let s^2=-23$
let Z^3=Z+1$
off nat$

phiZ:=(4*s+(9*s-23)*Z-6*s*Z^2)/46$
phi2Z:=(-4*s-(9*s+23)*Z+6*s*Z^2)/46$

ID3:=mat((1,0,0),
         (0,1,0),
         (0,0,1))$

ZEROMAT:=mat((0,0,0),
             (0,0,0),
             (0,0,0))$

SIG:=mat((0,1,0),
         (0,0,1),
         (2,0,0))$

ZMAT:=mat((Z,   0,    0),
          (0,phiZ,    0),
          (0,   0,phi2Z))$

FF:=mat((2,0,0),
        (0,0,1),
        (0,1,0))$

gendt:=(7+3*s)/16$
gendti:=(7-3*s)/16$

% The following two matrices generators of $\bar\Gamma$ in the case $(a=23,p=2,\emptyset)$:
AA:=mat(
(1/23*(-5*s-23)*z^2-4/23*s*z+1/23*(11*s+46),
1/46*(9*s+69)*z^2+1/23*(-s-46)*z-3/23*s,
1/46*(15*s+23)*z^2+1/46*(-11*s-23)*z-5/23*s),
(1/23*(-9*s+23)*z^2+1/23*(2*s+46)*z+6/23*s,
1/23*(7*s-23)*z^2+1/23*(s+23)*z+1/23*(3*s+46),
-3/23*s*z^2+1/23*(-7*s+23)*z+1/23*(2*s+23)),
(1/23*(-3*s-69)*z^2+1/23*(16*s+46)*z+1/23*(2*s+92),
1/23*(-6*s-46)*z^2+1/23*(9*s-23)*z+1/23*(4*s+46),
1/23*(-2*s+46)*z^2+1/23*(3*s-23)*z+9/23*s))$

BB:=mat(
(-2/23*s*z^2+1/92*(-11*s-23)*z+1/92*(13*s-23),0,0),
(0,1/92*(7*s-69)*z^2+1/92*(s+69)*z+1/92*(3*s+23),0),
(0,0,1/92*(s+69)*z^2+1/46*(5*s-23)*z+1/92*(7*s-69)))$

% The following two matrices generators of $\bar\Gamma$ in the case $(a=23,p=2,\{23\})$:

AD:=(1/46)*mat(
(s*z^2+10*s*z+7*s-23*z^2+92*z-23,10*s*z^2-2*s*z-15*s-60*z^2-2*z+63,4*s*z^2-6*s*z+5*s+69),
(2*(-2*s*z^2+3*s*z+9*s+23*z+69),-8*s*z^2+12*s*z+13*s+46*z^2-92*z-69,7*s*z^2-2*s*z-13*s+69*z^2-23),
(2*(-17*s*z^2+4*s*z+3*s-9*z^2+2*z+29),2*(-2*s*z^2+3*s*z+9*s-23*z+69),7*s*z^2-22*s*z+3*s-23*z^2-23))$

BD:=(1/92)*mat(
(-8*s*z^2-11*s*z+13*s-23*z-23,0,0),
(0,7*s*z^2+s*z+3*s-69*z^2+69*z+23,0),
(0,0,s*z^2+10*s*z+7*s+69*z^2-46*z-69))$

AAI:=mat((1/23*(5*s-23)*z^2+4/23*s*z+1/23*(-11*s+46),
1/46*(3*s-69)*z^2+1/23*(-8*s+23)*z+1/23*(-s+46),
1/46*(9*s+23)*z^2+1/23*(-s+23)*z-3/23*s),
(1/23*(-15*s+23)*z^2+1/23*(11*s-23)*z+10/23*s,
1/23*(2*s+46)*z^2+1/23*(-3*s-23)*z-9/23*s,
3/23*s*z^2+1/23*(7*s+23)*z+1/23*(-2*s+23)),
(1/23*(-9*s+69)*z^2+1/23*(2*s-92)*z+6/23*s,
1/23*(6*s-46)*z^2+1/23*(-9*s-23)*z+1/23*(-4*s+46),
1/23*(-7*s-23)*z^2+1/23*(-s+23)*z+1/23*(-3*s+46)))$

BBI:=mat(
(2/23*s*z^2+1/92*(11*s-23)*z+1/92*(-13*s-23),0,0),
(0,1/92*(-s+69)*z^2+1/46*(-5*s-23)*z+1/92*(-7*s-69),0),
(0,0,1/92*(-7*s-69)*z^2+1/92*(-s+69)*z+1/92*(-3*s+23)))$

ADI:=mat((1/46*(-s-23)*z^2+1/23*(-5*s+46)*z+1/46*(-7*s-23),
1/46*(17*s-9)*z^2+1/23*(-2*s+1)*z+1/46*(-3*s+29),
1/23*s*z^2+1/46*(-3*s+23)*z+1/46*(-9*s+69)),
(-4/23*s*z^2+6/23*s*z+1/23*(-5*s+69),
1/46*(-7*s-23)*z^2+11/23*s*z+1/46*(-3*s-23),
1/46*(-7*s+69)*z^2+1/23*s*z+1/46*(13*s-23)),
(1/23*(-10*s-60)*z^2+1/23*(2*s-2)*z+1/23*(15*s+63),
2/23*s*z^2+1/23*(-3*s-23)*z+1/23*(-9*s+69),
1/23*(4*s+23)*z^2+1/23*(-6*s-46)*z+1/46*(-13*s-69)))$

BDI:=mat(
(2/23*s*z^2+1/92*(11*s-23)*z+1/92*(-13*s-23),0,0),
(0,1/92*(-s+69)*z^2+1/46*(-5*s-23)*z+1/92*(-7*s-69),0),
(0,0,1/92*(-7*s-69)*z^2+1/92*(-s+69)*z+1/92*(-3*s+23)))$

a1:=2$ a2:=0$ a3:=0$ a4:=0$ a5:=-2$ a6:=-1/2$ a7:=-1$ a8:=3/2$ a9:=1/2$ a10:=11/23$ a11:=-3/23$ a12:=-5/23$ a13:=-4/23$ a14:=-1/23$ a15:=-11/46$ a16:=-5/23$ a17:=9/46$ a18:=15/46$ 

b1:=-1/4$ b2:=0$ b3:=0$ b4:=-1/4$ b5:=0$ b6:=0$ b7:=0$ b8:=0$ b9:=0$ b10:=13/92$ b11:=0$ b12:=0$ b13:=-11/92$ b14:=0$ b15:=0$ b16:=-2/23$ b17:=0$ b18:=0$ 

ad_1:=-1/2$ ad_2:=63/46$ ad_3:=3/2$ ad_4:=2$ ad_5:=-1/23$ ad_6:=0$ ad_7:=-1/2$ ad_8:=-30/23$ ad_9:=0$ ad_10:=7/46$ ad_11:=-15/46$ ad_12:=5/46$ ad_13:=5/23$ ad_14:=-1/23$ ad_15:=-3/23$ ad_16:=1/46$ ad_17:=5/23$ ad_18:=2/23$ 

bd_1:=-1/4$ bd_2:=0$ bd_3:=0$ bd_4:=-1/4$ bd_5:=0$ bd_6:=0$ bd_7:=0$ bd_8:=0$ bd_9:=0$ bd_10:=13/92$ bd_11:=0$ bd_12:=0$ bd_13:=-11/92$ bd_14:=0$ bd_15:=0$ bd_16:=-2/23$ bd_17:=0$ bd_18:=0$ 

avec:=mat((a1),(a2),(a3),(a4),(a5),(a6),(a7),(a8),(a9),(a10),(a11),(a12),(a13),(a14),(a15),(a16),(a17),(a18))$

bvec:=mat((b1),(b2),(b3),(b4),(b5),(b6),(b7),(b8),(b9),(b10),(b11),(b12),(b13),(b14),(b15),(b16),(b17),(b18))$

advec:=mat((ad_1),(ad_2),(ad_3),(ad_4),(ad_5),(ad_6),(ad_7),(ad_8),(ad_9),(ad_10),(ad_11),(ad_12),(ad_13),(ad_14),(ad_15),(ad_16),(ad_17),(ad_18))$

bdvec:=mat((bd_1),(bd_2),(bd_3),(bd_4),(bd_5),(bd_6),(bd_7),(bd_8),(bd_9),(bd_10),(bd_11),(bd_12),(bd_13),(bd_14),(bd_15),(bd_16),(bd_17),(bd_18))$

AA-(a1*ZMAT^0*SIG^0+a2*ZMAT^0*SIG^1+a3*ZMAT^0*SIG^2+
a4*ZMAT^1*SIG^0+a5*ZMAT^1*SIG^1+a6*ZMAT^1*SIG^2+
a7*ZMAT^2*SIG^0+a8*ZMAT^2*SIG^1+a9*ZMAT^2*SIG^2+
a10*s*ZMAT^0*SIG^0+a11*s*ZMAT^0*SIG^1+a12*s*ZMAT^0*SIG^2+
a13*s*ZMAT^1*SIG^0+a14*s*ZMAT^1*SIG^1+a15*s*ZMAT^1*SIG^2+
a16*s*ZMAT^2*SIG^0+a17*s*ZMAT^2*SIG^1+a18*s*ZMAT^2*SIG^2);

BB-(b1*ZMAT^0*SIG^0+b2*ZMAT^0*SIG^1+b3*ZMAT^0*SIG^2+
b4*ZMAT^1*SIG^0+b5*ZMAT^1*SIG^1+b6*ZMAT^1*SIG^2+
b7*ZMAT^2*SIG^0+b8*ZMAT^2*SIG^1+b9*ZMAT^2*SIG^2+
b10*s*ZMAT^0*SIG^0+b11*s*ZMAT^0*SIG^1+b12*s*ZMAT^0*SIG^2+
b13*s*ZMAT^1*SIG^0+b14*s*ZMAT^1*SIG^1+b15*s*ZMAT^1*SIG^2+
b16*s*ZMAT^2*SIG^0+b17*s*ZMAT^2*SIG^1+b18*s*ZMAT^2*SIG^2);

AD-(ad_1*ZMAT^0*SIG^0+ad_2*ZMAT^0*SIG^1+ad_3*ZMAT^0*SIG^2+
ad_4*ZMAT^1*SIG^0+ad_5*ZMAT^1*SIG^1+ad_6*ZMAT^1*SIG^2+
ad_7*ZMAT^2*SIG^0+ad_8*ZMAT^2*SIG^1+ad_9*ZMAT^2*SIG^2+
ad_10*s*ZMAT^0*SIG^0+ad_11*s*ZMAT^0*SIG^1+ad_12*s*ZMAT^0*SIG^2+
ad_13*s*ZMAT^1*SIG^0+ad_14*s*ZMAT^1*SIG^1+ad_15*s*ZMAT^1*SIG^2+
ad_16*s*ZMAT^2*SIG^0+ad_17*s*ZMAT^2*SIG^1+ad_18*s*ZMAT^2*SIG^2);

BD-(bd_1*ZMAT^0*SIG^0+bd_2*ZMAT^0*SIG^1+bd_3*ZMAT^0*SIG^2+
bd_4*ZMAT^1*SIG^0+bd_5*ZMAT^1*SIG^1+bd_6*ZMAT^1*SIG^2+
bd_7*ZMAT^2*SIG^0+bd_8*ZMAT^2*SIG^1+bd_9*ZMAT^2*SIG^2+
bd_10*s*ZMAT^0*SIG^0+bd_11*s*ZMAT^0*SIG^1+bd_12*s*ZMAT^0*SIG^2+
bd_13*s*ZMAT^1*SIG^0+bd_14*s*ZMAT^1*SIG^1+bd_15*s*ZMAT^1*SIG^2+
bd_16*s*ZMAT^2*SIG^0+bd_17*s*ZMAT^2*SIG^1+bd_18*s*ZMAT^2*SIG^2);


CondMtxDm23Type1 := mat(
( 1, 0, 0, 348, 0, 0, 492, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ),
( 0, 1, 0, 0, 348, 0, 0, 492, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ),
( 0, 0, 1, 0, 0, 348, 0, 0, 492, 0, 0, 0, 0, 0, 0, 0, 0, 0 ),
( 0, 0, 2, 0, 0, 181, 0, 0, 39, 0, 0, 0, 0, 0, 345, 0, 0, 23 ),
( 1, 0, 0, 355, 0, 0, 284, 0, 0, 0, 0, 0, 437, 0, 0, 276, 0, 0 ),
( 0, 1, 0, 0, 355, 0, 0, 284, 0, 0, 0, 0, 0, 437, 0, 0, 276, 0 ),
( 0, 2, 0, 0, 181, 0, 0, 39, 0, 0, 0, 0, 0, 184, 0, 0, 506, 0 ),
( 0, 0, 2, 0, 0, 181, 0, 0, 39, 0, 0, 0, 0, 0, 184, 0, 0, 506 ),
( 1, 0, 0, 355, 0, 0, 284, 0, 0, 0, 0, 0, 92, 0, 0, 253, 0, 0 ),
( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 348, 0, 0, 492, 0, 0 ),
( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 348, 0, 0, 492, 0 ),
( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 348, 0, 0, 492 ),
( 0, 0, 0, 0, 0, 307, 0, 0, 22, 0, 0, 2, 0, 0, 181, 0, 0, 39 ),
( 0, 0, 0, 418, 0, 0, 11, 0, 0, 1, 0, 0, 355, 0, 0, 284, 0, 0 ),
( 0, 0, 0, 0, 418, 0, 0, 11, 0, 0, 1, 0, 0, 355, 0, 0, 284, 0 ),
( 0, 0, 0, 0, 222, 0, 0, 507, 0, 0, 2, 0, 0, 181, 0, 0, 39, 0 ),
( 0, 0, 0, 0, 0, 222, 0, 0, 507, 0, 0, 2, 0, 0, 181, 0, 0, 39 ),
( 0, 0, 0, 111, 0, 0, 518, 0, 0, 1, 0, 0, 355, 0, 0, 284, 0, 0 ))$

CondMtxDM23Type2:=mat(
( 1, 0, 0, 348, 0, 0, 492, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ),
( 0, 1, 0, 0, 348, 0, 0, 492, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ),
( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 69, 0, 0, 207 ),
( 0, 0, 2, 0, 0, 181, 0, 0, 39, 0, 0, 0, 0, 0, 345, 0, 0, 23 ),
( 1, 0, 0, 355, 0, 0, 284, 0, 0, 0, 0, 0, 437, 0, 0, 276, 0, 0 ),
( 0, 0, 0, 0, 92, 0, 0, 253, 0, 0, 23, 0, 0, 230, 0, 0, 184, 0 ),
( 0, 0, 0, 0, 307, 0, 0, 22, 0, 0, 527, 0, 0, 348, 0, 0, 490, 0 ),
( 0, 0, 0, 0, 0, 307, 0, 0, 22, 0, 0, 527, 0, 0, 348, 0, 0, 490 ),
( 1, 0, 0, 355, 0, 0, 284, 0, 0, 0, 0, 0, 92, 0, 0, 253, 0, 0 ),
( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 348, 0, 0, 492, 0, 0 ),
( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 348, 0, 0, 492, 0 ),
( 0, 0, 528, 0, 0, 181, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0 ),
( 0, 0, 0, 0, 0, 307, 0, 0, 22, 0, 0, 2, 0, 0, 181, 0, 0, 39 ),
( 0, 0, 0, 418, 0, 0, 11, 0, 0, 1, 0, 0, 355, 0, 0, 284, 0, 0 ),
( 0, 528, 0, 0, 174, 0, 0, 245, 0, 0, 0, 0, 0, 92, 0, 0, 253, 0 ),
( 0, 2/23, 0, 0, 2826/23, 0, 0, 7445/23, 0, 0, 0, 0, 0, 307, 0, 0, 22, 0 ),
( 0, 0, 2/23, 0, 0, 2826/23, 0, 0, 7445/23, 0, 0, 0, 0, 0, 307, 0, 0, 22 ),
( 0, 0, 0, 111, 0, 0, 518, 0, 0, 1, 0, 0, 355, 0, 0, 284, 0, 0 ))$

AA*AAI-ID3;
BB*BBI-ID3;

AD*ADI-ID3;
BD*BDI-ID3;

det(AA)-1;
det(BB)-gendt;

det(AD)-1;
det(BD)-gendt;

AASTAR:=sub(S=-S,tp(AA))$
BBSTAR:=sub(S=-S,tp(BB))$

ADSTAR:=sub(S=-S,tp(AD))$
BDSTAR:=sub(S=-S,tp(BD))$

% The following are zero, checking that the elements are unitary with respect to $\iota$:
AASTAR*FF*AA-FF;
BBSTAR*FF*BB-FF;

ADSTAR*FF*AD-FF;
BDSTAR*FF*BD-FF;

% We now check the arithmeticity conditions:

avec-(1/46)*mat((92),(0),(0),(0),(-92),(-23),(-46),(69),(23),(22),(-6),(-10),(-8),(-2),(-11),(-10),(9),(15));
bvec-(1/92)*mat((-23),(0),(0),(-23),(0),(0),(0),(0),(0),(13),(0),(0),(-11),(0),(0),(-8),(0),(0));
advec-(1/46)*mat((-23),(63),(69),(92),(-2),(0),(-23),(-60),(0),(7),(-15),(5),(10),(-2),(-6),(1),(10),(4));
bdvec-(1/92)*mat((-23),(0),(0),(-23),(0),(0),(0),(0),(0),(13),(0),(0),(-11),(0),(0),(-8),(0),(0));

CondMtxDM23Type1*avec  - (1/2)*mat((-980),(84),(144),(-292),(-836),(-498),(-425),(100),(-706),(-334),(162),(154),(-347),(-268),(-1559),(632),(223),(-1282));
CondMtxDM23Type1*bvec  - (1/4)*mat((-349),(0),(0),(0),(-661),(0),(0),(0),(-488),(-337),(0),(0),(0),(-686),(0),(0),(0),(-379));
CondMtxDM23Type2*advec - (1/2)*mat((899),(-1311),(23),(-80),(1337),(-623),(-245),(109),(1186),(173),(183),(1584),(-40),(1828),(894),(-872),(-76),(93));
CondMtxDM23Type2*bdvec - (1/4)*mat((-349),(0),(0),(0),(-661),(0),(0),(0),(-488),(-337),(0),(0),(0),(-686),(0),(0),(0),(-379));

% Here are 37 relations satisfied by AA and BB:

BB^3*AAI*BBI*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB^2*AA*BBI^3*AAI*BBI*AA
*BB^8*AAI*BBI*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI - gendt^7*ID3;

BB^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI*AA*BBI^3
*AAI*BB*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3 - ID3;

AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^2
*AAI*BB*AA*BBI^5*AAI*BB*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^2 - ID3;

BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BB*AAI*BBI*AA*BB^3*AAI*BB^2*AA*BBI^3*AAI*BBI*AA
*BB^5*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BB^2*AA - ID3;

AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI
*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI^2*AAI*BB*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI - gendt^7*ID3;

BB*AA*BB^3*AAI*BB*AAI*BBI^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB*AAI*BB*AA*BB^3*AAI
*BB*AA*BB^3*AAI*BBI^2*AA*BB*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB^2 - gendt^7*ID3;

BB^5*AAI*BBI^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB*AAI*BB*AA*BB^3*AAI*BB*AA*BB^3*AAI
*BBI^7*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^2*AA - ID3;

BB*AA*BBI^3*AAI*BB*AA*BBI^2*AAI*BB*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3
*AAI*BBI^2*AAI*BBI*AA*BB^2*AAI*BBI*AA*BB^3*AAI*BB^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AA
*BBI^3*AAI*BBI*AA*BBI^3*AAI - ID3;

AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB^3*AAI*BBI^2*AA
*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB*AAI*BBI*AA
*BB^3*AAI*BB*AA*BB^3*AAI*BB^3 - ID3;

BB^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BBI
*AA*BBI^3*AAI*BB*AA*BBI^2*AAI*BB*AA*BBI^5*AAI*BB*AA*BB^3*AAI*BBI^3*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3 - ID3;

BBI^2*AAI*BBI^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB*AAI*BB^2*AA*BBI^3*AAI*BBI^3*AA*BBI^3
*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI^2*AAI*BBI*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB*AAI
*BB*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI^2 - gendti^7*ID3;

AAI*BBI^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI
*BB^4*AA*BB^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI^2*AA
*BB^3*AAI*BB*AA*BB^3*AAI*BB^3 - ID3;

BB*AA*BBI^6*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI^4*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI^4*AA
*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB^3*AA*BBI^3*AAI*BBI*AA*BB^2*AA*BBI^3*AAI*BBI*AA*BBI^3
*AAI*BB*AA*BBI^3*AAI - gendti^14*ID3;

BB*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB*AAI*BBI*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI
*BBI^2*AAI*BBI^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI*AAI*BB*AA*BBI^5*AAI*BB*AA
*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^2*AAI - ID3;

AA*BB*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB^2*AA
*BB^5*AAI*BBI*AA*BB^2*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AA*BB^3*AAI*BBI^3*AA
*BB^3*AAI*BB*AA*BB^3*AAI*BB^3 - gendt^14*ID3;

BB*AA*BB^3*AAI*BB*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI^3*AA*BBI^3*AAI*BBI*AA
*BBI^3*AAI*BB*AA*BBI^4*AAI*BB*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI*AA
*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB^2*AA*BB^3*AAI - gendti^7*ID3;

BBI^2*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB^3*AAI*BBI^2*AA
*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB*AAI*BB*AA*BB^3*AAI*BB^2*AA*BBI^3*AAI*BBI*AA
*BB^3*AAI*BB*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI - gendt^7*ID3;

AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB^2*AA*BBI^3*AAI*BBI*AA*BB^2*AAI*BBI*AA*BB^3*AAI*BB
*AA*BB^3*AAI*BB^2*AA*BBI^8*AAI*BBI*AA*BB*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3
*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB^2*AA - gendt^7*ID3;

AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI^2*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AA*BB^3*AAI*BBI
*AA*BB^3*AAI*BB^3*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB^2*AA*BBI^3*AAI*BBI*AA*BB^2*AAI
*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^2*AA*BBI - gendt^7*ID3;

BBI^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI^3*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB
*AA*BBI*AAI*BB^2*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BBI^2*AAI*BB*AA*BB^3*AAI*BBI^2*AA
*BBI^3*AAI*BB*AA*BBI^2*AAI*BB*AA*BB^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI - gendti^7*ID3;

BBI*AA*BBI^3*AAI*BBI*AA*BB^4*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI^2*AA*BB^3*AAI*BB*AA
*BB^3*AAI*BB^3*AA*BB^3*AAI*BBI*AA*BB^3*AAI^2*BBI*AA*BB*AAI*BBI*AA*BB^3*AAI*BB*AA
*BB^3*AAI*BB^3*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB^2*AA - gendt^7*ID3;

BBI*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI^2*AAI*BB*AA*BB^3*AAI*BBI*AA*BB^3*AAI
*BBI^5*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI*AAI*BB*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB
*AA*BBI^2*AAI*BB*AA*BB^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB^2*AAI*BBI - gendti^7*ID3;

BB^6*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI^3*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI*AA
*BB^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BB^2*AA*BB^3*AAI*BBI*AA*BB^3*AAI
*BB*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI - ID3;

BB^3*AAI*BB^3*AAI*BBI^2*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AA*BB^3*AAI*BBI*AA*BB^3*AAI
*BB^3*AA*BB^3*AAI*BBI^2*AA*BBI*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^2*AA^2*BB^3*AAI
*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB*AA - gendt^14*ID3;

BB^5*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI^2*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI
*BBI*AA*BBI^3*AAI*BB*AA*BBI*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^2*AA*BB*AA*BB^3
*AAI*BB*AA*BB^3*AAI*BB^4*AA*BB^3*AAI*BB*AA*BB^3*AAI - gendt^7*ID3;

BB^8*AAI*BBI*AA*BB^2*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^2*AA*BB^5*AAI*BBI*AA*BB^3
*AAI*BBI*AA*BB^3*AAI*BB^2*AA*BBI^3*AAI*BBI^2*AA*BB^2*AAI*BBI*AA*BB^3*AAI*BB^2*AA*BBI^3
*AAI*BBI*AA*BB^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI*AA - gendt^7*ID3;

BB^3*AAI*BB*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI^2*BBI^2*AA*BBI^3*AAI*BBI*AA*BBI^3
*AAI*BB*AA*BB*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AA*BB^2*AAI*BBI*AA*BB^3*AAI*BB^2
*AA*BBI^3*AAI*BBI*AA*BB^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI*AA - ID3;

BB*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB
*AAI*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB*AAI*BB*AA*BB^3*AAI*BB*AA
*BB^3*AAI*BBI^2*AA*BBI^2*AAI*BB*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BB - ID3;

BB^5*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI^2*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AA*BB*AAI*BB*AA
*BBI^5*AAI*BB*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI*AAI*BB*AA*BB^3*AAI*BB*AA*BB^3
*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB*AAI*BB*AA*BB^3*AAI - gendt^7*ID3;

BB*AA*BB^2*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BB*AA*BBI*AA*BBI^3*AAI*BBI*AA*BBI^3
*AAI*BBI*AA*BBI*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI*AA*BB^3
*AAI*BB^2*AA*BBI^3*AAI*BB^2*AA*BBI^3*AAI*BBI^3*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI^3*AA
*BBI^3*AAI*BBI*AA*BBI^3*AAI - gendti^7*ID3;

BBI*AA*BBI*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^2*AA*BBI*AA*BBI^3*AAI*BBI^3*AA
*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AAI
*BBI^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI^2*AAI*BB*AA*BBI^3*AAI*BBI*AA*BB^3
*AAI*BB*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI - ID3;

BB^5*AA*BBI^3*AAI*BBI^3*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI^2*AAI*BB*AA*BBI^5*AAI
*BB*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB*AA
*BB^3*AAI*BB^3*AAI*BBI*AA*BB^2*AAI*BBI*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^2 - gendt^7*ID3;

BBI*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI^4*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI^3
*AAI*BB*AA*BB*AAI*BB*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BBI^2
*AAI*BBI*AA*BBI*AAI*BBI*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI^2*AAI*BB*AA*BB^3
*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI - gendti^7*ID3;

BBI^2*AAI*BBI*AA*BB*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AA*BB^3*AAI*BBI*AA*BB^3
*AAI*BB^2*AA*BBI^5*AAI*BB*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^2*AAI*BB*AA*BBI^3*AA
*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BB^3
*AA*BB^3*AAI*BB*AA*BB^3*AAI - ID3;

BB^6*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI^3*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA
*BBI^2*AAI*BB*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^5*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI^2*AA
*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AA*BBI^2*AAI*BB*AA*BB^3*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BB*AA*BB^2 - ID3;

BB^8*AAI*BBI^2*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BBI^3*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA
*BBI^2*AAI^2*BBI^2*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB*AAI*BBI*AA*BB^3*AAI*BB*AA
*BB^3*AAI*BB^4*AA*BB^7*AA*BBI^3*AAI*BBI*AA*BBI^3*AAI*BBI^2*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^2*AA - ID3;

BB*AA*BB^3*AAI*BB*AA*BB^3*AAI*BB^3*AAI*BBI*AA*BB*AAI*BBI*AA*BB^3*AAI*BB*AA*BB^3*AAI
*BB^3*AA*BB^3*AAI*BBI*AA*BB^3*AAI*BB^2*AA*BBI^5*AAI*BB*AA*BB^3*AAI*BB*AAI*BBI^2*AA*BBI^3
*AAI*BBI*AA*BBI^3*AAI*BB*AA*BB*AAI*BB*AA*BB^3*AAI*BB*AA*BBI^2*AAI*BB*AA*BB^3*AAI*BBI^2
*AA*BBI^3*AAI*BB*AA*BBI^3*AAI*BB*AA - gendt^7*ID3;

%*********************************************************************************************
% Here are 79 relations satisfied by AD and BD:

BDI^5*ADI*BDI^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BDI^2*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI - gendti^5*ID3;

BD^2*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD^3*BDI^5*ADI*BDI^5*ADI*
BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI^3*ADI*BD^3*AD - gendt^3*ID3;

BD^3*ADI*BDI^2*AD*BDI^3*AD*BD^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^8*ADI*BD^3
*ADI^2*BDI^2*ADI*BDI^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI - gendti^7*ID3;

AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^8*AD*BD^5*ADI^2
*BD*AD*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^2 - gendt^10*ID3;

BD*ADI*BDI^2*AD*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^3*ADI*BD^3*AD*BD^5
*ADI^2*BD*AD*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^4 - gendt^11*ID3;

BDI*AD*BDI^8*ADI*BD^3*ADI*BDI*AD^2*BDI^10*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI
*AD*BD^5*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^8*ADI - gendt^2*ID3;

ADI*BDI^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI^4*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD^3
*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3*AD*BD^5*ADI*BDI^3*AD*BD^3 - gendti^3*ID3;

AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^10*ADI^2*BD
*AD*BDI^3*AD*BD^2*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2 - gendt^8*ID3;

BDI^5*ADI*BD^3*ADI*BD*AD*BDI^8*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^8*ADI
*BD^3*AD*BDI^10*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD*BDI^3 - gendti^9*ID3;

BD^5*ADI*BDI^3*ADI*BD^3*AD*BD^5*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^5*AD*BD^2*AD
*BDI^3*ADI*BD^3*AD*BD^5*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^5 - gendt^9*ID3;

BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD
*BDI^8*ADI*BD^3*ADI*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^5*AD*BDI^3*ADI*BD^3*AD*BDI^5*ADI - gendti^3*ID3;

BD^10*ADI*BDI^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BD^3*AD*BDI^10*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3
*AD*BD^5*ADI*BDI*AD*BD^2*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^3*ID3;

AD*BDI^5*ADI*BDI^3*AD^2*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^3*BD*AD*BDI^3*AD*BD^5*AD
*BD^3*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^10*ADI^2*BD^4 - gendt^2*ID3;

AD^2*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI^2*BD^3*AD*BD^5*ADI*BDI^3*ADI*BD^3*AD
*BD^2*ADI*BD^3*ADI*BD*AD*BDI^8*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^8 - gendti^2*ID3;

AD^2*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI^2*BD^3*AD*BD^5*ADI*BDI^3*ADI*BDI^2*ADI
*BD^3*ADI*BDI*AD*BDI^3*AD*BD^3*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^10*ADI^2*BD*AD - gendt^4*ID3;

AD^2*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^3*BD*AD*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD
*BD^10*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^5*AD*BD^2 - gendt^10*ID3;

AD*BD^5*ADI*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD*AD*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^10*ADI
*BDI*AD*BDI^3*AD*BD^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3 - gendt^8*ID3;

BDI^3*ADI*BD^3*AD*BD^2*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^8*ADI*BD^3
*ADI*BD^3*AD*BDI^5*ADI*BDI^3*AD*BDI^3*ADI*BD^3*AD*BD*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD - gendti^2*ID3;

AD*BD^2*AD*BD^2*AD*BD^5*ADI^2*BD*AD*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^7*AD*BD^5*AD*BD^5*ADI
*BDI^3*AD*BD^8*ADI*BD^2*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^5 - gendt^17*ID3;

AD*BDI^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BDI^10*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5
*ADI*BDI*AD*BDI^5*ADI*BD*AD*BDI^5*ADI*BDI^3*AD*BDI*AD*BDI^8*ADI*BD^3*ADI*BDI*AD^2*BDI^5*ADI*BDI^3 - gendti^13*ID3;

ADI*BD^3*AD*BD^5*ADI^2*BD*AD*BDI^3*AD*BD^8*ADI*BD*ADI*BD^3*AD*BD^5*ADI*BDI*AD*BDI^5*ADI
*BDI^3*AD*BD^3*AD*BDI^5*ADI*BDI^3*AD^2*BDI^5*ADI*BDI^3*AD^2*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD^3 - gendt*ID3;

BDI^4*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI^2*AD*BDI^3*AD*BD^2*AD*BD^8*ADI*BD^2*AD*BDI^3*AD
*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^5*AD*BD^2*AD*BDI*AD*BDI^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BD^3*ADI*BD*ADI*BDI^2*ADI*BDI - ID3;

BDI^7*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD*BDI^3*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI
*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^3*AD*BDI^3 - gendt^4*ID3;

BDI^3*ADI*BD^3*AD*BD^3*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^10*ADI*BDI^6*AD*BD^3*AD
*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^6*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^5*AD - gendt^8*ID3;

BDI^5*ADI*BD^3*AD*BDI^2*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^10*ADI^2*BD*ADI*BDI^2*ADI
*BD^3*ADI*BDI*AD*BDI^3*AD*BDI^5*ADI*BD^3*ADI*BD*AD^2*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI^3*ADI*BDI^2*ADI - gendti^2*ID3;

BD^5*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^8*ADI*BDI*AD*BDI^3*AD*BDI^5*ADI*BD^3*ADI*BD^2
*AD*BDI^5*ADI*BDI^3*AD*BDI*AD*BDI^8*ADI*BD^3*ADI*BDI*AD^3*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI - ID3;

BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD*AD*BDI^8*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD
*BDI^5*ADI*BDI^2*ADI*BDI^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD - gendti^8*ID3;

BD^3*AD*BD^5*ADI^2*BD*AD*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^2*AD*BDI*AD^2*BDI^10*ADI*BDI^5*ADI*BD^3*ADI^2
*BD^3*AD*BD^5*ADI*BDI*AD*BDI^3*ADI^2*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^8*ADI*BD^3*ADI*BD^2 - gendti*ID3;

BD^13*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^12*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI
*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^8*ADI*BD*ADI*BD^3*AD*BD^5*ADI*BDI^2*AD*BDI^3*AD - gendt^12*ID3;

BD^10*ADI^2*BD*ADI*BD^3*AD*BD^5*ADI*BDI*AD*BDI^3*AD*BD^8*AD*BDI^10*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5
*ADI*BDI*AD*BDI^3*ADI*BDI^3*AD*BD^2*AD*BDI^3*AD*BD^3*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^3*ID3;

AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3*AD*BD^5*AD^2*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5
*ADI^2*BD^3*AD*BD^5*ADI*BDI^3*ADI*BD^3*AD*BDI^3*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD*BDI^8*ADI*BD^3 - ID3;

BDI^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD^2*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD
*BD^5*ADI*BD^2*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD*BD^5*ADI*BDI*AD*BDI^3
*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^3 - ID3;

BD^3*ADI*BDI^2*AD^2*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^3
*AD*BD^5*AD*BD^4*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI^3*ADI*BDI^2*ADI
*BDI^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI - gendti^2*ID3;

ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^8*ADI*BD^3*AD^2*BDI^5*ADI*BDI^5*ADI*BD^3
*ADI^2*BD^3*AD*BD^5*ADI^2*BD^3*AD*BD^5*ADI*BDI^3*ADI*BDI^2*ADI*BDI^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5
*ADI*BD^3*ADI*BDI*AD*BDI^8 - gendti^8*ID3;

BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^8*ADI*BD^3*ADI*BDI*AD^2*BDI^5*ADI^2*BD*AD*BDI^3*AD
*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^8*ADI*BDI*AD*BDI^3*AD*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^10*ADI*BDI^3*AD^2*BDI^3*AD - gendti*ID3;

BD^10*ADI*BDI^2*AD*BDI^3*AD*BD^8*ADI*BD*ADI*BDI^2*ADI*BDI^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI
*BD^3*ADI*BDI*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^8*ADI*BD*AD*BD^5*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^5*ID3;

BDI^2*ADI*BD^3*AD*BDI*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI^3*ADI
*BD^3*AD*BDI^3*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI^2*AD^3*BDI^5*ADI*BDI^5*ADI*BD^3
*ADI^2*BD^3*AD*BD^5*ADI^2*BD^3*AD*BD^5*ADI*BDI^4 - gendt^4*ID3;

BD^10*ADI*BDI^3*AD*BDI*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI^3*ADI
*BD^3*AD*BD^2*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD^2*BDI^5*ADI*BDI^5*ADI*BDI^5*ADI*BD^3*AD*BD^3
*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendti*ID3;

BD^5*AD*BD^5*ADI^2*BD^3*ADI*BD^2*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^7*ADI*BDI^3*AD*BD^3
*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI*AD*BDI^6*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD^2*BDI^3*AD - gendt^7*ID3;

ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD^3
*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^6*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD
*BD^2*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI - gendt^6*ID3;

BD^10*ADI*BDI^3*AD^2*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI^2*BD^3*AD*BD^5*ADI^2*BD^3
*AD*BD^5*ADI^2*BDI^2*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI^3*ADI*BD^3*AD*BD^2*ADI
*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^5*ID3;

BD^10*ADI*BDI^3*ADI*BD*AD*BDI^3*AD*BD^8*ADI*BD*ADI*BD^3*AD*BD^5*ADI*BDI^2*AD^2*BDI^5*ADI
*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^9*ADI*BD
*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^8*ID3;

BD^15*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^8*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD*BDI^5*ADI
*BDI^3*AD*BD^3*AD*BDI^5*ADI*BDI^3*AD*BDI^3*ADI*BD^3*AD*BDI^3*ADI*BD^3*ADI*BD^2*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^6*ID3;

BD^10*ADI*BDI^4*AD*BDI^3*AD^2*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BDI^2*ADI*BD^3*AD*BDI^5*ADI*BDI^5
*ADI*BD^3*ADI*BDI^3*ADI*BD^3*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^10*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^2*ID3;

AD*BD^5*AD*BD^2*AD*BD^5*AD*BD^5*ADI^2*BD*AD*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^7*ADI*BDI^5
*ADI*BD^3*ADI*BDI*AD^2*BDI^5*ADI^3*BD*AD*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^10*ADI*BDI*AD*BDI^3*AD*BD^2 - gendt^14*ID3;

BDI^2*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BD^3*AD*BDI^5*ADI*BDI^3*AD^2*BDI^5*ADI*BDI^3*AD^2
*BDI^3*AD*BD^5*AD*BD^5*ADI^3*BD^2*AD*BD^5*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^10*ADI*BDI^2*AD*BDI^3*AD*BD^8*ADI - gendt*ID3;

BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD*AD*BDI^3*AD*BD^2*AD*BDI^3*ADI*BD^3*AD*BDI*ADI*BDI^3
*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI^3*ADI*BD^3*AD*BD^2*ADI*BDI^3*AD*BDI^3*ADI
*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI^3*ADI*BD^3*AD*BDI^5*ADI - gendt*ID3;

BD^10*ADI*BDI^3*AD*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^6*AD*BD^3*AD*BDI^3*AD*BD^5
*AD*BD^5*ADI*BDI^3*AD*BD^2*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD^3*AD*BD^3*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^8*ID3;

BD^10*ADI*BDI*AD*BD^5*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^10*ADI*BDI^2*AD*BDI^3*AD
*BD^8*ADI*BDI^2*ADI*BDI^2*ADI*BDI^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^8*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^3*ID3;

ADI*BDI^2*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI^3*ADI*BD^3*AD*BDI*ADI*BDI^3*AD*BD^3
*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI^3*ADI*BD^3*AD*BDI^3*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD
*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD^3 - gendt^4*ID3;

BDI^3*ADI*BD^3*AD*BD*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI^3*ADI*BD^3
*AD*BDI^3*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^3
*AD*BD^2*AD*BD^3*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^2 - gendt^2*ID3;

ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3*AD*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3
*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^8*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^5*ADI
*BDI^2*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI^3*ADI*BD^3*AD*BDI^3 - gendti^7*ID3;

BD^3*ADI*BD*AD*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^3*ADI*BDI^2*ADI*BDI^5
*ADI*BD^3*AD*BDI^2*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^10*ADI^2*BD*ADI*BD^3*AD*BD^2
*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3*AD*BDI^5*ADI*BDI^5*ADI - gendt^2*ID3;

BD^13*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^7*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3*AD
*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^3*ADI*BDI^3*AD*BD^3*ADI*BD^3*AD*BD^5
*ADI*BDI^3*ADI*BD^3*AD*BD^5*ADI*BDI*AD*BDI^3*AD - gendt^8*ID3;

BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD*AD*BDI^3*AD*BD^5*AD*BDI^2*ADI*BDI^5*ADI*BD^3*ADI*BDI
*AD*BDI^3*AD*BDI^5*ADI*BD^3*ADI*BD*ADI*BDI^2*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI^3
*ADI*BD^3*AD*BD^3*ADI*BDI^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD - gendt^4*ID3;

BD^10*ADI^2*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^5*AD*BD^2*AD*BDI^3*ADI*BD^3*AD*BDI^5*ADI
*BDI^5*ADI*BD^3*ADI*BDI^3*ADI*BD^3*AD*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3
*AD*BD^3*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^6*ID3;

BDI^7*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD^2*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD
*BD^5*ADI*BDI^3*ADI*BDI^2*ADI*BDI^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^10
*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD*BDI^8 - gendti^9*ID3;

AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^8*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3*AD*BD^5
*AD*BD^5*ADI^2*BD*AD*BDI^3*AD*BD^2*AD*BD^3*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BDI*AD
*BDI^8*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3 - gendti^4*ID3;

BDI*AD*BD^3*ADI*BDI^2*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI^3*ADI*BD^3*AD*BD*ADI
*BD^3*ADI*BD*AD*BDI^8*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^11*AD*BD^5*AD*BD^2
*AD*BD^2*AD*BDI^3*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^8*ADI*BD^3*ADI - gendti^9*ID3;

BD^8*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI^3*AD*BDI^3*AD*BD^5*AD*BD^5
*ADI*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5
*ADI^2*BD^2*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^6*ID3;

AD*BDI^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BD^3*ADI*BDI^2*ADI*BDI^2*ADI*BDI^5*ADI*BD^3*AD*BDI^5*ADI
*BDI^5*ADI^2*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI*AD*BDI^3*AD*BD^5*ADI
*BD^3*ADI*BD*ADI*BDI^2*ADI*BD^3*ADI*BDI*AD*BDI^8*ADI*BD^3*ADI*BDI*AD^2*BDI^5*ADI*BDI^6 - gendti^5*ID3;

BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI^3*ADI*BD^3*AD*BD^3*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5
*ADI*BDI^3*AD*BD^2*AD*BDI^3*ADI*BD^3*AD*BD^5*ADI*BDI*AD*BDI^3*AD*BD^13*ADI*BD*AD*BDI^5*ADI*BDI^3
*AD^2*BDI^3*AD*BD^5*AD*BD^9*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD - gendt^11*ID3;

BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD*AD*BDI^3*AD*BD^5*AD*BD^10*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2
*BDI^3*AD*BD^5*AD*BD^10*ADI*BDI*AD*BDI^10*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD*BDI^10*ADI*BDI^3*AD^2*BDI^3*AD - gendt^4*ID3;

BD^7*ADI*BDI^3*AD*BD^3*AD^2*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI^3*ADI*BDI^2*ADI
*BD^3*ADI*BDI*AD*BDI^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BDI^5*ADI*BD^3
*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD^2*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - ID3;

BD^10*ADI^2*BD*ADI*BD^3*AD*BD^5*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI^3
*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BD^3*ADI*BDI^2*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BDI^2
*ADI*BDI^5*ADI*BD^3*AD*BDI^2*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^5*ID3;

BDI^2*ADI*BDI^5*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI^2*AD*BDI^3*AD*BD^2*AD*BD^5*AD*BD^2
*AD*BD^5*AD*BD^2*AD*BD^2*AD*BDI^3*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^8*ADI
*BD^3*ADI*BDI*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^5*AD*BD^5*ADI*BD^3*ADI*BD*ADI - gendt^3*ID3;

BD^10*ADI*BDI^6*AD*BD^5*AD*BD^5*AD*BD^3*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^10*ADI
*BDI^8*ADI*BD^3*ADI*BDI*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^6*ADI
*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^10*ID3;

BD^5*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^3*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5
*ADI*BDI^3*AD*BD^2*AD*BDI^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BD^3*ADI*BD^6*AD*BD^5*ADI^2*BD*AD*BDI^3
*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^2*AD*BDI*AD*BDI^8*ADI*BD^3*ADI*BDI*AD*BDI^3*AD - gendt^13*ID3;

BDI^3*AD*BD^5*AD*BD^8*AD*BDI^10*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD*BDI^4*ADI
*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI^3*ADI*BD^3*AD*BD^2*ADI*BDI^3
*AD*BD^3*AD*BDI^5*ADI*BDI^3*AD^2*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^2 - ID3;

BDI^3*AD*BD^5*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BDI^2*ADI*BDI^5*ADI*BD^3*ADI
*BDI*AD*BDI^3*AD*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^2
*BD^3*ADI*BD*ADI*BDI^2*ADI*BD^3*ADI*BDI*AD*BDI^8*ADI*BD^3*ADI*BDI*AD^2*BDI^5*ADI
*BDI^6*AD^2*BDI^5*ADI*BDI^3*AD*BDI^3 - gendti^7*ID3;

BDI^3*AD*BD^5*AD*BD^8*AD*BDI^10*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD*BDI^3*ADI
*BDI^3*AD*BD^6*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BDI*AD*BDI^3*AD*BD^5*ADI*BD^3*AD
*BDI^10*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD*BDI^3*ADI - ID3;

BD^13*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^8*ADI^2*BD^3*AD*BD^5*ADI*BDI^2*AD^2*BDI^5
*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD*ADI
*BDI^5*ADI*BD^3*ADI*BDI*AD*BDI^3*AD*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD - gendt^10*ID3;

BD^5*AD*BD^5*ADI^2*BD^2*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD*BD^3*ADI*BDI^5*ADI*BD^3*ADI
*BDI*AD*BDI^3*AD*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD^2*AD*BDI^5*ADI*BDI^3
*AD*BDI^3*ADI*BD^3*AD*BDI*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI^3
*ADI*BD^3*AD*BDI^3*ADI*BD^3*ADI*BD*AD*BDI^3*AD - gendt^2*ID3;

BD^10*ADI^2*BD^4*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BDI^3*AD
*BD^5*AD*BD^2*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^6*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3
*AD*BD^3*ADI*BDI^5*ADI*BD^3*AD*BDI^2*ADI*BD*AD*BDI^5*ADI*BDI^3*AD^2*BDI^3*AD*BD^5*AD - gendt^14*ID3;

AD*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^3*ADI*BD*AD^2*BDI^5*ADI*BDI^5
*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI^3*ADI*BDI^2*ADI*BD^3*ADI*BDI*AD^2*BDI^5*ADI*BDI^5
*ADI*BDI^10*ADI*BD^3*ADI*BD*AD*BDI^5*ADI*BDI^3*AD*BD^3*ADI*BDI^2*ADI*BD^3*AD*BDI^5*ADI
*BDI^5*ADI*BD^3*ADI*BDI^3*ADI*BD^3*AD*BDI^3*ADI*BDI^3*AD - gendti^7*ID3;

BD^8*ADI*BDI*AD*BDI^3*AD*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^8*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI
*BD^3*ADI*BDI*AD*BDI^3*AD*BD^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BDI^2*ADI*BDI^5*ADI*BD^3
*ADI*BDI*AD*BDI^3*AD*BDI^5*ADI*BD^3*ADI*BD*AD^2*BDI^5*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD
*BD^5*ADI*BD^2*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD - gendti*ID3;

BD^3*ADI*BD^3*AD*BDI^10*ADI*BDI^5*ADI*BD^3*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD*BDI^7*ADI*BDI^3
*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^2*AD*BDI^3*AD*BDI^10*ADI*BDI^5*ADI*BD^3*ADI^2
*BD^3*AD*BD^5*ADI*BDI*AD*BDI^3*ADI*BD^3*ADI*BD*AD*BDI^8*ADI*BD^3*AD*BDI^5*ADI*BDI^5*ADI
*BD^3*ADI*BDI*AD*BDI^5*ADI*BDI^2*ADI - gendti^9*ID3;

BDI^5*ADI*BDI^5*ADI*BD^3*AD*BDI^3*ADI*BDI^3*AD*BD^3*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD
*BD^2*AD^2*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI^2*BD^2
*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD*BD^8*ADI*BDI*AD^2*BDI^10*ADI*BDI^5*ADI*BD^3
*ADI^2*BD^3*AD*BD^5*ADI*BDI*AD*BDI^3 - gendt^7*ID3;

BD^3*ADI*BDI^3*AD^2*BDI^3*AD*BD^8*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^8*ADI*BD^3*ADI
*BDI*AD^2*BDI^5*ADI*BDI^5*ADI*BD^3*AD*BD^5*ADI^2*BD*AD*BDI^3*AD*BD^8*ADI*BD*AD^2*BDI^5
*ADI*BDI^5*ADI*BD^3*ADI*BDI^3*ADI*BD^3*AD*BDI^2*ADI*BDI^5*ADI*BD^3*ADI*BDI*AD
*BDI^3*AD*BDI^5*ADI*BD^3*ADI*BD*AD*BDI^3*AD*BD^5*AD*BD^5*ADI*BDI^3*AD - ID3;

;end;