{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 "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 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 "" {MPLTEXT 1 0 258 "\n#\n# J\366rg Lem m\n#\n# Maple-Worksheet\n# zur Vorlesung Finanzmathematik und Risiko management\n# WS 2007/2008\n# Universit\344t M\374nster\n#\n# Beisp iel Gau\337sche Regression \n#\n# mit negativem Laplaceoperator \n# \+ als inverse Priorkovarianz\n# auf diskretem Gitter\n#\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "with(linalg):\n\n#n := 50; # Anzahl Gitterpunkte (50 geht noch gut)\nn := 10; # Anzahl Gitte rpunkte\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 548 "#\n# 1. Daten\n#\n\nnd := 6; # Anz ahl Datenpunkte\nData := array(1..nd,1..2): # Array f\374r Eingangsda ten \n\n# Datenpaare (x,y)\nData[1,1] := 1: Data[1,2] := 5: # x = \+ 1 und y = 5\nData[2,1] := 2: Data[2,2] := 4: # x = 2 und y = 4\nDa ta[3,1] := 2: Data[3,2] := 5: # x = 2 und y = 5\nData[4,1] := 5: D ata[4,2] := 5.5: # x = 5 und y = 5.5\nData[5,1] := 6: Data[5,2] := 6 : # x = 6 und y = 6\nData[6,1] := 7: Data[6,2] := 2: # x = 7 u nd y = 2\n# Umskalieren x-Werte\nfor i from 1 to nd do:\n Data[i,1] \+ := round(Data[i,1]*n/10);\nend:\nevalm(Data);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ndG\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matri xG6#7(7$\"\"\"\"\"&7$\"\"#\"\"%7$F+F)7$F)$\"#b!\"\"7$\"\"'F37$\"\"(F+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 257 "# \334bernahme Daten i n Gittervektor\nyData := vector(n,0): \nnData := vector(n,0): \nfor i \+ from 1 to nd do:\n nData[Data[i,1]] := nData[Data[i,1]] +1: # Z \344hler f\374r jeden x-Wert \n yData[Data[i,1]] := yData[Data[i,1]] + Data[i,2]: # \334bernahme y-Werte \nend:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "# Mittelwert von y pro x\nfor i from 1 to n do:\n \+ if (nData[i] > 0) then \n yData[i] := yData[i]/nData[i]: \n end if: \nend:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "evalm(nData);evalm( yData);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7,\"\"\"\"\"#\" \"!F)F'F'F'F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7,\" \"&#\"\"*\"\"#\"\"!F+$\"#b!\"\"\"\"'F*F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 166 "# Datenkern (data kernel) = inverse Datenkovari anz \n# Sigma=1 (konstantes Sigma ungleich 1 kann \374ber Lambda einfl ie\337en)\nKD := matrix(n,n,diag(seq(nData[i],i=1..n))); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#KDG-%'matrixG6#7,7,\"\"\"\"\"!F+F+F+F+F+F+F+ F+7,F+\"\"#F+F+F+F+F+F+F+F+7,F+F+F+F+F+F+F+F+F+F+F.7,F+F+F+F+F*F+F+F+F +F+7,F+F+F+F+F+F*F+F+F+F+7,F+F+F+F+F+F+F*F+F+F+F.F.F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 450 "#\n# 2. Prior (A-Priori-Informatio n)\n#\n\n# negativer Laplaceoperator auf dem Gitter \n# als Beispiel e iner inversen Priorkovarianz\n#\n# Definition der Wurzel der inversen \+ Kovarianz\n# Matrixelemente diskrete Rechtsableitung\nrder := proc(i,j ); \n if (i=j) then 1 elif (i-j=-1) then -1 else 0 end if;\nend proc: \n# diskrete Rechtsableitung als Matrix\nW := matrix(n,n,rder);\n# W[n ,1] := -1: # periodische Randbedingungen (K0 nicht mehr invertierbar) \nevalm(W);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"WG-%'matrixG6#7,7 ,\"\"\"!\"\"\"\"!F,F,F,F,F,F,F,7,F,F*F+F,F,F,F,F,F,F,7,F,F,F*F+F,F,F,F ,F,F,7,F,F,F,F*F+F,F,F,F,F,7,F,F,F,F,F*F+F,F,F,F,7,F,F,F,F,F,F*F+F,F,F ,7,F,F,F,F,F,F,F*F+F,F,7,F,F,F,F,F,F,F,F*F+F,7,F,F,F,F,F,F,F,F,F*F+7,F ,F,F,F,F,F,F,F,F,F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7,7 ,\"\"\"!\"\"\"\"!F*F*F*F*F*F*F*7,F*F(F)F*F*F*F*F*F*F*7,F*F*F(F)F*F*F*F *F*F*7,F*F*F*F(F)F*F*F*F*F*7,F*F*F*F*F(F)F*F*F*F*7,F*F*F*F*F*F(F)F*F*F *7,F*F*F*F*F*F*F(F)F*F*7,F*F*F*F*F*F*F*F(F)F*7,F*F*F*F*F*F*F*F*F(F)7,F *F*F*F*F*F*F*F*F*F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "# Tr ansponierte (=bis auf Randbedingung negative diskrete Linksableitung) \nWT := transpose(W);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#WTG-%'ma trixG6#7,7,\"\"\"\"\"!F+F+F+F+F+F+F+F+7,!\"\"F*F+F+F+F+F+F+F+F+7,F+F-F *F+F+F+F+F+F+F+7,F+F+F-F*F+F+F+F+F+F+7,F+F+F+F-F*F+F+F+F+F+7,F+F+F+F+F -F*F+F+F+F+7,F+F+F+F+F+F-F*F+F+F+7,F+F+F+F+F+F+F-F*F+F+7,F+F+F+F+F+F+F +F-F*F+7,F+F+F+F+F+F+F+F+F-F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 " \n# negativer Laplaceoperator NL = WT.W \nNL := multiply(WT,W) ;\nNL[1,1] :=2; # Randbedingung Null, bei period. Randbed. schon vorha nden\nevalm(NL);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#NLG-%'matrixG6# 7,7,\"\"\"!\"\"\"\"!F,F,F,F,F,F,F,7,F+\"\"#F+F,F,F,F,F,F,F,7,F,F+F.F+F ,F,F,F,F,F,7,F,F,F+F.F+F,F,F,F,F,7,F,F,F,F+F.F+F,F,F,F,7,F,F,F,F,F+F.F +F,F,F,7,F,F,F,F,F,F+F.F+F,F,7,F,F,F,F,F,F,F+F.F+F,7,F,F,F,F,F,F,F,F+F .F+7,F,F,F,F,F,F,F,F,F+F." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#NLG6$ \"\"\"F'\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7,7,\"\"# !\"\"\"\"!F*F*F*F*F*F*F*7,F)F(F)F*F*F*F*F*F*F*7,F*F)F(F)F*F*F*F*F*F*7, F*F*F)F(F)F*F*F*F*F*7,F*F*F*F)F(F)F*F*F*F*7,F*F*F*F*F)F(F)F*F*F*7,F*F* F*F*F*F)F(F)F*F*7,F*F*F*F*F*F*F)F(F)F*7,F*F*F*F*F*F*F*F)F(F)7,F*F*F*F* F*F*F*F*F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 545 "# aus Lapl aceoperator abgeleitete Priorkerne\n# negativer Laplaceoperator\nK0 := NL;\n\n# Radiale-Basis-Funktionen-Prior (truncated)\n# Varianz f\374r (truncated) Radiale-Basis-Funktionen-Prior\n#varRBF := 1/n: # glatte r, Bsp. ohne Delle\n#varRBF := 10/n: # rauher, Bsp. mit Delle\n#K0 := \+ 1+evalm(NL)/varRBF+multiply(NL,NL)/(2*varRBF^2) \\\n# + multiply( NL,NL,NL)/(6*varRBF^3);\n\n# Variante RBF ohne 1, keinen absoluten Bez ug zur Priortemplate\n#K0 := evalm(NL)/varRBF+multiply(NL,NL)/(2*varRB F^2) \\\n# + multiply(NL,NL,NL)/(6*varRBF^3); \n\nevalm(K0);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#K0G%#NLG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7,7,\"\"#!\"\"\"\"!F*F*F*F*F*F*F*7,F)F(F)F* F*F*F*F*F*F*7,F*F)F(F)F*F*F*F*F*F*7,F*F*F)F(F)F*F*F*F*F*7,F*F*F*F)F(F) F*F*F*F*7,F*F*F*F*F)F(F)F*F*F*7,F*F*F*F*F*F)F(F)F*F*7,F*F*F*F*F*F*F)F( F)F*7,F*F*F*F*F*F*F*F)F(F)7,F*F*F*F*F*F*F*F*F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 296 "# Invertieren liefert Priorkovarianz \n# (nu r m\366glich, wenn keine Nulleigenwerte vorhanden sind,\n# falls solch e Nulleigenwerte vorhanden sind, \n# dann m\374ssen erst die Daten hin zugef\374gt werden, \n# bevor invertiert werden kann.)\n# \nC0 := inve rse(K0);\n# Test: Inverses korrekt?\n# E:=multiply(K0,C0);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#C0G-%'matrixG6#7,7,#\"#5\"#6#\"\"*F,#\"\" )F,#\"\"(F,#\"\"'F,#\"\"&F,#\"\"%F,#\"\"$F,#\"\"#F,#\"\"\"F,7,F-#\"#=F ,#\"#;F,#\"#9F,#\"#7F,F*F/F3F7F;7,F/FB#\"#CF,#\"#@F,F@#\"#:F,FFF-F3F97 ,F1FDFK#\"#GF,FI#\"#?F,FBFFF/F77,F3FFF@FI#\"#IF,#\"#DF,FRFMF*F57,F5F*F MFRFWFUFIF@FFF37,F7F/FFFBFRFIFPFKFDF17,F9F3F-FFFMF@FKFIFBF/7,F;F7F3F/F *FFFDFBF@F-7,F=F;F9F7F5F3F1F/F-F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 358 "# Plot Priorkovarianz\nwith(plots):with(CurveFitting ):\nc:=array(1..n): # f\374r jede Spalte ein Datenvektor\ns:=array (1..n): # f\374r jede Spalte eine B-Spline-Kurve\nx:=[seq(i,i=1..n )]: # x-Werte\nfor i from 1 to n do; \n c := [seq(C0[j,i],j=1..n)]; \+ # Spalte i\n s[i] := BSplineCurve(x,c,v,order=2): # B-Spline- Kurve f\374r Spalte i\nend do:\nplot(s); \n \n" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6.-%'CURVESG6$7S7$$\"\"\"\"\"!$\"3g !4444444*!#=7$$\"3#*****\\(Quh>\"!#<$\"3!ROO'Q(oD\"*)F-7$$\"3/+]7tY'oO \"F1$\"3KXXq^dRd()F-7$$\"31++D^P#)e:F1$\"35OO'))\\()Ge)F-7$$\"3-++ve_0 _F1$\"3344M!R#RK#)F-7$$\"3**** \\7VsmA@F1$\"3+++D1DIq!)F-7$$\"3*)**\\7)R&G2BF1$\"3/kj))>yY-zF-7$$\"3- +]7ex@)\\#F1$\"3f!4fr%H*)GxF-7$$\"3%)**\\i&zP&)o#F1$\"3w++DJZ(eb(F-7$$ \"3A++]Z`I%)GF1$\"3WaaaHU!zP(F-7$$\"3#****\\P^Pn0$F1$\"3bEFx9x9@sF-7$$ \"3G++]#Hb3D$F1$\"3x!==o+xY/(F-7$$\"3%)****\\P,xXMF1$\"3M===$p\"[noF-7 $$\"3E++]2ngLOF1$\"3'******\\<@np'F-7$$\"3&)**\\73.=/QF1$\"3L44MlUlTlF -7$$\"3/++]<)3q+%F1$\"3-OOO6ZEdjF-7$$\"3[+++q6$)yTF1$\"3orsssD1,iF-7$$ \"3Q+]789qyVF1$\"3qWXq^BO>gF-7$$\"3u*****\\W?cb%F1$\"37===oo_eeF-7$$\" 3U+]7j'G(\\ZF1$\"3oWXq^[1#o&F-7$$\"3X+]P*elX$\\F1$\"3UijQ#GJS^&F-7$$\" 3s++DJNUF^F1$\"3t<=o!)eqQ`F-7$$\"32+]iDt_/`F1$\"3u***\\7V-x<&F-7$$\"3[ ***\\Ppdb\\&F1$\"3htsAg%QS+&F-7$$\"3#***\\7eX)Rp&F1$\"3iXXq,/lB[F-7$$ \"3K+](os:n'eF1$\"3%GFxk1Amm%F-7$$\"3u***\\77qK0'F1$\"3A++]ir-(\\%F-7$ $\"3Y*****\\1**fC'F1$\"3h#===.>=K%F-7$$\"3t***\\itYXV'F1$\"3gXX&z07/:% F-7$$\"3'***\\7.j(ph'F1$\"3C!4fr*pc%)RF-7$$\"3l***\\PBL&>oF1$\"32XX&HL C/!QF-7$$\"3P*****\\kR:+(F1$\"3(*444fR'\\j$F-7$$\"3e++]P.(e>(F1$\"3u<= =$p*HeMF-7$$\"3e**\\7GG'>P(F1$\"3Abaz5c@)H$F-7$$\"3_++]K%yWc(F1$\"3`** ***\\U,K7$F-7$$\"3S**\\781iXxF1$\"3%*34M:n_eHF-7$$\"3n**\\i&Qm\\$zF1$ \"3_jj)[>%R'y#F-7$$\"31++](['3?\")F1$\"3s<==$>.\"=EF-7$$\"3q)*\\7y+*QJ )F1$\"3tbaz5\"=>W#F-7$$\"3,,++qfa+&)F1$\"3/NOOO4BsAF-7$$\"3=***\\(y&G9 p)F1$\"31ba/#H,()4#F-7$$\"3_+]7$eI2)))F1$\"3F-7$$\"3a*****\\ YzY0*F1$\"3Wjjj8KZoG^U\"F-7$$\"3L**\\78%zCi*F1$\"3oOOhU9H_7F-7$$\"3v** \\(o\"*[W!)*F1$\"3IFF-@Y'o3\"F-7$$\"#5F*$\"3%G3444444*!#>-%'COLOURG6&% $RGBG$Ffz!\"\"$F*F*F`[l-F$6$7\\o7$F($\"3K#=======)F-7$$\"33++v$>(3)4\" F1$\"3Iba/n(\\V)*)F-7$F/$\"3;FFF_8)oy*F-7$$\"3++DJI&>:G\"F1$\"3-\"fY$z f^[5F17$F5$\"364fYBQM=6F17$$\"31+v=7U%GY\"F1$\"3G=VCPD(o>\"F17$F:$\"3] FF-^7Sv7F17$$\"3#******\\]Ral\"F1$\"3;444/0Xa8F17$F?$\"31\"4frv*\\L9F1 7$$\"3'**\\(o9=@[=F1$\"3ROh#HIt@^\"F17$FD$\"3#>=$p[o%3f\"F17$$\"3-+voH dlm>F1$\"3D4Mlg>34;F17$$\"3#****\\()3V*))>F1$\"3MOOhsqJF;F17$$\"3'\\i: &G\\^%*>F1$\"3A$p.1&e(=j\"F17$$\"3w\\7Gon3+?F1$\"38+DJgyMO;F17$$\"3duo /3'ec+#F1$\"3)>$p`)zM`j\"F17$$\"3#)*\\7yWI7,#F1$\"3hj8wO\"44f6C3I)F-7$F[u$\"3[!==V*R8pzF-7$F`u$\"39!44fm[3g (F-7$Feu$\"3%*>===z#*psF-7$Fju$\"3ZNOO'Q*f;pF-7$F_v$\"3W54f@7V'f'F-7$F dv$\"31******\\GSYiF-7$Fiv$\"3)y\"=oIM0%F-7$Fgx$\"3M34f@r@`QF-7$F\\y$\"3!psssUYp`$F-7$Fay$\"3=XXX?XYuJF-7 $Ffy$\"3?z\"==Qc-&GF-7$F[z$\"3NtsA&)Ge/DF-7$F`z$\"3eaa/U#HP<#F-7$Fez$ \"3d;=======F--F[[l6&F][lF`[lF^[lF`[l-F$6$7en7$F($\"3#HFFFFFFF(F-7$F/$ \"3/\"4444]%*p)F-7$F5$\"3ZPOO')R$3%**F-7$F:$\"3*3444+!pL6F17$F?$\"3[OO O1?Au7F17$FD$\"3tsss(3'399F17$FI$\"3*******\\*zvV:F17$FN$\"3)*344Wd-y; 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Daten und Prior\n#\n# Gesamtkern = inverse Gesamtkovarianz\n#\nLam bda := 1; # Regularisierungsfaktor\nK := KD + Lambda * K0;\nevalm(K) ; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'LambdaG\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"KG,&%#KDG\"\"\"%#NLGF'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7,7,\"\"$!\"\"\"\"!F*F*F*F*F*F*F*7,F)\"\"%F )F*F*F*F*F*F*F*7,F*F)\"\"#F)F*F*F*F*F*F*7,F*F*F)F.F)F*F*F*F*F*7,F*F*F* F)F(F)F*F*F*F*7,F*F*F*F*F)F(F)F*F*F*7,F*F*F*F*F*F)F(F)F*F*7,F*F*F*F*F* F*F)F.F)F*7,F*F*F*F*F*F*F*F)F.F)7,F*F*F*F*F*F*F*F*F)F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 391 "# Gesamtkovarianz\nC := inverse(K) :\n# Plot Gesamtkovarianz\nwith(plots):with(CurveFitting):\nc:=array(1 ..n): # f\374r jede Spalte ein Datenvektor\ns:=array(1..n): # \+ f\374r jede Spalte eine B-Spline-Kurve\nx:=[seq(i,i=1..n)]: # x-Werte \nfor i from 1 to n do; \n c := [seq(C[j,i],j=1..n)]; # Spal te i\n s[i] := BSplineCurve(x,c,v,order=2): # B-Spline-Kurve f\374r S palte i\nend do:\nplot(s); \n" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6.-%'CURVESG6$7fn7$$\"\"\"\"\"!$\"3@\\_8![/4r$!#=7$$ \"33++v$>(3)4\"!#<$\"3s(y'4cp,eMF-7$$\"3#*****\\(Quh>\"F1$\"3BE$e?VH^? $F-7$$\"3++DJI&>:G\"F1$\"3%Rqu&\\L4&)HF-7$$\"3/+]7tY'oO\"F1$\"3o\"3\"4 ns0lFF-7$$\"31+v=7U%GY\"F1$\"3kwF[zOgx\"F-7$$\"3'**\\(o9=@[=F1$\"3mO_rzB0C:F-7$$\"3!***\\iq$oV%>F1$\"3ME fy3C9w7F-7$$\"3#****\\()3V*))>F1$\"3?#e<*p-Ah6F-7$$\"3%***\\(o!y^L?F1$ \"3l7(H7$$ \"3%)**\\i&zP&)o#F1$\"3ax$Q(e\\jt\"*F^q7$$\"3A++]Z`I%)GF1$\"3?k@o@UMh& )F^q7$$\"3#****\\P^Pn0$F1$\"3rbi?2#Q?-)F^q7$$\"3G++]#Hb3D$F1$\"38.&)=p t!\\T(F^q7$$\"3%)****\\P,xXMF1$\"3'4#zh$f$G0oF^q7$$\"3E++]2ngLOF1$\"3] *)pJD\")zy] Y6x&Fiv7$$\"3'***\\7.j(ph'F1$\"3$3w`e:+,+&Fiv7$$\"3l***\\PBL&>oF1$\"3W 30!=k%)R9%Fiv7$$\"3P*****\\kR:+(F1$\"3[A:SvE$*zLFiv7$$\"3e++]P.(e>(F1$ \"3i'R5>Gjc@$Fiv7$$\"3e**\\7GG'>P(F1$\"3%*y\\<'z5o1$Fiv7$$\"3_++]K%yWc (F1$\"3VUC<7d2/HFiv7$$\"3S**\\781iXxF1$\"3+5xO!oa4v#Fiv7$$\"3n**\\i&Qm \\$zF1$\"3C>>J#3**3f#Fiv7$$\"31++](['3?\")F1$\"3%[f7(zaTMCFiv7$$\"3q)* \\7y+*QJ)F1$\"3W.m$*\\;fqAFiv7$$\"3,,++qfa+&)F1$\"3[\"HQ4$)4G6#Fiv7$$ \"3=***\\(y&G9p)F1$\"3uf%z?8b9&>Fiv7$$\"3_+]7$eI2)))F1$\"3+1MfJlV\"z\" Fiv7$$\"3a*****\\YzY0*F1$\"3%HnNm0'RW;Fiv7$$\"3Q***\\P^WSD*F1$\"3I@]#) y5(eZ\"Fiv7$$\"3*3+++**eBV*F1$\"3#*H.nH.9D8Fiv7$$\"3L**\\78%zCi*F1$\"3 ;ev#G\"*HW;\"Fiv7$$\"3v**\\(o\"*[W!)*F1$\"3\"R*=sP&41,\"Fiv7$$\"#5F*$ \"3C0B;w`3`%)!#@-%'COLOURG6&%$RGBG$Fe]l!\"\"$F*F*F_^l-F$6$7^o7$F($\"3. 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