######################################################################
##SINKHORN.txt: Save this file as  SINKHORN.txt                      #
## To use it, stay in the                                            #
##same directory, get into Maple (by typing: maple <Enter> )         #
##and then type:  SINKHORN.txt <Enter>                               #
##Then follow the instructions given there                           #
##                                                                   #
##Written by Doron Zeilberger, Rutgers University ,                  #
#DoronZeil at gmail dot com                                          #
######################################################################
 
#Created: 

Digits:=20:
 
print(`Created:  Jan. -Feb., 2019`):
print(` This is SINKHRORN.txt `):
print(`It  accompanies the article `):
print(`Answers to Some Questions about  Explicit Sinkhorn Limits posed by Mel Nathanson`):
print(`by Shalosh B. Ekhad and Doron Zeilberger`):

print(`and also available from Zeilberger's website`):
print(``):
print(`Please report bugs to DoronZeil at gmail dot com `):
print(``):
 print(`The most current version of this  package and paper`):
 print(` are  available from`):
 print(`http://sites.math.rutgers.edu/~zeilberg/  .`):

print(`---------------------------------------`):
 print(`For a list of the checking procedures type ezraC();, for help with`):
 print(`a specific procedure, type ezra(procedure_name);   .`):
 print(``):
print(`---------------------------------------`):

print(`---------------------------------------`):
 print(`For a list of the No Good procedures type ezraNG();, for help with`):
 print(`a specific procedure, type ezra(procedure_name);   .`):
 print(``):
print(`---------------------------------------`):

print(`---------------------------------------`):
 print(`For a list of the Supporting procedures type ezra1();, for help with`):
 print(`a specific procedure, type ezra(procedure_name);   .`):
 print(``):
print(`---------------------------------------`):

print(`---------------------------------------`):
 print(`For a list of the NICE procedures type ezraNice();, for help with`):
 print(`a specific procedure, type ezra(procedure_name);   .`):
 print(``):
print(`---------------------------------------`):

print(`---------------------------------------`):
 print(`For a list of the procedures concerning Mel Nathanson's questions in his article`):
 print(`Matrix Scaling, Explicit Sinkhorn Limits, and Arithmetic`):
 print(`type ezraMel();, for help with`):
 print(`a specific procedure, type ezra(procedure_name);   .`):
 print(``):
print(`---------------------------------------`):

print(`---------------------------------------`):
 print(`For a list of the MAIN procedures type ezra();, for help with`):
 print(`a specific procedure, type ezra(procedure_name);   .`):
 print(``):
print(`---------------------------------------`):

with(combinat):

ezraMel:=proc()

if args=NULL then
 print(` The procedures answering Mel Nathanson's questions posed in his interesting article`):
 print(` "Matrix Scaling, Explicit Sinkhorn Limits, and Arithmetic" are: MelMat `):
 print(`MelNprob1, MelNprob2a, MelNprob2b, MelNprob5, MelNprob5G, MelNprob5Gnice ,MelNprob5nice, MelNsec13 `):
 print(``):

else
ezra(args):
fi:

end:

ezraC:=proc()

if args=NULL then
 print(` The checking procedures are: CheckExacGS, CheckSinkPlusErr `):
 print(``):

else
ezra(args):
fi:

end:

ezraNG:=proc()

if args=NULL then
 print(` The No Good procedures are: Exac,ExacF, MelNold, RevRS, `):
 print(``):

else
ezra(args):
fi:

end:

ezraNice:=proc()

if args=NULL then
 print(` The Nice procedures are: ExacGSnice, ExacGSniceV,ExacGSsNice, ,ExacGSsNiceV `):
 print(``):

else
ezra(args):
fi:

end:

ezra1:=proc()

if args=NULL then
 print(` The supporting procedures are: CS, DSE, Err1, ExacFF, OneStepS, RandM, RandSM,  RS, Tra `):
 print(``):

else
ezra(args):
fi:

end:

ezra:=proc()

if args=NULL then
 print(`The main procedures are:  ExacG, ExacGS, ExacGSf, ExacGSs, ExacGSs2, ExacGSs3, ExacSF, KLM,`):
print(`MelN,  Sink, SinkPlus, SinkPlusErr, SinkPlusF, SinkE, SinkEe, SinkF `):
 print(` `):


elif nops([args])=1 and op(1,[args])=CheckExacGS then
print(`CheckExacGS(M,X,p,z,S): Inputs a symmetric square matrix M, a vector X representing a diagonal matrix X phrased`):
print(`in terms of z, a polynomial p that is the minimal polynomial satisfied by z and a tentative doubly-stochastic`):
print(`matrix. Checks that indeed XMX=S (mod p(z)) and that S is doubly stochastic mod p(z). Try:`):
print(`M:=RandSM(3,10): gu:=ExacGS(M,z):CheckExacGS(M,gu[1],gu[2],z,gu[3]); `):

elif nops([args])=1 and op(1,[args])=CheckSinkPlusErr then
print(`CheckSinkPlusErr(M,X,Y,S): Inputs a square matrix in floating point and outputs `):
print(`candidate X,Y,S`):
print(`checks that indeed S=XMY and S is approximately double-stochastic with error eps. Try:`):
print(`M:=RandM(4,30): gu:=SinkPlusErr(M,1/10^18): CheckSinkPlusErr(M,op(gu));`):

elif nops([args])=1 and op(1,[args])=CS then
print(`CS(M): inputs a matrix M with positive entries M and outputs the matrix obtained by scaling its columns. Try:`):
print(`CS([[1,2,3],[2,1,3],[3,2,1]]);`):


elif nops([args])=1 and op(1,[args])=DSE then
print(`DSE(A): inputs a symbolic matrix and outputs the set of conditions that will make it doubly-stochastic. Try:`):
print(`DSE([[a,b],[c,d]]);`):

elif nops([args])=1 and op(1,[args])=Exac then
print(`Exac(M): the exact values of the matrices X, Y and S such that X and Y are diagonal matrices, S=XMY , and S is doubly stochastic`):
print(` Using solve. `):
print(`WARNING: NOT EFFICIENT, and possibly wrong.`):
print(`Try: `):
print(` Exac([[3,4],[6,7]]); `):


elif nops([args])=1 and op(1,[args])=ExacF then
print(`ExacF(M): the exact values of the matrices X, Y and S such that X and Y are diagonal matrices, S=XMY , and S is doubly stochastic`):
print(` Using fsolve. May give negative entires. `):
print(`WARNING: NOT EFFICIENT, and possibly wrong, it may give negative entries.`):
print(`Try: `):
print(` ExacF([[3,4],[6,7]]); `):

elif nops([args])=1 and op(1,[args])=ExacFF then
print(`ExacFF(M): the exact values of the matrices X, Y and S such that X and Y are diagonal matrices, S=XMY , and S is doubly stochastic`):
print(` Using fsolve with the entries between 0 or 1. May FAIL. Try: `):
print(` ExacFF([[3,4],[6,7]]); `):


elif nops([args])=1 and op(1,[args])=ExacG then
print(`ExacG(M,x,y): Like Exca(M) but using Groebner basis where we normalize the (1,1) entry of the diagonal matrix X to be 1 and`):
print(`X=Diag(1,x[2], .., x[n]); Y=Diag(y[1], ..., y[n]). `):
print(`Try:`):
print(`ExacG([[3,4],[6,7]],x,y);`):


elif nops([args])=1 and op(1,[args])=ExacGS then

print(`ExacGS(M,z): Inputs a symmetric matrix M, and a variable name z and outputs the vector`):
print(` X=[x[1],x[2], .., x[n]]; such that if X denotes the diagonal matrix with entry X, XMX  is doubly-stochastic.`):
print(`It returns a triple whose first entry is a list of length n where x[1] is denoted by the variable z, and x[2], ..., x[n] `):
print(`are polynomials in z, and second entry is the minimal polynomial satisfied by z.`):
print(`and the third entry is the Sinkhorn limit. `):
print(` Try: `):
print(` ExacGS([[3,4],[4,5]],z); `):


elif nops([args])=1 and op(1,[args])=ExacGSf then
print(`ExacGSf(M): inputs a symmetric matrix M and outputs the Exact (numeric) value (in floating-point) of X and S such that S=XMX is doubly-stochastic`):
print(`using the  exact procedure ExacGS(M,z). `):
pritn(` Try:  `):
print(` ExacGSf([[3,4],[4,5]]); `):

elif nops([args])=1 and op(1,[args])=ExacGSnice then
print(`ExacGSnice(M,z):  Like ExacGS(M,z), but with z^2 replaced by z, and the first vector is divided by sqrt(z)`):
print(`(where z is the new z).`):
print(`Try:  `):
print(`ExacGSnice([[3,4],[4,5]],z);`):

elif nops([args])=1 and op(1,[args])=ExacGSniceV then
print(`ExacGSniceV(M,z):  Verbose version of ExacGSnice(M,z). `):
print(`Try:  `):
print(`ExacGSniceV([[3,4],[4,5]],z);`):

elif nops([args])=1 and op(1,[args])=ExacGSs then
print(`ExacGSs(a,k,z): Inputs a symbol a and a positive integer k, outputs the vector X and the doubly-stochatic matrix S`):
print(`such that if M is the generic SYMMERTY k by k matrix with entries a[i,j] the XMX=S `):
print(`It returns the minimal polynomial satisfied by X[1], called z, and X and S in terms of z and a[i,j].`):
print(` X=[x[1],x[2], .., x[n]]; such that if X denotes the diagonal matrix with entry X XMX  is doubly-stochastic.`):
print(`It returns a pair whose first entry is a list of length n where x[1] is denoted by the variable z, and x[2], ..., x[n] `):
print(`are polynomials in z, and second entry is the minimal polynomial satisfied by z.`):
print(` Try:  `):
print(` ExacGSs(a,2,z); `):

elif nops([args])=1 and op(1,[args])=ExacGSsNice then
print(`ExacGSsNice(a,k,z):  Like ExacGSs(a,k,z), but with z^2 replaced by z, and the first vector is divided by sqrt(z)`):
print(` (where z is the new z). `):
print(` Try:  `):
print(`ExacGSsNice(a,2,z); `):

elif nops([args])=1 and op(1,[args])=ExacGSsNiceV then
print(`ExacGSsNiceV(a,k,z):  Verbose version of ExacGSsNice(a,k,z) `):
print(` Try:  `):
print(`ExacGSsNiceV(a,2,z); `):


elif nops([args])=1 and op(1,[args])=ExacGSs2 then
print(`ExacGSs2(a,z): The pre-computed ExacGS(a,2,z). Try: `):
print(` ExacGSs2(a,z); `):

elif nops([args])=1 and op(1,[args])=ExacGSs3 then
print(`ExacGSs3(a,z): The pre-computed ExacGS(a,3,z). Try: `):
print(` ExacGSs3(a,z); `):

elif nops([args])=1 and op(1,[args])=ExacSF then
print(`ExacSF(M): Inputs a symmetric matrix M, outputs`):
print(`the exact values of the matrix X and S such that X is a diagonal matrix, S=XMX , and S is doubly stochastic in Floating point`):
print(`Try:`):
print(`ExacSF([[3,4],[4,9]]);`):

elif nops([args])=1 and op(1,[args])=Err1 then
print(`Err1(M): inputs a matrix M and finds out how far it is from a doubly-stochastic matrix. Try:`):
print(`Err1([[1/3,2/3],[2/3,1/3]]);`):


elif nops([args])=1 and op(1,[args])=KLM then
print(`KLM(K,L,M,n,k): Mel Nathanson's  KLM matrix where the K part is in the k by k upper-left block`):
print(`the L part is  in the k by n-k upper-right block and n-k by k bottom-left blocks and the`):
print(` M part is at the bottom (n-k) by (n-k) block. Try: `):
print(`KLM(3,4,5,4,2);`):

elif nops([args])=1 and op(1,[args])=MelMat then
print(`MelMat(r): The Nathanson matrix [[r*(r+1)/2,1,1],[1,1,1],[1,1,1]] followed by the limiting vector X, and its `):
print(`Sinkhorn limit of the Nathanson matrix [[r*(r+1)/2,1,1],[1,1,1],[1,1,1]]. Try:`):
print(`MelMat(r);`):


elif nops([args])=1 and op(1,[args])=MelN then
print(`MelN(a,k): inputs a symbol a and a positive integer k and outpus the Groebner basis and  the set of variables`):
print(`for a generic row-stochastic matrix to still be row-stochastic after one column scaling. Try:`):
print(`MelN(a,2);`):


elif nops([args])=1 and op(1,[args])=MelNold then
print(`MelNold(M,var): inputs a matrix M depending on a set of parameters var, outputs the conditions`):
print(`outputs the equations satisfied by the variables var`):
print(`for the Sinkhorn algorithm terminating after two steps (one Row scaling and one column scaling).`):
print(`Try: `):
print(`MelNold([[a,b],[c,d]],[a,b,c,d]); `):

elif nops([args])=1 and op(1,[args])=MelNprob1 then
print(`MelNprob1(a,z): answers problem 1 in  Mel Nathanson's article`):
print(`"Matrix Scaling, Explicit Sinkhorn limits, and Arithmetic". Try:`):
print(`MelNprob1(a,z):`) :

elif nops([args])=1 and op(1,[args])=MelNprob2a then
print(`MelNprob2a(K,L,z): answers the first part of problem 2 in  Mel Nathanson's article`):
print(` "Matrix Scaling, Explicit Sinkhorn limits, and Arithmetic". Try: `):
print(`MelNprob2a(K,L,z): `):

elif nops([args])=1 and op(1,[args])=MelNprob2b then
print(`MelNprob2b(K,L,M,z): answers the second part of problem 2 in  Mel Nathanson's article`):
print(` "Matrix Scaling, Explicit Sinkhorn limits, and Arithmetic". Try: `):
print(`MelNprob2b(K,L,M,z): `):


elif nops([args])=1 and op(1,[args])=MelNprob5 then
print(`MelNprob5(T,var): answers Mel Nathanson's Problem 1 (in the affirmative) in his interesting paper`):
print(`Alternate minimization and doubly stochastic matrices, arXiv:1812.11930v2 [math.CO] 4 Jan 2019 .`):
print(`that became Problem 5 in his equally interesting paper`):
print(` "Matrix Scaling, Explicit Sinkhorn Limits, and Arithmetic" `):
print(` Inputs a  template for row-stochastic matrices featuring the list of variables var`):
print(`for the first k-1 columns, with the  last column implied, tries to find a row-stochastic matrix with that template`):
print(`such that it is still row-stochastic after one column scaling. It outputs the list of length 2`):
print(`[M,M1] , where M is a positive row-stochastic matrix that is not column-stochastic,and M1`):
print(`is what M becomes after one column scaling, and is doubly stochastic. Try:`):
print(`MelNprob5([[x,x],[2*x,x],[3*x,x]],{x} );`):

elif nops([args])=1 and op(1,[args])=MelNprob5G then
print(`MelNprob5G(T,var,KAMA): inputs a  template for row-stochastic matrices featuring the list of variables var`):
print(`for the first k-1 columns, with the  last column implied, tries to find a choice of the variables`):
print(`such thati it still row-stochastic after one column scaling followed by KAMA-1 double iterations of Sinkhorn becomes double-stochastic`):
print(`It outputs the pairs, [matrix, SinkhornLimit] , try: `):
print(`MelNprob5G([[x,x],[2*x,x],[4*x,x]],{x},2 );`):

elif nops([args])=1 and op(1,[args])=MelNprob5Gnice then
print(`MelNprob5Gnice(T,var,KAMA): A verbose form of MelNprob5G(T,var,KAMA) (q.v.). Try:`):
print(`MelNprob5Gnice([[x,x],[2*x,x],[4*x,x]],{x},2 );`):

elif nops([args])=1 and op(1,[args])=MelNprob5nice then
print(`MelNprob5nice(T,var): verbose form of MelNprob5(T,var) (q.v.). Try: `):
print(`MelNprob5nice([[x,x],[2*x,x],[3*x,x]],{x} );`):


elif nops([args])=1 and op(1,[args])=MelNsec13 then
print(`MelNsec13(r,k): investigates Mel Nathanson's matrix [[r+1)*r/2,1,1,1],[1,1,1],[1,1,1]]. Try:`):
print(`MelNsec13(r,1);`):

elif nops([args])=1 and op(1,[args])=OneStepS then
print(`OneStepS(a,k): The algebraic conitions for a k by matrix terminate after one step in Sinkhorn's algorithm. Try:`):
print(`OneStepS(a,2);`):

elif nops([args])=1 and op(1,[args])=RandM then
print(`RandM(n,K):  A random n by n matrix with positive integer entries between 1 and K. Try:`):
print(`RandM(4,100);`):

elif nops([args])=1 and op(1,[args])=RevRS then
print(`RevRS(M,R): inputs  a row-stochastic matrix M and a list of numbers R (of the same size as the number of rows of M)`):
print(`outputs the matrix obtained by multiplying row i by R[i]`):
print(`Try: `):
print(`RevRS([[1/3,2/3],[2/3,1/3]],[2,3]);`);

elif nops([args])=1 and op(1,[args])=RSM then
print(`RandSM(n,K):  A random SYMMETRIC n by n matrix with positive integer entries between 1 and K. Try:`):
print(`RandSM(4,100);`):

elif nops([args])=1 and op(1,[args])=RS then
print(`RS(M): inputs a matrix M with positive entries M and outputs the matrix obtained by scaling its rows. Try:`):
print(`RS([[1,2,3],[2,1,3],[3,2,1]]);`):

elif nops([args])=1 and op(1,[args])=Sink then
print(`Sink(M,N): applies N iterations of Sinkhorn's algorithm to the matrix M. Try: `):
print(` Sink([[1,3],[2,5]],10); `):

elif nops([args])=1 and op(1,[args])=SinkE then
print(`SinkE(M,e): inputs a matrix M and an error e, and outputs an approximate doubly-stochastic matrix, as well as the number of iterations. `):
print(`It terminates as soon as the deviation from being doubly-stochastic is  less than e. Try:`):
print(`SinkE([[1,3],[2,7]],1/10^10);`):

elif nops([args])=1 and op(1,[args])=SinkEe then
print(`SinkEe(M,e): inputs a matrix M and an error e, and outputs an approximate doubly-stochastic matrix, as well as the number of iterations. `):
print(`It terminates as soon as the norm of the current iteration minus the actual limit is less than e.Try:`):
print(`It only works for symmetric matrices. Try:`):
print(`SinkEe([[1,3],[3,7]],1/10^10); `):

elif nops([args])=1 and op(1,[args])=SinkF then
print(`SinkF(M,N): Floating point version of Sink(M,N). Applies N iterations of Sinkhorn's algorithm to the matrix M. Try: `):
print(` SinkF([[1,3],[2,5]],10); `):

elif nops([args])=1 and op(1,[args])=SinkPlus then
print(`SinkPlus(M,N): applies N iterations of Sinkhorn's algorithm to the matrix M. Outputs the diagonal matrices X, and Y and S such that`):
print(` S=XMY is almost doubly-stochastic. The output is [X,Y,S]. Try `):
print(`SinkPlus([[1,3],[2,5]],10);`):

elif nops([args])=1 and op(1,[args])=SinkPlusErr then
print(`SinkPlusErr(M,eps): Inputs a square matrix in floating point and outputs [X,Y,M1] where M1=XMY and M1 is approximately`):
print(`double-stochastic with error eps. Try: `):
print(`SinkPlusErr([[1,3],[2,5]],1/10^9); `):

elif nops([args])=1 and op(1,[args])=SinkPlusF then
print(`SinkPlusF(M,N): floating point version of SinkPlus(M,N) (q.v.) . `):
print(` Try: `):
print(`SinkPlusF([[1,3],[2,5]],10);`):

elif nops([args])=1 and op(1,[args])=Tra then
print(`Tra(A), the transpose of the matrix, given as a list of lists. Try: `): 
print(`Tra([[3,4],[6,2]]);`):

else
print(`There is no ezra for`,args):
fi:
 
end:

#Start Precomputed
ExacGSs2:=proc(a,z):

[[z, -z*a[1,1]*(-a[2,2]-a[1,2]^2*z^2+a[2,2]*a[1,1]*z^2)/a[2,2]/a[1,2]], a[2,2]-2*a[2,2]*a[1,1]*z^2+(-a[1,2]^2*a[1,1]+a[2,2]*a[1,1]^2)*z^4, [[a[1,1]*z^2, 1-a[1,1]*z^
2], [1-a[1,1]*z^2, a[1,1]*z^2]]]:
:
end:



ExacGSs3:=proc(a,z):
[[z, -z*(-z^6*a[1,1]^2*a[1,3]^2*a[3,3]^4*a[2,2]*a[1,2]^9+3*z^2*a[1,1]^2*a[1,2]^4*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^3+27*z^2*a[1,1]^2*a[1,2]^5*a[1,3]^2*a[3,3]^3*a[2,3]
^2*a[2,2]^2+6*z^4*a[1,1]^5*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]^4-6*z^2*a[1,1]^2*a[1,2]^5*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]-3*z^4*a[1,1]^5*a[1,3]^3*a[3,3]^3*a[2,3]*a[2
,2]^5+5*z^6*a[1,1]^4*a[1,2]^2*a[1,3]^5*a[2,3]^5*a[2,2]^2-12*z^2*a[1,1]^2*a[1,2]^6*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]+2*z^6*a[1,1]^4*a[1,2]^5*a[1,3]^2*a[3,3]^3*a[2,3]^2
*a[2,2]^2+6*z^4*a[1,1]^5*a[1,2]^2*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]^3+5*z^4*a[1,1]*a[1,2]^4*a[1,3]^7*a[3,3]*a[2,3]*a[2,2]^3+2*z^2*a[1,1]*a[1,3]^8*a[2,3]^2*a[2,2]^4*a[
1,2]-z^4*a[1,1]*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[1,2]^9-5*z^2*a[1,1]*a[1,2]^2*a[1,3]^7*a[2,3]^3*a[2,2]^3-6*z^2*a[1,1]^2*a[1,2]*a[1,3]^6*a[2,3]^4*a[2,2]^3+7*z^2*a[1,1]^2
*a[1,2]^6*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^2-2*z^6*a[1,1]^4*a[1,2]*a[1,3]^6*a[3,3]^2*a[2,2]^5-3*z^4*a[1,1]^5*a[1,3]^3*a[3,3]*a[2,3]^5*a[2,2]^3+18*z^2*a[1,1]^3*a[1,2]*a
[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^3+2*z^2*a[1,1]^2*a[1,2]*a[1,3]^6*a[3,3]^2*a[2,2]^5-5*z^2*a[1,1]*a[1,2]^2*a[1,3]^7*a[3,3]*a[2,3]*a[2,2]^4+6*z^2*a[1,1]*a[1,2]^3*a[1,3]
^6*a[3,3]*a[2,3]^2*a[2,2]^3-z^2*a[1,1]^2*a[1,3]^7*a[3,3]*a[2,3]*a[2,2]^5+z^6*a[1,1]^6*a[1,2]^2*a[1,3]*a[3,3]^2*a[2,3]^5*a[2,2]^2+4*z^6*a[1,1]^6*a[1,2]*a[1,3]^2*a[3,
3]^3*a[2,3]^2*a[2,2]^4+2*z^2*a[1,1]^2*a[1,3]^7*a[2,3]^3*a[2,2]^4+4*z^2*a[1,1]*a[1,2]^4*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^3+14*z^2*a[1,1]*a[1,2]^5*a[1,3]^4*a[3,3]*a[2,
3]^4*a[2,2]+3*z^6*a[1,1]^2*a[1,2]^7*a[1,3]^4*a[3,3]*a[2,3]^4-8*z^6*a[1,1]^2*a[1,2]^7*a[1,3]^4*a[3,3]^3*a[2,2]^2+4*z^4*a[1,1]^4*a[1,2]^5*a[3,3]^3*a[2,3]^4*a[2,2]+3*z
^2*a[1,1]^4*a[1,2]^2*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^4-8*z^2*a[1,1]*a[1,2]^4*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^2+2*z^6*a[1,1]^5*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^4+12*z^2
*a[1,1]^2*a[1,2]^2*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^3-z^6*a[1,1]^4*a[1,3]^7*a[3,3]*a[2,3]*a[2,2]^5-z^6*a[1,1]^4*a[1,2]*a[1,3]^6*a[2,3]^4*a[2,2]^3-6*z^2*a[1,1]^4*a[1,
2]^2*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]^3+2*z^4*a[1,1]*a[1,2]^8*a[1,3]^3*a[3,3]^2*a[2,3]^3+8*z^6*a[1,1]^5*a[1,2]^3*a[1,3]^2*a[3,3]^4*a[2,2]^4-z^2*a[1,1]^2*a[1,2]*a[1,3
]^6*a[3,3]*a[2,3]^2*a[2,2]^4-4*z^4*a[1,1]^3*a[1,3]^7*a[2,3]^3*a[2,2]^4-2*z^6*a[1,1]^6*a[1,2]*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]^3+2*z^2*a[1,1]*a[1,3]*a[3,3]^3*a[2,3]
^3*a[1,2]^8+z^2*a[1,2]^3*a[1,3]^8*a[2,3]^2*a[2,2]^3-12*z^2*a[1,1]^2*a[1,2]^5*a[1,3]^2*a[3,3]^4*a[2,2]^3-4*z^4*a[1,1]^4*a[1,2]^5*a[3,3]^4*a[2,3]^2*a[2,2]^2-9*z^2*a[1
,1]^2*a[1,2]^2*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^4-27*z^2*a[1,1]^2*a[1,2]^3*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^2-2*z^6*a[1,1]^2*a[1,2]^8*a[1,3]^3*a[3,3]^2*a[2,3]^3-5*z^2
*a[1,2]^7*a[1,3]^4*a[3,3]*a[2,3]^4-2*z^2*a[1,1]^2*a[1,2]^7*a[3,3]^4*a[2,3]^2*a[2,2]+2*z^2*a[1,2]^7*a[1,3]^4*a[3,3]^3*a[2,2]^2+20*z^2*a[1,1]^3*a[1,2]^3*a[1,3]^2*a[3,
3]^4*a[2,2]^4-15*z^4*a[1,1]^4*a[1,2]*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^3+18*z^4*a[1,1]^4*a[1,2]*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^4-2*z^6*a[1,1]^4*a[1,2]^6*a[1,3]*a[3
,3]^3*a[2,3]^3*a[2,2]-18*z^2*a[1,1]*a[1,2]^5*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^2-14*z^4*a[1,1]*a[1,2]^4*a[1,3]^7*a[2,3]^3*a[2,2]^2+6*z^4*a[1,1]*a[1,2]^3*a[1,3]^8*a[
2,3]^2*a[2,2]^3+11*z^2*a[1,1]*a[1,2]^6*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]-z^2*a[1,1]^3*a[1,2]^4*a[1,3]*a[3,3]^2*a[2,3]^5*a[2,2]-2*z^4*a[1,1]^4*a[1,3]^5*a[3,3]^2*a[2,
3]*a[2,2]^5+13*z^2*a[1,1]*a[1,2]^6*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^2-z^4*a[1,1]*a[1,2]^3*a[1,3]^8*a[3,3]*a[2,2]^4+4*z^6*a[1,1]^3*a[1,2]^7*a[1,3]^2*a[3,3]^3*a[2,3]^2
*a[2,2]+18*z^6*a[1,1]^3*a[1,2]^6*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]+6*z^4*a[1,1]^5*a[1,2]*a[1,3]^2*a[3,3]^4*a[2,2]^5-11*z^4*a[1,1]^3*a[1,2]^2*a[1,3]^5*a[2,3]^5*a[2,2
]^2+7*z^6*a[1,1]^4*a[1,2]^6*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^2-3*z^6*a[1,1]^3*a[1,2]^8*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]-26*z^6*a[1,1]^3*a[1,2]^6*a[1,3]^3*a[3,3]^3*a[2,3]*
a[2,2]^2+2*z^4*a[1,1]^4*a[1,3]^5*a[2,3]^5*a[2,2]^3-15*z^6*a[1,1]^4*a[1,2]^3*a[1,3]^4*a[3,3]^3*a[2,2]^4-2*z^6*a[1,1]^6*a[1,2]*a[1,3]^2*a[3,3]^4*a[2,2]^5-z^6*a[1,1]^5
*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^5-z^4*a[1,1]*a[1,3]^9*a[2,3]*a[2,2]^4*a[1,2]^2-2*z^6*a[1,1]^4*a[1,2]^7*a[3,3]^4*a[2,3]^2*a[2,2]+6*z^6*a[1,1]^5*a[1,2]^4*a[1,3]*a[3,
3]^3*a[2,3]^3*a[2,2]^2-11*z^6*a[1,1]^4*a[1,2]^5*a[1,3]^2*a[3,3]^4*a[2,2]^3-z^6*a[1,1]^5*a[1,2]^4*a[1,3]*a[3,3]^2*a[2,3]^5*a[2,2]-4*z^6*a[1,1]^3*a[1,2]^5*a[1,3]^4*a[
3,3]^2*a[2,3]^2*a[2,2]^2+8*z^4*a[1,1]^2*a[1,2]^2*a[1,3]^7*a[2,3]^3*a[2,2]^3-16*z^4*a[1,1]^2*a[1,2]^3*a[1,3]^6*a[2,3]^4*a[2,2]^2-3*z^4*a[1,1]^3*a[1,2]^7*a[3,3]^3*a[2
,3]^4+4*z^2*a[1,2]^6*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]-14*z^2*a[1,1]*a[1,2]^7*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]+18*z^2*a[1,1]^3*a[1,2]^2*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[
2,2]^3-16*z^4*a[1,1]^2*a[1,2]^6*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]+10*z^4*a[1,1]^2*a[1,2]^6*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^2+38*z^4*a[1,1]^3*a[1,2]^4*a[1,3]^3*a[3,3
]^2*a[2,3]^3*a[2,2]^2+4*z^4*a[1,1]^2*a[1,2]^3*a[1,3]^6*a[3,3]^2*a[2,2]^4+12*z^4*a[1,1]^2*a[1,2]^4*a[1,3]^5*a[2,3]^5*a[2,2]-8*z^4*a[1,1]^2*a[1,2]^5*a[1,3]^4*a[3,3]^3
*a[2,2]^3+6*z^4*a[1,1]^2*a[1,2]^6*a[1,3]^3*a[3,3]*a[2,3]^5-19*z^4*a[1,1]^4*a[1,2]^3*a[1,3]^2*a[3,3]^4*a[2,2]^4+4*z^4*a[1,1]^3*a[1,2]^7*a[3,3]^4*a[2,3]^2*a[2,2]+14*z
^4*a[1,1]^3*a[1,2]^3*a[1,3]^4*a[3,3]^3*a[2,2]^4+16*z^4*a[1,1]^3*a[1,2]^5*a[1,3]^2*a[3,3]^4*a[2,2]^3-14*z^2*a[1,1]^3*a[1,2]*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^4+4*z^6
*a[1,1]^5*a[1,2]*a[1,3]^4*a[3,3]^3*a[2,2]^5-18*z^2*a[1,1]^3*a[1,2]^2*a[1,3]^3*a[3,3]*a[2,3]^5*a[2,2]^2+2*z^6*a[1,1]*a[1,2]^7*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]+2*z^2*a
[1,2]^8*a[1,3]^3*a[3,3]^2*a[2,3]^3+12*z^2*a[1,1]^3*a[1,2]^3*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]^2+z^6*a[1,1]^6*a[1,3]^3*a[3,3]*a[2,3]^5*a[2,2]^3-2*z^6*a[1,1]^6*a[1,3]
^3*a[3,3]^2*a[2,3]^3*a[2,2]^4-4*z^4*a[1,1]*a[1,2]^6*a[1,3]^5*a[2,3]^5+z^6*a[1,1]*a[1,2]^5*a[1,3]^8*a[3,3]*a[2,2]^3+4*z^6*a[1,1]*a[1,2]^6*a[1,3]^7*a[2,3]^3*a[2,2]-8*
z^6*a[1,1]^2*a[1,2]^5*a[1,3]^6*a[3,3]^2*a[2,2]^3+18*z^6*a[1,1]^3*a[1,2]^5*a[1,3]^4*a[3,3]^3*a[2,2]^3-24*z^4*a[1,1]^3*a[1,2]^4*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^3+8*z^
4*a[1,1]^3*a[1,2]^5*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]-15*z^4*a[1,1]^3*a[1,2]^5*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^2-3*z^4*a[1,1]^4*a[1,2]*a[1,3]^4*a[3,3]^3*a[2,2]^5-
z^4*a[1,1]^2*a[1,2]^7*a[1,3]^2*a[3,3]^2*a[2,3]^4-3*z^4*a[1,1]^2*a[1,2]^7*a[1,3]^2*a[3,3]^4*a[2,2]^2+5*z^4*a[1,1]^3*a[1,3]^7*a[3,3]*a[2,3]*a[2,2]^5-2*z^6*a[1,1]^3*a[
1,2]^6*a[1,3]^3*a[3,3]*a[2,3]^5+6*z^6*a[1,1]^3*a[1,2]^7*a[1,3]^2*a[3,3]^4*a[2,2]^2-2*z^6*a[1,1]^3*a[1,3]*a[3,3]^3*a[2,3]^3*a[1,2]^8-z^6*a[1,1]^5*a[1,2]^5*a[3,3]^3*a
[2,3]^4*a[2,2]-4*z^2*a[1,1]^3*a[1,2]*a[1,3]^4*a[3,3]^3*a[2,2]^5+3*z^2*a[1,1]^4*a[1,3]^3*a[3,3]*a[2,3]^5*a[2,2]^3-6*z^2*a[1,1]^4*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]^4+
3*z^2*a[1,1]^4*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^5+10*z^4*a[1,1]^3*a[1,2]*a[1,3]^6*a[2,3]^4*a[2,2]^3-4*z^4*a[1,1]^3*a[1,2]*a[1,3]^6*a[3,3]^2*a[2,2]^5-5*z^2*a[1,1]^3*a
[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^4+6*z^2*a[1,1]^3*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^5+8*z^4*a[1,1]^3*a[1,2]^2*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^4+19*z^4*a[1,1]^3*a[1,2]^3
*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^2-z^4*a[1,1]^2*a[1,3]^8*a[2,3]^2*a[2,2]^4*a[1,2]-z^4*a[1,2]^9*a[1,3]^4*a[3,3]^2*a[2,3]^2-38*z^4*a[1,1]^3*a[1,2]^3*a[1,3]^4*a[3,3]^2
*a[2,3]^2*a[2,2]^3-19*z^4*a[1,1]^3*a[1,2]^4*a[1,3]^3*a[3,3]*a[2,3]^5*a[2,2]-28*z^4*a[1,1]^4*a[1,2]^2*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]^3+10*z^4*a[1,1]^4*a[1,2]^2*a[
1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^4-11*z^4*a[1,1]^4*a[1,2]^3*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]^2+30*z^4*a[1,1]^4*a[1,2]^3*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^3-6*z^2*a[1,
1]^4*a[1,2]*a[1,3]^2*a[3,3]^4*a[2,2]^5+2*z^2*a[1,2]^4*a[1,3]^7*a[3,3]*a[2,3]*a[2,2]^3+3*z^2*a[1,2]^7*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]-2*z^2*a[1,2]^8*a[1,3]^3*a[3,3
]^3*a[2,3]*a[2,2]+z^4*a[1,1]^2*a[1,2]*a[1,3]^8*a[3,3]*a[2,2]^5-6*z^2*a[1,1]^3*a[1,2]^5*a[3,3]^3*a[2,3]^4*a[2,2]+6*z^2*a[1,1]^3*a[1,2]^5*a[3,3]^4*a[2,3]^2*a[2,2]^2-2
*z^2*a[1,1]^2*a[1,2]^3*a[1,3]^4*a[3,3]^3*a[2,2]^4-10*z^6*a[1,1]^3*a[1,2]^5*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]-4*z^6*a[1,1]*a[1,2]^6*a[1,3]^7*a[3,3]*a[2,3]*a[2,2]^2+3*z
^2*a[1,1]^2*a[1,2]^7*a[3,3]^3*a[2,3]^4-z^2*a[1,1]^3*a[1,3]^5*a[2,3]^5*a[2,2]^3+19*z^2*a[1,1]^3*a[1,2]^4*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]^2-32*z^2*a[1,1]^3*a[1,2]^3*a
[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^3+z^6*a[1,1]^5*a[1,2]^5*a[3,3]^4*a[2,3]^2*a[2,2]^2+3*z^2*a[1,1]^4*a[1,2]^2*a[1,3]*a[3,3]^2*a[2,3]^5*a[2,2]^2+11*z^6*a[1,1]^2*a[1,2]
^5*a[1,3]^6*a[2,3]^4*a[2,2]+12*z^2*a[1,1]^4*a[1,2]*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^4-6*z^2*a[1,1]^4*a[1,2]*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]^3-18*z^2*a[1,1]^3*a[1
,2]^4*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^3-z^6*a[1,1]*a[1,2]^5*a[1,3]^8*a[2,3]^2*a[2,2]^2-3*z^4*a[1,1]*a[1,2]^7*a[1,3]^4*a[3,3]^3*a[2,2]^2+24*z^2*a[1,1]^2*a[1,2]^3*a[1,3
]^4*a[3,3]^2*a[2,3]^2*a[2,2]^3-z^6*a[1,1]^2*a[1,2]^3*a[1,3]^8*a[3,3]*a[2,2]^4+4*z^4*a[1,2]^8*a[1,3]^5*a[3,3]*a[2,3]^3+2*z^4*a[1,1]^4*a[1,2]^4*a[1,3]*a[3,3]^2*a[2,3]
^5*a[2,2]-16*z^4*a[1,1]^4*a[1,2]^4*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]^2+6*z^4*a[1,1]^3*a[1,2]^6*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]-2*z^2*a[1,2]^4*a[1,3]^7*a[2,3]^3*a[2,2]
^2-z^2*a[1,2]^5*a[1,3]^6*a[2,3]^4*a[2,2]+z^2*a[1,2]^5*a[1,3]^6*a[3,3]^2*a[2,2]^3-6*z^2*a[1,1]*a[1,2]^4*a[1,3]^5*a[2,3]^5*a[2,2]-4*z^4*a[1,2]^8*a[1,3]^5*a[3,3]^2*a[2
,3]*a[2,2]-14*z^6*a[1,1]^2*a[1,2]^4*a[1,3]^7*a[2,3]^3*a[2,2]^2+2*z^4*a[1,1]*a[1,2]^7*a[1,3]^4*a[3,3]*a[2,3]^4-z^6*a[1,1]^2*a[1,3]^9*a[2,3]*a[2,2]^4*a[1,2]^2+6*z^6*a
[1,1]^2*a[1,2]^3*a[1,3]^8*a[2,3]^2*a[2,2]^3-11*z^4*a[1,1]^3*a[1,2]^6*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^2+21*z^4*a[1,1]^2*a[1,2]^5*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^2+18
*z^4*a[1,1]^4*a[1,2]^2*a[1,3]^3*a[3,3]*a[2,3]^5*a[2,2]^2+18*z^2*a[1,1]^2*a[1,2]^4*a[1,3]^3*a[3,3]*a[2,3]^5*a[2,2]+z^6*a[1,1]*a[1,2]^9*a[1,3]^4*a[3,3]^3*a[2,2]+4*z^6
*a[1,1]*a[1,2]^8*a[1,3]^5*a[3,3]*a[2,3]^3+2*z^4*a[1,2]^7*a[1,3]^6*a[3,3]^2*a[2,2]^2+10*z^6*a[1,1]^4*a[1,2]^2*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^4+4*z^6*a[1,1]^4*a[1,2]
^3*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^2+16*z^6*a[1,1]^4*a[1,2]^3*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^3-a[1,2]^7*a[1,3]^2*a[3,3]^2*a[2,3]^4+2*a[1,2]^6*a[1,3]^3*a[3,3]*a[2
,3]^5+2*a[1,1]^3*a[1,2]*a[1,3]^2*a[3,3]^4*a[2,2]^5-a[1,1]^3*a[1,3]^3*a[3,3]*a[2,3]^5*a[2,2]^3-3*a[1,1]^2*a[1,2]^5*a[3,3]^4*a[2,3]^2*a[2,2]^2-6*a[1,1]^2*a[1,2]*a[1,3
]^4*a[3,3]*a[2,3]^4*a[2,2]^3-3*a[1,1]^2*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^5+3*a[1,1]^2*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^4+3*a[1,1]^2*a[1,2]^5*a[3,3]^3*a[2,3]^4*a[2,2]-\
9*a[1,1]^2*a[1,2]^3*a[1,3]^2*a[3,3]^4*a[2,2]^4+3*a[1,1]^2*a[1,2]*a[1,3]^4*a[3,3]^3*a[2,2]^5-a[1,1]*a[1,2]^7*a[3,3]^3*a[2,3]^4-a[1,1]*a[1,3]^7*a[2,3]^3*a[2,2]^4+5*a[
1,1]*a[1,2]^6*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]+2*a[1,1]*a[1,2]^5*a[1,3]^2*a[3,3]^4*a[2,2]^3-12*a[1,1]*a[1,2]^5*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^2+a[1,1]*a[1,2]^5*a[
1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]-2*a[1,1]*a[1,2]^4*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^3+13*a[1,1]*a[1,2]^4*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]^2-6*a[1,1]*a[1,2]^4*a[1,3]^
3*a[3,3]*a[2,3]^5*a[2,2]+5*a[1,1]*a[1,2]^3*a[1,3]^4*a[3,3]^3*a[2,2]^4-6*a[1,1]*a[1,2]^3*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^3+6*a[1,1]*a[1,2]^3*a[1,3]^4*a[3,3]*a[2,3]
^4*a[2,2]^2-4*a[1,1]*a[1,2]^2*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^4-5*a[1,1]*a[1,2]^2*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^3-a[1,1]*a[1,2]*a[1,3]^6*a[3,3]^2*a[2,2]^5+6*a[1,1
]*a[1,2]*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^4+3*z^6*a[1,1]^5*a[1,2]*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^3-7*z^6*a[1,1]^5*a[1,2]*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^4-6*z^6*a
[1,1]^5*a[1,2]^2*a[1,3]^3*a[3,3]*a[2,3]^5*a[2,2]^2+16*z^6*a[1,1]^5*a[1,2]^2*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]^3+23*z^6*a[1,1]^2*a[1,2]^6*a[1,3]^5*a[3,3]^2*a[2,3]*a[
2,2]^2+6*z^4*a[1,1]^5*a[1,2]*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]^3-4*z^6*a[1,1]^2*a[1,2]^7*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]+8*z^6*a[1,1]^4*a[1,2]*a[1,3]^6*a[3,3]*a[2
,3]^2*a[2,2]^4-24*z^6*a[1,1]^4*a[1,2]^2*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^3+38*z^6*a[1,1]^3*a[1,2]^4*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^2-28*z^6*a[1,1]^3*a[1,2]^4*a[1,3]
^5*a[3,3]^2*a[2,3]*a[2,2]^3-20*z^6*a[1,1]^2*a[1,2]^6*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]-12*z^4*a[1,1]^5*a[1,2]*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^4+2*z^4*a[1,2]^7*a[1,3
]^6*a[3,3]*a[2,3]^2*a[2,2]-5*z^4*a[1,1]*a[1,2]^5*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^2-z^6*a[1,1]*a[1,2]^9*a[1,3]^4*a[3,3]^2*a[2,3]^2+8*z^6*a[1,1]^3*a[1,2]^3*a[1,3]^6*a
[3,3]^2*a[2,2]^4-6*z^6*a[1,1]^3*a[1,2]^4*a[1,3]^5*a[2,3]^5*a[2,2]+z^6*a[1,1]^6*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^5+7*z^6*a[1,1]^2*a[1,2]^8*a[1,3]^3*a[3,3]^3*a[2,3]*a[
2,2]-12*z^6*a[1,1]^3*a[1,2]^3*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^3-4*z^4*a[1,1]*a[1,2]^6*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]+6*a[1,1]^2*a[1,2]^2*a[1,3]^3*a[3,3]*a[2,3]^5*a
[2,2]^2-13*z^4*a[1,1]^2*a[1,2]^5*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]+3*z^4*a[1,1]*a[1,2]^8*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]+6*z^2*a[1,1]^2*a[1,2]^2*a[1,3]^5*a[2,3]^5*a[2
,2]^2+4*z^4*a[1,2]^6*a[1,3]^7*a[2,3]^3*a[2,2]-z^2*a[1,2]^3*a[1,3]^8*a[3,3]*a[2,2]^4+2*z^6*a[1,1]^2*a[1,2]^6*a[1,3]^5*a[2,3]^5+4*z^2*a[1,1]*a[1,2]^3*a[1,3]^6*a[3,3]^
2*a[2,2]^4+z^6*a[1,1]^3*a[3,3]^4*a[2,3]^2*a[1,2]^9+z^6*a[1,1]^4*a[1,2]^7*a[3,3]^3*a[2,3]^4+2*z^6*a[1,1]^2*a[1,2]^5*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^2-z^6*a[1,1]^5*a[
1,3]^5*a[2,3]^5*a[2,2]^3+z^6*a[1,1]^3*a[1,3]^9*a[2,3]*a[2,2]^5+2*z^6*a[1,1]*a[1,2]^7*a[1,3]^6*a[3,3]^2*a[2,2]^2-4*z^4*a[1,1]*a[1,2]^5*a[1,3]^6*a[3,3]^2*a[2,2]^3+10*
z^6*a[1,1]^3*a[1,2]^2*a[1,3]^7*a[2,3]^3*a[2,2]^3-6*z^6*a[1,1]^3*a[1,2]^3*a[1,3]^6*a[2,3]^4*a[2,2]^2+13*z^4*a[1,1]*a[1,2]^6*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^2-5*z^6*a
[1,1]^5*a[1,2]^4*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^3-8*z^4*a[1,1]*a[1,2]^7*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]-4*z^6*a[1,1]*a[1,2]^7*a[1,3]^6*a[2,3]^4+8*z^2*a[1,1]*a[1,2]
^3*a[1,3]^6*a[2,3]^4*a[2,2]^2+5*z^6*a[1,1]^2*a[1,2]^4*a[1,3]^7*a[3,3]*a[2,3]*a[2,2]^3-6*z^2*a[1,1]*a[1,2]^6*a[1,3]^3*a[3,3]*a[2,3]^5-8*z^4*a[1,1]^2*a[1,2]^2*a[1,3]^
7*a[3,3]*a[2,3]*a[2,2]^4+2*z^2*a[1,1]*a[1,2]^7*a[1,3]^2*a[3,3]^4*a[2,2]^2+12*z^4*a[1,1]^2*a[1,2]^3*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^3+z^4*a[1,2]^5*a[1,3]^8*a[3,3]*a[
2,2]^3-3*z^4*a[1,1]^5*a[1,2]^2*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^4+14*z^4*a[1,1]^4*a[1,2]^4*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^3+2*z^2*a[1,2]^6*a[1,3]^5*a[2,3]^5-4*z^4*a[1,2
]^7*a[1,3]^6*a[2,3]^4-2*z^6*a[1,1]^6*a[1,2]^2*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]^3+7*z^6*a[1,1]^4*a[1,2]^4*a[1,3]^3*a[3,3]*a[2,3]^5*a[2,2]-30*z^6*a[1,1]^4*a[1,2]^4*a[1
,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]^2-26*z^2*a[1,1]^2*a[1,2]^4*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]^2+14*z^4*a[1,1]*a[1,2]^5*a[1,3]^6*a[2,3]^4*a[2,2]-5*z^6*a[1,1]^3*a[1,3]^
8*a[2,3]^2*a[2,2]^4*a[1,2]+z^4*a[1,2]^9*a[1,3]^4*a[3,3]^3*a[2,2]-10*z^6*a[1,1]^5*a[1,2]^2*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^4+2*z^6*a[1,1]^5*a[1,2]^3*a[1,3]^2*a[3,3]^
2*a[2,3]^4*a[2,2]^2-10*z^6*a[1,1]^5*a[1,2]^3*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^3-4*z^4*a[1,2]^6*a[1,3]^7*a[3,3]*a[2,3]*a[2,2]^2+28*z^6*a[1,1]^4*a[1,2]^4*a[1,3]^3*a[
3,3]^3*a[2,3]*a[2,2]^3-3*z^4*a[1,1]^5*a[1,2]^2*a[1,3]*a[3,3]^2*a[2,3]^5*a[2,2]^2-4*z^6*a[1,1]*a[1,2]^8*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]+2*z^2*a[1,1]*a[1,2]^7*a[1,3]^
2*a[3,3]^2*a[2,3]^4-6*z^2*a[1,1]*a[1,2]^5*a[1,3]^4*a[3,3]^3*a[2,2]^3+z^6*a[1,1]^6*a[1,2]^2*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^4-4*z^4*a[1,1]^2*a[1,2]^4*a[1,3]^5*a[3,3]*a
[2,3]^3*a[2,2]^2-8*z^4*a[1,1]^2*a[1,2]^4*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^3-6*z^2*a[1,2]^6*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^2-z^4*a[1,2]^5*a[1,3]^8*a[2,3]^2*a[2,2]^2+
3*a[1,1]^2*a[1,2]*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^4-6*a[1,1]^2*a[1,2]^2*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]^3-3*a[1,1]^2*a[1,2]^3*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]^
2+12*a[1,1]^2*a[1,2]^3*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^3-9*a[1,1]^2*a[1,2]^4*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]^2+9*a[1,1]^2*a[1,2]^4*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^3
+2*a[1,1]^3*a[1,2]*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]^3-4*a[1,1]^3*a[1,2]*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^4+2*a[1,1]^3*a[1,2]^2*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]^3-a
[1,1]^3*a[1,2]^2*a[1,3]*a[3,3]^2*a[2,3]^5*a[2,2]^2-a[1,1]^3*a[1,2]^2*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^4-a[1,1]^3*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^5+2*a[1,1]^3*a[1,3]^3*
a[3,3]^2*a[2,3]^3*a[2,2]^4+a[1,2]^2*a[1,3]^7*a[3,3]*a[2,3]*a[2,2]^4-a[1,2]^3*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^3+2*a[1,2]^3*a[1,3]^6*a[2,3]^4*a[2,2]^2-a[1,2]^2*a[1,3]
^7*a[2,3]^3*a[2,2]^3+2*a[1,2]^4*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^3-2*a[1,2]^4*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^2+4*a[1,2]^5*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^2-3*a[1,
2]^5*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]-a[1,2]^5*a[1,3]^4*a[3,3]^3*a[2,2]^3-a[1,2]^3*a[1,3]^6*a[3,3]^2*a[2,2]^4-a[1,2]^6*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^2-a[1,2]^6*a[1
,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]+a[1,2]^7*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]+4*z^4*a[1,1]^2*a[1,2]^7*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]-11*z^4*a[1,1]^3*a[1,2]*a[1,3]^6*
a[3,3]*a[2,3]^2*a[2,2]^4+12*z^4*a[1,1]^3*a[1,2]^2*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^3)/a[2,2]/(a[1,2]^2*a[1,3]^6*a[2,3]^4*a[2,2]^2+a[1,2]^2*a[1,3]^6*a[3,3]^2*a[2,2]^4
+a[1,1]*a[1,3]^6*a[2,3]^4*a[2,2]^3-a[1,2]^6*a[1,3]^2*a[3,3]^4*a[2,2]^2-2*a[1,2]^3*a[1,3]^5*a[2,3]^5*a[2,2]-3*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^2-4*a
[1,1]*a[1,2]*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^3-2*a[1,2]^2*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^3+a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^2+3*a[1,1]*a[1,2]^2*a[1,
3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^3+4*a[1,2]^3*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^2-a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]+a[1,1]*a[1,2]^6*a[3,3]^4*a[2,3]^2*a[2
,2]+4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]+4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^4-4*a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]-2*a[1,2]^3*a[1,
3]^5*a[3,3]^2*a[2,3]*a[2,2]^3+2*a[1,2]^5*a[1,3]^3*a[3,3]*a[2,3]^5+2*a[1,2]^5*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^2-a[1,2]^6*a[1,3]^2*a[3,3]^2*a[2,3]^4-a[1,1]*a[1,3]^6*a
[3,3]*a[2,3]^2*a[2,2]^4+4*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^4*a[2,2]^3-4*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^3*a[2,2]^4+2*a[1,2]^6*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]-a[1,1
]*a[1,2]^6*a[3,3]^3*a[2,3]^4-4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^2), z*(-16*z^4*a[1,1]^2*a[1,2]^3*a[1,3]^6*a[2,3]^3*a[3,3]*a[2,2]^2+5*z^4*a[1,1]*a[1,2]^
7*a[1,3]^4*a[3,3]^3*a[2,3]*a[2,2]-z^6*a[1,1]^5*a[1,2]^5*a[2,3]*a[3,3]^5*a[2,2]^2-6*z^2*a[1,1]^4*a[1,2]*a[1,3]^2*a[2,3]^3*a[3,3]^3*a[2,2]^3+a[1,2]^7*a[1,3]^2*a[2,3]*
a[3,3]^4*a[2,2]+2*a[1,1]*a[1,2]^2*a[1,3]^5*a[3,3]^3*a[2,2]^4+5*a[1,1]*a[1,2]^4*a[1,3]^3*a[3,3]^4*a[2,2]^3-a[1,1]*a[1,2]^6*a[1,3]*a[3,3]^5*a[2,2]^2+3*a[1,1]^2*a[1,3]
^5*a[2,3]^4*a[3,3]*a[2,2]^3-3*a[1,1]^2*a[1,3]^5*a[2,3]^2*a[3,3]^2*a[2,2]^4-9*a[1,1]^2*a[1,2]^2*a[1,3]^3*a[3,3]^4*a[2,2]^4+3*a[1,1]^2*a[1,2]^4*a[1,3]*a[3,3]^5*a[2,2]
^3+3*a[1,1]^2*a[1,2]^5*a[2,3]^3*a[3,3]^4*a[2,2]-3*a[1,1]^2*a[1,2]^5*a[2,3]*a[3,3]^5*a[2,2]^2-3*a[1,2]^4*a[1,3]^5*a[2,3]^4*a[3,3]*a[2,2]+a[1,2]^2*a[1,3]^7*a[2,3]^2*a
[3,3]*a[2,2]^3-a[1,2]^3*a[1,3]^6*a[2,3]^3*a[3,3]*a[2,2]^2-a[1,1]*a[2,3]^4*a[2,2]^3*a[1,3]^7-a[1,1]*a[1,2]^7*a[2,3]^3*a[3,3]^4-a[1,2]^3*a[1,3]^6*a[2,3]*a[3,3]^2*a[2,
2]^3+4*a[1,2]^4*a[1,3]^5*a[2,3]^2*a[3,3]^2*a[2,2]^2-2*a[1,2]^5*a[1,3]^4*a[2,3]^3*a[3,3]^2*a[2,2]-a[1,2]^2*a[1,3]^7*a[2,3]^4*a[2,2]^2+2*a[1,2]^3*a[1,3]^6*a[2,3]^5*a[
2,2]-a[1,2]^4*a[1,3]^5*a[3,3]^3*a[2,2]^3+2*a[1,2]^6*a[1,3]^3*a[2,3]^4*a[3,3]^2-a[1,2]^6*a[1,3]^3*a[3,3]^4*a[2,2]^2-a[1,2]^7*a[1,3]^2*a[2,3]^3*a[3,3]^3+2*a[1,2]^5*a[
1,3]^4*a[2,3]*a[3,3]^3*a[2,2]^2-a[1,2]^6*a[1,3]^3*a[2,3]^2*a[3,3]^3*a[2,2]+2*z^6*a[1,1]^5*a[1,2]^5*a[2,3]^3*a[3,3]^4*a[2,2]-6*z^2*a[1,1]^2*a[1,2]^6*a[1,3]*a[2,3]^4*
a[3,3]^3+2*z^2*a[1,1]^2*a[1,2]^6*a[1,3]*a[3,3]^5*a[2,2]^2-2*z^2*a[1,1]^2*a[1,2]^4*a[1,3]^3*a[3,3]^4*a[2,2]^3-6*a[1,1]^2*a[1,2]^3*a[1,3]^2*a[2,3]^3*a[3,3]^3*a[2,2]^2
-6*a[1,1]^2*a[1,2]^4*a[1,3]*a[2,3]^4*a[3,3]^3*a[2,2]+6*z^2*a[1,1]^2*a[1,2]^5*a[1,3]^2*a[2,3]^5*a[3,3]^2+18*z^2*a[1,1]^3*a[1,2]^4*a[1,3]*a[2,3]^4*a[3,3]^3*a[2,2]-6*z
^2*a[1,1]^4*a[1,2]^2*a[1,3]*a[2,3]^4*a[3,3]^3*a[2,2]^2+3*z^2*a[1,1]^4*a[1,2]*a[1,3]^2*a[2,3]^5*a[3,3]^2*a[2,2]^2+2*a[1,1]^3*a[1,2]^2*a[1,3]*a[3,3]^5*a[2,2]^4-a[1,1]
^3*a[1,2]^3*a[2,3]^5*a[3,3]^3*a[2,2]+2*a[1,1]^3*a[1,2]^3*a[2,3]^3*a[3,3]^4*a[2,2]^2-a[1,1]^3*a[1,2]^3*a[2,3]*a[3,3]^5*a[2,2]^3-3*a[1,1]^2*a[1,2]^2*a[1,3]^3*a[2,3]^4
*a[3,3]^2*a[2,2]^2+12*a[1,1]^2*a[1,2]^2*a[1,3]^3*a[2,3]^2*a[3,3]^3*a[2,2]^3+6*a[1,1]^2*a[1,2]^3*a[1,3]^2*a[2,3]^5*a[3,3]^2*a[2,2]+6*a[1,1]*a[1,2]^6*a[1,3]*a[2,3]^2*
a[3,3]^4*a[2,2]-9*a[1,1]^2*a[1,2]*a[1,3]^4*a[2,3]^3*a[3,3]^2*a[2,2]^3+9*a[1,1]^2*a[1,2]*a[1,3]^4*a[2,3]*a[3,3]^3*a[2,2]^4+12*z^2*a[1,1]^4*a[1,2]^2*a[1,3]*a[2,3]^2*a
[3,3]^4*a[2,2]^3+3*z^2*a[1,1]^4*a[1,2]*a[1,3]^2*a[2,3]*a[3,3]^4*a[2,2]^4+16*z^6*a[1,1]^5*a[1,2]^3*a[1,3]^2*a[2,3]^3*a[3,3]^3*a[2,2]^2+6*z^2*a[1,1]^3*a[1,3]^5*a[2,3]
^2*a[3,3]^2*a[2,2]^4-12*a[1,1]*a[1,2]^2*a[1,3]^5*a[2,3]^2*a[3,3]^2*a[2,2]^3-6*a[1,1]*a[1,2]^3*a[1,3]^4*a[2,3]^5*a[3,3]*a[2,2]+13*a[1,1]*a[1,2]^3*a[1,3]^4*a[2,3]^3*a
[3,3]^2*a[2,2]^2-2*a[1,1]*a[1,2]^3*a[1,3]^4*a[2,3]*a[3,3]^3*a[2,2]^3+6*a[1,1]*a[1,2]^4*a[1,3]^3*a[2,3]^4*a[3,3]^2*a[2,2]-6*a[1,1]*a[1,2]^4*a[1,3]^3*a[2,3]^2*a[3,3]^
3*a[2,2]^2-5*a[1,1]*a[1,2]^5*a[1,3]^2*a[2,3]^3*a[3,3]^3*a[2,2]-4*a[1,1]*a[1,2]^5*a[1,3]^2*a[2,3]*a[3,3]^4*a[2,2]^2-a[1,1]^3*a[1,2]*a[1,3]^2*a[2,3]*a[3,3]^4*a[2,2]^4
+2*a[1,1]^3*a[1,2]^2*a[1,3]*a[2,3]^4*a[3,3]^3*a[2,2]^2-6*z^6*a[1,1]^5*a[1,2]^3*a[1,3]^2*a[2,3]^5*a[3,3]^2*a[2,2]+z^6*a[1,1]^5*a[1,3]^5*a[2,3]^2*a[3,3]^2*a[2,2]^4-z^
6*a[1,1]^5*a[1,3]^5*a[2,3]^4*a[3,3]*a[2,2]^3+2*z^2*a[1,1]*a[1,2]^2*a[1,3]^7*a[2,3]^4*a[2,2]^2-4*a[1,1]^3*a[1,2]^2*a[1,3]*a[2,3]^2*a[3,3]^4*a[2,2]^3+5*a[1,1]*a[1,2]*
a[2,3]^3*a[3,3]*a[2,2]^3*a[1,3]^6+a[1,1]*a[1,2]^2*a[1,3]^5*a[2,3]^4*a[3,3]*a[2,2]^2-a[1,1]^3*a[1,2]*a[1,3]^2*a[2,3]^5*a[3,3]^2*a[2,2]^2+2*a[1,1]^3*a[1,2]*a[1,3]^2*a
[2,3]^3*a[3,3]^3*a[2,2]^3+3*a[1,1]^2*a[1,2]^4*a[1,3]*a[2,3]^2*a[3,3]^4*a[2,2]^2+6*z^6*a[1,1]^5*a[1,2]*a[1,3]^4*a[2,3]^3*a[3,3]^2*a[2,2]^3-z^6*a[1,1]^5*a[1,2]*a[1,3]
^4*a[2,3]^5*a[3,3]*a[2,2]^2+2*z^6*a[1,1]^5*a[1,2]^2*a[1,3]^3*a[2,3]^4*a[3,3]^2*a[2,2]^2+8*z^6*a[1,1]^5*a[1,2]^2*a[1,3]^3*a[3,3]^4*a[2,2]^4-5*z^6*a[1,1]^5*a[1,2]*a[1
,3]^4*a[2,3]*a[3,3]^3*a[2,2]^4-10*z^6*a[1,1]^5*a[1,2]^2*a[1,3]^3*a[2,3]^2*a[3,3]^3*a[2,2]^3+2*z^2*a[1,1]*a[2,3]^3*a[2,2]^3*a[1,3]^8*a[1,2]+10*z^6*a[1,1]^4*a[1,2]^5*
a[1,3]^2*a[2,3]*a[3,3]^4*a[2,2]^2+18*z^4*a[1,1]^4*a[1,2]^3*a[1,3]^2*a[2,3]^5*a[3,3]^2*a[2,2]-4*z^4*a[1,1]*a[1,2]^6*a[1,3]^5*a[3,3]^3*a[2,2]^2-14*z^4*a[1,1]*a[1,2]^7
*a[1,3]^4*a[3,3]^2*a[2,3]^3-3*z^4*a[1,1]*a[1,2]^4*a[1,3]^7*a[3,3]^2*a[2,2]^3-4*z^4*a[1,2]^7*a[1,3]^6*a[3,3]^2*a[2,3]*a[2,2]+30*z^4*a[1,1]^4*a[1,2]^2*a[1,3]^3*a[2,3]
^2*a[3,3]^3*a[2,2]^3-16*z^4*a[1,1]^4*a[1,2]*a[1,3]^4*a[2,3]^3*a[3,3]^2*a[2,2]^3-11*z^4*a[1,1]^4*a[1,2]^2*a[1,3]^3*a[2,3]^4*a[3,3]^2*a[2,2]^2+z^6*a[1,1]^6*a[1,2]^3*a
[2,3]*a[3,3]^5*a[2,2]^3+z^2*a[1,2]^8*a[1,3]^3*a[3,3]^3*a[2,3]^2+14*z^4*a[1,1]*a[1,2]^6*a[1,3]^5*a[3,3]*a[2,3]^4+8*z^4*a[1,1]^3*a[1,2]^2*a[1,3]^5*a[2,3]^4*a[3,3]*a[2
,2]^2-15*z^4*a[1,1]^3*a[1,2]^2*a[1,3]^5*a[2,3]^2*a[3,3]^2*a[2,2]^3+2*z^2*a[1,2]^4*a[1,3]^7*a[3,3]^2*a[2,2]^3+5*z^6*a[1,1]^4*a[1,2]^5*a[1,3]^2*a[2,3]^5*a[3,3]^2-15*z
^6*a[1,1]^4*a[1,2]^4*a[1,3]^3*a[3,3]^4*a[2,2]^3-24*z^6*a[1,1]^4*a[1,2]^5*a[1,3]^2*a[2,3]^3*a[3,3]^3*a[2,2]-z^6*a[1,1]^4*a[1,2]^6*a[1,3]*a[2,3]^4*a[3,3]^3-6*z^2*a[1,
1]^3*a[1,3]^5*a[2,3]^4*a[3,3]*a[2,2]^3-6*z^2*a[1,1]*a[1,2]^3*a[1,3]^6*a[2,3]^5*a[2,2]+20*z^2*a[1,1]^3*a[1,2]^2*a[1,3]^3*a[3,3]^4*a[2,2]^4-z^2*a[1,1]^2*a[1,2]^7*a[2,
3]*a[3,3]^5*a[2,2]-2*z^6*a[1,1]^6*a[1,2]^3*a[2,3]^3*a[3,3]^4*a[2,2]^2+6*z^4*a[1,1]^3*a[1,2]*a[2,3]^3*a[3,3]*a[2,2]^3*a[1,3]^6-11*z^4*a[1,1]^3*a[1,2]*a[1,3]^6*a[2,3]
*a[3,3]^2*a[2,2]^4-z^2*a[1,2]^8*a[1,3]^3*a[3,3]^4*a[2,2]+14*z^4*a[1,1]^4*a[1,2]*a[1,3]^4*a[2,3]*a[3,3]^3*a[2,2]^4-11*z^4*a[1,1]^3*a[1,2]^6*a[1,3]*a[2,3]^2*a[3,3]^4*
a[2,2]-13*z^4*a[1,1]^2*a[1,2]^4*a[1,3]^5*a[2,3]^4*a[3,3]*a[2,2]+8*z^6*a[1,1]^4*a[1,2]^6*a[1,3]*a[2,3]^2*a[3,3]^4*a[2,2]-z^6*a[1,1]^4*a[1,2]^7*a[2,3]*a[3,3]^5*a[2,2]
-2*z^6*a[1,1]^4*a[1,2]^6*a[1,3]*a[3,3]^5*a[2,2]^2-6*z^2*a[1,1]*a[1,2]^4*a[1,3]^5*a[3,3]^3*a[2,2]^3+2*z^4*a[1,1]^4*a[1,2]*a[1,3]^4*a[2,3]^5*a[3,3]*a[2,2]^2+10*z^4*a[
1,1]^2*a[1,2]^3*a[1,3]^6*a[2,3]*a[3,3]^2*a[2,2]^3+21*z^4*a[1,1]^2*a[1,2]^4*a[1,3]^5*a[2,3]^2*a[3,3]^2*a[2,2]^2-4*z^4*a[1,1]^2*a[1,2]^5*a[1,3]^4*a[2,3]^3*a[3,3]^2*a[
2,2]-8*z^4*a[1,1]^2*a[1,2]^5*a[1,3]^4*a[2,3]*a[3,3]^3*a[2,2]^2+12*z^4*a[1,1]^2*a[1,2]^6*a[1,3]^3*a[2,3]^2*a[3,3]^3*a[2,2]-19*z^4*a[1,1]^3*a[1,2]^3*a[1,3]^4*a[2,3]^5
*a[3,3]*a[2,2]-5*z^2*a[1,2]^4*a[1,3]^7*a[2,3]^4*a[2,2]+8*z^2*a[1,1]*a[1,2]^6*a[1,3]^3*a[2,3]^4*a[3,3]^2+4*z^2*a[1,1]*a[1,2]^6*a[1,3]^3*a[3,3]^4*a[2,2]^2-5*z^2*a[1,1
]*a[1,2]^7*a[1,3]^2*a[2,3]^3*a[3,3]^3+2*z^2*a[1,1]*a[2,3]^2*a[3,3]^4*a[1,3]*a[1,2]^8+3*z^2*a[1,2]^4*a[1,3]^7*a[3,3]*a[2,3]^2*a[2,2]^2-2*z^2*a[1,2]^3*a[1,3]^8*a[3,3]
*a[2,3]*a[2,2]^3+2*z^2*a[1,2]^7*a[1,3]^4*a[3,3]^3*a[2,3]*a[2,2]+2*z^2*a[1,1]*a[1,2]^2*a[1,3]^7*a[3,3]^2*a[2,2]^4-6*z^2*a[1,1]*a[1,2]^5*a[1,3]^4*a[2,3]^5*a[3,3]+2*z^
2*a[1,2]^3*a[1,3]^8*a[2,3]^3*a[2,2]^2+z^2*a[1,2]^6*a[1,3]^5*a[3,3]^3*a[2,2]^2+11*z^2*a[1,1]*a[1,2]^3*a[1,3]^6*a[2,3]^3*a[3,3]*a[2,2]^2-6*z^2*a[1,2]^5*a[1,3]^6*a[3,3
]^2*a[2,3]*a[2,2]^2+4*z^2*a[1,2]^5*a[1,3]^6*a[3,3]*a[2,3]^3*a[2,2]-2*z^2*a[1,2]^7*a[1,3]^4*a[3,3]^2*a[2,3]^3-6*z^6*a[1,1]^3*a[1,2]^6*a[1,3]^3*a[2,3]^4*a[3,3]^2+8*z^
6*a[1,1]^3*a[1,2]^6*a[1,3]^3*a[3,3]^4*a[2,2]^2-12*z^6*a[1,1]^3*a[1,2]^6*a[1,3]^3*a[2,3]^2*a[3,3]^3*a[2,2]-2*z^6*a[1,1]^3*a[1,2]^3*a[1,3]^6*a[2,3]^5*a[2,2]-4*z^6*a[1
,1]^3*a[1,2]^4*a[1,3]^5*a[2,3]^2*a[3,3]^2*a[2,2]^2+38*z^6*a[1,1]^3*a[1,2]^5*a[1,3]^4*a[2,3]^3*a[3,3]^2*a[2,2]-6*z^6*a[1,1]^3*a[1,2]^5*a[1,3]^4*a[2,3]^5*a[3,3]-28*z^
6*a[1,1]^3*a[1,2]^5*a[1,3]^4*a[2,3]*a[3,3]^3*a[2,2]^2+z^6*a[1,1]^3*a[3,3]^5*a[2,3]*a[1,2]^9-10*z^6*a[1,1]^3*a[1,2]^4*a[1,3]^5*a[2,3]^4*a[3,3]*a[2,2]-26*z^6*a[1,1]^3
*a[1,2]^3*a[1,3]^6*a[2,3]*a[3,3]^2*a[2,2]^3+18*z^6*a[1,1]^3*a[1,2]^4*a[1,3]^5*a[3,3]^3*a[2,2]^3+4*z^2*a[1,1]*a[1,2]^5*a[1,3]^4*a[2,3]*a[3,3]^3*a[2,2]^2+6*z^2*a[1,1]
*a[1,2]^6*a[1,3]^3*a[2,3]^2*a[3,3]^3*a[2,2]-z^6*a[1,1]^5*a[1,2]^5*a[2,3]^5*a[3,3]^3+z^6*a[1,1]^4*a[2,3]^4*a[2,2]^3*a[1,3]^7+2*z^6*a[1,1]^4*a[1,2]^2*a[1,3]^5*a[2,3]^
2*a[3,3]^2*a[2,2]^3+7*z^6*a[1,1]^4*a[1,2]*a[1,3]^6*a[2,3]*a[3,3]^2*a[2,2]^4-2*z^6*a[1,1]^4*a[1,2]*a[2,3]^3*a[3,3]*a[2,2]^3*a[1,3]^6-2*z^6*a[1,1]^4*a[1,3]^7*a[2,3]^2
*a[3,3]*a[2,2]^4+7*z^6*a[1,1]^4*a[1,2]^3*a[1,3]^4*a[2,3]^5*a[3,3]*a[2,2]+28*z^6*a[1,1]^4*a[1,2]^3*a[1,3]^4*a[2,3]*a[3,3]^3*a[2,2]^3-30*z^6*a[1,1]^4*a[1,2]^3*a[1,3]^
4*a[2,3]^3*a[3,3]^2*a[2,2]^2-5*z^6*a[1,1]^3*a[2,3]^2*a[3,3]^4*a[1,3]*a[1,2]^8+14*z^2*a[1,1]*a[1,2]^4*a[1,3]^5*a[2,3]^4*a[3,3]*a[2,2]-14*z^2*a[1,1]*a[1,2]^2*a[1,3]^7
*a[2,3]^2*a[3,3]*a[2,2]^3-8*z^2*a[1,1]*a[1,2]^5*a[1,3]^4*a[2,3]^3*a[3,3]^2*a[2,2]-11*z^6*a[1,1]^4*a[1,2]^2*a[1,3]^5*a[3,3]^3*a[2,2]^4+16*z^6*a[1,1]^4*a[1,2]^4*a[1,3
]^3*a[2,3]^2*a[3,3]^3*a[2,2]^2+4*z^6*a[1,1]^4*a[1,2]^4*a[1,3]^3*a[2,3]^4*a[3,3]^2*a[2,2]+13*z^2*a[1,1]*a[1,2]^3*a[1,3]^6*a[2,3]*a[3,3]^2*a[2,2]^3+10*z^6*a[1,1]^3*a[
1,2]^7*a[1,3]^2*a[2,3]^3*a[3,3]^3-27*z^2*a[1,1]^2*a[1,2]^4*a[1,3]^3*a[2,3]^4*a[3,3]^2*a[2,2]+3*z^2*a[1,1]^2*a[1,2]^3*a[1,3]^4*a[2,3]*a[3,3]^3*a[2,2]^3-11*z^4*a[1,1]
^3*a[1,2]^5*a[1,3]^2*a[2,3]^5*a[3,3]^2-3*z^4*a[1,1]^5*a[1,2]*a[1,3]^2*a[2,3]^5*a[3,3]^2*a[2,2]^2+2*z^6*a[1,1]^2*a[1,2]^6*a[1,3]^5*a[3,3]^2*a[2,3]^2*a[2,2]+11*z^6*a[
1,1]^2*a[1,2]^6*a[1,3]^5*a[3,3]*a[2,3]^4-z^4*a[1,2]^4*a[1,3]^9*a[2,3]^2*a[2,2]^2+z^4*a[1,2]^4*a[1,3]^9*a[3,3]*a[2,2]^3-14*z^6*a[1,1]^2*a[1,2]^7*a[1,3]^4*a[3,3]^2*a[
2,3]^3+6*z^4*a[1,1]^5*a[1,2]*a[1,3]^2*a[2,3]^3*a[3,3]^3*a[2,2]^3+2*z^4*a[1,1]^4*a[1,2]^5*a[2,3]^5*a[3,3]^3+18*z^4*a[1,1]^4*a[1,2]^4*a[1,3]*a[2,3]^2*a[3,3]^4*a[2,2]^
2-z^6*a[1,1]^2*a[3,3]^4*a[2,3]*a[1,3]^2*a[1,2]^9-z^6*a[1,1]^2*a[1,2]^8*a[1,3]^3*a[3,3]^4*a[2,2]-2*z^6*a[1,1]^6*a[1,2]^2*a[1,3]*a[2,3]^4*a[3,3]^3*a[2,2]^2-8*z^6*a[1,
1]^2*a[1,2]^6*a[1,3]^5*a[3,3]^3*a[2,2]^2-26*z^2*a[1,1]^2*a[1,2]^3*a[1,3]^4*a[2,3]^3*a[3,3]^2*a[2,2]^2+24*z^2*a[1,1]^2*a[1,2]^4*a[1,3]^3*a[2,3]^2*a[3,3]^3*a[2,2]^2+6
*z^6*a[1,1]^2*a[1,2]^8*a[1,3]^3*a[3,3]^3*a[2,3]^2+5*z^6*a[1,1]^2*a[1,2]^7*a[1,3]^4*a[3,3]^3*a[2,3]*a[2,2]-12*z^2*a[1,1]^2*a[1,2]*a[2,3]^3*a[3,3]*a[2,2]^3*a[1,3]^6+7
*z^2*a[1,1]^2*a[1,2]*a[1,3]^6*a[2,3]*a[3,3]^2*a[2,2]^4-3*z^6*a[1,1]^3*a[1,2]*a[1,3]^8*a[3,3]*a[2,3]*a[2,2]^4-2*z^6*a[1,1]^3*a[2,3]^3*a[2,2]^3*a[1,3]^8*a[1,2]+4*z^6*
a[1,1]^3*a[1,2]^2*a[1,3]^7*a[2,3]^2*a[3,3]*a[2,2]^3+z^6*a[1,1]^3*a[2,3]^2*a[2,2]^4*a[1,3]^9+2*z^6*a[1,1]^2*a[1,2]^5*a[1,3]^6*a[2,3]^5-4*z^6*a[1,1]*a[1,2]^6*a[1,3]^7
*a[2,3]^4+18*z^6*a[1,1]^3*a[1,2]^3*a[1,3]^6*a[2,3]^3*a[3,3]*a[2,2]^2-5*z^2*a[1,1]*a[1,2]^7*a[1,3]^2*a[2,3]*a[3,3]^4*a[2,2]-18*z^2*a[1,1]*a[1,2]^4*a[1,3]^5*a[2,3]^2*
a[3,3]^2*a[2,2]^2+6*z^6*a[1,1]^3*a[1,2]^2*a[1,3]^7*a[3,3]^2*a[2,2]^4+10*z^4*a[1,1]^3*a[1,2]^6*a[1,3]*a[2,3]^4*a[3,3]^3+2*z^4*a[1,2]^6*a[1,3]^7*a[3,3]^2*a[2,2]^2+23*
z^6*a[1,1]^2*a[1,2]^5*a[1,3]^6*a[3,3]^2*a[2,3]*a[2,2]^2-20*z^6*a[1,1]^2*a[1,2]^5*a[1,3]^6*a[3,3]*a[2,3]^3*a[2,2]-z^2*a[1,1]^2*a[1,2]^6*a[1,3]*a[2,3]^2*a[3,3]^4*a[2,
2]-15*z^4*a[1,1]^4*a[1,2]^4*a[1,3]*a[2,3]^4*a[3,3]^3*a[2,2]-z^2*a[1,1]^3*a[1,2]*a[1,3]^4*a[2,3]^5*a[3,3]*a[2,2]^2-4*z^2*a[1,1]^3*a[1,2]^4*a[1,3]*a[3,3]^5*a[2,2]^3-6
*z^2*a[1,1]^2*a[1,2]^2*a[1,3]^5*a[2,3]^4*a[3,3]*a[2,2]^2+27*z^2*a[1,1]^2*a[1,2]^2*a[1,3]^5*a[2,3]^2*a[3,3]^2*a[2,2]^3+18*z^2*a[1,1]^2*a[1,2]^3*a[1,3]^4*a[2,3]^5*a[3
,3]*a[2,2]+z^4*a[1,1]^2*a[1,2]^8*a[1,3]*a[3,3]^5*a[2,2]-9*z^2*a[1,1]^2*a[1,2]^5*a[1,3]^2*a[2,3]*a[3,3]^4*a[2,2]^2+12*z^2*a[1,1]^2*a[1,2]^5*a[1,3]^2*a[2,3]^3*a[3,3]^
3*a[2,2]-6*z^2*a[1,1]^4*a[1,2]^2*a[1,3]*a[3,3]^5*a[2,2]^4-4*z^6*a[1,1]^2*a[1,2]^4*a[1,3]^7*a[3,3]*a[2,3]^2*a[2,2]^2-8*z^4*a[1,1]^2*a[1,2]^7*a[1,3]^2*a[2,3]*a[3,3]^4
*a[2,2]+12*z^4*a[1,1]^3*a[1,2]^5*a[1,3]^2*a[2,3]^3*a[3,3]^3*a[2,2]+8*z^4*a[1,1]^3*a[1,2]^5*a[1,3]^2*a[2,3]*a[3,3]^4*a[2,2]^2+4*z^4*a[1,1]^3*a[1,3]^7*a[2,3]^2*a[3,3]
*a[2,2]^4+16*z^4*a[1,1]^3*a[1,2]^2*a[1,3]^5*a[3,3]^3*a[2,2]^4-5*z^2*a[1,1]^3*a[1,2]^5*a[2,3]^3*a[3,3]^4*a[2,2]+19*z^2*a[1,1]^3*a[1,2]*a[1,3]^4*a[2,3]^3*a[3,3]^2*a[2
,2]^3+12*z^4*a[1,1]^2*a[1,2]^5*a[1,3]^4*a[2,3]^5*a[3,3]-16*z^4*a[1,1]^2*a[1,2]^6*a[1,3]^3*a[2,3]^4*a[3,3]^2+4*z^4*a[1,1]^2*a[1,2]^6*a[1,3]^3*a[3,3]^4*a[2,2]^2+14*z^
4*a[1,1]^3*a[1,2]^4*a[1,3]^3*a[3,3]^4*a[2,2]^3+18*z^2*a[1,1]^3*a[1,2]^3*a[1,3]^2*a[2,3]^3*a[3,3]^3*a[2,2]^2-14*z^2*a[1,1]^3*a[1,2]^4*a[1,3]*a[2,3]^2*a[3,3]^4*a[2,2]
^2-8*z^4*a[1,1]^2*a[1,2]^4*a[1,3]^5*a[3,3]^3*a[2,2]^3+4*z^4*a[1,2]^5*a[1,3]^8*a[2,3]^3*a[2,2]+3*z^2*a[1,1]^4*a[1,2]^3*a[2,3]^5*a[3,3]^3*a[2,2]+3*z^2*a[1,1]^4*a[1,2]
^3*a[2,3]*a[3,3]^5*a[2,2]^3+10*z^4*a[1,1]^4*a[1,2]^3*a[1,3]^2*a[3,3]^4*a[2,3]*a[2,2]^3+6*z^4*a[1,1]^2*a[1,2]^3*a[1,3]^6*a[2,3]^5*a[2,2]-4*z^4*a[1,1]^4*a[1,3]^5*a[2,
3]^2*a[3,3]^2*a[2,2]^4-4*z^4*a[1,1]*a[1,2]^5*a[1,3]^6*a[2,3]^5-2*z^6*a[1,1]^2*a[1,2]^3*a[1,3]^8*a[2,3]^3*a[2,2]^2-z^6*a[1,1]^2*a[3,3]*a[2,2]^4*a[1,3]^9*a[1,2]^2+z^4
*a[1,2]^8*a[1,3]^5*a[3,3]^3*a[2,2]+4*z^4*a[1,1]^4*a[1,3]^5*a[2,3]^4*a[3,3]*a[2,2]^3-3*z^4*a[1,1]^3*a[2,3]^4*a[2,2]^3*a[1,3]^7-4*z^4*a[1,1]^3*a[1,2]^7*a[2,3]^3*a[3,3
]^4+3*z^6*a[1,1]^2*a[1,2]^4*a[1,3]^7*a[2,3]^4*a[2,2]+7*z^6*a[1,1]^2*a[1,2]^3*a[1,3]^8*a[3,3]*a[2,3]*a[2,2]^3+5*z^4*a[1,1]^3*a[1,2]^7*a[2,3]*a[3,3]^5*a[2,2]-z^4*a[1,
2]^8*a[1,3]^5*a[3,3]^2*a[2,3]^2-32*z^2*a[1,1]^3*a[1,2]^2*a[1,3]^3*a[2,3]^2*a[3,3]^3*a[2,2]^3-4*z^4*a[1,1]^3*a[1,2]^6*a[1,3]*a[3,3]^5*a[2,2]^2+12*z^2*a[1,1]^3*a[1,2]
^2*a[1,3]^3*a[2,3]^4*a[3,3]^2*a[2,2]^2-18*z^2*a[1,1]^3*a[1,2]^3*a[1,3]^2*a[2,3]^5*a[3,3]^2*a[2,2]+6*z^2*a[1,1]^3*a[1,2]^5*a[2,3]*a[3,3]^5*a[2,2]^2-8*z^6*a[1,1]^2*a[
1,2]^4*a[1,3]^7*a[3,3]^2*a[2,2]^3-18*z^2*a[1,1]^3*a[1,2]*a[1,3]^4*a[2,3]*a[3,3]^3*a[2,2]^4+4*z^4*a[1,2]^7*a[1,3]^6*a[3,3]*a[2,3]^3-2*z^6*a[1,1]^6*a[1,2]*a[1,3]^2*a[
2,3]^3*a[3,3]^3*a[2,2]^3+z^6*a[1,1]^6*a[1,2]*a[1,3]^2*a[2,3]^5*a[3,3]^2*a[2,2]^2-2*z^6*a[1,1]^6*a[1,2]^2*a[1,3]*a[3,3]^5*a[2,2]^4+2*z^2*a[1,1]^2*a[1,2]^7*a[2,3]^3*a
[3,3]^4-3*z^4*a[1,1]^2*a[1,2]^2*a[1,3]^7*a[3,3]^2*a[2,2]^4+2*z^4*a[1,2]^6*a[1,3]^7*a[3,3]*a[2,3]^2*a[2,2]+z^6*a[1,1]*a[1,2]^8*a[1,3]^5*a[3,3]^3*a[2,2]-z^6*a[1,1]*a[
1,2]^8*a[1,3]^5*a[3,3]^2*a[2,3]^2-z^4*a[1,1]*a[3,3]^4*a[2,3]*a[1,3]^2*a[1,2]^9-z^4*a[1,1]^2*a[1,2]^2*a[1,3]^7*a[2,3]^4*a[2,2]^2+6*z^4*a[1,1]*a[1,2]^8*a[1,3]^3*a[3,3
]^3*a[2,3]^2-z^4*a[1,1]*a[1,2]^8*a[1,3]^3*a[3,3]^4*a[2,2]-12*z^2*a[1,1]^2*a[1,2]^2*a[1,3]^5*a[3,3]^3*a[2,2]^4-6*z^2*a[1,1]^4*a[1,2]^3*a[2,3]^3*a[3,3]^4*a[2,2]^2+8*z
^4*a[1,1]^2*a[1,2]^7*a[1,3]^2*a[2,3]^3*a[3,3]^3-z^4*a[1,1]^2*a[2,3]^2*a[3,3]^4*a[1,3]*a[1,2]^8+2*z^4*a[1,1]*a[1,2]^3*a[1,3]^8*a[2,3]^3*a[2,2]^2+2*z^4*a[1,1]*a[1,2]^
4*a[1,3]^7*a[2,3]^4*a[2,2]+z^6*a[1,1]*a[1,2]^4*a[1,3]^9*a[3,3]*a[2,2]^3-z^6*a[1,1]*a[1,2]^4*a[1,3]^9*a[2,3]^2*a[2,2]^2+6*z^4*a[1,1]^5*a[1,2]^2*a[1,3]*a[3,3]^5*a[2,2
]^4-z^4*a[1,1]*a[2,3]^2*a[2,2]^3*a[1,3]^9*a[1,2]^2-3*z^4*a[1,1]^5*a[1,2]^3*a[2,3]*a[3,3]^5*a[2,2]^3-4*z^4*a[1,2]^5*a[1,3]^8*a[3,3]*a[2,3]*a[2,2]^2+4*z^6*a[1,1]*a[1,
2]^5*a[1,3]^8*a[2,3]^3*a[2,2]-3*z^4*a[1,1]^5*a[1,2]^3*a[2,3]^5*a[3,3]^3*a[2,2]+6*z^4*a[1,1]^5*a[1,2]^3*a[2,3]^3*a[3,3]^4*a[2,2]^2-2*z^4*a[1,1]^4*a[1,2]^5*a[2,3]*a[3
,3]^5*a[2,2]^2+2*z^6*a[1,1]*a[1,2]^6*a[1,3]^7*a[3,3]^2*a[2,2]^2+2*z^6*a[1,1]*a[1,2]^6*a[1,3]^7*a[3,3]*a[2,3]^2*a[2,2]-4*z^6*a[1,1]*a[1,2]^5*a[1,3]^8*a[3,3]*a[2,3]*a
[2,2]^2-28*z^4*a[1,1]^4*a[1,2]^3*a[1,3]^2*a[2,3]^3*a[3,3]^3*a[2,2]^2-19*z^4*a[1,1]^4*a[1,2]^2*a[1,3]^3*a[3,3]^4*a[2,2]^4-3*z^4*a[1,1]^4*a[1,2]^4*a[1,3]*a[3,3]^5*a[2
,2]^3-4*z^6*a[1,1]*a[1,2]^7*a[1,3]^6*a[3,3]^2*a[2,3]*a[2,2]+4*z^6*a[1,1]*a[1,2]^7*a[1,3]^6*a[3,3]*a[2,3]^3+z^6*a[1,1]^6*a[1,2]*a[1,3]^2*a[2,3]*a[3,3]^4*a[2,2]^4+19*
z^4*a[1,1]^3*a[1,2]^4*a[1,3]^3*a[2,3]^4*a[3,3]^2*a[2,2]-38*z^4*a[1,1]^3*a[1,2]^4*a[1,3]^3*a[2,3]^2*a[3,3]^3*a[2,2]^2+2*z^2*a[1,2]^5*a[1,3]^6*a[2,3]^5-4*z^4*a[1,2]^6
*a[1,3]^7*a[2,3]^4+38*z^4*a[1,1]^3*a[1,2]^3*a[1,3]^4*a[2,3]^3*a[3,3]^2*a[2,2]^2-24*z^4*a[1,1]^3*a[1,2]^3*a[1,3]^4*a[2,3]*a[3,3]^3*a[2,2]^3+z^6*a[1,1]^6*a[1,2]^3*a[2
,3]^5*a[3,3]^3*a[2,2]-z^2*a[1,1]^3*a[1,2]^5*a[2,3]^5*a[3,3]^3+4*z^6*a[1,1]^6*a[1,2]^2*a[1,3]*a[2,3]^2*a[3,3]^4*a[2,2]^3-3*z^4*a[1,1]^5*a[1,2]*a[1,3]^2*a[2,3]*a[3,3]
^4*a[2,2]^4-2*z^2*a[1,1]^2*a[1,3]^7*a[2,3]^2*a[3,3]*a[2,2]^4-z^2*a[1,2]^6*a[1,3]^5*a[3,3]*a[2,3]^4-12*z^4*a[1,1]^5*a[1,2]^2*a[1,3]*a[2,3]^2*a[3,3]^4*a[2,2]^3+6*z^4*
a[1,1]^5*a[1,2]^2*a[1,3]*a[2,3]^4*a[3,3]^3*a[2,2]^2-4*z^4*a[1,1]*a[1,2]^5*a[1,3]^6*a[3,3]*a[2,3]^3*a[2,2]+3*z^4*a[1,1]*a[1,2]^3*a[1,3]^8*a[3,3]*a[2,3]*a[2,2]^3+3*z^
6*a[1,1]^5*a[1,2]^4*a[1,3]*a[2,3]^4*a[3,3]^3*a[2,2]-10*z^6*a[1,1]^5*a[1,2]^3*a[1,3]^2*a[3,3]^4*a[2,3]*a[2,2]^3+13*z^4*a[1,1]*a[1,2]^5*a[1,3]^6*a[3,3]^2*a[2,3]*a[2,2
]^2-8*z^4*a[1,1]*a[1,2]^4*a[1,3]^7*a[3,3]*a[2,3]^2*a[2,2]^2+4*z^6*a[1,1]^5*a[1,2]^4*a[1,3]*a[3,3]^5*a[2,2]^3+3*z^2*a[1,1]^2*a[2,3]^4*a[2,2]^3*a[1,3]^7-7*z^6*a[1,1]^
5*a[1,2]^4*a[1,3]*a[2,3]^2*a[3,3]^4*a[2,2]^2+4*z^4*a[1,1]^2*a[1,2]^2*a[1,3]^7*a[2,3]^2*a[3,3]*a[2,2]^3-5*z^4*a[1,1]*a[1,2]^6*a[1,3]^5*a[3,3]^2*a[2,3]^2*a[2,2])/a[3,
3]/(a[1,2]^2*a[1,3]^6*a[2,3]^4*a[2,2]^2+a[1,2]^2*a[1,3]^6*a[3,3]^2*a[2,2]^4+a[1,1]*a[1,3]^6*a[2,3]^4*a[2,2]^3-a[1,2]^6*a[1,3]^2*a[3,3]^4*a[2,2]^2-2*a[1,2]^3*a[1,3]^
5*a[2,3]^5*a[2,2]-3*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^2-4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^3-2*a[1,2]^2*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]
^3+a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^2+3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^3+4*a[1,2]^3*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^2-a[1,1]*a[1,2
]^4*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]+a[1,1]*a[1,2]^6*a[3,3]^4*a[2,3]^2*a[2,2]+4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]+4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]^2*a
[2,3]*a[2,2]^4-4*a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]-2*a[1,2]^3*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^3+2*a[1,2]^5*a[1,3]^3*a[3,3]*a[2,3]^5+2*a[1,2]^5*a[1,3]^3*a[3
,3]^3*a[2,3]*a[2,2]^2-a[1,2]^6*a[1,3]^2*a[3,3]^2*a[2,3]^4-a[1,1]*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^4+4*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^4*a[2,2]^3-4*a[1,1]*a[1,2]^2*a[
1,3]^4*a[3,3]^3*a[2,2]^4+2*a[1,2]^6*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]-a[1,1]*a[1,2]^6*a[3,3]^3*a[2,3]^4-4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^2)], -a[3,3]
*a[2,3]^2*a[2,2]+a[3,3]^2*a[2,2]^2+(-4*a[1,1]*a[3,3]^2*a[2,2]^2+2*a[3,3]*a[2,3]*a[2,2]*a[1,3]*a[1,2]-a[1,3]^2*a[2,3]^2*a[2,2]-a[1,2]^2*a[3,3]*a[2,3]^2+4*a[1,1]*a[3,
3]*a[2,3]^2*a[2,2])*z^2+(6*a[1,1]^2*a[3,3]^2*a[2,2]^2-2*a[1,1]*a[1,3]^2*a[3,3]*a[2,2]^2-6*a[1,1]^2*a[3,3]*a[2,3]^2*a[2,2]-2*a[1,1]*a[1,2]^2*a[3,3]^2*a[2,2]-a[1,2]^2
*a[1,3]^2*a[2,3]^2+2*a[2,3]*a[2,2]*a[1,3]^3*a[1,2]+3*a[1,1]*a[1,2]^2*a[3,3]*a[2,3]^2-2*a[1,1]*a[3,3]*a[2,3]*a[2,2]*a[1,3]*a[1,2]+3*a[1,1]*a[1,3]^2*a[2,3]^2*a[2,2]+2
*a[3,3]*a[2,3]*a[1,3]*a[1,2]^3-3*a[1,2]^2*a[1,3]^2*a[3,3]*a[2,2])*z^4+(-a[1,1]^4*a[3,3]*a[2,3]^2*a[2,2]-2*a[1,1]^3*a[1,2]^2*a[3,3]^2*a[2,2]+a[1,1]^3*a[1,2]^2*a[3,3]
*a[2,3]^2+2*a[1,1]^3*a[3,3]*a[2,3]*a[2,2]*a[1,3]*a[1,2]+a[1,1]^2*a[3,3]^2*a[1,2]^4+a[1,1]^4*a[3,3]^2*a[2,2]^2-2*a[1,1]^3*a[1,3]^2*a[3,3]*a[2,2]^2+a[1,1]^3*a[1,3]^2*
a[2,3]^2*a[2,2]-2*a[1,1]^2*a[3,3]*a[2,3]*a[1,3]*a[1,2]^3+3*a[1,1]^2*a[1,2]^2*a[1,3]^2*a[3,3]*a[2,2]-a[1,1]^2*a[1,2]^2*a[1,3]^2*a[2,3]^2-2*a[1,1]^2*a[2,3]*a[2,2]*a[1
,3]^3*a[1,2]+a[1,1]^2*a[2,2]^2*a[1,3]^4-a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]+2*a[1,1]*a[1,2]^3*a[2,3]*a[1,3]^3-a[1,1]*a[1,2]^2*a[1,3]^4*a[2,2])*z^8+(-4*a[2,2]^2*a[3,3]^2
*a[1,1]^3+4*a[2,3]^2*a[2,2]*a[1,1]^3*a[3,3]+4*a[1,2]^2*a[3,3]^2*a[1,1]^2*a[2,2]-3*a[1,2]^2*a[2,3]^2*a[1,1]^2*a[3,3]-2*a[1,2]*a[2,3]*a[1,3]*a[1,1]^2*a[2,2]*a[3,3]+4*
a[1,3]^2*a[2,2]^2*a[3,3]*a[1,1]^2-3*a[2,3]^2*a[1,3]^2*a[2,2]*a[1,1]^2-2*a[1,2]^2*a[1,3]^2*a[3,3]*a[1,1]*a[2,2]+2*a[1,2]^2*a[2,3]^2*a[1,3]^2*a[1,1]-a[1,2]^4*a[1,3]^2
*a[3,3]+2*a[1,2]^3*a[2,3]*a[1,3]^3-a[1,2]^2*a[1,3]^4*a[2,2])*z^6, [[a[1,1]*z^2, -(5*a[3,3]*a[1,1]*a[1,2]^5*a[1,3]^3*a[2,3]^2+2*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]^3+a[1
,1]^2*a[1,2]^6*a[2,3]*a[3,3]^3+a[3,3]^2*a[1,1]^3*a[1,2]^4*a[2,3]^3-5*a[3,3]^2*a[1,1]*a[1,2]^6*a[1,3]^2*a[2,3]-3*a[3,3]*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]^3+a[2,2]^3*
a[1,1]^2*a[1,3]^6*a[2,3]+a[2,2]^2*a[1,1]^3*a[1,3]^4*a[2,3]^3-a[3,3]^2*a[1,1]^2*a[1,2]^5*a[1,3]*a[2,3]^2+a[3,3]^3*a[1,1]*a[1,2]^7*a[1,3]+a[2,2]^3*a[1,1]*a[1,2]*a[1,3
]^7-2*a[2,2]^3*a[1,1]^4*a[1,2]*a[1,3]*a[3,3]^3+5*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^3+a[2,2]^3*a[3,3]^2*a[1,1]^4*a[1,3]^2*a[2,3]-4*a[2,2]^3*a[3,3]*a[1,1]^2*a[
1,2]*a[1,3]^5-2*a[2,2]^3*a[3,3]*a[1,1]^3*a[1,3]^4*a[2,3]+5*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]+a[2,2]^2*a[3,3]^3*a[1,1]^4*a[1,2]^2*a[2,3]-10*a[2,2]^2*a[3,3]^
2*a[1,1]^2*a[1,2]^3*a[1,3]^3+2*a[2,2]^2*a[3,3]^2*a[1,1]^4*a[1,2]*a[1,3]*a[2,3]^2-10*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]+14*a[2,2]^2*a[3,3]*a[1,1]^2*
a[1,2]^2*a[1,3]^4*a[2,3]-a[2,2]^2*a[3,3]*a[1,1]^4*a[1,3]^2*a[2,3]^3+6*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]^5-a[2,2]^2*a[3,3]*a[1,1]^3*a[1,2]*a[1,3]^3*a[2,3]^2-a[2
,2]^2*a[1,1]^2*a[1,2]*a[1,3]^5*a[2,3]^2-5*a[2,2]^2*a[1,1]*a[1,2]^2*a[1,3]^6*a[2,3]-2*a[2,2]*a[3,3]^3*a[1,1]^3*a[1,2]^4*a[2,3]-4*a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2]^5*a[
1,3]+14*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]-a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]*a[2,3]^2-a[2,2]*a[3,3]^2*a[1,1]^4*a[1,2]^2*a[2,3]^3+6*a[2,2]*a[3,
3]^2*a[1,1]*a[1,2]^5*a[1,3]^3-4*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]^2-16*a[2,2]*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]+4*a[2,2]*a[3,3]*a[1,1]^3*a[1,2]^2
*a[1,3]^2*a[2,3]^3-3*a[2,2]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]^3+5*a[2,2]*a[1,1]*a[1,2]^3*a[1,3]^5*a[2,3]^2+4*a[3,3]*a[1,2]^6*a[1,3]^4*a[2,3]-2*a[2,2]*a[3,3]*a[1,2]^
5*a[1,3]^5+4*a[2,2]*a[1,2]^4*a[1,3]^6*a[2,3]-4*a[1,2]^5*a[1,3]^5*a[2,3]^2-a[3,3]^2*a[1,2]^7*a[1,3]^3-a[2,2]^2*a[1,2]^3*a[1,3]^7)*a[1,3]*a[1,1]*a[1,2]/(-4*a[2,2]^3*a
[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,
1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2
]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a
[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3])*z^6+(-6*a[3,3]*
a[1,1]*a[1,2]^5*a[1,3]^3*a[2,3]^2+4*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]^3-a[1,1]^2*a[1,2]^6*a[2,3]*a[3,3]^3+2*a[3,3]^2*a[1,1]^3*a[1,2]^4*a[2,3]^3+2*a[3,3]^2*a[1,1]*a[1,
2]^6*a[1,3]^2*a[2,3]-7*a[3,3]*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]^3-a[2,2]^3*a[1,1]^2*a[1,3]^6*a[2,3]+2*a[2,2]^2*a[1,1]^3*a[1,3]^4*a[2,3]^3+5*a[3,3]^2*a[1,1]^2*a[1,2]
^5*a[1,3]*a[2,3]^2-6*a[2,2]^3*a[1,1]^4*a[1,2]*a[1,3]*a[3,3]^3+8*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^3+3*a[2,2]^3*a[3,3]^2*a[1,1]^4*a[1,3]^2*a[2,3]-2*a[2,2]^3*a
[3,3]*a[1,1]^2*a[1,2]*a[1,3]^5-2*a[2,2]^3*a[3,3]*a[1,1]^3*a[1,3]^4*a[2,3]+8*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]+3*a[2,2]^2*a[3,3]^3*a[1,1]^4*a[1,2]^2*a[2,3]-\
6*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^3*a[1,3]^3+6*a[2,2]^2*a[3,3]^2*a[1,1]^4*a[1,2]*a[1,3]*a[2,3]^2-12*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]+4*a[2,2]^2
*a[3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]-3*a[2,2]^2*a[3,3]*a[1,1]^4*a[1,3]^2*a[2,3]^3-2*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]^5-8*a[2,2]^2*a[3,3]*a[1,1]^3*a[1,2]*
a[1,3]^3*a[2,3]^2+5*a[2,2]^2*a[1,1]^2*a[1,2]*a[1,3]^5*a[2,3]^2+2*a[2,2]^2*a[1,1]*a[1,2]^2*a[1,3]^6*a[2,3]-2*a[2,2]*a[3,3]^3*a[1,1]^3*a[1,2]^4*a[2,3]-2*a[2,2]*a[3,3]
^3*a[1,1]^2*a[1,2]^5*a[1,3]+4*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]-8*a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]*a[2,3]^2-3*a[2,2]*a[3,3]^2*a[1,1]^4*a[1,2
]^2*a[2,3]^3-2*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^3+8*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]^2+8*a[2,2]*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]+12*a[2,2
]*a[3,3]*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]^3-7*a[2,2]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]^3-6*a[2,2]*a[1,1]*a[1,2]^3*a[1,3]^5*a[2,3]^2-4*a[3,3]*a[1,2]^6*a[1,3]^4*a[2,
3]+2*a[2,2]*a[3,3]*a[1,2]^5*a[1,3]^5-4*a[2,2]*a[1,2]^4*a[1,3]^6*a[2,3]+4*a[1,2]^5*a[1,3]^5*a[2,3]^2+a[3,3]^2*a[1,2]^7*a[1,3]^3+a[2,2]^2*a[1,2]^3*a[1,3]^7)*a[1,2]*a[
1,3]/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3
]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,
3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*
a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,
3])*z^4-(-a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^6+a[2,2]^2*a[1,2]^2*a[1,3]^7*a[2,3]-a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^4-3*a[2,2]*a[1,2]^3*a[1,3]^6*a[2,3]^2+4*a[2,2]*a[3,3]*
a[1,2]^4*a[1,3]^5*a[2,3]+2*a[1,2]^4*a[1,3]^5*a[2,3]^3+a[1,1]^2*a[1,2]^5*a[2,3]^2*a[3,3]^3+a[2,2]^2*a[2,3]^3*a[1,1]^2*a[1,3]^5+4*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^2*a[
2,3]^2+a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]*a[2,3]^3-6*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^3*a[2,3]^3+3*a[2,2]^3*a[3,3]^2*a[1,1]^2*a[1,2]*a[1,3]^4-a[2,2]^3*a[3,3]*a[1,1]*a[1
,2]*a[1,3]^6+a[2,2]^3*a[3,3]*a[1,1]^2*a[1,3]^5*a[2,3]+7*a[2,2]^2*a[3,3]^3*a[1,1]^2*a[1,2]^3*a[1,3]^2+3*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^2*a[1,3]*a[2,3]-4*a[2,2]^2*
a[3,3]^2*a[1,1]^2*a[1,2]^2*a[1,3]^3*a[2,3]+6*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^2*a[2,3]^2+a[2,2]^2*a[3,3]^2*a[1,1]*a[1,2]^3*a[1,3]^4-4*a[2,2]^2*a[3,3]*a[1,1]
*a[1,2]^2*a[1,3]^5*a[2,3]-10*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]*a[1,3]^4*a[2,3]^2-3*a[2,2]^2*a[3,3]*a[1,1]^3*a[1,3]^3*a[2,3]^3+3*a[2,2]^2*a[1,1]*a[1,2]*a[1,3]^6*a[2,3]
^2-2*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]^2-3*a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2]^4*a[1,3]*a[2,3]-2*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^3*a[2,3]-9*a[2,2]*a[3,3]^2*
a[1,1]^2*a[1,2]^3*a[1,3]^2*a[2,3]^2-3*a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]*a[2,3]^3+11*a[2,2]*a[3,3]*a[1,2]^3*a[2,3]^2*a[1,3]^4*a[1,1]+12*a[2,2]*a[3,3]*a[1,2]^2
*a[2,3]^3*a[1,3]^3*a[1,1]^2-4*a[2,2]*a[2,3]^3*a[1,1]*a[1,2]^2*a[1,3]^5-6*a[2,2]^3*a[1,1]^3*a[1,2]*a[1,3]^2*a[3,3]^3+3*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,3]^3*a[2,3]+a[3
,3]^2*a[1,2]^6*a[1,3]^3*a[2,3]-3*a[3,3]*a[1,2]^5*a[1,3]^4*a[2,3]^2)*a[1,2]/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a
[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,
3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3
]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3
+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3])*z^2+a[3,3]*a[1,2]*(-2*a[1,1]^2*a[2,2]^3*a[1,2]*a[1,3]^2*a[3,3]^2+a[1,1]^2*a[2,2]^3*a[2,3]*
a[1,3]^3*a[3,3]+a[1,1]^2*a[2,2]^2*a[1,2]^2*a[1,3]*a[2,3]*a[3,3]^2+2*a[1,1]^2*a[2,2]^2*a[1,2]*a[1,3]^2*a[2,3]^2*a[3,3]-a[1,1]^2*a[2,2]^2*a[1,3]^3*a[2,3]^3-a[1,1]^2*a
[1,2]^2*a[1,3]*a[2,3]^3*a[3,3]*a[2,2]+a[1,1]*a[1,3]^5*a[2,3]*a[2,2]^3+4*a[1,1]*a[2,2]^2*a[1,2]^3*a[1,3]^2*a[3,3]^2-2*a[1,1]*a[2,2]^2*a[1,2]^2*a[1,3]^3*a[2,3]*a[3,3]
-3*a[1,1]*a[2,2]^2*a[1,2]*a[1,3]^4*a[2,3]^2-3*a[1,1]*a[2,2]*a[1,2]^4*a[1,3]*a[2,3]*a[3,3]^2-2*a[1,1]*a[2,2]*a[1,2]^3*a[1,3]^2*a[2,3]^2*a[3,3]+4*a[1,1]*a[2,2]*a[1,2]
^2*a[1,3]^3*a[2,3]^3+a[1,1]*a[1,2]^5*a[2,3]^2*a[3,3]^2-a[1,2]^3*a[1,3]^4*a[3,3]*a[2,2]^2-a[2,2]*a[1,2]^5*a[1,3]^2*a[3,3]^2+2*a[2,2]*a[1,2]^4*a[1,3]^3*a[2,3]*a[3,3]+
a[2,2]*a[1,2]^3*a[1,3]^4*a[2,3]^2+a[1,2]^5*a[1,3]^2*a[2,3]^2*a[3,3]-2*a[1,2]^4*a[1,3]^3*a[2,3]^3)/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a
[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]
*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1
]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1
,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3]), (5*a[3,3]*a[1,1]*a[1,2]^5*a[1,3]^3*a[2,3]^2+2*a[1,1]*a[1,2]^4*a[1,
3]^4*a[2,3]^3+a[1,1]^2*a[1,2]^6*a[2,3]*a[3,3]^3+a[3,3]^2*a[1,1]^3*a[1,2]^4*a[2,3]^3-5*a[3,3]^2*a[1,1]*a[1,2]^6*a[1,3]^2*a[2,3]-3*a[3,3]*a[1,1]^2*a[1,2]^4*a[1,3]^2*a
[2,3]^3+a[2,2]^3*a[1,1]^2*a[1,3]^6*a[2,3]+a[2,2]^2*a[1,1]^3*a[1,3]^4*a[2,3]^3-a[3,3]^2*a[1,1]^2*a[1,2]^5*a[1,3]*a[2,3]^2+a[3,3]^3*a[1,1]*a[1,2]^7*a[1,3]+a[2,2]^3*a[
1,1]*a[1,2]*a[1,3]^7-2*a[2,2]^3*a[1,1]^4*a[1,2]*a[1,3]*a[3,3]^3+5*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^3+a[2,2]^3*a[3,3]^2*a[1,1]^4*a[1,3]^2*a[2,3]-4*a[2,2]^3*a
[3,3]*a[1,1]^2*a[1,2]*a[1,3]^5-2*a[2,2]^3*a[3,3]*a[1,1]^3*a[1,3]^4*a[2,3]+5*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]+a[2,2]^2*a[3,3]^3*a[1,1]^4*a[1,2]^2*a[2,3]-10
*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^3*a[1,3]^3+2*a[2,2]^2*a[3,3]^2*a[1,1]^4*a[1,2]*a[1,3]*a[2,3]^2-10*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]+14*a[2,2]^2
*a[3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]-a[2,2]^2*a[3,3]*a[1,1]^4*a[1,3]^2*a[2,3]^3+6*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]^5-a[2,2]^2*a[3,3]*a[1,1]^3*a[1,2]*a[1,
3]^3*a[2,3]^2-a[2,2]^2*a[1,1]^2*a[1,2]*a[1,3]^5*a[2,3]^2-5*a[2,2]^2*a[1,1]*a[1,2]^2*a[1,3]^6*a[2,3]-2*a[2,2]*a[3,3]^3*a[1,1]^3*a[1,2]^4*a[2,3]-4*a[2,2]*a[3,3]^3*a[1
,1]^2*a[1,2]^5*a[1,3]+14*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]-a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]*a[2,3]^2-a[2,2]*a[3,3]^2*a[1,1]^4*a[1,2]^2*a[2,3
]^3+6*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^3-4*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]^2-16*a[2,2]*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]+4*a[2,2]*a[3,3]*
a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]^3-3*a[2,2]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]^3+5*a[2,2]*a[1,1]*a[1,2]^3*a[1,3]^5*a[2,3]^2+4*a[3,3]*a[1,2]^6*a[1,3]^4*a[2,3]-2*a[2,
2]*a[3,3]*a[1,2]^5*a[1,3]^5+4*a[2,2]*a[1,2]^4*a[1,3]^6*a[2,3]-4*a[1,2]^5*a[1,3]^5*a[2,3]^2-a[3,3]^2*a[1,2]^7*a[1,3]^3-a[2,2]^2*a[1,2]^3*a[1,3]^7)*a[1,3]*a[1,1]*a[1,
2]/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^
2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]
^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[
1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3]
)*z^6-(-6*a[3,3]*a[1,1]*a[1,2]^5*a[1,3]^3*a[2,3]^2+4*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]^3-a[1,1]^2*a[1,2]^6*a[2,3]*a[3,3]^3+2*a[3,3]^2*a[1,1]^3*a[1,2]^4*a[2,3]^3+2*a[3
,3]^2*a[1,1]*a[1,2]^6*a[1,3]^2*a[2,3]-7*a[3,3]*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]^3-a[2,2]^3*a[1,1]^2*a[1,3]^6*a[2,3]+2*a[2,2]^2*a[1,1]^3*a[1,3]^4*a[2,3]^3+5*a[3,3]^
2*a[1,1]^2*a[1,2]^5*a[1,3]*a[2,3]^2-6*a[2,2]^3*a[1,1]^4*a[1,2]*a[1,3]*a[3,3]^3+8*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^3+3*a[2,2]^3*a[3,3]^2*a[1,1]^4*a[1,3]^2*a[
2,3]-2*a[2,2]^3*a[3,3]*a[1,1]^2*a[1,2]*a[1,3]^5-2*a[2,2]^3*a[3,3]*a[1,1]^3*a[1,3]^4*a[2,3]+8*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]+3*a[2,2]^2*a[3,3]^3*a[1,1]^4
*a[1,2]^2*a[2,3]-6*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^3*a[1,3]^3+6*a[2,2]^2*a[3,3]^2*a[1,1]^4*a[1,2]*a[1,3]*a[2,3]^2-12*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]^2*
a[2,3]+4*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]-3*a[2,2]^2*a[3,3]*a[1,1]^4*a[1,3]^2*a[2,3]^3-2*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]^5-8*a[2,2]^2*a[3,3]
*a[1,1]^3*a[1,2]*a[1,3]^3*a[2,3]^2+5*a[2,2]^2*a[1,1]^2*a[1,2]*a[1,3]^5*a[2,3]^2+2*a[2,2]^2*a[1,1]*a[1,2]^2*a[1,3]^6*a[2,3]-2*a[2,2]*a[3,3]^3*a[1,1]^3*a[1,2]^4*a[2,3
]-2*a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2]^5*a[1,3]+4*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]-8*a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]*a[2,3]^2-3*a[2,2]*a[3,3]
^2*a[1,1]^4*a[1,2]^2*a[2,3]^3-2*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^3+8*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]^2+8*a[2,2]*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^
4*a[2,3]+12*a[2,2]*a[3,3]*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]^3-7*a[2,2]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]^3-6*a[2,2]*a[1,1]*a[1,2]^3*a[1,3]^5*a[2,3]^2-4*a[3,3]*a[1,2
]^6*a[1,3]^4*a[2,3]+2*a[2,2]*a[3,3]*a[1,2]^5*a[1,3]^5-4*a[2,2]*a[1,2]^4*a[1,3]^6*a[2,3]+4*a[1,2]^5*a[1,3]^5*a[2,3]^2+a[3,3]^2*a[1,2]^7*a[1,3]^3+a[2,2]^2*a[1,2]^3*a[
1,3]^7)*a[1,2]*a[1,3]/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,
1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2
]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2
*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3
]^3*a[2,3]^3*a[3,3])*z^4+(-a[2,2]^2*a[3,3]*a[1,2]^4*a[1,3]^5+a[2,2]^2*a[1,2]^3*a[1,3]^6*a[2,3]-a[2,2]*a[3,3]^2*a[1,2]^6*a[1,3]^3-3*a[2,2]*a[1,2]^4*a[1,3]^5*a[2,3]^2
+4*a[2,2]*a[3,3]*a[1,2]^5*a[1,3]^4*a[2,3]+3*a[3,3]^2*a[1,1]*a[1,2]^6*a[1,3]*a[2,3]^2-4*a[3,3]*a[2,3]^3*a[1,1]*a[1,2]^5*a[1,3]^2-6*a[2,2]^3*a[1,1]^3*a[1,2]^2*a[1,3]*
a[3,3]^3+3*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^2*a[2,3]+7*a[2,2]^3*a[3,3]^2*a[1,1]^2*a[1,2]^2*a[1,3]^3-2*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^5-3*a[2,2]^3*a[
3,3]*a[1,1]^2*a[1,2]*a[1,3]^4*a[2,3]+3*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[2,3]+3*a[2,2]^2*a[3,3]^3*a[1,1]^2*a[1,2]^4*a[1,3]+a[2,2]^2*a[3,3]^2*a[1,1]*a[1,2]^4*a[1
,3]^3-4*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^3*a[1,3]^2*a[2,3]+6*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]*a[2,3]^2-9*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^3*a[2,3
]^2-2*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]^4*a[2,3]-3*a[2,2]^2*a[3,3]*a[1,1]^3*a[1,2]*a[1,3]^2*a[2,3]^3+4*a[2,2]^2*a[1,1]*a[1,2]^2*a[1,3]^5*a[2,3]^2+a[2,2]^2*a[1,
1]^2*a[1,2]*a[1,3]^4*a[2,3]^3-a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^6*a[1,3]+a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2]^5*a[2,3]-4*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^2*a[2,3]-3*a[
2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[2,3]^3-10*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]*a[2,3]^2+12*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^2*a[2,3]^3+11*a[2,2]*a[3,3]*
a[1,1]*a[1,2]^4*a[1,3]^3*a[2,3]^2-6*a[2,2]*a[1,1]*a[1,2]^3*a[1,3]^4*a[2,3]^3+2*a[1,2]^5*a[1,3]^4*a[2,3]^3+a[3,3]^2*a[2,3]^3*a[1,1]^2*a[1,2]^5+a[2,2]^3*a[1,1]^2*a[1,
3]^5*a[2,3]^2+a[3,3]^2*a[1,2]^7*a[1,3]^2*a[2,3]-3*a[3,3]*a[1,2]^6*a[1,3]^3*a[2,3]^2)*a[1,3]/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*
a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2
]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,
2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*
a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3])*z^2-a[2,2]*a[1,3]*(-2*a[1,1]^2*a[2,2]^2*a[1,2]^2*a[1,3]*a[3,3]^3+a[1,1]^2
*a[2,2]^2*a[1,2]*a[1,3]^2*a[2,3]*a[3,3]^2+a[1,1]^2*a[2,2]*a[1,2]^3*a[2,3]*a[3,3]^3+2*a[1,1]^2*a[2,2]*a[1,2]^2*a[1,3]*a[2,3]^2*a[3,3]^2-a[1,1]^2*a[2,2]*a[1,2]*a[1,3]
^2*a[2,3]^3*a[3,3]-a[1,1]^2*a[1,2]^3*a[2,3]^3*a[3,3]^2+4*a[1,1]*a[2,2]^2*a[1,2]^2*a[1,3]^3*a[3,3]^2-3*a[1,1]*a[2,2]^2*a[1,2]*a[1,3]^4*a[2,3]*a[3,3]+a[1,1]*a[2,2]^2*
a[1,3]^5*a[2,3]^2-2*a[1,1]*a[2,2]*a[1,2]^3*a[1,3]^2*a[2,3]*a[3,3]^2-2*a[1,1]*a[2,2]*a[1,2]^2*a[1,3]^3*a[2,3]^2*a[3,3]+a[1,1]*a[1,2]^5*a[2,3]*a[3,3]^3-3*a[1,1]*a[1,2
]^4*a[1,3]*a[2,3]^2*a[3,3]^2+4*a[1,1]*a[1,2]^3*a[1,3]^2*a[2,3]^3*a[3,3]-a[1,2]^2*a[1,3]^5*a[3,3]*a[2,2]^2-a[2,2]*a[1,2]^4*a[1,3]^3*a[3,3]^2+2*a[2,2]*a[1,2]^3*a[1,3]
^4*a[2,3]*a[3,3]+a[2,2]*a[1,2]^2*a[1,3]^5*a[2,3]^2+a[1,2]^4*a[1,3]^3*a[2,3]^2*a[3,3]-2*a[1,2]^3*a[1,3]^4*a[2,3]^3)/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*
a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2
]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,
2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[
2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3])], [-(5*a[3,3]*a[1,1]*a[1,2]^5*a[1,3]^3*a[2,3]^2+2*
a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]^3+a[1,1]^2*a[1,2]^6*a[2,3]*a[3,3]^3+a[3,3]^2*a[1,1]^3*a[1,2]^4*a[2,3]^3-5*a[3,3]^2*a[1,1]*a[1,2]^6*a[1,3]^2*a[2,3]-3*a[3,3]*a[1,1]^2
*a[1,2]^4*a[1,3]^2*a[2,3]^3+a[2,2]^3*a[1,1]^2*a[1,3]^6*a[2,3]+a[2,2]^2*a[1,1]^3*a[1,3]^4*a[2,3]^3-a[3,3]^2*a[1,1]^2*a[1,2]^5*a[1,3]*a[2,3]^2+a[3,3]^3*a[1,1]*a[1,2]^
7*a[1,3]+a[2,2]^3*a[1,1]*a[1,2]*a[1,3]^7-2*a[2,2]^3*a[1,1]^4*a[1,2]*a[1,3]*a[3,3]^3+5*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^3+a[2,2]^3*a[3,3]^2*a[1,1]^4*a[1,3]^2
*a[2,3]-4*a[2,2]^3*a[3,3]*a[1,1]^2*a[1,2]*a[1,3]^5-2*a[2,2]^3*a[3,3]*a[1,1]^3*a[1,3]^4*a[2,3]+5*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]+a[2,2]^2*a[3,3]^3*a[1,1]^
4*a[1,2]^2*a[2,3]-10*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^3*a[1,3]^3+2*a[2,2]^2*a[3,3]^2*a[1,1]^4*a[1,2]*a[1,3]*a[2,3]^2-10*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]^
2*a[2,3]+14*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]-a[2,2]^2*a[3,3]*a[1,1]^4*a[1,3]^2*a[2,3]^3+6*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]^5-a[2,2]^2*a[3,3]*
a[1,1]^3*a[1,2]*a[1,3]^3*a[2,3]^2-a[2,2]^2*a[1,1]^2*a[1,2]*a[1,3]^5*a[2,3]^2-5*a[2,2]^2*a[1,1]*a[1,2]^2*a[1,3]^6*a[2,3]-2*a[2,2]*a[3,3]^3*a[1,1]^3*a[1,2]^4*a[2,3]-4
*a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2]^5*a[1,3]+14*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]-a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]*a[2,3]^2-a[2,2]*a[3,3]^2*a[1
,1]^4*a[1,2]^2*a[2,3]^3+6*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^3-4*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]^2-16*a[2,2]*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^4*a[2
,3]+4*a[2,2]*a[3,3]*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]^3-3*a[2,2]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]^3+5*a[2,2]*a[1,1]*a[1,2]^3*a[1,3]^5*a[2,3]^2+4*a[3,3]*a[1,2]^6*a[
1,3]^4*a[2,3]-2*a[2,2]*a[3,3]*a[1,2]^5*a[1,3]^5+4*a[2,2]*a[1,2]^4*a[1,3]^6*a[2,3]-4*a[1,2]^5*a[1,3]^5*a[2,3]^2-a[3,3]^2*a[1,2]^7*a[1,3]^3-a[2,2]^2*a[1,2]^3*a[1,3]^7
)*a[1,3]*a[1,1]*a[1,2]/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1
,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,
2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+
2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,
3]^3*a[2,3]^3*a[3,3])*z^6+(-6*a[3,3]*a[1,1]*a[1,2]^5*a[1,3]^3*a[2,3]^2+4*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]^3-a[1,1]^2*a[1,2]^6*a[2,3]*a[3,3]^3+2*a[3,3]^2*a[1,1]^3*a[1
,2]^4*a[2,3]^3+2*a[3,3]^2*a[1,1]*a[1,2]^6*a[1,3]^2*a[2,3]-7*a[3,3]*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]^3-a[2,2]^3*a[1,1]^2*a[1,3]^6*a[2,3]+2*a[2,2]^2*a[1,1]^3*a[1,3]^
4*a[2,3]^3+5*a[3,3]^2*a[1,1]^2*a[1,2]^5*a[1,3]*a[2,3]^2-6*a[2,2]^3*a[1,1]^4*a[1,2]*a[1,3]*a[3,3]^3+8*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^3+3*a[2,2]^3*a[3,3]^2*
a[1,1]^4*a[1,3]^2*a[2,3]-2*a[2,2]^3*a[3,3]*a[1,1]^2*a[1,2]*a[1,3]^5-2*a[2,2]^3*a[3,3]*a[1,1]^3*a[1,3]^4*a[2,3]+8*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]+3*a[2,2]
^2*a[3,3]^3*a[1,1]^4*a[1,2]^2*a[2,3]-6*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^3*a[1,3]^3+6*a[2,2]^2*a[3,3]^2*a[1,1]^4*a[1,2]*a[1,3]*a[2,3]^2-12*a[2,2]^2*a[3,3]^2*a[1,1]^
3*a[1,2]^2*a[1,3]^2*a[2,3]+4*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]-3*a[2,2]^2*a[3,3]*a[1,1]^4*a[1,3]^2*a[2,3]^3-2*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]
^5-8*a[2,2]^2*a[3,3]*a[1,1]^3*a[1,2]*a[1,3]^3*a[2,3]^2+5*a[2,2]^2*a[1,1]^2*a[1,2]*a[1,3]^5*a[2,3]^2+2*a[2,2]^2*a[1,1]*a[1,2]^2*a[1,3]^6*a[2,3]-2*a[2,2]*a[3,3]^3*a[1
,1]^3*a[1,2]^4*a[2,3]-2*a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2]^5*a[1,3]+4*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]-8*a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]*a[2,
3]^2-3*a[2,2]*a[3,3]^2*a[1,1]^4*a[1,2]^2*a[2,3]^3-2*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^3+8*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]^2+8*a[2,2]*a[3,3]*a[1
,1]*a[1,2]^4*a[1,3]^4*a[2,3]+12*a[2,2]*a[3,3]*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]^3-7*a[2,2]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]^3-6*a[2,2]*a[1,1]*a[1,2]^3*a[1,3]^5*a[2
,3]^2-4*a[3,3]*a[1,2]^6*a[1,3]^4*a[2,3]+2*a[2,2]*a[3,3]*a[1,2]^5*a[1,3]^5-4*a[2,2]*a[1,2]^4*a[1,3]^6*a[2,3]+4*a[1,2]^5*a[1,3]^5*a[2,3]^2+a[3,3]^2*a[1,2]^7*a[1,3]^3+
a[2,2]^2*a[1,2]^3*a[1,3]^7)*a[1,2]*a[1,3]/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[
1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a
[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4
*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3
]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3])*z^4-(-a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^6+a[2,2]^2*a[1,2]^2*a[1,3]^7*a[2,3]-a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^4-3*a[2,2]*a[1,2]
^3*a[1,3]^6*a[2,3]^2+4*a[2,2]*a[3,3]*a[1,2]^4*a[1,3]^5*a[2,3]+2*a[1,2]^4*a[1,3]^5*a[2,3]^3+a[1,1]^2*a[1,2]^5*a[2,3]^2*a[3,3]^3+a[2,2]^2*a[2,3]^3*a[1,1]^2*a[1,3]^5+4
*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^2*a[2,3]^2+a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]*a[2,3]^3-6*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^3*a[2,3]^3+3*a[2,2]^3*a[3,3]^2*a[1,1]^2*a[1,2
]*a[1,3]^4-a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^6+a[2,2]^3*a[3,3]*a[1,1]^2*a[1,3]^5*a[2,3]+7*a[2,2]^2*a[3,3]^3*a[1,1]^2*a[1,2]^3*a[1,3]^2+3*a[2,2]^2*a[3,3]^3*a[1,1]
^3*a[1,2]^2*a[1,3]*a[2,3]-4*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^2*a[1,3]^3*a[2,3]+6*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^2*a[2,3]^2+a[2,2]^2*a[3,3]^2*a[1,1]*a[1,2
]^3*a[1,3]^4-4*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^5*a[2,3]-10*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]*a[1,3]^4*a[2,3]^2-3*a[2,2]^2*a[3,3]*a[1,1]^3*a[1,3]^3*a[2,3]^3+3*a
[2,2]^2*a[1,1]*a[1,2]*a[1,3]^6*a[2,3]^2-2*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]^2-3*a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2]^4*a[1,3]*a[2,3]-2*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]
^4*a[1,3]^3*a[2,3]-9*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^3*a[1,3]^2*a[2,3]^2-3*a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]*a[2,3]^3+11*a[2,2]*a[3,3]*a[1,2]^3*a[2,3]^2*a[1,
3]^4*a[1,1]+12*a[2,2]*a[3,3]*a[1,2]^2*a[2,3]^3*a[1,3]^3*a[1,1]^2-4*a[2,2]*a[2,3]^3*a[1,1]*a[1,2]^2*a[1,3]^5-6*a[2,2]^3*a[1,1]^3*a[1,2]*a[1,3]^2*a[3,3]^3+3*a[2,2]^3*
a[3,3]^2*a[1,1]^3*a[1,3]^3*a[2,3]+a[3,3]^2*a[1,2]^6*a[1,3]^3*a[2,3]-3*a[3,3]*a[1,2]^5*a[1,3]^4*a[2,3]^2)*a[1,2]/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2
,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2
*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*
a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3
]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3])*z^2+a[3,3]*a[1,2]*(-2*a[1,1]^2*a[2,2]^3*a[1,2]*a[1,3]
^2*a[3,3]^2+a[1,1]^2*a[2,2]^3*a[2,3]*a[1,3]^3*a[3,3]+a[1,1]^2*a[2,2]^2*a[1,2]^2*a[1,3]*a[2,3]*a[3,3]^2+2*a[1,1]^2*a[2,2]^2*a[1,2]*a[1,3]^2*a[2,3]^2*a[3,3]-a[1,1]^2*
a[2,2]^2*a[1,3]^3*a[2,3]^3-a[1,1]^2*a[1,2]^2*a[1,3]*a[2,3]^3*a[3,3]*a[2,2]+a[1,1]*a[1,3]^5*a[2,3]*a[2,2]^3+4*a[1,1]*a[2,2]^2*a[1,2]^3*a[1,3]^2*a[3,3]^2-2*a[1,1]*a[2
,2]^2*a[1,2]^2*a[1,3]^3*a[2,3]*a[3,3]-3*a[1,1]*a[2,2]^2*a[1,2]*a[1,3]^4*a[2,3]^2-3*a[1,1]*a[2,2]*a[1,2]^4*a[1,3]*a[2,3]*a[3,3]^2-2*a[1,1]*a[2,2]*a[1,2]^3*a[1,3]^2*a
[2,3]^2*a[3,3]+4*a[1,1]*a[2,2]*a[1,2]^2*a[1,3]^3*a[2,3]^3+a[1,1]*a[1,2]^5*a[2,3]^2*a[3,3]^2-a[1,2]^3*a[1,3]^4*a[3,3]*a[2,2]^2-a[2,2]*a[1,2]^5*a[1,3]^2*a[3,3]^2+2*a[
2,2]*a[1,2]^4*a[1,3]^3*a[2,3]*a[3,3]+a[2,2]*a[1,2]^3*a[1,3]^4*a[2,3]^2+a[1,2]^5*a[1,3]^2*a[2,3]^2*a[3,3]-2*a[1,2]^4*a[1,3]^3*a[2,3]^3)/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*
a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1
,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,
2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*
a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3]), -(2*a[2,3]^5*a[1,1]*a[1,2]^5*
a[1,3]^5+a[3,3]^3*a[1,1]^3*a[1,2]^6*a[2,3]^4-a[3,3]^2*a[1,2]^8*a[1,3]^4*a[2,3]^2+4*a[3,3]*a[1,2]^7*a[1,3]^5*a[2,3]^3+7*a[2,2]*a[1,1]*a[1,2]^4*a[1,3]^6*a[2,3]^4+4*a[
2,2]*a[1,2]^5*a[1,3]^7*a[2,3]^3-2*a[3,3]*a[1,1]^2*a[1,2]^5*a[1,3]^3*a[2,3]^5+3*a[3,3]*a[1,1]*a[1,2]^6*a[1,3]^4*a[2,3]^4-4*a[2,2]*a[1,1]^2*a[1,2]^3*a[1,3]^5*a[2,3]^5
-2*a[3,3]^2*a[2,3]^3*a[1,1]*a[1,2]^7*a[1,3]^3+2*a[2,2]^4*a[1,1]^4*a[1,2]^2*a[1,3]^2*a[3,3]^4-5*a[2,2]^4*a[3,3]^3*a[1,1]^3*a[1,2]^2*a[1,3]^4-a[2,2]^4*a[3,3]^2*a[1,1]
^4*a[1,3]^4*a[2,3]^2-5*a[2,2]^3*a[3,3]^4*a[1,1]^3*a[1,2]^4*a[1,3]^2-2*a[2,2]^3*a[3,3]^4*a[1,1]^4*a[1,2]^3*a[1,3]*a[2,3]+4*a[2,2]^4*a[3,3]^2*a[1,1]^2*a[1,2]^2*a[1,3]
^6+2*a[2,2]^4*a[3,3]*a[1,1]^3*a[1,3]^6*a[2,3]^2+a[2,2]^3*a[3,3]*a[1,2]^4*a[1,3]^8+10*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]^4*a[2,3]^2-6*a[2,2]^3*a[3,3]^2*a[1,1
]*a[1,2]^4*a[1,3]^6+2*a[2,2]^3*a[3,3]^2*a[1,1]^4*a[1,2]*a[1,3]^3*a[2,3]^3+10*a[2,2]^3*a[3,3]^3*a[1,1]^2*a[1,2]^4*a[1,3]^4+10*a[2,2]^3*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1
,3]^3*a[2,3]-4*a[2,2]^3*a[3,3]^3*a[1,1]^4*a[1,2]^2*a[1,3]^2*a[2,3]^2-a[2,2]^4*a[1,1]^2*a[1,3]^8*a[2,3]^2-8*a[2,2]^3*a[3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-6*a[2
,2]^3*a[3,3]*a[2,3]^3*a[1,1]^3*a[1,2]*a[1,3]^5+a[2,2]^3*a[3,3]*a[1,1]^4*a[1,3]^4*a[2,3]^4-a[2,2]*a[3,3]^4*a[1,1]*a[1,2]^8*a[1,3]^2-2*a[2,2]*a[3,3]^4*a[1,1]^2*a[1,2]
^7*a[1,3]*a[2,3]+4*a[2,2]^2*a[3,3]^4*a[1,1]^2*a[1,2]^6*a[1,3]^2+a[2,2]^2*a[3,3]^4*a[1,1]^4*a[1,2]^4*a[2,3]^2+4*a[2,2]^2*a[3,3]^4*a[1,1]^3*a[1,2]^5*a[1,3]*a[2,3]-a[2
,2]^3*a[1,1]^3*a[1,3]^6*a[2,3]^4+2*a[2,2]^2*a[3,3]^2*a[1,2]^6*a[1,3]^6-a[2,2]^2*a[1,2]^4*a[1,3]^8*a[2,3]^2+a[2,2]*a[3,3]^3*a[1,2]^8*a[1,3]^4+4*a[2,2]^3*a[3,3]*a[1,1
]*a[1,2]^3*a[1,3]^7*a[2,3]+2*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^8*a[2,3]^2+4*a[2,2]^3*a[1,1]^2*a[1,2]*a[2,3]^3*a[1,3]^7-4*a[1,2]^6*a[1,3]^6*a[2,3]^4+2*a[2,2]^2*a[3,3]^
3*a[1,1]^3*a[1,2]^4*a[1,3]^2*a[2,3]^2-16*a[2,2]^2*a[3,3]^3*a[1,1]^2*a[1,2]^5*a[1,3]^3*a[2,3]-6*a[2,2]^2*a[3,3]^3*a[1,1]*a[1,2]^6*a[1,3]^4-a[2,2]^4*a[3,3]*a[1,1]*a[1
,2]^2*a[1,3]^8+a[1,1]^2*a[1,2]^8*a[2,3]^2*a[3,3]^4+2*a[2,2]^2*a[3,3]^3*a[1,1]^4*a[1,2]^3*a[1,3]*a[2,3]^3+2*a[2,2]^2*a[3,3]^2*a[1,1]^4*a[1,2]^2*a[1,3]^2*a[2,3]^4-8*a
[2,2]^2*a[1,1]*a[1,2]^3*a[1,3]^7*a[2,3]^3-6*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^4*a[2,3]^2+16*a[2,2]^2*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^5*a[2,3]-4*a[2,2]^2*a[
3,3]*a[1,2]^5*a[1,3]^7*a[2,3]-14*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]^3*a[2,3]^3+4*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^6*a[2,3]^2-2*a[2,2]^2*a[1,1]^2*a[1,2
]^2*a[1,3]^6*a[2,3]^4+20*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^5*a[2,3]^3+2*a[2,2]^2*a[1,1]^3*a[1,2]*a[1,3]^5*a[2,3]^5-2*a[2,2]^2*a[3,3]*a[1,1]^4*a[1,2]*a[1,3]^3
*a[2,3]^5-12*a[2,2]^3*a[3,3]^2*a[1,1]^2*a[1,2]^3*a[1,3]^5*a[2,3]-2*a[2,2]*a[1,1]^3*a[1,2]^6*a[2,3]^2*a[3,3]^4+2*a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2]^6*a[1,3]^2*a[2,3]^2-
a[2,2]*a[3,3]^3*a[1,1]^4*a[1,2]^4*a[2,3]^4+6*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^7*a[1,3]^3*a[2,3]-4*a[2,2]*a[3,3]^2*a[1,2]^7*a[1,3]^5*a[2,3]-2*a[3,3]^3*a[2,3]^3*a[1,1]^2
*a[1,2]^7*a[1,3]-2*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^6*a[1,3]^4*a[2,3]^2-18*a[2,2]*a[3,3]*a[1,1]*a[1,2]^5*a[1,3]^5*a[2,3]^3-2*a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^4*a[1,3]^2
*a[2,3]^4+14*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^5*a[1,3]^3*a[2,3]^3+4*a[2,2]*a[3,3]*a[1,1]^3*a[1,2]^3*a[1,3]^3*a[2,3]^5-4*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^4*a[1,3]^4*a[2,
3]^4+2*a[2,2]*a[3,3]*a[2,3]^2*a[1,2]^6*a[1,3]^6)*a[1,1]/(a[1,2]^2*a[1,3]^6*a[2,3]^4*a[2,2]^2+a[1,2]^2*a[1,3]^6*a[3,3]^2*a[2,2]^4+a[1,1]*a[1,3]^6*a[2,3]^4*a[2,2]^3-a
[1,2]^6*a[1,3]^2*a[3,3]^4*a[2,2]^2-2*a[1,2]^3*a[1,3]^5*a[2,3]^5*a[2,2]-3*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^2-4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]*a[2,3]^
3*a[2,2]^3-2*a[1,2]^2*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^3+a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^2+3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^3+4*a[
1,2]^3*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^2-a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]+a[1,1]*a[1,2]^6*a[3,3]^4*a[2,3]^2*a[2,2]+4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^
3*a[2,3]^3*a[2,2]+4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^4-4*a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]-2*a[1,2]^3*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^3+2*a[1,
2]^5*a[1,3]^3*a[3,3]*a[2,3]^5+2*a[1,2]^5*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^2-a[1,2]^6*a[1,3]^2*a[3,3]^2*a[2,3]^4-a[1,1]*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^4+4*a[1,1]*a[1
,2]^4*a[1,3]^2*a[3,3]^4*a[2,2]^3-4*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^3*a[2,2]^4+2*a[1,2]^6*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]-a[1,1]*a[1,2]^6*a[3,3]^3*a[2,3]^4-4*a[1,1
]*a[1,2]^5*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^2)*z^6+(4*a[2,3]^5*a[1,1]*a[1,2]^5*a[1,3]^5+a[3,3]^3*a[1,1]*a[1,2]^8*a[1,3]^2*a[2,3]^2+3*a[3,3]^3*a[1,1]^3*a[1,2]^6*a[2,3]^
4+a[3,3]^2*a[1,2]^8*a[1,3]^4*a[2,3]^2-4*a[3,3]*a[1,2]^7*a[1,3]^5*a[2,3]^3-10*a[2,2]*a[1,1]*a[1,2]^4*a[1,3]^6*a[2,3]^4-4*a[2,2]*a[1,2]^5*a[1,3]^7*a[2,3]^3-6*a[3,3]*a
[1,1]^2*a[1,2]^5*a[1,3]^3*a[2,3]^5-2*a[3,3]*a[1,1]*a[1,2]^6*a[1,3]^4*a[2,3]^4-8*a[2,2]*a[1,1]^2*a[1,2]^3*a[1,3]^5*a[2,3]^5+a[3,3]^2*a[1,1]^2*a[1,2]^6*a[1,3]^2*a[2,3
]^4-2*a[3,3]^2*a[2,3]^3*a[1,1]*a[1,2]^7*a[1,3]^3+6*a[2,2]^4*a[1,1]^4*a[1,2]^2*a[1,3]^2*a[3,3]^4+2*a[2,2]^4*a[3,3]^3*a[1,1]^4*a[1,2]*a[1,3]^3*a[2,3]-8*a[2,2]^4*a[3,3
]^3*a[1,1]^3*a[1,2]^2*a[1,3]^4-4*a[2,2]^4*a[3,3]^2*a[1,1]^4*a[1,3]^4*a[2,3]^2+2*a[2,2]^4*a[3,3]*a[1,1]^2*a[1,2]*a[1,3]^7*a[2,3]-8*a[2,2]^3*a[3,3]^4*a[1,1]^3*a[1,2]^
4*a[1,3]^2-8*a[2,2]^3*a[3,3]^4*a[1,1]^4*a[1,2]^3*a[1,3]*a[2,3]-4*a[2,2]^4*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^5*a[2,3]+2*a[2,2]^4*a[3,3]^2*a[1,1]^2*a[1,2]^2*a[1,3]^6+4*
a[2,2]^4*a[3,3]*a[1,1]^3*a[1,3]^6*a[2,3]^2-a[2,2]^3*a[3,3]*a[1,2]^4*a[1,3]^8+24*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]^4*a[2,3]^2+2*a[2,2]^3*a[3,3]^2*a[1,1]*a[1
,2]^4*a[1,3]^6+4*a[2,2]^3*a[3,3]^2*a[1,1]^4*a[1,2]*a[1,3]^3*a[2,3]^3+6*a[2,2]^3*a[3,3]^3*a[1,1]^2*a[1,2]^4*a[1,3]^4+12*a[2,2]^3*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]^3*
a[2,3]-12*a[2,2]^3*a[3,3]^3*a[1,1]^4*a[1,2]^2*a[1,3]^2*a[2,3]^2-11*a[2,2]^3*a[3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-4*a[2,2]^3*a[3,3]*a[2,3]^3*a[1,1]^3*a[1,2]*a[
1,3]^5+4*a[2,2]^3*a[3,3]*a[1,1]^4*a[1,3]^4*a[2,3]^4+2*a[2,2]^2*a[3,3]^4*a[1,1]^2*a[1,2]^6*a[1,3]^2+4*a[2,2]^2*a[3,3]^4*a[1,1]^4*a[1,2]^4*a[2,3]^2+8*a[2,2]^2*a[3,3]^
4*a[1,1]^3*a[1,2]^5*a[1,3]*a[2,3]-3*a[2,2]^3*a[1,1]^3*a[1,3]^6*a[2,3]^4-2*a[2,2]^2*a[3,3]^2*a[1,2]^6*a[1,3]^6+a[2,2]^2*a[1,2]^4*a[1,3]^8*a[2,3]^2-a[2,2]*a[3,3]^3*a[
1,2]^8*a[1,3]^4-2*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]^7*a[2,3]-a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^8*a[2,3]^2-2*a[2,2]^3*a[1,1]^2*a[1,2]*a[2,3]^3*a[1,3]^7+4*a[1,2]^6
*a[1,3]^6*a[2,3]^4+8*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^4*a[1,3]^2*a[2,3]^2-8*a[2,2]^2*a[3,3]^3*a[1,1]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]^2*a[3,3]^3*a[1,1]*a[1,2]^6
*a[1,3]^4+8*a[2,2]^2*a[3,3]^3*a[1,1]^4*a[1,2]^3*a[1,3]*a[2,3]^3+6*a[2,2]^2*a[3,3]^2*a[1,1]^4*a[1,2]^2*a[1,3]^2*a[2,3]^4+6*a[2,2]^2*a[1,1]*a[1,2]^3*a[1,3]^7*a[2,3]^3
-14*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^4*a[2,3]^2-8*a[2,2]^2*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^5*a[2,3]+4*a[2,2]^2*a[3,3]*a[1,2]^5*a[1,3]^7*a[2,3]-24*a[2,2]^2
*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]^3*a[2,3]^3+3*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^6*a[2,3]^2+9*a[2,2]^2*a[1,1]^2*a[1,2]^2*a[1,3]^6*a[2,3]^4-11*a[2,2]^2*a[3,3]*
a[1,1]^3*a[1,2]^2*a[1,3]^4*a[2,3]^4+8*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^5*a[2,3]^3+4*a[2,2]^2*a[1,1]^3*a[1,2]*a[1,3]^5*a[2,3]^5-6*a[2,2]^2*a[3,3]*a[1,1]^4*a[
1,2]*a[1,3]^3*a[2,3]^5-4*a[2,2]*a[1,1]^3*a[1,2]^6*a[2,3]^2*a[3,3]^4-3*a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2]^6*a[1,3]^2*a[2,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]^4*a[1,2]^4*a[2,3]
^4-2*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^7*a[1,3]^3*a[2,3]-4*a[2,2]*a[3,3]^3*a[1,1]^3*a[1,2]^5*a[1,3]*a[2,3]^3+4*a[2,2]*a[3,3]^2*a[1,2]^7*a[1,3]^5*a[2,3]+5*a[2,2]*a[3,3]^
2*a[1,1]*a[1,2]^6*a[1,3]^4*a[2,3]^2+4*a[2,2]*a[3,3]*a[1,1]*a[1,2]^5*a[1,3]^5*a[2,3]^3-5*a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^4*a[1,3]^2*a[2,3]^4+14*a[2,2]*a[3,3]^2*a[1,1
]^2*a[1,2]^5*a[1,3]^3*a[2,3]^3+12*a[2,2]*a[3,3]*a[1,1]^3*a[1,2]^3*a[1,3]^3*a[2,3]^5+8*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^4*a[1,3]^4*a[2,3]^4-2*a[2,2]*a[3,3]*a[2,3]^2*a[1
,2]^6*a[1,3]^6)/(a[1,2]^2*a[1,3]^6*a[2,3]^4*a[2,2]^2+a[1,2]^2*a[1,3]^6*a[3,3]^2*a[2,2]^4+a[1,1]*a[1,3]^6*a[2,3]^4*a[2,2]^3-a[1,2]^6*a[1,3]^2*a[3,3]^4*a[2,2]^2-2*a[1
,2]^3*a[1,3]^5*a[2,3]^5*a[2,2]-3*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^2-4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^3-2*a[1,2]^2*a[1,3]^6*a[3,3]*a[
2,3]^2*a[2,2]^3+a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^2+3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^3+4*a[1,2]^3*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^2
-a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]+a[1,1]*a[1,2]^6*a[3,3]^4*a[2,3]^2*a[2,2]+4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]+4*a[1,1]*a[1,2]*a[1,3]
^5*a[3,3]^2*a[2,3]*a[2,2]^4-4*a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]-2*a[1,2]^3*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^3+2*a[1,2]^5*a[1,3]^3*a[3,3]*a[2,3]^5+2*a[1,2]^5
*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^2-a[1,2]^6*a[1,3]^2*a[3,3]^2*a[2,3]^4-a[1,1]*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^4+4*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^4*a[2,2]^3-4*a[1,1
]*a[1,2]^2*a[1,3]^4*a[3,3]^3*a[2,2]^4+2*a[1,2]^6*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]-a[1,1]*a[1,2]^6*a[3,3]^3*a[2,3]^4-4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]
^2)*z^4-(2*a[2,3]^5*a[1,2]^5*a[1,3]^5+2*a[3,3]^2*a[1,1]*a[1,2]^6*a[1,3]^2*a[2,3]^4-6*a[3,3]*a[1,1]*a[1,2]^5*a[1,3]^3*a[2,3]^5+2*a[3,3]^2*a[1,2]^7*a[1,3]^3*a[2,3]^3-\
5*a[3,3]*a[1,2]^6*a[1,3]^4*a[2,3]^4+2*a[3,3]^3*a[1,1]*a[1,2]^7*a[1,3]*a[2,3]^3+3*a[3,3]^3*a[1,1]^2*a[1,2]^6*a[2,3]^4-4*a[2,2]^4*a[3,3]^2*a[1,1]^2*a[1,2]*a[1,3]^5*a[
2,3]+a[2,2]^3*a[3,3]^2*a[1,2]^4*a[1,3]^6+4*a[2,2]^4*a[3,3]^3*a[1,1]^3*a[1,2]*a[1,3]^3*a[2,3]-5*a[2,2]^4*a[3,3]^2*a[1,1]^3*a[1,3]^4*a[2,3]^2+a[2,2]^4*a[3,3]^2*a[1,1]
*a[1,2]^2*a[1,3]^6+6*a[2,2]^4*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[3,3]^4-3*a[2,2]^4*a[3,3]^3*a[1,1]^2*a[1,2]^2*a[1,3]^4-10*a[2,2]^3*a[3,3]^4*a[1,1]^3*a[1,2]^3*a[1,3]*a[2,3
]+a[2,2]^4*a[1,1]^2*a[1,3]^6*a[2,3]^2*a[3,3]-7*a[2,2]^3*a[3,3]^4*a[1,1]^2*a[1,2]^4*a[1,3]^2+4*a[2,2]^3*a[3,3]^3*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]-a[2,2]*a[1,2]^4*a[
1,3]^6*a[2,3]^4-12*a[2,2]^3*a[3,3]^3*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]^2-a[2,2]^3*a[3,3]^3*a[1,1]*a[1,2]^4*a[1,3]^4+14*a[2,2]^3*a[3,3]^2*a[1,1]^2*a[1,2]^2*a[1,3]^4*
a[2,3]^2+2*a[2,2]^2*a[3,3]^4*a[1,1]*a[1,2]^6*a[1,3]^2+2*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^3*a[2,3]^3-2*a[2,2]^3*a[1,1]^2*a[1,3]^6*a[2,3]^4+2*a[2,2]^3*a[3,3]*
a[1,1]*a[1,2]^2*a[1,3]^6*a[2,3]^2+5*a[2,2]^3*a[3,3]*a[1,1]^3*a[1,3]^4*a[2,3]^4+6*a[2,2]^2*a[3,3]^4*a[1,1]^2*a[1,2]^5*a[1,3]*a[2,3]+5*a[2,2]^2*a[3,3]^4*a[1,1]^3*a[1,
2]^4*a[2,3]^2+6*a[2,2]^3*a[3,3]*a[1,1]^2*a[1,2]*a[1,3]^5*a[2,3]^3-2*a[2,2]^3*a[1,1]*a[1,2]*a[2,3]^3*a[1,3]^7+15*a[2,2]^2*a[3,3]^3*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]^
2+6*a[2,2]^2*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]^3*a[2,3]+4*a[2,2]*a[3,3]^2*a[1,2]^6*a[1,3]^4*a[2,3]^2+10*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]*a[2,3]^3+a[2,2]^2*a
[3,3]^3*a[1,2]^6*a[1,3]^4-10*a[2,2]^2*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]^2-5*a[2,2]*a[3,3]^3*a[1,1]^3*a[1,2]^4*a[2,3]^4+6*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^2*
a[1,3]^2*a[2,3]^4-2*a[2,2]*a[1,1]^2*a[1,2]^6*a[2,3]^2*a[3,3]^4-16*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]^3-4*a[2,2]^2*a[3,3]^2*a[1,2]^5*a[1,3]^5*a[2,3]
-6*a[2,2]^2*a[3,3]*a[1,1]^3*a[1,2]*a[1,3]^3*a[2,3]^5+5*a[2,2]^2*a[1,1]*a[2,3]^4*a[1,2]^2*a[1,3]^6-6*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]^5*a[2,3]^3-16*a[2,2]^2*a[
3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]^4+2*a[2,2]^2*a[1,1]^2*a[1,2]*a[1,3]^5*a[2,3]^5-12*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^6*a[1,3]^2*a[2,3]^2-10*a[2,2]*a[3,3]^3*a[1,1]
^2*a[1,2]^5*a[1,3]*a[2,3]^3-2*a[2,2]*a[3,3]^3*a[1,2]^7*a[1,3]^3*a[2,3]+10*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^3*a[2,3]^3-3*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,
3]^2*a[2,3]^4+2*a[2,2]*a[3,3]*a[1,2]^5*a[1,3]^5*a[2,3]^3+12*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]^5+11*a[2,2]*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]^4-4*a
[2,2]*a[1,1]*a[1,2]^3*a[1,3]^5*a[2,3]^5)/(a[1,2]^2*a[1,3]^6*a[2,3]^4*a[2,2]^2+a[1,2]^2*a[1,3]^6*a[3,3]^2*a[2,2]^4+a[1,1]*a[1,3]^6*a[2,3]^4*a[2,2]^3-a[1,2]^6*a[1,3]^
2*a[3,3]^4*a[2,2]^2-2*a[1,2]^3*a[1,3]^5*a[2,3]^5*a[2,2]-3*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^2-4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^3-2*a[
1,2]^2*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^3+a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^2+3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^3+4*a[1,2]^3*a[1,3]^5
*a[3,3]*a[2,3]^3*a[2,2]^2-a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]+a[1,1]*a[1,2]^6*a[3,3]^4*a[2,3]^2*a[2,2]+4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,
2]+4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^4-4*a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]-2*a[1,2]^3*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^3+2*a[1,2]^5*a[1,3]^3*a
[3,3]*a[2,3]^5+2*a[1,2]^5*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^2-a[1,2]^6*a[1,3]^2*a[3,3]^2*a[2,3]^4-a[1,1]*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^4+4*a[1,1]*a[1,2]^4*a[1,3]^2*
a[3,3]^4*a[2,2]^3-4*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^3*a[2,2]^4+2*a[1,2]^6*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]-a[1,1]*a[1,2]^6*a[3,3]^3*a[2,3]^4-4*a[1,1]*a[1,2]^5*a[1,
3]*a[3,3]^4*a[2,3]*a[2,2]^2)*z^2+a[3,3]*(2*a[1,1]^2*a[2,2]^3*a[1,3]^4*a[2,3]^4-2*a[1,2]^5*a[1,3]^3*a[2,3]^5-2*a[1,1]^2*a[2,2]^4*a[1,3]^4*a[2,3]^2*a[3,3]+2*a[1,1]^2*
a[2,2]^4*a[1,2]^2*a[1,3]^2*a[3,3]^3-2*a[1,1]^2*a[1,2]^4*a[2,3]^4*a[3,3]^2*a[2,2]-2*a[1,1]^2*a[2,2]^2*a[1,2]*a[1,3]^3*a[2,3]^5+2*a[1,1]^2*a[2,2]^2*a[1,2]^4*a[2,3]^2*
a[3,3]^3+4*a[1,1]*a[2,2]*a[1,2]^3*a[1,3]^3*a[2,3]^5-5*a[1,1]*a[2,2]^2*a[1,2]^2*a[1,3]^4*a[2,3]^4+2*a[1,1]*a[2,2]^3*a[2,3]^3*a[1,2]*a[1,3]^5-4*a[1,1]*a[2,2]^4*a[1,2]
^2*a[1,3]^4*a[3,3]^2+2*a[1,1]^2*a[2,2]^4*a[1,2]*a[1,3]^3*a[2,3]*a[3,3]^2-4*a[1,1]^2*a[2,2]^3*a[1,2]^3*a[1,3]*a[2,3]*a[3,3]^3-4*a[1,1]^2*a[2,2]^3*a[1,2]^2*a[1,3]^2*a
[2,3]^2*a[3,3]^2+4*a[1,1]^2*a[2,2]^2*a[1,2]^3*a[1,3]*a[2,3]^3*a[3,3]^2-a[1,1]*a[2,2]^4*a[1,3]^6*a[2,3]^2+2*a[1,1]*a[2,2]^4*a[1,2]*a[1,3]^5*a[2,3]*a[3,3]+2*a[1,1]^2*
a[2,2]^2*a[1,2]^2*a[1,3]^2*a[2,3]^4*a[3,3]+2*a[1,1]*a[2,2]^3*a[1,2]^3*a[2,3]*a[1,3]^3*a[3,3]^2+4*a[1,1]*a[2,2]^3*a[1,2]^2*a[1,3]^4*a[2,3]^2*a[3,3]+a[1,2]^6*a[1,3]^2
*a[2,3]^4*a[3,3]+5*a[1,1]*a[2,2]^2*a[1,2]^4*a[1,3]^2*a[2,3]^2*a[3,3]^2+a[1,2]^2*a[1,3]^6*a[3,3]*a[2,2]^4-6*a[1,1]*a[2,2]^2*a[1,2]^3*a[1,3]^3*a[2,3]^3*a[3,3]-a[2,2]^
3*a[1,2]^2*a[1,3]^6*a[2,3]^2+a[2,2]^3*a[1,2]^4*a[1,3]^4*a[3,3]^2+2*a[2,2]^2*a[1,2]^3*a[1,3]^5*a[2,3]^3-2*a[2,2]^3*a[1,2]^3*a[1,3]^5*a[2,3]*a[3,3]-2*a[2,2]^2*a[1,2]^
4*a[1,3]^4*a[2,3]^2*a[3,3]-a[2,2]*a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2+2*a[2,2]*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3]-4*a[1,1]*a[2,2]*a[1,2]^5*a[1,3]*a[2,3]^3*a[3,3]^2+a
[2,2]*a[1,2]^4*a[1,3]^4*a[2,3]^4+a[1,1]*a[1,2]^6*a[2,3]^4*a[3,3]^2)/(a[1,2]^2*a[1,3]^6*a[2,3]^4*a[2,2]^2+a[1,2]^2*a[1,3]^6*a[3,3]^2*a[2,2]^4+a[1,1]*a[1,3]^6*a[2,3]^
4*a[2,2]^3-a[1,2]^6*a[1,3]^2*a[3,3]^4*a[2,2]^2-2*a[1,2]^3*a[1,3]^5*a[2,3]^5*a[2,2]-3*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^2-4*a[1,1]*a[1,2]*a[1,3]^5*a[
3,3]*a[2,3]^3*a[2,2]^3-2*a[1,2]^2*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^3+a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^2+3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2*a[2,3]^2*a
[2,2]^3+4*a[1,2]^3*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^2-a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]+a[1,1]*a[1,2]^6*a[3,3]^4*a[2,3]^2*a[2,2]+4*a[1,1]*a[1,2]^5*a[
1,3]*a[3,3]^3*a[2,3]^3*a[2,2]+4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^4-4*a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]-2*a[1,2]^3*a[1,3]^5*a[3,3]^2*a[2,3]*a[2
,2]^3+2*a[1,2]^5*a[1,3]^3*a[3,3]*a[2,3]^5+2*a[1,2]^5*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^2-a[1,2]^6*a[1,3]^2*a[3,3]^2*a[2,3]^4-a[1,1]*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^4+
4*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^4*a[2,2]^3-4*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^3*a[2,2]^4+2*a[1,2]^6*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]-a[1,1]*a[1,2]^6*a[3,3]^3*a[2,
3]^4-4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^2), (-a[2,2]^3*a[3,3]*a[1,2]*a[1,1]*a[1,3]^5-a[2,2]*a[3,3]^3*a[1,2]^5*a[1,1]*a[1,3]+a[1,2]^6*a[1,1]*a[2,3]*a[3,
3]^3+a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]+a[1,2]^3*a[1,3]^5*a[3,3]*a[2,2]^2-a[3,3]*a[1,2]^3*a[1,1]^2*a[1,3]*a[2,3]^4-4*a[2,2]*a[3,3]*a[1,2]^4*a[1,3]^4*a[2,3]-3*a[3,3]^2*
a[1,2]^5*a[1,1]*a[1,3]*a[2,3]^2+a[3,3]*a[1,2]^4*a[1,3]^2*a[2,3]^3*a[1,1]-a[3,3]^2*a[1,2]^6*a[1,3]^2*a[2,3]+a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,2]+a[3,3]^2*a[1,2]^4*a[1,1
]^2*a[2,3]^3+a[1,1]^2*a[1,3]^4*a[2,3]^3*a[2,2]^2-a[2,2]^3*a[1,2]*a[1,1]^3*a[1,3]*a[3,3]^3+a[2,2]^3*a[3,3]^2*a[1,3]^2*a[1,1]^3*a[2,3]+2*a[2,2]^3*a[3,3]^2*a[1,2]*a[1,
3]^3*a[1,1]^2-2*a[2,2]^3*a[1,1]^2*a[1,3]^4*a[2,3]*a[3,3]+a[2,2]^2*a[3,3]^3*a[1,2]^2*a[1,1]^3*a[2,3]+2*a[2,2]^2*a[3,3]^3*a[1,2]^3*a[1,1]^2*a[1,3]-3*a[2,2]^2*a[3,3]^2
*a[1,2]^3*a[1,1]*a[1,3]^3-6*a[2,2]^2*a[3,3]^2*a[1,2]^2*a[1,1]^2*a[1,3]^2*a[2,3]+3*a[2,2]^2*a[3,3]*a[1,2]*a[1,3]^3*a[1,1]^2*a[2,3]^2-a[2,2]^2*a[3,3]*a[1,3]^2*a[1,1]^
3*a[2,3]^3+6*a[2,2]^2*a[3,3]*a[1,2]^2*a[1,3]^4*a[1,1]*a[2,3]-3*a[2,2]^2*a[1,2]*a[1,1]*a[1,3]^5*a[2,3]^2-2*a[2,2]*a[1,2]^4*a[1,1]^2*a[2,3]*a[3,3]^3+3*a[2,2]*a[3,3]^2
*a[1,2]^3*a[1,1]^2*a[1,3]*a[2,3]^2+6*a[2,2]*a[3,3]^2*a[1,2]^4*a[1,1]*a[1,3]^2*a[2,3]-a[2,2]*a[3,3]^2*a[1,2]^2*a[1,1]^3*a[2,3]^3-6*a[2,2]*a[3,3]*a[1,2]^3*a[1,1]*a[1,
3]^3*a[2,3]^2+a[2,2]*a[3,3]*a[1,2]*a[1,1]^3*a[1,3]*a[2,3]^4-a[2,2]*a[1,2]*a[1,3]^3*a[1,1]^2*a[2,3]^4+a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^3*a[1,1]+a[1,2]^3*a[1,1]*a[1,3]
^3*a[2,3]^4-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]+3*a[3,3]*a[1,2]^5*a[1,3]^3*a[2,3]^2+3*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^2-2*a[1,2]^4*a[1,3]^4*a[2,3]^3)*a[1,1]^2*a[2,3]/
(a[3,3]*a[2,2]-a[2,3]^2)/(4*a[1,2]^2*a[3,3]^2*a[1,1]*a[1,3]^2*a[2,2]^2-4*a[2,2]^2*a[3,3]*a[1,2]*a[1,3]^3*a[1,1]*a[2,3]-a[1,2]^2*a[1,3]^4*a[3,3]*a[2,2]^2+a[2,2]^2*a[
1,1]*a[1,3]^4*a[2,3]^2-4*a[2,2]*a[3,3]^2*a[1,2]^3*a[1,1]*a[1,3]*a[2,3]-a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,2]+2*a[2,2]*a[3,3]*a[1,2]^3*a[2,3]*a[1,3]^3+2*a[2,2]*a[3,3]*a[
1,2]^2*a[2,3]^2*a[1,3]^2*a[1,1]+a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^2+a[1,2]^4*a[1,1]*a[2,3]^2*a[3,3]^2+a[1,2]^4*a[1,3]^2*a[2,3]^2*a[3,3]-2*a[1,2]^3*a[1,3]^3*a[2,3]^3)*
z^6-(-a[2,2]^3*a[3,3]*a[1,2]*a[1,1]*a[1,3]^5-a[2,2]*a[3,3]^3*a[1,2]^5*a[1,1]*a[1,3]-2*a[3,3]*a[1,2]^3*a[1,1]^2*a[1,3]*a[2,3]^4+2*a[2,2]*a[3,3]*a[1,2]^4*a[1,3]^4*a[2
,3]+a[3,3]^2*a[1,2]^5*a[1,1]*a[1,3]*a[2,3]^2-4*a[3,3]*a[1,2]^4*a[1,3]^2*a[2,3]^3*a[1,1]+a[3,3]^2*a[1,2]^6*a[1,3]^2*a[2,3]+3*a[3,3]^2*a[1,2]^4*a[1,1]^2*a[2,3]^3+3*a[
1,1]^2*a[1,3]^4*a[2,3]^3*a[2,2]^2-5*a[2,2]^3*a[1,2]*a[1,1]^3*a[1,3]*a[3,3]^3+4*a[2,2]^3*a[3,3]^2*a[1,3]^2*a[1,1]^3*a[2,3]+6*a[2,2]^3*a[3,3]^2*a[1,2]*a[1,3]^3*a[1,1]
^2-4*a[2,2]^3*a[1,1]^2*a[1,3]^4*a[2,3]*a[3,3]+4*a[2,2]^2*a[3,3]^3*a[1,2]^2*a[1,1]^3*a[2,3]+6*a[2,2]^2*a[3,3]^3*a[1,2]^3*a[1,1]^2*a[1,3]-5*a[2,2]^2*a[3,3]^2*a[1,2]^3
*a[1,1]*a[1,3]^3+2*a[2,2]^2*a[3,3]^2*a[1,2]*a[1,1]^3*a[1,3]*a[2,3]^2-12*a[2,2]^2*a[3,3]^2*a[1,2]^2*a[1,1]^2*a[1,3]^2*a[2,3]-4*a[2,2]^2*a[3,3]*a[1,3]^2*a[1,1]^3*a[2,
3]^3+4*a[2,2]^2*a[3,3]*a[1,2]^2*a[1,3]^4*a[1,1]*a[2,3]+a[2,2]^2*a[1,2]*a[1,1]*a[1,3]^5*a[2,3]^2-4*a[2,2]*a[1,2]^4*a[1,1]^2*a[2,3]*a[3,3]^3+4*a[2,2]*a[3,3]^2*a[1,2]^
4*a[1,1]*a[1,3]^2*a[2,3]-4*a[2,2]*a[3,3]^2*a[1,2]^2*a[1,1]^3*a[2,3]^3+4*a[2,2]*a[3,3]*a[1,2]^3*a[1,1]*a[1,3]^3*a[2,3]^2+6*a[2,2]*a[3,3]*a[1,2]^2*a[1,1]^2*a[1,3]^2*a
[2,3]^3+3*a[2,2]*a[3,3]*a[1,2]*a[1,1]^3*a[1,3]*a[2,3]^4-2*a[2,2]*a[1,2]*a[1,3]^3*a[1,1]^2*a[2,3]^4-4*a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^3*a[1,1]+a[1,2]^3*a[1,1]*a[1,3]
^3*a[2,3]^4+a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]-4*a[3,3]*a[1,2]^5*a[1,3]^3*a[2,3]^2-4*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^2+4*a[1,2]^4*a[1,3]^4*a[2,3]^3)*a[1,1]*a[2,3]/(a
[3,3]*a[2,2]-a[2,3]^2)/(4*a[1,2]^2*a[3,3]^2*a[1,1]*a[1,3]^2*a[2,2]^2-4*a[2,2]^2*a[3,3]*a[1,2]*a[1,3]^3*a[1,1]*a[2,3]-a[1,2]^2*a[1,3]^4*a[3,3]*a[2,2]^2+a[2,2]^2*a[1,
1]*a[1,3]^4*a[2,3]^2-4*a[2,2]*a[3,3]^2*a[1,2]^3*a[1,1]*a[1,3]*a[2,3]-a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,2]+2*a[2,2]*a[3,3]*a[1,2]^3*a[2,3]*a[1,3]^3+2*a[2,2]*a[3,3]*a[1,
2]^2*a[2,3]^2*a[1,3]^2*a[1,1]+a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^2+a[1,2]^4*a[1,1]*a[2,3]^2*a[3,3]^2+a[1,2]^4*a[1,3]^2*a[2,3]^2*a[3,3]-2*a[1,2]^3*a[1,3]^3*a[2,3]^3)*z^
4+(-a[1,2]^3*a[1,3]^5*a[3,3]*a[2,2]^2-a[3,3]*a[1,2]^3*a[1,1]^2*a[1,3]*a[2,3]^4+2*a[2,2]*a[3,3]*a[1,2]^4*a[1,3]^4*a[2,3]+2*a[3,3]^2*a[1,2]^5*a[1,1]*a[1,3]*a[2,3]^2-2
*a[3,3]*a[1,2]^4*a[1,3]^2*a[2,3]^3*a[1,1]-a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,2]+2*a[3,3]^2*a[1,2]^4*a[1,1]^2*a[2,3]^3+2*a[1,1]^2*a[1,3]^4*a[2,3]^3*a[2,2]^2-7*a[2,2]^3*a
[1,2]*a[1,1]^3*a[1,3]*a[3,3]^3+5*a[2,2]^3*a[3,3]^2*a[1,3]^2*a[1,1]^3*a[2,3]+3*a[2,2]^3*a[3,3]^2*a[1,2]*a[1,3]^3*a[1,1]^2-a[2,2]^3*a[1,1]^2*a[1,3]^4*a[2,3]*a[3,3]+5*
a[2,2]^2*a[3,3]^3*a[1,2]^2*a[1,1]^3*a[2,3]+3*a[2,2]^2*a[3,3]^3*a[1,2]^3*a[1,1]^2*a[1,3]+4*a[2,2]^2*a[3,3]^2*a[1,2]^3*a[1,1]*a[1,3]^3+4*a[2,2]^2*a[3,3]^2*a[1,2]*a[1,
1]^3*a[1,3]*a[2,3]^2-2*a[2,2]^2*a[3,3]^2*a[1,2]^2*a[1,1]^2*a[1,3]^2*a[2,3]-6*a[2,2]^2*a[3,3]*a[1,2]*a[1,3]^3*a[1,1]^2*a[2,3]^2-5*a[2,2]^2*a[3,3]*a[1,3]^2*a[1,1]^3*a
[2,3]^3-6*a[2,2]^2*a[3,3]*a[1,2]^2*a[1,3]^4*a[1,1]*a[2,3]+2*a[2,2]^2*a[1,2]*a[1,1]*a[1,3]^5*a[2,3]^2-a[2,2]*a[1,2]^4*a[1,1]^2*a[2,3]*a[3,3]^3-6*a[2,2]*a[3,3]^2*a[1,
2]^3*a[1,1]^2*a[1,3]*a[2,3]^2-6*a[2,2]*a[3,3]^2*a[1,2]^4*a[1,1]*a[1,3]^2*a[2,3]-5*a[2,2]*a[3,3]^2*a[1,2]^2*a[1,1]^3*a[2,3]^3+8*a[2,2]*a[3,3]*a[1,2]^3*a[1,1]*a[1,3]^
3*a[2,3]^2+8*a[2,2]*a[3,3]*a[1,2]^2*a[1,1]^2*a[1,3]^2*a[2,3]^3+3*a[2,2]*a[3,3]*a[1,2]*a[1,1]^3*a[1,3]*a[2,3]^4-a[2,2]*a[1,2]*a[1,3]^3*a[1,1]^2*a[2,3]^4-2*a[2,2]*a[1
,2]^2*a[1,3]^4*a[2,3]^3*a[1,1]+a[3,3]*a[1,2]^5*a[1,3]^3*a[2,3]^2+a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^2-2*a[1,2]^4*a[1,3]^4*a[2,3]^3)*a[2,3]/(a[3,3]*a[2,2]-a[2,3]^2)/(4*
a[1,2]^2*a[3,3]^2*a[1,1]*a[1,3]^2*a[2,2]^2-4*a[2,2]^2*a[3,3]*a[1,2]*a[1,3]^3*a[1,1]*a[2,3]-a[1,2]^2*a[1,3]^4*a[3,3]*a[2,2]^2+a[2,2]^2*a[1,1]*a[1,3]^4*a[2,3]^2-4*a[2
,2]*a[3,3]^2*a[1,2]^3*a[1,1]*a[1,3]*a[2,3]-a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,2]+2*a[2,2]*a[3,3]*a[1,2]^3*a[2,3]*a[1,3]^3+2*a[2,2]*a[3,3]*a[1,2]^2*a[2,3]^2*a[1,3]^2*a[1
,1]+a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^2+a[1,2]^4*a[1,1]*a[2,3]^2*a[3,3]^2+a[1,2]^4*a[1,3]^2*a[2,3]^2*a[3,3]-2*a[1,2]^3*a[1,3]^3*a[2,3]^3)*z^2-(-3*a[1,1]^2*a[2,2]^3*a[
1,2]*a[1,3]*a[3,3]^3+2*a[1,1]^2*a[2,2]^3*a[1,3]^2*a[2,3]*a[3,3]^2+2*a[1,1]^2*a[2,2]^2*a[2,3]*a[1,2]^2*a[3,3]^3+2*a[1,1]^2*a[2,2]^2*a[1,2]*a[1,3]*a[2,3]^2*a[3,3]^2-2
*a[1,1]^2*a[2,2]^2*a[2,3]^3*a[1,3]^2*a[3,3]-2*a[1,1]^2*a[2,2]*a[1,2]^2*a[2,3]^3*a[3,3]^2+a[1,1]^2*a[2,2]*a[1,2]*a[1,3]*a[2,3]^4*a[3,3]+a[1,2]*a[1,3]^3*a[2,2]^3*a[1,
1]*a[3,3]^2+a[1,2]^3*a[1,1]*a[1,3]*a[2,2]^2*a[3,3]^3+2*a[1,1]*a[2,2]^2*a[1,3]^2*a[1,2]^2*a[2,3]*a[3,3]^2-5*a[1,1]*a[2,2]^2*a[1,2]*a[1,3]^3*a[2,3]^2*a[3,3]+a[1,1]*a[
1,3]^4*a[2,3]^3*a[2,2]^2-5*a[1,1]*a[2,2]*a[1,2]^3*a[1,3]*a[2,3]^2*a[3,3]^2+4*a[1,1]*a[2,2]*a[1,2]^2*a[1,3]^2*a[2,3]^3*a[3,3]+a[1,1]*a[1,2]^4*a[2,3]^3*a[3,3]^2-a[1,2
]^2*a[1,3]^4*a[2,3]*a[3,3]*a[2,2]^2-a[2,2]*a[1,2]^4*a[1,3]^2*a[2,3]*a[3,3]^2+2*a[2,2]*a[1,2]^3*a[1,3]^3*a[2,3]^2*a[3,3]+a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^3+a[1,2]^4*a
[1,3]^2*a[2,3]^3*a[3,3]-2*a[1,2]^3*a[1,3]^3*a[2,3]^4)*a[2,3]/(a[3,3]*a[2,2]-a[2,3]^2)/(4*a[1,2]^2*a[3,3]^2*a[1,1]*a[1,3]^2*a[2,2]^2-4*a[2,2]^2*a[3,3]*a[1,2]*a[1,3]^
3*a[1,1]*a[2,3]-a[1,2]^2*a[1,3]^4*a[3,3]*a[2,2]^2+a[2,2]^2*a[1,1]*a[1,3]^4*a[2,3]^2-4*a[2,2]*a[3,3]^2*a[1,2]^3*a[1,1]*a[1,3]*a[2,3]-a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,2
]+2*a[2,2]*a[3,3]*a[1,2]^3*a[2,3]*a[1,3]^3+2*a[2,2]*a[3,3]*a[1,2]^2*a[2,3]^2*a[1,3]^2*a[1,1]+a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^2+a[1,2]^4*a[1,1]*a[2,3]^2*a[3,3]^2+a[1
,2]^4*a[1,3]^2*a[2,3]^2*a[3,3]-2*a[1,2]^3*a[1,3]^3*a[2,3]^3)], [(5*a[3,3]*a[1,1]*a[1,2]^5*a[1,3]^3*a[2,3]^2+2*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]^3+a[1,1]^2*a[1,2]^6*a[
2,3]*a[3,3]^3+a[3,3]^2*a[1,1]^3*a[1,2]^4*a[2,3]^3-5*a[3,3]^2*a[1,1]*a[1,2]^6*a[1,3]^2*a[2,3]-3*a[3,3]*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]^3+a[2,2]^3*a[1,1]^2*a[1,3]^6
*a[2,3]+a[2,2]^2*a[1,1]^3*a[1,3]^4*a[2,3]^3-a[3,3]^2*a[1,1]^2*a[1,2]^5*a[1,3]*a[2,3]^2+a[3,3]^3*a[1,1]*a[1,2]^7*a[1,3]+a[2,2]^3*a[1,1]*a[1,2]*a[1,3]^7-2*a[2,2]^3*a[
1,1]^4*a[1,2]*a[1,3]*a[3,3]^3+5*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^3+a[2,2]^3*a[3,3]^2*a[1,1]^4*a[1,3]^2*a[2,3]-4*a[2,2]^3*a[3,3]*a[1,1]^2*a[1,2]*a[1,3]^5-2*a
[2,2]^3*a[3,3]*a[1,1]^3*a[1,3]^4*a[2,3]+5*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]+a[2,2]^2*a[3,3]^3*a[1,1]^4*a[1,2]^2*a[2,3]-10*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]
^3*a[1,3]^3+2*a[2,2]^2*a[3,3]^2*a[1,1]^4*a[1,2]*a[1,3]*a[2,3]^2-10*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]+14*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^4
*a[2,3]-a[2,2]^2*a[3,3]*a[1,1]^4*a[1,3]^2*a[2,3]^3+6*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]^5-a[2,2]^2*a[3,3]*a[1,1]^3*a[1,2]*a[1,3]^3*a[2,3]^2-a[2,2]^2*a[1,1]^2*a[
1,2]*a[1,3]^5*a[2,3]^2-5*a[2,2]^2*a[1,1]*a[1,2]^2*a[1,3]^6*a[2,3]-2*a[2,2]*a[3,3]^3*a[1,1]^3*a[1,2]^4*a[2,3]-4*a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2]^5*a[1,3]+14*a[2,2]*a[
3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]-a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]*a[2,3]^2-a[2,2]*a[3,3]^2*a[1,1]^4*a[1,2]^2*a[2,3]^3+6*a[2,2]*a[3,3]^2*a[1,1]*a[1,2
]^5*a[1,3]^3-4*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]^2-16*a[2,2]*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]+4*a[2,2]*a[3,3]*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]^
3-3*a[2,2]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]^3+5*a[2,2]*a[1,1]*a[1,2]^3*a[1,3]^5*a[2,3]^2+4*a[3,3]*a[1,2]^6*a[1,3]^4*a[2,3]-2*a[2,2]*a[3,3]*a[1,2]^5*a[1,3]^5+4*a[2,
2]*a[1,2]^4*a[1,3]^6*a[2,3]-4*a[1,2]^5*a[1,3]^5*a[2,3]^2-a[3,3]^2*a[1,2]^7*a[1,3]^3-a[2,2]^2*a[1,2]^3*a[1,3]^7)*a[1,3]*a[1,1]*a[1,2]/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[
1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3
]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]
^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[
1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3])*z^6-(-6*a[3,3]*a[1,1]*a[1,2]^5*a
[1,3]^3*a[2,3]^2+4*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]^3-a[1,1]^2*a[1,2]^6*a[2,3]*a[3,3]^3+2*a[3,3]^2*a[1,1]^3*a[1,2]^4*a[2,3]^3+2*a[3,3]^2*a[1,1]*a[1,2]^6*a[1,3]^2*a[2
,3]-7*a[3,3]*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]^3-a[2,2]^3*a[1,1]^2*a[1,3]^6*a[2,3]+2*a[2,2]^2*a[1,1]^3*a[1,3]^4*a[2,3]^3+5*a[3,3]^2*a[1,1]^2*a[1,2]^5*a[1,3]*a[2,3]^
2-6*a[2,2]^3*a[1,1]^4*a[1,2]*a[1,3]*a[3,3]^3+8*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^3+3*a[2,2]^3*a[3,3]^2*a[1,1]^4*a[1,3]^2*a[2,3]-2*a[2,2]^3*a[3,3]*a[1,1]^2*a[
1,2]*a[1,3]^5-2*a[2,2]^3*a[3,3]*a[1,1]^3*a[1,3]^4*a[2,3]+8*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]+3*a[2,2]^2*a[3,3]^3*a[1,1]^4*a[1,2]^2*a[2,3]-6*a[2,2]^2*a[3,3]
^2*a[1,1]^2*a[1,2]^3*a[1,3]^3+6*a[2,2]^2*a[3,3]^2*a[1,1]^4*a[1,2]*a[1,3]*a[2,3]^2-12*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]+4*a[2,2]^2*a[3,3]*a[1,1]^2*
a[1,2]^2*a[1,3]^4*a[2,3]-3*a[2,2]^2*a[3,3]*a[1,1]^4*a[1,3]^2*a[2,3]^3-2*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]^5-8*a[2,2]^2*a[3,3]*a[1,1]^3*a[1,2]*a[1,3]^3*a[2,3]^2
+5*a[2,2]^2*a[1,1]^2*a[1,2]*a[1,3]^5*a[2,3]^2+2*a[2,2]^2*a[1,1]*a[1,2]^2*a[1,3]^6*a[2,3]-2*a[2,2]*a[3,3]^3*a[1,1]^3*a[1,2]^4*a[2,3]-2*a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2
]^5*a[1,3]+4*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]-8*a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]*a[2,3]^2-3*a[2,2]*a[3,3]^2*a[1,1]^4*a[1,2]^2*a[2,3]^3-2*a[
2,2]*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^3+8*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]^2+8*a[2,2]*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]+12*a[2,2]*a[3,3]*a[1,1]^3
*a[1,2]^2*a[1,3]^2*a[2,3]^3-7*a[2,2]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]^3-6*a[2,2]*a[1,1]*a[1,2]^3*a[1,3]^5*a[2,3]^2-4*a[3,3]*a[1,2]^6*a[1,3]^4*a[2,3]+2*a[2,2]*a[3,3
]*a[1,2]^5*a[1,3]^5-4*a[2,2]*a[1,2]^4*a[1,3]^6*a[2,3]+4*a[1,2]^5*a[1,3]^5*a[2,3]^2+a[3,3]^2*a[1,2]^7*a[1,3]^3+a[2,2]^2*a[1,2]^3*a[1,3]^7)*a[1,2]*a[1,3]/(-4*a[2,2]^3
*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[
1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2
,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3
*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3])*z^4+(-a[2,2]^
2*a[3,3]*a[1,2]^4*a[1,3]^5+a[2,2]^2*a[1,2]^3*a[1,3]^6*a[2,3]-a[2,2]*a[3,3]^2*a[1,2]^6*a[1,3]^3-3*a[2,2]*a[1,2]^4*a[1,3]^5*a[2,3]^2+4*a[2,2]*a[3,3]*a[1,2]^5*a[1,3]^4
*a[2,3]+3*a[3,3]^2*a[1,1]*a[1,2]^6*a[1,3]*a[2,3]^2-4*a[3,3]*a[2,3]^3*a[1,1]*a[1,2]^5*a[1,3]^2-6*a[2,2]^3*a[1,1]^3*a[1,2]^2*a[1,3]*a[3,3]^3+3*a[2,2]^3*a[3,3]^2*a[1,1
]^3*a[1,2]*a[1,3]^2*a[2,3]+7*a[2,2]^3*a[3,3]^2*a[1,1]^2*a[1,2]^2*a[1,3]^3-2*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^5-3*a[2,2]^3*a[3,3]*a[1,1]^2*a[1,2]*a[1,3]^4*a[2,
3]+3*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[2,3]+3*a[2,2]^2*a[3,3]^3*a[1,1]^2*a[1,2]^4*a[1,3]+a[2,2]^2*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^3-4*a[2,2]^2*a[3,3]^2*a[1,1]^2
*a[1,2]^3*a[1,3]^2*a[2,3]+6*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]*a[2,3]^2-9*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^3*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,1]*a[1,2
]^3*a[1,3]^4*a[2,3]-3*a[2,2]^2*a[3,3]*a[1,1]^3*a[1,2]*a[1,3]^2*a[2,3]^3+4*a[2,2]^2*a[1,1]*a[1,2]^2*a[1,3]^5*a[2,3]^2+a[2,2]^2*a[1,1]^2*a[1,2]*a[1,3]^4*a[2,3]^3-a[2,
2]*a[3,3]^3*a[1,1]*a[1,2]^6*a[1,3]+a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2]^5*a[2,3]-4*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^2*a[2,3]-3*a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[
2,3]^3-10*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]*a[2,3]^2+12*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^2*a[2,3]^3+11*a[2,2]*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^3*a[2,3]^2-\
6*a[2,2]*a[1,1]*a[1,2]^3*a[1,3]^4*a[2,3]^3+2*a[1,2]^5*a[1,3]^4*a[2,3]^3+a[3,3]^2*a[2,3]^3*a[1,1]^2*a[1,2]^5+a[2,2]^3*a[1,1]^2*a[1,3]^5*a[2,3]^2+a[3,3]^2*a[1,2]^7*a[
1,3]^2*a[2,3]-3*a[3,3]*a[1,2]^6*a[1,3]^3*a[2,3]^2)*a[1,3]/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,3]^5*a[2,3]+a[2,2]^3*a[
3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^2*a
[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]*a[2,3]+a[2,2]*a[3,3]^2
*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[3,3]^3+a[1,2]^6*a[1,3]^
2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3])*z^2-a[2,2]*a[1,3]*(-2*a[1,1]^2*a[2,2]^2*a[1,2]^2*a[1,3]*a[3,3]^3+a[1,1]^2*a[2,2]^2*a[1,2]*a[1,3]^2*a[2,3]*a
[3,3]^2+a[1,1]^2*a[2,2]*a[1,2]^3*a[2,3]*a[3,3]^3+2*a[1,1]^2*a[2,2]*a[1,2]^2*a[1,3]*a[2,3]^2*a[3,3]^2-a[1,1]^2*a[2,2]*a[1,2]*a[1,3]^2*a[2,3]^3*a[3,3]-a[1,1]^2*a[1,2]
^3*a[2,3]^3*a[3,3]^2+4*a[1,1]*a[2,2]^2*a[1,2]^2*a[1,3]^3*a[3,3]^2-3*a[1,1]*a[2,2]^2*a[1,2]*a[1,3]^4*a[2,3]*a[3,3]+a[1,1]*a[2,2]^2*a[1,3]^5*a[2,3]^2-2*a[1,1]*a[2,2]*
a[1,2]^3*a[1,3]^2*a[2,3]*a[3,3]^2-2*a[1,1]*a[2,2]*a[1,2]^2*a[1,3]^3*a[2,3]^2*a[3,3]+a[1,1]*a[1,2]^5*a[2,3]*a[3,3]^3-3*a[1,1]*a[1,2]^4*a[1,3]*a[2,3]^2*a[3,3]^2+4*a[1
,1]*a[1,2]^3*a[1,3]^2*a[2,3]^3*a[3,3]-a[1,2]^2*a[1,3]^5*a[3,3]*a[2,2]^2-a[2,2]*a[1,2]^4*a[1,3]^3*a[3,3]^2+2*a[2,2]*a[1,2]^3*a[1,3]^4*a[2,3]*a[3,3]+a[2,2]*a[1,2]^2*a
[1,3]^5*a[2,3]^2+a[1,2]^4*a[1,3]^3*a[2,3]^2*a[3,3]-2*a[1,2]^3*a[1,3]^4*a[2,3]^3)/(-4*a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2+4*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]*a[1,
3]^5*a[2,3]+a[2,2]^3*a[3,3]*a[1,2]^2*a[1,3]^6-a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]^2+4*a[2,2]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3-a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^
4*a[2,3]^2-2*a[2,2]^2*a[3,3]*a[1,2]^3*a[1,3]^5*a[2,3]-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,2]^6*a[1,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^5*a[1,3]
*a[2,3]+a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,2]^5*a[1,3]^3*a[2,3]+2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3+a[1,1]*a[1,2]^6*a[2,3]^2*a[
3,3]^3+a[1,2]^6*a[1,3]^2*a[2,3]^2*a[3,3]^2-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3]), (-a[2,2]^3*a[3,3]*a[1,2]*a[1,1]*a[1,3]^5-a[2,2]*a[3,3]^3*a[1,2]^5*a[1,1]*a[1,3]+a[1
,2]^6*a[1,1]*a[2,3]*a[3,3]^3+a[2,2]^3*a[1,1]*a[1,3]^6*a[2,3]+a[1,2]^3*a[1,3]^5*a[3,3]*a[2,2]^2-a[3,3]*a[1,2]^3*a[1,1]^2*a[1,3]*a[2,3]^4-4*a[2,2]*a[3,3]*a[1,2]^4*a[1
,3]^4*a[2,3]-3*a[3,3]^2*a[1,2]^5*a[1,1]*a[1,3]*a[2,3]^2+a[3,3]*a[1,2]^4*a[1,3]^2*a[2,3]^3*a[1,1]-a[3,3]^2*a[1,2]^6*a[1,3]^2*a[2,3]+a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,2]
+a[3,3]^2*a[1,2]^4*a[1,1]^2*a[2,3]^3+a[1,1]^2*a[1,3]^4*a[2,3]^3*a[2,2]^2-a[2,2]^3*a[1,2]*a[1,1]^3*a[1,3]*a[3,3]^3+a[2,2]^3*a[3,3]^2*a[1,3]^2*a[1,1]^3*a[2,3]+2*a[2,2
]^3*a[3,3]^2*a[1,2]*a[1,3]^3*a[1,1]^2-2*a[2,2]^3*a[1,1]^2*a[1,3]^4*a[2,3]*a[3,3]+a[2,2]^2*a[3,3]^3*a[1,2]^2*a[1,1]^3*a[2,3]+2*a[2,2]^2*a[3,3]^3*a[1,2]^3*a[1,1]^2*a[
1,3]-3*a[2,2]^2*a[3,3]^2*a[1,2]^3*a[1,1]*a[1,3]^3-6*a[2,2]^2*a[3,3]^2*a[1,2]^2*a[1,1]^2*a[1,3]^2*a[2,3]+3*a[2,2]^2*a[3,3]*a[1,2]*a[1,3]^3*a[1,1]^2*a[2,3]^2-a[2,2]^2
*a[3,3]*a[1,3]^2*a[1,1]^3*a[2,3]^3+6*a[2,2]^2*a[3,3]*a[1,2]^2*a[1,3]^4*a[1,1]*a[2,3]-3*a[2,2]^2*a[1,2]*a[1,1]*a[1,3]^5*a[2,3]^2-2*a[2,2]*a[1,2]^4*a[1,1]^2*a[2,3]*a[
3,3]^3+3*a[2,2]*a[3,3]^2*a[1,2]^3*a[1,1]^2*a[1,3]*a[2,3]^2+6*a[2,2]*a[3,3]^2*a[1,2]^4*a[1,1]*a[1,3]^2*a[2,3]-a[2,2]*a[3,3]^2*a[1,2]^2*a[1,1]^3*a[2,3]^3-6*a[2,2]*a[3
,3]*a[1,2]^3*a[1,1]*a[1,3]^3*a[2,3]^2+a[2,2]*a[3,3]*a[1,2]*a[1,1]^3*a[1,3]*a[2,3]^4-a[2,2]*a[1,2]*a[1,3]^3*a[1,1]^2*a[2,3]^4+a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^3*a[1,1
]+a[1,2]^3*a[1,1]*a[1,3]^3*a[2,3]^4-a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]+3*a[3,3]*a[1,2]^5*a[1,3]^3*a[2,3]^2+3*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^2-2*a[1,2]^4*a[1,3]^4*a[
2,3]^3)*a[1,1]^2*a[2,3]/(a[3,3]*a[2,2]-a[2,3]^2)/(4*a[1,2]^2*a[3,3]^2*a[1,1]*a[1,3]^2*a[2,2]^2-4*a[2,2]^2*a[3,3]*a[1,2]*a[1,3]^3*a[1,1]*a[2,3]-a[1,2]^2*a[1,3]^4*a[3
,3]*a[2,2]^2+a[2,2]^2*a[1,1]*a[1,3]^4*a[2,3]^2-4*a[2,2]*a[3,3]^2*a[1,2]^3*a[1,1]*a[1,3]*a[2,3]-a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,2]+2*a[2,2]*a[3,3]*a[1,2]^3*a[2,3]*a[1
,3]^3+2*a[2,2]*a[3,3]*a[1,2]^2*a[2,3]^2*a[1,3]^2*a[1,1]+a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^2+a[1,2]^4*a[1,1]*a[2,3]^2*a[3,3]^2+a[1,2]^4*a[1,3]^2*a[2,3]^2*a[3,3]-2*a[1,
2]^3*a[1,3]^3*a[2,3]^3)*z^6-(-a[2,2]^3*a[3,3]*a[1,2]*a[1,1]*a[1,3]^5-a[2,2]*a[3,3]^3*a[1,2]^5*a[1,1]*a[1,3]-2*a[3,3]*a[1,2]^3*a[1,1]^2*a[1,3]*a[2,3]^4+2*a[2,2]*a[3,
3]*a[1,2]^4*a[1,3]^4*a[2,3]+a[3,3]^2*a[1,2]^5*a[1,1]*a[1,3]*a[2,3]^2-4*a[3,3]*a[1,2]^4*a[1,3]^2*a[2,3]^3*a[1,1]+a[3,3]^2*a[1,2]^6*a[1,3]^2*a[2,3]+3*a[3,3]^2*a[1,2]^
4*a[1,1]^2*a[2,3]^3+3*a[1,1]^2*a[1,3]^4*a[2,3]^3*a[2,2]^2-5*a[2,2]^3*a[1,2]*a[1,1]^3*a[1,3]*a[3,3]^3+4*a[2,2]^3*a[3,3]^2*a[1,3]^2*a[1,1]^3*a[2,3]+6*a[2,2]^3*a[3,3]^
2*a[1,2]*a[1,3]^3*a[1,1]^2-4*a[2,2]^3*a[1,1]^2*a[1,3]^4*a[2,3]*a[3,3]+4*a[2,2]^2*a[3,3]^3*a[1,2]^2*a[1,1]^3*a[2,3]+6*a[2,2]^2*a[3,3]^3*a[1,2]^3*a[1,1]^2*a[1,3]-5*a[
2,2]^2*a[3,3]^2*a[1,2]^3*a[1,1]*a[1,3]^3+2*a[2,2]^2*a[3,3]^2*a[1,2]*a[1,1]^3*a[1,3]*a[2,3]^2-12*a[2,2]^2*a[3,3]^2*a[1,2]^2*a[1,1]^2*a[1,3]^2*a[2,3]-4*a[2,2]^2*a[3,3
]*a[1,3]^2*a[1,1]^3*a[2,3]^3+4*a[2,2]^2*a[3,3]*a[1,2]^2*a[1,3]^4*a[1,1]*a[2,3]+a[2,2]^2*a[1,2]*a[1,1]*a[1,3]^5*a[2,3]^2-4*a[2,2]*a[1,2]^4*a[1,1]^2*a[2,3]*a[3,3]^3+4
*a[2,2]*a[3,3]^2*a[1,2]^4*a[1,1]*a[1,3]^2*a[2,3]-4*a[2,2]*a[3,3]^2*a[1,2]^2*a[1,1]^3*a[2,3]^3+4*a[2,2]*a[3,3]*a[1,2]^3*a[1,1]*a[1,3]^3*a[2,3]^2+6*a[2,2]*a[3,3]*a[1,
2]^2*a[1,1]^2*a[1,3]^2*a[2,3]^3+3*a[2,2]*a[3,3]*a[1,2]*a[1,1]^3*a[1,3]*a[2,3]^4-2*a[2,2]*a[1,2]*a[1,3]^3*a[1,1]^2*a[2,3]^4-4*a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^3*a[1,1
]+a[1,2]^3*a[1,1]*a[1,3]^3*a[2,3]^4+a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]-4*a[3,3]*a[1,2]^5*a[1,3]^3*a[2,3]^2-4*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^2+4*a[1,2]^4*a[1,3]^4*a[
2,3]^3)*a[1,1]*a[2,3]/(a[3,3]*a[2,2]-a[2,3]^2)/(4*a[1,2]^2*a[3,3]^2*a[1,1]*a[1,3]^2*a[2,2]^2-4*a[2,2]^2*a[3,3]*a[1,2]*a[1,3]^3*a[1,1]*a[2,3]-a[1,2]^2*a[1,3]^4*a[3,3
]*a[2,2]^2+a[2,2]^2*a[1,1]*a[1,3]^4*a[2,3]^2-4*a[2,2]*a[3,3]^2*a[1,2]^3*a[1,1]*a[1,3]*a[2,3]-a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,2]+2*a[2,2]*a[3,3]*a[1,2]^3*a[2,3]*a[1,3
]^3+2*a[2,2]*a[3,3]*a[1,2]^2*a[2,3]^2*a[1,3]^2*a[1,1]+a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^2+a[1,2]^4*a[1,1]*a[2,3]^2*a[3,3]^2+a[1,2]^4*a[1,3]^2*a[2,3]^2*a[3,3]-2*a[1,2]
^3*a[1,3]^3*a[2,3]^3)*z^4+(-a[1,2]^3*a[1,3]^5*a[3,3]*a[2,2]^2-a[3,3]*a[1,2]^3*a[1,1]^2*a[1,3]*a[2,3]^4+2*a[2,2]*a[3,3]*a[1,2]^4*a[1,3]^4*a[2,3]+2*a[3,3]^2*a[1,2]^5*
a[1,1]*a[1,3]*a[2,3]^2-2*a[3,3]*a[1,2]^4*a[1,3]^2*a[2,3]^3*a[1,1]-a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,2]+2*a[3,3]^2*a[1,2]^4*a[1,1]^2*a[2,3]^3+2*a[1,1]^2*a[1,3]^4*a[2,3]
^3*a[2,2]^2-7*a[2,2]^3*a[1,2]*a[1,1]^3*a[1,3]*a[3,3]^3+5*a[2,2]^3*a[3,3]^2*a[1,3]^2*a[1,1]^3*a[2,3]+3*a[2,2]^3*a[3,3]^2*a[1,2]*a[1,3]^3*a[1,1]^2-a[2,2]^3*a[1,1]^2*a
[1,3]^4*a[2,3]*a[3,3]+5*a[2,2]^2*a[3,3]^3*a[1,2]^2*a[1,1]^3*a[2,3]+3*a[2,2]^2*a[3,3]^3*a[1,2]^3*a[1,1]^2*a[1,3]+4*a[2,2]^2*a[3,3]^2*a[1,2]^3*a[1,1]*a[1,3]^3+4*a[2,2
]^2*a[3,3]^2*a[1,2]*a[1,1]^3*a[1,3]*a[2,3]^2-2*a[2,2]^2*a[3,3]^2*a[1,2]^2*a[1,1]^2*a[1,3]^2*a[2,3]-6*a[2,2]^2*a[3,3]*a[1,2]*a[1,3]^3*a[1,1]^2*a[2,3]^2-5*a[2,2]^2*a[
3,3]*a[1,3]^2*a[1,1]^3*a[2,3]^3-6*a[2,2]^2*a[3,3]*a[1,2]^2*a[1,3]^4*a[1,1]*a[2,3]+2*a[2,2]^2*a[1,2]*a[1,1]*a[1,3]^5*a[2,3]^2-a[2,2]*a[1,2]^4*a[1,1]^2*a[2,3]*a[3,3]^
3-6*a[2,2]*a[3,3]^2*a[1,2]^3*a[1,1]^2*a[1,3]*a[2,3]^2-6*a[2,2]*a[3,3]^2*a[1,2]^4*a[1,1]*a[1,3]^2*a[2,3]-5*a[2,2]*a[3,3]^2*a[1,2]^2*a[1,1]^3*a[2,3]^3+8*a[2,2]*a[3,3]
*a[1,2]^3*a[1,1]*a[1,3]^3*a[2,3]^2+8*a[2,2]*a[3,3]*a[1,2]^2*a[1,1]^2*a[1,3]^2*a[2,3]^3+3*a[2,2]*a[3,3]*a[1,2]*a[1,1]^3*a[1,3]*a[2,3]^4-a[2,2]*a[1,2]*a[1,3]^3*a[1,1]
^2*a[2,3]^4-2*a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^3*a[1,1]+a[3,3]*a[1,2]^5*a[1,3]^3*a[2,3]^2+a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^2-2*a[1,2]^4*a[1,3]^4*a[2,3]^3)*a[2,3]/(a[3
,3]*a[2,2]-a[2,3]^2)/(4*a[1,2]^2*a[3,3]^2*a[1,1]*a[1,3]^2*a[2,2]^2-4*a[2,2]^2*a[3,3]*a[1,2]*a[1,3]^3*a[1,1]*a[2,3]-a[1,2]^2*a[1,3]^4*a[3,3]*a[2,2]^2+a[2,2]^2*a[1,1]
*a[1,3]^4*a[2,3]^2-4*a[2,2]*a[3,3]^2*a[1,2]^3*a[1,1]*a[1,3]*a[2,3]-a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,2]+2*a[2,2]*a[3,3]*a[1,2]^3*a[2,3]*a[1,3]^3+2*a[2,2]*a[3,3]*a[1,2]
^2*a[2,3]^2*a[1,3]^2*a[1,1]+a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^2+a[1,2]^4*a[1,1]*a[2,3]^2*a[3,3]^2+a[1,2]^4*a[1,3]^2*a[2,3]^2*a[3,3]-2*a[1,2]^3*a[1,3]^3*a[2,3]^3)*z^2-
(-3*a[1,1]^2*a[2,2]^3*a[1,2]*a[1,3]*a[3,3]^3+2*a[1,1]^2*a[2,2]^3*a[1,3]^2*a[2,3]*a[3,3]^2+2*a[1,1]^2*a[2,2]^2*a[2,3]*a[1,2]^2*a[3,3]^3+2*a[1,1]^2*a[2,2]^2*a[1,2]*a[
1,3]*a[2,3]^2*a[3,3]^2-2*a[1,1]^2*a[2,2]^2*a[2,3]^3*a[1,3]^2*a[3,3]-2*a[1,1]^2*a[2,2]*a[1,2]^2*a[2,3]^3*a[3,3]^2+a[1,1]^2*a[2,2]*a[1,2]*a[1,3]*a[2,3]^4*a[3,3]+a[1,2
]*a[1,3]^3*a[2,2]^3*a[1,1]*a[3,3]^2+a[1,2]^3*a[1,1]*a[1,3]*a[2,2]^2*a[3,3]^3+2*a[1,1]*a[2,2]^2*a[1,3]^2*a[1,2]^2*a[2,3]*a[3,3]^2-5*a[1,1]*a[2,2]^2*a[1,2]*a[1,3]^3*a
[2,3]^2*a[3,3]+a[1,1]*a[1,3]^4*a[2,3]^3*a[2,2]^2-5*a[1,1]*a[2,2]*a[1,2]^3*a[1,3]*a[2,3]^2*a[3,3]^2+4*a[1,1]*a[2,2]*a[1,2]^2*a[1,3]^2*a[2,3]^3*a[3,3]+a[1,1]*a[1,2]^4
*a[2,3]^3*a[3,3]^2-a[1,2]^2*a[1,3]^4*a[2,3]*a[3,3]*a[2,2]^2-a[2,2]*a[1,2]^4*a[1,3]^2*a[2,3]*a[3,3]^2+2*a[2,2]*a[1,2]^3*a[1,3]^3*a[2,3]^2*a[3,3]+a[2,2]*a[1,2]^2*a[1,
3]^4*a[2,3]^3+a[1,2]^4*a[1,3]^2*a[2,3]^3*a[3,3]-2*a[1,2]^3*a[1,3]^3*a[2,3]^4)*a[2,3]/(a[3,3]*a[2,2]-a[2,3]^2)/(4*a[1,2]^2*a[3,3]^2*a[1,1]*a[1,3]^2*a[2,2]^2-4*a[2,2]
^2*a[3,3]*a[1,2]*a[1,3]^3*a[1,1]*a[2,3]-a[1,2]^2*a[1,3]^4*a[3,3]*a[2,2]^2+a[2,2]^2*a[1,1]*a[1,3]^4*a[2,3]^2-4*a[2,2]*a[3,3]^2*a[1,2]^3*a[1,1]*a[1,3]*a[2,3]-a[1,2]^4
*a[1,3]^2*a[3,3]^2*a[2,2]+2*a[2,2]*a[3,3]*a[1,2]^3*a[2,3]*a[1,3]^3+2*a[2,2]*a[3,3]*a[1,2]^2*a[2,3]^2*a[1,3]^2*a[1,1]+a[2,2]*a[1,2]^2*a[1,3]^4*a[2,3]^2+a[1,2]^4*a[1,
1]*a[2,3]^2*a[3,3]^2+a[1,2]^4*a[1,3]^2*a[2,3]^2*a[3,3]-2*a[1,2]^3*a[1,3]^3*a[2,3]^3), -(-2*a[2,3]^5*a[1,1]*a[1,2]^5*a[1,3]^5-2*a[3,3]^3*a[1,1]*a[1,2]^8*a[1,3]^2*a[2
,3]^2+a[3,3]^3*a[1,1]^3*a[1,2]^6*a[2,3]^4+a[3,3]^2*a[1,2]^8*a[1,3]^4*a[2,3]^2-4*a[3,3]*a[1,2]^7*a[1,3]^5*a[2,3]^3-3*a[2,2]*a[1,1]*a[1,2]^4*a[1,3]^6*a[2,3]^4-4*a[2,2
]*a[1,2]^5*a[1,3]^7*a[2,3]^3+4*a[3,3]*a[1,1]^2*a[1,2]^5*a[1,3]^3*a[2,3]^5-7*a[3,3]*a[1,1]*a[1,2]^6*a[1,3]^4*a[2,3]^4+2*a[2,2]*a[1,1]^2*a[1,2]^3*a[1,3]^5*a[2,3]^5+2*
a[3,3]^2*a[1,1]^2*a[1,2]^6*a[1,3]^2*a[2,3]^4+8*a[3,3]^2*a[2,3]^3*a[1,1]*a[1,2]^7*a[1,3]^3-2*a[2,2]^4*a[1,1]^4*a[1,2]^2*a[1,3]^2*a[3,3]^4+2*a[2,2]^4*a[3,3]^3*a[1,1]^
4*a[1,2]*a[1,3]^3*a[2,3]+5*a[2,2]^4*a[3,3]^3*a[1,1]^3*a[1,2]^2*a[1,3]^4-a[2,2]^4*a[3,3]^2*a[1,1]^4*a[1,3]^4*a[2,3]^2+2*a[2,2]^4*a[3,3]*a[1,1]^2*a[1,2]*a[1,3]^7*a[2,
3]+5*a[2,2]^3*a[3,3]^4*a[1,1]^3*a[1,2]^4*a[1,3]^2-4*a[2,2]^4*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^5*a[2,3]-4*a[2,2]^4*a[3,3]^2*a[1,1]^2*a[1,2]^2*a[1,3]^6+2*a[2,2]^4*a[3,
3]*a[1,1]^3*a[1,3]^6*a[2,3]^2+2*a[2,2]*a[3,3]^2*a[1,1]^4*a[1,2]^3*a[1,3]*a[2,3]^5-a[2,2]^3*a[3,3]*a[1,2]^4*a[1,3]^8-2*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]^4*a
[2,3]^2+6*a[2,2]^3*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^6-2*a[2,2]^3*a[3,3]^2*a[1,1]^4*a[1,2]*a[1,3]^3*a[2,3]^3-10*a[2,2]^3*a[3,3]^3*a[1,1]^2*a[1,2]^4*a[1,3]^4-10*a[2,2]
^3*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]^3*a[2,3]+4*a[2,2]^3*a[3,3]^3*a[1,1]^4*a[1,2]^2*a[1,3]^2*a[2,3]^2-a[2,2]^4*a[1,1]^2*a[1,3]^8*a[2,3]^2-2*a[2,2]^3*a[3,3]*a[1,1]^2
*a[1,2]^2*a[1,3]^6*a[2,3]^2+a[2,2]^3*a[3,3]*a[1,1]^4*a[1,3]^4*a[2,3]^4+a[2,2]*a[3,3]^4*a[1,1]*a[1,2]^8*a[1,3]^2-4*a[2,2]^2*a[3,3]^4*a[1,1]^2*a[1,2]^6*a[1,3]^2+a[2,2
]^2*a[3,3]^4*a[1,1]^4*a[1,2]^4*a[2,3]^2-a[2,2]^3*a[1,1]^3*a[1,3]^6*a[2,3]^4-2*a[2,2]^2*a[3,3]^2*a[1,2]^6*a[1,3]^6+a[2,2]^2*a[1,2]^4*a[1,3]^8*a[2,3]^2-a[2,2]*a[3,3]^
3*a[1,2]^8*a[1,3]^4-6*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]^7*a[2,3]+2*a[2,2]^3*a[1,1]^2*a[1,2]*a[2,3]^3*a[1,3]^7+4*a[1,2]^6*a[1,3]^6*a[2,3]^4-10*a[2,2]^2*a[3,3]^3
*a[1,1]^3*a[1,2]^4*a[1,3]^2*a[2,3]^2+12*a[2,2]^2*a[3,3]^3*a[1,1]^2*a[1,2]^5*a[1,3]^3*a[2,3]+6*a[2,2]^2*a[3,3]^3*a[1,1]*a[1,2]^6*a[1,3]^4+a[2,2]^4*a[3,3]*a[1,1]*a[1,
2]^2*a[1,3]^8+a[1,1]^2*a[1,2]^8*a[2,3]^2*a[3,3]^4-2*a[2,2]^2*a[3,3]^3*a[1,1]^4*a[1,2]^3*a[1,3]*a[2,3]^3-2*a[2,2]^2*a[3,3]^2*a[1,1]^4*a[1,2]^2*a[1,3]^2*a[2,3]^4+2*a[
2,2]^2*a[1,1]*a[1,2]^3*a[1,3]^7*a[2,3]^3+6*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^4*a[2,3]^2-16*a[2,2]^2*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^5*a[2,3]+4*a[2,2]^2*a[3
,3]*a[1,2]^5*a[1,3]^7*a[2,3]+14*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]^3*a[2,3]^3+2*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^6*a[2,3]^2+2*a[2,2]^2*a[3,3]*a[1,1]^3
*a[1,2]^2*a[1,3]^4*a[2,3]^4-14*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^5*a[2,3]^3+16*a[2,2]^3*a[3,3]^2*a[1,1]^2*a[1,2]^3*a[1,3]^5*a[2,3]-2*a[3,3]^2*a[1,1]^3*a[1,2]
^5*a[1,3]*a[2,3]^5-2*a[2,2]*a[1,1]^3*a[1,2]^6*a[2,3]^2*a[3,3]^4+8*a[2,2]*a[3,3]^3*a[1,1]^2*a[1,2]^6*a[1,3]^2*a[2,3]^2-a[2,2]*a[3,3]^3*a[1,1]^4*a[1,2]^4*a[2,3]^4-4*a
[2,2]*a[3,3]^3*a[1,1]*a[1,2]^7*a[1,3]^3*a[2,3]+6*a[2,2]*a[3,3]^3*a[1,1]^3*a[1,2]^5*a[1,3]*a[2,3]^3+4*a[2,2]*a[3,3]^2*a[1,2]^7*a[1,3]^5*a[2,3]-4*a[3,3]^3*a[2,3]^3*a[
1,1]^2*a[1,2]^7*a[1,3]-4*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^6*a[1,3]^4*a[2,3]^2+18*a[2,2]*a[3,3]*a[1,1]*a[1,2]^5*a[1,3]^5*a[2,3]^3-20*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^5*a
[1,3]^3*a[2,3]^3-4*a[2,2]*a[3,3]*a[1,1]^3*a[1,2]^3*a[1,3]^3*a[2,3]^5+4*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^4*a[1,3]^4*a[2,3]^4-2*a[2,2]*a[3,3]*a[2,3]^2*a[1,2]^6*a[1,3]^6)
*a[1,1]/(a[1,2]^2*a[1,3]^6*a[2,3]^4*a[2,2]^2+a[1,2]^2*a[1,3]^6*a[3,3]^2*a[2,2]^4+a[1,1]*a[1,3]^6*a[2,3]^4*a[2,2]^3-a[1,2]^6*a[1,3]^2*a[3,3]^4*a[2,2]^2-2*a[1,2]^3*a[
1,3]^5*a[2,3]^5*a[2,2]-3*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^2-4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^3-2*a[1,2]^2*a[1,3]^6*a[3,3]*a[2,3]^2*a
[2,2]^3+a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^2+3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^3+4*a[1,2]^3*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^2-a[1,1]*
a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]+a[1,1]*a[1,2]^6*a[3,3]^4*a[2,3]^2*a[2,2]+4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]+4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3
]^2*a[2,3]*a[2,2]^4-4*a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]-2*a[1,2]^3*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^3+2*a[1,2]^5*a[1,3]^3*a[3,3]*a[2,3]^5+2*a[1,2]^5*a[1,3]^
3*a[3,3]^3*a[2,3]*a[2,2]^2-a[1,2]^6*a[1,3]^2*a[3,3]^2*a[2,3]^4-a[1,1]*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^4+4*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^4*a[2,2]^3-4*a[1,1]*a[1,2]
^2*a[1,3]^4*a[3,3]^3*a[2,2]^4+2*a[1,2]^6*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]-a[1,1]*a[1,2]^6*a[3,3]^3*a[2,3]^4-4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^2)*z^6+
(-4*a[2,3]^5*a[1,1]*a[1,2]^5*a[1,3]^5+a[3,3]^3*a[1,1]*a[1,2]^8*a[1,3]^2*a[2,3]^2+3*a[3,3]^3*a[1,1]^3*a[1,2]^6*a[2,3]^4-a[3,3]^2*a[1,2]^8*a[1,3]^4*a[2,3]^2+4*a[3,3]*
a[1,2]^7*a[1,3]^5*a[2,3]^3+2*a[2,2]*a[1,1]*a[1,2]^4*a[1,3]^6*a[2,3]^4+4*a[2,2]*a[1,2]^5*a[1,3]^7*a[2,3]^3+8*a[3,3]*a[1,1]^2*a[1,2]^5*a[1,3]^3*a[2,3]^5+10*a[3,3]*a[1
,1]*a[1,2]^6*a[1,3]^4*a[2,3]^4+6*a[2,2]*a[1,1]^2*a[1,2]^3*a[1,3]^5*a[2,3]^5-9*a[3,3]^2*a[1,1]^2*a[1,2]^6*a[1,3]^2*a[2,3]^4-6*a[3,3]^2*a[2,3]^3*a[1,1]*a[1,2]^7*a[1,3
]^3-6*a[2,2]^4*a[1,1]^4*a[1,2]^2*a[1,3]^2*a[3,3]^4+8*a[2,2]^4*a[3,3]^3*a[1,1]^4*a[1,2]*a[1,3]^3*a[2,3]+8*a[2,2]^4*a[3,3]^3*a[1,1]^3*a[1,2]^2*a[1,3]^4-4*a[2,2]^4*a[3
,3]^2*a[1,1]^4*a[1,3]^4*a[2,3]^2+8*a[2,2]^3*a[3,3]^4*a[1,1]^3*a[1,2]^4*a[1,3]^2-2*a[2,2]^3*a[3,3]^4*a[1,1]^4*a[1,2]^3*a[1,3]*a[2,3]-8*a[2,2]^4*a[3,3]^2*a[1,1]^3*a[1
,2]*a[1,3]^5*a[2,3]-2*a[2,2]^4*a[3,3]^2*a[1,1]^2*a[1,2]^2*a[1,3]^6+4*a[2,2]^4*a[3,3]*a[1,1]^3*a[1,3]^6*a[2,3]^2+6*a[2,2]*a[3,3]^2*a[1,1]^4*a[1,2]^3*a[1,3]*a[2,3]^5+
a[2,2]^3*a[3,3]*a[1,2]^4*a[1,3]^8-8*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]^4*a[2,3]^2-2*a[2,2]^3*a[3,3]^2*a[1,1]*a[1,2]^4*a[1,3]^6-8*a[2,2]^3*a[3,3]^2*a[1,1]^4*
a[1,2]*a[1,3]^3*a[2,3]^3-6*a[2,2]^3*a[3,3]^3*a[1,1]^2*a[1,2]^4*a[1,3]^4-12*a[2,2]^3*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]^3*a[2,3]+12*a[2,2]^3*a[3,3]^3*a[1,1]^4*a[1,2]^
2*a[1,3]^2*a[2,3]^2+3*a[2,2]^3*a[3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2+4*a[2,2]^3*a[3,3]*a[2,3]^3*a[1,1]^3*a[1,2]*a[1,3]^5+4*a[2,2]^3*a[3,3]*a[1,1]^4*a[1,3]^4*a[
2,3]^4-2*a[2,2]*a[3,3]^4*a[1,1]^2*a[1,2]^7*a[1,3]*a[2,3]-2*a[2,2]^2*a[3,3]^4*a[1,1]^2*a[1,2]^6*a[1,3]^2+4*a[2,2]^2*a[3,3]^4*a[1,1]^4*a[1,2]^4*a[2,3]^2+4*a[2,2]^2*a[
3,3]^4*a[1,1]^3*a[1,2]^5*a[1,3]*a[2,3]-3*a[2,2]^3*a[1,1]^3*a[1,3]^6*a[2,3]^4+2*a[2,2]^2*a[3,3]^2*a[1,2]^6*a[1,3]^6-a[2,2]^2*a[1,2]^4*a[1,3]^8*a[2,3]^2+a[2,2]*a[3,3]
^3*a[1,2]^8*a[1,3]^4+2*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]^3*a[1,3]^7*a[2,3]-a[2,2]^3*a[1,1]*a[1,2]^2*a[1,3]^8*a[2,3]^2-4*a[1,2]^6*a[1,3]^6*a[2,3]^4-24*a[2,2]^2*a[3,3]^3*
a[1,1]^3*a[1,2]^4*a[1,3]^2*a[2,3]^2-2*a[2,2]^2*a[3,3]^3*a[1,1]*a[1,2]^6*a[1,3]^4-4*a[2,2]^2*a[3,3]^3*a[1,1]^4*a[1,2]^3*a[1,3]*a[2,3]^3-6*a[2,2]^2*a[3,3]^2*a[1,1]^4*
a[1,2]^2*a[1,3]^2*a[2,3]^4+2*a[2,2]^2*a[1,1]*a[1,2]^3*a[1,3]^7*a[2,3]^3+14*a[2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^4*a[2,3]^2+8*a[2,2]^2*a[3,3]^2*a[1,1]*a[1,2]^5
*a[1,3]^5*a[2,3]-4*a[2,2]^2*a[3,3]*a[1,2]^5*a[1,3]^7*a[2,3]+24*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]^3*a[2,3]^3-5*a[2,2]^2*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^6*a[2,
3]^2-a[2,2]^2*a[1,1]^2*a[1,2]^2*a[1,3]^6*a[2,3]^4+5*a[2,2]^2*a[3,3]*a[1,1]^3*a[1,2]^2*a[1,3]^4*a[2,3]^4-14*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^5*a[2,3]^3+8*a[2
,2]^3*a[3,3]^2*a[1,1]^2*a[1,2]^3*a[1,3]^5*a[2,3]-4*a[3,3]^2*a[1,1]^3*a[1,2]^5*a[1,3]*a[2,3]^5-4*a[2,2]*a[1,1]^3*a[1,2]^6*a[2,3]^2*a[3,3]^4+11*a[2,2]*a[3,3]^3*a[1,1]
^2*a[1,2]^6*a[1,3]^2*a[2,3]^2-4*a[2,2]*a[3,3]^3*a[1,1]^4*a[1,2]^4*a[2,3]^4+2*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^7*a[1,3]^3*a[2,3]+4*a[2,2]*a[3,3]^3*a[1,1]^3*a[1,2]^5*a[1
,3]*a[2,3]^3-4*a[2,2]*a[3,3]^2*a[1,2]^7*a[1,3]^5*a[2,3]+2*a[3,3]^3*a[2,3]^3*a[1,1]^2*a[1,2]^7*a[1,3]-3*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^6*a[1,3]^4*a[2,3]^2-4*a[2,2]*a[
3,3]*a[1,1]*a[1,2]^5*a[1,3]^5*a[2,3]^3+11*a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^4*a[1,3]^2*a[2,3]^4-8*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^5*a[1,3]^3*a[2,3]^3-12*a[2,2]*a[3,3]
*a[1,1]^3*a[1,2]^3*a[1,3]^3*a[2,3]^5-8*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^4*a[1,3]^4*a[2,3]^4+2*a[2,2]*a[3,3]*a[2,3]^2*a[1,2]^6*a[1,3]^6)/(a[1,2]^2*a[1,3]^6*a[2,3]^4*a[2
,2]^2+a[1,2]^2*a[1,3]^6*a[3,3]^2*a[2,2]^4+a[1,1]*a[1,3]^6*a[2,3]^4*a[2,2]^3-a[1,2]^6*a[1,3]^2*a[3,3]^4*a[2,2]^2-2*a[1,2]^3*a[1,3]^5*a[2,3]^5*a[2,2]-3*a[1,1]*a[1,2]^
4*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^2-4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^3-2*a[1,2]^2*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^3+a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]
*a[2,3]^4*a[2,2]^2+3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^3+4*a[1,2]^3*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^2-a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2
,2]+a[1,1]*a[1,2]^6*a[3,3]^4*a[2,3]^2*a[2,2]+4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]+4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^4-4*a[1,2]^5*a[1,3]^3
*a[3,3]^2*a[2,3]^3*a[2,2]-2*a[1,2]^3*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^3+2*a[1,2]^5*a[1,3]^3*a[3,3]*a[2,3]^5+2*a[1,2]^5*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^2-a[1,2]^6*a[1
,3]^2*a[3,3]^2*a[2,3]^4-a[1,1]*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^4+4*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^4*a[2,2]^3-4*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^3*a[2,2]^4+2*a[1,2]^
6*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]-a[1,1]*a[1,2]^6*a[3,3]^3*a[2,3]^4-4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^2)*z^4-(-2*a[2,3]^5*a[1,2]^5*a[1,3]^5-5*a[3,3]
^2*a[1,1]*a[1,2]^6*a[1,3]^2*a[2,3]^4+4*a[3,3]*a[1,1]*a[1,2]^5*a[1,3]^3*a[2,3]^5+a[3,3]*a[1,2]^6*a[1,3]^4*a[2,3]^4+2*a[3,3]^3*a[1,1]*a[1,2]^7*a[1,3]*a[2,3]^3+2*a[3,3
]^3*a[1,1]^2*a[1,2]^6*a[2,3]^4-6*a[2,2]^3*a[3,3]^2*a[1,1]*a[1,2]^3*a[1,3]^5*a[2,3]+2*a[2,2]^3*a[3,3]*a[1,3]^7*a[2,3]*a[1,2]^3-4*a[2,2]^2*a[3,3]*a[1,2]^4*a[1,3]^6*a[
2,3]^2+6*a[2,2]*a[3,3]^2*a[1,1]^3*a[1,2]^3*a[1,3]*a[2,3]^5-6*a[2,2]^4*a[3,3]^2*a[1,1]^2*a[1,2]*a[1,3]^5*a[2,3]-a[2,2]^3*a[3,3]^2*a[1,2]^4*a[1,3]^6+10*a[2,2]^4*a[3,3
]^3*a[1,1]^3*a[1,2]*a[1,3]^3*a[2,3]-5*a[2,2]^4*a[3,3]^2*a[1,1]^3*a[1,3]^4*a[2,3]^2-2*a[2,2]^4*a[3,3]^2*a[1,1]*a[1,2]^2*a[1,3]^6-2*a[2,2]^2*a[1,2]^3*a[1,3]^7*a[2,3]^
3-6*a[2,2]^4*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[3,3]^4+7*a[2,2]^4*a[3,3]^3*a[1,1]^2*a[1,2]^2*a[1,3]^4-2*a[3,3]^2*a[1,1]^2*a[1,2]^5*a[1,3]*a[2,3]^5-4*a[2,2]^3*a[3,3]^4*a[1
,1]^3*a[1,2]^3*a[1,3]*a[2,3]+2*a[2,2]^4*a[1,1]^2*a[1,3]^6*a[2,3]^2*a[3,3]+3*a[2,2]^3*a[3,3]^4*a[1,1]^2*a[1,2]^4*a[1,3]^2-4*a[2,2]^3*a[3,3]^3*a[1,1]^2*a[1,2]^3*a[1,3
]^3*a[2,3]+5*a[2,2]*a[1,2]^4*a[1,3]^6*a[2,3]^4+12*a[2,2]^3*a[3,3]^3*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]^2+a[2,2]^3*a[3,3]^3*a[1,1]*a[1,2]^4*a[1,3]^4-15*a[2,2]^3*a[3,3
]^2*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]^2-a[2,2]^2*a[3,3]^4*a[1,1]*a[1,2]^6*a[1,3]^2-10*a[2,2]^3*a[3,3]^2*a[1,1]^3*a[1,2]*a[1,3]^3*a[2,3]^3-3*a[2,2]^3*a[1,1]^2*a[1,3]
^6*a[2,3]^4+12*a[2,2]^3*a[3,3]*a[1,1]*a[1,2]^2*a[1,3]^6*a[2,3]^2+5*a[2,2]^3*a[3,3]*a[1,1]^3*a[1,3]^4*a[2,3]^4+4*a[2,2]^2*a[3,3]^4*a[1,1]^2*a[1,2]^5*a[1,3]*a[2,3]+5*
a[2,2]^2*a[3,3]^4*a[1,1]^3*a[1,2]^4*a[2,3]^2+10*a[2,2]^3*a[3,3]*a[1,1]^2*a[1,2]*a[1,3]^5*a[2,3]^3-2*a[2,2]^3*a[1,1]*a[1,2]*a[2,3]^3*a[1,3]^7-14*a[2,2]^2*a[3,3]^3*a[
1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]^2-2*a[2,2]^2*a[3,3]^3*a[1,1]^3*a[1,2]^3*a[1,3]*a[2,3]^3-a[2,2]^2*a[3,3]^3*a[1,2]^6*a[1,3]^4+10*a[2,2]^2*a[3,3]^2*a[1,1]*a[1,2]^4*a[1
,3]^4*a[2,3]^2-5*a[2,2]*a[3,3]^3*a[1,1]^3*a[1,2]^4*a[2,3]^4-6*a[2,2]^2*a[3,3]^2*a[1,1]^3*a[1,2]^2*a[1,3]^2*a[2,3]^4-a[2,2]*a[1,1]^2*a[1,2]^6*a[2,3]^2*a[3,3]^4+16*a[
2,2]^2*a[3,3]^2*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]^3+4*a[2,2]^2*a[3,3]^2*a[1,2]^5*a[1,3]^5*a[2,3]-2*a[2,2]^2*a[1,1]*a[2,3]^4*a[1,2]^2*a[1,3]^6-10*a[2,2]^2*a[3,3]*a[1
,1]*a[1,2]^3*a[1,3]^5*a[2,3]^3+3*a[2,2]^2*a[3,3]*a[1,1]^2*a[1,2]^2*a[1,3]^4*a[2,3]^4-2*a[2,2]*a[3,3]^3*a[1,1]*a[1,2]^6*a[1,3]^2*a[2,3]^2-6*a[2,2]*a[3,3]^3*a[1,1]^2*
a[1,2]^5*a[1,3]*a[2,3]^3+6*a[2,2]*a[3,3]^2*a[1,1]*a[1,2]^5*a[1,3]^3*a[2,3]^3+16*a[2,2]*a[3,3]^2*a[1,1]^2*a[1,2]^4*a[1,3]^2*a[2,3]^4-2*a[2,2]*a[3,3]*a[1,2]^5*a[1,3]^
5*a[2,3]^3-12*a[2,2]*a[3,3]*a[1,1]^2*a[1,2]^3*a[1,3]^3*a[2,3]^5-11*a[2,2]*a[3,3]*a[1,1]*a[1,2]^4*a[1,3]^4*a[2,3]^4+6*a[2,2]*a[1,1]*a[1,2]^3*a[1,3]^5*a[2,3]^5)/(a[1,
2]^2*a[1,3]^6*a[2,3]^4*a[2,2]^2+a[1,2]^2*a[1,3]^6*a[3,3]^2*a[2,2]^4+a[1,1]*a[1,3]^6*a[2,3]^4*a[2,2]^3-a[1,2]^6*a[1,3]^2*a[3,3]^4*a[2,2]^2-2*a[1,2]^3*a[1,3]^5*a[2,3]
^5*a[2,2]-3*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^2-4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^3-2*a[1,2]^2*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^3+a[1,1
]*a[1,2]^2*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^2+3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^3+4*a[1,2]^3*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^2-a[1,1]*a[1,2]^4*a[1,
3]^2*a[3,3]^2*a[2,3]^4*a[2,2]+a[1,1]*a[1,2]^6*a[3,3]^4*a[2,3]^2*a[2,2]+4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]+4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]^2*a[2,3]*a[
2,2]^4-4*a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]-2*a[1,2]^3*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^3+2*a[1,2]^5*a[1,3]^3*a[3,3]*a[2,3]^5+2*a[1,2]^5*a[1,3]^3*a[3,3]^3*a[
2,3]*a[2,2]^2-a[1,2]^6*a[1,3]^2*a[3,3]^2*a[2,3]^4-a[1,1]*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^4+4*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^4*a[2,2]^3-4*a[1,1]*a[1,2]^2*a[1,3]^4*a
[3,3]^3*a[2,2]^4+2*a[1,2]^6*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]-a[1,1]*a[1,2]^6*a[3,3]^3*a[2,3]^4-4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^4*a[2,3]*a[2,2]^2)*z^2+a[2,2]*(a[1,2
]^6*a[1,3]^2*a[2,3]^2*a[3,3]^3-2*a[1,2]^5*a[1,3]^3*a[2,3]^3*a[3,3]^2-a[1,2]^4*a[1,3]^4*a[2,3]^4*a[3,3]-a[2,2]^2*a[1,2]^4*a[1,3]^4*a[3,3]^3-a[2,2]*a[1,2]^6*a[1,3]^2*
a[3,3]^4-a[2,2]*a[1,2]^2*a[1,3]^6*a[2,3]^4-2*a[1,1]^2*a[2,2]^3*a[1,2]^2*a[1,3]^2*a[3,3]^4+4*a[1,1]^2*a[2,2]^3*a[1,2]*a[1,3]^3*a[2,3]*a[3,3]^3-2*a[1,1]^2*a[1,3]^4*a[
3,3]^2*a[2,3]^2*a[2,2]^3-2*a[1,1]^2*a[2,2]^2*a[1,2]^3*a[1,3]*a[2,3]*a[3,3]^4+4*a[1,1]^2*a[2,2]^2*a[1,2]^2*a[1,3]^2*a[2,3]^2*a[3,3]^3+2*a[1,1]^2*a[1,3]^4*a[3,3]*a[2,
3]^4*a[2,2]^2-4*a[1,1]^2*a[2,2]^2*a[1,2]*a[1,3]^3*a[2,3]^3*a[3,3]^2+2*a[1,1]^2*a[2,2]*a[1,2]^4*a[2,3]^2*a[3,3]^4-2*a[1,1]^2*a[2,2]*a[1,2]^2*a[1,3]^2*a[2,3]^4*a[3,3]
^2+2*a[1,1]^2*a[1,2]^3*a[1,3]*a[2,3]^5*a[3,3]^2+4*a[1,1]*a[2,2]^2*a[1,2]^4*a[1,3]^2*a[3,3]^4-2*a[1,1]*a[2,2]^2*a[1,2]^3*a[2,3]*a[1,3]^3*a[3,3]^3-5*a[1,1]*a[2,2]^2*a
[1,2]^2*a[1,3]^4*a[2,3]^2*a[3,3]^2+4*a[1,1]*a[2,2]^2*a[1,2]*a[1,3]^5*a[2,3]^3*a[3,3]-2*a[1,1]*a[2,2]*a[1,2]^5*a[1,3]*a[2,3]*a[3,3]^4-4*a[1,1]*a[2,2]*a[1,2]^4*a[1,3]
^2*a[2,3]^2*a[3,3]^3+6*a[1,1]*a[2,2]*a[1,2]^3*a[1,3]^3*a[2,3]^3*a[3,3]^2-2*a[1,1]*a[2,3]^3*a[1,2]^5*a[1,3]*a[3,3]^3+5*a[1,1]*a[1,2]^4*a[1,3]^2*a[2,3]^4*a[3,3]^2-4*a
[1,1]*a[1,2]^3*a[1,3]^3*a[2,3]^5*a[3,3]+2*a[1,2]^3*a[1,3]^5*a[2,3]^5+a[2,2]^2*a[1,2]^2*a[1,3]^6*a[2,3]^2*a[3,3]+2*a[2,2]*a[1,2]^5*a[1,3]^3*a[2,3]*a[3,3]^3+2*a[2,2]*
a[1,2]^4*a[1,3]^4*a[2,3]^2*a[3,3]^2-2*a[2,2]*a[1,2]^3*a[1,3]^5*a[2,3]^3*a[3,3]-2*a[1,1]^2*a[1,2]^4*a[2,3]^4*a[3,3]^3-a[1,1]*a[1,3]^6*a[2,3]^4*a[2,2]^2+a[1,1]*a[1,2]
^6*a[2,3]^2*a[3,3]^4)/(a[1,2]^2*a[1,3]^6*a[2,3]^4*a[2,2]^2+a[1,2]^2*a[1,3]^6*a[3,3]^2*a[2,2]^4+a[1,1]*a[1,3]^6*a[2,3]^4*a[2,2]^3-a[1,2]^6*a[1,3]^2*a[3,3]^4*a[2,2]^2
-2*a[1,2]^3*a[1,3]^5*a[2,3]^5*a[2,2]-3*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]^2-4*a[1,1]*a[1,2]*a[1,3]^5*a[3,3]*a[2,3]^3*a[2,2]^3-2*a[1,2]^2*a[1,3]^6*a[3
,3]*a[2,3]^2*a[2,2]^3+a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]*a[2,3]^4*a[2,2]^2+3*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^2*a[2,3]^2*a[2,2]^3+4*a[1,2]^3*a[1,3]^5*a[3,3]*a[2,3]^3*a[
2,2]^2-a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^2*a[2,3]^4*a[2,2]+a[1,1]*a[1,2]^6*a[3,3]^4*a[2,3]^2*a[2,2]+4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^3*a[2,3]^3*a[2,2]+4*a[1,1]*a[1,2]*
a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^4-4*a[1,2]^5*a[1,3]^3*a[3,3]^2*a[2,3]^3*a[2,2]-2*a[1,2]^3*a[1,3]^5*a[3,3]^2*a[2,3]*a[2,2]^3+2*a[1,2]^5*a[1,3]^3*a[3,3]*a[2,3]^5+2*a[
1,2]^5*a[1,3]^3*a[3,3]^3*a[2,3]*a[2,2]^2-a[1,2]^6*a[1,3]^2*a[3,3]^2*a[2,3]^4-a[1,1]*a[1,3]^6*a[3,3]*a[2,3]^2*a[2,2]^4+4*a[1,1]*a[1,2]^4*a[1,3]^2*a[3,3]^4*a[2,2]^3-4
*a[1,1]*a[1,2]^2*a[1,3]^4*a[3,3]^3*a[2,2]^4+2*a[1,2]^6*a[1,3]^2*a[3,3]^3*a[2,3]^2*a[2,2]-a[1,1]*a[1,2]^6*a[3,3]^3*a[2,3]^4-4*a[1,1]*a[1,2]^5*a[1,3]*a[3,3]^4*a[2,3]*
a[2,2]^2)]]]
:
end:

#end Precomputed


#Tra(M): The transpose of the matrix M
Tra:=proc(M) local i,j:
[seq([seq(M[i][j],i=1..nops(M))],j=1..nops(M[1]))]:
end:


#RS(M): inputs a matrix M with positive entries M and outputs the matrix obtained by scaling its rows. Try:
#RS([[1,2,3],[2,1,3],[3,2,1]]);
RS:=proc(M) local i,su,M1,j:
M1:=[]:
for i from 1 to nops(M) do
 su:=convert(M[i],`+`):
 if su=0 then
   RETURN(FAIL):
  else
 M1:=[op(M1),[seq(M[i][j]/su,j=1..nops(M[i]))]]:
 fi:
od:

M1:
end:


#CS(M): inputs a matrix M with positive entries M and outputs the matrix obtained by scaling its columns. Try:
#CS([[1,2,3],[2,1,3],[3,2,1]]);
CS:=proc(M):
Tra(RS(Tra(M))):
end:


#Sink(M,N): applies N iterations of Sinkhorn's algorithm to the matrix M. Try
#Sink([[1,3],[2,5]],10);
Sink:=proc(M,N) local i, M1:
M1:=M:
for i from 1 to N do
M1:=normal(CS(RS(M1))):
od:
M1:
end:

#Err1(M): inputs a matrix M and finds out how far it is from a doubly-stochastic matrix. Try:
#Err1([[1/3,2/3],[2/3,1/3]]);
Err1:=proc(M) local i,M1, eR,eC:
eR:=max(seq(abs(convert(M[i],`+`)-1) ,i=1..nops(M))):
M1:=Tra(M):
eC:=max(seq(abs(convert(M1[i],`+`)-1) ,i=1..nops(M1))):
max(eR,eC):
end:

#SinkF(M,N): applies N iterations of Sinkhorn's algorithm to the matrix M using floating point. Try
#SinkF([[1,3],[2,5]],10);
SinkF:=proc(M,N) local i, M1:
M1:=evalf(M):
for i from 1 to N do
M1:=evalf(CS(RS(M1))):
od:
M1:
end:

#SinkE(M,e): inputs a matrix M and an error e, and outputs an approximate doubly-stochastic matrix, as well as the number of iterations. 
#It terminates as soon as the deviation from being doubly-stochastic is  less than e
#SinkE([[1,3],[2,7]],1/10^10);
SinkE:=proc(M,e) local i,M1:
if e<1/10^(Digits-5) then
 print(` e must be at most`, 1/10^(Digits-5)):
 RETURN(FAIL):
fi:

i:=0:
M1:=evalf(M):
for i from 1 while Err1(M1)>e do
 M1:=CS(RS(M1)):
od:

M1,i:

end:

#SinkEe(M,e): inputs a matrix M and an error e, and outputs an approximate doubly-stochastic matrix, as well as the number of iterations. 
#It terminates as soon as the norm of the current iteration minus the actual limit is less than e.Try:
#It only works for symmetric matrices. Try:
#SinkEe([[1,3],[3,7]],1/10^10); 

SinkEe:=proc(M,e) local i,M1,M0,i1,j1:
if e<1/10^(Digits-5) then
 print(` e must be at most`, 1/10^(Digits-5)):
 RETURN(FAIL):
fi:

if Tra(M)<>M then
 print(M, `must be symmetric`):
 RETURN(FAIL):
fi:

M0:=ExacGSf(M):

if M0=FAIL then
 RETURN(FAIL):
fi:
M0:=M0[2]:

i:=0:
M1:=evalf(M):
for i from 1 while 
max(seq(seq(abs(M1[i1][j1]-M0[i1][j1]),j1=1..nops(M[i1])),i1=1..nops(M)))>e do
 M1:=CS(RS(M1)):
od:

M1,i:

end:



#RandM(n,K):  A random n by n matrix with positive integer entries between 1 and K. Try:
#RandM(4,100);
RandM:=proc(n,K) local ra,i,j:
ra:=rand(1..K):
[seq([seq(ra(),j=1..n)],i=1..n)]:
end:

#RandSM(n,K):  A random SYMMETRIC n by n matrix with positive integer entries between 1 and K. Try:
#RandSM(4,100);
RandSM:=proc(n,K) local ra,i,j,T:
ra:=rand(1..K):
for i from 1 to n do
 for j from i to n do
   T[i,j]:=ra():
 od:
od:

[seq([seq(T[j,i],j=1..i-1),seq(T[i,j],j=i..n)],i=1..n)]:

end:




#SinkPlus(M,N): applies N iterations of Sinkhorn's algorithm to the matrix M. Outputs the diagonal matrices X, and Y and S such that
#S=XMY is almost doubly-stochastic. The output is [X,Y,S]. Try
#SinkPlus([[1,3],[2,5]],10);
SinkPlus:=proc(M,N) local i, n,M1,X1,Y1,i1,j1,D1,M2:
if not type(M,list) then
 RETURN(FAIL):
fi:
n:=nops(M):

if not ({seq(type(M[i],list),i=1..n)}={true} and {seq(nops(M[i]),i=1..n)}={n} and min(seq(op(M[i]),i=1..n))>0) then
 print(`Bad input`):
 RETURN(FAIL):
fi:

M1:=M:
X1:=[1$n]:
Y1:=[1$n]:

for i from 1 to N do
D1:=[seq(1/add(M1[i1][j1],j1=1..n),i1=1..n)]:
X1:=[seq(X1[i1]*D1[i1],i1=1..n)]:
M1:=[seq([seq(M1[i1][j1]*D1[i1],j1=1..n)],i1=1..n)]:

D1:=[seq(1/add(M1[i1][j1],i1=1..n),j1=1..n)]:
Y1:=[seq(Y1[i1]*D1[i1],i1=1..n)]:
M1:=[seq([seq(M1[i1][j1]*D1[j1],j1=1..n)],i1=1..n)]:
od:

M2:=[seq([seq(M[i1][j1]*X1[i1],j1=1..n)],i1=1..n)]:
M2:=[seq([seq(M2[i1][j1]*Y1[j1],j1=1..n)],i1=1..n)]:
if M1<>M2 then
 print(`Something terrible happened`):
 RETURN(FAIL):
fi:
[X1,Y1,M1]:
end:


#SinkPlusF(M,N): Floating point version of SinkPlus(M,N) (q.v.). Try:
#SinkPlusF([[1,3],[2,5]],10);
SinkPlusF:=proc(M,N) local i, n,M1,X1,Y1,i1,j1,D1:
if not type(M,list) then
 RETURN(FAIL):
fi:
n:=nops(M):

if not ({seq(type(M[i],list),i=1..n)}={true} and {seq(nops(M[i]),i=1..n)}={n} and min(seq(op(M[i]),i=1..n))>0) then
 print(`Bad input`):
 RETURN(FAIL):
fi:

M1:=evalf(M):
X1:=[1$n]:
Y1:=[1$n]:

for i from 1 to N do
D1:=[seq(1/add(M1[i1][j1],j1=1..n),i1=1..n)]:
X1:=[seq(X1[i1]*D1[i1],i1=1..n)]:
M1:=[seq([seq(M1[i1][j1]*D1[i1],j1=1..n)],i1=1..n)]:

D1:=[seq(1/add(M1[i1][j1],i1=1..n),j1=1..n)]:
Y1:=[seq(Y1[i1]*D1[i1],i1=1..n)]:
M1:=[seq([seq(M1[i1][j1]*D1[j1],j1=1..n)],i1=1..n)]:
od:


[X1,Y1,M1]:
end:

#SinkPlusErr(M,eps): Inputs a square matrix in floating point and outputs [X,Y,M1] where M1=XMY and M1 is approximately
#double-stochastic with error eps. Try:
#SinkPlusErr([[1,3],[2,5]],1/10^9);
SinkPlusErr:=proc(M,eps) local i, n,M1,X1,Y1,i1,j1,D1,k:
if not type(M,list) then
 RETURN(FAIL):
fi:
n:=nops(M):

if not ({seq(type(M[i],list),i=1..n)}={true} and {seq(nops(M[i]),i=1..n)}={n} and min(seq(op(M[i]),i=1..n))>0) then
 print(`Bad input`):
 RETURN(FAIL):
fi:

M1:=evalf(M):
X1:=[1$n]:
Y1:=[1$n]:


 while Err1(M1)>eps do

D1:=[seq(1/add(M1[i1][j1],j1=1..n),i1=1..n)]:
X1:=[seq(X1[i1]*D1[i1],i1=1..n)]:
M1:=[seq([seq(M1[i1][j1]*D1[i1],j1=1..n)],i1=1..n)]:

D1:=[seq(1/add(M1[i1][j1],i1=1..n),j1=1..n)]:
Y1:=[seq(Y1[i1]*D1[i1],i1=1..n)]:

M1:=[seq([seq(M1[i1][j1]*D1[j1],j1=1..n)],i1=1..n)]:
od:

k:=X1[1]:
X1:=[seq(X1[i1]/k,i1=1..n)]:
Y1:=[seq(Y1[i1]*k,i1=1..n)]:
[X1,Y1,M1]:
end:


#ExacF(M): the exact values of the matrices X, Y and S such that X and Y are diagonal matrices, S=XMY , and S is doubly stochastic in Floating point
#May give negative entries
#Try:
#ExacF([[3,4],[6,7]]);
ExacF:=proc(M) local n,x,y,i,eq,var,M1,i1,j1,X,Y:
n:=nops(M):

X:=[1,seq(x[i],i=2..n)]:
Y:=[seq(y[i],i=1..n)]:

var:={seq(x[i],i=2..n),seq(y[i],i=1..n)}:
M1:=[seq([seq(M[i1][j1]*x[i1],j1=1..n)],i1=1..n)]:
M1:=subs(x[1]=1,M1):
M1:=[seq([seq(M1[i1][j1]*y[j1],j1=1..n)],i1=1..n)]:
eq:={seq(add(M1[i1][j1],j1=1..n)-1,i1=2..n),
     seq(add(M1[i1][j1],i1=1..n)-1,j1=1..n)}:



var:=fsolve(eq,var):

[subs(var,X), subs(var,Y), subs(var,M1)]:

end:

#ExacFF(M): the exact values of the matrices X, Y and S such that X and Y are diagonal matrices, S=XMY , and S is doubly stochastic in Floating point
#restricted to [0,1]
#Try:
#ExacFF([[3,4],[6,7]]);
ExacFF:=proc(M) local n,x,y,i,eq,var,M1,i1,j1,X,Y:
n:=nops(M):

X:=[1,seq(x[i],i=2..n)]:
Y:=[seq(y[i],i=1..n)]:

var:={seq(x[i]=0..1,i=2..n),seq(y[i]=0..1,i=1..n)}:
M1:=[seq([seq(M[i1][j1]*x[i1],j1=1..n)],i1=1..n)]:
M1:=subs(x[1]=1,M1):
M1:=[seq([seq(M1[i1][j1]*y[j1],j1=1..n)],i1=1..n)]:
eq:={seq(add(M1[i1][j1],j1=1..n)-1,i1=2..n),
     seq(add(M1[i1][j1],i1=1..n)-1,j1=1..n)}:



var:=fsolve(eq,var):

if type(var,set) then
 [subs(var,X), subs(var,Y), subs(var,M1)]:
  else
 FAIL:
fi:

end:


#Exac(M): the exact values of the matrices X, Y and S such that X and Y are diagonal matrices, S=XMY , and S is doubly stochastic in Floating point
#Try:
#Exac([[3,4],[6,7]]);
Exac:=proc(M) local n,x,y,i,eq,var,M1,i1,j1,X,Y:

if not (type(M,list) and type(M[1],list) and nops(M)=nops(M[1])) then
print(`Bad input`):
RETURN(FAIL):
fi:


 _EnvAllSolutions := true:

n:=nops(M):

X:=[1,seq(x[i],i=2..n)]:
Y:=[seq(y[i],i=1..n)]:

var:={seq(x[i],i=2..n),seq(y[i],i=1..n)}:
M1:=[seq([seq(M[i1][j1]*x[i1],j1=1..n)],i1=1..n)]:
M1:=subs(x[1]=1,M1):
M1:=[seq([seq(M1[i1][j1]*y[j1],j1=1..n)],i1=1..n)]:
eq:={seq(add(M1[i1][j1],j1=1..n)-1,i1=2..n),
     seq(add(M1[i1][j1],i1=1..n)-1,j1=1..n)}:

var:=solve(eq,var):


[subs(var,X), subs(var,Y), subs(var,M1)]:

end:




#ExacSF(M): Inputs a symmetric matrix M, outputs
#the exact values of the matrix X and S such that X is a diagonal matrix, S=XMX , and S is doubly stochastic in Floating point
#Try:
#ExacSF([[3,4],[4,9]]);
ExacSF:=proc(M) local n,x,y,i,eq,var,M1,i1,j1,X,Y:

if Tra(M)<>M then
 print(`Not symmetric`):
  RETURN(FAIL):
fi:

n:=nops(M):


X:=[seq(x[i],i=1..n)]:

var:={seq(x[i],i=1..n)}:
M1:=[seq([seq(M[i1][j1]*x[i1],j1=1..n)],i1=1..n)]:
M1:=[seq([seq(M1[i1][j1]*x[j1],j1=1..n)],i1=1..n)]:
eq:={seq(add(M1[i1][j1],j1=1..n)-1,i1=1..n)}:



var:=fsolve(eq,var):
X:=subs(var,X):

M1:=subs(var,M1):

if X[1]<0 then
 X:=-X:
fi:


if min(seq(seq(M1[i1][j1],i1=1..n),j1=1..n))<0 then
 print(`There are negative entries`):
fi:

[X,M1]:

end:

#ExacG(M,x,y): Like Exca(M) but using Groebner basis where we normalize the (1,1) entry of the diagonal matrix X to be 1 and
#X=Diag(1,x[2], .., x[n]); Y=Diag(y[1], ..., y[n]). 
#Try:
#ExacG([[3,4],[6,7]],x,y);
ExacG:=proc(M,x,y) local n,i,eq,var,M1,i1,j1,X,Y:
if not (type(M,list) and type(M[1],list) and nops(M)=nops(M[1])) then
print(`Bad input`):
RETURN(FAIL):
fi:

n:=nops(M):

X:=[1,seq(x[i],i=2..n)]:
Y:=[seq(y[i],i=1..n)]:

var:=[seq(y[i],i=1..n),seq(x[i],i=2..n)]:
M1:=[seq([seq(M[i1][j1]*x[i1],j1=1..n)],i1=1..n)]:
M1:=subs(x[1]=1,M1):
M1:=[seq([seq(M1[i1][j1]*y[j1],j1=1..n)],i1=1..n)]:
eq:={seq(add(M1[i1][j1],j1=1..n)-1,i1=2..n),
     seq(add(M1[i1][j1],i1=1..n)-1,j1=1..n)}:


Groebner[Basis](eq,plex(op(var) ));

end:


#ExacGS(M,z): Inputs a symmetric matrix M, and a variable name z and outputs the vector
# X=[x[1],x[2], .., x[n]]; such that if X denotes the diagonal matrix with entry X XMX  is doubly-stochastic.
#It returns a triple whose first entry is a list of length n where x[1] is denoted by the variable z, and x[2], ..., x[n] 
#are polynomials in z, and second entry is the minimal polynomial satisfied by z, and the third is the limiting 
#doubly-stochastic matrix
#Try: 
#ExacGS([[3,4],[4,5]],z);
ExacGS:=proc(M,z) local n,i,x,eq,var,M1,i1,j1,lu,vu:

if not (type(M,list) and type(M[1],list) and nops(M)=nops(M[1])) then
print(`Bad input`):
RETURN(FAIL):
fi:


if Tra(M)<>M then
 print(M, `is not symmetric `):
 RETURN(FAIL):
fi:

n:=nops(M):

var:=[seq(x[n-i+1],i=1..n)]:
M1:=[seq([seq(M[i1][j1]*x[i1],j1=1..n)],i1=1..n)]:
M1:=[seq([seq(M1[i1][j1]*x[j1],j1=1..n)],i1=1..n)]:
eq:={seq(add(M1[i1][j1],j1=1..n)-1,i1=1..n)}:


lu:=Groebner[Basis](eq,plex(op(var) ));


vu:=[]:
vu:=[x[1]]:

for i from 2 to n do
 if degree(lu[i],x[i])<>1 then
  print(`Something is wrong`):
  RETURN(FAIL):
 else
 vu:=[op(vu),-normal(coeff(lu[i],x[i],0)/coeff(lu[i],x[i],1))]:
 fi:
od:

vu:=subs(x[1]=z,vu):
lu:=subs(x[1]=z,lu[1]):

M1:=expand(subs({seq(x[i1]=vu[i1],i1=1..n)},M1)):

M1:=[seq([seq(rem(M1[i1][j1],lu,z),j1=1..n)],i1=1..n)]:

[vu,lu, M1 ]:

end:





#CheckSinkPlusErr(M,X,Y,S): Inputs a square matrix in floating point and outputs 
#candidate X,Y,S
#checks that indeed S=XMY and S is approximately double-stochastic with error eps. Try:
#gu:=SinkPlusErr([[1,3],[2,5]],1/10^18);
#CheckSinkPlusErr([[1,3],[2,5]],op(gu),1/10^18);

CheckSinkPlusErr:=proc(M,X,Y,S) local i1, j1,n,S1:

n:=nops(M):

S1:=[seq(X[i1]*M[i1],i1=1..n)]:
S1:=[seq([seq(S1[i1][j1]*Y[i1],j1=1..n)],i1=1..n)]:

min(seq(seq(abs(S[i1][j1]-S1[i1][j1]),j1=1..n),i1=1..n)):
end:




#KefelM(A,B): the products of matrices A and B try:
#KefelM([[1,2],[3,4]],[[5,6],[7,8]]);
KefelM:=proc(A,B) local m,n,r,i,j,k,T:
m:=nops(A):
n:=nops(A[1]):

if nops(B)<>n then
 RETURN(FAIL):
fi:

r:=nops(B[1]):

for i from 1 to m do
for j from 1 to r do
 T[i,j]:=expand(add(A[i][k]*B[k][j],k=1..n)):
od:
od:

[seq([seq(T[i,j],j=1..n)],i=1..n)]:
end:


#CheckExacGS(M,X,p,z,S): Inputs a symmetric square matrix M, a vector X representing a diagonal matrix X phrased
#in terms of z, a polynomial p that is the minimal polynomial satisfied by z and a tentative doubly-stochastic
#matrix. Checks that indeed XMX=S (mod p(z)) and that S is doubly stochastic mod p(z). Try:
#M:=RandSM(3,10): gu:=ExacGS(M,z):CheckExacGS(M,gu[1],gu[2],z,gu[3]):

CheckExacGS:=proc(M,X,p,z,S) local i1, j1,n,S1,MatX:

n:=nops(M):

if {seq(rem(1-convert(S[i1],`+`),p,z),i1=1..n)}<>{0} then
 print(`Not doubly stochastic`):
 RETURN(false):
fi:

S1:=Tra(S):
if {seq(rem(1-convert(S1[i1],`+`),p,z),i1=1..n)}<>{0} then
 print(`Not doubly stochastic`):
 RETURN(false):
fi:

MatX:=[seq( [0$(i1-1),X[i1],0$(n-i1)],i1=1..n)]:

S1:=KefelM(MatX,M):
S1:=KefelM(S1,MatX):

S1:=[seq([seq(rem(S1[i1][j1],p,z),j1=1..n)],i1=1..n)]:

evalb(S=S1):
end:




#ExacGSf(M): inputs a symmetric matrix M and outputs the Exact (numeric) value (in floating-point) of X and S such that S=XMX is doubly-stochastic
#using the  exact procedure ExacGS(M,z).
#Try: 
#ExacGSf([[3,4],[4,5]]);
ExacGSf:=proc(M) local z,X,p,S1,lu,gu,i,z1,X1,i1:
gu:=ExacGS(M,z):
X:=gu[1]:
p:=gu[2]:
S1:=gu[3]:

if {seq(coeff(p,z,2*i+1),i=0..degree(p,z)/2)}<>{0} then
  RETURN(FAIL):
fi:

p:=subs(z=sqrt(z),p):

lu:=[fsolve(p,z)]:

for i from 1 to nops(lu) do
 if lu[i]>0 then
   z1:=sqrt(lu[i]):
   X1:=subs(z=z1,X):
   S1:=subs(z=z1,S1):
    if min(op(X1))>0 and min(seq(op(S1[i1]),i1=1..nops(S1))) >0 then
     RETURN([X1,S1]):
    fi:
 fi:
od:

FAIL:
end:





#ExacGSs(a,k,z): Inputs a symbol a and a positive integer k, outputs the vector X and the doubly-stochatic matrix S
#such that if M is the generic SYMMERTY k by k matrix with entries a[i,j] the XMX=S #
#It returns the minimal polynomial satisfied by X[1], called z, and X and S in terms of z and a[i,j].
# X=[x[1],x[2], .., x[n]]; such that if X denotes the diagonal matrix with entry X XMX  is doubly-stochastic.
#It returns a pair whose first entry is a list of length n where x[1] is denoted by the variable z, and x[2], ..., x[n] 
#are polynomials in z, and second entry is the minimal polynomial satisfied by z.
#Try: 
#ExacGSs(a,2,z);
ExacGSs:=proc(a,k,z) local M,i,j:
M:=[seq([seq(a[j,i],j=1..i-1),seq(a[i,j],j=i..k)],i=1..k)]:
ExacGS(M,z):
end:


#MelNold(M,var): inputs a matrix M depending on a set of parameters var, 
#outputs the equations satisfied by the variables var
#for the Sinkhorn algorithm terminating after two steps (one Row scaling and one column scaling).
#Try:
#MelNold([[a,b],[c,d]],[a,b,c,d]);
MelNold:=proc(M,var) local gu,i,eq:
gu:=normal(Sink(M,1));

eq:={seq(numer(convert(gu[i],`+`)-1),i=1..nops(gu))}:

Groebner[Basis](eq,plex(op(var) ));

end:


#KLM(K,L,M,n,k): Mel Nathanson's  KLM matrix where the K part is in the k by k upper-left block
#the L part is  in the k by n-k upper-right block and n-k by k bottom-left blocks and the
#M part is at the bottom (n-k) by (n-k) block. Try:
#KLM(3,4,5,4,2);
KLM:=proc(K,L,M,n,k):
[[K$k,L$(n-k)]$k,[L$k,M$(n-k)]$(n-k)]:
end:


#MelN(a,k): inputs a symbol a and a positive integer k and outpus the Groebner basis and  the set of variables
#for a generic row-stochastic matrix to still be row-stochastic after one column scaling. Try:
#MelN(a,2);
MelN:=proc(a,k) local M,i,j,var,M1,eq:
M:=[seq([seq(a[i,j],j=1..k-1),1-add(a[i,j],j=1..k-1)],i=1..k)]:
var:=[seq(seq(a[i,j],j=1..k-1),i=1..k)]:
M1:=CS(M):
eq:={seq(numer(normal(convert(M1[i],`+`)-1)),i=1..k)}:

eq,var:
#Groebner[Basis](eq,plex(op(var) ));
end:

#RevRS(M,R): inputs  a row-stochacstic matrix M and a list of numbers R (of the same size as the number of rows of M)
#outputs the matrix obtained by multiplying row i by R[i]
RevRS:=proc(M,R) local i:

if nops(M)<>nops(R) then
 print(`bad input`):
 RETURN(FAIL):
fi:

if {seq(convert(M[i],`+`),i=1..nops(M))}<>{1} then
 print(`not row-stochastic`):
 RETURN(FAIL):
fi:

[seq(R[i]*M[i],i=1..nops(R))]:

end:

#MelNprob5(T,var): inputs a  template for row-stochastic matrices featuring the list of variables var
#for the first k-1 columns, with the  last column implied, tries to find a chose of the variables
#such thati it still row-stochastic after one column scaling. Try:
#MelNprob5([[x,x],[2*x,x],[3*x,x]],{x} );
MelNprob5:=proc(T,var) local M,i,j,M1,eq,k,var1,v:
k:=nops(T):
if nops(T[1])<>k-1 then
  RETURN(FAIL):
fi:

M:=[seq([seq(T[i][j],j=1..k-1),1-add(T[i][j],j=1..k-1)],i=1..k)]:
M1:=CS(M):
eq:={seq(numer(normal(convert(M1[i],`+`)-1)),i=1..k)}:
var1:=solve(eq,var):
if var1=NULL then
print(`No solution`):
 RETURN(FAIL):
fi:


for v in var1 do
if op(1,v)=op(2,v) then
  print(`Not unique solution`):
 RETURN(FAIL):
fi:
od:

M:=subs(var1,M):



if min(seq(op(M[i]),i=1..nops(M)))<0 then
 print(M, `is not non-negative`):
 RETURN(FAIL):
fi:

M1:=subs(var1,M1):

if min(seq(op(M1[i]),i=1..nops(M1)))<0 then
 print(M1, `is not non-negative`):
 RETURN(FAIL):
fi:

if M=M1 then
 FAIL:
else
[M,M1]:
fi:

end:






#ExacGSnice(M,z):  Like ExacGS(M,z), but with z^2 replaced by z, and the first vector is divided by sqrt(z)
#(where z is the new z).
#Try: 
#ExacGSnice([[3,4],[4,5]],z);
ExacGSnice:=proc(M,z) local gu,gu1,gu2,gu3,i1,j1,lu,mu3,mu3a:
gu:=ExacGS(M,z):

if gu=FAIL then
 RETURN(FAIL):
fi:

gu1:=sort(collect(expand(subs(z=sqrt(z),normal(gu[1]/z))),z)):
gu2:=sort(collect(expand(subs(z=sqrt(z),gu[2])),z)):
gu3:=gu[3]:


mu3:=[]:

for i1 from 1 to nops(gu3) do
  mu3a:=[]:
 for j1 from 1 to nops(gu3[i1]) do
   lu:=gu3[i1][j1]:
   lu:=subs(z=sqrt(z),lu):
   lu:=sort(collect(lu,z)):
   mu3a:=[op(mu3a),lu]:
 od:
 mu3:=[op(mu3),mu3a]:
 od:

[gu1,gu2,mu3]:

end:


#ExacGSsNice(M,k,a):  Like ExacGSs(M,a), but with z^2 replaced by z, and the first vector is divided by sqrt(z)
#(where z is the new z).
#Try: 
#ExacGSsNice(a,z);
ExacGSsNice:=proc(a,k,z) local gu,gu1,gu2,gu3,i1,j1,lu,mu3,mu3a:
gu:=ExacGSs(a,k,z):

if gu=FAIL then
 RETURN(FAIL):
fi:

gu1:=sort(collect(expand(subs(z=sqrt(z),normal(gu[1]/z))),z)):
gu2:=sort(collect(expand(subs(z=sqrt(z),gu[2])),z)):
gu3:=gu[3]:


mu3:=[]:

for i1 from 1 to nops(gu3) do
  mu3a:=[]:
 for j1 from 1 to nops(gu3[i1]) do
   lu:=gu3[i1][j1]:
   lu:=subs(z=sqrt(z),lu):
   lu:=sort(collect(lu,z)):
   mu3a:=[op(mu3a),lu]:
 od:
 mu3:=[op(mu3),mu3a]:
 od:

[gu1,gu2,mu3]:

end:





#ExacGSniceV(M,z):   ExacGSniceV(M,z): verbose version of ExacGSnice(M,z) (q.v.).   
#Try: 
#ExacGSniceV([[3,4],[4,5]],z);
ExacGSniceV:=proc(M,z) local gu,lu,i:
gu:=ExacGSnice(M,z):

if gu=FAIL then
 RETURN(FAIL):
fi:

print(`The exact value of the Sinkhorn limit for a certain symmetric matrix of size`, nops(M[1])):
print(``):
print(`By Shalsoh B. Ekhad `):
print(``):
print(`Consider the following symmetric matrix`):
print(``):
print(matrix(M)):
print(``):
print(` Let `, z, ` be the smallest real positive root of the polynomial equation `):
print(``):
lu:=add(factor(coeff(gu[2],z,i))*z^i,i=0..degree(gu[2],z)):
print(lu=0):
print(``):
print(`and in Maple notation`):
print(``):
lprint(lu=0):
print(``):
print(`and in LaTex`):
print(``):
lprint(latex(lu=0)):
print(``):
print(`Then the diagonal matrix X such that S=XMX is doubly stochastic has in its diagonal`):
print(``):
print(sqrt(z)*gu[1]):
print(``):
print(`and in Maple notation`):
print(``):
lprint(sqrt(z)*gu[1]):
print(``):
print(`and the Sinkhorn limit is`):
print(``):
print(gu[3]):
print(``):
print(``):
print(`and in Maple notation`):
print(``):
lprint(gu[3]):
print(``):
end:



#ExacGSsNiceV(a,k,z):   ExacGSsNice(a,k,z): verbose version of ExacGSsNice(M,z) (q.v.).   
#Try: 
#ExacGSsNiceV(a,2,z);
ExacGSsNiceV:=proc(a,k,z) local gu,i,j:
gu:=ExacGSsNice(a,k,z):

if gu=FAIL then
 RETURN(FAIL):
fi:

print(`The exact value of the Sinkhorn limit for a certain symmetric matrix of size`, k):
print(``):
print(`By Shalsoh B. Ekhad `):
print(``):
print(`Consider the generic  symmetric matrix of size`,k):
print(``):
print(matrix([seq([seq(a[j,i],j=1..i-1),seq(a[i,j],j=i..k)],i=1..k)])):
print(``):
print(` Let `, z, ` be the smallest real positive root of the polynomial equation `):
print(``):
lprint(gu[2]=0):
print(``):
print(`Then the diagonal matrix X such that S=XMX is doubly stochastic has in its diagonal`):
print(``):
lprint(sqrt(z)*gu[1]):
print(``):
print(`and the Sinkhorn limit is`):
print(``):
lprint(gu[3]):
print(``):
end:


#OneStepS(a,k): The algebraic conitions for a k by matrix terminate after one step in Sinkhorn's algorithm. Try:
#OneStepS(a,2);
OneStepS:=proc(a,k) local M,i,j:

 M:=[seq([seq(a[i,j],j=1..k)],i=1..k)]:

M:=Sink(M,1):

{seq(numer(normal(convert(M[i],`+`)-1)),i=1..k),
seq(numer(normal(convert(Tra(M)[i],`+`)-1)),i=1..k)} minus {0} :
end:




#MelNprob5nice(T,var): A verbose version of  MelNprob5(T,var) (q.v.). Try:
#MelNprob5nice([[x,x],[2*x,x],[3*x,x]],{x} );
MelNprob5nice:=proc(T,var) local gu,A,T1,i,j:
gu:=MelNprob5(T,var):

if gu=FAIL then
 RETURN(FAIL):
fi:

print(`A Positive 3x3 matrix that is Row Stochastic, but not Column Stochastic, and becomes Doubly Stochastic after one Column Scaling`):
print(``):
print(`By Shalosh B. Ekhad `):
print(``):
print(`Mel Nathanson asked in his JMM 2019 talk, and also as problem 1 in "Alternate Minomization and Doubly Stochastic Matrices"`):
print(` arXiv:1812.119302v2 and as problem 5 in his paper "Matrix Scaling, Explicit Sinkhorn limits, and Arithmetic" `):
print(`whether  there exists a positive 3x3 matrix that is row stochastic, but not column stochastic, and becomes doubly stochastic after one column scaling`):
print(`Here I answer the question in the affirmative. Indeed the matrix`):
print(``):
print(matrix(gu[1])):
print(``):
print(`and in LaTex`):
print(``):
lprint(latex(matrix(gu[1]))):
print(``):
print(` is row stochastic, but not column stochastic`):
print(``):
print(`Applying column scaling, we get the doubly-stochastic matrix`):
print(``):
print(matrix(gu[2])):
print(``):
print(`and in LaTex`):
print(``):
lprint(latex(matrix(gu[2]))):

print(``):

A:=gu[1]:

if {seq(seq(type(A[i][j],fraction) or evalb(A[i][j]=0) ,j=1..nops(A[i])),i=1..nops(A))}={true} then

  T1:=[seq(lcm(op(denom(A[i]))),i=1..nops(A))]:
 A:=[seq(T1[i]*A[i],i=1..nops(A))]:

  print(`By multiplying the `, nops(A), `rows, respectively, by,`, op(T1), `we get a matrix with integer coefficients `):
 print(` `):
 print(matrix(A)):
  print(` `):
 print(`and in LaTex`):
  print(` `):
 lprint(latex(matrix(A))):
  print(` `):

  print(`this becomes doubly-stochastic after TWO applications of the Sinkhorn process (or one double-application)`):
 print(` `):
fi:
A:


end:




#MelNprob1(a,z): answers problem 1 in  Mel Nathanson's article
#"Matrix Scaling, Explicit Sinkhorn limits, and Arithmetic". Try:
#MelNprob1(a,z):

MelNprob1:=proc(a,z) local gu,i,j:

print(`This article answers problem 1 in Mel Nathanson's article`):
print(` "Matrix Scaling, Explicit Sinkhorn limits, and Arithmetic" `):

gu:=ExacGSsNice(a,3,z):



print(`The exact value of the Sinkhorn limit for the general 3 by 3 symmetric positive matrix` ):
print(``):
print(`By Shalsoh B. Ekhad `):
print(``):
print(`Consider the generic 3 by 3 symmetric matrix` ):
print(``):
print(matrix([seq([seq(a[j,i],j=1..i-1),seq(a[i,j],j=i..3)],i=1..3)])):
print(``):
print(` Let `, z, ` be the smallest real positive root of the polynomial equation `):
print(``):
lprint(gu[2]=0):
print(``):
print(`Then the diagonal matrix X such that S=XMX is doubly stochastic has in its diagonal`):
print(``):
lprint(sqrt(z)*gu[1]):
print(``):
print(`and the Sinkhorn limit is`):
print(``):
lprint(gu[3]):
print(``):
end:


#MelNprob2a(K,L,z): answers the first part of problem 2 in  Mel Nathanson's article
#"Matrix Scaling, Explicit Sinkhorn limits, and Arithmetic". Try:
#MelNprob2a(K,L,z):

MelNprob2a:=proc(K,L,z):

print(`This article answers the first part of problem 2 in Mel Nathanson's article`):
print(` "Matrix Scaling, Explicit Sinkhorn limits, and Arithmetic" `):

ExacGSniceV([[K,1,1],[1,L,1],[1,1,1]],z):

end:

#MelNprob2b(K,L,M,z): answers the second part of problem 2 in  Mel Nathanson's article
#"Matrix Scaling, Explicit Sinkhorn limits, and Arithmetic". Try:
#MelNprob2b(K,L,M,z):

MelNprob2b:=proc(K,L,M,z):

print(`This article answers the second part of problem 2 in Mel Nathanson's article`):
print(` "Matrix Scaling, Explicit Sinkhorn limits, and Arithmetic" `):

ExacGSniceV([[K,1,1],[1,L,1],[1,1,M]],z):

end:




#MelNsec13(r,k): investigates Mel Nathanson's matrix [[r+1)*r/2,1,1,1],[1,1,1],[1,1,1]]
MelNsec13:=proc(r,k) local M,mu:
M:=[ [(r+1)*r/2,1,1],[1,1,1],[1,1,1]]:
mu:=Tra(normal(Sink(M,k))):

mu:=convert(mu,`+`):

factor(normal(mu[1]-mu[2]));

end:




MelMat:=proc(r) local gu,z,gu2,lu,M, M1,M2:

M:=[[r*(r+1)/2,1,1],[1,1,1],[1,1,1]]:
gu:=ExacGS([[r*(r+1)/2,1,1],[1,1,1],[1,1,1]],z):

gu:=simplify(subs(z=sqrt(z),gu)):

gu2:=gu[2]:

lu:=solve(gu2,z):

#[[ normal(simplify(subs(z=lu[1],gu[1]))),normal(subs(z=lu[1],gu[3]))],
#[ normal(simplify(subs(z=lu[2],gu[1]))),normal(subs(z=lu[2],gu[3]))]]

M1:=normal(subs(z=lu[1],gu[3])):
M2:=normal(subs(z=lu[2],gu[3])):

if min(op(ListTools[Flatten](subs(r=3,M1)))) >0 then
  RETURN([M,simplify(normal(subs(z=lu[1],gu[1]))), M1]):
else
  RETURN([M,simplify(normal(subs(z=lu[1],gu[1]))),M2]):
fi:

end:

#DSE(A): inputs a symbolic matrix and outputs the set of conditions that will make it doubly-stochastic. Try:
#DSE([[a,b],[c,d]]);
DSE:=proc(A) local i,j,eq:
eq:={seq( normal(add(A[i][j],j=1..nops(A[i]))-1),i=1..nops(A)),
seq( normal(add(A[i][j],j=1..nops(A))-1),i=1..nops(A[1]))}
minus {0}:
numer(eq):
end:



IsDS:=proc(M): evalb(convert(M,`+`)=[1$nops(M)] and convert(Tra(M),`+`)=[1$nops(M)]):end:

#MelNprob5G(T,var,KAMA): inputs a  template for row-stochastic matrices featuring the list of variables var
#for the first k-1 columns, with the  last column implied, tries to find a chose of the variables
#such thati it still row-stochastic after one column scaling followed by KAMA-1 double iterations of Sinkhorn. Try:
#MelNprob5G([[x,x],[2*x,x],[4*x,x]],{x},2 );
MelNprob5G:=proc(T,var,KAMA) local M,i,j,M1,eq,k,var1,k1,gu,lu,gu1:
k:=nops(T):
if nops(T[1])<>k-1 then
  RETURN(FAIL):
fi:

M:=[seq([seq(T[i][j],j=1..k-1),1-add(T[i][j],j=1..k-1)],i=1..k)]:

M1:=normal(CS(M)):

for k1 from 1 to KAMA-1 do
M1:=normal(RS(M1)):
M1:=normal(CS(M1)):
od:

eq:={seq(numer(normal(convert(M1[i],`+`)-1)),i=1..k)}:
var1:=solve(eq,var):
if var1=NULL then
print(`No solution`):
 RETURN(FAIL):
fi:

lu:=[var1]:

gu:={}:

for i from 1 to nops(lu) do
 gu:=gu union {subs(lu[i],M)}:
od:
gu:



lu:={}:

for gu1 in gu do
if not IsDS(simplify(Sink(gu1,KAMA-1))) then
  lu:=lu union {[gu1,simplify(Sink(gu1,KAMA))]}:
fi:
od:

lu:

end:


#MelNprob5Gnice(T,var,KAMA):  A verbose form of MelNprob5G(T,var,KAMA)(q.v.). Try:
#MelNprob5Gnice([[x,x],[2*x,x],[4*x,x]],{x},2 );
MelNprob5Gnice:=proc(T,var,KAMA) local gu,gu1,i:

gu:=MelNprob5G(T,var,KAMA):

if gu=FAIL or gu={} then
 RETURN(FAIL):
fi:

print(`Examples of Matrices for which the Sinkhorn algorithm terminates after EXACTLY`, KAMA,` steps `):
print(``):
print(`By Shalosh B. Ekhad `):
print(``):

for i from 1 to nops(gu) do 
gu1:=gu[i]:

print(`The Sinkorhn algorithm terminates after exactly`, KAMA, `steps for the following matrix `):
print(``):
print(matrix(gu1[1])):
print(``):
print(`and in floating point`):
print(``):
print(matrix(evalf(gu1[1]))):
print(``):
if min(op(ListTools[Flatten](evalf(gu1[1])) )) <0 then
print(`Alas it has negative entries.`):
else
print(`Yea, we found such a matrix with non-negative entries`):
fi:
print(``):

print(`Its Sinkhorn limit is`):
print(``):
print(matrix(gu1[2])):
print(``):
print(`and in floating point`):
print(``):
print(matrix(evalf(gu1[2]))):
print(``):


od:

gu:

end: