{VERSION 4 0 "IBM INTEL NT" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 256 "" 1 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
257 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 277 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 
278 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 280 "" 0 1 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "" 1 12 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 
0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading
 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }
1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 
-1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 
2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 
0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Map
le Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 
1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 
{CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 
0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 40 "The work integral in clas
sical mechanics" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 103 "Let us demonstrate the path independence of the work int
egral for a conservative curl-free force field," }}{PARA 0 "" 0 "" 
{TEXT -1 44 "such as the gravitational field of a sphere." }}{PARA 0 "
" 0 "" {TEXT -1 58 "Let us define the potential energy for a particle \+
of mass " }{TEXT 258 1 "m" }{TEXT -1 46 " in the field of the star (or
 planet) of mass " }{TEXT 257 1 "M" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 12 "V:=-G*M*m/r;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"VG,$*&*(%\"GG\"\"\"%\"MGF)%\"mGF)F)%\"rG!\"\"F-" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" 
{TEXT -1 80 "Warning, the protected names norm and trace have been red
efined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 
"F:=-grad(V,[x,y,z]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG,$-%'ve
ctorG6#7%\"\"!F*F*!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "That d
idn't work!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "F:=-grad(V,[
r,theta,phi],coords=spherical);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"FG,$-%'vectorG6#7%*&*(%\"GG\"\"\"%\"MGF-%\"mGF-F-*$)%\"rG\"\"#F-!\"
\"\"\"!F5F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(F[1]);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#&,$-%'vectorG6#7%*&*(%\"GG\"\"\"%
\"MGF,%\"mGF,F,*$)%\"rG\"\"#F,!\"\"\"\"!F4F36#F," }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 181 "The - sign on front of the grad throws Maple off,
 because the grad procedure returns a vector, and not a list. The fix \+
is to put the minus sign with the scalar potential function V." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "F:=grad(-V,[r,theta,phi],coo
rds=spherical);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG-%'vectorG6#7
%,$*&*(%\"GG\"\"\"%\"MGF-%\"mGF-F-*$)%\"rG\"\"#F-!\"\"F4\"\"!F5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "F[1];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*&*(%\"GG\"\"\"%\"MGF'%\"mGF'F'*$)%\"rG\"\"#F'!\"\"F.
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 85 "OK, Maple has its peculiar fe
atures! It didn't like the '-' sign before the gradient." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "curl(F,[r,theta,phi],coords=spheric
al);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%\"\"!F'F'" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "The force field is curl-free by co
nstruction: it has been derived from a scalar potential." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 132 "For plotting the \+
potential energy we need to switch to Cartesian coordinates. We choose
 the show the potential at a fixed z=1 plane:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 99 "PL1:=plot3d(subs(r=sqrt(x^2+y^2+1),G=1,M=1,m=1,V
),x=-5..5,y=-5..5,axes=boxed): plots[display](PL1);" }}{PARA 13 "" 1 "
" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6%-%%GRIDG6%;$!\"&\"\"!$\"\"&F)F&
X,%)anythingG6\"6\"][[[[]\\q\\bm\":\":BFC1EC70124E98F9BFC2AB59D92B962F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-%+AXESLABELSG6%%\"xG%\"yGQ!6\"-%*AXESSTYL
EG6#%$BOXG" 1 2 0 1 10 0 2 1 1 2 2 1.000000 45.000000 45.000000 0 0 "C
urve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Let us choose a straig
ht-line path:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "r_i:=[2,2,
1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$r_iG7%\"\"#F&\"\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "r_f:=[-2,0,1];" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%$r_fG7%!\"#\"\"!\"\"\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 21 "r_t:=r_i+(r_f-r_i)*t;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$r_tG,&7%\"\"#F'\"\"\"F(*&7%!\"%!\"#\"\"!F(%\"tGF(F(
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "evalm(r_t);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7%,&\"\"#\"\"\"*&\"\"%F)%\"tGF)!
\"\",&F(F)*&F(F)F,F)F-F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 120 "Note
: here t is a parameter, not necessarily time. Nevertheless, we call t
he derivative of the parameter representation " }{TEXT 264 1 "v" }
{TEXT -1 3 "_t:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "v_t:=dif
f(r_t,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$v_tG7%!\"%!\"#\"\"!" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "Now the work integral is reduced
 to a parameter integral using the dotproduct of " }{TEXT 263 1 "F" }
{TEXT -1 6 " with " }{TEXT 262 1 "v" }{TEXT -1 28 "_t, but also realiz
ing that " }{TEXT 261 1 "F" }{TEXT -1 38 " needs to be evaluated along
 the path," }}{PARA 0 "" 0 "" {TEXT -1 9 "i.e., as " }{TEXT 260 1 "F" 
}{TEXT -1 1 "(" }{TEXT 259 1 "r" }{TEXT -1 7 "_t) !!!" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 228 "Also: we have defined
 the parameter representation in Cartesian coordinates, so we should u
se these coordinates for the dot product calculation, which means that
 the force has to be translated into Cartesians. How do we do this?" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 46 "F:=grad(-subs(r=sqrt(x^2+y^2+z^2),V),[x,y,z]);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%\"FG-%'vectorG6#7%,$*&**%\"GG\"\"\"%\"MGF-%\"mGF-%
\"xGF-F-*$),(*$)F0\"\"#F-F-*$)%\"yGF6F-F-*$)%\"zGF6F-F-#\"\"$F6F-!\"\"
F?,$*&**F,F-F.F-F/F-F9F-F-*$)F3#F>F6F-F?F?,$*&**F,F-F.F-F/F-F<F-F-*$)F
3#F>F6F-F?F?" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "We start with the
 common mistake made by many beginners:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "Work:=int(dotprod(F,v_t),t=0..1);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%%WorkG,&*&**%\"GG\"\"\"%\"MGF)%\"mGF)%\"xGF)F)*$),(
*$)F,\"\"#F)F)*$)%\"yGF2F)F)*$)%\"zGF2F)F)#\"\"$F2F)!\"\"\"\"%*&*,F2F)
F(F)F*F)F+F)F5F)F)*$)F/#F:F2F)F;F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 41 "This is a bad answer for several reasons:" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "1) the work has to come o
ut as a number (we have specified initial and final points)." }}{PARA 
0 "" 0 "" {TEXT -1 57 "2) we have not evaluated the force along the ch
osen path." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "r_t:=evalm(r_
t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$r_tG-%'vectorG6#7%,&\"\"#\"
\"\"*&\"\"%F+%\"tGF+!\"\",&F*F+*&F*F+F.F+F/F+" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 66 "Work:=int(dotprod(subs(x=r_t[1],y=r_t[2],z=r_t[3
],F),v_t),t=0..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%WorkG,&*&**%
\"GG\"\"\"%\"MGF)%\"mGF)%\"xGF)F)*$),(*$)F,\"\"#F)F)*$)%\"yGF2F)F)*$)%
\"zGF2F)F)#\"\"$F2F)!\"\"\"\"%*&*,F2F)F(F)F*F)F+F)F5F)F)*$)F/#F:F2F)F;
F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "This is frustrating: we do \+
apparently the right thing, yet we get the same wrong answer!!!" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 29 "How do we
 avoid this pitfall?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 73 "1) look at subexpressions, and then realize that someth
ing hasn't worked." }}{PARA 0 "" 0 "" {TEXT -1 77 "Substitutions into \+
vectors and matrices in Maple require the use of the op():" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "dotprod(subs(x=r_t[1],y=r_t[2],z=r_
t[3],op(F)),v_t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&**%\"GG\"\"\"
%\"MGF'%\"mGF',&!\"\"F'*&\"\"#F'%\"tGF'F'F'F'*$),(\"\"*F'*&\"#CF'F.F'F
+*&\"#?F')F.F-F'F'#\"\"$F-F'F+!\")*&*,\"\"%F'F&F'F(F'F)F',&F+F'F.F'F'F
'*$)F1#F9F-F'F+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "This is the \+
correct integrand: it no longer depends on " }{TEXT 268 1 "x" }{TEXT 
-1 2 ", " }{TEXT 267 1 "y" }{TEXT -1 2 ", " }{TEXT 266 1 "z" }{TEXT 
-1 24 "  just on the parameter " }{TEXT 265 1 "t" }{TEXT -1 1 "." }}
{PARA 0 "" 0 "" {TEXT -1 20 "Now do the integral:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 70 "Work:=int(dotprod(subs(x=r_t[1],y=r_t[2],z=r
_t[3],op(F)),v_t),t=0..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%WorkG
,&**-%%sqrtG6#\"\"&\"\"\"%\"GGF+%\"MGF+%\"mGF+#F+F**&#F+\"\"$F+*(F,F+F
-F+F.F+F+!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "An alternative \+
to using op() is to convert the vector produced by grad into a list." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "FL:=convert(F,list);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#FLG7%,$*&**%\"GG\"\"\"%\"MGF*%\"mGF
*%\"xGF*F**$),(*$)F-\"\"#F*F**$)%\"yGF3F*F**$)%\"zGF3F*F*#\"\"$F3F*!\"
\"F<,$*&**F)F*F+F*F,F*F6F*F**$)F0#F;F3F*F<F<,$*&**F)F*F+F*F,F*F9F*F**$
)F0#F;F3F*F<F<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "Work:=int
(dotprod(subs(x=r_t[1],y=r_t[2],z=r_t[3],FL),v_t),t=0..1);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%%WorkG,&**-%%sqrtG6#\"\"&\"\"\"%\"GGF+%\"M
GF+%\"mGF+#F+F**&#F+\"\"$F+*(F,F+F-F+F.F+F+!\"\"" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,
$*(%\"GG\"\"\"%\"MGF&%\"mGF&$\"+BE!)Q6!#5" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 78 "The work integral tells us by how much the kinetic energy
 has changed between " }{TEXT 271 1 "r" }{TEXT -1 7 "_i and " }{TEXT 
270 1 "r" }{TEXT -1 45 "_f due to the work done by the force on mass \+
" }{TEXT 269 1 "m" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 68 "Now \+
let us compare this result with the potential energy difference:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "r_i;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7%\"\"#F$\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 
"We need a function to calculate the magnitude of the position vector:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "v_mag:=v->sqrt(add(v[i]
^2,i=1..3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&v_magGR6#%\"vG6\"6$
%)operatorG%&arrowGF(-%%sqrtG6#-%$addG6$*$)&9$6#%\"iG\"\"#\"\"\"/F7;F9
\"\"$F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "v_mag(r_i),v
_mag(r_f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"$*$-%%sqrtG6#\"\"&\"
\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "subs(r=v_mag(r_i),V
)-subs(r=v_mag(r_f),V);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&**-%%sqrt
G6#\"\"&\"\"\"%\"GGF)%\"MGF)%\"mGF)#F)F(*&#F)\"\"$F)*(F*F)F+F)F,F)F)!
\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 180 "We recognize that the di
fference between the potential energy at the initial and final points \+
amounts to the same as the work done on the particle, or the change in
 kinetic energy." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Work-%;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 16 "with(plottools);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6
#7F%$arcG%&arrowG%'circleG%%coneG%'cuboidG%&curveG%&cutinG%'cutoutG%)c
ylinderG%%diskG%-dodecahedronG%(ellipseG%,ellipticArcG%+hemisphereG%+h
exahedronG%*homothetyG%*hyperbolaG%,icosahedronG%%lineG%+octahedronG%)
piesliceG%&pointG%(polygonG%(projectG%*rectangleG%(reflectG%'rotateG%&
scaleG%*semitorusG%'sphereG%)stellateG%,tetrahedronG%&torusG%*transfor
mG%*translateG%%vrmlG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "l \+
:= line(r_i, r_f, color=red, linestyle=2, thickness=3): plots[display]
(l,PL1);" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6&-%'C
URVESG6&7$7%$\"\"#\"\"!F($\"\"\"F*7%$!\"#F*$F*F*F+-%*THICKNESSG6#\"\"$
-%*LINESTYLEG6#F)-%'COLOURG6&%$RGBG$\"*++++\"!\")F0F0-%%GRIDG6%;$!\"&F
*$\"\"&F*FBX,%)anythingG6\"6\"][[[[]\\q\\bm\":\":BFC1EC70124E98F9BFC2A
B59D92B962FBFC37038CB24744CBFC4390861AA78CFBFC502F49F9D6955BFC5CA3BC0E
092E4BFC68A1F80D71818BFC73CF2A377B47FBFC7DC50378E0408BFC8618618618619B
FC8C6318C6318C7BFC904FC246766CBBFC91A556151761CBFC904FC246766CBBFC8C63
18C6318C7BFC8618618618619BFC7DC50378E0408BFC73CF2A377B47FBFC68A1F80D71
818BFC5CA3BC0E092E4BFC502F49F9D6955BFC4390861AA78CFBFC37038CB24744CBFC
2AB59D92B962FBFC1EC70124E98F9BFC2AB59D92B962FBFC384442E05C1C4BFC4667E7
8FF99C9BFC55012CDC31B76BFC63E0030F579A2BFC72C000B101E41BFC81459C53FF0A
EBFC8EFD9031F6F35BFC9B6001CDFE531BFCA5D8E901FAD9CBFCADD641D8114F9BFCB2
DAB1AB5DB26BFCB490F0851E53FBFCB2DAB1AB5DB26BFCADD641D8114F9BFCA5D8E901
FAD9CBFC9B6001CDFE531BFC8EFD9031F6F35BFC81459C53FF0AEBFC72C000B101E41B
FC63E0030F579A2BFC55012CDC31B76BFC4667E78FF99C9BFC384442E05C1C4BFC2AB5
9D92B962FBFC37038CB24744CBFC4667E78FF99C9BFC56A86A8DD715ABFC67AA7844C6
C64BFC793EB95DD6386BFC8B1AB80301514BFC9CD2CC8BF8863BFCADD641D8114F9BFC
BD708D08935F7BFCCAD2E3A4771A5BFCD528740128724BFCDBB4411CC7150BFCDDF2A3
7538475BFCDBB4411CC7150BFCD528740128724BFCCAD2E3A4771A5BFCBD708D08935F
7BFCADD641D8114F9BFC9CD2CC8BF8863BFC8B1AB80301514BFC793EB95DD6386BFC67
AA7844C6C64BFC56A86A8DD715ABFC4667E78FF99C9BFC37038CB24744CBFC4390861A
A78CFBFC55012CDC31B76BFC67AA7844C6C64BFC7B7CB0BF1D6F6BFC904FC246766CCB
FCA5D8E901FAD9CBFCBB9F25E1EE4D6BFCD0F0F00C22941BFCE4DFD0B45B7B9BFCF648
A3A321F8EBFD01F78597005D3BFD0656C9FBD8B2BBFD07D8B7C63AADDBFD0656C9FBD8
B2BBFD01F78597005D3BFCF648A3A321F8EBFCE4DFD0B45B7B9BFCD0F0F00C22941BFC
BB9F25E1EE4D6BFCA5D8E901FAD9CBFC904FC246766CCBFC7B7CB0BF1D6F6BFC67AA78
44C6C64BFC55012CDC31B76BFC4390861AA78CFBFC502F49F9D6955BFC63E0030F579A
2BFC793EB95DD6386BFC904FC246766CCBFCA8FD472123D18BFCC307DBAC15D76BFCDD
F2A37538475BFCF8ED557B1670DBFD0961609B1A4D5BFD14EC2D2D958D2BFD1E279469
63306BFD24285CCB18F4EBFD263E862C542D5BFD24285CCB18F4EBFD1E27946963306B
FD14EC2D2D958D2BFD0961609B1A4D5BFCF8ED557B1670DBFCDDF2A37538475BFCC307
DBAC15D76BFCA8FD472123D18BFC904FC246766CCBFC793EB95DD6386BFC63E0030F57
9A2BFC502F49F9D6955BFC5CA3BC0E092E4BFC72C000B101E41BFC8B1AB80301514BFC
A5D8E901FAD9CBFCC307DBAC15D76BFCE28837E8D09B2BFD01F78597005D3BFD132E5D
89F9B22BFD24285CCB18F4EBFD33C7126FEB930BFD409AE1F10DABEBFD491DDAE347FA
3BFD4C1BACF914C1CBFD491DDAE347FA3BFD409AE1F10DABEBFD33C7126FEB930BFD24
285CCB18F4EBFD132E5D89F9B22BFD01F78597005D3BFCE28837E8D09B2BFCC307DBAC
15D76BFCA5D8E901FAD9CBFC8B1AB80301514BFC72C000B101E41BFC5CA3BC0E092E4B
FC68A1F80D71818BFC81459C53FF0AEBFC9CD2CC8BF8863BFCBB9F25E1EE4D6BFCDDF2
A37538475BFD01F78597005D3BFD16B28F55D72D4BFD2CC8673C6804DBFD435E50D794
35EBFD58F2077ECA743BFD6B4D65E5FB662BFD77D4AE44BF43BBFD7C4DD663EBB88BFD
77D4AE44BF43BBFD6B4D65E5FB662BFD58F2077ECA743BFD435E50D79435EBFD2CC867
3C6804DBFD16B28F55D72D4BFD01F78597005D3BFCDDF2A37538475BFCBB9F25E1EE4D
6BFC9CD2CC8BF8863BFC81459C53FF0AEBFC68A1F80D71818BFC73CF2A377B47FBFC8E
FD9031F6F35BFCADD641D8114F9BFCD0F0F00C22941BFCF8ED557B1670DBFD132E5D89
F9B22BFD2CC8673C6804DBFD491DDAE347FA2BFD676586A60B525BFD85C06EF5EC461B
FDA0D78377B313EBFDB415B597DE13FBFDBB1DDA5CF5834BFDB415B597DE13EBFDA0D7
8377B313EBFD85C06EF5EC461BFD676586A60B525BFD491DDAE347FA2BFD2CC8673C68
04DBFD132E5D89F9B22BFCF8ED557B1670DBFCD0F0F00C22941BFCADD641D8114F9BFC
8EFD9031F6F35BFC73CF2A377B47FBFC7DC50378E0408BFC9B6001CDFE531BFCBD708D
08935F7BFCE4DFD0B45B7B9BFD0961609B1A4D5BFD24285CCB18F4EBFD435E50D79435
EBFD676586A60B525BFD8FF0B9C392ECCBFDBB1DDA5CF5834BFDE4370C710AC79BFE01
91E395DC880BFE076BFCD6FBECDBFE0191E395DC880BFDE4370C710AC78BFDBB1DDA5C
F5834BFD8FF0B9C392ECCBFD676586A60B525BFD435E50D79435EBFD24285CCB18F4EB
FD0961609B1A4D5BFCE4DFD0B45B7B9BFCBD708D08935F7BFC9B6001CDFE531BFC7DC5
0378E0408BFC8618618618619BFCA5D8E901FAD9CBFCCAD2E3A4771A5BFCF648A3A321
F8EBFD14EC2D2D958D2BFD33C7126FEB930BFD58F2077ECA743BFD85C06EF5EC461BFD
BB1DDA5CF5834BFDF82EC882C0F9BBFE1BB41C8400209BFE3587BE5A71417BFE3FD807
7E70577BFE3587BE5A71417BFE1BB41C8400208BFDF82EC882C0F9ABFDBB1DDA5CF583
4BFD85C06EF5EC461BFD58F2077ECA743BFD33C7126FEB930BFD14EC2D2D958D2BFCF6
48A3A321F8EBFCCAD2E3A4771A5BFCA5D8E901FAD9CBFC8618618618619BFC8C6318C6
318C7BFCADD641D8114F9BFCD528740128724BFD01F78597005D3BFD1E27946963306B
FD409AE1F10DABEBFD6B4D65E5FB662BFDA0D78377B313EBFDE4370C710AC79BFE1BB4
1C8400209BFE4B4324BC26276BFE769B35EAE2887BFE89544CAFEC8B8BFE769B35EAE2
887BFE4B4324BC26276BFE1BB41C8400208BFDE4370C710AC78BFDA0D78377B313EBFD
6B4D65E5FB662BFD409AE1F10DABEBFD1E27946963306BFD01F78597005D3BFCD52874
0128724BFCADD641D8114F9BFC8C6318C6318C7BFC904FC246766CBBFCB2DAB1AB5DB2
6BFCDBB4411CC7150BFD0656C9FBD8B2BBFD24285CCB18F4EBFD491DDAE347FA3BFD77
D4AE44BF43BBFDB415B597DE13FBFE0191E395DC880BFE3587BE5A71417BFE769B35EA
E2887BFEB91D0DDAC86FFBFED89D89D89D89EBFEB91D0DDAC86FEBFE769B35EAE2887B
FE3587BE5A71416BFE0191E395DC880BFDB415B597DE13FBFD77D4AE44BF43BBFD491D
DAE347FA3BFD24285CCB18F4EBFD0656C9FBD8B2BBFCDBB4411CC7150BFCB2DAB1AB5D
B26BFC904FC246766CBBFC91A556151761CBFCB490F0851E53FBFCDDF2A37538475BFD
07D8B7C63AADDBFD263E862C542D5BFD4C1BACF914C1CBFD7C4DD663EBB88BFDBB1DDA
5CF5834BFE076BFCD6FBECDBFE3FD8077E70577BFE89544CAFEC8B8BFED89D89D89D89
EBFF0000000000000BFED89D89D89D89DBFE89544CAFEC8B6BFE3FD8077E70576BFE07
6BFCD6FBECCBFDBB1DDA5CF5834BFD7C4DD663EBB88BFD4C1BACF914C1CBFD263E862C
542D5BFD07D8B7C63AADDBFCDDF2A37538475BFCB490F0851E53FBFC91A556151761CB
FC904FC246766CBBFCB2DAB1AB5DB26BFCDBB4411CC7150BFD0656C9FBD8B2BBFD2428
5CCB18F4EBFD491DDAE347FA3BFD77D4AE44BF43BBFDB415B597DE13EBFE0191E395DC
880BFE3587BE5A71417BFE769B35EAE2887BFEB91D0DDAC86FEBFED89D89D89D89DBFE
B91D0DDAC86FEBFE769B35EAE2887BFE3587BE5A71416BFE0191E395DC880BFDB415B5
97DE13EBFD77D4AE44BF43BBFD491DDAE347FA3BFD24285CCB18F4EBFD0656C9FBD8B2
BBFCDBB4411CC7150BFCB2DAB1AB5DB26BFC904FC246766CBBFC8C6318C6318C7BFCAD
D641D8114F9BFCD528740128724BFD01F78597005D3BFD1E27946963306BFD409AE1F1
0DABEBFD6B4D65E5FB662BFDA0D78377B313EBFDE4370C710AC78BFE1BB41C8400208B
FE4B4324BC26276BFE769B35EAE2887BFE89544CAFEC8B6BFE769B35EAE2887BFE4B43
24BC26275BFE1BB41C8400208BFDE4370C710AC78BFDA0D78377B313EBFD6B4D65E5FB
662BFD409AE1F10DABEBFD1E27946963306BFD01F78597005D3BFCD528740128724BFC
ADD641D8114F9BFC8C6318C6318C7BFC8618618618619BFCA5D8E901FAD9CBFCCAD2E3
A4771A5BFCF648A3A321F8EBFD14EC2D2D958D2BFD33C7126FEB930BFD58F2077ECA74
3BFD85C06EF5EC461BFDBB1DDA5CF5834BFDF82EC882C0F9ABFE1BB41C8400208BFE35
87BE5A71416BFE3FD8077E70576BFE3587BE5A71416BFE1BB41C8400208BFDF82EC882
C0F99BFDBB1DDA5CF5833BFD85C06EF5EC461BFD58F2077ECA743BFD33C7126FEB930B
FD14EC2D2D958D2BFCF648A3A321F8EBFCCAD2E3A4771A5BFCA5D8E901FAD9CBFC8618
618618619BFC7DC50378E0408BFC9B6001CDFE531BFCBD708D08935F7BFCE4DFD0B45B
7B9BFD0961609B1A4D5BFD24285CCB18F4EBFD435E50D79435EBFD676586A60B525BFD
8FF0B9C392ECCBFDBB1DDA5CF5834BFDE4370C710AC78BFE0191E395DC880BFE076BFC
D6FBECCBFE0191E395DC880BFDE4370C710AC78BFDBB1DDA5CF5833BFD8FF0B9C392EC
CBFD676586A60B525BFD435E50D79435EBFD24285CCB18F4EBFD0961609B1A4D5BFCE4
DFD0B45B7B9BFCBD708D08935F7BFC9B6001CDFE531BFC7DC50378E0408BFC73CF2A37
7B47FBFC8EFD9031F6F35BFCADD641D8114F9BFCD0F0F00C22941BFCF8ED557B1670DB
FD132E5D89F9B22BFD2CC8673C6804DBFD491DDAE347FA2BFD676586A60B525BFD85C0
6EF5EC461BFDA0D78377B313EBFDB415B597DE13FBFDBB1DDA5CF5834BFDB415B597DE
13EBFDA0D78377B313EBFD85C06EF5EC461BFD676586A60B525BFD491DDAE347FA2BFD
2CC8673C6804DBFD132E5D89F9B22BFCF8ED557B1670DBFCD0F0F00C22941BFCADD641
D8114F9BFC8EFD9031F6F35BFC73CF2A377B47FBFC68A1F80D71818BFC81459C53FF0A
EBFC9CD2CC8BF8863BFCBB9F25E1EE4D6BFCDDF2A37538475BFD01F78597005D3BFD16
B28F55D72D4BFD2CC8673C6804DBFD435E50D79435EBFD58F2077ECA743BFD6B4D65E5
FB662BFD77D4AE44BF43BBFD7C4DD663EBB88BFD77D4AE44BF43BBFD6B4D65E5FB662B
FD58F2077ECA743BFD435E50D79435EBFD2CC8673C6804DBFD16B28F55D72D4BFD01F7
8597005D3BFCDDF2A37538475BFCBB9F25E1EE4D6BFC9CD2CC8BF8863BFC81459C53FF
0AEBFC68A1F80D71818BFC5CA3BC0E092E4BFC72C000B101E41BFC8B1AB80301514BFC
A5D8E901FAD9CBFCC307DBAC15D76BFCE28837E8D09B2BFD01F78597005D3BFD132E5D
89F9B22BFD24285CCB18F4EBFD33C7126FEB930BFD409AE1F10DABEBFD491DDAE347FA
3BFD4C1BACF914C1CBFD491DDAE347FA3BFD409AE1F10DABEBFD33C7126FEB930BFD24
285CCB18F4EBFD132E5D89F9B22BFD01F78597005D3BFCE28837E8D09B2BFCC307DBAC
15D76BFCA5D8E901FAD9CBFC8B1AB80301514BFC72C000B101E41BFC5CA3BC0E092E4B
FC502F49F9D6955BFC63E0030F579A2BFC793EB95DD6386BFC904FC246766CCBFCA8FD
472123D18BFCC307DBAC15D76BFCDDF2A37538475BFCF8ED557B1670DBFD0961609B1A
4D5BFD14EC2D2D958D2BFD1E27946963306BFD24285CCB18F4EBFD263E862C542D5BFD
24285CCB18F4EBFD1E27946963306BFD14EC2D2D958D2BFD0961609B1A4D5BFCF8ED55
7B1670DBFCDDF2A37538475BFCC307DBAC15D76BFCA8FD472123D18BFC904FC246766C
CBFC793EB95DD6386BFC63E0030F579A2BFC502F49F9D6955BFC4390861AA78CFBFC55
012CDC31B76BFC67AA7844C6C64BFC7B7CB0BF1D6F6BFC904FC246766CCBFCA5D8E901
FAD9CBFCBB9F25E1EE4D6BFCD0F0F00C22941BFCE4DFD0B45B7B9BFCF648A3A321F8EB
FD01F78597005D3BFD0656C9FBD8B2BBFD07D8B7C63AADDBFD0656C9FBD8B2BBFD01F7
8597005D3BFCF648A3A321F8EBFCE4DFD0B45B7B9BFCD0F0F00C22941BFCBB9F25E1EE
4D6BFCA5D8E901FAD9CBFC904FC246766CCBFC7B7CB0BF1D6F6BFC67AA7844C6C64BFC
55012CDC31B76BFC4390861AA78CFBFC37038CB24744CBFC4667E78FF99C9BFC56A86A
8DD715ABFC67AA7844C6C64BFC793EB95DD6386BFC8B1AB80301514BFC9CD2CC8BF886
3BFCADD641D8114F9BFCBD708D08935F7BFCCAD2E3A4771A5BFCD528740128724BFCDB
B4411CC7150BFCDDF2A37538475BFCDBB4411CC7150BFCD528740128724BFCCAD2E3A4
771A5BFCBD708D08935F7BFCADD641D8114F9BFC9CD2CC8BF8863BFC8B1AB80301514B
FC793EB95DD6386BFC67AA7844C6C64BFC56A86A8DD715ABFC4667E78FF99C9BFC3703
8CB24744CBFC2AB59D92B962FBFC384442E05C1C4BFC4667E78FF99C9BFC55012CDC31
B76BFC63E0030F579A2BFC72C000B101E41BFC81459C53FF0AEBFC8EFD9031F6F35BFC
9B6001CDFE531BFCA5D8E901FAD9CBFCADD641D8114F9BFCB2DAB1AB5DB26BFCB490F0
851E53FBFCB2DAB1AB5DB26BFCADD641D8114F9BFCA5D8E901FAD9CBFC9B6001CDFE53
1BFC8EFD9031F6F35BFC81459C53FF0AEBFC72C000B101E41BFC63E0030F579A2BFC55
012CDC31B76BFC4667E78FF99C9BFC384442E05C1C4BFC2AB59D92B962FBFC1EC70124
E98F9BFC2AB59D92B962FBFC37038CB24744CBFC4390861AA78CFBFC502F49F9D6955B
FC5CA3BC0E092E4BFC68A1F80D71818BFC73CF2A377B47FBFC7DC50378E0408BFC8618
618618619BFC8C6318C6318C7BFC904FC246766CBBFC91A556151761CBFC904FC24676
6CBBFC8C6318C6318C7BFC8618618618619BFC7DC50378E0408BFC73CF2A377B47FBFC
68A1F80D71818BFC5CA3BC0E092E4BFC502F49F9D6955BFC4390861AA78CFBFC37038C
B24744CBFC2AB59D92B962FBFC1EC70124E98F9-%+AXESLABELSG6%%\"xG%\"yGQ!6\"
-%*AXESSTYLEG6#%$BOXG" 1 2 0 1 10 0 2 1 1 2 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
78 "We want to indicate with the height the amount of potential energy
, therefore:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "r_iV:=r_i: \+
r_iV[3]:=subs(r=v_mag(r_i),G=1,M=1,m=1,V): r_iV;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7%\"\"#F$#!\"\"\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 59 "r_fV:=r_f: r_fV[3]:=subs(r=v_mag(r_f),G=1,M=1,m=1,V):
 r_fV;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%!\"#\"\"!,$*$-%%sqrtG6#\"
\"&\"\"\"#!\"\"F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "l := l
ine(r_iV, r_fV, color=red, linestyle=2, thickness=3): plots[display](l
,PL1);" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "6&-%'CUR
VESG6&7$7%$\"\"#\"\"!F($!+LLLLL!#57%$!\"#F*$F*F*$!+cf8sWF--%*THICKNESS
G6#\"\"$-%*LINESTYLEG6#F)-%'COLOURG6&%$RGBG$\"*++++\"!\")F1F1-%%GRIDG6
%;$!\"&F*$\"\"&F*FEX,%)anythingG6\"6\"][[[[]\\q\\bm\":\":BFC1EC70124E9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-%+AXESLABELSG6%%\"xG%
\"yGQ!6\"-%*AXESSTYLEG6#%$BOXG" 1 2 0 1 10 0 2 1 1 2 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 159 "As the particle traverses the potential well it picks \+
up a lot of kinetic energy on the way down, in order to give up a good
 fraction as it climbs up the hill." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 75 "We can verify this by calculating the wo
rk done at some intermediate point." }}{PARA 0 "" 0 "" {TEXT -1 43 "Fi
rst recall the total kinetic energy gain:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 12 "evalf(Work);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*
(%\"GG\"\"\"%\"MGF&%\"mGF&$\"+BE!)Q6!#5" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 79 "Now break the path up into two halves, just by looking at
 what happens between " }{TEXT 275 1 "t" }{TEXT -1 7 "=0 and " }{TEXT 
274 1 "t" }{TEXT -1 23 "=0.5, and then between " }{TEXT 273 1 "t" }
{TEXT -1 9 "=0.5 and " }{TEXT 272 1 "t" }{TEXT -1 3 "=1:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "Work1:=int(dotprod(subs(x=r_t[1],y=
r_t[2],z=r_t[3],op(F)),v_t),t=0..1/2);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%&Work1G,&**-%%sqrtG6#\"\"#\"\"\"%\"GGF+%\"MGF+%\"mGF+#F+F**&#F
+\"\"$F+*(F,F+F-F+F.F+F+!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 73 "Work2:=int(dotprod(subs(x=r_t[1],y=r_t[2],z=r_t[3],op(F)),v_t),t
=1/2..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&Work2G,&**-%%sqrtG6#\"
\"&\"\"\"%\"GGF+%\"MGF+%\"mGF+#F+F**&#F+\"\"#F+**-F(6#F2F+F,F+F-F+F.F+
F+!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "evalf([Work1,Wor
k2,Work1+Work2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%,$*(%\"GG\"\"\"
%\"MGF'%\"mGF'$\"+xWtPP!#5,$F%$!+a=$*)f#F,,$F%$\"+BE!)Q6F," }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 323 "Notice the large amount of work done on \+
the particle on the first 'half', then the particle works against the \+
potential well, but still has a net gain of kinetic energy at the fina
l point. It is, however, at a lower value of potential energy at this \+
point, i.e., it gained kinetic energy at the expense of potential ener
gy." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 177 "Now consider a non-conservative force. It will have no direct \+
physical meaning, i.e., it is a made-up problem to demonstrate what ha
ppens when a force field is not conservative." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "F:=[x^2+2*y-z,y+z-x,z^3+x*2
];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG7%,(*$)%\"xG\"\"#\"\"\"F+*
&F*F+%\"yGF+F+%\"zG!\"\",(F-F+F.F+F)F/,&*$)F.\"\"$F+F+*&F*F+F)F+F+" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "
" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have b
een redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 16 "curl(F,[x,y,z]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG
6#7%!\"\"!\"$F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 132 "This force fi
eld is not curl-free, which means that it cannot be derived from a sca
lar potential. We choose the same path as before." }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "r_i:=[2,2,1];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$r_iG7%\"\"#F&\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "r_f:=[-2,0,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$r_fG7%!\"#
\"\"!\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "r_t:=evalm(r
_i+(r_f-r_i)*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$r_tG-%'vectorG6
#7%,&\"\"#\"\"\"*&\"\"%F+%\"tGF+!\"\",&F*F+*&F*F+F.F+F/F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "v_t:=diff(r_t,t);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%$v_tG\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 
"Another one of these Maple-quirks. We defined " }{TEXT 19 3 "r_t" }
{TEXT -1 36 " as a combination of lists, but the " }{TEXT 19 5 "evalm
" }{TEXT -1 21 " did something funny." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "whattype(r_t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%'s
ymbolG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "The evalm turned " }
{TEXT 19 3 "r_t" }{TEXT -1 15 " into a symbol." }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 21 "v_t:=map(diff,r_t,t);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$v_tG-%'vectorG6#7%!\"%!\"#\"\"!" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 22 "If we had avoided the " }{TEXT 19 5 "evalm" }
{TEXT -1 139 ", the simple differentiation would have worked because t
 appeared as a factor of one of the lists (as carried out in the previ
ous section)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "Work1:=int
(dotprod(subs(x=r_t[1],y=r_t[2],z=r_t[3],F),v_t),t=0..1/2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%&Work1G#!#\\\"\"'" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 69 "Work2:=int(dotprod(subs(x=r_t[1],y=r_t[2],z=r_t[
3],F),v_t),t=1/2..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&Work2G#!#J
\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "Work:=int(dotprod(
subs(x=r_t[1],y=r_t[2],z=r_t[3],F),v_t),t=0..1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%WorkG#!#S\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 38 "evalf([Work1,Work2,Work1+Work2,Work]);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#7&$!+nmmm\")!\"*$!+nmmm^F&$!+LLLL8!\")F)" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 229 "Of course, the work integral is a
dditive. What we want to demonstrate is that if we connect the two end
points in some different way, then a different result will be found fo
r the work done on the particle as it moves from A to B." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 122 "Let us choose as \+
an alternative to the direct connection from A to B a path that goes v
ia the origin [0,0,1] in the plane." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "r_1:=[0,0,1];" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%$r_1G7%\"\"!F&\"\"\"" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 30 "r_tp1:=evalm(r_i+(r_1-r_i)*t);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%&r_tp1G-%'vectorG6#7%,&\"\"#\"\"\"*&F*F+%\"tGF+!\"
\"F)F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "v_tp1:=map(diff,r
_tp1,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&v_tp1G-%'vectorG6#7%!\"
#F)\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "r_tp2:=evalm(r_
1+(r_f-r_1)*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&r_tp2G-%'vectorG
6#7%,$%\"tG!\"#\"\"!\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "v_tp2:=map(diff,r_tp2,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&v_
tp2G-%'vectorG6#7%!\"#\"\"!F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "
Now we are ready to calculate the work integral." }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 75 "Work1:=int(dotprod(subs(x=r_tp1[1],y=r_tp1[2]
,z=r_tp1[3],F),v_tp1),t=0..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&W
ork1G#!#?\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "Work2:=in
t(dotprod(subs(x=r_tp2[1],y=r_tp2[2],z=r_tp2[3],F),v_tp2),t=0..1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&Work2G#!\"#\"\"$" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 26 "evalf([Work1+Work2,Work]);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#7$$!+LLLLt!\"*$!+LLLL8!\")" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 109 "The amount work done on the particle as it moves \+
through the force field along a different path is different!" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 77 "What can we do \+
to visualize the force field, and how it affects the particle?" }}
{PARA 0 "" 0 "" {TEXT -1 36 "First define the force field in the " }
{TEXT 277 1 "z" }{TEXT -1 90 "=1 plane and ignore the z-component of t
he force, as we are not moving the particle along " }{TEXT 278 1 "z" }
{TEXT -1 51 " (no work is done by this component of the force!)." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "Fzeq1:=subs(z=1,F);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&Fzeq1G7%,(*$)%\"xG\"\"#\"\"\"F+*&F*
F+%\"yGF+F+F+!\"\",(F-F+F+F+F)F.,&F+F+*&F*F+F)F+F+" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 25 "F2d:=[Fzeq1[1],Fzeq1[2]];" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%$F2dG7$,(*$)%\"xG\"\"#\"\"\"F+*&F*F+%\"yGF+F+F+!\"
\",(F-F+F+F+F)F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(pl
ots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords h
as been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "PL1:
=fieldplot(F2d,x=-2..2,y=-2..2,arrows=thick,color=blue,axes=boxed,grid
=[12,12]): display(PL1);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 
{PLOTDATA 2 "6%-%)POLYGONSG6]t7*7$$!3(G;<V$f8@?!#<$!39PGolS')y>F*7$F($
!3b&fZ1za(3?F*7$$!3#*4*G$fB<6?F*$!3#GMfc@\"z)*>F*7$$!3gjp<`e%Q)>F*$!38
*G6=s<h-#F*7$$!3m5()=yA)Q(>F*$!3iOI#o9ah,#F*7$$!3(plSVy37+#F*$!33!4r1k
F)))>F*7$$!3C/CN4_C\"*>F*F+F'7*7$$!3gE&zN\"zW&o\"F*$!3M()*z*f)\\l)>F*7
$$!3o*eENx]-m\"F*$!3AV]Yq$o2.#F*7$$!3I$)er;.\"Rl\"F*$!3N7dG?)Hw+#F*7$$
!31*4`ve\\/f\"F*$!34y'4^T>]-#F*7$$!3o#RU284Te\"F*$!3BZ.$\\'3)=+#F*7$$!
3!p<0*f)pvk\"F*$!3]\"Q1,F\"\\%)>F*7$$!3_qW4.%H7k\"F*$!3S]q#*>FNh>F*FH7
*7$$!3%\\9iUAqTM\"F*$!3MPrFacB%*>F*7$$!3Q%f8nVGxH\"F*$!3cn^sd%H)[?F*7$
$!3eM/3)46]H\"F*$!3vtHRF4::?F*7$$!3%*z*30*Hk-7F*$!38f*))3h.E-#F*7$$!35
?e(=lD**>\"F*$!3wlnb!3D*))>F*7$$!3wusWfPH#H\"F*$!3Q!ygqRs9)>F*7$$!3%\\
693Uw&*G\"F*$!3y'eGn'QzZ>F*Ffo7*7$$!3qz,lj'GI(**!#=$!3L(Gu&[9#>+#F*7$$
!3qu<yQ#*oN$*F]r$!37ozU_!QH1#F*7$$!37TcAMquW$*F]r$!3mF6)p`a8-#F*7$$!3T
kgW?1E/#)F]r$!3oK\"\\\"4.()=?F*7$$!3tH**)eT=L@)F]r$!3A#H-Pz'Gx>F*7$$!3
W1&p'H[!QN*F]r$!3?(GM:-r(z>F*7$$!3'GP8^iiGO*F]r$!3sYu31v=Q>F*Fjq7*7$$!
3m`9)))Re%[kF]r$!3bP9(GC2'4?F*7$$!3W#Q.-NAxn&F]r$!3OXMdaT4t?F*7$$!3Y8F
UF8,BdF]r$!3lt,0\\1CE?F*7$$!37%y*f@!))zV%F]r$!3J)>!*)4&>Q,#F*7$$!37:\"
>))*pF$[%F]r$!3gEpO/g'p'>F*7$$!3YW?k/.IodF]r$!3;-p_VrQz>F*7$$!3Zv8'=G*
e8eF]r$!3VIO+QO`K>F*F_t7*7$$!3)HF:$[9*z'GF]r$!3x(eor.$H<?F*7$$!3Qp2S,P
Q.?F]r$!3G*fhTw(Hz?F*7$$!3_lbRgQ!\\3#F]r$!3;7,gj#4)H?F*7$$!3I(f4b3@hF(
!#>$!3-c@687X2?F*7$$!3uevXvEK\"4)Few$!3oo1b7F'z&>F*7$$!3mh.R>SUm@F]r$!
3#[iQIw?.)>F*7$$!3!y:&QyT%zC#F]r$!3YPrZiA$3$>F*Fcv7*7$$\"3#\\j$[!)=s$o
(Few$!3)ztl9$)y\\-#F*7$$\"3'R1EwqEto\"F]r$!3')HC>\"))[:3#F*7$$\"3C.e&o
Ov&p:F]r$!3IU4j!Qg?.#F*7$$\"3<4/q=r'o#HF]r$!3!e+:)=aw**>F*7$$\"3)y9Izx
:\"4GF]r$!3o=ND=pF]>F*7$$\"3AUb3ES#=X\"F]r$!3=b%p+)=d#)>F*7$$\"3A\"G:`
osSL\"F]r$!3#y'z]zL3L>F*Fhx7*7$$\"3=b%4-^K1Y%F]r$!3w()GwDYmK?F*7$$\"35
=r(o()3WR&F]r$!3COfm0v%)z?F*7$$\"3O$RJVNE/C&F]r$!3^kE9+S*H.#F*7$$\"3:A
V:g'\\a_'F]r$!3)yu)*p7i2*>F*7$$\"3G'f3w8n9P'F]r$!3;waZ@'3R%>F*7$$\"3]n
cyJQW'3&F]r$!3-$R>Y\\Sh)>F*7$$\"34T*R#48YK\\F]r$!3^@h4*)pGR>F*F\\[l7*7
$$\"3i-!o\"=&*y3#)F]r$!3(z.g+U]./#F*7$$\"3x%R_j!G'y6*F]r$!3s>@ePO>u?F*
7$$\"3@.7.-\"\\w#*)F]r$!3qz_8A,hK?F*7$$\"35y5e^N\"o+\"F*$!3E#QjwLT/)>F
*7$$\"3[*e*[6=#z()*F]r$!3zTl@Ay&)Q>F*7$$\"3w7+r(RNut)F]r$!3AR%)o1m-\"*
>F*7$$\"3KA))Q$p@sa)F]r$!3w)fT74V%\\>F*F`]l7*7$$\"3Z+C>@VG,7F*$!3?)=dV
@O![?F*7$$\"37*=0'\\)odG\"F*$!3))z4%pF(ek?F*7$$\"3iBb*4OCJE\"F*$!3^'y3
mu34.#F*7$$\"3CypcoC\\b8F*$!3]3*330.)o>F*7$$\"3_7t&*zz%GL\"F*$!38:nZ?X
7N>F*7$$\"3*y&eQs)z/C\"F*$!39$fwi@Is*>F*7$$\"3Q#>wPQNy@\"F*$!3c*RWfo^N
'>F*Fd_l7*7$$\"3KYx9f$zse\"F*$!3SQVl3?sb?F*7$$\"3%3c(f%f)Qh;F*$!3q;DuB
%G50#F*7$$\"3w[.\"y)47N;F*$!3%e=jN()*)y-#F*7$$\"3'H8tpr\"e)p\"F*$!3CF`
Vms%e&>F*7$$\"37@f=5TJs;F*$!3Q'*fD;(3F$>F*7$$\"3pOJ-\"Q`)3;F*$!3)\\&QQ
B8v/?F*7$$\"3iCfBude#e\"F*$!3!R_/Kx7;)>F*Fhal7*7$$\"3!y$GolS')y>F*$!3=
)[^H!ySj?F*7$$\"3&[N7c^X'Q?F*$!3wHn)z2<N.#F*7$$\"3V'fZ1za(3?F*$!3\"oZ)
*H]`N-#F*7$$\"3`U&*z'H\"3O?F*$!32QEa%)RdT>F*7$$\"36%yM=d!>1?F*$!37&Qa&
4/hJ>F*7$F]dl$!3&QA5!G**e8?F*7$$\"3;z!=2Mt*[>F*$!3Mr>-`ji.?F*F\\dl7*7$
$!3WiGsXVw0?F*$!3PB$\\x!>a2;F*7$$!3y@=_x$o?-#F*$!3;ixWbz*>j\"F*7$$!3EA
gN%o\"[3?F*$!3N-Y\"oh!GH;F*7$$!3)o.g3+H5+#F*$!3-HXHMSam;F*7$$!3ePUp2BW
()>F*$!3?p8m&pEQm\"F*7$$!3'HA!>\"*\\*[*>F*$!3`U9=yKcE;F*7$$!3mBW-)H38)
>F*$!3\\#G[&Rf%Qi\"F*F^fl7*7$$!3SE_)\\Kw+n\"F*$!3Ptk/-xA:;F*7$$!3e[7t;
K=h;F*$!3i4_EN:,a;F*7$$!3%e*HuT'>7l\"F*$!3mr4W@#>\"Q;F*7$$!3cshBNFj2;F
*$!3?=HfFdWl;F*7$$!3g>zCg\"pwf\"F*$!3/!ooPT`&\\;F*7$$!3*Guan1c7k\"F*$!
3sLnh2pAA;F*7$$!3;!\\m<\\#HJ;F*$!3b&\\#z$fMjg\"F*Fbhl7*7$$!3&\\%ymN')z
G8F*$!3fBOM'\\8Hi\"F*7$$!3u`#=*z3m)H\"F*$!3%RLDDis?n\"F*7$$!3OZv5B/K#H
\"F*$!3GL#[&G.kX;F*7$$!3@`?>Qh#)>7F*$!3C*>sL#*HIm\"F*7$$!3$oM\"Q\"o&[8
7F*$!3c)4&RHwfO;F*7$$!3)4%oHm*zfG\"F*$!3$G8rX.3#>;F*7$$!3eMh[4&R'z7F*$
!3OKSfSdx#f\"F*Ffjl7*7$$!3fxrqxFJ>)*F]r$!3et2k!H*fI;F*7$$!3([OG3n8]M*F
]r$!3_M\"Gs@\"='o\"F*7$$!3gln\\%GSyJ*F]r$!3?(QO\"QR%=l\"F*7$$!3E)zws4#
4w$)F]r$!3esBj@mHf;F*7$$!35+_%4r=*[$)F]r$!3CD1aU$f\\i\"F*7$$!3Wn^;)*om
!H*F]r$!3kRY/fm]<;F*7$$!3=oN$=^$\\j#*F]r$!3I#*G&*z$pJe\"F*Fj\\m7*7$$!3
a^%QH^UZH'F]r$!3!Q#z$\\3&GQ;F*7$$!3is*\\AyYqo&F]r$!3w6OP>tL'p\"F*7$$!3
%z$QpxX5'p&F]r$!3=La?]+tc;F*7$$!3_=0V)\\>)4YF]r$!3)zVtB#eCa;F*7$$!3&\\
QuQHx)=YF]r$!3Sf_?`&QYh\"F*7$$!3O/x8tB;0dF]r$!3gas.\"yArh\"F*7$$!3yq:e
o,A9dF]r$!3!e2p=^:vd\"F*F^_m7*7$$!3'3FsBcvUr#F]r$!3!Q2N#z3(fk\"F*7$$!3
bftWL\"3F,#F]r$!3ol<'*G4a-<F*7$$!3%3pm16(*z0#F]r$!3Cr`vk')Hg;F*7$$!3aX
p\"Q&eV%**)Few$!3#fR&fDv(yk\"F*7$$!3ib-,EcKZ%*Few$!3[,!*Qh_j0;F*7$$!3%
=-')y3'G.@F]r$!3/x*[0Sc!=;F*7$$!37``5l]d[@F]r$!3g#eUj89ed\"F*Fbam7*7$$
\"3[dO\"*R2)3A*Few$!3-CA`tml`;F*7$$\"3Mu%zbF-!y;F]r$!3/'f#*f/#z/<F*7$$
\"3?yYe;@['f\"F]r$!3#=?'y\"y\\Dm\"F*7$$\"3?u'p=kN]v#F]r$!3pX#)HJ<>S;F*
7$$\"3iy[(G[:Nn#F]r$!3E^=4n%\\zf\"F*7$$\"31#))*ed>'\\^\"F]r$!3S2)zv^2.
i\"F*7$$\"3>'3&f)zTMV\"F]r$!3=8MP`_1y:F*Ffcm7*7$$\"3%yX_hR[Vh%F]r$!3+u
$HyYU8m\"F*7$$\"31H0$[W%3&Q&F]r$!3&G5m/n!4.<F*7$$\"3yn-1/JLn_F]r$!3ECz
H,M[j;F*7$$\"3=(eBL==ON'F]r$!3x()>[R%)=J;F*7$$\"3-FLbUo'eB'F]r$!3=4QJq
6e\"f\"F*7$$\"3g2+Hj<e\\^F]r$!3ZX(H@8wQi\"F*7$$\"3LY(>DUI=.&F]r$!3)och
H')oUe\"F*Fjem7*7$$\"3u/56/a]i$)F]r$!3ACl7i#G!p;F*7$$\"3g/eIu$Q&3\"*F]
r$!3a'G#Q-oV(p\"F*7$$\"3uy+w^eba*)F]r$!3+R0HB&*4j;F*7$$\"31Y+)*QSI'*)*
F]r$!3$>iY,ln3i\"F*7$$\"3??VV;:KU(*F]r$!3gu[0r.`'e\"F*7$$\"3(GN9#HLd+)
)F]r$!3o\"z)>WAwG;F*7$$\"3+F'om!3fY')F]r$!37Wq5l\\U%f\"F*F^hm7*7$$\"3o
+ny4fl;7F*$!3?uOUcSrw;F*7$$\"3)*H0S1k$[G\"F*$!3[Y6uT/$yo\"F*7$$\"316%o
f.:eE\"F*$!3#e/kx9)Rh;F*7$$\"3v/R)3K4$Q8F*$!3h[@Hj$H#4;F*7$$\"3g&y^/&z
G>8F*$!3%z/:$pqz#e\"F*7$$\"3!>HObm$zY7F*$!3PXpy`e'\\j\"F*7$$\"3'H</^Hs
xA\"F*$!3\"\\%)4)fN`3;F*Fbjm7*7$$\"3`Y?uZ4l-;F*$!3UC3s])*R%o\"F*7$$\"3
#>!HR^hXg;F*$!35$oU&)erUn\"F*7$$\"3UOKyi;\"yj\"F*$!3;X%=ZFz$e;F*7$$\"3
qf+Hp&)R\"o\"F*$!39n&=*yNF'f\"F*7$$\"3)RR!o!3a(e;F*$!3'*GV4l7Q!e\"F*7$
$\"3qqN<ur;:;F*$!3?2U*3'p[U;F*7$$\"3=0Rc&oADf\"F*$!3/p*pqk%fE;F*Ff\\n7
*7$$\"3+QrFacB%*>F*$!3Uuz,Xc3#p\"F*7$$\"3&fp2C28x.#F*$!3;'*oyU-wc;F*7$
$\"3l$[?cYX9,#F*$!3MOP:/H/a;F*7$$\"3.pk6\\\")*)=?F*$!3'z(e-(H+?e\"F*7$
$\"3'pDHBaIE*>F*$!39=FReHGz:F*7$$\"3!=FL)ey<&)>F*$!3_w0_lbK^;F*7$$\"3s
fg/_-\"*e>F*$!3[;u)oA3'[;F*Fj^n7*7$$!3Yi&Grv#R!*>F*$!3S4e\")\\(>iB\"F*
7$$!3p![E2#3+B?F*$!3cGzC?6Cb7F*7$$!3/NJQ45z0?F*$!3mh)pz,q(f7F*7$$!3P5J
a[@@=?F*$!3\"*oxxY.(pI\"F*7$$!3sk(*>PB+,?F*$!3B-(*\\W#*\\68F*7$$!3=*yR
!)>\"e))>F*$!3w%z\"p:*)Hk7F*7$$!3IVkp'Qr8(>F*$!3'ys8M\"y#)o7F*F^an7*7$
$!3?E4ROZqa;F*$!3ifH6Wb!RC\"F*7$$!3q2f$*fc6i;F*$!3Aw`1+ZDx7F*7$$!3S3,x
m*G&[;F*$!3?JifA'3'o7F*7$$!31Y#>H)e\"[i\"F*$!3(y:w+/seI\"F*7$$!3`YMv*=
H7h\"F*$!3%G,2E'fA(H\"F*7$$!3))3VgtA%\\j\"F*$!3;'3F^ai*f7F*7$$!3e4&Q/e
b8i\"F*$!39TzlnkJ^7F*Fbcn7*7$$!3_WN2ZqU88F*$!3i4,TQ8f^7F*7$$!3U7H7BLf*
H\"F*$!37+bK(y:`H\"F*7$$!3qfY8[(H'*G\"F*$!3g#\\.(H(HhF\"F*7$$!3$p7veG4
qB\"F*$!38Ra&eBcMI\"F*7$$!3(R(o)3rXqA\"F*$!3gJMBy,F%G\"F*7$$!3u1k9thmz
7F*$!31&[\"3sO%pD\"F*7$$!3+a\"e\")f-(p7F*$!3_x%fWhdxB\"F*Ffen7*7$$!3Yv
Tw\"*ofl'*F]r$!3%)fsqKrFf7F*7$$!3#R&\\(G5QVN*F]r$!3#4IG?QC%48F*7$$!3=
\"*ywMN$4H*F]r$!3]Y;HRLL#G\"F*7$$!3ALv5uN#za)F]r$!3Y7c6MHs*H\"F*7$$!3Q
p/+1!>X[)F]r$!3#y&*y8*=js7F*7$$!3MF3mm*GvA*F]r$!35#*\\b'HU_D\"F*7$$!3[
jPb)RCT;*F]r$!3nP$=QD^\"G7F*Fjgn7*7$$!3W\\a*piE59'F]r$!3#)4W+FH'pE\"F*
7$$!3ohlH97P'p&F]r$!3;yP<%[!e>8F*7$$!3_j\\'z#y>pcF]r$!3]#pg8X>sG\"F*7$
$!3%HDh_(4l\"y%F]r$!33ym&[8sYH\"F*7$$!3ya'H*)exWv%F]r$!3?#fV?56BE\"F*7
$$!3DkLjTW-UcF]r$!3#ogZ&=%e[D\"F*7$$!34m<Ib5&[h&F]r$!3;@Xt&Q(\\A7F*F^j
n7*7$$!3uo#Hknf0c#F]r$!3/g:I@([YF\"F*7$$!3s\\R\\lD.A?F]r$!32K>w$4%yD8F
*7$$!3(e\"y$4O!4J?F]r$!3yI1\"f1)y!H\"F*7$$!3CHC@i]Fr5F]r$!3eN'y!QQI)G
\"F*7$$!3Q&Hcw&GL!3\"F]r$!3GMtA5yI`7F*7$$!3H#o\"Qc\"[,/#F]r$!3[H$f!Q?z
b7F*7$$!3W[b#=&f?\\?F]r$!3>G!3-,'z?7F*Fb\\o7*7$$\"3'yOM*fR!e2\"F]r$!3/
5()f:XL#G\"F*7$$\"3=%)G`Vyno;F]r$!3ViFz5_.G8F*7$$\"3<`NJm))QB;F]r$!3#4
YTH=RIH\"F*7$$\"3!)R*Q];/Ke#F]r$!3e&[\"yV!=1G\"F*7$$\"3z3'>y=:z`#F]r$!
3I%=If,AcC\"F*7$$\"3)=A%4*))*4y:F]r$!3if,4bJ/e7F*7$$\"3)3*[(=\"4\"G`\"
F]r$!3Le)Qs7ZIA\"F*Ff^o7*7$$\"3'*fa4#Gk!oZF]r$!3Ege*)4.-!H\"F*7$$\"3!*
QRy7+wv`F]r$!3ZpiENQLE8F*7$$\"3IV\"*y`)RUH&F]r$!3e$=`C!G(RH\"F*7$$\"3K
`G\\1ny\"='F]r$!3mF_'>v9;F\"F*7$$\"3kc!)\\ZlE+hF]r$!3yT@:>PDR7F*7$$\"3
rZVz%p>F@&F]r$!3#z4S'p<hh7F*7$$\"3,^&*zN&*>J^F]r$!3D7q#ot]#H7F*Fj`o7*7
$$\"3&o+a+H@i^)F]r$!3C5I>/hq(H\"F*7$$\"3U9#fA%R@*4*F]r$!3t_C=n*z1K\"F*
7$$\"3;`*)[,EY\")*)F]r$!3K)zXW#*)e$H\"F*7$$\"366$\\@csWs*F]r$!3/i)HE'R
Hh7F*7$$\"3$40z8A@ng*F]r$!3T2K*)>H?M7F*7$$\"3)Hp=2E6P'))F]r$!3!R94<)y
\\m7F*7$$\"3qJ%[*>*ffu)F]r$!3\\*[s*QoSR7F*F^co7*7$$\"3!4+\"Q)\\F?B\"F*
$!3Yg,\\)*=R08F*7$$\"33re>jR!RG\"F*$!3*GJTlgt5J\"F*7$$\"3])HT4r0&o7F*$
!3M0$>*[v)=H\"F*7$$\"3EJ3?th7@8F*$!3G)Qvdnb'\\7F*7$$\"3nei%4#zs08F*$!3
u!Q`\"='p/B\"F*7$$\"3!fs'oeu5`7F*$!3#yH(H\"\\,FF\"F*7$$\"3K`@V1#4xB\"F
*$!3G!HvOV:ND\"F*Fbeo7*7$$\"3uYjLOD-=;F*$!3Y5ty#pxIJ\"F*7$$\"3!GC)=3P_
f;F*$!3[\\GM`Z^(H\"F*7$$\"3'Q7cxL-0k\"F*$!3Y/P(eno))G\"F*7$$\"3?')pg@a
@k;F*$!3.2=S\"*)*pO7F*7$$\"31n[<^S>X;F*$!3+iE$R\"Q0G7F*7$$\"3r/SKn4[@;
F*$!3WfXS)fA-G\"F*7$$\"3x&)=*offCg\"F*$!3S9a$4_w:F\"F*Ffgo7*7$$\"3*zVr
GC2'4?F*$!3ngW3([j2K\"F*7$$\"3gOI?H1yO?F*$!3aiqe2M+!G\"F*7$$\"3(3P$fSh
89?F*$!3)e**3`IKXG\"F*7$$\"3a&RL9+:<+#F*$!3j<\"4&4mUA7F*7$$\"3#)HP#G^q
!z>F*$!3'40Js]bpA\"F*7$$\"3e0P)>l\"\\\"*>F*$!3)*G4..71*G\"F*7$$\"3))RS
Pjr%)o>F*$!31iGv+,f$H\"F*Fjio7*7$$!3CiU`o6-v>F*$!3edH#)=f(*[')F]r7$$!3
/S6$RELR-#F*$!3e]4[]G%[y)F]r7$$!3PZ-TM.5.?F*$!3(=@^7>%f-*)F]r7$$!3J%=E
iH&RN?F*$!37*35EfmRZ*F]r7$$!3l\"H0nOiX,#F*$!3E\\.QLzr\"f*F]r7$$!3;b$*)
[SnA)>F*$!3;t9-KbM?!*F]r7$$!3%HYo`ZM9'>F*$!3LL<zso4Q\"*F]rF^\\p7*7$$!3
)fi'zZJLR;F*$!3keWzhQ$es)F]r7$$!3gm09.\"[Im\"F*$!3IFal['y\\+*F]r7$$!3u
?sz\"HQek\"F*$!3;1\\^P-)4**)F]r7$$!3L>BgI!**>k\"F*$!3syRfDN)HY*F]r7$$!
3ot*e#>#*yC;F*$!3edMX9^)*[%*F]r7$$!35vQX![G'G;F*$!37'Quj#=)p(*)F]r7$$!
3AH06p'=9h\"F*$!3)\\'QB:M)H'*)F]rFb^p7*7$$!3_W#z%ea0)H\"F*$!3pffw/=p-)
)F]r7$$!3yrvKmd_+8F*$!3]omD@&*e&=*F]r7$$!3Es<;t!RpG\"F*$!3KAve38>m!*F]
r7$$!3?+#eNV#>a7F*$!3<!z'Q$[D)Q%*F]r7$$!3o+CRSdgS7F*$!3)Rk<2FF%>$*F]r7
$$!3'H(f**zBNt7F*$!3Cx$=f4$zY*)F]r7$$!3mt,$ool(f7F*$!30J#\\K)[RF))F]rF
f`p7*7$$!3Nt6#e+\")=^*F]r$!3wgutZ(\\&z))F]r7$$!35W:#\\`iOO*F]r$!3JvYGo
anE$*F]r7$$!3m:!R]yESE*F]r$!3Mg!pWSF#G\"*F]r7$$!3>o#Q40b(>()F]r$!3^B&)
)fY#\\,%*F]r7$$!3lQd0,$>,i)F]r$!3`3H<-W/.#*F]r7$$!3C([c^.\"Rk\"*F]r$!3
ZYMlS$z(H*)F]r7$$!3!)eRF&GbZ1*F]r$!3]Jy$oFJ8t)F]rFjbp7*7$$!3KZC0T2J()f
F]r$!3!='*32p2k&*)F]r7$$!3&=:Vjk&p0dF]r$!3sZ%R(*[O#G%*F]r7$$!3*z3O#y5H
UcF]r$!3A?&f^_)3x\"*F]r7$$!3!z)>4_C[`\\F]r$!3qy\"*RtW)4N*F]r7$$!3/C\\)
R)y2!*[F]r$!3?^#>)3l$)*4*F]r7$$!3ED!H,^'))ybF]r$!3%Qfz0cSf#*)F]r7$$!3S
h>-U>[:bF]r$!3Mm'**ff#zu')F]rF^ep7*7$$!3imi[!zVoS#F]r$!3(GY!oLcEL!*F]r
7$$!3hR0a(*pNJ?F]r$!3u&)4i&es-\\*F]r7$$!3!4%*37h$=/?F]r$!35.*e1nuF@*F]
r7$$!3ljJ/Rl5V7F]r$!3yb(=c],tG*F]r7$$!3%\\c6F:Lf@\"F]r$!3-sml!f.)4!*F]
r7$$!3=Ut([A5q(>F]r$!3M>opbnFN*)F]r7$$!3uVdaQo$)\\>F]r$!3eNZtS)yxl)F]r
Fbgp7*7$$\"3%)pt(e%)>&H7F]r$!3$R'>lwN75\"*F]r7$$\"3G%H'[6MNf;F]r$!3Q*G
Hfv$y7&*F]r7$$\"39GC/;cH];F]r$!3t1s'4%eGN#*F]r7$$\"3Q0#3#)os8T#F]r$!3s
askiNW5#*F]r7$$\"3'*QVw#*[J-CF]r$!3(4<&oZc%H$*)F]r7$$\"3sh&)f?yBT;F]r$
!3'H70g#zyd*)F]r7$$\"3d&pa^-!=K;F]r$!3?RI/6+H!o)F]rFfip7*7$$\"3_h%Q!o,
y@\\F]r$!3)\\YB'>:)p=*F]r7$$\"3s[tt!eNkO&F]r$!3geVm++x&\\*F]r7$$\"3r<!
=NgY6K&F]r$!3AKW3O?iW#*F]r7$$\"3P=@mH_&*4gF]r$!3`vY[W1T?\"*F]r7$$\"3O(
yUCDmY'fF]r$!3/[Z!*zEEp))F]r7$$\"3q'o)HEw&eF&F]r$!3s/X]rSZ$**)F]r7$$\"
3qb$z!\\'o0B&F]r$!3MyX#p5EBu)F]rFj[q7*7$$\"3)*3q*f<P*p')F]r$!3/m\\fi%R
QE*F]r7$$\"3ECE@5&*))*3*F]r$!3Y$>E)>8BR%*F]r7$$\"3nGy@^$p$3!*F]r$!3fz0
,cKyS#*F]r7$$\"3Ex&=`3TEb*F]r$!3@=58^F?<!*F]r7$$\"3c!yBj#47r%*F]r$!3C.
aJ(oa(=))F]r7$$\"33LIA#>\\o#*)F]r$!3ik\\>#>NB/*F]r7$$\"3QO#GK.H`%))F]r
$!3w]$z$Gr)Q%))F]rF^^q7*7$$\"37,`(p3*RZ7F*$!35nkc0upS$*F]r7$$\"3=77**>
:(HG\"F*$!3!Rz9MrnJM*F]r7$$\"3%f=9fQ'>r7F*$!3$)[cu+&pPA*F]r7$$\"3wdx^D
I%RI\"F*$!3w#G'e#))>3!*)F]r7$$\"3uJ2W\"*y;#H\"F*$!3cOr\"*p;U\"y)F]r7$$
\"3#*fr$=D@%f7F*$!3k-l2)GrV5*F]r7$$\"3!R8gx6YwC\"F*$!3edtSvI(\\)*)F]rF
b`q7*7$$\"3&pkI\\7%RL;F*$!3;oz`[`b<%*F]r7$$\"3!Re$)\\E\"fe;F*$!3(*f,V
\"=zv?*F]r7$$\"3I6!HF,$>V;F*$!3%*R'*Gq2e$>*F]r7$$\"3s7R#RFKqk\"F*$!3=p
/&)Q?Er()F]r7$$\"38S$p;-M;j\"F*$!3/[*4xijsv)F]r7$$\"3sQWZgZzF;F*$!3!)=
\"\\\"fBez\"*F]r7$$\"38m)>#3lR7;F*$!3y)f3![Rel\"*F]rFfbq7*7$$\"3VQdYJ)
y\\-#F*$!3?p%4:H8W\\*F]r7$$\"3px$)*f=[e.#F*$!3j\"HsQslC.*F]r7$$\"3)*ei
c:o#o,#F*$!3#HbUY1<-:*F]r7$$\"3/A.v`=`%)>F*$!3YxN#*>#H&G')F]r7$$\"3)G?
=L[5b'>F*$!3kPQpg0GY()F]r7$$\"3#)RT8Xa!y*>F*$!3?9GT0%ozE*F]r7$$\"3o??q
uSyy>F*$!3OuI=Y(>dQ*F]rFjdq7*7$$!3-i*R*z&\\'f>F*$!30?y[RVvN\\F]r7$$!3%
*)zNrql[-#F*$!3k:E[)\\us,&F]r7$$!3:gtVf'4/+#F*$!3?2Q!G?)[2_F]r7$$!3Od#
4RWyD0#F*$!3-)[UurH#yeF]r7$$!3e=3@'RA\"G?F*$!3czOw@MWogF]r7$$!3;@*Q<h`
f(>F*$!3k(*\\72>q(R&F]r7$$!3O#[SSc(\\^>F*$!35)=Y9h:ze&F]rF^gq7*7$$!3xD
B?f:'Ri\"F*$!36@$fCG7E,&F]r7$$!3_D_MY0)Rm\"F*$!3N#4dmH5uB&F]r7$$!3ILV#
ohZJk\"F*$!3[,v1\\U(eH&F]r7$$!3%GR&Gy@=f;F*$!3gxjU]mCneF]r7$$!3h+Xw[#
\\$Q;F*$!3&yyOGg5d#fF]r7$$!33TMI(o9Bi\"F*$!3i5zZ,#QVN&F]r7$$!3k[Dyd<[,
;F*$!3w>$))Q:-GT&F]rFbiq7*7$$!3KW\\))pQo#G\"F*$!3;A3VD-Z*3&F]r7$$!3oIA
`4#e9I\"F*$!3bL$e#p6-=aF]r7$$!3#[)))=)R[UG\"F*$!3k<,9?`3r`F]r7$$!3[t7C
\"ev8F\"F*$!32*=>#3')3VeF]r7$$!3%y#z*)pd;a7F*$!3Eu45fF:'z&F]r7$$!3%*Qb
%oeQqE\"F*$!3s,>-r%\\TK&F]r7$$!3I$>-bxG)\\7F*$!3!eo.>i8sF&F]rFf[r7*7$$
!3Cr\"y)>^;e$*F]r$!3ABBSo\"Gj;&F]r7$$!3EM\"op'p)HP*F]r$!3OSjG;r5fbF]r7
$$!3DT,JN+7P#*F]r$!3mb;-;97LaF]r7$$!3/-!px_'e\"*))F]r$!3_B4#3fbd!eF]r7
$$!3/456'f>dv)F]r$!3sPib!*)p(zcF]r7$$!38Z@l.JD,\"*F]r$!3'4(pv:d82`F]r7
$$!35aT*><'Ql*)F]r$!3E'G#\\:+:\"=&F]rFj]r7*7$$!3?X%4^&[fLeF]r$!3GCQP6h
=V_F]r7$$!3-U(*Qy+-:dF]r$!3w76uP\"o1m&F]r7$$!3f8s]GVQ:cF]r$!3a:@rOD)>[
&F]r7$$!3UBF#*GRJD^F]r$!3sy:B)fZ_v&F]r7$$!3(Q>S!z\"yc-&F]r$!3Q!e-s*>cw
bF]r7$$!3:&oC'y&[d^&F]r$!3L=JoNpH.`F]r7$$!3sc@uGG6;aF]r$!36@TlM8hC^F]r
F^`r7*7$$!3]kKa/z7`AF]r$!3MD`MaS/?`F]r7$$!3]HreH9oS?F]r$!3z]EiLUqAdF]r
7$$!3%f1![hoFx>F]r$!3J(\\6Aoow^&F]r7$$!3M)*Q(e,Q\\T\"F]r$!3!e:^/jk:p&F
]r7$$!3[MowZM`^8F]r$!3?,+/z!Hl[&F]r7$$!3N-IP$HsQ\">F]r$!3$QM+38LEJ&F]r
7$$!3yQfEDxY]=F]r$!3N!>*Qzvf2^F]rFbbr7*7$$\"3'>P?=tNKQ\"F]r$!3SEoJ(*>!
pR&F]r7$$\"37/(R%z*G+l\"F]r$!3Ua4$RS:_u&F]r7$$\"3#GIrdO-sn\"F]r$!3%4!)
>D&)z,a&F]r7$$\"3pquP67aRAF]r$!3ta'zuo1Zh&F]r7$$\"3Sp!4xf9nE#F]r$!39+&
og8r'4aF]r7$$\"3a,H5_dP/<F]r$!3YZ'36IW^L&F]r7$$\"3E+XVQ\"\\:t\"F]r$!3(
R\\(p\\(3,8&F]rFfdr7*7$$\"3?k9)R0'\\v]F]r$!3YF$)GS*fPZ&F]r7$$\"3mf2p[6
6d`F]r$!3mBgm[;?GdF]r7$$\"3C$*oC`L0[`F]r$!3WEqjZg^\\bF]r7$$\"3T$QJGvB
\"QeF]r$!3avqJpPnCbF]r7$$\"34=vQdf1HeF]r$!3Ax!)Go\"))fM&F]r7$$\"3\"o-.
yb&**Q`F]r$!3AH!3mWI3P&F]r7$$\"3Rg\"fBwP*H`F]r$!3)>.zb%[9#>&F]rFjfr7*7
$$\"346+%>1`O#))F]r$!3_G)fK)yh]bF]r7$$\"3?Ng;y]c!3*F]r$!3]ey#y'HmrcF]r
7$$\"33.n%45w_.*F]r$!3!Q<jvExca&F]r7$$\"3GUy[3'43Q*F]r$!36<M'f(eY@aF]r
7$$\"3G6&o7j?bL*F]r$!3_L()pv,[&H&F]r7$$\"33stsBr)**)*)F]r$!36*[)Hn:p>a
F]r7$$\"32T!3l9)pW*)F]r$!3S/Q.neq$H&F]rF^ir7*7$$\"3K,'pbnqFE\"F*$!3eH8
BEeZFcF]r7$$\"3/`lyw!R?G\"F*$!3'*ekTh$*fvbF]r7$$\"3Qtq)31()QF\"F*$!3/V
#)H7NmGbF]r7$$\"3E%oMy()fnG\"F*$!3m\"o=u+$30`F]r7$$\"3#[?N>'ygy7F*$!3'
oY+$er9e_F]r7$$\"3#Rf()\\/NdE\"F*$!37F+=jws\"[&F]r7$$\"3E9\")3HIed7F*$
!3L7=19=zMaF]rFb[s7*7$$\"3;Z\\_8dw[;F*$!3kIG?pPL/dF]r7$$\"3)\\#*y<#)ew
l\"F*$!3,D=VH3,SaF]r7$$\"3u)*=q(o$)ek\"F*$!39MA%=yu%)\\&F]r7$$\"3AR3CE
\"\\)H;F*$!33oGoj^_v^F]r7$$\"3?8Q;#*R2=;F*$!3LyK4;\"*)RB&F]r7$$\"3ts[i
`&3Tj\"F*$!3SWEDM(Qpb&F]r7$$\"3rYya>MLA;F*$!3``Im'o-ah&F]rFf]s7*7$$\"3
UQ+1?/NS?F*$!3qJV<7<>\"y&F]r7$$\"3y=PzUd\"\\.#F*$!3ocR(=P(*[E&F]r7$$\"
3?Y\"R0\\<&>?F*$!37Z^>w56baF]r7$$\"3a[s11([t'>F*$!3PwfvWBzK]F]r7$$\"3'
fn7QX]>&>F*$!3#z;x!\\g+B_F]r7$$\"3htXGQ#>T+#F*$!3oQj^!yC`k&F]r7$$\"3!3
+Ig)4s))>F*$!38Hv$[[Qb$eF]rFj_s7*7$$!3\"=mX8*zFW>F*$!3D#o_,wKDA\"F]r7$
$!3&yXS.:)zD?F*$!3%3G%[Yhq\\7F]r7$$!3[sWY%)*=x*>F*$!3T,kN9AQ7:F]r7$$!3
'3L#f\"fh(p?F*$!3I))[FUG\\#G#F]r7$$!3&fM;dU#oT?F*$!3u3q95*o^a#F]r7$$!3
O([)e=)R'p>F*$!39A&GAGe]x\"F]r7$$!3+-Dr_1cT>F*$!3eU15]VtP?F]rF^bs7*7$$
!3bD!31(**e3;F*$!3I$=CJq!R*H\"F]r7$$!3k%))\\&*)H\"\\m\"F*$!3%oveY%>%)p
9F]r7$$!3'eW^=%pXS;F*$!3(f4?1Eo2g\"F]r7$$!3Km%ofKljn\"F*$!3=y(e_x4:F#F
]r7$$!3aF+Fy#4>l\"F*$!3.<,A\"4OCS#F]r7$$!322I:%*3+;;F*$!36N9ewXpJ<F]r7
$$!3GoXXY[a\"f\"F*$!3'RxUD*3ii=F]rFbds7*7$$!35W1H\"G7tE\"F*$!3O%o&4Y'[
iP\"F]r7$$!3f*)ot_1R-8F*$!3K)**fs\"GX];F]r7$$!3Q(*f@Bxb\"G\"F*$!377FpJ
$zfn\"F]r7$$!3)pMC*G(e&)G\"F*$!3k*e^It^tC#F]r7$$!3waMS*zDxE\"F*$!3W.V[
Z#yGF#F]r7$$!3%\\5&p$zC2E\"F*$!3@Ea7Ye],<F]r7$$!3r7U<k=*)R7F*$!3-S\"e0
OKqs\"F]rFffs7*7$$!37p^$RB\\W?*F]r$!3U&=n!*e1JX\"F]r7$$!3WCZ,*R6BQ*F]r
$!370!)Gk(Q:z\"F]r7$$!3tl7e&G8-@*F]r$!3V]UdFa,Q<F]r7$$!3-P(*f/!=M1*F]r
$!3(HK`cr=+@#F]r7$$!3Iyi;\"*)>8*))F]r$!3+o&R*y`\\c@F]r7$$!3-2y9s^6Q!*F
]r$!3Y&\\g34#\\%o\"F]r7$$!3U\\Vreq,m))F]r$!3[Sn9a(o4j\"F]rFjhs7*7$$!33
Vk;p*y)zcF]r$!3\\'oQ?`k*H:F]r7$$!3>KjV5XMCdF]r$!3!yxUdy*4$*=F]r7$$!31Q
$y(yvZ)e&F]r$!3K5ZE[l(oy\"F]r7$$!3EdMv0a9(H&F]r$!3=yR1B2^f@F]r7$$!3Eka
4u%y7;&F]r$!3o5fe&[(G`?F]r7$$!3/X.7Z1h_aF]r$!3#Gk'y5Ll!o\"F]r7$$!3._BY
:Pu;`F]r$!3Kv&3L2IWd\"F]rF^[t7*7$$!3Qi-g=?T*4#F]r$!3b(=5]ZAog\"F]r7$$!
3S>Pjhe+]?F]r$!3%eJC;)e8b>F]r7$$!3'4>^<6q.&>F]r$!33#4kPpiD#=F]r7$$!3uK
Yq#\\pne\"F]r$!3CbNGbx#e4#F]r7$$!3K/@#GuLr[\"F]r$!3]JLUnXDj>F]r7$$!3_i
'o=OM2&=F]r$!3KoQ!f]*)**o\"F]r7$$!35Mh)>h)4^<F]r$!3cWO/=jTd:F]rFb]t7*7
$$\"33uLw<;&p`\"F]r$!3g)o\")zT!o$o\"F]r7$$\"3A9JRZXqS;F]r$!3[>E$>0Zw(>
F]r7$$\"3!y<+b64Tq\"F]r$!3q&RsS'Q2X=F]r7$$\"3IOnaM(4x1#F]r$!3>a?J7)p*=
?F]r7$$\"3f*z`EI968#F]r$!3UI=XCmR')=F]r7$$\"3OTsg$o8vw\"F]r$!3&><7in+D
r\"F]r7$$\"3&\\I9<D=4$=F]r$!3Y[>N)[F*z:F]rFf_t7*7$$\"3JmW#*R>@H_F]r$!3
m*=`4OQ0w\"F]r7$$\"3]pTk;nyZ`F]r$!3s)onmHL1'>F]r7$$\"3mnd(H5g\\P&F]r$!
3[@'*=f+Ta=F]r7$$\"3a\\1+wAHmcF]r$!3+v%\\T*o$*G>F]r7$$\"3sZALicY$p&F]r
$!3]29ncOrA=F]r7$$\"3#pO2$*[L@S&F]r$!3)Rb6<#o=[<F]r7$$\"33l*Qc(oIHaF]r
$!3['[LUej>k\"F]rFjat7*7$$\"3?8I)y%*ot(*)F]r$!3s!pCRI'RP=F]r7$$\"3/X%>
hkS72*F]r$!3bB&Heh%4/>F]r7$$\"3gybn]G=i!*F]r$!3')od6z7d]=F]r7$$\"3K2rl
J\"y*3#*F]r$!3o<ez+!Hd#=F]r7$$\"3+UK@O.#**>*F]r$!3qi?3kc?s<F]r7$$\"3=7
<Bb]7`!*F]r$!3'Q,-C%z/(z\"F]r7$$\"3wXyyfs1W!*F]r$!3=f#)o0Y_V<F]rF^dt7*
7$$\"3a,R;kA9y7F*$!3y\">'*oCaU\">F]r7$$\"39%*=eLm5\"G\"F*$!3+C\"=%45.3
=F]r7$$\"3/h*fetxlF\"F*$!34Q3&Q_dN$=F]r7$$\"3+6;:Indp7F*$!3B#3^A8Y$4<F
]r7$$\"3mx'HC$y/l7F*$!3/'z$oYE([t\"F]r7$$\"3%z-Q\"Q)[?F\"F*$!3=_NGQS3f
=F]r7$$\"3%[4;/%*>vE\"F*$!3Emir_0h%)=F]rFbft7*7$$\"3OZ#>@IPTm\"F*$!3#G
pn)*=76*>F]r7$$\"3'eEu&yjsc;F*$!31!\\LuZUCn\"F]r7$$\"3U'yuEOu&[;F*$!3>
H[R$zoL!=F]r7$$\"3slxbyfm7;F*$!3ko_^)G)yz:F]r7$$\"3F'GeE'R^/;F*$!3]2mZ
/Yr5<F]r7$$\"3u1`xYBUS;F*$!3LohN4^HM>F]r7$$\"32Fe(3LqAj\"F*$!3Y2vJD9Al
?F]rFfht7*7$$\"3')QVl3?sb?F*$!3!R>RG8qz1#F]r7$$\"3))f!*e*H$)R.#F*$!3W@
c()>!Ht\\\"F]r7$$\"3'Q.7b;3A-#F*$!3;Uxu(30+w\"F]r7$$\"3/vTQeb;]>F*$!3m
w$)epa0P9F]r7$$\"3.\\rIC/RQ>F*$!3Q(\\gu`J(*p\"F]r7$$\"3%y+N9.L/,#F*$!3
*G')>c:\"oA?F]r7$$\"3g\")zN(*yl)*>F*$!3i$)>\\BsN&G#F]rFjjt7*7$$!3gh8v-
k!*G>F*$\"3EbC=>))o!\\#F]r7$$!3v;^a$fIn-#F*$\"3r`S^0A'y^#F]r7$$!3/&e\"
\\4$G]*>F*$\"3c.54uPs#=#F]r7$$!3O/aFRZ%p3#F*$\"3'>r#*G.WKJ\"F]r7$$!3Ws
=AbCCb?F*$\"3C:mp9g0\"y*Few7$$!3O`!Qa-EL'>F*$\"3Q`zmU`eZ=F]r7$$!3U@XQT
PiJ>F*$\"3%H!\\C6pW7:F]rF^]u7*7$$!3MDP,#Q=Kf\"F*$\"3@a4@w3$QT#F]r7$$!3
aVXvKa%em\"F*$\"37y&RtSExH#F]r7$$!3Ue&yoEmxj\"F*$\"3C4t#ysPV4#F]r7$$!3
!)R:lt%[Np\"F*$\"34A)3**4FUK\"F]r7$$!3Yabx2$pam\"F*$\"3P`lR?%Q37\"F]r7
$$!31tD+,ro4;F*$\"3SS]J[!\\4*=F]r7$$!3q(eE^$zg\"e\"F*$\"3GrF!)o.c(o\"F
]rFb_u7*7$$!3!RM'p#pS>D\"F*$\"3:`%RK$H(pL#F]r7$$!3r[:%f4BLI\"F*$\"3jO$
QZ`:r6#F]r7$$!3#*4JC[q')y7F*$\"3$GpanlE\">?F]r7$$!3Z?ugw=u08F*$\"3i5g6
U^Q[8F]r7$$!3o\")*3*GeG\"G\"F*$\"35nB8kiR]7F]r7$$!39rYa+5Ta7F*$\"3I\\5
xyx8@>F]r7$$!38Ki%G&\\&*H7F*$\"3\\0uy+*[J#=F]rFfau7*7$$!3+n@*zML20*F]r
$\"3#=&zE!*\\6gAF]r7$$!3]881Jej\"R*F]r$\"3GH.r(eHg(>F]r7$$!3K\"R_e`1L=
*F]r$\"3aaJ(3c!4d>F]r7$$!3'3ZI9[\\_B*F]r$\"3exU^f\"=dQ\"F]r7$$!3o[:A'=
?p-*F]r$\"3#G5xE8znO\"F]r7$$!3-oMkSs(\\(*)F]r$\"3yzf.M::Q>F]r7$$!3uWXV
Xzkm()F]r$\"3w/))>2D@>>F]rFjcu7*7$$!3'4WBK3jh_&F]r$\"3w]kHZqD$=#F]r7$$
!3D@H[U*oOt&F]r$\"3'obbicoW(=F]r7$$!3kj%\\!H3dhbF]r$\"3k%p#=S%H#3>F]r7
$$!3C#>%e#)o(*oaF]r$\"3PAO5_hAO9F]r7$$!3_L2:p(yoH&F]r$\"39g2.Eq)*p9F]r
7$$!3%\\+;crs%*Q&F]r$\"3UK)4TJ!*>%>F]r7$$!3MZD=-YP<_F]r$\"3#*pp.)=^d(>
F]rF^fu7*7$$!3GgslKhpX>F]r$\"3)*\\\\K/\"*R1@F]r7$$!3G4.o$HI$f?F]r$\"3$
)=SPqCV7=F]r7$$!3*fJA?OjM#>F]r$\"3)GJ$o%HVD(=F]r7$$!3Wn``p4ge<F]r$\"3-
XS))>\"4**\\\"F]r7$$!3'QPxy.MFi\"F]r$\"31RL>W*>+c\"F]r7$$!3qAVOIkf(y\"
F]r$\"3#pg#**=TlK>F]r7$$!37Hjq)\\H<l\"F]r$\"3%4!>IV\\w#*>F]rFbhu7*7$$
\"3?wjq.vm!p\"F]r$\"3#*[MNh6aH?F]r7$$\"3LClM:,QJ;F]r$\"3?:d1+8#**y\"F]
r7$$\"3/`!H_'e,J<F]r$\"3C4]PC@.]=F]r7$$\"3g,grd#ye*=F]r$\"33Yb&G1nnd\"
F]r7$$\"3-I&)f2S^&*>F]r$\"37S[;()y(oj\"F]r7$$\"3[\"e6^h^1$=F]r$\"3H.Vo
[H95>F]r7$$\"3\"*4T*\\O(GI>F]r$\"31(f$*Hx`-(>F]rFfju7*7$$\"3Uou'e#y#HQ
&F]r$\"3'y%>Q=Ko_>F]r7$$\"3Kzvf%Gi%Q`F]r$\"3(fkI`0Np!=F]r7$$\"3<VYq_o'
=S&F]r$\"3u$yd#HfpS=F]r7$$\"3e9*p\"*zgW\\&F]r$\"3ED\"=5)**zm;F]r7$$\"3
WypFn`'yb&F]r$\"30j_%\\&3c+<F]r7$$\"3-2<\"3Ur_Y&F]r$\"3C@\\=.oXu=F]r7$
$\"3xp(=*))fnGbF]r$\"3.f?6xw@3>F]rFj\\v7*7$$\"3L:g#Q$[3J\"*F]r$\"3!oW5
aFDe(=F]r7$$\"3'[&G29i\">1*F]r$\"376)ohttM'=F]r7$$\"37aWS+'*3*3*F]r$\"
3QO;L4Z`W=F]r7$$\"3Ztj#[lYr.*F]r$\"3e#yrV(y+q<F]r7$$\"3krz:T+Kk!*F]r$
\"3%ygMv%)o5v\"F]r7$$\"3H_gt')HE;\"*F]r$\"3OhW\\#o&fD=F]r7$$\"3X]w1tjV
V\"*F]r$\"3M'Gdclcm!=F]rF^_v7*7$$\"3u,#eF&Q^$H\"F*$\"3uX*QCLn*)z\"F]r7
$$\"3-NsP!>u,G\"F*$\"3o5-eUt`f>F]r7$$\"3[[G$3To#z7F*$\"3'oc'fk%[:'=F]r
7$$\"3]P&oCe$R_7F*$\"3K=l\"Hu!R')=F]r7$$\"3u]T#H!y[^7F*$\"3AuG$\\'=S)y
\"F]r7$$\"3'>Y)GJEOy7F*$\"31BHh'efNw\"F]r7$$\"3?vSu^oXx7F*$\"3Ez#H'32d
l;F]rFbav7*7$$\"3eZNr!*)3&z;F*$\"3oWuY*Q4@s\"F]r7$$\"3'pgp`$Rzb;F*$\"3
)[%[cue7&4#F]r7$$\"3'QnZw.l7l\"F*$\"3wvD0&>P<*=F]r7$$\"3W#pu3$G[&f\"F*
$\"3!>L_me[f,#F]r7$$\"37fF:LR&4f\"F*$\"3wi+92*fD\"=F]r7$$\"3wSd#*RhtY;
F*$\"3!pISb^[$)o\"F]r7$$\"3l2Q?Us?U;F*$\"31Q!Gg$)f\\[\"F]rFfcv7*7$$\"3
%)Q'[sf$4r?F*$\"3iVf\\Y9DX;F]r7$$\"3`+WQc30L?F*$\"3]8F7K$R-F#F]r7$$\"3
3@\\[S))*[-#F*$\"3yi'*p+45N>F]r7$$\"3b,6q5C)H$>F*$\"3iB#zbS\"oe@F]r7$$
\"35A;![RI[#>F*$\"3<th:uHaB=F]r7$$\"3jTaeCou;?F*$\"3M7mFpC'**f\"F]r7$$
\"3uhfo3[f3?F*$\"3!>c`y.C[E\"F]rFjev7*7$$!3Rhq:9[`8>F*$\"3_#f<&)R5R?'F
]r7$$!3mv(\\n.jw-#F*$\"35)Q7vbIaG'F]r7$$!3g(p=XjPB*>F*$\"3%zSQDwHy(eF]
r7$$!3'yZep)y7/@F*$\"3^7.134)*3\\F]r7$$!3!)*RFZ[-)o?F*$\"3NKj38,Q,XF]r
7$$!3M>wGKA,d>F*$\"3yFWcn*G-Z&F]r7$$!31Tl0Ioo@>F*$\"3s[/fs\"GE1&F]rF^h
v7*7$$!39D%>MzYyd\"F*$\"3Y\"4YbX_q7'F]r7$$!3o-#ff(yxm;F*$\"3]7zLfZHlgF
]r7$$!3wqc!>fv]j\"F*$\"3m8ZF;PW*y&F]r7$$!3K8YL@;t5<F*$\"3\"HUw](R'*>\\
F]r7$$!3Q\"3\"GP$H!z;F*$\"31CK,KH6WYF]r7$$!30R@&yItLg\"F*$\"3#f^6Kn#f8
bF]r7$$!3M2')zB5nr:F*$\"31<$[,jTxB&F]rFbjv7*7$$!3oV?5/\"plB\"F*$\"3S!f
uD^%>]gF]r7$$!3i2i9RbD/8F*$\"3Irmt')Qo%)eF]r7$$!3EA-Ftj<w7F*$\"3^(4-_k
KUr&F]r7$$!3(R\\!HC]#HK\"F*$\"3X6OG<?7W\\F]r7$$!3g3XTee%[H\"F*$\"3kP!
\\dxqOx%F]r7$$!39PUR2s4[7F*$\"3\"[_nOS\"yVbF]r7$$!3x^#=:/=+A\"F*$\"3+^
H8i,Lt`F]rFf\\w7*7$$!3)[;\\?Y<q*))F]r$\"3M*3.'plLtfF]r7$$!3n.z5j-'4S*F
]r$\"3]k'3(RzfVdF]r7$$!3!e^Bhy*Rc\"*F]r$\"3[f0K\\l>_cF]r7$$!3$e?h#e432
%*F]r$\"37y=oM]X\")\\F]r7$$!3'z\"oF\"[?D;*F]r$\"35tPHWO0!*[F]r7$$!3#z7
R\"4$R=\"*)F]r$\"3YaC$*e^zgbF]r7$$!3/SZ:K)ysm)F]r$\"3c]VaoPRpaF]rFj^w7
*7$$!3%)Q/G(>ZCP&F]r$\"3G)eJmiyk*eF]r7$$!3U6&HXP$*Hu&F]r$\"33#*QD=p.Uc
F]r7$$!37)e?$zSmMbF]r$\"3f*4I'GaL.cF]r7$$!33E\\Tf$33k&F]r$\"3OA7FFI'>.
&F]r7$$!3\"R+1U1zCV&F]r$\"3UIukP:E$*\\F]r7$$!3%fm6TyMjK&F]r$\"352j+RRj
kbF]r7$$!3lUF!*)[0!=^F]r$\"3r:DQ\\C$f_&F]rF^aw7*7$$!39eUrY-)>z\"F]r$\"
3A(3gOo?'>eF]r7$$!3=**osDZlo?F]r$\"31aBPA3+!e&F]r7$$!3-TMH7mb'*=F]r$\"
3#yrIJG\\wc&F]r7$$!3%=5mjWK/$>F]r$\"3GX;0&*fk&4&F]r7$$!3oVE$HLM$e<F]r$
\"3;5+\"eX%H$3&F]r7$$!3f#)*f))\\eWs\"F]r$\"3g\"3*)Qu(HbbF]r7$$!3WClU&Q
gBb\"F]r$\"3ZYuk/i%Ha&F]rFbcw7*7$$\"3Jy$\\'*Q$QW=F]r$\"3<'e)oSFwUdF]r7
$$\"3WM**H$ob?i\"F]r$\"3K\\S1_'*[dbF]r7$$\"3+Gz&\\hAzv\"F]r$\"3?9C#G6Q
^a&F]r7$$\"3#pE&)3yYSs\"F]r$\"3MYJ-QR]s^F]r7$$\"3[gKa7P\"*f=F]r$\"3A6:
y)R_,;&F]r7$$\"3I@fhY&*y$*=F]r$\"3(zx!etlyKbF]r7$$\"3g9RFyklH?F]r$\"3%
G9RV.N/_&F]rFfew7*7$$\"3bq/\"=rVm`&F]r$\"35&3<xz/fm&F]r7$$\"3:*)4b_y8H
`F]r$\"33!)*GtS.Xd&F]r7$$\"3f<NV-OxGaF]r$\"3q)=0x\">!e`&F]r7$$\"3iz\"R
BKHEK&F]r$\"3_Dd=co`i_F]r7$$\"3<4<As]EAaF]r$\"3:M>cm`$QA&F]r7$$\"3-YgJ
_$4%GbF]r$\"3?'R\"3G/5(\\&F]r7$$\"3dv&)>-^/GcF]r$\"3s.wXQ*)ReaF]rFjgw7
*7$$\"3W<!p(>2![G*F]r$\"31%eXZ&o/*e&F]r7$$\"3qki-#y\"f_!*F]r$\"3CXr;)3
U5j&F]r7$$\"3aGL8]j*f6*F]r$\"3LT!zxpS'RbF]r7$$\"3]Qc*z<:`'))F]r$\"3'GQ
R&\\Zul`F]r7$$\"3O-F5Y(>(G*)F]r$\"3%*y7:fLMu_F]r7$$\"3S#RS#=4Sz\"*F]r$
\"3KO4R2$R#[aF]r7$$\"3CcuM'[0GC*F]r$\"3IJG+<z$oN&F]rF^jw7*7$$\"3'>]_8W
&))38F*$\"3*H3u<\"*)=7bF]r7$$\"35wD<Z<Cz7F*$\"3!fayXp0rs&F]r7$$\"3#ft0
e3f>G\"F*$\"35sR/`WlcbF]r7$$\"3+kayM/@N7F*$\"3I=T3=w7#[&F]r7$$\"3\"Qi=
MxFzB\"F*$\"3hX&\\lPw;J&F]r7$$\"3u&*)QWUwYG\"F*$\"3G)R4:@.iQ&F]r7$$\"3
yb?2jPR(G\"F*$\"3\\C[(*p>v:_F]rFb\\x7*7$$\"3yZyIz/)[p\"F*$\"3$>e-)o4LN
aF]r7$$\"3#y%\\;#\\h[l\"F*$\"3%)zJcEUpieF]r7$$\"3Ih0i7d&Rl\"F*$\"3+\")
**\\$=Voe&F]r7$$\"3'*=;>$o*Hy:F*$\"3*=$*>=Y&o6cF]r7$$\"3?Ksk.RRx:F*$\"
39Mnv=W$eL&F]r7$$\"3wuh2L*\\Il\"F*$\"39#yO/9#*4J&F]r7$$\"3+)yJN:W@l\"F
*$\"3H$ett4T^.&F]rFf^x7*7$$\"3GRH%e=lk3#F*$\"3)33Je-t%e`F]r7$$\"32U(zJ
T=@.#F*$\"3=[57%o2y.'F]r7$$\"3u3yX:&*eF?F*$\"3-oq9*)o?IcF]r7$$\"3FG!=I
E*z:>F*$\"3sCou!G=Wv&F]r7$$\"3&\\4'Hl.F6>F*$\"3WVGx&[<oM&F]r7$$\"3(e(e
t<11B?F*$\"3'y3tT41EA&F]r7$$\"3aUR,?<`=?F*$\"392\"*>*H0]\"[F]rFj`x7*7$
$!3=hFcDK;)*=F*$\"3/IF&y(>8<**F]r7$$!3,NW&*zafG?F*$\"3Us5&4*)*H05F*7$$
!3%*4eafpk*)>F*$\"3u8e)4vNHd*F]r7$$!3N^:kM5J@@F*$\"308zA$y<Z])F]r7$$!3
GEHB9DO#3#F*$\"3h-IqCYlC!)F]r7$$!3K&=P\"R%)p]>F*$\"3G.4Y#fsG4*F]r7$$!3
[g&G(=*\\<\">F*$\"3'R*f$RV4Gh)F]rF^cx7*7$$!3#\\7D[?vCc\"F*$\"3**G7)[.u
-%)*F]r7$$!3ehQ;>.rn;F*$\"3YZiL6J'G$)*F]r7$$!3K$yKp\"\\QK;F*$\"3W>@s/(
\\X[*F]r7$$!3f'o<!pZ\"zs\"F*$\"3YBSC]3q:&)F]r7$$!3_3mym$*e#p\"F*$\"3K%
*)HOW(Qn\")F]r7$$!3/0<q9&fqf\"F*$\"3K!*z5)HOi8*F]r7$$!3wE1Z7Tth:F*$\"3
GiQ\\\"*G#zy)F]rFbex7*7$$!3ZVx]:v>@7F*$\"3#zs4>4;Mw*F]r7$$!3`m3N#)z=08
F*$\"3E1]tQAD_'*F]r7$$!3#[L(H)p&[t7F*$\"3H.&\\OjQ$4%*F]r7$$!3YnN(><3,M
\"F*$\"3*>@^C*)e)R&)F]r7$$!3aN+#z)eS38F*$\"3!zqltGXpH)F]r7$$!37.QC9MyT
7F*$\"3A**RcG]Um\"*F]r7$$!3>r->I6357F*$\"3C'\\yMU6N#*)F]rFfgx7*7$$!3xi
h5w:IV()F]r$\"3)oAQ*[\"elo*F]r7$$!3%Q\\a^p%G5%*F]r$\"3X**pq\"Hm6^*F]r7
$$!3QTYROI\\H\"*F]r$\"3;kzwPDIZ$*F]r7$$!3yS>4NC\"*y&*F]r$\"3my%\\)4>>x
&)F]r7$$!3A(3Kjx?\")H*F]r$\"3OV/\"f:GLT)F]r7$$!3#yyMwP,([))F]r$\"3)*H*
GQyQM=*F]r7$$!3ON\\()=(4zc)F]r$\"3z&*)*))H]d>!*F]rFjix7*7$$!3tOuL68t=_
F]r$\"3\"esmf?+(4'*F]r7$$!3g,hd1yJ_dF]r$\"3/FADq_g4%*F]r7$$!3r8<fHtv2b
F]r$\"3E/v2<9W)H*F]r7$$!30hcCO)RE\"eF]r$\"3XB)QC!**pF')F]r7$$!3=t7Ef$z
!obF]r$\"3o+TE\\g`;&)F]r7$$!3%eK2E&o>j_F]r$\"3g#y-Rcxs=*F]r7$$!3'z$Hiv
jj=]F]r$\"3%41G2r8h2*F]rF^\\y7*7$$!3/c7xgVEQ;F]r$\"3vC_*HEUG`*F]r7$$!3
3*[tx:zz2#F]r$\"3!zoqV<pvM*F]r7$$!31mXci)\\'p=F]r$\"3]A\"y:FbFE*F]r7$$
!3`Oo>BRE-@F]r$\"3OY#>-(GQ\"p)F]r7$$!3A8z)ziMR*=F]r$\"3()zmUn*olg)F]r7
$$!3wUcNn0Kh;F]r$\"35dbyo8%z<*F]r7$$!3u>n9s7*HX\"F]r$\"3q\"*H*fYFJ4*F]
rFb^y7*7$$\"3U!Q#fv#*4)*>F]r$\"3qBP-?V)fX*F]r7$$\"3#[M`7DJFh\"F]r$\"3G
%QiS+e]K*F]r7$$\"3)H!ook$H[y\"F]r$\"3))=)p75W-C*F]r7$$\"3_KX0/`@_:F]r$
\"3WZ2>83Co()F]r7$$\"3m!*z[<MJC<F]r$\"3#4=)R5pU$o)F]r7$$\"39h-7yu#p&>F
]r$\"3[`sZ)>Ia:*F]r7$$\"3H>Pb\"fD!H@F]r$\"33)o%o&H;12*F]rFf`y7*7$$\"3m
sMv(ff.p&F]r$\"3iAA0xj7z$*F]r7$$\"34+W]?M\")>`F]r$\"3/:tKf<2U$*F]r7$$
\"37$Ri@N!obaF]r$\"3Q$f_h!z!4B*F]r7$$\"3yX%3b%yz]^F]r$\"3iELNJPFe))F]r
7$$\"3yQk;xZm'G&F]r$\"3'Qgy\"y)4ru)F]r7$$\"37'Q?QGZ:f&F]r$\"3sry(H0W(>
\"*F]r7$$\"3D!Qya@9us&F]r$\"31]J!)*>!e3!*F]rFjby7*7$$\"3c>?r0m^Q%*F]r$
\"3d@23M%oAI*F]r7$$\"3jv'z*\\tEV!*F]r$\"3=![l,W5')R*F]r7$$\"31/A')*4.H
9*F]r$\"3,YkA'oYZB*F]r7$$\"3a.\\;,P[$p)F]r$\"3%R)pqC;[h*)F]r7$$\"33Lu/
^%>Jz)F]r$\"3k[zwqyh(z)F]r7$$\"3]KZu\\)QDC*F]r$\"3#=T(GKH)32*F]r7$$\"3
$4EF'*fu@M*F]r$\"3kx$[$y\">q!*)F]rF^ey7*7$$\"3<-o%*HqDC8F*$\"3^?#46\\5
aA*F]r7$$\"3?<z'RI4$y7F*$\"3uzodYSn%\\*F]r7$$\"3eB'y2w\\YG\"F*$\"3yw8
\\T/w^#*F]r7$$\"3]!R-rGF!=7F*$\"3S><D$\\ky2*F]r7$$\"3)o48RunVA\"F*$\"3
K:i;))3&\\$))F]r7$$\"3uH$*e<-*4H\"F*$\"3!Q(eSOo%)3!*F]r7$$\"37O+Su1L(H
\"F*$\"3sp.KJK$fw)F]rFbgy7*7$$\"3,[@!z1_-r\"F*$\"3Y>x8[Db[\"*F]r7$$\"3
#*)Gg*[!HRl\"F*$\"3![^h&yDEI'*F]r7$$\"3u[Mf(QYml\"F*$\"3m&QZ><\\>G*F]r
7$$\"3YX&3b`;6c\"F*$\"3*H`()pLAu?*F]r7$$\"3G0<9uQ$Qc\"F*$\"3'QSt.$*3\"
f))F]r7$$\"3y3mAEPOf;F*$\"3ldKLldjL*)F]r7$$\"3eo(f[1\"3i;F*$\"3_G\">(e
BK&e)F]rFfiy7*7$$\"3ERsVun$=5#F*$\"3S=i;0Ypr!*F]r7$$\"3s#3v*pf=J?F*$\"
38$Q>h.w`!)*F]r7$$\"3'fpI/>!GI?F*$\"3qsWfxGJD$*F]r7$$\"3+b\\L:hh)*=F*$
\"3qCW\"f:b,N*F]r7$$\"3Co0zN.r(*=F*$\"3E9&*Q(*>4q))F]r7$$\"3l4j)3Tu$H?
F*$\"3Ei&p!>(\\_%))F]r7$$\"3!H#>MJ'o%G?F*$\"3#HlW0c'=l$)F]rFj[z7*7$$!3
'4Yopj\"z#)=F*$\"3k'y=dNNIO\"F*7$$!3#R4fJ#z_H?F*$\"3!e!4:En0#Q\"F*7$$!
3]AHd%Gcp)>F*$\"3%=KVR</oK\"F*7$$!3&[iCB=%\\Q@F*$\"3>^&ReYX+@\"F*7$$!3
m`%QPaAf4#F*$\"3Cn>j8Hza6F*7$$!3J^n)fk%QW>F*$\"3mPdt@;br7F*7$$!37!e+u+
8=!>F*$\"3q`\"G&p!*H;7F*F^^z7*7$$!3qC3B;O5Z:F*$\"3kO;Uh&\\`N\"F*7$$!3[
?&oBwU'o;F*$\"3OeMLYJ/g8F*7$$!3(e*)f>C%pH;F*$\"3I_pJpb'zJ\"F*7$$!35g2q
;z4X<F*$\"3,i6asP967F*7$$!3ZN@H'R\\hq\"F*$\"3ScY_&>m!p6F*7$$!3-r7b@du!
f\"F*$\"3qY/I#*z)eF\"F*7$$!3UYE9,sz^:F*$\"3lSRG:/\"QB\"F*Fb`z7*7$$!3EV
M\"p#f#e?\"F*$\"3W'[CrwjwM\"F*7$$!3lDbbD/718F*$\"3,ML2f?)>M\"F*7$$!3QZ
WKB]zq7F*$\"3p!p4AYW/J\"F*7$$!3uSml>8Hd8F*$\"3)4)=ww&fN@\"F*7$$!3pibU<
f'>K\"F*$\"3'yB)*)z>-#=\"F*7$$!36pL4@'paB\"F*$\"3OZgMlo!*y7F*7$$!3$3Hi
)=U9+7F*$\"3//C[o#ptC\"F*Ffbz7*7$$!3kgJ;!p&e*e)F]r$\"3WOt#G(z(*R8F*7$$
!3,%3,s74'>%*F]r$\"3WL0PkM(yK\"F*7$$!3'ewlmG'e-\"*F]r$\"3*p`@E&3C/8F*7
$$!3kuE#>\"Ru](*F]r$\"3k2<]yGH<7F*7$$!3gdtQr5sL%*F]r$\"3=6Fvm-m$>\"F*7
$$!3qZ/8YMc&y)F]r$\"3cSD(3C31G\"F*7$$!3mI^f01ao%)F]r$\"35WN7Hc(pD\"F*F
jdz7*7$$!3iMWRDa,l]F]r$\"3A'=I&y@HK8F*7$$!3w\"pA'QAkhdF]r$\"3)f0DAO<xJ
\"F*7$$!3=QG')z0&3[&F]r$\"3y!\\_0ua$*H\"F*7$$!3-'RwIJrW)fF]r$\"3BU1wxO
MA7F*7$$!3XUlJa'zOq&F]r$\"3/x!)3c5)R?\"F*7$$!3t&)H5@*e+?&F]r$\"3gD*z)=
@*4G\"F*7$$!3sKJMisE>\\F]r$\"3igt?(\\HEE\"F*F^gz7*7$$!3#RDG[Z[X[\"F]r$
\"3BOIB%Q1YK\"F*7$$!3Cz+#)*e.t3#F]r$\"3H-pj_P^68F*7$$!33\"pNG6VF%=F]r$
\"3s_D+Ehy&H\"F*7$$!3%4dF+S&4uAF]r$\"3I%oQX(>rG7F*7$$!31$=VI#\\`H?F]r$
\"3'\\L/zM%)H@\"F*7$$!3%HI^ej#=)f\"F]r$\"3;.#o$*\\e+G\"F*7$$!3y9p')e@i
`8F]r$\"3!Q&Qts3Lk7F*Fbiz7*7$$\"3a#QN:;:=:#F]r$\"3,')e$**e?pJ\"F*7$$\"
3$\\v1#>oS.;F]r$\"3#>21cji#48F*7$$\"3%zn:W6O<\"=F]r$\"3OA<(*3]`$H\"F*7
$$\"3#yzBs#QQ!Q\"F]r$\"3_Me$)oxRO7F*7$$\"37@FVAJr)e\"F]r$\"3<&[,A9q1A
\"F*7$$\"3'4gC'4a1??F]r$\"3!GPPBQ2yF\"F*7$$\"3ECN$[q%RGAF]r$\"3ABIqb(z
?E\"F*Ff[[l7*7$$\"3ntkp$[vS%eF]r$\"3-O(QczM#48F*7$$\"3\")3yX))*)[5`F]r
$\"36lD86S'4J\"F*7$$\"3_n7*=5(e#[&F]r$\"3#****f%*Q,EH\"F*7$$\"3#>rx'oj
'*y\\F]r$\"3W#4_11,aC\"F*7$$\"3iq66#[k5:&F]r$\"3DF&z*Q%QqA\"F*7$$\"37D
ZK:_oacF]r$\"3sMuyn(QUF\"F*7$$\"3$Q=e(GLyEeF]r$\"3ap[6Yh(eD\"F*Fj][l7*
7$$\"3m@]l\"\\KAf*F]r$\"3!eeT8+\\:I\"F*7$$\"3Y&3Lz\"H%R.*F]r$\"3S\"Q;#
zyh;8F*7$$\"3[y5f\\)4)p\"*F]r$\"3'\\QnuE&)HH\"F*7$$\"3ppTLCAl@&)F]r$\"
3Geu)*\\=sb7F*7$$\"3si@*f:>vl)F]r$\"3%=YQ#Q#*3K7F*7$$\"3\\r!\\7ywcI*F]
r$\"3_)Q=dl_$p7F*7$$\"3jlq!HrV:W*F]r$\"33#RpR/?dC\"F*F^`[l7*7$$\"3:-6a
='G'R8F*$\"3!eVWq?jQH\"F*7$$\"3'yDj2'oPx7F*$\"3Z@v&)RUAE8F*7$$\"3!3^^d
VStG\"F*$\"39yQ*Hk'o%H\"F*7$$\"3A<$>%RT%3?\"F*$\"3gJ>%o8gtE\"F*7$$\"3=
qvS9x!3@\"F*$\"3^)Gy*RD#eB\"F*7$$\"3aj(R2,/tH\"F*$\"3#[BIh/\\JE\"F*7$$
\"3\\;!GdensI\"F*$\"3]\"fm#\\9hJ7F*Fbb[l7*7$$\"3A[k\\cOiD<F*$\"3e&GZFT
xhG\"F*7$$\"3-Icv0m*Hl\"F*$\"3'[)f0$4$yR8F*7$$\"3SOjciqLf;F*$\"3/z%Rg^
0xH\"F*7$$\"3'>ZDyQLRa\"F*$\"338b@@fJ!G\"F*7$$\"3MyhjWQF]:F*$\"3Z2!*>W
$Q#Q7F*7$$\"3cUqP>vnl;F*$\"3?tH-Rzib7F*7$$\"3%*[x=wz,s;F*$\"3Qnk+i.b87
F*Ffd[l7*7$$\"3qR:.j$3s6#F*$\"3gN,X=;\\y7F*7$$\"3\"QUqn_`-.#F*$\"3!=x6
)QWHd8F*7$$\"3j$e.a'3(H.#F*$\"3&y=/m)=/-8F*7$$\"3G\")=lnHV\")=F*$\"3C-
#3J?*e%H\"F*7$$\"35T]G1.:%)=F*$\"3H=1!4lO$R7F*7$$\"3WVn./#)oN?F*$\"3!R
g'RM$*yY7F*7$$\"3q.*pEa0%Q?F*$\"3#*>!*=#yO:>\"F*Fjf[l7*7$$!3wgTP[+Un=F
*$\"3i+Bl8vNM<F*7$$!3#GvjjOg/.#F*$\"3UR2NhN\")e<F*7$$!31N+g4cE%)>F*$\"
3_i!)ysZJ'p\"F*7$$!3!zp2+Lxc:#F*$\"3I6jN`\">'p:F*7$$!3f!)RCtD[4@F*$\"3
?MOzk.72:F*7$$!3I<j$G&32Q>F*$\"3V&QDU)f\"Qj\"F*7$$!3a*fsg4w=*=F*$\"3c3
Fm&><8d\"F*F^i[l7*7$$!3]CljF?tJ:F*$\"3S]^N><nE<F*7$$!3izJd0_dp;F*$\"3u
\"HL:)**zO<F*7$$!3@3q)pc.qi\"F*$\"3)Hph\"ohZ(o\"F*7$$!3eLQQk5Gi<F*$\"3
MAz0gurq:F*7$$!3RiwzD%4(><F*$\"3gBjoYOR@:F*7$$!3-P3SG>V%e\"F*$\"3-%4!z
aB:Q;F*7$$!3$em9)*Gg=a\"F*$\"3G&\\=9aG))e\"F*Fb[\\l7*7$$!3/V\">$QVX!>
\"F*$\"3T+!e]#f)*=<F*7$$!3c%=g(oG028F*$\"3inJF%*)Q(=<F*7$$!3%*f:N[V5o7
F*$\"3OJW0h]&*z;F*7$$!3C9(RtYuWP\"F*$\"33T'yUELJd\"F*7$$!3h*3Jp%f_N8F*
$\"3%[!*f5V\\V`\"F*7$$!35NH%z#e:H7F*$\"39&pNyAr6k\"F*7$$!3C5V`2t?!>\"F
*$\"3*)eph%R(Q-;F*Ff]\\l7*7$$!3`e,A/)peV)F]r$\"3>]3wI,I6<F*7$$!3=uwCfN
$*G%*F]r$\"3#oOq&*HIYq\"F*7$$!3W\"*o$p`zc2*F]r$\"3YxiY^9vt;F*7$$!3h4Mv
)QvD#**F]r$\"3)zY=gcmod\"F*7$$!3)oiUkO@$p&*F]r$\"3SyV\"zr()fa\"F*7$$!3
r3hi9bUA()F]r$\"35)=iLgsGk\"F*7$$!3)fK:B\\r\"p$)F]r$\"3u)4e_v$*>h\"F*F
j_\\l7*7$$!30L9XR&*H6\\F]r$\"3?+PYOVh.<F*7$$!3%>Gp1nm4x&F]r$\"3!)*)[U(
>uWp\"F*7$$!3yjR8IQ%RX&F]r$\"3oJsRR`')o;F*7$$!3))Hr!**y-j:'F]r$\"3M-uF
lt\">e\"F*7$$!3$G\"=P\\*z#ReF]r$\"3-W(\\s]3jb\"F*7$$!3tY')f*)4#p8&F]r$
\"3Ot&p8[cKk\"F*7$$!3eGL1\\\")*)>[F]r$\"3D:>MBwk<;F*F^b\\l7*7$$!3!=D&)
))eK3L\"F]r$\"3'*\\l;U&Gfp\"F*7$$!3%)om'=-Gm4#F]r$\"3)etOyeq#)o\"F*7$$
!3%e\"o5jj$e\"=F]r$\"3S$HZ[s'Hl;F*7$$!3i0$eo(o#fW#F]r$\"3kWa0icG)e\"F*
7$$!3g_%)4=_8l@F]r$\"3;-g1*z6`c\"F*7$$!36jpM/Z/N:F]r$\"3q]y&='GKU;F*7$
$!355reXIDa7F]r$\"3A3%o))**[$>;F*Fbd\\l7*7$$\"3n%Qyu/JbI#F]r$\"3)**Rpy
uU#)o\"F*7$$\"3wk,;(Q#3%f\"F]r$\"3_0f!3Z>go\"F*7$$\"3\"HbWT'GkQ=F]r$\"
3/jk\"ygXIm\"F*7$$\"3FjIR]Bb37F]r$\"3i%f_jXrff\"F*7$$\"3G^uPFG6`9F]r$
\"39_JO$f(*Hd\"F*7$$\"3yS*G6M.K3#F]r$\"3c?q#[ur+k\"F*7$$\"3%*GL6=QwFBF
]r$\"33yv$=)y4<;F*Fff\\l7*7$$\"3!pZR'p8z(*fF]r$\"3w\\Ad`pb!o\"F*7$$\"3
v>7TcX;,`F]r$\"3[)RKj%3s(o\"F*7$$\"30V,i^Q\\4bF]r$\"3QSZI))>6i;F*7$$\"
3&p(p%=*[82[F]r$\"3x_)o\"[Z(\\g\"F*7$$\"3D+f0(=ka,&F]r$\"3W%>T,*eOz:F*
7$$\"3Mm!Ho9Byr&F]r$\"3G#3x-8.lj\"F*7$$\"3j*)z.UC:EfF]r$\"3;C%\\AF%*3h
\"F*Fjh\\l7*7$$\"3!Q-)fx$[fu*F]r$\"3w*4v#f6(Gn\"F*7$$\"3H&\\')e[=Y-*F]
r$\"3A:iT9ZP$p\"F*7$$\"3+a*>$*f;n>*F]r$\"3kD@Jme\\i;F*7$$\"3sMM]Z2#)\\
$)F]r$\"3R=U]PbH:;F*7$$\"3W$*o$4')=>_)F]r$\"3!)G,S*o;We\"F*7$$\"3g6Mv7
Z\")o$*F]r$\"3HO!3#=qhJ;F*7$$\"3Jqo=EG\"4a*F]r$\"3#p%R5q\"Q2g\"F*F^[]l
7*7$$\"3e-a82-+b8F*$\"3c\\z(\\O&=l;F*7$$\"3;*fevTWkF\"F*$\"33bt0v5)Hq
\"F*7$$\"3Y)RC26J+H\"F*$\"3g='Q=C(>k;F*7$$\"3]Vit\"*4m$=\"F*$\"3%>peV#
Q$pi\"F*7$$\"3-V?!\\oZs>\"F*$\"3qb*R6**\\\")e\"F*7$$\"3x(>!*Q!yh.8F*$
\"3P#))>'3MTD;F*7$$\"32(*f0(\\/sJ\"F*$\"37Y6Sv&Hme\"F*Fb]]l7*7$$\"3W[2
4X_*4u\"F*$\"3c*z!oq&*\\d;F*7$$\"3)3(4biT1_;F*$\"3Z=eDG*Rlr\"F*7$$\"3%
QARvtF?m\"F*$\"3s>U)[6;sm\"F*7$$\"3Y)RU,C]n_\"F*$\"3>tAt3'*))R;F*7$$\"
3U^18:QrO:F*$\"3Wu1O&zl0f\"F*7$$\"3cwu_78*>n\"F*$\"3)4i7:I#*yh\"F*7$$
\"3_Hd^()[&>o\"F*$\"3-A59)[o&o:F*Ff_]l7*7$$\"3pRei^*zD8#F*$\"3M\\OQwP
\")\\;F*7$$\"3Ykdc$3@$H?F*$\"3?0;,u70M<F*7$$\"3&3Zw.ahc.#F*$\"3KG*[a[_
:n\"F*7$$\"3y2)o*>)\\U'=F*$\"3ei\\i!*G;a;F*7$$\"3;9&znF!fq=F*$\"3[&Gi?
5k;f\"F*7$$\"3Bxr=(*>+U?F*$\"3A^i)op`!4;F*7$$\"3i$)y*RXU$[?F*$\"3MuNK3
\\bY:F*Fja]l7*7$$!3ag)z(f%[?&=F*$\"3P9eer'zc5#F*7$$!3t6%o&4GRJ?F*$\"3z
s0b'Rqb8#F*7$$!3iZriM\\d\")>F*$\"3+.Gjr`#e1#F*7$$!3%=x!px/'G<#F*$\"3Tr
I(3%G>H>F*7$$!3^2&\\FgUI7#F*$\"3i,`&f\"yWf=F*7$$!3H$)eofqvJ>F*$\"3)H.:
nM!3'*>F*7$$!3=>Yu%=R>)=F*$\"3>jsz@`LE>F*F^d]l7*7$$!3GCA/R/O;:F*$\"39k
')GxQ*z4#F*7$$!3_Qyx[w]q;F*$\"37DJt;ob8@F*7$$!3x?T,#*GJC;F*$\"3CLk+nn)
p0#F*7$$!332p17UYz<F*$\"3X#ouv9\"HI>F*7$$!3K*=.`XpKt\"F*$\"3c!*z%y4@P(
=F*7$$!3+./DN\"=\"y:F*$\"3!=uzsr;/+#F*7$$!3D&o'[yL#>`\"F*$\"3\"*\\Ibnm
%Q%>F*Fbf]l7*7$$!3#G%[s\\F3v6F*$\"3Q9:*H33.4#F*7$$!3pV['>J&)zI\"F*$\"3
A,IZHd\\&4#F*7$$!3Gs'yLn8aE\"F*$\"3Gs\"**)fcY\\?F*7$$!3s(yA]hd;R\"F*$
\"3U,az^pqK>F*7$$!3a;mVwf3\\8F*$\"3/s:A#)on')=F*7$$!34,DzM?%GA\"F*$\"3
\"HMD.fNM+#F*7$$!3!*Hj?'Rq-=\"F*$\"3_8:v?bSd>F*Ffh]l7*7$$!3UcrF=R:#G)F
]r$\"3;kVp)GAE3#F*7$$!3CjUH\"*zDQ%*F]r$\"3m+-xMrQ\"3#F*7$$!3#f,3sys([!
*F]r$\"3P=5J]?EV?F*7$$!3Y9%eloS%45F*$\"3'yANNDSk$>F*7$$!3:'*y\\h;#\\q*
F]r$\"3eXg2p^J)*=F*7$$!3go<7$e(Gf')F]r$\"3lN=&e'p80?F*7$$!3I@b.zB!)p#)
F]r$\"3Q`ER\")=,n>F*Fjj]l7*7$$!3%4V3Nl$edZF]r$\"3%R@(R%\\O\\2#F*7$$!35
ser-6H!y&F]r$\"3UBZiK5Br?F*7$$!3P*30/3PqU&F]r$\"3%>(>CQfPQ?F*7$$!3$['y
tmU8GjF]r$\"3XiTz_5\\T>F*7$$!35#3FWC!)[(fF]r$\"3V69Tefj3>F*7$$!3k1V4eI
yt]F]r$\"3\"4AfQ%3_0?F*7$$!3!R_$yN!H0s%F]r$\"3!*pkZ\\dms>F*F^]^l7*7$$!
3o\\A%Hq;r<\"F]r$\"3uj+5+2Dn?F*7$$!3.fK\"RX_f5#F]r$\"3]pl.Bu-l?F*7$$!3
;TzP8'H*)y\"F]r$\"3)Q.#pBt![.#F*7$$!3JS!*o`$exh#F]r$\"3u/Ad\\$fy%>F*7$
$!3;AP:8bt+BF]r$\"37pwA]#Rw\">F*7$$!3GBE%Gx1>Z\"F]r$\"3D)\\ZVA(e/?F*7$
$!3S0tIKR)[:\"F]r$\"3'G'H+DrOu>F*Fb_^l7*7$$\"3y'Q@M$pCfCF]r$\"3'R\"H!e
!\\cf?F*7$$\"3)[d8^&zv%e\"F]r$\"3ORd+1jxi?F*7$$\"3)yUtQh\\b'=F]r$\"3u.
7m1ibK?F*7$$\"3()GBct3sO5F]r$\"3'\\NpQ9Xb&>F*7$$\"3u\"=AB`7vJ\"F]r$\"3
M>[_W]KD>F*7$$\"3!4GLEFTj9#F]r$\"36omJ2hL-?F*7$$\"3jLJRJH8FCF]r$\"3sK@
(z+;@(>F*Ffa^l7*7$$\"3-zCebs]^hF]r$\"3ujd]6\"z=0#F*7$$\"3eHYOC,%=H&F]r
$\"35KA`\"oxW1#F*7$$\"3Y<!\\8g+k`&F]r$\"32\"[\\reA;.#F*7$$\"3*>C;]T.`j
%F]r$\"3m7coN%[X'>F*7$$\"3')H1+#*Q')z[F]r$\"3jhGITLpJ>F*7$$\"3W1MLy5'4
y&F]r$\"3/Inw#\\n()*>F*7$$\"3K%z<`b@b-'F]r$\"3!)yRQ)R7f'>F*Fjc^l7*7$$
\"3!f-TNEk'**)*F]r$\"3_8'3sJ$>W?F*7$$\"370*RQ0%H:!*F]r$\"3i[gh\\:8q?F*
7$$\"3TG)[!\\LiB#*F]r$\"3Mmo:lk+K?F*7$$\"3'3qs1F*)z<)F]r$\"3]y4-D#p[(>
F*7$$\"31B;)ec=jQ)F]r$\"3A'zh09Wn$>F*7$$\"3r^xDWE&>V*F]r$\"3%Qo(p!Q\")
Q*>F*7$$\"3+vmYR>GS'*F]r$\"3c,&QiHcd&>F*F^f^l7*7$$\"3!GqHdzr.P\"F*$\"3
Jj9\"H_2l.#F*7$$\"3/SRNu>^v7F*$\"3Y)=d-\"ztz?F*7$$\"3!fG(p&y@FH\"F*$\"
33fLoSyqL?F*7$$\"3AqJ0WyZm6F*$\"31_a(=^2l)>F*7$$\"3)e^'Rbwo$=\"F*$\"3n
A;IUuZS>F*7$$\"3yJ1/(fJ*48F*$\"3#*H&46xxw)>F*7$$\"3lxRQ399F8F*$\"3a+d`
,xkT>F*Fbh^l7*7$$\"3k[]oLoOc<F*$\"3a8VhG<#)G?F*7$$\"3)>JY$><8^;F*$\"31
_cXjnH$4#F*7$$\"3G6@^7%=Zm\"F*$\"3kg*GPrEn.#F*7$$\"3(\\KfC4n&4:F*$\"3_
L!\\iHj%**>F*7$$\"3\\C^i&y`J_\"F*$\"3jTB_YK*G%>F*7$$\"3e5zn0^Iy;F*$\"3
aoA+km:!)>F*7$$\"3')4P%))z\"*=p\"F*$\"3(odvUh'eB>F*Ffj^l7*7$$\"37S,AS:
&z9#F*$\"3KjrJMf8@?F*7$$\"3+16OS')QG?F*$\"3-R9@4\"336#F*7$$\"3&*e$\\`@
_$Q?F*$\"3BpOH%3j5/#F*7$$\"3GMdGsm1Z=F*$\"3pA<9ylt8?F*7$$\"3C()RFZ-.d=
F*$\"3n_RA`:*R%>F*7$$\"3Y6wL!z:$[?F*$\"3+**ePf!=8(>F*7$$\"3UkeKl$z#e?F
*$\"3?H\"eW.t:!>F*Fj\\_l-%&COLORG6&%$RGBG$\"\"!Fb__lFa__l$\"*++++\"!\"
)-%*AXESSTYLEG6#%$BOXG-%+AXESLABELSG6$%\"xG%\"yG" 1 2 0 1 10 0 2 9 1 
2 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 16 "with(plottools):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 84 "l1 := line([r_i[1],r_i[2]], [r_f[1], r_f[2]], color=r
ed, linestyle=2, thickness=3): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 86 "l2 := line([r_i[1],r_i[2]], [r_1[1], r_1[2]], color=green, lin
estyle=2, thickness=3): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 
"l3 := line([r_1[1],r_1[2]], [r_f[1], r_f[2]], color=green, linestyle=
2, thickness=3): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "displa
y(l1,l2,l3,PL1);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 
2 "6(-%'CURVESG6&7$7$$\"\"#\"\"!F(7$$!\"#F*$F*F*-%'COLOURG6&%$RGBG$\"*
++++\"!\")F.F.-%*THICKNESSG6#\"\"$-%*LINESTYLEG6#F)-F$6&7$F'7$F.F.-F06
&F2F.F3F.F6F:-F$6&7$F@F+FAF6F:-%)POLYGONSG6]t7*7$$!3(G;<V$f8@?!#<$!39P
GolS')y>FM7$FK$!3b&fZ1za(3?FM7$$!3#*4*G$fB<6?FM$!3#GMfc@\"z)*>FM7$$!3g
jp<`e%Q)>FM$!38*G6=s<h-#FM7$$!3m5()=yA)Q(>FM$!3iOI#o9ah,#FM7$$!3(plSVy
37+#FM$!33!4r1kF)))>FM7$$!3C/CN4_C\"*>FMFNFJ7*7$$!3gE&zN\"zW&o\"FM$!3M
()*z*f)\\l)>FM7$$!3o*eENx]-m\"FM$!3AV]Yq$o2.#FM7$$!3I$)er;.\"Rl\"FM$!3
N7dG?)Hw+#FM7$$!31*4`ve\\/f\"FM$!34y'4^T>]-#FM7$$!3o#RU284Te\"FM$!3BZ.
$\\'3)=+#FM7$$!3!p<0*f)pvk\"FM$!3]\"Q1,F\"\\%)>FM7$$!3_qW4.%H7k\"FM$!3
S]q#*>FNh>FMFeo7*7$$!3%\\9iUAqTM\"FM$!3MPrFacB%*>FM7$$!3Q%f8nVGxH\"FM$
!3cn^sd%H)[?FM7$$!3eM/3)46]H\"FM$!3vtHRF4::?FM7$$!3%*z*30*Hk-7FM$!38f*
))3h.E-#FM7$$!35?e(=lD**>\"FM$!3wlnb!3D*))>FM7$$!3wusWfPH#H\"FM$!3Q!yg
qRs9)>FM7$$!3%\\693Uw&*G\"FM$!3y'eGn'QzZ>FMFiq7*7$$!3qz,lj'GI(**!#=$!3
L(Gu&[9#>+#FM7$$!3qu<yQ#*oN$*F`t$!37ozU_!QH1#FM7$$!37TcAMquW$*F`t$!3mF
6)p`a8-#FM7$$!3TkgW?1E/#)F`t$!3oK\"\\\"4.()=?FM7$$!3tH**)eT=L@)F`t$!3A
#H-Pz'Gx>FM7$$!3W1&p'H[!QN*F`t$!3?(GM:-r(z>FM7$$!3'GP8^iiGO*F`t$!3sYu3
1v=Q>FMF]t7*7$$!3m`9)))Re%[kF`t$!3bP9(GC2'4?FM7$$!3W#Q.-NAxn&F`t$!3OXM
daT4t?FM7$$!3Y8FUF8,BdF`t$!3lt,0\\1CE?FM7$$!37%y*f@!))zV%F`t$!3J)>!*)4
&>Q,#FM7$$!37:\">))*pF$[%F`t$!3gEpO/g'p'>FM7$$!3YW?k/.IodF`t$!3;-p_VrQ
z>FM7$$!3Zv8'=G*e8eF`t$!3VIO+QO`K>FMFbv7*7$$!3)HF:$[9*z'GF`t$!3x(eor.$
H<?FM7$$!3Qp2S,PQ.?F`t$!3G*fhTw(Hz?FM7$$!3_lbRgQ!\\3#F`t$!3;7,gj#4)H?F
M7$$!3I(f4b3@hF(!#>$!3-c@687X2?FM7$$!3uevXvEK\"4)Fhy$!3oo1b7F'z&>FM7$$
!3mh.R>SUm@F`t$!3#[iQIw?.)>FM7$$!3!y:&QyT%zC#F`t$!3YPrZiA$3$>FMFfx7*7$
$\"3#\\j$[!)=s$o(Fhy$!3)ztl9$)y\\-#FM7$$\"3'R1EwqEto\"F`t$!3')HC>\"))[
:3#FM7$$\"3C.e&oOv&p:F`t$!3IU4j!Qg?.#FM7$$\"3<4/q=r'o#HF`t$!3!e+:)=aw*
*>FM7$$\"3)y9Izx:\"4GF`t$!3o=ND=pF]>FM7$$\"3AUb3ES#=X\"F`t$!3=b%p+)=d#
)>FM7$$\"3A\"G:`osSL\"F`t$!3#y'z]zL3L>FMF[[l7*7$$\"3=b%4-^K1Y%F`t$!3w(
)GwDYmK?FM7$$\"35=r(o()3WR&F`t$!3COfm0v%)z?FM7$$\"3O$RJVNE/C&F`t$!3^kE
9+S*H.#FM7$$\"3:AV:g'\\a_'F`t$!3)yu)*p7i2*>FM7$$\"3G'f3w8n9P'F`t$!3;wa
Z@'3R%>FM7$$\"3]ncyJQW'3&F`t$!3-$R>Y\\Sh)>FM7$$\"34T*R#48YK\\F`t$!3^@h
4*)pGR>FMF_]l7*7$$\"3i-!o\"=&*y3#)F`t$!3(z.g+U]./#FM7$$\"3x%R_j!G'y6*F
`t$!3s>@ePO>u?FM7$$\"3@.7.-\"\\w#*)F`t$!3qz_8A,hK?FM7$$\"35y5e^N\"o+\"
FM$!3E#QjwLT/)>FM7$$\"3[*e*[6=#z()*F`t$!3zTl@Ay&)Q>FM7$$\"3w7+r(RNut)F
`t$!3AR%)o1m-\"*>FM7$$\"3KA))Q$p@sa)F`t$!3w)fT74V%\\>FMFc_l7*7$$\"3Z+C
>@VG,7FM$!3?)=dV@O![?FM7$$\"37*=0'\\)odG\"FM$!3))z4%pF(ek?FM7$$\"3iBb*
4OCJE\"FM$!3^'y3mu34.#FM7$$\"3CypcoC\\b8FM$!3]3*330.)o>FM7$$\"3_7t&*zz
%GL\"FM$!38:nZ?X7N>FM7$$\"3*y&eQs)z/C\"FM$!39$fwi@Is*>FM7$$\"3Q#>wPQNy
@\"FM$!3c*RWfo^N'>FMFgal7*7$$\"3KYx9f$zse\"FM$!3SQVl3?sb?FM7$$\"3%3c(f
%f)Qh;FM$!3q;DuB%G50#FM7$$\"3w[.\"y)47N;FM$!3%e=jN()*)y-#FM7$$\"3'H8tp
r\"e)p\"FM$!3CF`Vms%e&>FM7$$\"37@f=5TJs;FM$!3Q'*fD;(3F$>FM7$$\"3pOJ-\"
Q`)3;FM$!3)\\&QQB8v/?FM7$$\"3iCfBude#e\"FM$!3!R_/Kx7;)>FMF[dl7*7$$\"3!
y$GolS')y>FM$!3=)[^H!ySj?FM7$$\"3&[N7c^X'Q?FM$!3wHn)z2<N.#FM7$$\"3V'fZ
1za(3?FM$!3\"oZ)*H]`N-#FM7$$\"3`U&*z'H\"3O?FM$!32QEa%)RdT>FM7$$\"36%yM
=d!>1?FM$!37&Qa&4/hJ>FM7$F`fl$!3&QA5!G**e8?FM7$$\"3;z!=2Mt*[>FM$!3Mr>-
`ji.?FMF_fl7*7$$!3WiGsXVw0?FM$!3PB$\\x!>a2;FM7$$!3y@=_x$o?-#FM$!3;ixWb
z*>j\"FM7$$!3EAgN%o\"[3?FM$!3N-Y\"oh!GH;FM7$$!3)o.g3+H5+#FM$!3-HXHMSam
;FM7$$!3ePUp2BW()>FM$!3?p8m&pEQm\"FM7$$!3'HA!>\"*\\*[*>FM$!3`U9=yKcE;F
M7$$!3mBW-)H38)>FM$!3\\#G[&Rf%Qi\"FMFahl7*7$$!3SE_)\\Kw+n\"FM$!3Ptk/-x
A:;FM7$$!3e[7t;K=h;FM$!3i4_EN:,a;FM7$$!3%e*HuT'>7l\"FM$!3mr4W@#>\"Q;FM
7$$!3cshBNFj2;FM$!3?=HfFdWl;FM7$$!3g>zCg\"pwf\"FM$!3/!ooPT`&\\;FM7$$!3
*Guan1c7k\"FM$!3sLnh2pAA;FM7$$!3;!\\m<\\#HJ;FM$!3b&\\#z$fMjg\"FMFejl7*
7$$!3&\\%ymN')zG8FM$!3fBOM'\\8Hi\"FM7$$!3u`#=*z3m)H\"FM$!3%RLDDis?n\"F
M7$$!3OZv5B/K#H\"FM$!3GL#[&G.kX;FM7$$!3@`?>Qh#)>7FM$!3C*>sL#*HIm\"FM7$
$!3$oM\"Q\"o&[87FM$!3c)4&RHwfO;FM7$$!3)4%oHm*zfG\"FM$!3$G8rX.3#>;FM7$$
!3eMh[4&R'z7FM$!3OKSfSdx#f\"FMFi\\m7*7$$!3fxrqxFJ>)*F`t$!3et2k!H*fI;FM
7$$!3([OG3n8]M*F`t$!3_M\"Gs@\"='o\"FM7$$!3gln\\%GSyJ*F`t$!3?(QO\"QR%=l
\"FM7$$!3E)zws4#4w$)F`t$!3esBj@mHf;FM7$$!35+_%4r=*[$)F`t$!3CD1aU$f\\i
\"FM7$$!3Wn^;)*om!H*F`t$!3kRY/fm]<;FM7$$!3=oN$=^$\\j#*F`t$!3I#*G&*z$pJ
e\"FMF]_m7*7$$!3a^%QH^UZH'F`t$!3!Q#z$\\3&GQ;FM7$$!3is*\\AyYqo&F`t$!3w6
OP>tL'p\"FM7$$!3%z$QpxX5'p&F`t$!3=La?]+tc;FM7$$!3_=0V)\\>)4YF`t$!3)zVt
B#eCa;FM7$$!3&\\QuQHx)=YF`t$!3Sf_?`&QYh\"FM7$$!3O/x8tB;0dF`t$!3gas.\"y
Arh\"FM7$$!3yq:eo,A9dF`t$!3!e2p=^:vd\"FMFaam7*7$$!3'3FsBcvUr#F`t$!3!Q2
N#z3(fk\"FM7$$!3bftWL\"3F,#F`t$!3ol<'*G4a-<FM7$$!3%3pm16(*z0#F`t$!3Cr`
vk')Hg;FM7$$!3aXp\"Q&eV%**)Fhy$!3#fR&fDv(yk\"FM7$$!3ib-,EcKZ%*Fhy$!3[,
!*Qh_j0;FM7$$!3%=-')y3'G.@F`t$!3/x*[0Sc!=;FM7$$!37``5l]d[@F`t$!3g#eUj8
9ed\"FMFecm7*7$$\"3[dO\"*R2)3A*Fhy$!3-CA`tml`;FM7$$\"3Mu%zbF-!y;F`t$!3
/'f#*f/#z/<FM7$$\"3?yYe;@['f\"F`t$!3#=?'y\"y\\Dm\"FM7$$\"3?u'p=kN]v#F`
t$!3pX#)HJ<>S;FM7$$\"3iy[(G[:Nn#F`t$!3E^=4n%\\zf\"FM7$$\"31#))*ed>'\\^
\"F`t$!3S2)zv^2.i\"FM7$$\"3>'3&f)zTMV\"F`t$!3=8MP`_1y:FMFiem7*7$$\"3%y
X_hR[Vh%F`t$!3+u$HyYU8m\"FM7$$\"31H0$[W%3&Q&F`t$!3&G5m/n!4.<FM7$$\"3yn
-1/JLn_F`t$!3ECzH,M[j;FM7$$\"3=(eBL==ON'F`t$!3x()>[R%)=J;FM7$$\"3-FLbU
o'eB'F`t$!3=4QJq6e\"f\"FM7$$\"3g2+Hj<e\\^F`t$!3ZX(H@8wQi\"FM7$$\"3LY(>
DUI=.&F`t$!3)ochH')oUe\"FMF]hm7*7$$\"3u/56/a]i$)F`t$!3ACl7i#G!p;FM7$$
\"3g/eIu$Q&3\"*F`t$!3a'G#Q-oV(p\"FM7$$\"3uy+w^eba*)F`t$!3+R0HB&*4j;FM7
$$\"31Y+)*QSI'*)*F`t$!3$>iY,ln3i\"FM7$$\"3??VV;:KU(*F`t$!3gu[0r.`'e\"F
M7$$\"3(GN9#HLd+))F`t$!3o\"z)>WAwG;FM7$$\"3+F'om!3fY')F`t$!37Wq5l\\U%f
\"FMFajm7*7$$\"3o+ny4fl;7FM$!3?uOUcSrw;FM7$$\"3)*H0S1k$[G\"FM$!3[Y6uT/
$yo\"FM7$$\"316%of.:eE\"FM$!3#e/kx9)Rh;FM7$$\"3v/R)3K4$Q8FM$!3h[@Hj$H#
4;FM7$$\"3g&y^/&zG>8FM$!3%z/:$pqz#e\"FM7$$\"3!>HObm$zY7FM$!3PXpy`e'\\j
\"FM7$$\"3'H</^HsxA\"FM$!3\"\\%)4)fN`3;FMFe\\n7*7$$\"3`Y?uZ4l-;FM$!3UC
3s])*R%o\"FM7$$\"3#>!HR^hXg;FM$!35$oU&)erUn\"FM7$$\"3UOKyi;\"yj\"FM$!3
;X%=ZFz$e;FM7$$\"3qf+Hp&)R\"o\"FM$!39n&=*yNF'f\"FM7$$\"3)RR!o!3a(e;FM$
!3'*GV4l7Q!e\"FM7$$\"3qqN<ur;:;FM$!3?2U*3'p[U;FM7$$\"3=0Rc&oADf\"FM$!3
/p*pqk%fE;FMFi^n7*7$$\"3+QrFacB%*>FM$!3Uuz,Xc3#p\"FM7$$\"3&fp2C28x.#FM
$!3;'*oyU-wc;FM7$$\"3l$[?cYX9,#FM$!3MOP:/H/a;FM7$$\"3.pk6\\\")*)=?FM$!
3'z(e-(H+?e\"FM7$$\"3'pDHBaIE*>FM$!39=FReHGz:FM7$$\"3!=FL)ey<&)>FM$!3_
w0_lbK^;FM7$$\"3sfg/_-\"*e>FM$!3[;u)oA3'[;FMF]an7*7$$!3Yi&Grv#R!*>FM$!
3S4e\")\\(>iB\"FM7$$!3p![E2#3+B?FM$!3cGzC?6Cb7FM7$$!3/NJQ45z0?FM$!3mh)
pz,q(f7FM7$$!3P5Ja[@@=?FM$!3\"*oxxY.(pI\"FM7$$!3sk(*>PB+,?FM$!3B-(*\\W
#*\\68FM7$$!3=*yR!)>\"e))>FM$!3w%z\"p:*)Hk7FM7$$!3IVkp'Qr8(>FM$!3'ys8M
\"y#)o7FMFacn7*7$$!3?E4ROZqa;FM$!3ifH6Wb!RC\"FM7$$!3q2f$*fc6i;FM$!3Aw`
1+ZDx7FM7$$!3S3,xm*G&[;FM$!3?JifA'3'o7FM7$$!31Y#>H)e\"[i\"FM$!3(y:w+/s
eI\"FM7$$!3`YMv*=H7h\"FM$!3%G,2E'fA(H\"FM7$$!3))3VgtA%\\j\"FM$!3;'3F^a
i*f7FM7$$!3e4&Q/eb8i\"FM$!39TzlnkJ^7FMFeen7*7$$!3_WN2ZqU88FM$!3i4,TQ8f
^7FM7$$!3U7H7BLf*H\"FM$!37+bK(y:`H\"FM7$$!3qfY8[(H'*G\"FM$!3g#\\.(H(Hh
F\"FM7$$!3$p7veG4qB\"FM$!38Ra&eBcMI\"FM7$$!3(R(o)3rXqA\"FM$!3gJMBy,F%G
\"FM7$$!3u1k9thmz7FM$!31&[\"3sO%pD\"FM7$$!3+a\"e\")f-(p7FM$!3_x%fWhdxB
\"FMFign7*7$$!3YvTw\"*ofl'*F`t$!3%)fsqKrFf7FM7$$!3#R&\\(G5QVN*F`t$!3#4
IG?QC%48FM7$$!3=\"*ywMN$4H*F`t$!3]Y;HRLL#G\"FM7$$!3ALv5uN#za)F`t$!3Y7c
6MHs*H\"FM7$$!3Qp/+1!>X[)F`t$!3#y&*y8*=js7FM7$$!3MF3mm*GvA*F`t$!35#*\\
b'HU_D\"FM7$$!3[jPb)RCT;*F`t$!3nP$=QD^\"G7FMF]jn7*7$$!3W\\a*piE59'F`t$
!3#)4W+FH'pE\"FM7$$!3ohlH97P'p&F`t$!3;yP<%[!e>8FM7$$!3_j\\'z#y>pcF`t$!
3]#pg8X>sG\"FM7$$!3%HDh_(4l\"y%F`t$!33ym&[8sYH\"FM7$$!3ya'H*)exWv%F`t$
!3?#fV?56BE\"FM7$$!3DkLjTW-UcF`t$!3#ogZ&=%e[D\"FM7$$!34m<Ib5&[h&F`t$!3
;@Xt&Q(\\A7FMFa\\o7*7$$!3uo#Hknf0c#F`t$!3/g:I@([YF\"FM7$$!3s\\R\\lD.A?
F`t$!32K>w$4%yD8FM7$$!3(e\"y$4O!4J?F`t$!3yI1\"f1)y!H\"FM7$$!3CHC@i]Fr5
F`t$!3eN'y!QQI)G\"FM7$$!3Q&Hcw&GL!3\"F`t$!3GMtA5yI`7FM7$$!3H#o\"Qc\"[,
/#F`t$!3[H$f!Q?zb7FM7$$!3W[b#=&f?\\?F`t$!3>G!3-,'z?7FMFe^o7*7$$\"3'yOM
*fR!e2\"F`t$!3/5()f:XL#G\"FM7$$\"3=%)G`Vyno;F`t$!3ViFz5_.G8FM7$$\"3<`N
Jm))QB;F`t$!3#4YTH=RIH\"FM7$$\"3!)R*Q];/Ke#F`t$!3e&[\"yV!=1G\"FM7$$\"3
z3'>y=:z`#F`t$!3I%=If,AcC\"FM7$$\"3)=A%4*))*4y:F`t$!3if,4bJ/e7FM7$$\"3
)3*[(=\"4\"G`\"F`t$!3Le)Qs7ZIA\"FMFi`o7*7$$\"3'*fa4#Gk!oZF`t$!3Ege*)4.
-!H\"FM7$$\"3!*QRy7+wv`F`t$!3ZpiENQLE8FM7$$\"3IV\"*y`)RUH&F`t$!3e$=`C!
G(RH\"FM7$$\"3K`G\\1ny\"='F`t$!3mF_'>v9;F\"FM7$$\"3kc!)\\ZlE+hF`t$!3yT
@:>PDR7FM7$$\"3rZVz%p>F@&F`t$!3#z4S'p<hh7FM7$$\"3,^&*zN&*>J^F`t$!3D7q#
ot]#H7FMF]co7*7$$\"3&o+a+H@i^)F`t$!3C5I>/hq(H\"FM7$$\"3U9#fA%R@*4*F`t$
!3t_C=n*z1K\"FM7$$\"3;`*)[,EY\")*)F`t$!3K)zXW#*)e$H\"FM7$$\"366$\\@csW
s*F`t$!3/i)HE'RHh7FM7$$\"3$40z8A@ng*F`t$!3T2K*)>H?M7FM7$$\"3)Hp=2E6P')
)F`t$!3!R94<)y\\m7FM7$$\"3qJ%[*>*ffu)F`t$!3\\*[s*QoSR7FMFaeo7*7$$\"3!4
+\"Q)\\F?B\"FM$!3Yg,\\)*=R08FM7$$\"33re>jR!RG\"FM$!3*GJTlgt5J\"FM7$$\"
3])HT4r0&o7FM$!3M0$>*[v)=H\"FM7$$\"3EJ3?th7@8FM$!3G)Qvdnb'\\7FM7$$\"3n
ei%4#zs08FM$!3u!Q`\"='p/B\"FM7$$\"3!fs'oeu5`7FM$!3#yH(H\"\\,FF\"FM7$$
\"3K`@V1#4xB\"FM$!3G!HvOV:ND\"FMFego7*7$$\"3uYjLOD-=;FM$!3Y5ty#pxIJ\"F
M7$$\"3!GC)=3P_f;FM$!3[\\GM`Z^(H\"FM7$$\"3'Q7cxL-0k\"FM$!3Y/P(eno))G\"
FM7$$\"3?')pg@a@k;FM$!3.2=S\"*)*pO7FM7$$\"31n[<^S>X;FM$!3+iE$R\"Q0G7FM
7$$\"3r/SKn4[@;FM$!3WfXS)fA-G\"FM7$$\"3x&)=*offCg\"FM$!3S9a$4_w:F\"FMF
iio7*7$$\"3*zVrGC2'4?FM$!3ngW3([j2K\"FM7$$\"3gOI?H1yO?FM$!3aiqe2M+!G\"
FM7$$\"3(3P$fSh89?FM$!3)e**3`IKXG\"FM7$$\"3a&RL9+:<+#FM$!3j<\"4&4mUA7F
M7$$\"3#)HP#G^q!z>FM$!3'40Js]bpA\"FM7$$\"3e0P)>l\"\\\"*>FM$!3)*G4..71*
G\"FM7$$\"3))RSPjr%)o>FM$!31iGv+,f$H\"FMF]\\p7*7$$!3CiU`o6-v>FM$!3edH#
)=f(*[')F`t7$$!3/S6$RELR-#FM$!3e]4[]G%[y)F`t7$$!3PZ-TM.5.?FM$!3(=@^7>%
f-*)F`t7$$!3J%=EiH&RN?FM$!37*35EfmRZ*F`t7$$!3l\"H0nOiX,#FM$!3E\\.QLzr
\"f*F`t7$$!3;b$*)[SnA)>FM$!3;t9-KbM?!*F`t7$$!3%HYo`ZM9'>FM$!3LL<zso4Q
\"*F`tFa^p7*7$$!3)fi'zZJLR;FM$!3keWzhQ$es)F`t7$$!3gm09.\"[Im\"FM$!3IFa
l['y\\+*F`t7$$!3u?sz\"HQek\"FM$!3;1\\^P-)4**)F`t7$$!3L>BgI!**>k\"FM$!3
syRfDN)HY*F`t7$$!3ot*e#>#*yC;FM$!3edMX9^)*[%*F`t7$$!35vQX![G'G;FM$!37'
Quj#=)p(*)F`t7$$!3AH06p'=9h\"FM$!3)\\'QB:M)H'*)F`tFe`p7*7$$!3_W#z%ea0)
H\"FM$!3pffw/=p-))F`t7$$!3yrvKmd_+8FM$!3]omD@&*e&=*F`t7$$!3Es<;t!RpG\"
FM$!3KAve38>m!*F`t7$$!3?+#eNV#>a7FM$!3<!z'Q$[D)Q%*F`t7$$!3o+CRSdgS7FM$
!3)Rk<2FF%>$*F`t7$$!3'H(f**zBNt7FM$!3Cx$=f4$zY*)F`t7$$!3mt,$ool(f7FM$!
30J#\\K)[RF))F`tFibp7*7$$!3Nt6#e+\")=^*F`t$!3wgutZ(\\&z))F`t7$$!35W:#
\\`iOO*F`t$!3JvYGoanE$*F`t7$$!3m:!R]yESE*F`t$!3Mg!pWSF#G\"*F`t7$$!3>o#
Q40b(>()F`t$!3^B&))fY#\\,%*F`t7$$!3lQd0,$>,i)F`t$!3`3H<-W/.#*F`t7$$!3C
([c^.\"Rk\"*F`t$!3ZYMlS$z(H*)F`t7$$!3!)eRF&GbZ1*F`t$!3]Jy$oFJ8t)F`tF]e
p7*7$$!3KZC0T2J()fF`t$!3!='*32p2k&*)F`t7$$!3&=:Vjk&p0dF`t$!3sZ%R(*[O#G
%*F`t7$$!3*z3O#y5HUcF`t$!3A?&f^_)3x\"*F`t7$$!3!z)>4_C[`\\F`t$!3qy\"*Rt
W)4N*F`t7$$!3/C\\)R)y2!*[F`t$!3?^#>)3l$)*4*F`t7$$!3ED!H,^'))ybF`t$!3%Q
fz0cSf#*)F`t7$$!3Sh>-U>[:bF`t$!3Mm'**ff#zu')F`tFagp7*7$$!3imi[!zVoS#F`
t$!3(GY!oLcEL!*F`t7$$!3hR0a(*pNJ?F`t$!3u&)4i&es-\\*F`t7$$!3!4%*37h$=/?
F`t$!35.*e1nuF@*F`t7$$!3ljJ/Rl5V7F`t$!3yb(=c],tG*F`t7$$!3%\\c6F:Lf@\"F
`t$!3-sml!f.)4!*F`t7$$!3=Ut([A5q(>F`t$!3M>opbnFN*)F`t7$$!3uVdaQo$)\\>F
`t$!3eNZtS)yxl)F`tFeip7*7$$\"3%)pt(e%)>&H7F`t$!3$R'>lwN75\"*F`t7$$\"3G
%H'[6MNf;F`t$!3Q*GHfv$y7&*F`t7$$\"39GC/;cH];F`t$!3t1s'4%eGN#*F`t7$$\"3
Q0#3#)os8T#F`t$!3saskiNW5#*F`t7$$\"3'*QVw#*[J-CF`t$!3(4<&oZc%H$*)F`t7$
$\"3sh&)f?yBT;F`t$!3'H70g#zyd*)F`t7$$\"3d&pa^-!=K;F`t$!3?RI/6+H!o)F`tF
i[q7*7$$\"3_h%Q!o,y@\\F`t$!3)\\YB'>:)p=*F`t7$$\"3s[tt!eNkO&F`t$!3geVm+
+x&\\*F`t7$$\"3r<!=NgY6K&F`t$!3AKW3O?iW#*F`t7$$\"3P=@mH_&*4gF`t$!3`vY[
W1T?\"*F`t7$$\"3O(yUCDmY'fF`t$!3/[Z!*zEEp))F`t7$$\"3q'o)HEw&eF&F`t$!3s
/X]rSZ$**)F`t7$$\"3qb$z!\\'o0B&F`t$!3MyX#p5EBu)F`tF]^q7*7$$\"3)*3q*f<P
*p')F`t$!3/m\\fi%RQE*F`t7$$\"3ECE@5&*))*3*F`t$!3Y$>E)>8BR%*F`t7$$\"3nG
y@^$p$3!*F`t$!3fz0,cKyS#*F`t7$$\"3Ex&=`3TEb*F`t$!3@=58^F?<!*F`t7$$\"3c
!yBj#47r%*F`t$!3C.aJ(oa(=))F`t7$$\"33LIA#>\\o#*)F`t$!3ik\\>#>NB/*F`t7$
$\"3QO#GK.H`%))F`t$!3w]$z$Gr)Q%))F`tFa`q7*7$$\"37,`(p3*RZ7FM$!35nkc0up
S$*F`t7$$\"3=77**>:(HG\"FM$!3!Rz9MrnJM*F`t7$$\"3%f=9fQ'>r7FM$!3$)[cu+&
pPA*F`t7$$\"3wdx^DI%RI\"FM$!3w#G'e#))>3!*)F`t7$$\"3uJ2W\"*y;#H\"FM$!3c
Or\"*p;U\"y)F`t7$$\"3#*fr$=D@%f7FM$!3k-l2)GrV5*F`t7$$\"3!R8gx6YwC\"FM$
!3edtSvI(\\)*)F`tFebq7*7$$\"3&pkI\\7%RL;FM$!3;oz`[`b<%*F`t7$$\"3!Re$)
\\E\"fe;FM$!3(*f,V\"=zv?*F`t7$$\"3I6!HF,$>V;FM$!3%*R'*Gq2e$>*F`t7$$\"3
s7R#RFKqk\"FM$!3=p/&)Q?Er()F`t7$$\"38S$p;-M;j\"FM$!3/[*4xijsv)F`t7$$\"
3sQWZgZzF;FM$!3!)=\"\\\"fBez\"*F`t7$$\"38m)>#3lR7;FM$!3y)f3![Rel\"*F`t
Fidq7*7$$\"3VQdYJ)y\\-#FM$!3?p%4:H8W\\*F`t7$$\"3px$)*f=[e.#FM$!3j\"HsQ
slC.*F`t7$$\"3)*eic:o#o,#FM$!3#HbUY1<-:*F`t7$$\"3/A.v`=`%)>FM$!3YxN#*>
#H&G')F`t7$$\"3)G?=L[5b'>FM$!3kPQpg0GY()F`t7$$\"3#)RT8Xa!y*>FM$!3?9GT0
%ozE*F`t7$$\"3o??quSyy>FM$!3OuI=Y(>dQ*F`tF]gq7*7$$!3-i*R*z&\\'f>FM$!30
?y[RVvN\\F`t7$$!3%*)zNrql[-#FM$!3k:E[)\\us,&F`t7$$!3:gtVf'4/+#FM$!3?2Q
!G?)[2_F`t7$$!3Od#4RWyD0#FM$!3-)[UurH#yeF`t7$$!3e=3@'RA\"G?FM$!3czOw@M
WogF`t7$$!3;@*Q<h`f(>FM$!3k(*\\72>q(R&F`t7$$!3O#[SSc(\\^>FM$!35)=Y9h:z
e&F`tFaiq7*7$$!3xDB?f:'Ri\"FM$!36@$fCG7E,&F`t7$$!3_D_MY0)Rm\"FM$!3N#4d
mH5uB&F`t7$$!3ILV#ohZJk\"FM$!3[,v1\\U(eH&F`t7$$!3%GR&Gy@=f;FM$!3gxjU]m
CneF`t7$$!3h+Xw[#\\$Q;FM$!3&yyOGg5d#fF`t7$$!33TMI(o9Bi\"FM$!3i5zZ,#QVN
&F`t7$$!3k[Dyd<[,;FM$!3w>$))Q:-GT&F`tFe[r7*7$$!3KW\\))pQo#G\"FM$!3;A3V
D-Z*3&F`t7$$!3oIA`4#e9I\"FM$!3bL$e#p6-=aF`t7$$!3#[)))=)R[UG\"FM$!3k<,9
?`3r`F`t7$$!3[t7C\"ev8F\"FM$!32*=>#3')3VeF`t7$$!3%y#z*)pd;a7FM$!3Eu45f
F:'z&F`t7$$!3%*Qb%oeQqE\"FM$!3s,>-r%\\TK&F`t7$$!3I$>-bxG)\\7FM$!3!eo.>
i8sF&F`tFi]r7*7$$!3Cr\"y)>^;e$*F`t$!3ABBSo\"Gj;&F`t7$$!3EM\"op'p)HP*F`
t$!3OSjG;r5fbF`t7$$!3DT,JN+7P#*F`t$!3mb;-;97LaF`t7$$!3/-!px_'e\"*))F`t
$!3_B4#3fbd!eF`t7$$!3/456'f>dv)F`t$!3sPib!*)p(zcF`t7$$!38Z@l.JD,\"*F`t
$!3'4(pv:d82`F`t7$$!35aT*><'Ql*)F`t$!3E'G#\\:+:\"=&F`tF]`r7*7$$!3?X%4^
&[fLeF`t$!3GCQP6h=V_F`t7$$!3-U(*Qy+-:dF`t$!3w76uP\"o1m&F`t7$$!3f8s]GVQ
:cF`t$!3a:@rOD)>[&F`t7$$!3UBF#*GRJD^F`t$!3sy:B)fZ_v&F`t7$$!3(Q>S!z\"yc
-&F`t$!3Q!e-s*>cwbF`t7$$!3:&oC'y&[d^&F`t$!3L=JoNpH.`F`t7$$!3sc@uGG6;aF
`t$!36@TlM8hC^F`tFabr7*7$$!3]kKa/z7`AF`t$!3MD`MaS/?`F`t7$$!3]HreH9oS?F
`t$!3z]EiLUqAdF`t7$$!3%f1![hoFx>F`t$!3J(\\6Aoow^&F`t7$$!3M)*Q(e,Q\\T\"
F`t$!3!e:^/jk:p&F`t7$$!3[MowZM`^8F`t$!3?,+/z!Hl[&F`t7$$!3N-IP$HsQ\">F`
t$!3$QM+38LEJ&F`t7$$!3yQfEDxY]=F`t$!3N!>*Qzvf2^F`tFedr7*7$$\"3'>P?=tNK
Q\"F`t$!3SEoJ(*>!pR&F`t7$$\"37/(R%z*G+l\"F`t$!3Ua4$RS:_u&F`t7$$\"3#GIr
dO-sn\"F`t$!3%4!)>D&)z,a&F`t7$$\"3pquP67aRAF`t$!3ta'zuo1Zh&F`t7$$\"3Sp
!4xf9nE#F`t$!39+&og8r'4aF`t7$$\"3a,H5_dP/<F`t$!3YZ'36IW^L&F`t7$$\"3E+X
VQ\"\\:t\"F`t$!3(R\\(p\\(3,8&F`tFifr7*7$$\"3?k9)R0'\\v]F`t$!3YF$)GS*fP
Z&F`t7$$\"3mf2p[66d`F`t$!3mBgm[;?GdF`t7$$\"3C$*oC`L0[`F`t$!3WEqjZg^\\b
F`t7$$\"3T$QJGvB\"QeF`t$!3avqJpPnCbF`t7$$\"34=vQdf1HeF`t$!3Ax!)Go\"))f
M&F`t7$$\"3\"o-.yb&**Q`F`t$!3AH!3mWI3P&F`t7$$\"3Rg\"fBwP*H`F`t$!3)>.zb
%[9#>&F`tF]ir7*7$$\"346+%>1`O#))F`t$!3_G)fK)yh]bF`t7$$\"3?Ng;y]c!3*F`t
$!3]ey#y'HmrcF`t7$$\"33.n%45w_.*F`t$!3!Q<jvExca&F`t7$$\"3GUy[3'43Q*F`t
$!36<M'f(eY@aF`t7$$\"3G6&o7j?bL*F`t$!3_L()pv,[&H&F`t7$$\"33stsBr)**)*)
F`t$!36*[)Hn:p>aF`t7$$\"32T!3l9)pW*)F`t$!3S/Q.neq$H&F`tFa[s7*7$$\"3K,'
pbnqFE\"FM$!3eH8BEeZFcF`t7$$\"3/`lyw!R?G\"FM$!3'*ekTh$*fvbF`t7$$\"3Qtq
)31()QF\"FM$!3/V#)H7NmGbF`t7$$\"3E%oMy()fnG\"FM$!3m\"o=u+$30`F`t7$$\"3
#[?N>'ygy7FM$!3'oY+$er9e_F`t7$$\"3#Rf()\\/NdE\"FM$!37F+=jws\"[&F`t7$$
\"3E9\")3HIed7FM$!3L7=19=zMaF`tFe]s7*7$$\"3;Z\\_8dw[;FM$!3kIG?pPL/dF`t
7$$\"3)\\#*y<#)ewl\"FM$!3,D=VH3,SaF`t7$$\"3u)*=q(o$)ek\"FM$!39MA%=yu%)
\\&F`t7$$\"3AR3CE\"\\)H;FM$!33oGoj^_v^F`t7$$\"3?8Q;#*R2=;FM$!3LyK4;\"*
)RB&F`t7$$\"3ts[i`&3Tj\"FM$!3SWEDM(Qpb&F`t7$$\"3rYya>MLA;FM$!3``Im'o-a
h&F`tFi_s7*7$$\"3UQ+1?/NS?FM$!3qJV<7<>\"y&F`t7$$\"3y=PzUd\"\\.#FM$!3oc
R(=P(*[E&F`t7$$\"3?Y\"R0\\<&>?FM$!37Z^>w56baF`t7$$\"3a[s11([t'>FM$!3Pw
fvWBzK]F`t7$$\"3'fn7QX]>&>FM$!3#z;x!\\g+B_F`t7$$\"3htXGQ#>T+#FM$!3oQj^
!yC`k&F`t7$$\"3!3+Ig)4s))>FM$!38Hv$[[Qb$eF`tF]bs7*7$$!3\"=mX8*zFW>FM$!
3D#o_,wKDA\"F`t7$$!3&yXS.:)zD?FM$!3%3G%[Yhq\\7F`t7$$!3[sWY%)*=x*>FM$!3
T,kN9AQ7:F`t7$$!3'3L#f\"fh(p?FM$!3I))[FUG\\#G#F`t7$$!3&fM;dU#oT?FM$!3u
3q95*o^a#F`t7$$!3O([)e=)R'p>FM$!39A&GAGe]x\"F`t7$$!3+-Dr_1cT>FM$!3eU15
]VtP?F`tFads7*7$$!3bD!31(**e3;FM$!3I$=CJq!R*H\"F`t7$$!3k%))\\&*)H\"\\m
\"FM$!3%oveY%>%)p9F`t7$$!3'eW^=%pXS;FM$!3(f4?1Eo2g\"F`t7$$!3Km%ofKljn
\"FM$!3=y(e_x4:F#F`t7$$!3aF+Fy#4>l\"FM$!3.<,A\"4OCS#F`t7$$!322I:%*3+;;
FM$!36N9ewXpJ<F`t7$$!3GoXXY[a\"f\"FM$!3'RxUD*3ii=F`tFefs7*7$$!35W1H\"G
7tE\"FM$!3O%o&4Y'[iP\"F`t7$$!3f*)ot_1R-8FM$!3K)**fs\"GX];F`t7$$!3Q(*f@
Bxb\"G\"FM$!377FpJ$zfn\"F`t7$$!3)pMC*G(e&)G\"FM$!3k*e^It^tC#F`t7$$!3wa
MS*zDxE\"FM$!3W.V[Z#yGF#F`t7$$!3%\\5&p$zC2E\"FM$!3@Ea7Ye],<F`t7$$!3r7U
<k=*)R7FM$!3-S\"e0OKqs\"F`tFihs7*7$$!37p^$RB\\W?*F`t$!3U&=n!*e1JX\"F`t
7$$!3WCZ,*R6BQ*F`t$!370!)Gk(Q:z\"F`t7$$!3tl7e&G8-@*F`t$!3V]UdFa,Q<F`t7
$$!3-P(*f/!=M1*F`t$!3(HK`cr=+@#F`t7$$!3Iyi;\"*)>8*))F`t$!3+o&R*y`\\c@F
`t7$$!3-2y9s^6Q!*F`t$!3Y&\\g34#\\%o\"F`t7$$!3U\\Vreq,m))F`t$!3[Sn9a(o4
j\"F`tF][t7*7$$!33Vk;p*y)zcF`t$!3\\'oQ?`k*H:F`t7$$!3>KjV5XMCdF`t$!3!yx
Udy*4$*=F`t7$$!31Q$y(yvZ)e&F`t$!3K5ZE[l(oy\"F`t7$$!3EdMv0a9(H&F`t$!3=y
R1B2^f@F`t7$$!3Eka4u%y7;&F`t$!3o5fe&[(G`?F`t7$$!3/X.7Z1h_aF`t$!3#Gk'y5
Ll!o\"F`t7$$!3._BY:Pu;`F`t$!3Kv&3L2IWd\"F`tFa]t7*7$$!3Qi-g=?T*4#F`t$!3
b(=5]ZAog\"F`t7$$!3S>Pjhe+]?F`t$!3%eJC;)e8b>F`t7$$!3'4>^<6q.&>F`t$!33#
4kPpiD#=F`t7$$!3uKYq#\\pne\"F`t$!3CbNGbx#e4#F`t7$$!3K/@#GuLr[\"F`t$!3]
JLUnXDj>F`t7$$!3_i'o=OM2&=F`t$!3KoQ!f]*)**o\"F`t7$$!35Mh)>h)4^<F`t$!3c
WO/=jTd:F`tFe_t7*7$$\"33uLw<;&p`\"F`t$!3g)o\")zT!o$o\"F`t7$$\"3A9JRZXq
S;F`t$!3[>E$>0Zw(>F`t7$$\"3!y<+b64Tq\"F`t$!3q&RsS'Q2X=F`t7$$\"3IOnaM(4
x1#F`t$!3>a?J7)p*=?F`t7$$\"3f*z`EI968#F`t$!3UI=XCmR')=F`t7$$\"3OTsg$o8
vw\"F`t$!3&><7in+Dr\"F`t7$$\"3&\\I9<D=4$=F`t$!3Y[>N)[F*z:F`tFiat7*7$$
\"3JmW#*R>@H_F`t$!3m*=`4OQ0w\"F`t7$$\"3]pTk;nyZ`F`t$!3s)onmHL1'>F`t7$$
\"3mnd(H5g\\P&F`t$!3[@'*=f+Ta=F`t7$$\"3a\\1+wAHmcF`t$!3+v%\\T*o$*G>F`t
7$$\"3sZALicY$p&F`t$!3]29ncOrA=F`t7$$\"3#pO2$*[L@S&F`t$!3)Rb6<#o=[<F`t
7$$\"33l*Qc(oIHaF`t$!3['[LUej>k\"F`tF]dt7*7$$\"3?8I)y%*ot(*)F`t$!3s!pC
RI'RP=F`t7$$\"3/X%>hkS72*F`t$!3bB&Heh%4/>F`t7$$\"3gybn]G=i!*F`t$!3')od
6z7d]=F`t7$$\"3K2rlJ\"y*3#*F`t$!3o<ez+!Hd#=F`t7$$\"3+UK@O.#**>*F`t$!3q
i?3kc?s<F`t7$$\"3=7<Bb]7`!*F`t$!3'Q,-C%z/(z\"F`t7$$\"3wXyyfs1W!*F`t$!3
=f#)o0Y_V<F`tFaft7*7$$\"3a,R;kA9y7FM$!3y\">'*oCaU\">F`t7$$\"39%*=eLm5
\"G\"FM$!3+C\"=%45.3=F`t7$$\"3/h*fetxlF\"FM$!34Q3&Q_dN$=F`t7$$\"3+6;:I
ndp7FM$!3B#3^A8Y$4<F`t7$$\"3mx'HC$y/l7FM$!3/'z$oYE([t\"F`t7$$\"3%z-Q\"
Q)[?F\"FM$!3=_NGQS3f=F`t7$$\"3%[4;/%*>vE\"FM$!3Emir_0h%)=F`tFeht7*7$$
\"3OZ#>@IPTm\"FM$!3#Gpn)*=76*>F`t7$$\"3'eEu&yjsc;FM$!31!\\LuZUCn\"F`t7
$$\"3U'yuEOu&[;FM$!3>H[R$zoL!=F`t7$$\"3slxbyfm7;FM$!3ko_^)G)yz:F`t7$$
\"3F'GeE'R^/;FM$!3]2mZ/Yr5<F`t7$$\"3u1`xYBUS;FM$!3LohN4^HM>F`t7$$\"32F
e(3LqAj\"FM$!3Y2vJD9Al?F`tFijt7*7$$\"3')QVl3?sb?FM$!3!R>RG8qz1#F`t7$$
\"3))f!*e*H$)R.#FM$!3W@c()>!Ht\\\"F`t7$$\"3'Q.7b;3A-#FM$!3;Uxu(30+w\"F
`t7$$\"3/vTQeb;]>FM$!3mw$)epa0P9F`t7$$\"3.\\rIC/RQ>FM$!3Q(\\gu`J(*p\"F
`t7$$\"3%y+N9.L/,#FM$!3*G')>c:\"oA?F`t7$$\"3g\")zN(*yl)*>FM$!3i$)>\\Bs
N&G#F`tF]]u7*7$$!3gh8v-k!*G>FM$\"3EbC=>))o!\\#F`t7$$!3v;^a$fIn-#FM$\"3
r`S^0A'y^#F`t7$$!3/&e\"\\4$G]*>FM$\"3c.54uPs#=#F`t7$$!3O/aFRZ%p3#FM$\"
3'>r#*G.WKJ\"F`t7$$!3Ws=AbCCb?FM$\"3C:mp9g0\"y*Fhy7$$!3O`!Qa-EL'>FM$\"
3Q`zmU`eZ=F`t7$$!3U@XQTPiJ>FM$\"3%H!\\C6pW7:F`tFa_u7*7$$!3MDP,#Q=Kf\"F
M$\"3@a4@w3$QT#F`t7$$!3aVXvKa%em\"FM$\"37y&RtSExH#F`t7$$!3Ue&yoEmxj\"F
M$\"3C4t#ysPV4#F`t7$$!3!)R:lt%[Np\"FM$\"34A)3**4FUK\"F`t7$$!3Yabx2$pam
\"FM$\"3P`lR?%Q37\"F`t7$$!31tD+,ro4;FM$\"3SS]J[!\\4*=F`t7$$!3q(eE^$zg
\"e\"FM$\"3GrF!)o.c(o\"F`tFeau7*7$$!3!RM'p#pS>D\"FM$\"3:`%RK$H(pL#F`t7
$$!3r[:%f4BLI\"FM$\"3jO$QZ`:r6#F`t7$$!3#*4JC[q')y7FM$\"3$GpanlE\">?F`t
7$$!3Z?ugw=u08FM$\"3i5g6U^Q[8F`t7$$!3o\")*3*GeG\"G\"FM$\"35nB8kiR]7F`t
7$$!39rYa+5Ta7FM$\"3I\\5xyx8@>F`t7$$!38Ki%G&\\&*H7FM$\"3\\0uy+*[J#=F`t
Ficu7*7$$!3+n@*zML20*F`t$\"3#=&zE!*\\6gAF`t7$$!3]881Jej\"R*F`t$\"3GH.r
(eHg(>F`t7$$!3K\"R_e`1L=*F`t$\"3aaJ(3c!4d>F`t7$$!3'3ZI9[\\_B*F`t$\"3ex
U^f\"=dQ\"F`t7$$!3o[:A'=?p-*F`t$\"3#G5xE8znO\"F`t7$$!3-oMkSs(\\(*)F`t$
\"3yzf.M::Q>F`t7$$!3uWXVXzkm()F`t$\"3w/))>2D@>>F`tF]fu7*7$$!3'4WBK3jh_
&F`t$\"3w]kHZqD$=#F`t7$$!3D@H[U*oOt&F`t$\"3'obbicoW(=F`t7$$!3kj%\\!H3d
hbF`t$\"3k%p#=S%H#3>F`t7$$!3C#>%e#)o(*oaF`t$\"3PAO5_hAO9F`t7$$!3_L2:p(
yoH&F`t$\"39g2.Eq)*p9F`t7$$!3%\\+;crs%*Q&F`t$\"3UK)4TJ!*>%>F`t7$$!3MZD
=-YP<_F`t$\"3#*pp.)=^d(>F`tFahu7*7$$!3GgslKhpX>F`t$\"3)*\\\\K/\"*R1@F`
t7$$!3G4.o$HI$f?F`t$\"3$)=SPqCV7=F`t7$$!3*fJA?OjM#>F`t$\"3)GJ$o%HVD(=F
`t7$$!3Wn``p4ge<F`t$\"3-XS))>\"4**\\\"F`t7$$!3'QPxy.MFi\"F`t$\"31RL>W*
>+c\"F`t7$$!3qAVOIkf(y\"F`t$\"3#pg#**=TlK>F`t7$$!37Hjq)\\H<l\"F`t$\"3%
4!>IV\\w#*>F`tFeju7*7$$\"3?wjq.vm!p\"F`t$\"3#*[MNh6aH?F`t7$$\"3LClM:,Q
J;F`t$\"3?:d1+8#**y\"F`t7$$\"3/`!H_'e,J<F`t$\"3C4]PC@.]=F`t7$$\"3g,grd
#ye*=F`t$\"33Yb&G1nnd\"F`t7$$\"3-I&)f2S^&*>F`t$\"37S[;()y(oj\"F`t7$$\"
3[\"e6^h^1$=F`t$\"3H.Vo[H95>F`t7$$\"3\"*4T*\\O(GI>F`t$\"31(f$*Hx`-(>F`
tFi\\v7*7$$\"3Uou'e#y#HQ&F`t$\"3'y%>Q=Ko_>F`t7$$\"3Kzvf%Gi%Q`F`t$\"3(f
kI`0Np!=F`t7$$\"3<VYq_o'=S&F`t$\"3u$yd#HfpS=F`t7$$\"3e9*p\"*zgW\\&F`t$
\"3ED\"=5)**zm;F`t7$$\"3WypFn`'yb&F`t$\"30j_%\\&3c+<F`t7$$\"3-2<\"3Ur_
Y&F`t$\"3C@\\=.oXu=F`t7$$\"3xp(=*))fnGbF`t$\"3.f?6xw@3>F`tF]_v7*7$$\"3
L:g#Q$[3J\"*F`t$\"3!oW5aFDe(=F`t7$$\"3'[&G29i\">1*F`t$\"376)ohttM'=F`t
7$$\"37aWS+'*3*3*F`t$\"3QO;L4Z`W=F`t7$$\"3Ztj#[lYr.*F`t$\"3e#yrV(y+q<F
`t7$$\"3krz:T+Kk!*F`t$\"3%ygMv%)o5v\"F`t7$$\"3H_gt')HE;\"*F`t$\"3OhW\\
#o&fD=F`t7$$\"3X]w1tjVV\"*F`t$\"3M'Gdclcm!=F`tFaav7*7$$\"3u,#eF&Q^$H\"
FM$\"3uX*QCLn*)z\"F`t7$$\"3-NsP!>u,G\"FM$\"3o5-eUt`f>F`t7$$\"3[[G$3To#
z7FM$\"3'oc'fk%[:'=F`t7$$\"3]P&oCe$R_7FM$\"3K=l\"Hu!R')=F`t7$$\"3u]T#H
!y[^7FM$\"3AuG$\\'=S)y\"F`t7$$\"3'>Y)GJEOy7FM$\"31BHh'efNw\"F`t7$$\"3?
vSu^oXx7FM$\"3Ez#H'32dl;F`tFecv7*7$$\"3eZNr!*)3&z;FM$\"3oWuY*Q4@s\"F`t
7$$\"3'pgp`$Rzb;FM$\"3)[%[cue7&4#F`t7$$\"3'QnZw.l7l\"FM$\"3wvD0&>P<*=F
`t7$$\"3W#pu3$G[&f\"FM$\"3!>L_me[f,#F`t7$$\"37fF:LR&4f\"FM$\"3wi+92*fD
\"=F`t7$$\"3wSd#*RhtY;FM$\"3!pISb^[$)o\"F`t7$$\"3l2Q?Us?U;FM$\"31Q!Gg$
)f\\[\"F`tFiev7*7$$\"3%)Q'[sf$4r?FM$\"3iVf\\Y9DX;F`t7$$\"3`+WQc30L?FM$
\"3]8F7K$R-F#F`t7$$\"33@\\[S))*[-#FM$\"3yi'*p+45N>F`t7$$\"3b,6q5C)H$>F
M$\"3iB#zbS\"oe@F`t7$$\"35A;![RI[#>FM$\"3<th:uHaB=F`t7$$\"3jTaeCou;?FM
$\"3M7mFpC'**f\"F`t7$$\"3uhfo3[f3?FM$\"3!>c`y.C[E\"F`tF]hv7*7$$!3Rhq:9
[`8>FM$\"3_#f<&)R5R?'F`t7$$!3mv(\\n.jw-#FM$\"35)Q7vbIaG'F`t7$$!3g(p=Xj
PB*>FM$\"3%zSQDwHy(eF`t7$$!3'yZep)y7/@FM$\"3^7.134)*3\\F`t7$$!3!)*RFZ[
-)o?FM$\"3NKj38,Q,XF`t7$$!3M>wGKA,d>FM$\"3yFWcn*G-Z&F`t7$$!31Tl0Ioo@>F
M$\"3s[/fs\"GE1&F`tFajv7*7$$!39D%>MzYyd\"FM$\"3Y\"4YbX_q7'F`t7$$!3o-#f
f(yxm;FM$\"3]7zLfZHlgF`t7$$!3wqc!>fv]j\"FM$\"3m8ZF;PW*y&F`t7$$!3K8YL@;
t5<FM$\"3\"HUw](R'*>\\F`t7$$!3Q\"3\"GP$H!z;FM$\"31CK,KH6WYF`t7$$!30R@&
yItLg\"FM$\"3#f^6Kn#f8bF`t7$$!3M2')zB5nr:FM$\"31<$[,jTxB&F`tFe\\w7*7$$
!3oV?5/\"plB\"FM$\"3S!fuD^%>]gF`t7$$!3i2i9RbD/8FM$\"3Irmt')Qo%)eF`t7$$
!3EA-Ftj<w7FM$\"3^(4-_kKUr&F`t7$$!3(R\\!HC]#HK\"FM$\"3X6OG<?7W\\F`t7$$
!3g3XTee%[H\"FM$\"3kP!\\dxqOx%F`t7$$!39PUR2s4[7FM$\"3\"[_nOS\"yVbF`t7$
$!3x^#=:/=+A\"FM$\"3+^H8i,Lt`F`tFi^w7*7$$!3)[;\\?Y<q*))F`t$\"3M*3.'plL
tfF`t7$$!3n.z5j-'4S*F`t$\"3]k'3(RzfVdF`t7$$!3!e^Bhy*Rc\"*F`t$\"3[f0K\\
l>_cF`t7$$!3$e?h#e432%*F`t$\"37y=oM]X\")\\F`t7$$!3'z\"oF\"[?D;*F`t$\"3
5tPHWO0!*[F`t7$$!3#z7R\"4$R=\"*)F`t$\"3YaC$*e^zgbF`t7$$!3/SZ:K)ysm)F`t
$\"3c]VaoPRpaF`tF]aw7*7$$!3%)Q/G(>ZCP&F`t$\"3G)eJmiyk*eF`t7$$!3U6&HXP$
*Hu&F`t$\"33#*QD=p.UcF`t7$$!37)e?$zSmMbF`t$\"3f*4I'GaL.cF`t7$$!33E\\Tf
$33k&F`t$\"3OA7FFI'>.&F`t7$$!3\"R+1U1zCV&F`t$\"3UIukP:E$*\\F`t7$$!3%fm
6TyMjK&F`t$\"352j+RRjkbF`t7$$!3lUF!*)[0!=^F`t$\"3r:DQ\\C$f_&F`tFacw7*7
$$!39eUrY-)>z\"F`t$\"3A(3gOo?'>eF`t7$$!3=**osDZlo?F`t$\"31aBPA3+!e&F`t
7$$!3-TMH7mb'*=F`t$\"3#yrIJG\\wc&F`t7$$!3%=5mjWK/$>F`t$\"3GX;0&*fk&4&F
`t7$$!3oVE$HLM$e<F`t$\"3;5+\"eX%H$3&F`t7$$!3f#)*f))\\eWs\"F`t$\"3g\"3*
)Qu(HbbF`t7$$!3WClU&QgBb\"F`t$\"3ZYuk/i%Ha&F`tFeew7*7$$\"3Jy$\\'*Q$QW=
F`t$\"3<'e)oSFwUdF`t7$$\"3WM**H$ob?i\"F`t$\"3K\\S1_'*[dbF`t7$$\"3+Gz&
\\hAzv\"F`t$\"3?9C#G6Q^a&F`t7$$\"3#pE&)3yYSs\"F`t$\"3MYJ-QR]s^F`t7$$\"
3[gKa7P\"*f=F`t$\"3A6:y)R_,;&F`t7$$\"3I@fhY&*y$*=F`t$\"3(zx!etlyKbF`t7
$$\"3g9RFyklH?F`t$\"3%G9RV.N/_&F`tFigw7*7$$\"3bq/\"=rVm`&F`t$\"35&3<xz
/fm&F`t7$$\"3:*)4b_y8H`F`t$\"33!)*GtS.Xd&F`t7$$\"3f<NV-OxGaF`t$\"3q)=0
x\">!e`&F`t7$$\"3iz\"RBKHEK&F`t$\"3_Dd=co`i_F`t7$$\"3<4<As]EAaF`t$\"3:
M>cm`$QA&F`t7$$\"3-YgJ_$4%GbF`t$\"3?'R\"3G/5(\\&F`t7$$\"3dv&)>-^/GcF`t
$\"3s.wXQ*)ReaF`tF]jw7*7$$\"3W<!p(>2![G*F`t$\"31%eXZ&o/*e&F`t7$$\"3qki
-#y\"f_!*F`t$\"3CXr;)3U5j&F`t7$$\"3aGL8]j*f6*F`t$\"3LT!zxpS'RbF`t7$$\"
3]Qc*z<:`'))F`t$\"3'GQR&\\Zul`F`t7$$\"3O-F5Y(>(G*)F`t$\"3%*y7:fLMu_F`t
7$$\"3S#RS#=4Sz\"*F`t$\"3KO4R2$R#[aF`t7$$\"3CcuM'[0GC*F`t$\"3IJG+<z$oN
&F`tFa\\x7*7$$\"3'>]_8W&))38FM$\"3*H3u<\"*)=7bF`t7$$\"35wD<Z<Cz7FM$\"3
!fayXp0rs&F`t7$$\"3#ft0e3f>G\"FM$\"35sR/`WlcbF`t7$$\"3+kayM/@N7FM$\"3I
=T3=w7#[&F`t7$$\"3\"Qi=MxFzB\"FM$\"3hX&\\lPw;J&F`t7$$\"3u&*)QWUwYG\"FM
$\"3G)R4:@.iQ&F`t7$$\"3yb?2jPR(G\"FM$\"3\\C[(*p>v:_F`tFe^x7*7$$\"3yZyI
z/)[p\"FM$\"3$>e-)o4LNaF`t7$$\"3#y%\\;#\\h[l\"FM$\"3%)zJcEUpieF`t7$$\"
3Ih0i7d&Rl\"FM$\"3+\")**\\$=Voe&F`t7$$\"3'*=;>$o*Hy:FM$\"3*=$*>=Y&o6cF
`t7$$\"3?Ksk.RRx:FM$\"39Mnv=W$eL&F`t7$$\"3wuh2L*\\Il\"FM$\"39#yO/9#*4J
&F`t7$$\"3+)yJN:W@l\"FM$\"3H$ett4T^.&F`tFi`x7*7$$\"3GRH%e=lk3#FM$\"3)3
3Je-t%e`F`t7$$\"32U(zJT=@.#FM$\"3=[57%o2y.'F`t7$$\"3u3yX:&*eF?FM$\"3-o
q9*)o?IcF`t7$$\"3FG!=IE*z:>FM$\"3sCou!G=Wv&F`t7$$\"3&\\4'Hl.F6>FM$\"3W
VGx&[<oM&F`t7$$\"3(e(et<11B?FM$\"3'y3tT41EA&F`t7$$\"3aUR,?<`=?FM$\"392
\"*>*H0]\"[F`tF]cx7*7$$!3=hFcDK;)*=FM$\"3/IF&y(>8<**F`t7$$!3,NW&*zafG?
FM$\"3Us5&4*)*H05FM7$$!3%*4eafpk*)>FM$\"3u8e)4vNHd*F`t7$$!3N^:kM5J@@FM
$\"308zA$y<Z])F`t7$$!3GEHB9DO#3#FM$\"3h-IqCYlC!)F`t7$$!3K&=P\"R%)p]>FM
$\"3G.4Y#fsG4*F`t7$$!3[g&G(=*\\<\">FM$\"3'R*f$RV4Gh)F`tFaex7*7$$!3#\\7
D[?vCc\"FM$\"3**G7)[.u-%)*F`t7$$!3ehQ;>.rn;FM$\"3YZiL6J'G$)*F`t7$$!3K$
yKp\"\\QK;FM$\"3W>@s/(\\X[*F`t7$$!3f'o<!pZ\"zs\"FM$\"3YBSC]3q:&)F`t7$$
!3_3mym$*e#p\"FM$\"3K%*)HOW(Qn\")F`t7$$!3/0<q9&fqf\"FM$\"3K!*z5)HOi8*F
`t7$$!3wE1Z7Tth:FM$\"3GiQ\\\"*G#zy)F`tFegx7*7$$!3ZVx]:v>@7FM$\"3#zs4>4
;Mw*F`t7$$!3`m3N#)z=08FM$\"3E1]tQAD_'*F`t7$$!3#[L(H)p&[t7FM$\"3H.&\\Oj
Q$4%*F`t7$$!3YnN(><3,M\"FM$\"3*>@^C*)e)R&)F`t7$$!3aN+#z)eS38FM$\"3!zql
tGXpH)F`t7$$!37.QC9MyT7FM$\"3A**RcG]Um\"*F`t7$$!3>r->I6357FM$\"3C'\\yM
U6N#*)F`tFiix7*7$$!3xih5w:IV()F`t$\"3)oAQ*[\"elo*F`t7$$!3%Q\\a^p%G5%*F
`t$\"3X**pq\"Hm6^*F`t7$$!3QTYROI\\H\"*F`t$\"3;kzwPDIZ$*F`t7$$!3yS>4NC
\"*y&*F`t$\"3my%\\)4>>x&)F`t7$$!3A(3Kjx?\")H*F`t$\"3OV/\"f:GLT)F`t7$$!
3#yyMwP,([))F`t$\"3)*H*GQyQM=*F`t7$$!3ON\\()=(4zc)F`t$\"3z&*)*))H]d>!*
F`tF]\\y7*7$$!3tOuL68t=_F`t$\"3\"esmf?+(4'*F`t7$$!3g,hd1yJ_dF`t$\"3/FA
Dq_g4%*F`t7$$!3r8<fHtv2bF`t$\"3E/v2<9W)H*F`t7$$!30hcCO)RE\"eF`t$\"3XB)
QC!**pF')F`t7$$!3=t7Ef$z!obF`t$\"3o+TE\\g`;&)F`t7$$!3%eK2E&o>j_F`t$\"3
g#y-Rcxs=*F`t7$$!3'z$Hivjj=]F`t$\"3%41G2r8h2*F`tFa^y7*7$$!3/c7xgVEQ;F`
t$\"3vC_*HEUG`*F`t7$$!33*[tx:zz2#F`t$\"3!zoqV<pvM*F`t7$$!31mXci)\\'p=F
`t$\"3]A\"y:FbFE*F`t7$$!3`Oo>BRE-@F`t$\"3OY#>-(GQ\"p)F`t7$$!3A8z)ziMR*
=F`t$\"3()zmUn*olg)F`t7$$!3wUcNn0Kh;F`t$\"35dbyo8%z<*F`t7$$!3u>n9s7*HX
\"F`t$\"3q\"*H*fYFJ4*F`tFe`y7*7$$\"3U!Q#fv#*4)*>F`t$\"3qBP-?V)fX*F`t7$
$\"3#[M`7DJFh\"F`t$\"3G%QiS+e]K*F`t7$$\"3)H!ook$H[y\"F`t$\"3))=)p75W-C
*F`t7$$\"3_KX0/`@_:F`t$\"3WZ2>83Co()F`t7$$\"3m!*z[<MJC<F`t$\"3#4=)R5pU
$o)F`t7$$\"39h-7yu#p&>F`t$\"3[`sZ)>Ia:*F`t7$$\"3H>Pb\"fD!H@F`t$\"33)o%
o&H;12*F`tFiby7*7$$\"3msMv(ff.p&F`t$\"3iAA0xj7z$*F`t7$$\"34+W]?M\")>`F
`t$\"3/:tKf<2U$*F`t7$$\"37$Ri@N!obaF`t$\"3Q$f_h!z!4B*F`t7$$\"3yX%3b%yz
]^F`t$\"3iELNJPFe))F`t7$$\"3yQk;xZm'G&F`t$\"3'Qgy\"y)4ru)F`t7$$\"37'Q?
QGZ:f&F`t$\"3sry(H0W(>\"*F`t7$$\"3D!Qya@9us&F`t$\"31]J!)*>!e3!*F`tF]ey
7*7$$\"3c>?r0m^Q%*F`t$\"3d@23M%oAI*F`t7$$\"3jv'z*\\tEV!*F`t$\"3=![l,W5
')R*F`t7$$\"31/A')*4.H9*F`t$\"3,YkA'oYZB*F`t7$$\"3a.\\;,P[$p)F`t$\"3%R
)pqC;[h*)F`t7$$\"33Lu/^%>Jz)F`t$\"3k[zwqyh(z)F`t7$$\"3]KZu\\)QDC*F`t$
\"3#=T(GKH)32*F`t7$$\"3$4EF'*fu@M*F`t$\"3kx$[$y\">q!*)F`tFagy7*7$$\"3<
-o%*HqDC8FM$\"3^?#46\\5aA*F`t7$$\"3?<z'RI4$y7FM$\"3uzodYSn%\\*F`t7$$\"
3eB'y2w\\YG\"FM$\"3yw8\\T/w^#*F`t7$$\"3]!R-rGF!=7FM$\"3S><D$\\ky2*F`t7
$$\"3)o48RunVA\"FM$\"3K:i;))3&\\$))F`t7$$\"3uH$*e<-*4H\"FM$\"3!Q(eSOo%
)3!*F`t7$$\"37O+Su1L(H\"FM$\"3sp.KJK$fw)F`tFeiy7*7$$\"3,[@!z1_-r\"FM$
\"3Y>x8[Db[\"*F`t7$$\"3#*)Gg*[!HRl\"FM$\"3![^h&yDEI'*F`t7$$\"3u[Mf(QYm
l\"FM$\"3m&QZ><\\>G*F`t7$$\"3YX&3b`;6c\"FM$\"3*H`()pLAu?*F`t7$$\"3G0<9
uQ$Qc\"FM$\"3'QSt.$*3\"f))F`t7$$\"3y3mAEPOf;FM$\"3ldKLldjL*)F`t7$$\"3e
o(f[1\"3i;FM$\"3_G\">(eBK&e)F`tFi[z7*7$$\"3ERsVun$=5#FM$\"3S=i;0Ypr!*F
`t7$$\"3s#3v*pf=J?FM$\"38$Q>h.w`!)*F`t7$$\"3'fpI/>!GI?FM$\"3qsWfxGJD$*
F`t7$$\"3+b\\L:hh)*=FM$\"3qCW\"f:b,N*F`t7$$\"3Co0zN.r(*=FM$\"3E9&*Q(*>
4q))F`t7$$\"3l4j)3Tu$H?FM$\"3Ei&p!>(\\_%))F`t7$$\"3!H#>MJ'o%G?FM$\"3#H
lW0c'=l$)F`tF]^z7*7$$!3'4Yopj\"z#)=FM$\"3k'y=dNNIO\"FM7$$!3#R4fJ#z_H?F
M$\"3!e!4:En0#Q\"FM7$$!3]AHd%Gcp)>FM$\"3%=KVR</oK\"FM7$$!3&[iCB=%\\Q@F
M$\"3>^&ReYX+@\"FM7$$!3m`%QPaAf4#FM$\"3Cn>j8Hza6FM7$$!3J^n)fk%QW>FM$\"
3mPdt@;br7FM7$$!37!e+u+8=!>FM$\"3q`\"G&p!*H;7FMFa`z7*7$$!3qC3B;O5Z:FM$
\"3kO;Uh&\\`N\"FM7$$!3[?&oBwU'o;FM$\"3OeMLYJ/g8FM7$$!3(e*)f>C%pH;FM$\"
3I_pJpb'zJ\"FM7$$!35g2q;z4X<FM$\"3,i6asP967FM7$$!3ZN@H'R\\hq\"FM$\"3Sc
Y_&>m!p6FM7$$!3-r7b@du!f\"FM$\"3qY/I#*z)eF\"FM7$$!3UYE9,sz^:FM$\"3lSRG
:/\"QB\"FMFebz7*7$$!3EVM\"p#f#e?\"FM$\"3W'[CrwjwM\"FM7$$!3lDbbD/718FM$
\"3,ML2f?)>M\"FM7$$!3QZWKB]zq7FM$\"3p!p4AYW/J\"FM7$$!3uSml>8Hd8FM$\"3)
4)=ww&fN@\"FM7$$!3pibU<f'>K\"FM$\"3'yB)*)z>-#=\"FM7$$!36pL4@'paB\"FM$
\"3OZgMlo!*y7FM7$$!3$3Hi)=U9+7FM$\"3//C[o#ptC\"FMFidz7*7$$!3kgJ;!p&e*e
)F`t$\"3WOt#G(z(*R8FM7$$!3,%3,s74'>%*F`t$\"3WL0PkM(yK\"FM7$$!3'ewlmG'e
-\"*F`t$\"3*p`@E&3C/8FM7$$!3kuE#>\"Ru](*F`t$\"3k2<]yGH<7FM7$$!3gdtQr5s
L%*F`t$\"3=6Fvm-m$>\"FM7$$!3qZ/8YMc&y)F`t$\"3cSD(3C31G\"FM7$$!3mI^f01a
o%)F`t$\"35WN7Hc(pD\"FMF]gz7*7$$!3iMWRDa,l]F`t$\"3A'=I&y@HK8FM7$$!3w\"
pA'QAkhdF`t$\"3)f0DAO<xJ\"FM7$$!3=QG')z0&3[&F`t$\"3y!\\_0ua$*H\"FM7$$!
3-'RwIJrW)fF`t$\"3BU1wxOMA7FM7$$!3XUlJa'zOq&F`t$\"3/x!)3c5)R?\"FM7$$!3
t&)H5@*e+?&F`t$\"3gD*z)=@*4G\"FM7$$!3sKJMisE>\\F`t$\"3igt?(\\HEE\"FMFa
iz7*7$$!3#RDG[Z[X[\"F`t$\"3BOIB%Q1YK\"FM7$$!3Cz+#)*e.t3#F`t$\"3H-pj_P^
68FM7$$!33\"pNG6VF%=F`t$\"3s_D+Ehy&H\"FM7$$!3%4dF+S&4uAF`t$\"3I%oQX(>r
G7FM7$$!31$=VI#\\`H?F`t$\"3'\\L/zM%)H@\"FM7$$!3%HI^ej#=)f\"F`t$\"3;.#o
$*\\e+G\"FM7$$!3y9p')e@i`8F`t$\"3!Q&Qts3Lk7FMFe[[l7*7$$\"3a#QN:;:=:#F`
t$\"3,')e$**e?pJ\"FM7$$\"3$\\v1#>oS.;F`t$\"3#>21cji#48FM7$$\"3%zn:W6O<
\"=F`t$\"3OA<(*3]`$H\"FM7$$\"3#yzBs#QQ!Q\"F`t$\"3_Me$)oxRO7FM7$$\"37@F
VAJr)e\"F`t$\"3<&[,A9q1A\"FM7$$\"3'4gC'4a1??F`t$\"3!GPPBQ2yF\"FM7$$\"3
ECN$[q%RGAF`t$\"3ABIqb(z?E\"FMFi][l7*7$$\"3ntkp$[vS%eF`t$\"3-O(QczM#48
FM7$$\"3\")3yX))*)[5`F`t$\"36lD86S'4J\"FM7$$\"3_n7*=5(e#[&F`t$\"3#****
f%*Q,EH\"FM7$$\"3#>rx'oj'*y\\F`t$\"3W#4_11,aC\"FM7$$\"3iq66#[k5:&F`t$
\"3DF&z*Q%QqA\"FM7$$\"37DZK:_oacF`t$\"3sMuyn(QUF\"FM7$$\"3$Q=e(GLyEeF`
t$\"3ap[6Yh(eD\"FMF]`[l7*7$$\"3m@]l\"\\KAf*F`t$\"3!eeT8+\\:I\"FM7$$\"3
Y&3Lz\"H%R.*F`t$\"3S\"Q;#zyh;8FM7$$\"3[y5f\\)4)p\"*F`t$\"3'\\QnuE&)HH
\"FM7$$\"3ppTLCAl@&)F`t$\"3Geu)*\\=sb7FM7$$\"3si@*f:>vl)F`t$\"3%=YQ#Q#
*3K7FM7$$\"3\\r!\\7ywcI*F`t$\"3_)Q=dl_$p7FM7$$\"3jlq!HrV:W*F`t$\"33#Rp
R/?dC\"FMFab[l7*7$$\"3:-6a='G'R8FM$\"3!eVWq?jQH\"FM7$$\"3'yDj2'oPx7FM$
\"3Z@v&)RUAE8FM7$$\"3!3^^dVStG\"FM$\"39yQ*Hk'o%H\"FM7$$\"3A<$>%RT%3?\"
FM$\"3gJ>%o8gtE\"FM7$$\"3=qvS9x!3@\"FM$\"3^)Gy*RD#eB\"FM7$$\"3aj(R2,/t
H\"FM$\"3#[BIh/\\JE\"FM7$$\"3\\;!GdensI\"FM$\"3]\"fm#\\9hJ7FMFed[l7*7$
$\"3A[k\\cOiD<FM$\"3e&GZFTxhG\"FM7$$\"3-Icv0m*Hl\"FM$\"3'[)f0$4$yR8FM7
$$\"3SOjciqLf;FM$\"3/z%Rg^0xH\"FM7$$\"3'>ZDyQLRa\"FM$\"338b@@fJ!G\"FM7
$$\"3MyhjWQF]:FM$\"3Z2!*>W$Q#Q7FM7$$\"3cUqP>vnl;FM$\"3?tH-Rzib7FM7$$\"
3%*[x=wz,s;FM$\"3Qnk+i.b87FMFif[l7*7$$\"3qR:.j$3s6#FM$\"3gN,X=;\\y7FM7
$$\"3\"QUqn_`-.#FM$\"3!=x6)QWHd8FM7$$\"3j$e.a'3(H.#FM$\"3&y=/m)=/-8FM7
$$\"3G\")=lnHV\")=FM$\"3C-#3J?*e%H\"FM7$$\"35T]G1.:%)=FM$\"3H=1!4lO$R7
FM7$$\"3WVn./#)oN?FM$\"3!Rg'RM$*yY7FM7$$\"3q.*pEa0%Q?FM$\"3#*>!*=#yO:>
\"FMF]i[l7*7$$!3wgTP[+Un=FM$\"3i+Bl8vNM<FM7$$!3#GvjjOg/.#FM$\"3UR2NhN
\")e<FM7$$!31N+g4cE%)>FM$\"3_i!)ysZJ'p\"FM7$$!3!zp2+Lxc:#FM$\"3I6jN`\"
>'p:FM7$$!3f!)RCtD[4@FM$\"3?MOzk.72:FM7$$!3I<j$G&32Q>FM$\"3V&QDU)f\"Qj
\"FM7$$!3a*fsg4w=*=FM$\"3c3Fm&><8d\"FMFa[\\l7*7$$!3]CljF?tJ:FM$\"3S]^N
><nE<FM7$$!3izJd0_dp;FM$\"3u\"HL:)**zO<FM7$$!3@3q)pc.qi\"FM$\"3)Hph\"o
hZ(o\"FM7$$!3eLQQk5Gi<FM$\"3MAz0gurq:FM7$$!3RiwzD%4(><FM$\"3gBjoYOR@:F
M7$$!3-P3SG>V%e\"FM$\"3-%4!zaB:Q;FM7$$!3$em9)*Gg=a\"FM$\"3G&\\=9aG))e
\"FMFe]\\l7*7$$!3/V\">$QVX!>\"FM$\"3T+!e]#f)*=<FM7$$!3c%=g(oG028FM$\"3
inJF%*)Q(=<FM7$$!3%*f:N[V5o7FM$\"3OJW0h]&*z;FM7$$!3C9(RtYuWP\"FM$\"33T
'yUELJd\"FM7$$!3h*3Jp%f_N8FM$\"3%[!*f5V\\V`\"FM7$$!35NH%z#e:H7FM$\"39&
pNyAr6k\"FM7$$!3C5V`2t?!>\"FM$\"3*)eph%R(Q-;FMFi_\\l7*7$$!3`e,A/)peV)F
`t$\"3>]3wI,I6<FM7$$!3=uwCfN$*G%*F`t$\"3#oOq&*HIYq\"FM7$$!3W\"*o$p`zc2
*F`t$\"3YxiY^9vt;FM7$$!3h4Mv)QvD#**F`t$\"3)zY=gcmod\"FM7$$!3)oiUkO@$p&
*F`t$\"3SyV\"zr()fa\"FM7$$!3r3hi9bUA()F`t$\"35)=iLgsGk\"FM7$$!3)fK:B\\
r\"p$)F`t$\"3u)4e_v$*>h\"FMF]b\\l7*7$$!30L9XR&*H6\\F`t$\"3?+PYOVh.<FM7
$$!3%>Gp1nm4x&F`t$\"3!)*)[U(>uWp\"FM7$$!3yjR8IQ%RX&F`t$\"3oJsRR`')o;FM
7$$!3))Hr!**y-j:'F`t$\"3M-uFlt\">e\"FM7$$!3$G\"=P\\*z#ReF`t$\"3-W(\\s]
3jb\"FM7$$!3tY')f*)4#p8&F`t$\"3Ot&p8[cKk\"FM7$$!3eGL1\\\")*)>[F`t$\"3D
:>MBwk<;FMFad\\l7*7$$!3!=D&)))eK3L\"F`t$\"3'*\\l;U&Gfp\"FM7$$!3%)om'=-
Gm4#F`t$\"3)etOyeq#)o\"FM7$$!3%e\"o5jj$e\"=F`t$\"3S$HZ[s'Hl;FM7$$!3i0$
eo(o#fW#F`t$\"3kWa0icG)e\"FM7$$!3g_%)4=_8l@F`t$\"3;-g1*z6`c\"FM7$$!36j
pM/Z/N:F`t$\"3q]y&='GKU;FM7$$!355reXIDa7F`t$\"3A3%o))**[$>;FMFef\\l7*7
$$\"3n%Qyu/JbI#F`t$\"3)**RpyuU#)o\"FM7$$\"3wk,;(Q#3%f\"F`t$\"3_0f!3Z>g
o\"FM7$$\"3\"HbWT'GkQ=F`t$\"3/jk\"ygXIm\"FM7$$\"3FjIR]Bb37F`t$\"3i%f_j
Xrff\"FM7$$\"3G^uPFG6`9F`t$\"39_JO$f(*Hd\"FM7$$\"3yS*G6M.K3#F`t$\"3c?q
#[ur+k\"FM7$$\"3%*GL6=QwFBF`t$\"33yv$=)y4<;FMFih\\l7*7$$\"3!pZR'p8z(*f
F`t$\"3w\\Ad`pb!o\"FM7$$\"3v>7TcX;,`F`t$\"3[)RKj%3s(o\"FM7$$\"30V,i^Q
\\4bF`t$\"3QSZI))>6i;FM7$$\"3&p(p%=*[82[F`t$\"3x_)o\"[Z(\\g\"FM7$$\"3D
+f0(=ka,&F`t$\"3W%>T,*eOz:FM7$$\"3Mm!Ho9Byr&F`t$\"3G#3x-8.lj\"FM7$$\"3
j*)z.UC:EfF`t$\"3;C%\\AF%*3h\"FMF][]l7*7$$\"3!Q-)fx$[fu*F`t$\"3w*4v#f6
(Gn\"FM7$$\"3H&\\')e[=Y-*F`t$\"3A:iT9ZP$p\"FM7$$\"3+a*>$*f;n>*F`t$\"3k
D@Jme\\i;FM7$$\"3sMM]Z2#)\\$)F`t$\"3R=U]PbH:;FM7$$\"3W$*o$4')=>_)F`t$
\"3!)G,S*o;We\"FM7$$\"3g6Mv7Z\")o$*F`t$\"3HO!3#=qhJ;FM7$$\"3Jqo=EG\"4a
*F`t$\"3#p%R5q\"Q2g\"FMFa]]l7*7$$\"3e-a82-+b8FM$\"3c\\z(\\O&=l;FM7$$\"
3;*fevTWkF\"FM$\"33bt0v5)Hq\"FM7$$\"3Y)RC26J+H\"FM$\"3g='Q=C(>k;FM7$$
\"3]Vit\"*4m$=\"FM$\"3%>peV#Q$pi\"FM7$$\"3-V?!\\oZs>\"FM$\"3qb*R6**\\
\")e\"FM7$$\"3x(>!*Q!yh.8FM$\"3P#))>'3MTD;FM7$$\"32(*f0(\\/sJ\"FM$\"37
Y6Sv&Hme\"FMFe_]l7*7$$\"3W[24X_*4u\"FM$\"3c*z!oq&*\\d;FM7$$\"3)3(4biT1
_;FM$\"3Z=eDG*Rlr\"FM7$$\"3%QARvtF?m\"FM$\"3s>U)[6;sm\"FM7$$\"3Y)RU,C]
n_\"FM$\"3>tAt3'*))R;FM7$$\"3U^18:QrO:FM$\"3Wu1O&zl0f\"FM7$$\"3cwu_78*
>n\"FM$\"3)4i7:I#*yh\"FM7$$\"3_Hd^()[&>o\"FM$\"3-A59)[o&o:FMFia]l7*7$$
\"3pRei^*zD8#FM$\"3M\\OQwP\")\\;FM7$$\"3Ykdc$3@$H?FM$\"3?0;,u70M<FM7$$
\"3&3Zw.ahc.#FM$\"3KG*[a[_:n\"FM7$$\"3y2)o*>)\\U'=FM$\"3ei\\i!*G;a;FM7
$$\"3;9&znF!fq=FM$\"3[&Gi?5k;f\"FM7$$\"3Bxr=(*>+U?FM$\"3A^i)op`!4;FM7$
$\"3i$)y*RXU$[?FM$\"3MuNK3\\bY:FMF]d]l7*7$$!3ag)z(f%[?&=FM$\"3P9eer'zc
5#FM7$$!3t6%o&4GRJ?FM$\"3zs0b'Rqb8#FM7$$!3iZriM\\d\")>FM$\"3+.Gjr`#e1#
FM7$$!3%=x!px/'G<#FM$\"3TrI(3%G>H>FM7$$!3^2&\\FgUI7#FM$\"3i,`&f\"yWf=F
M7$$!3H$)eofqvJ>FM$\"3)H.:nM!3'*>FM7$$!3=>Yu%=R>)=FM$\"3>jsz@`LE>FMFaf
]l7*7$$!3GCA/R/O;:FM$\"39k')GxQ*z4#FM7$$!3_Qyx[w]q;FM$\"37DJt;ob8@FM7$
$!3x?T,#*GJC;FM$\"3CLk+nn)p0#FM7$$!332p17UYz<FM$\"3X#ouv9\"HI>FM7$$!3K
*=.`XpKt\"FM$\"3c!*z%y4@P(=FM7$$!3+./DN\"=\"y:FM$\"3!=uzsr;/+#FM7$$!3D
&o'[yL#>`\"FM$\"3\"*\\Ibnm%Q%>FMFeh]l7*7$$!3#G%[s\\F3v6FM$\"3Q9:*H33.4
#FM7$$!3pV['>J&)zI\"FM$\"3A,IZHd\\&4#FM7$$!3Gs'yLn8aE\"FM$\"3Gs\"**)fc
Y\\?FM7$$!3s(yA]hd;R\"FM$\"3U,az^pqK>FM7$$!3a;mVwf3\\8FM$\"3/s:A#)on')
=FM7$$!34,DzM?%GA\"FM$\"3\"HMD.fNM+#FM7$$!3!*Hj?'Rq-=\"FM$\"3_8:v?bSd>
FMFij]l7*7$$!3UcrF=R:#G)F`t$\"3;kVp)GAE3#FM7$$!3CjUH\"*zDQ%*F`t$\"3m+-
xMrQ\"3#FM7$$!3#f,3sys([!*F`t$\"3P=5J]?EV?FM7$$!3Y9%eloS%45FM$\"3'yANN
DSk$>FM7$$!3:'*y\\h;#\\q*F`t$\"3eXg2p^J)*=FM7$$!3go<7$e(Gf')F`t$\"3lN=
&e'p80?FM7$$!3I@b.zB!)p#)F`t$\"3Q`ER\")=,n>FMF]]^l7*7$$!3%4V3Nl$edZF`t
$\"3%R@(R%\\O\\2#FM7$$!35ser-6H!y&F`t$\"3UBZiK5Br?FM7$$!3P*30/3PqU&F`t
$\"3%>(>CQfPQ?FM7$$!3$['ytmU8GjF`t$\"3XiTz_5\\T>FM7$$!35#3FWC!)[(fF`t$
\"3V69Tefj3>FM7$$!3k1V4eIyt]F`t$\"3\"4AfQ%3_0?FM7$$!3!R_$yN!H0s%F`t$\"
3!*pkZ\\dms>FMFa_^l7*7$$!3o\\A%Hq;r<\"F`t$\"3uj+5+2Dn?FM7$$!3.fK\"RX_f
5#F`t$\"3]pl.Bu-l?FM7$$!3;TzP8'H*)y\"F`t$\"3)Q.#pBt![.#FM7$$!3JS!*o`$e
xh#F`t$\"3u/Ad\\$fy%>FM7$$!3;AP:8bt+BF`t$\"37pwA]#Rw\">FM7$$!3GBE%Gx1>
Z\"F`t$\"3D)\\ZVA(e/?FM7$$!3S0tIKR)[:\"F`t$\"3'G'H+DrOu>FMFea^l7*7$$\"
3y'Q@M$pCfCF`t$\"3'R\"H!e!\\cf?FM7$$\"3)[d8^&zv%e\"F`t$\"3ORd+1jxi?FM7
$$\"3)yUtQh\\b'=F`t$\"3u.7m1ibK?FM7$$\"3()GBct3sO5F`t$\"3'\\NpQ9Xb&>FM
7$$\"3u\"=AB`7vJ\"F`t$\"3M>[_W]KD>FM7$$\"3!4GLEFTj9#F`t$\"36omJ2hL-?FM
7$$\"3jLJRJH8FCF`t$\"3sK@(z+;@(>FMFic^l7*7$$\"3-zCebs]^hF`t$\"3ujd]6\"
z=0#FM7$$\"3eHYOC,%=H&F`t$\"35KA`\"oxW1#FM7$$\"3Y<!\\8g+k`&F`t$\"32\"[
\\reA;.#FM7$$\"3*>C;]T.`j%F`t$\"3m7coN%[X'>FM7$$\"3')H1+#*Q')z[F`t$\"3
jhGITLpJ>FM7$$\"3W1MLy5'4y&F`t$\"3/Inw#\\n()*>FM7$$\"3K%z<`b@b-'F`t$\"
3!)yRQ)R7f'>FMF]f^l7*7$$\"3!f-TNEk'**)*F`t$\"3_8'3sJ$>W?FM7$$\"370*RQ0
%H:!*F`t$\"3i[gh\\:8q?FM7$$\"3TG)[!\\LiB#*F`t$\"3Mmo:lk+K?FM7$$\"3'3qs
1F*)z<)F`t$\"3]y4-D#p[(>FM7$$\"31B;)ec=jQ)F`t$\"3A'zh09Wn$>FM7$$\"3r^x
DWE&>V*F`t$\"3%Qo(p!Q\")Q*>FM7$$\"3+vmYR>GS'*F`t$\"3c,&QiHcd&>FMFah^l7
*7$$\"3!GqHdzr.P\"FM$\"3Jj9\"H_2l.#FM7$$\"3/SRNu>^v7FM$\"3Y)=d-\"ztz?F
M7$$\"3!fG(p&y@FH\"FM$\"33fLoSyqL?FM7$$\"3AqJ0WyZm6FM$\"31_a(=^2l)>FM7
$$\"3)e^'Rbwo$=\"FM$\"3nA;IUuZS>FM7$$\"3yJ1/(fJ*48FM$\"3#*H&46xxw)>FM7
$$\"3lxRQ399F8FM$\"3a+d`,xkT>FMFej^l7*7$$\"3k[]oLoOc<FM$\"3a8VhG<#)G?F
M7$$\"3)>JY$><8^;FM$\"31_cXjnH$4#FM7$$\"3G6@^7%=Zm\"FM$\"3kg*GPrEn.#FM
7$$\"3(\\KfC4n&4:FM$\"3_L!\\iHj%**>FM7$$\"3\\C^i&y`J_\"FM$\"3jTB_YK*G%
>FM7$$\"3e5zn0^Iy;FM$\"3aoA+km:!)>FM7$$\"3')4P%))z\"*=p\"FM$\"3(odvUh'
eB>FMFi\\_l7*7$$\"37S,AS:&z9#FM$\"3KjrJMf8@?FM7$$\"3+16OS')QG?FM$\"3-R
9@4\"336#FM7$$\"3&*e$\\`@_$Q?FM$\"3BpOH%3j5/#FM7$$\"3GMdGsm1Z=FM$\"3pA
<9ylt8?FM7$$\"3C()RFZ-.d=FM$\"3n_RA`:*R%>FM7$$\"3Y6wL!z:$[?FM$\"3+**eP
f!=8(>FM7$$\"3UkeKl$z#e?FM$\"3?H\"eW.t:!>FMF]__l-%&COLORG6&F2F.F.F3-%*
AXESSTYLEG6#%$BOXG-%+AXESLABELSG6$%\"xG%\"yG" 1 2 0 1 10 0 2 9 1 2 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve \+
4" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 210 "The amount of work done on
 the particle as it moves through this field is different, because in \+
different regions of space the the force vectors are allowed to have d
ifferent lengths and different orientations." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 118 "For a force field which is not
 curl-free, the travel over a closed contour (loop) allows one to gain
 (or lose) energy." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 79 "The graph also shows visually why we refer to the field a
s not being curl-free." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "e
valf([Work1,Work2,Work1+Work2,Work]);" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#7&$!+nmmmm!\"*$F%!#5$!+LLLLtF&$!+LLLL8!\")" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 169 "Note that the amount of work done by the force on the
 particle is negative. We start the particle at [2,2] (top right-hand \+
corner), and it moves against the force field." }}{PARA 0 "" 0 "" 
{TEXT -1 278 "The fact that it arrives at location [0,-2] with a negat
ive amount of work (it worked against the force field) means that its \+
kinetic energy will be less than it was at A. It will be less at B tha
n at A by a different amount depending on whether the red or green pat
h is chosen." }}{PARA 0 "" 0 "" {TEXT -1 24 "An interesting question:
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 280 9 "Exerc
ise:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 114 "
Calculate the work done on the particle along a path such that it gain
s energy to go from A=[2,2,1] to B=[-2,0,1]." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 281 8 "Solutio
n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "r_i,r_f;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6$7%\"\"#F$\"\"\"7%!\"#\"\"!F%" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 14 "r_1:=[2,-2,1];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$r_1G7%\"\"#!\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 30 "r_tp1:=evalm(r_i+(r_1-r_i)*t);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%&r_tp1G-%'vectorG6#7%\"\"#,&F)\"\"\"*&\"\"%F+%\"tGF+!\"\"F+" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "r_2:=[-2,-2,1];" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$r_2G7%!\"#F&\"\"\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 25 "v_tp1:=map(diff,r_tp1,t);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&v_tp1G-%'vectorG6#7%\"\"!!\"%F)" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 30 "r_tp2:=evalm(r_1+(r_2-r_1)*t);" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 25 "v_tp2:=map(diff,r_tp2,t);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%&r_tp2G-%'vectorG6#7%,&\"\"#\"\"\"*&\"\"%F+%\"tGF+!
\"\"!\"#F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&v_tp2G-%'vectorG6#7%!
\"%\"\"!F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "r_tp3:=evalm(
r_2+(r_f-r_2)*t);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "v_tp3:=map(dif
f,r_tp3,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&r_tp3G-%'vectorG6#7%
!\"#,&F)\"\"\"*&\"\"#F+%\"tGF+F+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%&v_tp3G-%'vectorG6#7%\"\"!\"\"#F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 48 "Now we are ready to calculate the work integral." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "Work1:=int(dotprod(subs(x=r_tp1[1],
y=r_tp1[2],z=r_tp1[3],F),v_tp1),t=0..1);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%&Work1G\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "Wor
k2:=int(dotprod(subs(x=r_tp2[1],y=r_tp2[2],z=r_tp2[3],F),v_tp2),t=0..1
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&Work2G#\"#W\"\"$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "Work3:=int(dotprod(subs(x=r_tp3[1],
y=r_tp3[2],z=r_tp3[3],F),v_tp3),t=0..1);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%&Work3G\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "eva
lf(Work1+Work2+Work3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+nmmmA!\"
)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 5 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }