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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "\"Frame-Field\"  calculati
on of Ricci and Weyl and Ricci and Weyl invariants " }}{PARA 0 "" 0 "
" {TEXT -1 59 "for the mixmaster metric with constant basis inner prod
uct." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 7 "grtw():" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%
=GRTensorII~Version~1.79~(R6)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%02~
February~2001G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%ZDeveloped~by~Peter
~Musgrave,~Denis~Pollney~and~Kayll~LakeG" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%DCopyright~1994-2001~by~the~authors.G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%inLatest~version~available~from:~http://grtensor.phy.q
ueensu.ca/G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "qload(mix1);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%2Default~spacetimeG%%mix1G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%8For~the~mix1~spacetime:G" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%,CoordinatesG" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#-%\"xG6#%#upG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/)%#x~G%\"aG-%'
vectorG6#7&%&ThetaG%$PhiG%$PsiG%\"TG" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#%4Basis~inner~productG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$etaG6$%
$bupGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&)%$etaG%$(a)G\"\"\")%!G%
$(b)GF(-%'matrixG6#7&7&F(\"\"!F1F17&F1F(F1F17&F1F1F(F17&F1F1F1!\"\"" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#%=Basis~(covariant~components)G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#w1G6#%#dnG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/&%'omega1G6#%\"aG-%'vectorG6#7&,$*&*&-%$expG6#-F'6#%\"
TG\"\"\"-%%sqrtG6#,&F5F5*$)%$PsiG\"\"#F5!\"\"F5F5*$-F76#,&F5F5*$)%&The
taGF=F5F>F5F>F>*(F/F5F<F5-F76#FBF5\"\"!FI" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%#w2G6#%#dnG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%'om
ega2G6#%\"aG-%'vectorG6#7&,$*&*&-%$expG6#-%\"bG6#%\"TG\"\"\"%$PsiGF6F6
*$-%%sqrtG6#,&F6F6*$)%&ThetaG\"\"#F6!\"\"F6FAFA,$*(F/F6-F:6#F<F6-F:6#,
&F6F6*$)F7F@F6FAF6FA\"\"!FK" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#w3G6
#%#dnG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%'omega3G6#%\"aG-%'vectorG
6#7&\"\"!*&%&ThetaG\"\"\"-%$expG6#-%\"cG6#%\"TGF/*&F0F/*$-%%sqrtG6#,&F
/F/*$)%$PsiG\"\"#F/!\"\"F/FAF," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#w
4G6#%#dnG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%'omega4G6#%\"aG-%'vect
orG6#7&\"\"!F,F,-%$expG6#,(-F'6#%\"TG\"\"\"-%\"bGF2F4-%\"cGF2F4" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%coMixmaster~metric~(e.g.~MTW~Box~30.1
,~Theta~=~cos(theta),~Psi~=~sin(psi))G" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "grcalcalter(R(bdn,bdn),8);" }}{PARA 6 "" 1 "" {TEXT 
-1 40 "Created definition for rot(bdn,bup,bdn) " }}{PARA 6 "" 1 "" 
{TEXT -1 38 "Created a definition for e(bdn,dn,pdn)" }}{PARA 6 "" 1 "
" {TEXT -1 50 "Simplification will be applied during calculation." }}
{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 42 "Applying \+
routine normal to object g(up,up)" }}{PARA 6 "" 1 "" {TEXT -1 43 "Appl
ying routine normal to object e(bdn,up)" }}{PARA 6 "" 1 "" {TEXT -1 
47 "Applying routine normal to object e(bdn,dn,pdn)" }}{PARA 6 "" 1 "
" {TEXT -1 53 "Applying routine normal to object lambda(bdn,bdn,bdn)" 
}}{PARA 6 "" 1 "" {TEXT -1 50 "Applying routine normal to object rot(b
dn,bdn,bdn)" }}{PARA 6 "" 1 "" {TEXT -1 50 "Applying routine normal to
 object rot(bdn,bup,bdn)" }}{PARA 6 "" 1 "" {TEXT -1 52 "Applying rout
ine normal to object R(bdn,bdn,bdn,bdn)" }}{PARA 6 "" 1 "" {TEXT -1 
44 "Applying routine normal to object R(bdn,bdn)" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/%*CPU~Time~G$\"$\">!\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "gralter(_,6,7);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Compo
nent simplification of a GRTensorII object:" }}{PARA 6 "" 1 "" {TEXT 
-1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 44 "Applying routine expand to obje
ct R(bdn,bdn)" }}{PARA 6 "" 1 "" {TEXT -1 44 "Applying routine factor \+
to object R(bdn,bdn)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$
\"#?!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "grmap(_,autoAli
as,`x`);" }}{PARA 6 "" 1 "" {TEXT -1 40 "Applying routine autoAlias to
 R(bdn,bdn)" }}{PARA 7 "" 1 "" {TEXT -1 51 "Warning, alias or macro a[
T] defined in terms of a\n" }}{PARA 7 "" 1 "" {TEXT -1 51 "Warning, al
ias or macro b[T] defined in terms of b\n" }}{PARA 7 "" 1 "" {TEXT -1 
51 "Warning, alias or macro c[T] defined in terms of c\n" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "grdisplay(_);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%\"RG6$%$bdnGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&
&%\"RG6#%$(a)G\"\"\"&%!G6#%$(b)GF)-%'matrixG6#7&7&,$*&,,*&)-%$expG6#%
\"cG\"\"#F))-F96#%\"bGF<F)F<*$)F8\"\"%F)!\"\"*$)-F96#%\"aGFCF)F)*$)F>F
CF)FD*&F<F)&FI6$%\"TGFOF)F)F)*(F7F))FGF<F)F=F)FD#F)F<\"\"!FSFS7&FS,$*&
,,*&FQF)F7F)!\"#FAF)FEF)FJFD*&F<F)&F@FNF)FDF)*(F7F)FQF)F=F)FD#FDF<FSFS
7&FSFS,$*&,,*&FQF)F=F)FYFJF)FEF)FAFD*&F<F)&F;FNF)FDF)*(F7F)FQF)F=F)FDF
gnFS7&FSFSFS*&,.FMFD*(F<F)&FI6#FOF)&F@FeoF)F)*(F<F)FdoF)&F;FeoF)F)FenF
D*(F<F)FfoF)FhoF)F)F^oFDF)*(F7F)FQF)F=F)FD" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 115 "### WARNING: calls to `C` for generating C code sh
ould be replaced by codegen[C]\ngrcalcalter(C(bdn,bdn,bdn,bdn),8);" }}
{PARA 6 "" 1 "" {TEXT -1 50 "Simplification will be applied during cal
culation." }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 
46 "Applying routine normal to object bRicciscalar" }}{PARA 6 "" 1 "" 
{TEXT -1 52 "Applying routine normal to object C(bdn,bdn,bdn,bdn)" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#I!\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gralter(_,6,7);" }}{PARA 6 "" 1 "" 
{TEXT -1 48 "Component simplification of a GRTensorII object:" }}
{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 52 "Applying \+
routine expand to object C(bdn,bdn,bdn,bdn)" }}{PARA 6 "" 1 "" {TEXT 
-1 52 "Applying routine factor to object C(bdn,bdn,bdn,bdn)" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"#R!\"$" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 23 "grmap(_,autoAlias,`x`);" }}{PARA 6 "" 1 "" 
{TEXT -1 48 "Applying routine autoAlias to C(bdn,bdn,bdn,bdn)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "grdisplay(_);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#%8For~the~mix1~spacetime:G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%/Covariant~WeylG" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/&
%\"CG6#%0(1)~(2)~(1)~(2)G,$*&,:*&)-%$expG6#%\"aG\"\"#\"\"\")-F.6#%\"bG
F1F2!\"#*&)-F.6#%\"cGF1F2F3F2F2*&F,F2F9F2F2*$)F-\"\"%F2F2*$)F4F@F2F2*&
F1F2)F:F@F2!\"\"*(F@F2&F06#%\"TGF2&F6FHF2F2*(F1F2FGF2&F<FHF2FE*(F1F2FJ
F2FLF2FE&F06$FIFIFE&F6FOFE*&F1F2&F<FOF2F2F2*(F9F2F,F2F3F2FE#F2\"\"'" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%\"CG6#%0(1)~(2)~(3)~(4)G,$*&,0*&)-
%$expG6#%\"cG\"\"#\"\"\"&F06#%\"TGF2!\"#*&)-F.6#%\"bGF1F2&F;F4F2F2*&)-
F.6#%\"aGF1F2&FAF4F2F2*&FBF2F8F2!\"\"*&FBF2F,F2F2*&F<F2F>F2FD*&F<F2F,F
2F2F2*(F,F2F>F2F8F2FD#F2F1" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/&%\"CG6
#%0(1)~(3)~(1)~(3)G,$*&,:*&)-%$expG6#%\"aG\"\"#\"\"\")-F.6#%\"bGF1F2F2
*&)-F.6#%\"cGF1F2F3F2F2*(F1F2F,F2F8F2!\"\"*$)F-\"\"%F2F2*&F1F2)F4F@F2F
=*$)F9F@F2F2*(F@F2&F06#%\"TGF2&F;FGF2F2*(F1F2FFF2&F6FGF2F=*(F1F2FKF2FI
F2F=&F06$FHFHF=*&F1F2&F6FNF2F2&F;FNF=F2*(F8F2F,F2F3F2F=#F2\"\"'" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%\"CG6#%0(1)~(3)~(2)~(4)G,$*&,0*&)-%
$expG6#%\"bG\"\"#\"\"\"&F06#%\"TGF2!\"#*&)-F.6#%\"cGF1F2&F;F4F2F2*&)-F
.6#%\"aGF1F2&FAF4F2F2*&F<F2F>F2!\"\"*&F<F2F,F2F2*&FBF2F8F2FD*&FBF2F,F2
F2F2*(F8F2F>F2F,F2FD#FDF1" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/&%\"CG6#
%0(1)~(4)~(1)~(4)G,$*&,:*&)-%$expG6#%\"aG\"\"#\"\"\")-F.6#%\"bGF1F2!\"
\"*(F1F2)-F.6#%\"cGF1F2F3F2F2*&F,F2F9F2F7*&F1F2)F-\"\"%F2F2*$)F4F@F2F7
*$)F:F@F2F7*(F1F2&F06#%\"TGF2&F6FGF2F2*&F1F2&F06$FHFHF2F7*(F1F2FFF2&F<
FGF2F2*(F@F2FIF2FNF2F7&F6FLF2&F<FLF2F2*(F9F2F,F2F3F2F7#F2\"\"'" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/&%\"CG6#%0(1)~(4)~(2)~(3)G,$*&,0*&)-%
$expG6#%\"aG\"\"#\"\"\"&F06#%\"TGF2F1*&)-F.6#%\"bGF1F2&F:F4F2!\"\"*&F;
F2F,F2F<*&F;F2)-F.6#%\"cGF1F2F2*&F?F2&FBF4F2F<*&FDF2F,F2F<*&FDF2F7F2F2
F2*(F?F2F,F2F7F2F<#F<F1" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/&%\"CG6#%0
(2)~(3)~(2)~(3)G,$*&,:*&)-%$expG6#%\"aG\"\"#\"\"\")-F.6#%\"bGF1F2!\"\"
*(F1F2)-F.6#%\"cGF1F2F3F2F2*&F,F2F9F2F7*&F1F2)F-\"\"%F2F2*$)F4F@F2F7*$
)F:F@F2F7*(F1F2&F06#%\"TGF2&F6FGF2F2*&F1F2&F06$FHFHF2F7*(F1F2FFF2&F<FG
F2F2*(F@F2FIF2FNF2F7&F6FLF2&F<FLF2F2*(F9F2F,F2F3F2F7#F7\"\"'" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#/&%\"CG6#%0(2)~(4)~(2)~(4)G,$*&,:*&)-%$expG6
#%\"aG\"\"#\"\"\")-F.6#%\"bGF1F2F2*&)-F.6#%\"cGF1F2F3F2F2*(F1F2F,F2F8F
2!\"\"*$)F-\"\"%F2F2*&F1F2)F4F@F2F=*$)F9F@F2F2*(F@F2&F06#%\"TGF2&F;FGF
2F2*(F1F2FFF2&F6FGF2F=*(F1F2FKF2FIF2F=&F06$FHFHF=*&F1F2&F6FNF2F2&F;FNF
=F2*(F8F2F,F2F3F2F=#F=\"\"'" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/&%\"CG
6#%0(3)~(4)~(3)~(4)G,$*&,:*&)-%$expG6#%\"aG\"\"#\"\"\")-F.6#%\"bGF1F2!
\"#*&)-F.6#%\"cGF1F2F3F2F2*&F,F2F9F2F2*$)F-\"\"%F2F2*$)F4F@F2F2*&F1F2)
F:F@F2!\"\"*(F@F2&F06#%\"TGF2&F6FHF2F2*(F1F2FGF2&F<FHF2FE*(F1F2FJF2FLF
2FE&F06$FIFIFE&F6FOFE*&F1F2&F<FOF2F2F2*(F9F2F,F2F3F2FE#FE\"\"'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "grcalc(Rinvars);" }}{PARA 6 
"" 1 "" {TEXT -1 25 "Scalar invariant library." }}{PARA 6 "" 1 "" 
{TEXT -1 28 "Last modified 25 March 1997." }}{PARA 6 "" 1 "" {TEXT -1 
34 "Created definition for S(bup,bdn) " }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/%*CPU~Time~G$\"$6%!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 15 "gralter(_,6,7);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component simpli
fication of a GRTensorII object:" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}
{PARA 6 "" 1 "" {TEXT -1 45 "Applying routine expand to object Riccisc
alar" }}{PARA 6 "" 1 "" {TEXT -1 36 "Applying routine expand to object
 R1" }}{PARA 6 "" 1 "" {TEXT -1 36 "Applying routine expand to object \+
R2" }}{PARA 6 "" 1 "" {TEXT -1 36 "Applying routine expand to object R
3" }}{PARA 6 "" 1 "" {TEXT -1 45 "Applying routine factor to object Ri
cciscalar" }}{PARA 6 "" 1 "" {TEXT -1 36 "Applying routine factor to o
bject R1" }}{PARA 6 "" 1 "" {TEXT -1 36 "Applying routine factor to ob
ject R2" }}{PARA 6 "" 1 "" {TEXT -1 36 "Applying routine factor to obj
ect R3" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"$T&!\"$" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "To save space here we display onl
y R and R2.Increase grOptionDisplayLimit to display the other invarian
ts." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "grdisplay(Ricciscalar,R2);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#%8For~the~mix1~spacetime:G" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%-Ricci~scalarG" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#/%#R~G,$*&,:*&)-%$expG6#%\"cG\"\"#\"\"\")-F+6#%\"bGF.F/
F.*$)F*\"\"%F/!\"\"*$)-F+6#%\"aGF6F/F7*$)F1F6F/F7*&F6F/&F<6$%\"TGFBF/F
/*(F.F/)F:F.F/F)F/F/*&F6F/&F3FAF/F/*(F.F/FDF/F0F/F/*&F6F/&F-FAF/F/*(F6
F/&F<6#FBF/&F3FLF/F7*(F6F/FKF/&F-FLF/F7*(F6F/FMF/FOF/F7F/*(F)F/FDF/F0F
/F7#F/F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0CM~invariant~R2G" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#/%$R2~G,$*&*(,6&%\"bG6$%\"TGF,!\"%*(\"
\"#\"\"\")-%$expG6#%\"aGF/F0)-F36#F*F/F0F0*(F/F0F1F0)-F36#%\"cGF/F0!\"
\"*(F/F0F:F0F6F0F0*$)F;\"\"%F0F0*$)F2FBF0F0*&\"\"$F0)F7FBF0F>*(FBF0&F*
6#F,F0&F=FJF0F0*(FBF0&F5FJF0FIF0F0*(FBF0FMF0FKF0F0F0,6*&FMF0FKF0FB*(FB
F0FMF0FIF0F0*(FBF0FIF0FKF0F0*&FFF0FDF0F>*(F/F0F:F0F6F0F>F@F0*$FGF0F0*&
FBF0&F5F+F0F>*(F/F0F1F0F6F0F0*(F/F0F1F0F:F0F0F0,6FPF-*(FBF0FMF0FIF0F>*
(FBF0FIF0FKF0F>*(F/F0F1F0F6F0F0*&FFF0FAF0F0*(F/F0F1F0F:F0F>FUF>*&FBF0&
F=F+F0F0FCF>*(F/F0F:F0F6F0F>F0F0*()F;\"\"'F0)F2F_oF0)F7F_oF0F>#!\"$\"$
7&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "grcalc(Winvars);" }}
{PARA 6 "" 1 "" {TEXT -1 42 "Created definition for C(bdn,bdn,bup,bup)
 " }}{PARA 6 "" 1 "" {TEXT -1 42 "Created definition for C(bup,bup,bup
,bup) " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"$@%!\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gralter(_,6,7);" }}{PARA 6 "
" 1 "" {TEXT -1 48 "Component simplification of a GRTensorII object:" 
}}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 6 "" 1 "" {TEXT -1 37 "Applyin
g routine expand to object W1R" }}{PARA 6 "" 1 "" {TEXT -1 37 "Applyin
g routine expand to object W1I" }}{PARA 6 "" 1 "" {TEXT -1 37 "Applyin
g routine expand to object W2R" }}{PARA 6 "" 1 "" {TEXT -1 37 "Applyin
g routine expand to object W2I" }}{PARA 6 "" 1 "" {TEXT -1 37 "Applyin
g routine factor to object W1R" }}{PARA 6 "" 1 "" {TEXT -1 37 "Applyin
g routine factor to object W1I" }}{PARA 6 "" 1 "" {TEXT -1 37 "Applyin
g routine factor to object W2R" }}{PARA 6 "" 1 "" {TEXT -1 37 "Applyin
g routine factor to object W2I" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*C
PU~Time~G$\"$\"p!\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 110 "To save \+
space here we display only W1R and W1I. Increase grOptionDisplayLimit \+
to display the other invariants." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 
"grdisplay(W1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%8For~the~mix1~spac
etime:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%4CM~invariant~Re(W1)G" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#/%%W1R~G,$*&,^u*&)-%$expG6#%\"aG\"\"'
\"\"\")-F+6#%\"bG\"\"#F/!\"\"*&)-F+6#%\"cGF.F/F0F/F5*(\"\"%F/)&F36#%\"
TGF4F/)&F:F?F4F/F/*(F<F/)&F-F?F4F/FAF/F/*,F<F/)F*F4F/)F8F4F/FEF/F>F/F5
*,F4F/FGF/FHF/FEF/FBF/F/*,F<F/FGF/F0F/F>F/FBF/F5*,F<F/FGF/F0F/FEF/FBF/
F5*(F<F/FDF/F=F/F/*$)F8\"\")F/F/*$)F*FOF/F/*$)F1FOF/F/*,F4F/FHF/F0F/F>
F/FBF/F/*,F<F/FHF/F0F/FEF/F>F/F5*,F<F/FGF/FHF/F>F/FBF/F5*,F4F/FGF/F0F/
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