 w^5+16 a^2 b^18 c^4 u^4 v^3 w^5-128 a^16 b^2 c^6 u^4 v^3 w^5-832 a^14 b^4 c^6 u^4 v^3 w^5+192 a^12 b^6 c^6 u^4 v^3 w^5-2176 a^10 b^8 c^6 u^4 v^3 w^5+5376 a^8 b^10 c^6 u^4 v^3 w^5-64 a^6 b^12 c^6 u^4 v^3 w^5-2368 a^4 b^14 c^6 u^4 v^3 w^5-112 a^14 b^2 c^8 u^4 v^3 w^5+576 a^12 b^4 c^8 u^4 v^3 w^5+4976 a^10 b^6 c^8 u^4 v^3 w^5+5248 a^8 b^8 c^8 u^4 v^3 w^5-528 a^6 b^10 c^8 u^4 v^3 w^5+2112 a^4 b^12 c^8 u^4 v^3 w^5+16 a^2 b^14 c^8 u^4 v^3 w^5+336 a^12 b^2 c^10 u^4 v^3 w^5-368 a^10 b^4 c^10 u^4 v^3 w^5-5536 a^8 b^6 c^10 u^4 v^3 w^5-928 a^6 b^8 c^10 u^4 v^3 w^5+336 a^4 b^10 c^10 u^4 v^3 w^5+16 a^2 b^12 c^10 u^4 v^3 w^5-224 a^10 b^2 c^12 u^4 v^3 w^5+704 a^8 b^4 c^12 u^4 v^3 w^5+1728 a^6 b^6 c^12 u^4 v^3 w^5-1088 a^4 b^8 c^12 u^4 v^3 w^5-96 a^2 b^10 c^12 u^4 v^3 w^5-64 a^8 b^2 c^14 u^4 v^3 w^5-768 a^6 b^4 c^14 u^4 v^3 w^5+64 a^2 b^8 c^14 u^4 v^3 w^5+168 a^6 b^2 c^16 u^4 v^3 w^5+352 a^4 b^4 c^16 u^4 v^3 w^5+40 a^2 b^6 c^16 u^4 v^3 w^5-88 a^4 b^2 c^18 u^4 v^3 w^5-56 a^2 b^4 c^18 u^4 v^3 w^5+16 a^2 b^2 c^20 u^4 v^3 w^5+2 a^24 u^3 v^4 w^5+10 a^22 b^2 u^3 v^4 w^5-98 a^20 b^4 u^3 v^4 w^5+246 a^18 b^6 u^3 v^4 w^5-236 a^16 b^8 u^3 v^4 w^5-28 a^14 b^10 u^3 v^4 w^5+252 a^12 b^12 u^3 v^4 w^5-212 a^10 b^14 u^3 v^4 w^5+74 a^8 b^16 u^3 v^4 w^5-14 a^6 b^18 u^3 v^4 w^5+6 a^4 b^20 u^3 v^4 w^5-2 a^2 b^22 u^3 v^4 w^5-10 a^22 c^2 u^3 v^4 w^5-76 a^20 b^2 c^2 u^3 v^4 w^5+318 a^18 b^4 c^2 u^3 v^4 w^5-240 a^16 b^6 c^2 u^3 v^4 w^5-340 a^14 b^8 c^2 u^3 v^4 w^5+728 a^12 b^10 c^2 u^3 v^4 w^5-724 a^10 b^12 c^2 u^3 v^4 w^5+592 a^8 b^14 c^2 u^3 v^4 w^5-290 a^6 b^16 c^2 u^3 v^4 w^5+20 a^4 b^18 c^2 u^3 v^4 w^5+22 a^2 b^20 c^2 u^3 v^4 w^5+14 a^20 c^4 u^3 v^4 w^5+194 a^18 b^2 c^4 u^3 v^4 w^5-616 a^16 b^4 c^4 u^3 v^4 w^5-1560 a^14 b^6 c^4 u^3 v^4 w^5+5124 a^12 b^8 c^4 u^3 v^4 w^5-2788 a^10 b^10 c^4 u^3 v^4 w^5-1928 a^8 b^12 c^4 u^3 v^4 w^5+1672 a^6 b^14 c^4 u^3 v^4 w^5-34 a^4 b^16 c^4 u^3 v^4 w^5-78 a^2 b^18 c^4 u^3 v^4 w^5+10 a^18 c^6 u^3 v^4 w^5-176 a^16 b^2 c^6 u^3 v^4 w^5+664 a^14 b^4 c^6 u^3 v^4 w^5+336 a^12 b^6 c^6 u^3 v^4 w^5-868 a^10 b^8 c^6 u^3 v^4 w^5+2928 a^8 b^10 c^6 u^3 v^4 w^5-2728 a^6 b^12 c^6 u^3 v^4 w^5-272 a^4 b^14 c^6 u^3 v^4 w^5+106 a^2 b^16 c^6 u^3 v^4 w^5-44 a^16 c^8 u^3 v^4 w^5-44 a^14 b^2 c^8 u^3 v^4 w^5+548 a^12 b^4 c^8 u^3 v^4 w^5+4708 a^10 b^6 c^8 u^3 v^4 w^5+828 a^8 b^8 c^8 u^3 v^4 w^5+1468 a^6 b^10 c^8 u^3 v^4 w^5+716 a^4 b^12 c^8 u^3 v^4 w^5+12 a^2 b^14 c^8 u^3 v^4 w^5+28 a^14 c^10 u^3 v^4 w^5+152 a^12 b^2 c^10 u^3 v^4 w^5-2076 a^10 b^4 c^10 u^3 v^4 w^5-4048 a^8 b^6 c^10 u^3 v^4 w^5-60 a^6 b^8 c^10 u^3 v^4 w^5-456 a^4 b^10 c^10 u^3 v^4 w^5-196 a^2 b^12 c^10 u^3 v^4 w^5+28 a^12 c^12 u^3 v^4 w^5-44 a^10 b^2 c^12 u^3 v^4 w^5+1528 a^8 b^4 c^12 u^3 v^4 w^5+40 a^6 b^6 c^12 u^3 v^4 w^5-340 a^4 b^8 c^12 u^3 v^4 w^5+196 a^2 b^10 c^12 u^3 v^4 w^5-44 a^10 c^14 u^3 v^4 w^5+16 a^8 b^2 c^14 u^3 v^4 w^5-8 a^6 b^4 c^14 u^3 v^4 w^5+624 a^4 b^6 c^14 u^3 v^4 w^5-12 a^2 b^8 c^14 u^3 v^4 w^5+10 a^8 c^16 u^3 v^4 w^5-94 a^6 b^2 c^16 u^3 v^4 w^5-338 a^4 b^4 c^16 u^3 v^4 w^5-106 a^2 b^6 c^16 u^3 v^4 w^5+14 a^6 c^18 u^3 v^4 w^5+84 a^4 b^2 c^18 u^3 v^4 w^5+78 a^2 b^4 c^18 u^3 v^4 w^5-10 a^4 c^20 u^3 v^4 w^5-22 a^2 b^2 c^20 u^3 v^4 w^5+2 a^2 c^22 u^3 v^4 w^5+4 a^24 u^2 v^5 w^5-16 a^22 b^2 u^2 v^5 w^5+12 a^20 b^4 u^2 v^5 w^5+32 a^18 b^6 u^2 v^5 w^5-56 a^16 b^8 u^2 v^5 w^5+56 a^12 b^12 u^2 v^5 w^5-32 a^10 b^14 u^2 v^5 w^5-12 a^8 b^16 u^2 v^5 w^5+16 a^6 b^18 u^2 v^5 w^5-4 a^4 b^20 u^2 v^5 w^5-16 a^22 c^2 u^2 v^5 w^5+8 a^20 b^2 c^2 u^2 v^5 w^5-32 a^18 b^4 c^2 u^2 v^5 w^5+352 a^16 b^6 c^2 u^2 v^5 w^5-512 a^14 b^8 c^2 u^2 v^5 w^5-144 a^12 b^10 c^2 u^2 v^5 w^5+672 a^10 b^12 c^2 u^2 v^5 w^5-288 a^8 b^14 c^2 u^2 v^5 w^5-112 a^6 b^16 c^2 u^2 v^5 w^5+72 a^4 b^18 c^2 u^2 v^5 w^5+12 a^20 c^4 u^2 v^5 w^5-32 a^18 b^2 c^4 u^2 v^5 w^5-1296 a^16 b^4 c^4 u^2 v^5 w^5+2304 a^14 b^6 c^4 u^2 v^5 w^5+1160 a^12 b^8 c^4 u^2 v^5 w^5-3872 a^10 b^10 c^4 u^2 v^5 w^5+1392 a^8 b^12 c^4 u^2 v^5 w^5+576 a^6 b^14 c^4 u^2 v^5 w^5-244 a^4 b^16 c^4 u^2 v^5 w^5+32 a^18 c^6 u^2 v^5 w^5+352 a^16 b^2 c^6 u^2 v^5 w^5+2304 a^14 b^4 c^6 u^2 v^5 w^5-5216 a^12 b^6 c^6 u^2 v^5 w^5+3232 a^10 b^8 c^6 u^2 v^5 w^5+288 a^8 b^10 c^6 u^2 v^5 w^5-1216 a^6 b^12 c^6 u^2 v^5 w^5+224 a^4 b^14 c^6 u^2 v^5 w^5-56 a^16 c^8 u^2 v^5 w^5-512 a^14 b^2 c^8 u^2 v^5 w^5+1160 a^12 b^4 c^8 u^2 v^5 w^5+3232 a^10 b^6 c^8 u^2 v^5 w^5-2760 a^8 b^8 c^8 u^2 v^5 w^5+736 a^6 b^10 c^8 u^2 v^5 w^5+248 a^4 b^12 c^8 u^2 v^5 w^5-144 a^12 b^2 c^10 u^2 v^5 w^5-3872 a^10 b^4 c^10 u^2 v^5 w^5+288 a^8 b^6 c^10 u^2 v^5 w^5+736 a^6 b^8 c^10 u^2 v^5 w^5-592 a^4 b^10 c^10 u^2 v^5 w^5+56 a^12 c^12 u^2 v^5 w^5+672 a^10 b^2 c^12 u^2 v^5 w^5+1392 a^8 b^4 c^12 u^2 v^5 w^5-1216 a^6 b^6 c^12 u^2 v^5 w^5+248 a^4 b^8 c^12 u^2 v^5 w^5-32 a^10 c^14 u^2 v^5 w^5-288 a^8 b^2 c^14 u^2 v^5 w^5+576 a^6 b^4 c^14 u^2 v^5 w^5+224 a^4 b^6 c^14 u^2 v^5 w^5-12 a^8 c^16 u^2 v^5 w^5-112 a^6 b^2 c^16 u^2 v^5 w^5-244 a^4 b^4 c^16 u^2 v^5 w^5+16 a^6 c^18 u^2 v^5 w^5+72 a^4 b^2 c^18 u^2 v^5 w^5-4 a^4 c^20 u^2 v^5 w^5-64 a^20 b^2 c^2 u v^6 w^5+192 a^18 b^4 c^2 u v^6 w^5-64 a^16 b^6 c^2 u v^6 w^5-320 a^14 b^8 c^2 u v^6 w^5+320 a^12 b^10 c^2 u v^6 w^5+64 a^10 b^12 c^2 u v^6 w^5-192 a^8 b^14 c^2 u v^6 w^5+64 a^6 b^16 c^2 u v^6 w^5-192 a^18 b^2 c^4 u v^6 w^5-128 a^16 b^4 c^4 u v^6 w^5+1216 a^14 b^6 c^4 u v^6 w^5-768 a^12 b^8 c^4 u v^6 w^5-832 a^10 b^10 c^4 u v^6 w^5+896 a^8 b^12 c^4 u v^6 w^5-192 a^6 b^14 c^4 u v^6 w^5+960 a^16 b^2 c^6 u v^6 w^5-1216 a^14 b^4 c^6 u v^6 w^5-1152 a^12 b^6 c^6 u v^6 w^5+2176 a^10 b^8 c^6 u v^6 w^5-832 a^8 b^10 c^6 u v^6 w^5+64 a^6 b^12 c^6 u v^6 w^5-704 a^14 b^2 c^8 u v^6 w^5+2304 a^12 b^4 c^8 u v^6 w^5-1152 a^10 b^6 c^8 u v^6 w^5-768 a^8 b^8 c^8 u v^6 w^5+320 a^6 b^10 c^8 u v^6 w^5-704 a^12 b^2 c^10 u v^6 w^5-1216 a^10 b^4 c^10 u v^6 w^5+1216 a^8 b^6 c^10 u v^6 w^5-320 a^6 b^8 c^10 u v^6 w^5+960 a^10 b^2 c^12 u v^6 w^5-128 a^8 b^4 c^12 u v^6 w^5-64 a^6 b^6 c^12 u v^6 w^5-192 a^8 b^2 c^14 u v^6 w^5+192 a^6 b^4 c^14 u v^6 w^5-64 a^6 b^2 c^16 u v^6 w^5+64 a^14 b^8 c^2 u^6 w^6-128 a^12 b^10 c^2 u^6 w^6-64 a^10 b^12 c^2 u^6 w^6+256 a^8 b^14 c^2 u^6 w^6-64 a^6 b^16 c^2 u^6 w^6-128 a^4 b^18 c^2 u^6 w^6+64 a^2 b^20 c^2 u^6 w^6-128 a^12 b^8 c^4 u^6 w^6+384 a^10 b^10 c^4 u^6 w^6-256 a^8 b^12 c^4 u^6 w^6-256 a^6 b^14 c^4 u^6 w^6+384 a^4 b^16 c^4 u^6 w^6-128 a^2 b^18 c^4 u^6 w^6-64 a^10 b^8 c^6 u^6 w^6-256 a^8 b^10 c^6 u^6 w^6+640 a^6 b^12 c^6 u^6 w^6-256 a^4 b^14 c^6 u^6 w^6-64 a^2 b^16 c^6 u^6 w^6+256 a^8 b^8 c^8 u^6 w^6-256 a^6 b^10 c^8 u^6 w^6-256 a^4 b^12 c^8 u^6 w^6+256 a^2 b^14 c^8 u^6 w^6-64 a^6 b^8 c^10 u^6 w^6+384 a^4 b^10 c^10 u^6 w^6-64 a^2 b^12 c^10 u^6 w^6-128 a^4 b^8 c^12 u^6 w^6-128 a^2 b^10 c^12 u^6 w^6+64 a^2 b^8 c^14 u^6 w^6+64 a^16 b^6 c^2 u^5 v w^6+192 a^14 b^8 c^2 u^5 v w^6-960 a^12 b^10 c^2 u^5 v w^6+704 a^10 b^12 c^2 u^5 v w^6+704 a^8 b^14 c^2 u^5 v w^6-960 a^6 b^16 c^2 u^5 v w^6+192 a^4 b^18 c^2 u^5 v w^6+64 a^2 b^20 c^2 u^5 v w^6-192 a^14 b^6 c^4 u^5 v w^6+128 a^12 b^8 c^4 u^5 v w^6+1216 a^10 b^10 c^4 u^5 v w^6-2304 a^8 b^12 c^4 u^5 v w^6+1216 a^6 b^14 c^4 u^5 v w^6+128 a^4 b^16 c^4 u^5 v w^6-192 a^2 b^18 c^4 u^5 v w^6+64 a^12 b^6 c^6 u^5 v w^6-1216 a^10 b^8 c^6 u^5 v w^6+1152 a^8 b^10 c^6 u^5 v w^6+1152 a^6 b^12 c^6 u^5 v w^6-1216 a^4 b^14 c^6 u^5 v w^6+64 a^2 b^16 c^6 u^5 v w^6+320 a^10 b^6 c^8 u^5 v w^6+768 a^8 b^8 c^8 u^5 v w^6-2176 a^6 b^10 c^8 u^5 v w^6+768 a^4 b^12 c^8 u^5 v w^6+320 a^2 b^14 c^8 u^5 v w^6-320 a^8 b^6 c^10 u^5 v w^6+832 a^6 b^8 c^10 u^5 v w^6+832 a^4 b^10 c^10 u^5 v w^6-320 a^2 b^12 c^10 u^5 v w^6-64 a^6 b^6 c^12 u^5 v w^6-896 a^4 b^8 c^12 u^5 v w^6-64 a^2 b^10 c^12 u^5 v w^6+192 a^4 b^6 c^14 u^5 v w^6+192 a^2 b^8 c^14 u^5 v w^6-64 a^2 b^6 c^16 u^5 v w^6+16 a^18 b^4 c^2 u^4 v^2 w^6+192 a^16 b^6 c^2 u^4 v^2 w^6-192 a^14 b^8 c^2 u^4 v^2 w^6-1216 a^12 b^10 c^2 u^4 v^2 w^6+2400 a^10 b^12 c^2 u^4 v^2 w^6-1216 a^8 b^14 c^2 u^4 v^2 w^6-192 a^6 b^16 c^2 u^4 v^2 w^6+192 a^4 b^18 c^2 u^4 v^2 w^6+16 a^2 b^20 c^2 u^4 v^2 w^6-64 a^16 b^4 c^4 u^4 v^2 w^6-320 a^14 b^6 c^4 u^4 v^2 w^6+1344 a^12 b^8 c^4 u^4 v^2 w^6-960 a^10 b^10 c^4 u^4 v^2 w^6-960 a^8 b^12 c^4 u^4 v^2 w^6+1344 a^6 b^14 c^4 u^4 v^2 w^6-320 a^4 b^16 c^4 u^4 v^2 w^6-64 a^2 b^18 c^4 u^4 v^2 w^6+64 a^14 b^4 c^6 u^4 v^2 w^6-448 a^12 b^6 c^6 u^4 v^2 w^6-1344 a^10 b^8 c^6 u^4 v^2 w^6+3456 a^8 b^10 c^6 u^4 v^2 w^6-1344 a^6 b^12 c^6 u^4 v^2 w^6-448 a^4 b^14 c^6 u^4 v^2 w^6+64 a^2 b^16 c^6 u^4 v^2 w^6+64 a^12 b^4 c^8 u^4 v^2 w^6+1088 a^10 b^6 c^8 u^4 v^2 w^6-1152 a^8 b^8 c^8 u^4 v^2 w^6-1152 a^6 b^10 c^8 u^4 v^2 w^6+1088 a^4 b^12 c^8 u^4 v^2 w^6+64 a^2 b^14 c^8 u^4 v^2 w^6-160 a^10 b^4 c^10 u^4 v^2 w^6-192 a^8 b^6 c^10 u^4 v^2 w^6+1984 a^6 b^8 c^10 u^4 v^2 w^6-192 a^4 b^10 c^10 u^4 v^2 w^6-160 a^2 b^12 c^10 u^4 v^2 w^6+64 a^8 b^4 c^12 u^4 v^2 w^6-704 a^6 b^6 c^12 u^4 v^2 w^6-704 a^4 b^8 c^12 u^4 v^2 w^6+64 a^2 b^10 c^12 u^4 v^2 w^6+64 a^6 b^4 c^14 u^4 v^2 w^6+448 a^4 b^6 c^14 u^4 v^2 w^6+64 a^2 b^8 c^14 u^4 v^2 w^6-64 a^4 b^4 c^16 u^4 v^2 w^6-64 a^2 b^6 c^16 u^4 v^2 w^6+16 a^2 b^4 c^18 u^4 v^2 w^6-16 a^20 b^2 c^2 u^2 v^4 w^6-192 a^18 b^4 c^2 u^2 v^4 w^6+192 a^16 b^6 c^2 u^2 v^4 w^6+1216 a^14 b^8 c^2 u^2 v^4 w^6-2400 a^12 b^10 c^2 u^2 v^4 w^6+1216 a^10 b^12 c^2 u^2 v^4 w^6+192 a^8 b^14 c^2 u^2 v^4 w^6-192 a^6 b^16 c^2 u^2 v^4 w^6-16 a^4 b^18 c^2 u^2 v^4 w^6+64 a^18 b^2 c^4 u^2 v^4 w^6+320 a^16 b^4 c^4 u^2 v^4 w^6-1344 a^14 b^6 c^4 u^2 v^4 w^6+960 a^12 b^8 c^4 u^2 v^4 w^6+960 a^10 b^10 c^4 u^2 v^4 w^6-1344 a^8 b^12 c^4 u^2 v^4 w^6+320 a^6 b^14 c^4 u^2 v^4 w^6+64 a^4 b^16 c^4 u^2 v^4 w^6-64 a^16 b^2 c^6 u^2 v^4 w^6+448 a^14 b^4 c^6 u^2 v^4 w^6+1344 a^12 b^6 c^6 u^2 v^4 w^6-3456 a^10 b^8 c^6 u^2 v^4 w^6+1344 a^8 b^10 c^6 u^2 v^4 w^6+448 a^6 b^12 c^6 u^2 v^4 w^6-64 a^4 b^14 c^6 u^2 v^4 w^6-64 a^14 b^2 c^8 u^2 v^4 w^6-1088 a^12 b^4 c^8 u^2 v^4 w^6+1152 a^10 b^6 c^8 u^2 v^4 w^6+1152 a^8 b^8 c^8 u^2 v^4 w^6-1088 a^6 b^10 c^8 u^2 v^4 w^6-64 a^4 b^12 c^8 u^2 v^4 w^6+160 a^12 b^2 c^10 u^2 v^4 w^6+192 a^10 b^4 c^10 u^2 v^4 w^6-1984 a^8 b^6 c^10 u^2 v^4 w^6+192 a^6 b^8 c^10 u^2 v^4 w^6+160 a^4 b^10 c^10 u^2 v^4 w^6-64 a^10 b^2 c^12 u^2 v^4 w^6+704 a^8 b^4 c^12 u^2 v^4 w^6+704 a^6 b^6 c^12 u^2 v^4 w^6-64 a^4 b^8 c^12 u^2 v^4 w^6-64 a^8 b^2 c^14 u^2 v^4 w^6-448 a^6 b^4 c^14 u^2 v^4 w^6-64 a^4 b^6 c^14 u^2 v^4 w^6+64 a^6 b^2 c^16 u^2 v^4 w^6+64 a^4 b^4 c^16 u^2 v^4 w^6-16 a^4 b^2 c^18 u^2 v^4 w^6-64 a^20 b^2 c^2 u v^5 w^6-192 a^18 b^4 c^2 u v^5 w^6+960 a^16 b^6 c^2 u v^5 w^6-704 a^14 b^8 c^2 u v^5 w^6-704 a^12 b^10 c^2 u v^5 w^6+960 a^10 b^12 c^2 u v^5 w^6-192 a^8 b^14 c^2 u v^5 w^6-64 a^6 b^16 c^2 u v^5 w^6+192 a^18 b^2 c^4 u v^5 w^6-128 a^16 b^4 c^4 u v^5 w^6-1216 a^14 b^6 c^4 u v^5 w^6+2304 a^12 b^8 c^4 u v^5 w^6-1216 a^10 b^10 c^4 u v^5 w^6-128 a^8 b^12 c^4 u v^5 w^6+192 a^6 b^14 c^4 u v^5 w^6-64 a^16 b^2 c^6 u v^5 w^6+1216 a^14 b^4 c^6 u v^5 w^6-1152 a^12 b^6 c^6 u v^5 w^6-1152 a^10 b^8 c^6 u v^5 w^6+1216 a^8 b^10 c^6 u v^5 w^6-64 a^6 b^12 c^6 u v^5 w^6-320 a^14 b^2 c^8 u v^5 w^6-768 a^12 b^4 c^8 u v^5 w^6+2176 a^10 b^6 c^8 u v^5 w^6-768 a^8 b^8 c^8 u v^5 w^6-320 a^6 b^10 c^8 u v^5 w^6+320 a^12 b^2 c^10 u v^5 w^6-832 a^10 b^4 c^10 u v^5 w^6-832 a^8 b^6 c^10 u v^5 w^6+320 a^6 b^8 c^10 u v^5 w^6+64 a^10 b^2 c^12 u v^5 w^6+896 a^8 b^4 c^12 u v^5 w^6+64 a^6 b^6 c^12 u v^5 w^6-192 a^8 b^2 c^14 u v^5 w^6-192 a^6 b^4 c^14 u v^5 w^6+64 a^6 b^2 c^16 u v^5 w^6-64 a^20 b^2 c^2 v^6 w^6+128 a^18 b^4 c^2 v^6 w^6+64 a^16 b^6 c^2 v^6 w^6-256 a^14 b^8 c^2 v^6 w^6+64 a^12 b^10 c^2 v^6 w^6+128 a^10 b^12 c^2 v^6 w^6-64 a^8 b^14 c^2 v^6 w^6+128 a^18 b^2 c^4 v^6 w^6-384 a^16 b^4 c^4 v^6 w^6+256 a^14 b^6 c^4 v^6 w^6+256 a^12 b^8 c^4 v^6 w^6-384 a^10 b^10 c^4 v^6 w^6+128 a^8 b^12 c^4 v^6 w^6+64 a^16 b^2 c^6 v^6 w^6+256 a^14 b^4 c^6 v^6 w^6-640 a^12 b^6 c^6 v^6 w^6+256 a^10 b^8 c^6 v^6 w^6+64 a^8 b^10 c^6 v^6 w^6-256 a^14 b^2 c^8 v^6 w^6+256 a^12 b^4 c^8 v^6 w^6+256 a^10 b^6 c^8 v^6 w^6-256 a^8 b^8 c^8 v^6 w^6+64 a^12 b^2 c^10 v^6 w^6-384 a^10 b^4 c^10 v^6 w^6+64 a^8 b^6 c^10 v^6 w^6+128 a^10 b^2 c^12 v^6 w^6+128 a^8 b^4 c^12 v^6 w^6-64 a^8 b^2 c^14 v^6 w^6)

Angel Montesdeoca, 30 Nov. 2013