{VERSION 5 0 "IBM INTEL NT" "5.0" }
{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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 }
{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 "Text Output" -1 6 
1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 2 1 3 1 }1 1 
0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Co
urier" 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 "Maple Out
put" -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 -1 120 "dyn_of_lev.mws  Equations
 based on \"Dynamics of the Levitron\" Roger F Gans et al (J. Phys. D:
 Appl.Phys.31 1998 671-679)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 19 "23 nov 2003 Koepken" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 82 "with a test of a second order R
unge-Kutta integration method and C code generation" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "6 dec 2003" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 32 "(c) 2003-2005 Hans
-Georg Koepken" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "PDEtools[declare]( (q1,q2
,q3,q4,q5,q6,p1,p2,p3,p4,p5,p6)(t), prime=t, quiet );" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "Phi[1]:=Z/(1+Z^2)^(3/2)-3/4*(2*Z^2-
3)*Z/(1+Z^2)^(7/2)*(X^2+Y^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 35 "Phi:=subs(\{X=q1,Y=q2,Z=q3\},Phi[1]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$PhiG,&*&%#q3G\"\"\",&F(F(*$)F'\"\"#F(F(#!\"$F,F(*.\"
\"$F(\"\"%!\"\",&*&F,F(F+F(F(F0F2F(F'F(F)#!\"(F,,&*$)%#q1GF,F(F(*$)%#q
2GF,F(F(F(F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "H:=1/2*(p1
^2+p2^2+p3^2+p4^2/a+(p5-p6*cos(q4))^2/(a*sin(q4)^2)+p6^2/c)\n-M*(sin(q
4)*(cos(q5)*diff(Phi,q1)+sin(q5)*diff(Phi,q2))+cos(q4)*diff(Phi,q3))\n
+q3;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"HG,2*&\"\"#!\"\"%#p1GF'\"
\"\"*&F'F(%#p2GF'F**&F'F(%#p3GF'F**(F'F(%#p4GF'%\"aGF(F**&#F*F'F**(,&%
#p5GF**&%#p6GF*-%$cosG6#%#q4GF*F(F'F1F(-%$sinGF;!\"#F*F**(F'F(F8F'%\"c
GF(F**&%\"MGF*,&*&F=F*,&*&#\"\"$F'F**,-F:6#%#q5GF*,&*&F'F*)%#q3GF'F*F*
FIF(F*FQF*,&F*F**$FPF*F*#!\"(F'%#q1GF*F*F(*&#FIF'F**,-F>FLF*FNF*FQF*FR
FT%#q2GF*F*F(F*F**&F9F*,,*&F*F**$)FR#FIF'F*F(F**(FIF*FQF'FR#!\"&F'F(**
FIF*FQF'FRFT,&*$)FVF'F*F**$)FenF'F*F*F*F(*,FIF*\"\"%F(FNF*FRFTF`oF*F(*
.\"#@F*FfoF(FNF*FQF'FR#!\"*F'F`oF*F*F*F*F*F(FQF*" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 120 "eqgen:=\{p1=q[7],p2=q[8],p3=q[9],p4=q[10],p5
=q[11],p6=q[12],\n        q1=q[1],q2=q[2],q3=q[3],q4=q[ 4],q5=q[ 5],q6
=q[ 6]\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 278 "CodeGeneratio
n[C](subs(eqgen,[dq[1]=diff(H,p1),dq[2]=diff(H,p2),dq[3]=diff(H,p3),dq
[4]=diff(H,p4),dq[5]=diff(H,p5),dq[6]=diff(H,p6),\n        dq[7]=diff(
-H,q1),dq[8]=diff(-H,q2),dq[9]=diff(-H,q3),dq[10]=diff(-H,q4),dq[11]=d
iff(-H,q5),dq[12]=diff(-H,q6)]),\n        optimize=true);" }}{PARA 6 "
" 1 "" {TEXT -1 13 "dq[0] = q[6];" }}{PARA 6 "" 1 "" {TEXT -1 13 "dq[1
] = q[7];" }}{PARA 6 "" 1 "" {TEXT -1 13 "dq[2] = q[8];" }}{PARA 6 "" 
1 "" {TEXT -1 16 "t2 = 0.10e1 / a;" }}{PARA 6 "" 1 "" {TEXT -1 18 "dq[
3] = q[9] * t2;" }}{PARA 6 "" 1 "" {TEXT -1 11 "t4 = q[11];" }}{PARA 
6 "" 1 "" {TEXT -1 10 "t5 = q[3];" }}{PARA 6 "" 1 "" {TEXT -1 13 "t6 =
 cos(t5);" }}{PARA 6 "" 1 "" {TEXT -1 21 "t8 = q[10] - t4 * t6;" }}
{PARA 6 "" 1 "" {TEXT -1 13 "t9 = t8 * t2;" }}{PARA 6 "" 1 "" {TEXT 
-1 14 "t10 = sin(t5);" }}{PARA 6 "" 1 "" {TEXT -1 16 "t11 = t10 * t10;
" }}{PARA 6 "" 1 "" {TEXT -1 19 "t12 = 0.10e1 / t11;" }}{PARA 6 "" 1 "
" {TEXT -1 17 "dq[4] = t9 * t12;" }}{PARA 6 "" 1 "" {TEXT -1 32 "dq[5]
 = -t9 * t12 * t6 + t4 / c;" }}{PARA 6 "" 1 "" {TEXT -1 11 "t17 = q[4]
;" }}{PARA 6 "" 1 "" {TEXT -1 15 "t18 = cos(t17);" }}{PARA 6 "" 1 "" 
{TEXT -1 11 "t20 = q[2];" }}{PARA 6 "" 1 "" {TEXT -1 16 "t21 = t20 * t
20;" }}{PARA 6 "" 1 "" {TEXT -1 26 "t23 = 0.2e1 * t21 - 0.3e1;" }}
{PARA 6 "" 1 "" {TEXT -1 18 "t25 = 0.1e1 + t21;" }}{PARA 6 "" 1 "" 
{TEXT -1 16 "t26 = t25 * t25;" }}{PARA 6 "" 1 "" {TEXT -1 16 "t28 = sq
rt(t25);" }}{PARA 6 "" 1 "" {TEXT -1 31 "t30 = 0.10e1 / t28 / t26 / t2
5;" }}{PARA 6 "" 1 "" {TEXT -1 22 "t31 = t23 * t20 * t30;" }}{PARA 6 "
" 1 "" {TEXT -1 16 "t34 = t21 * t30;" }}{PARA 6 "" 1 "" {TEXT -1 11 "t
35 = q[0];" }}{PARA 6 "" 1 "" {TEXT -1 16 "t38 = t23 * t30;" }}{PARA 
6 "" 1 "" {TEXT -1 16 "t41 = t23 * t21;" }}{PARA 6 "" 1 "" {TEXT -1 
16 "t42 = t26 * t26;" }}{PARA 6 "" 1 "" {TEXT -1 25 "t44 = 0.10e1 / t2
8 / t42;" }}{PARA 6 "" 1 "" {TEXT -1 138 "dq[6] = M * (-0.3e1 / 0.2e1 \+
* t10 * t18 * t31 + t6 * (-0.6e1 * t34 * t35 - 0.3e1 / 0.2e1 * t38 * t
35 + 0.21e2 / 0.2e1 * t41 * t44 * t35));" }}{PARA 6 "" 1 "" {TEXT -1 
15 "t51 = sin(t17);" }}{PARA 6 "" 1 "" {TEXT -1 11 "t55 = q[1];" }}
{PARA 6 "" 1 "" {TEXT -1 138 "dq[7] = M * (-0.3e1 / 0.2e1 * t10 * t51 \+
* t31 + t6 * (-0.6e1 * t34 * t55 - 0.3e1 / 0.2e1 * t38 * t55 + 0.21e2 \+
/ 0.2e1 * t41 * t44 * t55));" }}{PARA 6 "" 1 "" {TEXT -1 16 "t67 = t30
 * t35;" }}{PARA 6 "" 1 "" {TEXT -1 16 "t70 = t18 * t23;" }}{PARA 6 "
" 1 "" {TEXT -1 16 "t73 = t21 * t44;" }}{PARA 6 "" 1 "" {TEXT -1 16 "t
78 = t30 * t55;" }}{PARA 6 "" 1 "" {TEXT -1 16 "t81 = t51 * t23;" }}
{PARA 6 "" 1 "" {TEXT -1 25 "t90 = 0.10e1 / t28 / t26;" }}{PARA 6 "" 
1 "" {TEXT -1 16 "t93 = t21 * t20;" }}{PARA 6 "" 1 "" {TEXT -1 16 "t96
 = t20 * t30;" }}{PARA 6 "" 1 "" {TEXT -1 16 "t97 = t35 * t35;" }}
{PARA 6 "" 1 "" {TEXT -1 16 "t98 = t55 * t55;" }}{PARA 6 "" 1 "" 
{TEXT -1 16 "t99 = t97 + t98;" }}{PARA 6 "" 1 "" {TEXT -1 398 "dq[8] =
 M * (t10 * (-0.6e1 * t18 * t21 * t67 - 0.3e1 / 0.2e1 * t70 * t67 + 0.
21e2 / 0.2e1 * t70 * t73 * t35 - 0.6e1 * t51 * t21 * t78 - 0.3e1 / 0.2
e1 * t81 * t78 + 0.21e2 / 0.2e1 * t81 * t73 * t55) + t6 * (-0.9e1 * t9
0 * t20 + 0.15e2 * t93 * t30 - 0.9e1 * t96 * t99 + 0.42e2 * t93 * t44 \+
* t99 + 0.63e2 / 0.4e1 * t23 * t44 * t99 * t20 - 0.189e3 / 0.4e1 * t23
 * t93 / t28 / t42 / t25 * t99)) - 0.1e1;" }}{PARA 6 "" 1 "" {TEXT -1 
15 "t123 = t8 * t8;" }}{PARA 6 "" 1 "" {TEXT -1 17 "t129 = t96 * t35;
" }}{PARA 6 "" 1 "" {TEXT -1 17 "t131 = t96 * t55;" }}{PARA 6 "" 1 "" 
{TEXT -1 256 "dq[9] = -t9 / t10 * t4 + t123 * t2 / t11 / t10 * t6 + M \+
* (t6 * (-0.3e1 / 0.2e1 * t70 * t129 - 0.3e1 / 0.2e1 * t81 * t131) - t
10 * (0.10e1 / t28 / t25 - 0.3e1 * t21 * t90 - 0.3e1 * t34 * t99 - 0.3
e1 / 0.4e1 * t38 * t99 + 0.21e2 / 0.4e1 * t41 * t44 * t99));" }}{PARA 
6 "" 1 "" {TEXT -1 77 "dq[10] = M * t10 * (0.3e1 / 0.2e1 * t81 * t129 \+
- 0.3e1 / 0.2e1 * t70 * t131);" }}{PARA 6 "" 1 "" {TEXT -1 15 "dq[11] \+
= 0.0e0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "pqt:=\{p1=p1(t),p2=p2(t),p3=p3(t),
p4=p4(t),p5=p5(t),p6=p6(t),\n            q1=q1(t),q2=q2(t),q3=q3(t),q4
=q4(t),q5=q5(t),q6=q6(t)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$pqtG
<./%#q1GF'/%#q2GF)/%#q3GF+/%#q4GF-/%#q5GF//%#q6GF1/%#p1GF3/%#p3GF5/%#p
4GF7/%#p5GF9/%#p6GF;/%#p2GF=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 232 "eqdp:=\{diff(p1(t),t)=subs(pqt,diff(-H,q1)),diff(p2(t),t)=subs(
pqt,diff(-H,q2)),diff(p3(t),t)=subs(pqt,diff(-H,q3)),\n       diff(p4(
t),t)=subs(pqt,diff(-H,q4)),diff(p5(t),t)=subs(pqt,diff(-H,q5)),diff(p
6(t),t)=subs(pqt,diff(-H,q6))\}:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 226 "eqdq:=\{diff(q1(t),t)=subs(pqt,diff(H,p1)),diff(q2(t
),t)=subs(pqt,diff(H,p2)),diff(q3(t),t)=subs(pqt,diff(H,p3)),\n       \+
diff(q4(t),t)=subs(pqt,diff(H,p4)),diff(q5(t),t)=subs(pqt,diff(H,p5)),
diff(q6(t),t)=subs(pqt,diff(H,p6))\}:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 194 "eq0:=\{p1(0)=0,p2(0)=0,p3(0)=0,p4(0)=0,p5(0)=Omega*(
a*sin(alpha)^2+c*cos(alpha)^2)+c*omega*cos(alpha),p6(0)=c*(omega+Omega
*cos(alpha)),\n      q1(0)=0,q2(0)=0,q3(0)=h,q4(0)=alpha,q5(0)=0,q6(0)
=0\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "omega[T]:=7.5;Ome
ga:=1.2;alpha:=0.005;omega:=omega[T]-Omega*cos(alpha);a:=0.089;c:=0.13
9;M:=8.2;h:=1.72;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%&omegaG6#%\"TG
$\"#v!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&OmegaG$\"#7!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&alphaG$\"\"&!\"$" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%&omegaG$\"++],+j!\"*" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"aG$\"#*)!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG$\"$R
\"!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG$\"##)!\"\"" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"hG$\"$s\"!\"#" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 11 "evalf(eq0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<./
-%#p5G6#\"\"!$\"+R'*[U5!\"*/-%#q3GF'$\"$s\"!\"#/-%#q4GF'$\"\"&!\"$/-%#
p1GF'$F(F(/-%#p2GF'F;/-%#p3GF'F;/-%#p4GF'F;/-%#q1GF'F;/-%#q2GF'F;/-%#q
5GF'F;/-%#q6GF'F;/-%#p6GF'$\"+++]U5F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 241 "sol:=dsolve(eqdp union eqdq union eq0,\{p1(t),p2(t),
p3(t),p4(t),p5(t),p6(t),\n                             q1(t),q2(t),q3(
t),q4(t),q5(t),q6(t)\},type=numeric,relerr=1e-5,abserr=1e-5,stiff=true
,output=array([seq(0.1*i,i=0..500)]),\nmaxfun=30000):" }}}{PARA 11 "" 
1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "q5d:=ev
alf(subs(\{q4(t)=1.5,p5(t)=0,p6(t)=1\},eval(diff(q5(t),t),eqdq)));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$q5dG$!+3+(z)z!#5" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 138 "P1[0]:=subs(eq0,p1(0));P2[0]:=subs(eq0,p
2(0));P3[0]:=subs(eq0,p3(0));P4[0]:=subs(eq0,p4(0));P5[0]:=subs(eq0,p5
(0));P6[0]:=subs(eq0,p6(0));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#P1
G6#\"\"!F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#P2G6#\"\"!F'" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#P3G6#\"\"!F'" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%#P4G6#\"\"!F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%
#P5G6#\"\"!$\"+R'*[U5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#P6G6#
\"\"!$\"+++]U5!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "Q1[0
]:=subs(eq0,q1(0));Q2[0]:=subs(eq0,q2(0));Q3[0]:=subs(eq0,q3(0));Q4[0]
:=subs(eq0,q4(0));Q5[0]:=subs(eq0,q5(0));Q6[0]:=subs(eq0,q6(0));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#Q1G6#\"\"!F'" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%#Q2G6#\"\"!F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%
#Q3G6#\"\"!$\"$s\"!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#Q4G6#\"
\"!$\"\"&!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#Q5G6#\"\"!F'" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#Q6G6#\"\"!F'" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 184 "eqPQ:=\{p1(t)=P1[i-1],p2(t)=P2[i-1],p3(t)=P3
[i-1],p4(t)=P4[i-1],p5(t)=P5[i-1],p6(t)=P6[i-1],\n       q1(t)=Q1[i-1]
,q2(t)=Q2[i-1],q3(t)=Q3[i-1],q4(t)=Q4[i-1],q5(t)=Q5[i-1],q6(t)=Q6[i-1]
\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%eqPQG<./%#p3G&%#P3G6#,&%\"iG
\"\"\"F-!\"\"/%#p4G&%#P4GF*/%#p5G&%#P5GF*/%#p6G&%#P6GF*/%#q1G&%#Q1GF*/
%#q2G&%#Q2GF*/%#q3G&%#Q3GF*/%#q4G&%#Q4GF*/%#q5G&%#Q5GF*/%#q6G&%#Q6GF*/
%#p1G&%#P1GF*/%#p2G&%#P2GF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
137 "eqPQm:=\{p1(t)=P1m,p2(t)=P2m,p3(t)=P3m,p4(t)=P4m,p5(t)=P5m,p6(t)=
P6m,\n       q1(t)=Q1m,q2(t)=Q2m,q3(t)=Q3m,q4(t)=Q4m,q5(t)=Q5m,q6(t)=Q
6m\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&eqPQmG<./%#q1G%$Q1mG/%#q2G
%$Q2mG/%#q3G%$Q3mG/%#q4G%$Q4mG/%#q5G%$Q5mG/%#q6G%$Q6mG/%#p1G%$P1mG/%#p
2G%$P2mG/%#p3G%$P3mG/%#p4G%$P4mG/%#p5G%$P5mG/%#p6G%$P6mG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "i:=1;evalf(subs(eqPQ,eval(diff(q5(t
),t),eqdq)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG\"\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++,+7!\"*" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 840 "T[0]:=0:dt:=0.0025;for i from 1 to 1 do\n  T[i]
:=T[i-1]+dt*0.060;\n  P1[i]:=P1[i-1]+dt*evalf(subs(eqPQ,eval(diff(p1(t
),t),eqdp))):\n  P2[i]:=P2[i-1]+dt*evalf(subs(eqPQ,eval(diff(p2(t),t),
eqdp))):\n  P3[i]:=P3[i-1]+dt*evalf(subs(eqPQ,eval(diff(p3(t),t),eqdp)
)):\n  P4[i]:=P4[i-1]+dt*evalf(subs(eqPQ,eval(diff(p4(t),t),eqdp))):\n
  P5[i]:=P5[i-1]+dt*evalf(subs(eqPQ,eval(diff(p5(t),t),eqdp))):\n  P6[
i]:=P6[i-1]+dt*evalf(subs(eqPQ,eval(diff(p6(t),t),eqdp))):\n  Q1[i]:=Q
1[i-1]+dt*evalf(subs(eqPQ,eval(diff(q1(t),t),eqdq))):\n  Q2[i]:=Q2[i-1
]+dt*evalf(subs(eqPQ,eval(diff(q2(t),t),eqdq))):\n  Q3[i]:=Q3[i-1]+dt*
evalf(subs(eqPQ,eval(diff(q3(t),t),eqdq))):\n  Q4[i]:=Q4[i-1]+dt*evalf
(subs(eqPQ,eval(diff(q4(t),t),eqdq))):\n  Q5[i]:=Q5[i-1]+dt*evalf(subs
(eqPQ,eval(diff(q5(t),t),eqdq))):\n  Q6[i]:=Q6[i-1]+dt*evalf(subs(eqPQ
,eval(diff(q6(t),t),eqdq))):\nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%#dtG$\"#D!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1615 "T[0
]:=0:dt:=0.01;for i from 1 to 1000 do\n  T[i]:=T[i-1]+dt;\n  P1m:=P1[i
-1]+dt/2*evalf(subs(eqPQ,eval(diff(p1(t),t),eqdp))):\n  P2m:=P2[i-1]+d
t/2*evalf(subs(eqPQ,eval(diff(p2(t),t),eqdp))):\n  P3m:=P3[i-1]+dt/2*e
valf(subs(eqPQ,eval(diff(p3(t),t),eqdp))):\n  P4m:=P4[i-1]+dt/2*evalf(
subs(eqPQ,eval(diff(p4(t),t),eqdp))):\n  P5m:=P5[i-1]+dt/2*evalf(subs(
eqPQ,eval(diff(p5(t),t),eqdp))):\n  P6m:=P6[i-1]+dt/2*evalf(subs(eqPQ,
eval(diff(p6(t),t),eqdp))):\n  Q1m:=Q1[i-1]+dt/2*evalf(subs(eqPQ,eval(
diff(q1(t),t),eqdq))):\n  Q2m:=Q2[i-1]+dt/2*evalf(subs(eqPQ,eval(diff(
q2(t),t),eqdq))):\n  Q3m:=Q3[i-1]+dt/2*evalf(subs(eqPQ,eval(diff(q3(t)
,t),eqdq))):\n  Q4m:=Q4[i-1]+dt/2*evalf(subs(eqPQ,eval(diff(q4(t),t),e
qdq))):\n  Q5m:=Q5[i-1]+dt/2*evalf(subs(eqPQ,eval(diff(q5(t),t),eqdq))
):\n  Q6m:=Q6[i-1]+dt/2*evalf(subs(eqPQ,eval(diff(q6(t),t),eqdq))):\n \+
 P1[i]:=P1[i-1]+dt*evalf(subs(eqPQm,eval(diff(p1(t),t),eqdp))):\n  P2[
i]:=P2[i-1]+dt*evalf(subs(eqPQm,eval(diff(p2(t),t),eqdp))):\n  P3[i]:=
P3[i-1]+dt*evalf(subs(eqPQm,eval(diff(p3(t),t),eqdp))):\n  P4[i]:=P4[i
-1]+dt*evalf(subs(eqPQm,eval(diff(p4(t),t),eqdp))):\n  P5[i]:=P5[i-1]+
dt*evalf(subs(eqPQm,eval(diff(p5(t),t),eqdp))):\n  P6[i]:=P6[i-1]+dt*e
valf(subs(eqPQm,eval(diff(p6(t),t),eqdp))):\n  Q1[i]:=Q1[i-1]+dt*evalf
(subs(eqPQm,eval(diff(q1(t),t),eqdq))):\n  Q2[i]:=Q2[i-1]+dt*evalf(sub
s(eqPQm,eval(diff(q2(t),t),eqdq))):\n  Q3[i]:=Q3[i-1]+dt*evalf(subs(eq
PQm,eval(diff(q3(t),t),eqdq))):\n  Q4[i]:=Q4[i-1]+dt*evalf(subs(eqPQm,
eval(diff(q4(t),t),eqdq))):\n  Q5[i]:=Q5[i-1]+dt*evalf(subs(eqPQm,eval
(diff(q5(t),t),eqdq))):\n  Q6[i]:=Q6[i-1]+dt*evalf(subs(eqPQm,eval(dif
f(q6(t),t),eqdq))):\nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#dtG
$\"\"\"!\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" 
{TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "listplot([seq([T[i],Q4[i]],i
=1..1000)]);" }}{PARA 13 "" 1 "" {GLPLOT2D 683 683 683 {PLOTDATA 2 "6#
-%'CURVESG6#7din7$$\"\"\"!\"#$\"+t(y/+&!#77$$\"\"#F*$\"+pD\">+&F-7$$\"
\"$F*$\"+S/H/]F-7$$\"\"%F*$\"+c8f2]F-7$$\"\"&F*$\"+'Q)y6]F-7$$\"\"'F*$
\"+nb%o,&F-7$$\"\"(F*$\"+g?sA]F-7$$\"\")F*$\"+\"*zOH]F-7$$\"\"*F*$\"+Q
1tO]F-7$$\"#5F*$\"+l-vW]F-7$$\"#6F*$\"+.,O`]F-7$$\"#7F*$\"+19\\i]F-7$$
\"#8F*$\"+D82s]F-7$$\"#9F*$\"+<=-#3&F-7$$\"#:F*$\"+olE#4&F-7$$\"#;F*$
\"+YGs-^F-7$$\"#<F*$\"+D.J8^F-7$$\"#=F*$\"+Ap%R7&F-7$$\"#>F*$\"+='\\X8
&F-7$$\"#?F*$\"+xr.X^F-7$$\"#@F*$\"+M=Lb^F-7$$\"#AF*$\"+bhNl^F-7$$\"#B
F*$\"+IZ.v^F-7$$\"#CF*$\"+GeH%=&F-7$$\"#DF*$\"+9I2$>&F-7$$\"#EF*$\"+%*
HI,_F-7$$\"#FF*$\"+?j#*3_F-7$$\"#GF*$\"+n3*e@&F-7$$\"#HF*$\"+*z[@A&F-7
$$\"#IF*$\"+S\"fwA&F-7$$\"#JF*$\"+^mQK_F-7$$\"#KF*$\"+j;IO_F-7$$\"#LF*
$\"+tEQR_F-7$$\"#MF*$\"+tDhT_F-7$$\"#NF*$\"+6A)HC&F-7$$\"#OF*$\"+!p'[V
_F-7$$\"#PF*$\"+z)HJC&F-7$$\"#QF*$\"+#p@>C&F-7$$\"#RF*$\"+:\"y)R_F-7$$
\"#SF*$\"+!4BqB&F-7$$\"#TF*$\"+\")eQL_F-7$$\"#UF*$\"+-@+H_F-7$$\"#VF*$
\"+]H\"RA&F-7$$\"#WF*$\"+q`;=_F-7$$\"#XF*$\"+1/\"=@&F-7$$\"#YF*$\"+mh!
\\?&F-7$$\"#ZF*$\"+9i^(>&F-7$$\"#[F*$\"+*))3(*=&F-7$$\"#\\F*$\"+4Qb\"=
&F-7$$\"#]F*$\"+%zEJ<&F-7$$\"#^F*$\"+\"Q1X;&F-7$$\"#_F*$\"+57xb^F-7$$
\"#`F*$\"+-J+Z^F-7$$\"#aF*$\"+LWGQ^F-7$$\"#bF*$\"+7$*pH^F-7$$\"#cF*$\"
+;*H87&F-7$$\"#dF*$\"+S:E8^F-7$$\"#eF*$\"+u\\d0^F-7$$\"#fF*$\"+s&\\$)4
&F-7$$\"#gF*$\"+A%f;4&F-7$$\"#hF*$\"+<%zb3&F-7$$\"#iF*$\"+#Rx,3&F-7$$
\"#jF*$\"+$=;b2&F-7$$\"#kF*$\"+Gxlr]F-7$$\"#lF*$\"+UIlo]F-7$$\"#mF*$\"
+-$[l1&F-7$$\"#nF*$\"+!)QQl]F-7$$\"#oF*$\"+<8>l]F-7$$\"#pF*$\"+.k*f1&F
-7$$\"#qF*$\"+Rh\"y1&F-7$$\"#rF*$\"+-3mq]F-7$$\"#sF*$\"+ZH`u]F-7$$\"#t
F*$\"+%QD%z]F-7$$\"#uF*$\"+'GD`3&F-7$$\"#vF*$\"+X6@#4&F-7$$\"#wF*$\"+W
e0+^F-7$$\"#xF*$\"+>E#)3^F-7$$\"#yF*$\"+@\"p%=^F-7$$\"#zF*$\"+0u%*G^F-
7$$\"#!)F*$\"+;>?S^F-7$$\"#\")F*$\"+fa<_^F-7$$\"##)F*$\"+oT![;&F-7$$\"
#$)F*$\"+\"\\<!y^F-7$$\"#%)F*$\"+>Su\">&F-7$$\"#&)F*$\"+Y8\"f?&F-7$$\"
#')F*$\"+06W?_F-7$$\"#()F*$\"+^YDN_F-7$$\"#))F*$\"+xZF]_F-7$$\"#*)F*$
\"+B<Ul_F-7$$\"#!*F*$\"+Peh!G&F-7$$\"#\"*F*$\"+&4\"y&H&F-7$$\"##*F*$\"
++-%3J&F-7$$\"#$*F*$\"+<3sD`F-7$$\"#%*F*$\"+C;NS`F-7$$\"#&*F*$\"+:[ma`
F-7$$\"#'*F*$\"+Hnfo`F-7$$\"#(*F*$\"+(e(3#Q&F-7$$\"#)*F*$\"+e.3&R&F-7$
$\"#**F*$\"+i\\_2aF-7$$\"$+\"F*$\"+DrP>aF-7$$\"$,\"F*$\"+g\")fIaF-7$$
\"$-\"F*$\"+?I:TaF-7$$\"$.\"F*$\"+v`,^aF-7$$\"$/\"F*$\"+*3j,Y&F-7$$\"$
0\"F*$\"+VCeoaF-7$$\"$1\"F*$\"+mXEwaF-7$$\"$2\"F*$\"+Ti?$[&F-7$$\"$3\"
F*$\"+*e6%*[&F-7$$\"$4\"F*$\"+g?*[\\&F-7$$\"$5\"F*$\"+qQm*\\&F-7$$\"$6
\"F*$\"+*\\^P]&F-7$$\"$7\"F*$\"+!>&=2bF-7$$\"$8\"F*$\"+*>++^&F-7$$\"$9
\"F*$\"+<pB7bF-7$$\"$:\"F*$\"+FO%R^&F-7$$\"$;\"F*$\"+;1<:bF-7$$\"$<\"F
*$\"+6t(f^&F-7$$\"$=\"F*$\"+tYU;bF-7$$\"$>\"F*$\"++Ce;bF-7$$\"$?\"F*$
\"+k'=l^&F-7$$\"$@\"F*$\"+ubI;bF-7$$\"$A\"F*$\"+,7-;bF-7$$\"$B\"F*$\"+
g4u:bF-7$$\"$C\"F*$\"+(fZb^&F-7$$\"$D\"F*$\"+ND_:bF-7$$\"$E\"F*$\"+ayu
:bF-7$$\"$F\"F*$\"+/lI;bF-7$$\"$G\"F*$\"+z)ys^&F-7$$\"$H\"F*$\"+oHu=bF
-7$$\"$I\"F*$\"+]sx?bF-7$$\"$J\"F*$\"+^WXBbF-7$$\"$K\"F*$\"+;`%o_&F-7$
$\"$L\"F*$\"+o'>5`&F-7$$\"$M\"F*$\"+>#Qg`&F-7$$\"$N\"F*$\"+K+'>a&F-7$$
\"$O\"F*$\"+0_$)[bF-7$$\"$P\"F*$\"+o&4nb&F-7$$\"$Q\"F*$\"+n>ilbF-7$$\"
$R\"F*$\"+^_gvbF-7$$\"$S\"F*$\"+\"o\"o'e&F-7$$\"$T\"F*$\"+b&o))f&F-7$$
\"$U\"F*$\"+9O<7cF-7$$\"$V\"F*$\"+C(*fEcF-7$$\"$W\"F*$\"+Fv8UcF-7$$\"$
X\"F*$\"+tGxecF-7$$\"$Y\"F*$\"+;/[wcF-7$$\"$Z\"F*$\"+\"3I_p&F-7$$\"$[
\"F*$\"+:D)\\r&F-7$$\"$\\\"F*$\"+cFpNdF-7$$\"$]\"F*$\"+@%3tv&F-7$$\"$^
\"F*$\"+/LxzdF-7$$\"$_\"F*$\"+jY-.eF-7$$\"$`\"F*$\"+%>$*p#eF-7$$\"$a\"
F*$\"+Flg^eF-7$$\"$b\"F*$\"+****yweF-7$$\"$c\"F*$\"+LRY-fF-7$$\"$d\"F*
$\"+.qaGfF-7$$\"$e\"F*$\"+!yd\\&fF-7$$\"$f\"F*$\"+U6h\")fF-7$$\"$g\"F*
$\"+fBU3gF-7$$\"$h\"F*$\"+-xINgF-7$$\"$i\"F*$\"+H]=igF-7$$\"$j\"F*$\"+
VN(*)3'F-7$$\"$k\"F*$\"+#=&f:hF-7$$\"$l\"F*$\"+[V(>9'F-7$$\"$m\"F*$\"+
To.ohF-7$$\"$n\"F*$\"+K_r$>'F-7$$\"$o\"F*$\"+oX%*=iF-7$$\"$p\"F*$\"+,h
mViF-7$$\"$q\"F*$\"+Xa#yE'F-7$$\"$r\"F*$\"+%yq8H'F-7$$\"$s\"F*$\"+*ofU
J'F-7$$\"$t\"F*$\"+`lXOjF-7$$\"$u\"F*$\"+?$HzN'F-7$$\"$v\"F*$\"+oRlyjF
-7$$\"$w\"F*$\"+tVh)R'F-7$$\"$x\"F*$\"+V\"*z<kF-7$$\"$y\"F*$\"+Vh?OkF-
7$$\"$z\"F*$\"+P'QQX'F-7$$\"$!=F*$\"+lvqqkF-7$$\"$\"=F*$\"+43$o['F-7$$
\"$#=F*$\"+([KA]'F-7$$\"$$=F*$\"+)yVp^'F-7$$\"$%=F*$\"+23+JlF-7$$\"$&=
F*$\"+j%[Wa'F-7$$\"$'=F*$\"+%RQtb'F-7$$\"$(=F*$\"+'4E(plF-7$$\"$)=F*$
\"+cTn\"e'F-7$$\"$*=F*$\"+h'[Kf'F-7$$\"$!>F*$\"+P4_/mF-7$$\"$\">F*$\"+
DZc:mF-7$$\"$#>F*$\"++(eki'F-7$$\"$$>F*$\"+2@GPmF-7$$\"$%>F*$\"+b!=\"[
mF-7$$\"$&>F*$\"+V90fmF-7$$\"$'>F*$\"+lo;qmF-7$$\"$(>F*$\"+(e\\:o'F-7$
$\"$)>F*$\"+x\\G$p'F-7$$\"$*>F*$\"+(ebaq'F-7$$\"$+#F*$\"+&4U\"=nF-7$$
\"$,#F*$\"+*oA9t'F-7$$\"$-#F*$\"+PCPXnF-7$$\"$.#F*$\"+6&f+w'F-7$$\"$/#
F*$\"+z2bvnF-7$$\"$0#F*$\"+*4/>z'F-7$$\"$1#F*$\"+4J<4oF-7$$\"$2#F*$\"+
V=SFoF-7$$\"$3#F*$\"+#HIm%oF-7$$\"$4#F*$\"+H#))o'oF-7$$\"$5#F*$\"+8%)>
))oF-7$$\"$6#F*$\"+(4v0\"pF-7$$\"$7#F*$\"+)4CS$pF-7$$\"$8#F*$\"+28aepF
-7$$\"$9#F*$\"+/V6%)pF-7$$\"$:#F*$\"+gis5qF-7$$\"$;#F*$\"+@vMQqF-7$$\"
$<#F*$\"+t-%p1(F-7$$\"$=#F*$\"+\"4gk4(F-7$$\"$>#F*$\"+Xf&o7(F-7$$\"$?#
F*$\"+)>q!erF-7$$\"$@#F*$\"+bj.!>(F-7$$\"$A#F*$\"+5]oAsF-7$$\"$B#F*$\"
+$GUfD(F-7$$\"$C#F*$\"+Vvs*G(F-7$$\"$D#F*$\"+-q&RK(F-7$$\"$E#F*$\"+%eV
&etF-7$$\"$F#F*$\"+c*)R$R(F-7$$\"$G#F*$\"+MEVGuF-7$$\"$H#F*$\"+HKbjuF-
7$$\"$I#F*$\"+^#o')\\(F-7$$\"$J#F*$\"+&p'oLvF-7$$\"$K#F*$\"+'[>&ovF-7$
$\"$L#F*$\"+)f!3.wF-7$$\"$M#F*$\"+USGPwF-7$$\"$N#F*$\"+j(\\5n(F-7$$\"$
O#F*$\"+%f)H/xF-7$$\"$P#F*$\"+F%fpt(F-7$$\"$Q#F*$\"+YN'*oxF-7$$\"$R#F*
$\"+F(\\-!yF-7$$\"$S#F*$\"+UEwIyF-7$$\"$T#F*$\"+2YXgyF-7$$\"$U#F*$\"+D
9G*)yF-7$$\"$V#F*$\"+&z1s\"zF-7$$\"$W#F*$\"+OM?WzF-7$$\"$X#F*$\"+S;Dqz
F-7$$\"$Y#F*$\"+kyL&*zF-7$$\"$Z#F*$\"+UsX>!)F-7$$\"$[#F*$\"+zGhU!)F-7$
$\"$\\#F*$\"+Oe\"[1)F-7$$\"$]#F*$\"+(\\%3'3)F-7$$\"$^#F*$\"+]_W1\")F-7
$$\"$_#F*$\"+UQ$f7)F-7$$\"$`#F*$\"+A(*eW\")F-7$$\"$a#F*$\"+z7Yi\")F-7$
$\"$b#F*$\"+qSgz\")F-7$$\"$c#F*$\"+hr2'>)F-7$$\"$d#F*$\"+wx%>@)F-7$$\"
$e#F*$\"+FqGF#)F-7$$\"$f#F*$\"+19<U#)F-7$$\"$g#F*$\"+E<oc#)F-7$$\"$h#F
*$\"+l?!4F)F-7$$\"$i#F*$\"+3(=\\G)F-7$$\"$j#F*$\"+j;#))H)F-7$$\"$k#F*$
\"+P(*p7$)F-7$$\"$l#F*$\"+I?kE$)F-7$$\"$m#F*$\"+'yQ2M)F-7$$\"$n#F*$\"+
l'z]N)F-7$$\"$o#F*$\"+%p](p$)F-7$$\"$p#F*$\"+$QO[Q)F-7$$\"$q#F*$\"+(H<
/S)F-7$$\"$r#F*$\"+d#olT)F-7$$\"$s#F*$\"+C<OL%)F-7$$\"$t#F*$\"+O9'3X)F
-7$$\"$u#F*$\"+<x7p%)F-7$$\"$v#F*$\"+T<@)[)F-7$$\"$w#F*$\"+E#e\"3&)F-7
$$\"$x#F*$\"+v[+H&)F-7$$\"$y#F*$\"+=#z2b)F-7$$\"$z#F*$\"+N1]t&)F-7$$\"
$!GF*$\"+z%yrf)F-7$$\"$\"GF*$\"+EZ\"=i)F-7$$\"$#GF*$\"+!Q.uk)F-7$$\"$$
GF*$\"+rm#Rn)F-7$$\"$%GF*$\"+%ef8q)F-7$$\"$&GF*$\"++nmH()F-7$$\"$'GF*$
\"+)R0)e()F-7$$\"$(GF*$\"+!fC()y)F-7$$\"$)GF*$\"+UsO>))F-7$$\"$*GF*$\"
+Fym]))F-7$$\"$!HF*$\"+,[b#)))F-7$$\"$\"HF*$\"+h6&\\\"*)F-7$$\"$#HF*$
\"+_PxZ*)F-7$$\"$$HF*$\"+bo$4)*)F-7$$\"$%HF*$\"+<-N9!*F-7$$\"$&HF*$\"+
]2#z/*F-7$$\"$'HF*$\"+sTb\"3*F-7$$\"$(HF*$\"+;[::\"*F-7$$\"$)HF*$\"+?m
i[\"*F-7$$\"$*HF*$\"+1N(==*F-7$$\"$+$F*$\"+&4-[@*F-7$$\"$,$F*$\"+T9KZ#
*F-7$$\"$-$F*$\"+/;Mz#*F-7$$\"$.$F*$\"+#*ox5$*F-7$$\"$/$F*$\"+6taT$*F-
7$$\"$0$F*$\"+jldr$*F-7$$\"$1$F*$\"+%3%z+%*F-7$$\"$2$F*$\"+_O8H%*F-7$$
\"$3$F*$\"+&pPlX*F-7$$\"$4$F*$\"+_`&H[*F-7$$\"$5$F*$\"+X6M3&*F-7$$\"$6
$F*$\"+a)fE`*F-7$$\"$7$F*$\"+3T)eb*F-7$$\"$8$F*$\"+PJ*zd*F-7$$\"$9$F*$
\"+;g(*)f*F-7$$\"$:$F*$\"+5)G)='*F-7$$\"$;$F*$\"+lybP'*F-7$$\"$<$F*$\"
+Bq<b'*F-7$$\"$=$F*$\"+`(3<n*F-7$$\"$>$F*$\"+(4$=(o*F-7$$\"$?$F*$\"+-s
j,(*F-7$$\"$@$F*$\"+Iw6:(*F-7$$\"$A$F*$\"+%=xws*F-7$$\"$B$F*$\"+ohPR(*
F-7$$\"$C$F*$\"+,)z-v*F-7$$\"$D$F*$\"+n+Yg(*F-7$$\"$E$F*$\"+s`**p(*F-7
$$\"$F$F*$\"+Xu'*y(*F-7$$\"$G$F*$\"+f:Y(y*F-7$$\"$H$F*$\"+ryc&z*F-7$$
\"$I$F*$\"+bmP.)*F-7$$\"$J$F*$\"+AC)4\")*F-7$$\"$K$F*$\"+%pz%=)*F-7$$
\"$L$F*$\"+jE'f#)*F-7$$\"$M$F*$\"+vU_L)*F-7$$\"$N$F*$\"+oeDT)*F-7$$\"$
O$F*$\"+#[[#\\)*F-7$$\"$P$F*$\"+^&)ed)*F-7$$\"$Q$F*$\"+$=fj')*F-7$$\"$
R$F*$\"+%\\Pc()*F-7$$\"$S$F*$\"+Lk\\&))*F-7$$\"$T$F*$\"+a4+'*)*F-7$$\"
$U$F*$\"+&Q5s!**F-7$$\"$V$F*$\"+oX<>**F-7$$\"$W$F*$\"+qn$>$**F-7$$\"$X
$F*$\"+O4`X**F-7$$\"$Y$F*$\"+b<)*f**F-7$$\"$Z$F*$\"+=ZIv**F-7$$\"$[$F*
$\"+kh]\"***F-7$$\"$\\$F*$\"+w#e3+\"!#67$$\"$]$F*$\"+4Al-5Fdhq7$$\"$^$
F*$\"+P/`/5Fdhq7$$\"$_$F*$\"+'z*[15Fdhq7$$\"$`$F*$\"+Uk_35Fdhq7$$\"$a$
F*$\"+eaj55Fdhq7$$\"$b$F*$\"+*H6G,\"Fdhq7$$\"$c$F*$\"+2v/:5Fdhq7$$\"$d
$F*$\"+`rL<5Fdhq7$$\"$e$F*$\"+QCn>5Fdhq7$$\"$f$F*$\"+#HX?-\"Fdhq7$$\"$
g$F*$\"+zpWC5Fdhq7$$\"$h$F*$\"+s&oo-\"Fdhq7$$\"$i$F*$\"+p1IH5Fdhq7$$\"
$j$F*$\"+aPtJ5Fdhq7$$\"$k$F*$\"+D\"eT.\"Fdhq7$$\"$l$F*$\"+ERcO5Fdhq7$$
\"$m$F*$\"+X9%*Q5Fdhq7$$\"$n$F*$\"+X6GT5Fdhq7$$\"$o$F*$\"+KNdV5Fdhq7$$
\"$p$F*$\"+Z%4e/\"Fdhq7$$\"$q$F*$\"+X,)z/\"Fdhq7$$\"$r$F*$\"+st2]5Fdhq
7$$\"$s$F*$\"+NK4_5Fdhq7$$\"$t$F*$\"+V0-a5Fdhq7$$\"$u$F*$\"+CE&e0\"Fdh
q7$$\"$v$F*$\"+2Med5Fdhq7$$\"$w$F*$\"+5x?f5Fdhq7$$\"$x$F*$\"+i4sg5Fdhq
7$$\"$y$F*$\"+Y&>@1\"Fdhq7$$\"$z$F*$\"+!e+M1\"Fdhq7$$\"$!QF*$\"+0?ck5F
dhq7$$\"$\"QF*$\"+zDgl5Fdhq7$$\"$#QF*$\"+q>_m5Fdhq7$$\"$$QF*$\"+c1Kn5F
dhq7$$\"$%QF*$\"+q***z1\"Fdhq7$$\"$&QF*$\"+d@co5Fdhq7$$\"$'QF*$\"+#Q5!
p5Fdhq7$$\"$(QF*$\"+&e[$p5Fdhq7$$\"$)QF*$\"+U9ep5Fdhq7$$\"$*QF*$\"+\"Q
9(p5Fdhq7$$\"$!RF*$\"+[Nvp5Fdhq7$$\"$\"RF*$\"+Cdqp5Fdhq7$$\"$#RF*$\"+V
#y&p5Fdhq7$$\"$$RF*$\"+;\"z$p5Fdhq7$$\"$%RF*$\"+*z;\"p5Fdhq7$$\"$&RF*$
\"+o,!)o5Fdhq7$$\"$'RF*$\"+M$Q%o5Fdhq7$$\"$(RF*$\"+@2/o5Fdhq7$$\"$)RF*
$\"+#)ohn5Fdhq7$$\"$*RF*$\"+sk<n5Fdhq7$$\"$+%F*$\"+:\"Hn1\"Fdhq7$$\"$,
%F*$\"+BWGm5Fdhq7$$\"$-%F*$\"+7=&e1\"Fdhq7$$\"$.%F*$\"+=0Wl5Fdhq7$$\"$
/%F*$\"+3%f]1\"Fdhq7$$\"$0%F*$\"+*)ork5Fdhq7$$\"$1%F*$\"+q3Uk5Fdhq7$$
\"$2%F*$\"+C(yT1\"Fdhq7$$\"$3%F*$\"+Xs*R1\"Fdhq7$$\"$4%F*$\"+[C)Q1\"Fd
hq7$$\"$5%F*$\"+H'RQ1\"Fdhq7$$\"$6%F*$\"+4J(Q1\"Fdhq7$$\"$7%F*$\"+]k)R
1\"Fdhq7$$\"$8%F*$\"+hC=k5Fdhq7$$\"$9%F*$\"+IGYk5Fdhq7$$\"$:%F*$\"+%RG
[1\"Fdhq7$$\"$;%F*$\"+D*y_1\"Fdhq7$$\"$<%F*$\"+XL\"e1\"Fdhq7$$\"$=%F*$
\"+s'Hk1\"Fdhq7$$\"$>%F*$\"+h[7n5Fdhq7$$\"$?%F*$\"+r^*y1\"Fdhq7$$\"$@%
F*$\"+#zN(o5Fdhq7$$\"$A%F*$\"+47kp5Fdhq7$$\"$B%F*$\"+W^gq5Fdhq7$$\"$C%
F*$\"+d2ir5Fdhq7$$\"$D%F*$\"+\"[!os5Fdhq7$$\"$E%F*$\"+ohxt5Fdhq7$$\"$F
%F*$\"+L#**[2\"Fdhq7$$\"$G%F*$\"+\"pSg2\"Fdhq7$$\"$H%F*$\"+&>\">x5Fdhq
7$$\"$I%F*$\"+E8My5Fdhq7$$\"$J%F*$\"+t9[z5Fdhq7$$\"$K%F*$\"+j=g!3\"Fdh
q7$$\"$L%F*$\"+)*Gp\"3\"Fdhq7$$\"$M%F*$\"+y\\u#3\"Fdhq7$$\"$N%F*$\"+&y
[P3\"Fdhq7$$\"$O%F*$\"+/_p%3\"Fdhq7$$\"$P%F*$\"+/bd&3\"Fdhq7$$\"$Q%F*$
\"+9:Q'3\"Fdhq7$$\"$R%F*$\"+(H0r3\"Fdhq7$$\"$S%F*$\"+G(Rx3\"Fdhq7$$\"$
T%F*$\"+s#y#)3\"Fdhq7$$\"$U%F*$\"+7]r)3\"Fdhq7$$\"$V%F*$\"+z[/*3\"Fdhq
7$$\"$W%F*$\"+(Qj#*3\"Fdhq7$$\"$X%F*$\"+9qO*3\"Fdhq7$$\"$Y%F*$\"+%z_$*
3\"Fdhq7$$\"$Z%F*$\"+-)=#*3\"Fdhq7$$\"$[%F*$\"+*4k*)3\"Fdhq7$$\"$\\%F*
$\"+z%)e)3\"Fdhq7$$\"$]%F*$\"+>D4)3\"Fdhq7$$\"$^%F*$\"+GyZ(3\"Fdhq7$$
\"$_%F*$\"+dnu'3\"Fdhq7$$\"$`%F*$\"+`D!f3\"Fdhq7$$\"$a%F*$\"+t$\\\\3\"
Fdhq7$$\"$b%F*$\"+,?*Q3\"Fdhq7$$\"$c%F*$\"+4gt#3\"Fdhq7$$\"$d%F*$\"+!o
([\"3\"Fdhq7$$\"$e%F*$\"+ER:!3\"Fdhq7$$\"$f%F*$\"+8Cuy5Fdhq7$$\"$g%F*$
\"+!=hs2\"Fdhq7$$\"$h%F*$\"+n)=d2\"Fdhq7$$\"$i%F*$\"+&QCT2\"Fdhq7$$\"$
j%F*$\"+!*p[s5Fdhq7$$\"$k%F*$\"+1h\"32\"Fdhq7$$\"$l%F*$\"++97p5Fdhq7$$
\"$m%F*$\"+.FTn5Fdhq7$$\"$n%F*$\"+C(*pl5Fdhq7$$\"$o%F*$\"+D@*R1\"Fdhq7
$$\"$p%F*$\"+$Q*Hi5Fdhq7$$\"$q%F*$\"+02jg5Fdhq7$$\"$r%F*$\"+)4&**e5Fdh
q7$$\"$s%F*$\"+m4Sd5Fdhq7$$\"$t%F*$\"+zi&e0\"Fdhq7$$\"$u%F*$\"+![oV0\"
Fdhq7$$\"$v%F*$\"+QV%H0\"Fdhq7$$\"$w%F*$\"+g+f^5Fdhq7$$\"$x%F*$\"+u3J]
5Fdhq7$$\"$y%F*$\"+%>6\"\\5Fdhq7$$\"$z%F*$\"+qX*z/\"Fdhq7$$\"$![F*$\"+
!pjp/\"Fdhq7$$\"$\"[F*$\"+)[?g/\"Fdhq7$$\"$#[F*$\"+kc;X5Fdhq7$$\"$$[F*
$\"+t#*RW5Fdhq7$$\"$%[F*$\"+%=?P/\"Fdhq7$$\"$&[F*$\"+ek7V5Fdhq7$$\"$'[
F*$\"+'G:E/\"Fdhq7$$\"$([F*$\"+NH=U5Fdhq7$$\"$)[F*$\"+$zC=/\"Fdhq7$$\"
$*[F*$\"+zb`T5Fdhq7$$\"$!\\F*$\"+t\"48/\"Fdhq7$$\"$\"\\F*$\"+;(Q6/\"Fd
hq7$$\"$#\\F*$\"+>p,T5Fdhq7$$\"$$\\F*$\"+Xf$4/\"Fdhq7$$\"$%\\F*$\"+Tt)
3/\"Fdhq7$$\"$&\\F*$\"+_C'3/\"Fdhq7$$\"$'\\F*$\"+UA&3/\"Fdhq7$$\"$(\\F
*$\"+'QZ3/\"Fdhq7$$\"$)\\F*$\"+g%Q3/\"Fdhq7$$\"$*\\F*$\"+\"3;3/\"Fdhq7
$$\"$+&F*$\"+y2xS5Fdhq7$$\"$,&F*$\"+NKpS5Fdhq7$$\"$-&F*$\"+qVdS5Fdhq7$
$\"$.&F*$\"+9`SS5Fdhq7$$\"$/&F*$\"+*px,/\"Fdhq7$$\"$0&F*$\"+FM))R5Fdhq
7$$\"$1&F*$\"+`[^R5Fdhq7$$\"$2&F*$\"+y]1R5Fdhq7$$\"$3&F*$\"+7w_Q5Fdhq7
$$\"$4&F*$\"+?n*y.\"Fdhq7$$\"$5&F*$\"+_t;P5Fdhq7$$\"$6&F*$\"+H_LO5Fdhq
7$$\"$7&F*$\"+ynRN5Fdhq7$$\"$8&F*$\"+w#\\V.\"Fdhq7$$\"$9&F*$\"+%*3>L5F
dhq7$$\"$:&F*$\"+O0#>.\"Fdhq7$$\"$;&F*$\"+Ny`I5Fdhq7$$\"$<&F*$\"+lM/H5
Fdhq7$$\"$=&F*$\"+!**Qu-\"Fdhq7$$\"$>&F*$\"+5msD5Fdhq7$$\"$?&F*$\"+%[4
R-\"Fdhq7$$\"$@&F*$\"+v8*>-\"Fdhq7$$\"$A&F*$\"+'3x*>5Fdhq7$$\"$B&F*$\"
+Z=(y,\"Fdhq7$$\"$C&F*$\"+7>o:5Fdhq7$$\"$D&F*$\"++RT85Fdhq7$$\"$E&F*$
\"+J^265Fdhq7$$\"$F&F*$\"+\"Gt'35Fdhq7$$\"$G&F*$\"+yn@15Fdhq7$$\"$H&F*
$\"+.Wr.5Fdhq7$$\"$I&F*$\"+d^<,5Fdhq7$$\"$J&F*$\"+dL3')**F-7$$\"$K&F*$
\"+2XBg**F-7$$\"$L&F*$\"+)*3IM**F-7$$\"$M&F*$\"+pxP3**F-7$$\"$N&F*$\"+
B5c#))*F-7$$\"$O&F*$\"+,e%p&)*F-7$$\"$P&F*$\"+cLiJ)*F-7$$\"$Q&F*$\"+IM
o1)*F-7$$\"$R&F*$\"+s5@#y*F-7$$\"$S&F*$\"+TcGe(*F-7$$\"$T&F*$\"+J?)\\t
*F-7$$\"$U&F*$\"+T'pBr*F-7$$\"$V&F*$\"+)=50p*F-7$$\"$W&F*$\"+B$e%p'*F-
7$$\"$X&F*$\"+-6E\\'*F-7$$\"$Y&F*$\"+9!e*H'*F-7$$\"$Z&F*$\"+v#z:h*F-7$
$\"$[&F*$\"+Fe9%f*F-7$$\"$\\&F*$\"+^5nx&*F-7$$\"$]&F*$\"+#Hd@c*F-7$$\"
$^&F*$\"+[/gZ&*F-7$$\"$_&F*$\"+mk)R`*F-7$$\"$`&F*$\"+v=H@&*F-7$$\"$a&F
*$\"+ta[4&*F-7$$\"$b&F*$\"+0r_)\\*F-7$$\"$c&F*$\"+s\"o$)[*F-7$$\"$d&F*
$\"+#H`*y%*F-7$$\"$e&F*$\"+/-Aq%*F-7$$\"$f&F*$\"+D35i%*F-7$$\"$g&F*$\"
+O6_a%*F-7$$\"$h&F*$\"+5ASZ%*F-7$$\"$i&F*$\"+\\1mS%*F-7$$\"$j&F*$\"+g,
@M%*F-7$$\"$k&F*$\"+5J'zU*F-7$$\"$l&F*$\"+T!G=U*F-7$$\"$m&F*$\"+\"39dT
*F-7$$\"$n&F*$\"+1!H&4%*F-7$$\"$o&F*$\"+@8=.%*F-7$$\"$p&F*$\"+31e'R*F-
7$$\"$q&F*$\"+P,k*Q*F-7$$\"$r&F*$\"+!\\vAQ*F-7$$\"$s&F*$\"+QgSu$*F-7$$
\"$t&F*$\"+v_&fO*F-7$$\"$u&F*$\"+aG&oN*F-7$$\"$v&F*$\"+.Q.Z$*F-7$$\"$w
&F*$\"+G$QkL*F-7$$\"$x&F*$\"+@L,D$*F-7$$\"$y&F*$\"+cFr7$*F-7$$\"$z&F*$
\"+7k\\*H*F-7$$\"$!eF*$\"+KJL&G*F-7$$\"$\"eF*$\"+r%)>q#*F-7$$\"$#eF*$
\"+<j2a#*F-7$$\"$$eF*$\"+\\)epB*F-7$$\"$%eF*$\"+%4Z)=#*F-7$$\"$&eF*$\"
+!p[(*>*F-7$$\"$'eF*$\"+*>!oz\"*F-7$$\"$(eF*$\"+dgme\"*F-7$$\"$)eF*$\"
+F)Rn8*F-7$$\"$*eF*$\"+`.%R6*F-7$$\"$!fF*$\"+/UJ!4*F-7$$\"$\"fF*$\"+ST
\"f1*F-7$$\"$#fF*$\"+r/!3/*F-7$$\"$$fF*$\"+,%Q],*F-7$$\"$%fF*$\"+A%*p)
)*)F-7$$\"$&fF*$\"+2/'='*)F-7$$\"$'fF*$\"+P:gM*)F-7$$\"$(fF*$\"+Qr+2*)
F-7$$\"$)fF*$\"+j`;z))F-7$$\"$*fF*$\"+ws;^))F-7$$\"$+'F*$\"+FN5B))F-7$
$\"$,'F*$\"+wj1&z)F-7$$\"$-'F*$\"+N*\\rw)F-7$$\"$.'F*$\"+]bWR()F-7$$\"
$/'F*$\"+5Q/7()F-7$$\"$0'F*$\"+mf.&o)F-7$$\"$1'F*$\"+3h]e')F-7$$\"$2'F
*$\"+So`K')F-7$$\"$3'F*$\"+7j?2')F-7$$\"$4'F*$\"+tqe#e)F-7$$\"$5'F*$\"
+tnue&)F-7$$\"$6'F*$\"+7duN&)F-7$$\"$7'F*$\"+Oij8&)F-7$$\"$8'F*$\"+YfY
#\\)F-7$$\"$9'F*$\"+%)>Fs%)F-7$$\"$:'F*$\"+<U3`%)F-7$$\"$;'F*$\"+^R#\\
V)F-7$$\"$<'F*$\"+Se!yT)F-7$$\"$='F*$\"+_Lt,%)F-7$$\"$>'F*$\"+k1q'Q)F-
7$$\"$?'F*$\"+2Rps$)F-7$$\"$@'F*$\"+@6pf$)F-7$$\"$A'F*$\"+)*3mZ$)F-7$$
\"$B'F*$\"+kUcO$)F-7$$\"$C'F*$\"+gRNE$)F-7$$\"$D'F*$\"+cp(pJ)F-7$$\"$E
'F*$\"+7CP3$)F-7$$\"$F'F*$\"+vTZ+$)F-7$$\"$G'F*$\"+<+@$H)F-7$$\"$H'F*$
\"+-T]'G)F-7$$\"$I'F*$\"+4\\F!G)F-7$$\"$J'F*$\"+,'RWF)F-7$$\"$K'F*$\"+
z7\"*o#)F-7$$\"$L'F*$\"+F?gj#)F-7$$\"$M'F*$\"+=FUe#)F-7$$\"$N'F*$\"+;G
G`#)F-7$$\"$O'F*$\"+EF4[#)F-7$$\"$P'F*$\"+YnwU#)F-7$$\"$Q'F*$\"+#Q=sB)
F-7$$\"$R'F*$\"+sEOJ#)F-7$$\"$S'F*$\"+(Q?^A)F-7$$\"$T'F*$\"+#)eT=#)F-7
$$\"$U'F*$\"+8v<6#)F-7$$\"$V'F*$\"+p'QL?)F-7$$\"$W'F*$\"+qv$[>)F-7$$\"
$X'F*$\"+2-i&=)F-7$$\"$Y'F*$\"+cwjv\")F-7$$\"$Z'F*$\"+D%[[;)F-7$$\"$['
F*$\"+\\*=K:)F-7$$\"$\\'F*$\"+aGsS\")F-7$$\"$]'F*$\"+D'Rt7)F-7$$\"$^'F
*$\"+#pdI6)F-7$$\"$_'F*$\"+]J(y4)F-7$$\"$`'F*$\"+V\"*y\"3)F-7$$\"$a'F*
$\"+jr\"[1)F-7$$\"$b'F*$\"+$fup/)F-7$$\"$c'F*$\"+q)*GG!)F-7$$\"$d'F*$
\"+`cz3!)F-7$$\"$e'F*$\"+1:`))zF-7$$\"$f'F*$\"+f`anzF-7$$\"$g'F*$\"+;0
*e%zF-7$$\"$h'F*$\"+=liBzF-7$$\"$i'F*$\"+P(=3!zF-7$$\"$j'F*$\"+&oOv(yF
-7$$\"$k'F*$\"+Ai&Q&yF-7$$\"$l'F*$\"+*fa)HyF-7$$\"$m'F*$\"+sEh0yF-7$$
\"$n'F*$\"+'\\;7y(F-7$$\"$o'F*$\"+COvcxF-7$$\"$p'F*$\"+aLJKxF-7$$\"$q'
F*$\"+zU)zq(F-7$$\"$r'F*$\"+t^&Qo(F-7$$\"$s'F*$\"+VQ,gwF-7$$\"$t'F*$\"
+EmaOwF-7$$\"$u'F*$\"+c#RNh(F-7$$\"$v'F*$\"+yG2\"f(F-7$$\"$w'F*$\"+YiA
pvF-7$$\"$x'F*$\"+V42[vF-7$$\"$y'F*$\"+]UnFvF-7$$\"$z'F*$\"+,y43vF-7$$
\"$!oF*$\"+SwR*[(F-7$$\"$\"oF*$\"+SNiruF-7$$\"$#oF*$\"+wo\"[X(F-7$$\"$
$oF*$\"+S8,RuF-7$$\"$%oF*$\"+5ABCuF-7$$\"$&oF*$\"+Fj\\5uF-7$$\"$'oF*$
\"+=N\"yR(F-7$$\"$(oF*$\"+jO='Q(F-7$$\"$)oF*$\"+2\")fvtF-7$$\"$*oF*$\"
+o5/mtF-7$$\"$!pF*$\"+ym[dtF-7$$\"$\"pF*$\"+!Q+*\\tF-7$$\"$#pF*$\"+(yT
KM(F-7$$\"$$pF*$\"+\"phuL(F-7$$\"$%pF*$\"+CF]KtF-7$$\"$&pF*$\"+nVIGtF-
7$$\"$'pF*$\"+$[)zCtF-7$$\"$(pF*$\"+[G\">K(F-7$$\"$)pF*$\"+c)o&>tF-7$$
\"$*pF*$\"+fko<tF-7$$\"$+(F*$\"++/=;tF-7$$\"$,(F*$\"+HA'\\J(F-7$$\"$-(
F*$\"+a^%RJ(F-7$$\"$.(F*$\"+>)QIJ(F-7$$\"$/(F*$\"+:M:7tF-7$$\"$0(F*$\"
+i,?6tF-7$$\"$1(F*$\"+$4\"45tF-7$$\"$2(F*$\"+T-u3tF-7$$\"$3(F*$\"+Gi12
tF-7$$\"$4(F*$\"+.#*)\\I(F-7$$\"$5(F*$\"+GMV-tF-7$$\"$6(F*$\"+]xK*H(F-
7$$\"$7(F*$\"+y`g&H(F-7$$\"$8(F*$\"+p]?\"H(F-7$$\"$9(F*$\"+>I2'G(F-7$$
\"$:(F*$\"+&Gh,G(F-7$$\"$;(F*$\"+PpUtsF-7$$\"$<(F*$\"+*4OeE(F-7$$\"$=(
F*$\"+f'ftD(F-7$$\"$>(F*$\"+lt(zC(F-7$$\"$?(F*$\"+()\\nPsF-7$$\"$@(F*$
\"+&QYkA(F-7$$\"$A(F*$\"+1\\H9sF-7$$\"$B(F*$\"+]#H7?(F-7$$\"$C(F*$\"+K
xE(=(F-7$$\"$D(F*$\"+$>MC<(F-7$$\"$E(F*$\"+I-wcrF-7$$\"$F(F*$\"+`RGSrF
-7$$\"$G(F*$\"+n,0BrF-7$$\"$H(F*$\"+q)4^5(F-7$$\"$I(F*$\"+`!>l3(F-7$$
\"$J(F*$\"+0=MnqF-7$$\"$K(F*$\"+^bkZqF-7$$\"$L(F*$\"+0U]FqF-7$$\"$M(F*
$\"+)4%*p+(F-7$$\"$N(F*$\"+g\\>')pF-7$$\"$O(F*$\"+;()=lpF-7$$\"$P(F*$
\"+s>1WpF-7$$\"$Q(F*$\"+)3,H#pF-7$$\"$R(F*$\"+WJz,pF-7$$\"$S(F*$\"+@p#
3)oF-7$$\"$T(F*$\"+'e)3goF-7$$\"$U(F*$\"+QTmRoF-7$$\"$V(F*$\"+_dj>oF-7
$$\"$W(F*$\"+QM3+oF-7$$\"$X(F*$\"+^G3\"y'F-7$$\"$Y(F*$\"+`hqinF-7$$\"$
Z(F*$\"+1@-XnF-7$$\"$[(F*$\"+*y$4GnF-7$$\"$\\(F*$\"+ca(>r'F-7$$\"$](F*
$\"+;\\r'p'F-7$$\"$^(F*$\"+YVN#o'F-7$$\"$_(F*$\"+*3F*omF-7$$\"$`(F*$\"
+T#fkl'F-7$$\"$a(F*$\"+-s'\\k'F-7$$\"$b(F*$\"+p+YMmF-7$$\"$c(F*$\"+!zQ
\\i'F-7$$\"$d(F*$\"+(o$R;mF-7$$\"$e(F*$\"+Xo!)3mF-7$$\"$f(F*$\"+\")G:-
mF-7$$\"$g(F*$\"+p!)R'f'F-7$$\"$h(F*$\"+/6]\"f'F-7$$\"$i(F*$\"+nYT(e'F
-7$$\"$j(F*$\"+)G\"3%e'F-7$$\"$k(F*$\"+y(R9e'F-7$$\"$l(F*$\"+z5UzlF-7$
$\"$m(F*$\"+DA&zd'F-7$$\"$n(F*$\"+:a&pd'F-7$$\"$o(F*$\"+-([jd'F-7$$\"$
p(F*$\"+hm/wlF-7$$\"$q(F*$\"+W='fd'F-7$$\"$r(F*$\"+3a+wlF-7$$\"$s(F*$
\"+Ex3wlF-7$$\"$t(F*$\"+!>=hd'F-7$$\"$u(F*$\"+>U+wlF-7$$\"$v(F*$\"+C0m
vlF-7$$\"$w(F*$\"+e4+vlF-7$$\"$x(F*$\"+n1%Rd'F-7$$\"$y(F*$\"+]0SslF-7$
$\"$z(F*$\"+;iIqlF-7$$\"$!yF*$\"+;aenlF-7$$\"$\"yF*$\"+<<<klF-7$$\"$#y
F*$\"+DF+glF-7$$\"$$yF*$\"+EX-blF-7$$\"$%yF*$\"+Iw=\\lF-7$$\"$&yF*$\"+
q1XUlF-7$$\"$'yF*$\"+$[zZ`'F-7$$\"$(yF*$\"+Ji9ElF-7$$\"$)yF*$\"+I;`;lF
-7$$\"$*yF*$\"+Y5#f]'F-7$$\"$!zF*$\"+A$3V\\'F-7$$\"$\"zF*$\"+hlp\"['F-
7$$\"$#zF*$\"+#3&4okF-7$$\"$$zF*$\"+V5_`kF-7$$\"$%zF*$\"+q()*zV'F-7$$
\"$&zF*$\"+y1c@kF-7$$\"$'zF*$\"+?VC/kF-7$$\"$(zF*$\"+ET4'Q'F-7$$\"$)zF
*$\"+C;;njF-7$$\"$*zF*$\"+'*[]ZjF-7$$\"$+)F*$\"+Xs=FjF-7$$\"$,)F*$\"+f
uF1jF-7$$\"$-)F*$\"+\"[[[G'F-7$$\"$.)F*$\"+(oxHE'F-7$$\"$/)F*$\"+FZuSi
F-7$$\"$0)F*$\"+/EB=iF-7$$\"$1)F*$\"+Dr_&>'F-7$$\"$2)F*$\"+8IrshF-7$$
\"$3)F*$\"+o*z)\\hF-7$$\"$4)F*$\"+nq6FhF-7$$\"$5)F*$\"+8@^/hF-7$$\"$6)
F*$\"+0=:#3'F-7$$\"$7)F*$\"+]57ggF-7$$\"$8)F*$\"+m8]QgF-7$$\"$9)F*$\"+
>,P<gF-7$$\"$:)F*$\"+'[,o*fF-7$$\"$;)F*$\"+$)Q'o(fF-7$$\"$<)F*$\"+=#=w
&fF-7$$\"$=)F*$\"+n97RfF-7$$\"$>)F*$\"+9\\U@fF-7$$\"$?)F*$\"+V0d/fF-7$
$\"$@)F*$\"+FYf))eF-7$$\"$A)F*$\"+tS_teF-7$$\"$B)F*$\"+0#y$feF-7$$\"$C
)F*$\"+/y;YeF-7$$\"$D)F*$\"+p]*Q$eF-7$$\"$E)F*$\"+'[aD#eF-7$$\"$F)F*$
\"+P487eF-7$$\"$G)F*$\"+a'*f-eF-7$$\"$H)F*$\"+6!GRz&F-7$$\"$I)F*$\"+qa
2'y&F-7$$\"$J)F*$\"+FN**ydF-7$$\"$K)F*$\"+U$HEx&F-7$$\"$L)F*$\"+`5#pw&
F-7$$\"$M)F*$\"+CB!=w&F-7$$\"$N)F*$\"+D8?ddF-7$$\"$O)F*$\"+$RVIv&F-7$$
\"$P)F*$\"+y!\\#\\dF-7$$\"$Q)F*$\"+lntXdF-7$$\"$R)F*$\"+A;UUdF-7$$\"$S
)F*$\"+ea@RdF-7$$\"$T)F*$\"+w5.OdF-7$$\"$U)F*$\"+l?yKdF-7$$\"$V)F*$\"+
.<QHdF-7$$\"$W)F*$\"+5suDdF-7$$\"$X)F*$\"+Rfz@dF-7$$\"$Y)F*$\"+'\\]ur&
F-7$$\"$Z)F*$\"+vJj7dF-7$$\"$[)F*$\"+o,F2dF-7$$\"$\\)F*$\"+dRH,dF-7$$
\"$])F*$\"+C8k%p&F-7$$\"$^)F*$\"+s[D(o&F-7$$\"$_)F*$\"+CG3zcF-7$$\"$`)
F*$\"+o03qcF-7$$\"$a)F*$\"+X(3-m&F-7$$\"$b)F*$\"+`[V\\cF-7$$\"$c)F*$\"
+')RtPcF-7$$\"$d)F*$\"+.q3DcF-7$$\"$e)F*$\"+)fz9h&F-7$$\"$f)F*$\"+Y$3p
f&F-7$$\"$g)F*$\"+BsP\"e&F-7$$\"$h)F*$\"+on*[c&F-7$$\"$i)F*$\"+E][ZbF-
7$$\"$j)F*$\"+!*e;HbF-7$$\"$k)F*$\"+.,(*4bF-7$$\"$l)F*$\"+)HO**[&F-7$$
\"$m)F*$\"+Ww5paF-7$$\"$n)F*$\"+/c`ZaF-7$$\"$o)F*$\"+2dFDaF-7$$\"$p)F*
$\"+y')Q-aF-7$$\"$q)F*$\"+(pS*y`F-7$$\"$r)F*$\"+a=+b`F-7$$\"$s)F*$\"+8
kkI`F-7$$\"$t)F*$\"+R7&fI&F-7$$\"$u)F*$\"+0q*4G&F-7$$\"$v)F*$\"+w%oeD&
F-7$$\"$w)F*$\"+l>lI_F-7$$\"$x)F*$\"+xOV0_F-7$$\"$y)F*$\"+^*)H!=&F-7$$
\"$z)F*$\"+*QM`:&F-7$$\"$!))F*$\"+7riI^F-7$$\"$\"))F*$\"+E!fi5&F-7$$\"
$#))F*$\"+f[J#3&F-7$$\"$$))F*$\"+i8()e]F-7$$\"$%))F*$\"+xV+O]F-7$$\"$&
))F*$\"+sQy8]F-7$$\"$'))F*$\"+n!yA*\\F-7$$\"$())F*$\"+@tar\\F-7$$\"$))
)F*$\"+$>Y;&\\F-7$$\"$*))F*$\"+W8iK\\F-7$$\"$!*)F*$\"+eY^9\\F-7$$\"$\"
*)F*$\"+=!ft*[F-7$$\"$#*)F*$\"+\"\\#=\")[F-7$$\"$$*)F*$\"+xS+m[F-7$$\"
$%*)F*$\"+[O$=&[F-7$$\"$&*)F*$\"+5>nQ[F-7$$\"$'*)F*$\"+I9^E[F-7$$\"$(*
)F*$\"+X(Q`\"[F-7$$\"$)*)F*$\"+![O^![F-7$$\"$**)F*$\"+XO(ez%F-7$$\"$+*
F*$\"+8U^(y%F-7$$\"$,*F*$\"+5g,!y%F-7$$\"$-*F*$\"+q1LtZF-7$$\"$.*F*$\"
+TdSnZF-7$$\"$/*F*$\"+#Hz@w%F-7$$\"$0*F*$\"+.%)edZF-7$$\"$1*F*$\"+jPc`
ZF-7$$\"$2*F*$\"+#yK+v%F-7$$\"$3*F*$\"+)oBpu%F-7$$\"$4*F*$\"+*=hTu%F-7
$$\"$5*F*$\"+K%o;u%F-7$$\"$6*F*$\"+#)*p$RZF-7$$\"$7*F*$\"+_k=PZF-7$$\"
$8*F*$\"+EO/NZF-7$$\"$9*F*$\"+`g'Gt%F-7$$\"$:*F*$\"+lHeIZF-7$$\"$;*F*$
\"+iR7GZF-7$$\"$<*F*$\"+TGUDZF-7$$\"$=*F*$\"+GtTAZF-7$$\"$>*F*$\"+`e/>
ZF-7$$\"$?*F*$\"+\"Gb_r%F-7$$\"$@*F*$\"+tc*4r%F-7$$\"$A*F*$\"+\"3@iq%F
-7$$\"$B*F*$\"+uA*3q%F-7$$\"$C*F*$\"+(ft\\p%F-7$$\"$D*F*$\"+,nV)o%F-7$
$\"$E*F*$\"+G%e7o%F-7$$\"$F*F*$\"+Z;UtYF-7$$\"$G*F*$\"+#3<\\m%F-7$$\"$
H*F*$\"+\"QQdl%F-7$$\"$I*F*$\"+6p)ek%F-7$$\"$J*F*$\"+Q<PNYF-7$$\"$K*F*
$\"+;n?CYF-7$$\"$L*F*$\"+g&4Ch%F-7$$\"$M*F*$\"+Ux++YF-7$$\"$N*F*$\"+<)
Hqe%F-7$$\"$O*F*$\"+`L^tXF-7$$\"$P*F*$\"+B#)\\fXF-7$$\"$Q*F*$\"+qE.XXF
-7$$\"$R*F*$\"+k&p,`%F-7$$\"$S*F*$\"+JY'\\^%F-7$$\"$T*F*$\"+YwZ*\\%F-7
$$\"$U*F*$\"+p;x$[%F-7$$\"$V*F*$\"+Bj\"zY%F-7$$\"$W*F*$\"+)*H)>X%F-7$$
\"$X*F*$\"+^S/OWF-7$$\"$Y*F*$\"+Oh<?WF-7$$\"$Z*F*$\"+%=`WS%F-7$$\"$[*F
*$\"+3R&*)Q%F-7$$\"$\\*F*$\"+L*ePP%F-7$$\"$]*F*$\"+pn%*eVF-7$$\"$^*F*$
\"+xrfWVF-7$$\"$_*F*$\"+rfyIVF-7$$\"$`*F*$\"+x0f<VF-7$$\"$a*F*$\"+SZ30
VF-7$$\"$b*F*$\"+A(RLH%F-7$$\"$c*F*$\"+4WU#G%F-7$$\"$d*F*$\"+Z?SsUF-7$
$\"$e*F*$\"+DDLjUF-7$$\"$f*F*$\"+;8FbUF-7$$\"$g*F*$\"+#Qo#[UF-7$$\"$h*
F*$\"+'>oBC%F-7$$\"$i*F*$\"+<'3wB%F-7$$\"$j*F*$\"+)>BSB%F-7$$\"$k*F*$
\"+)HM;B%F-7$$\"$l*F*$\"+N)e/B%F-7$$\"$m*F*$\"+*)f]IUF-7$$\"$n*F*$\"+K
=yJUF-7$$\"$o*F*$\"+lNGMUF-7$$\"$p*F*$\"+'Q)*zB%F-7$$\"$q*F*$\"+s:\"HC
%F-7$$\"$r*F*$\"+Oh**[UF-7$$\"$s*F*$\"+`(>iD%F-7$$\"$t*F*$\"+MqakUF-7$
$\"$u*F*$\"+\"pKRF%F-7$$\"$v*F*$\"+>1L%G%F-7$$\"$w*F*$\"+APo&H%F-7$$\"
$x*F*$\"+AS$zI%F-7$$\"$y*F*$\"+O9-@VF-7$$\"$z*F*$\"+\"4x[L%F-7$$\"$!)*
F*$\"+$4K%\\VF-7$$\"$\")*F*$\"+ithkVF-7$$\"$#)*F*$\"+T-O!Q%F-7$$\"$$)*
F*$\"+Hle'R%F-7$$\"$%)*F*$\"+/NA8WF-7$$\"$&)*F*$\"+V')>IWF-7$$\"$')*F*
$\"+c_VZWF-7$$\"$()*F*$\"+N1'[Y%F-7$$\"$))*F*$\"+HZS#[%F-7$$\"$*)*F*$
\"+Ry***\\%F-7$$\"$!**F*$\"+RWd<XF-7$$\"$\"**F*$\"+'))o]`%F-7$$\"$#**F
*$\"+w6U_XF-7$$\"$$**F*$\"+<<dpXF-7$$\"$%**F*$\"+&*zY'e%F-7$$\"$&**F*$
\"+!QgIg%F-7$$\"$'**F*$\"+N[I>YF-7$$\"$(**F*$\"+%zf^j%F-7$$\"$)**F*$\"
+S)*e]YF-7$$\"$***F*$\"+[EclYF-7$$\"%+5F*$\"+tk0!o%F-" 1 2 0 1 10 0 2 
9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 78 "eval(sol[1,1]);listplot([eval(seq([sol[2,1]
[i,1],sol[2,1][i,11]],i=1..500))]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#-%'vectorG6#7/%\"tG%#p1G%#p2G%#p3G%#p4G%#p5G%#p6G%#q1G%#q2G%#q3G%#q4G
%#q5G%#q6G" }}{PARA 13 "" 1 "" {GLPLOT2D 683 683 683 {PLOTDATA 2 "6#-%
'CURVESG6#7`jl7$$\"\"!F)$\"+++++]!#77$$\"+++++5!#5$\"+TSjW]F,7$$\"++++
+?F0$\"+J(yZ9&F,7$$\"+++++IF0$\"+3NsF_F,7$$\"+++++SF0$\"+(\\ezB&F,7$$F
+F0$\"+d'Q[<&F,7$$\"+++++gF0$\"+SPQ$4&F,7$$\"+++++qF0$\"+4fRo]F,7$$\"+
++++!)F0$\"+SaSR^F,7$$\"+++++!*F0$\"+bPPz_F,7$$\"\"\"F)$\"+3>7>aF,7$$
\"+++++6!\"*$\"+S_H,bF,7$$\"+++++7F\\o$\"+r:g>bF,7$$\"+++++8F\\o$\"+(
\\tP_&F,7$$\"+++++9F\\o$\"+&*)Rye&F,7$$\"+++++:F\\o$\"+E,zbdF,7$$\"+++
++;F\\o$\"+X:A0gF,7$$\"+++++<F\\o$\"+BFSliF,7$$\"+++++=F\\o$\"+`r7rkF,
7$$\"+++++>F\\o$\"+'3Czg'F,7$$\"\"#F)$\"+AP<AnF,7$$\"+++++@F\\o$\"+e)*
=*)oF,7$$\"+++++AF\\o$\"+f&yT:(F,7$$\"+++++BF\\o$\"+'*o)>\\(F,7$$\"+++
++CF\\o$\"+G\"*pDyF,7$$\"+++++DF\\o$\"+JD'e3)F,7$$\"+++++EF\\o$\"+xO(3
E)F,7$$\"+++++FF\\o$\"+UM!\\S)F,7$$\"+++++GF\\o$\"+.eF(f)F,7$$\"+++++H
F\\o$\"+8G#p())F,7$$\"\"$F)$\"+`@l1#*F,7$$\"+++++JF\\o$\"+!\\2K]*F,7$$
\"+++++KF\\o$\"+B$zEq*F,7$$\"+++++LF\\o$\"+A`#)3)*F,7$$\"+++++MF\\o$\"
+&\\`(*))*F,7$$\"+++++NF\\o$\"+&RRC+\"!#67$$\"+++++OF\\o$\"+Q(yN-\"Fgv
7$$\"+++++PF\\o$\"+:Y*p/\"Fgv7$$\"+++++QF\\o$\"+hW5k5Fgv7$$\"+++++RF\\
o$\"+4/0q5Fgv7$$\"\"%F)$\"+5OSn5Fgv7$$\"+++++TF\\o$\"+1+;k5Fgv7$$\"+++
++UF\\o$\"+V9Rn5Fgv7$$\"+++++VF\\o$\"+/uAx5Fgv7$$\"+++++WF\\o$\"+;Uv'3
\"Fgv7$$\"+++++XF\\o$\"+w&yy3\"Fgv7$$\"+++++YF\\o$\"+EK*y2\"Fgv7$$\"++
+++ZF\\o$\"+0*\\91\"Fgv7$$\"+++++[F\\o$\"+U`7Z5Fgv7$$\"+++++\\F\\o$\"+
S)f//\"Fgv7$$\"\"&F)$\"+;>XR5Fgv7$$\"+++++^F\\o$\"+'o0j.\"Fgv7$$\"++++
+_F\\o$\"+))42C5Fgv7$$\"+++++`F\\o$\"+\"HE@+\"Fgv7$$\"+++++aF\\o$\"+EX
mm(*F,7$$\"+++++bF\\o$\"+>F&3c*F,7$$\"+++++cF\\o$\"+$H4FW*F,7$$\"+++++
dF\\o$\"+R+4v$*F,7$$\"+++++eF\\o$\"+CC*yF*F,7$$\"+++++fF\\o$\"+w&)=%4*
F,7$$\"\"'F)$\"+%GlO$))F,7$$\"+++++hF\\o$\"+,$3ec)F,7$$\"+++++iF\\o$\"
+No?o$)F,7$$\"+++++jF\\o$\"+fiRl#)F,7$$\"+++++kF\\o$\"+/6H4#)F,7$$\"++
+++lF\\o$\"+f')o?\")F,7$$\"+++++mF\\o$\"+S(>:&zF,7$$\"+++++nF\\o$\"+DW
d>xF,7$$\"+++++oF\\o$\"+2La&\\(F,7$$\"+++++pF\\o$\"+J%*[]tF,7$$\"\"(F)
$\"+:kq)H(F,7$$\"+++++rF\\o$\"+B?I&G(F,7$$\"+++++sF\\o$\"+Tu@JsF,7$$\"
+++++tF\\o$\"+R!*3$4(F,7$$\"+++++uF\\o$\"+CN$H*oF,7$$\"+++++vF\\o$\"+v
B0-nF,7$$\"+++++wF\\o$\"+`o](e'F,7$$\"+++++xF\\o$\"+!*3kclF,7$$\"+++++
yF\\o$\"+u-m\\lF,7$$\"+++++zF\\o$\"+0%3%)['F,7$$\"\")F)$\"+nf.NjF,7$$
\"+++++\")F\\o$\"+15U<hF,7$$\"+++++#)F\\o$\"+i%p$4fF,7$$\"+++++$)F\\o$
\"+<PcvdF,7$$\"+++++%)F\\o$\"+\"HV%=dF,7$$\"+++++&)F\\o$\"+QVqwcF,7$$
\"+++++')F\\o$\"+$pGpd&F,7$$\"+++++()F\\o$\"+.Ey)Q&F,7$$\"+++++))F\\o$
\"+bX)\\9&F,7$$\"+++++*)F\\o$\"+j0g>\\F,7$$\"\"*F)$\"+C\\4wZF,7$$\"+++
++\"*F\\o$\"+J&f\">ZF,7$$\"+++++#*F\\o$\"+4/F&p%F,7$$\"+++++$*F\\o$\"+
'Q=&RYF,7$$\"+++++%*F\\o$\"+1/*Q_%F,7$$\"+++++&*F\\o$\"+x8cuVF,7$$\"++
+++'*F\\o$\"+*e_oD%F,7$$\"+++++(*F\\o$\"+IZ=NUF,7$$\"+++++)*F\\o$\"+h2
'yK%F,7$$\"+++++**F\\o$\"+z!3Y\\%F,7$$\"#5F)$\"+*>N(oYF,7$$\"++++55!\"
)$\"+Ux\\-[F,7$$\"++++?5F`[m$\"+vY!o*[F,7$$\"++++I5F`[m$\"+DYv**\\F,7$
$\"++++S5F`[m$\"+T2ox^F,7$$\"++++]5F`[m$\"++F6iaF,7$$\"++++g5F`[m$\"+2
[)*=eF,7$$\"++++q5F`[m$\"+IscrhF,7$$\"++++!3\"F`[m$\"+jD5ckF,7$$\"++++
!4\"F`[m$\"+iDOlmF,7$$\"#6F)$\"+pl%G&oF,7$$\"++++56F`[m$\"+#o`S4(F,7$$
\"++++?6F`[m$\"+MB1BuF,7$$\"++++I6F`[m$\"+vyq,yF,7$$\"++++S6F`[m$\"+\"
\\sn9)F,7$$\"++++]6F`[m$\"+nvl'R)F,7$$\"++++g6F`[m$\"+%y6lb)F,7$$\"+++
+q6F`[m$\"+>8B$p)F,7$$\"++++!=\"F`[m$\"+B=9%)))F,7$$\"++++!>\"F`[m$\"+
\"*G%>:*F,7$$\"#7F)$\"+O5TV%*F,7$$\"++++57F`[m$\"+'HlHn*F,7$$\"++++?7F
`[m$\"+@j]$z*F,7$$\"++++I7F`[m$\"+%p@&H)*F,7$$\"++++S7F`[m$\"+CGBf)*F,
7$$\"++++]7F`[m$\"+%f!>a**F,7$$\"++++g7F`[m$\"+JYk65Fgv7$$\"++++q7F`[m
$\"+=3&y-\"Fgv7$$\"++++!G\"F`[m$\"+!o&4O5Fgv7$$\"++++!H\"F`[m$\"+*3^M.
\"Fgv7$$\"#8F)$\"+h)fV-\"Fgv7$$\"++++58F`[m$\"+StM<5Fgv7$$\"++++?8F`[m
$\"+yX%z,\"Fgv7$$\"++++I8F`[m$\"+`ZiC5Fgv7$$\"++++S8F`[m$\"+l'3(H5Fgv7
$$\"++++]8F`[m$\"+(>\"=E5Fgv7$$\"++++g8F`[m$\"+]r885Fgv7$$\"++++q8F`[m
$\"+8EZj**F,7$$\"++++!Q\"F`[m$\"+g-VU)*F,7$$\"++++!R\"F`[m$\"+\"4=*3)*
F,7$$\"#9F)$\"+\"f^/$)*F,7$$\"++++59F`[m$\"+[YgG)*F,7$$\"++++?9F`[m$\"
+F-JU(*F,7$$\"++++I9F`[m$\"+W-Gx&*F,7$$\"++++S9F`[m$\"+Q3x*R*F,7$$\"++
++]9F`[m$\"+XXC(G*F,7$$\"++++g9F`[m$\"+1oro#*F,7$$\"++++q9F`[m$\"+&)oK
(H*F,7$$\"++++![\"F`[m$\"+d$zOH*F,7$$\"++++!\\\"F`[m$\"+pf(f?*F,7$$\"#
:F)$\"+(\\m%[!*F,7$$\"++++5:F`[m$\"+\"o+?*))F,7$$\"++++?:F`[m$\"+DXz3)
)F,7$$\"++++I:F`[m$\"+E*QL\"))F,7$$\"++++S:F`[m$\"+C)*G]))F,7$$\"++++]
:F`[m$\"+WF^Q))F,7$$\"++++g:F`[m$\"+ue)Ht)F,7$$\"++++q:F`[m$\"+>o-h&)F
,7$$\"++++!e\"F`[m$\"+&oL]R)F,7$$\"++++!f\"F`[m$\"+>Jp-$)F,7$$\"#;F)$
\"+q#\\fG)F,7$$\"++++5;F`[m$\"+p%Q*y#)F,7$$\"++++?;F`[m$\"+0[@.#)F,7$$
\"++++I;F`[m$\"+b]BE!)F,7$$\"++++S;F`[m$\"+(o4_y(F,7$$\"++++];F`[m$\"+
?DtgvF,7$$\"++++g;F`[m$\"+_2))4uF,7$$\"++++q;F`[m$\"+,bkAtF,7$$\"++++!
o\"F`[m$\"+E_3FsF,7$$\"++++!p\"F`[m$\"+:>F]qF,7$$\"#<F)$\"+>].vnF,7$$
\"++++5<F`[m$\"+ydk]kF,7$$\"++++?<F`[m$\"+4fIdhF,7$$\"++++I<F`[m$\"+E#
*eXfF,7$$\"++++S<F`[m$\"+'pL_z&F,7$$\"++++]<F`[m$\"+KGrNcF,7$$\"++++g<
F`[m$\"+^[p0aF,7$$\"++++q<F`[m$\"+HyG*4&F,7$$\"++++!y\"F`[m$\"+7a**oZF
,7$$\"++++!z\"F`[m$\"+0#f9\\%F,7$$\"#=F)$\"+Pld:VF,7$$\"++++5=F`[m$\"+
OOSHUF,7$$\"++++?=F`[m$\"+!zGu<%F,7$$\"++++I=F`[m$\"+OuS2TF,7$$\"++++S
=F`[m$\"+N,$f+%F,7$$\"++++]=F`[m$\"+W]w/RF,7$$\"++++g=F`[m$\"+8.ljQF,7
$$\"++++q=F`[m$\"+oDaMRF,7$$\"++++!)=F`[m$\"+@.NCTF,7$$\"++++!*=F`[m$
\"+ts*\\Q%F,7$$\"#>F)$\"+q&R]k%F,7$$\"++++5>F`[m$\"+87qa[F,7$$\"++++?>
F`[m$\"+$Q9l,&F,7$$\"++++I>F`[m$\"+2w\"3=&F,7$$\"++++S>F`[m$\"+rQ[8aF,
7$$\"++++]>F`[m$\"+/c!*QdF,7$$\"++++g>F`[m$\"+0(\\@6'F,7$$\"++++q>F`[m
$\"+KlYakF,7$$\"++++!)>F`[m$\"+c?44nF,7$$\"++++!*>F`[m$\"+kp(=)oF,7$$
\"#?F)$\"+\"\\ms.(F,7$$\"++++5?F`[m$\"+$fT'[sF,7$$\"++++??F`[m$\"+Wn<Q
vF,7$$\"++++I?F`[m$\"+<76ayF,7$$\"++++S?F`[m$\"+]x_9\")F,7$$\"++++]?F`
[m$\"+%[K?F)F,7$$\"++++g?F`[m$\"+$=^mM)F,7$$\"++++q?F`[m$\"+-)))\\T)F,
7$$\"++++!3#F`[m$\"+vq\\Y&)F,7$$\"++++!4#F`[m$\"+Y8v\\()F,7$$\"#@F)$\"
+s_Bh*)F,7$$\"++++5@F`[m$\"+q%HQ5*F,7$$\"++++?@F`[m$\"+'3oM9*F,7$$\"++
++I@F`[m$\"+[C'p6*F,7$$\"++++S@F`[m$\"+GoD1\"*F,7$$\"++++]@F`[m$\"+eNJ
r\"*F,7$$\"++++g@F`[m$\"+a^D0$*F,7$$\"++++q@F`[m$\"+DB;Q%*F,7$$\"++++!
=#F`[m$\"+,7^)\\*F,7$$\"++++!>#F`[m$\"+WgGl%*F,7$$\"#AF)$\"+@N***Q*F,7
$$\"++++5AF`[m$\"+xgW^$*F,7$$\"++++?AF`[m$\"+M$zDS*F,7$$\"++++IAF`[m$
\"+\\3I=&*F,7$$\"++++SAF`[m$\"+EI[G'*F,7$$\"++++]AF`[m$\"+n-jj'*F,7$$
\"++++gAF`[m$\"+/.(yh*F,7$$\"++++qAF`[m$\"+y%R_a*F,7$$\"++++!G#F`[m$\"
+bixE&*F,7$$\"++++!H#F`[m$\"+`*z$*f*F,7$$\"#BF)$\"+$\\s6t*F,7$$\"++++5
BF`[m$\"+=e)=%)*F,7$$\"++++?BF`[m$\"+OF^r)*F,7$$\"++++IBF`[m$\"+U)f1#)
*F,7$$\"++++SBF`[m$\"+yO]a(*F,7$$\"++++]BF`[m$\"+%)R;Y(*F,7$$\"++++gBF
`[m$\"+QdoC)*F,7$$\"++++qBF`[m$\"+FT^S**F,7$$\"++++!Q#F`[m$\"+lAb,5Fgv
7$$\"++++!R#F`[m$\"+uVb$***F,7$$\"#CF)$\"+V-6#*)*F,7$$\"++++5CF`[m$\"+
I/L!y*F,7$$\"++++?CF`[m$\"+i<mJ(*F,7$$\"++++ICF`[m$\"+%GHhv*F,7$$\"+++
+SCF`[m$\"+1XZ&z*F,7$$\"++++]CF`[m$\"+9GZn(*F,7$$\"++++gCF`[m$\"+>?%Qj
*F,7$$\"++++qCF`[m$\"+,esD%*F,7$$\"++++![#F`[m$\"+:E\"GA*F,7$$\"++++!
\\#F`[m$\"+[]@(3*F,7$$\"#DF)$\"+Y2s8!*F,7$$\"++++5DF`[m$\"+.-;K*)F,7$$
\"++++?DF`[m$\"+/a<n()F,7$$\"++++IDF`[m$\"+LVM)\\)F,7$$\"++++SDF`[m$\"
+yNps\")F,7$$\"++++]DF`[m$\"+#e\"ztyF,7$$\"++++gDF`[m$\"+>I\"3l(F,7$$
\"++++qDF`[m$\"+)>AI[(F,7$$\"++++!e#F`[m$\"+mC]&H(F,7$$\"++++!f#F`[m$
\"+=YkCqF,7$$\"#EF)$\"+Cw$pm'F,7$$\"++++5EF`[m$\"+\"H([ziF,7$$\"++++?E
F`[m$\"+eL[UfF,7$$\"++++IEF`[m$\"+P;8'p&F,7$$\"++++SEF`[m$\"+/We7bF,7$
$\"++++]EF`[m$\"+BgOC`F,7$$\"++++gEF`[m$\"+$pz+3&F,7$$\"++++qEF`[m$\"+
/(*p\"y%F,7$$\"++++!o#F`[m$\"+)enQ[%F,7$$\"++++!p#F`[m$\"+FK.eUF,7$$\"
#FF)$\"+V9qYTF,7$$\"++++5FF`[m$\"+N,nNTF,7$$\"++++?FF`[m$\"+!*y]nTF,7$
$\"++++IFF`[m$\"+#zMz=%F,7$$\"++++SFF`[m$\"+<^.wTF,7$$\"++++]FF`[m$\"+
-')ecTF,7$$\"++++gFF`[m$\"+lO'\\=%F,7$$\"++++qFF`[m$\"+1\"y2J%F,7$$\"+
+++!y#F`[m$\"+'>rj`%F,7$$\"++++!z#F`[m$\"+cGY1[F,7$$\"#GF)$\"+9!=!\\]F
,7$$\"++++5GF`[m$\"+ms->_F,7$$\"++++?GF`[m$\"+&\\j7L&F,7$$\"++++IGF`[m
$\"+$4O[W&F,7$$\"++++SGF`[m$\"+8b=DcF,7$$\"++++]GF`[m$\"+[RT&)eF,7$$\"
++++gGF`[m$\"++\"RB<'F,7$$\"++++qGF`[m$\"+xvJ5kF,7$$\"++++!)GF`[m$\"+!
y$4alF,7$$\"++++!*GF`[m$\"++9LEmF,7$$\"#HF)$\"+H%pap'F,7$$\"++++5HF`[m
$\"+8O5JoF,7$$\"++++?HF`[m$\"+/h-SqF,7$$\"++++IHF`[m$\"+)p7qE(F,7$$\"+
+++SHF`[m$\"+Y,MMuF,7$$\"++++]HF`[m$\"+08a4vF,7$$\"++++gHF`[m$\"+PA(3_
(F,7$$\"++++qHF`[m$\"+QQ,YvF,7$$\"++++!)HF`[m$\"+1:6YwF,7$$\"++++!*HF`
[m$\"+gUcByF,7$$\"#IF)$\"+K2\"R,)F,7$$\"++++5IF`[m$\"+)ekq9)F,7$$\"+++
+?IF`[m$\"+@aM$>)F,7$$\"++++IIF`[m$\"+-H:'>)F,7$$\"++++SIF`[m$\"+$=ogA
)F,7$$\"++++]IF`[m$\"+qyqU$)F,7$$\"++++gIF`[m$\"+$Gqo`)F,7$$\"++++qIF`
[m$\"+$Q67u)F,7$$\"++++!3$F`[m$\"+k]q')))F,7$$\"++++!4$F`[m$\"+VD?\\*)
F,7$$\"#JF)$\"+^/@x*)F,7$$\"++++5JF`[m$\"+Y8GT!*F,7$$\"++++?JF`[m$\"+#
f'3%>*F,7$$\"++++IJF`[m$\"+$o/dT*F,7$$\"++++SJF`[m$\"+'HoIj*F,7$$\"+++
+]JF`[m$\"+!4!**y(*F,7$$\"++++gJF`[m$\"+*4!pO)*F,7$$\"++++qJF`[m$\"+G)
\\B')*F,7$$\"++++!=$F`[m$\"+9bwF**F,7$$\"++++!>$F`[m$\"+xh]25Fgv7$$\"#
KF)$\"+'p4t-\"Fgv7$$\"++++5KF`[m$\"+$=iT/\"Fgv7$$\"++++?KF`[m$\"+KF._5
Fgv7$$\"++++IKF`[m$\"+^Af]5Fgv7$$\"++++SKF`[m$\"+g#\\k/\"Fgv7$$\"++++]
KF`[m$\"+>V)o/\"Fgv7$$\"++++gKF`[m$\"+m\"oY0\"Fgv7$$\"++++qKF`[m$\"+:9
8l5Fgv7$$\"++++!G$F`[m$\"+Fj0q5Fgv7$$\"++++!H$F`[m$\"+v?kk5Fgv7$$\"#LF
)$\"+;IQ]5Fgv7$$\"++++5LF`[m$\"+;/'\\.\"Fgv7$$\"++++?LF`[m$\"+q.1D5Fgv
7$$\"++++ILF`[m$\"+U_t@5Fgv7$$\"++++SLF`[m$\"+?p))=5Fgv7$$\"++++]LF`[m
$\"+JXq35Fgv7$$\"++++gLF`[m$\"+vQR!))*F,7$$\"++++qLF`[m$\"+eN]-'*F,7$$
\"++++!Q$F`[m$\"+qX4O$*F,7$$\"++++!R$F`[m$\"+K([l8*F,7$$\"#MF)$\"+,:c)
**)F,7$$\"++++5MF`[m$\"+MQz^))F,7$$\"++++?MF`[m$\"+z(*=F')F,7$$\"++++I
MF`[m$\"+z;g4$)F,7$$\"++++SMF`[m$\"+60GZzF,7$$\"++++]MF`[m$\"+#oQ7i(F,
7$$\"++++gMF`[m$\"+GwiwtF,7$$\"++++qMF`[m$\"+?R2'>(F,7$$\"++++![$F`[m$
\"+OP03qF,7$$\"++++!\\$F`[m$\"+#*4$\\v'F,7$$\"#NF)$\"+$QR-V'F,7$$\"+++
+5NF`[m$\"+\"pA')3'F,7$$\"++++?NF`[m$\"+^j8.eF,7$$\"++++INF`[m$\"+88=<
cF,7$$\"++++SNF`[m$\"+Gqc1bF,7$$\"++++]NF`[m$\"+?`)3T&F,7$$\"++++gNF`[
m$\"+y]es_F,7$$\"++++qNF`[m$\"+/YE%3&F,7$$\"++++!e$F`[m$\"+1S$y)[F,7$$
\"++++!f$F`[m$\"+MkD\\ZF,7$$\"#OF)$\"+nOw7ZF,7$$\"++++5OF`[m$\"+\"GtRw
%F,7$$\"++++?OF`[m$\"+-LuV[F,7$$\"++++IOF`[m$\"+A%\\m)[F,7$$\"++++SOF`
[m$\"+wAiq[F,7$$\"++++]OF`[m$\"+\"oB5#[F,7$$\"++++gOF`[m$\"+]!)y+[F,7$
$\"++++qOF`[m$\"+'Gl8'[F,7$$\"++++!o$F`[m$\"+g!*)>+&F,7$$\"++++!p$F`[m
$\"+UN(Q;&F,7$$\"#PF)$\"+^$z(z_F,7$$\"++++5PF`[m$\"+;\"[`J&F,7$$\"++++
?PF`[m$\"+)42#)H&F,7$$\"++++IPF`[m$\"+eO.#H&F,7$$\"++++SPF`[m$\"+%*)o%
e`F,7$$\"++++]PF`[m$\"+ro7+bF,7$$\"++++gPF`[m$\"+q\"zam&F,7$$\"++++qPF
`[m$\"+SF;$y&F,7$$\"++++!y$F`[m$\"+#e3S#eF,7$$\"++++!z$F`[m$\"+`yh5eF,
7$$\"#QF)$\"+UhP8eF,7$$\"++++5QF`[m$\"+cP(>*eF,7$$\"++++?QF`[m$\"+_WBc
gF,7$$\"++++IQF`[m$\"+?hQ_iF,7$$\"++++SQF`[m$\"+Y1j8kF,7$$\"++++]QF`[m
$\"+c0O.lF,7$$\"++++gQF`[m$\"+ujuZlF,7$$\"++++qQF`[m$\"+q(4Mh'F,7$$\"+
+++!)QF`[m$\"+TQ5fnF,7$$\"++++!*QF`[m$\"+[CM'*pF,7$$\"#RF)$\"+])oyE(F,
7$$\"++++5RF`[m$\"+rEC0vF,7$$\"++++?RF`[m$\"+B'>wm(F,7$$\"++++IRF`[m$
\"+_.r!y(F,7$$\"++++SRF`[m$\"+Q*fG\"zF,7$$\"++++]RF`[m$\"+q$f-7)F,7$$
\"++++gRF`[m$\"+TX\"3T)F,7$$\"++++qRF`[m$\"+Qll@()F,7$$\"++++!)RF`[m$
\"+4imz*)F,7$$\"++++!*RF`[m$\"+VV^^\"*F,7$$\"#SF)$\"+uD8k#*F,7$$\"++++
5SF`[m$\"++h%QR*F,7$$\"++++?SF`[m$\"+d0c%f*F,7$$\"++++ISF`[m$\"+$Qs)e)
*F,7$$\"++++SSF`[m$\"+`(R@,\"Fgv7$$\"++++]SF`[m$\"+P+[I5Fgv7$$\"++++gS
F`[m$\"+U!R#R5Fgv7$$\"++++qSF`[m$\"+0KKU5Fgv7$$\"++++!3%F`[m$\"+aZ`Z5F
gv7$$\"++++!4%F`[m$\"+gNzf5Fgv7$$\"#TF)$\"+p`<w5Fgv7$$\"++++5TF`[m$\"+
ea(**3\"Fgv7$$\"++++?TF`[m$\"+/rO%4\"Fgv7$$\"++++ITF`[m$\"+2/f)3\"Fgv7
$$\"++++STF`[m$\"+C]0z5Fgv7$$\"++++]TF`[m$\"+Ss(G2\"Fgv7$$\"++++gTF`[m
$\"+b(fK2\"Fgv7$$\"++++qTF`[m$\"+R-&o2\"Fgv7$$\"++++!=%F`[m$\"+'y#[v5F
gv7$$\"++++!>%F`[m$\"+WkCk5Fgv7$$\"#UF)$\"+]jRW5Fgv7$$\"++++5UF`[m$\"+
\\x[A5Fgv7$$\"++++?UF`[m$\"+6`615Fgv7$$\"++++IUF`[m$\"+:l>k**F,7$$\"++
++SUF`[m$\"+>lP())*F,7$$\"++++]UF`[m$\"+&HVov*F,7$$\"++++gUF`[m$\"+I0%
4`*F,7$$\"++++qUF`[m$\"+)R1GC*F,7$$\"++++!G%F`[m$\"+iu\")f*)F,7$$\"+++
+!H%F`[m$\"+i[BZ()F,7$$\"#VF)$\"+n+t5')F,7$$\"++++5VF`[m$\"+2j%)*[)F,7
$$\"++++?VF`[m$\"+8_Q>$)F,7$$\"++++IVF`[m$\"+.j6o!)F,7$$\"++++SVF`[m$
\"+t*pVx(F,7$$\"++++]VF`[m$\"+pHm3vF,7$$\"++++gVF`[m$\"+*R6iK(F,7$$\"+
+++qVF`[m$\"+))Q$\\A(F,7$$\"++++!Q%F`[m$\"+P`oUrF,7$$\"++++!R%F`[m$\"+
vsg;qF,7$$\"#WF)$\"+Ct`>oF,7$$\"++++5WF`[m$\"+*f0/f'F,7$$\"++++?WF`[m$
\"+n=N%R'F,7$$\"++++IWF`[m$\"+YB/%G'F,7$$\"++++SWF`[m$\"+Cw9_iF,7$$\"+
+++]WF`[m$\"+;&)yPiF,7$$\"++++gWF`[m$\"+7h$f<'F,7$$\"++++qWF`[m$\"+_I
\\RgF,7$$\"++++![%F`[m$\"+f(of'eF,7$$\"++++!\\%F`[m$\"+'p(y:dF,7$$\"#X
F)$\"+))[dUcF,7$$\"++++5XF`[m$\"+MuvRcF,7$$\"++++?XF`[m$\"+)>N![cF,7$$
\"++++IXF`[m$\"+T^B-cF,7$$\"++++SXF`[m$\"+K?#eZ&F,7$$\"++++]XF`[m$\"+]
iW0`F,7$$\"++++gXF`[m$\"+\\vQ_^F,7$$\"++++qXF`[m$\"+Q![N2&F,7$$\"++++!
e%F`[m$\"+0x5k]F,7$$\"++++!f%F`[m$\"+nIBs]F,7$$\"#YF)$\"+#f+\\.&F,7$$
\"++++5YF`[m$\"+%z:)G\\F,7$$\"++++?YF`[m$\"+'4^Cy%F,7$$\"++++IYF`[m$\"
+`YyhYF,7$$\"++++SYF`[m$\"+D=hAYF,7$$\"++++]YF`[m$\"+xfytYF,7$$\"++++g
YF`[m$\"+v(**)oZF,7$$\"++++qYF`[m$\"+p]#*\\[F,7$$\"++++!o%F`[m$\"+1o$H
)[F,7$$\"++++!p%F`[m$\"+'RUe)[F,7$$\"#ZF)$\"+$=5X\"\\F,7$$\"++++5ZF`[m
$\"+>QWC]F,7$$\"++++?ZF`[m$\"+X3>P_F,7$$\"++++IZF`[m$\"+=pM5bF,7$$\"++
++SZF`[m$\"+y5E!y&F,7$$\"++++]ZF`[m$\"+%p=e*fF,7$$\"++++gZF`[m$\"+&*)*
fghF,7$$\"++++qZF`[m$\"+!f\\xK'F,7$$\"++++!y%F`[m$\"+jvoclF,7$$\"++++!
z%F`[m$\"+9d([(oF,7$$\"#[F)$\"+>5RSsF,7$$\"++++5[F`[m$\"+3,!*yvF,7$$\"
++++?[F`[m$\"+,JgVyF,7$$\"++++I[F`[m$\"+_zqN!)F,7$$\"++++S[F`[m$\"+]\"
yI@)F,7$$\"++++][F`[m$\"+y)pcW)F,7$$\"++++g[F`[m$\"+4'ppu)F,7$$\"++++q
[F`[m$\"+5)=e2*F,7$$\"++++!)[F`[m$\"+zo'eN*F,7$$\"++++!*[F`[m$\"+LOrP&
*F,7$$\"#\\F)$\"+gP#fk*F,7$$\"++++5\\F`[m$\"+C3vU(*F,7$$\"++++?\\F`[m$
\"+_S,#*)*F,7$$\"++++I\\F`[m$\"+:,R55Fgv7$$\"++++S\\F`[m$\"+]\"3;.\"Fg
v7$$\"++++]\\F`[m$\"+>tyX5Fgv7$$\"++++g\\F`[m$\"+p9D]5Fgv7$$\"++++q\\F
`[m$\"+g%*eZ5Fgv7$$\"++++!)\\F`[m$\"+MxRX5Fgv7$$\"++++!*\\F`[m$\"+xaY
\\5Fgv" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve
 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 8 0" 
9 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }