From 1c9924dc727651a3660d3b3ed9731ec2b890b04f Mon Sep 17 00:00:00 2001
From: NotXia <35894453+NotXia@users.noreply.github.com>
Date: Sat, 2 Dec 2023 18:20:18 +0100
Subject: [PATCH] Add ML/DM data preprocessing

---
 .../img/mahalanobis.png                       | Bin 0 -> 35665 bytes
 src/machine-learning-and-data-mining/main.tex |   2 +
 .../sections/_classification.tex              |  37 +++-
 .../sections/_clustering.tex                  | 137 +++++++++++++++
 .../sections/_data_prepro.tex                 | 163 ++++++++++++++++++
 5 files changed, 331 insertions(+), 8 deletions(-)
 create mode 100644 src/machine-learning-and-data-mining/img/mahalanobis.png
 create mode 100644 src/machine-learning-and-data-mining/sections/_clustering.tex
 create mode 100644 src/machine-learning-and-data-mining/sections/_data_prepro.tex

diff --git a/src/machine-learning-and-data-mining/img/mahalanobis.png b/src/machine-learning-and-data-mining/img/mahalanobis.png
new file mode 100644
index 0000000000000000000000000000000000000000..fc5520df6fcd91472f5fc8673dd30f781ad5bdf8
GIT binary patch
literal 35665
zcmeFZXIN9|7d;wLWCSaU4Jk?@QWOON>CA{iLeqpIT?Gq4K<ORSK@g>dCLmx5Xiz}F
zNC#06gA@g%S839FZ+D-d=x><0&;Ne8AMSH`o^e1)a?X3+cki{=T6^C;qo%ltc`q{x
zh1!HwQoy57Yy06plRwtO-yD{FBm@6jV~tn*3zb;5uLpiucjZsjKT)V;f0p?RjPUb@
z>q<J-DAeZn$bV~!ET5aeUmBZgoU<WVm|j=CWOKpfg3Sf^I~2<Kfblic>t`%YEo`h0
zNa{Hsa5x}&RPcZ!{OKx4|LNG#qsRaKFHVS^`0+c-uRwk_aE({hDng-r?6C@eYB(77
zH!;}+pPDKfsS`9HGgm11Ji7R}cIz2Qp95lN<hK<t{LyQ6GM4Xv-Hv1d{$ZwVorSwj
zDa1ZKB<92TXJ*B=9!x-~oVEQysosO+YboV}ZgSny-S%4!1YC=5ifWA9V?^AG+%F0x
zjiI6G-wbcv32Oyk4qI95=-)_tGfL6F;Vg)=K6})vLy4ws=y(b*pp!zT(EnlNrBdL5
zIDGF@e_4|BWUVpAz@~N$@-M^OlKp3|mq~Oh$<BU%O4`doe@CT_rIF&|A$TMA1*%C?
zrtNRP{`0fXMEe#Dwd5ID)umh_>E30<pv|hD@2AWxxDhaZW94#2qjgteLaO?c=pXYf
zQfg7wuKyhN^f&s?-rM%r)p~8=vfz)k8*Jp0u=#$5c3*mNx;+k0{1~vG<h7ZDWb^f<
zPNfDeXMXe($-Mq`pvt=CYv#W3<pL9O?c8^g&(ptods}$l-J$A)NJ?=18}rDH*QS-|
zrJjMbmeBq$Prb<1DVLOKM+`ERh*|bSp%0H<xJ909_m{&RIrmB)|3W({n(}Qs&j|94
z0qMK%{&?$C<oC_b&+=fW{AYV#B&mdCtlzX(DcZ3soK*k)%TrahnD4LF!YkyzJ$b(w
zd8zzH<9zxz9!#f9@)OHVYicHHjAGm_eLbAkc%X)aQLYd|eh<aUvAo78=|jpalWUna
zf3%$*ZX5q(JJT8ViF)DvopFH|xl4=A8GcfO>EkTOOFR@5y*Q9>P+Knk{E$lyo1Lcy
zn^a?~9vm}9v+Oz|NXh7q3**<sS>@kiB-PK)jA8m}l7uJ=BSl=K_jfi0RW&>H9j5Iv
zayg5yjQm_EQbu1zkAgyp<?U4PYNJ#?jYflQ5@zHUsGseSOn!6q%K?I?TaygQyz2Q`
z5{INsK$W5MfGEu{#|cYxogEL{Ct*b<hX(IxX;FNHtb~WdrJ8MSc}93^Gt`eg=4~qY
zW3xTlsQAsg?_(ejiII6nK$Vz9<Dor&tV2`zHRB)f-#E&;1$n*I^za1&pXT#3`w5=&
zu!bbNR3i76W5_=u%ls*oF>CN;R+DW4J{D)ylbD%<{C&Zjq}*Bl1?DR~6|q)pK5|O_
z^N1WO7mNB7FXKF^l-WLZ>fTOK&BX|D%V<ilQ@gLY3Y%jPuX?D<x4XP(YJ+87lLqop
z{Sn7aNgbAX3kNAO)2+AT7#=0}>_a{bbxg3AW3nPvS^14clP=zQC}&C~Bu^{J(40SZ
zr{KBs@gK8hx*{=L?(;XW1BqFK!feQkxT9C^+b6QDat_1iX}VM*mS~V=C#vZpi5$-u
z*GV1hK&YO@G32El3dxr~?WEmi+JYnUMms#AY)x9(rz=OmN}6?O(NZ?1T%*pu_3avh
zr$XPp$@zCm((ncW>5~HuSNLOnb_rR;2h^orQ5G|+R$(3S3UolO40Z8b=+1tp!lb0$
zuP>e%o$}d%%`1~za>>Yrvj^KT)28QucA7=g@(%XahK;A1_l{39K3E_1b2G1mpy0MR
z>lpXN3`#JuGS1heGENmkJ*XP-07tQJan-gejSwZ(LwpdbOS3eh-Pd>Q3?VVH><q4I
zb{>);6!MBiA;;>Gc}uQ=)y!xoNw@ujud1g*VH`wz_@Zx8*oH?nuM^gp&yM$ymQ0qs
zy*Qne@a&Q{&pY63VyM^Ii@#jh^5bCMy}5ZgI3BzIGfD=xDa}iCKQxa2d}!{ASb+7W
z-ACm|d!EIFR>i4C9;}Pk6u|lhPIE8ED(++SeM#SX*Ygc2_}Fo?>X$lJmx^9pc;C@m
zMIp?_il<c8z;>uyKH<ZbE5UUoTHc8)Q+;^iiw4fXePM#slw}`QWsx-?2KzkE&6Tjw
z5Xhsb!Y0|^I@p*&(uI(UVLyJAoAP77aU1^Hc<(o7nSKBKnB=rw;?uyZtf+4#`y_3Y
zQnZr{>46C&W!Ha*@?)bF2>dt(1xHsdB=q#R1lULsI7*b1J^abc#{YnSZs!sGLm9Bg
zunDenlW{)k_Y0PT+eI`dvg#hYLlZVj9k{)`lISC=-u7QI(XD?*td*U5jvhHtt$+Ru
z3*0}i?*D(A|1YnNl?f7@XIyf}`=(ml!&owk{;@|s24>p!6?ew#QsebM%KX=+;8yG^
z3FiqjgHvL)f9jtLCQ<R)l#qcZ5Gs=hY7(c8ba1W$Njm}=vp8I9-<a#oQjLo?XCONq
zB|rJ&(7e6vLdg_$+rch&Er6cf#BO|3Ab2j$!4X9pU~s`lL-1eYHG{5wjSnG<nS9(z
z`&M{Q`QR;Me;KW1%wv(!xs!0|$i$1J+oy6e^HtgfbgPhrf<h&|&=Y?h%`Rp4l00X&
z^It-z(mbqyN~}iEK~=P?Yz(<N*;o-`#M9H8Xu_9@m57s5ne62WI;p3vD#%z;#6sVd
zvWI*WI#3$n%i<Zi={Tkuq9tz5A?UMX!{xn3k)iq5TGa4k)GYLaA}*l~$VCjV{|Uk_
z00^6#95CaL4HeWmAYuGrBR1iB+q<~p-1lBvB5{;A<_$Q=(dY1~>|Y9B^xM@oc^!&1
znK^&<mHg4lX^R}bb1!w+OO8`w+&Bf*BqSb~l2n+Q?Po5LB9h7|aSX_Zbug`p6=&}7
zjMzPuNYG2OAnC{mNK1Y2W#^rF$0DRe1Q>H%)1|mnqMvUdF<?BZ<qV$X{vU3G^IWQ-
zJFbWZC`C!B<CPbN+s~`bDB*VqUiEpsw3JYTcHL#jO}{s9>HoR6i9SerkfZq}oW`%x
zlzIUTc9ca)VW_mAD772=idDU2hNlT6N<*45F;^@Bz1HA%j55ISO!CnEN{k38(}Y5)
z*e89cO=?IVi`<TU$Lbso*wYBG66Cw8=Yh-lt}ijGOaljxg^+TsE`_9v#}7NNfyf+C
zRh_sgdb_OKyaN^>ttn}6&(L7Yc7H1o))-04ToYX0B1!jV((SyR4oi6?-PST^^upK`
z98q@c1RXX%`IWHmaM;xphX`PtC;Ry*rQsq)8aPIVHH1s5FSPPiD_$=y+>ZLzRT>E!
zQ{T3>^uu+&O9D9J;s86w_0&Ba@#a}e#<4HFXwjuxt;St1G_b75-32TygId(q_bbOr
zXYbuDyb=<18n^_bJi`hL{%0JrF6UB6B5nq;I5w=kb*4gaWS~Qz(t8$_*x)5f5j>1L
zZl%o99J5jkmW<_Jrrh_;-dJxGF8p&ttURHg;s4P-{{qG0Xc=cT%Z@|b6gFEssdDu!
zy8+=4JiGXMd&6>;D>1HbItc1A7|KLXWs!zXkd?X|Ay&q_h=VtL{QUQtcUZ^kk4$>+
z>yRScC$Gfe=B#~oi7$h$q?PP_&&eytrl*1g8!vPjZFDAWk)3|4frI@2RwHn#FDVbV
zdGB#R62d0ll$3)<XWZlP{9i2&ii?h$g=2eqY{uMKqLY&_uA`61N!Ks@=Z^RnROeG5
z(NCG1isVml8)2i7-KLZ{Rf*i^`C}OjERJeM+-Aa%4(13@W*(NJ=ubMMhz{I-Kuv`m
zcQ-qe$(*v+-~|Ion|F48ViZxW_<oio8>7Db=%jvv?F+w_Rj76Xos(nL{`ThDrOW_#
z7e<yiBWw_FaY!c7c9w0rT*iw2S);ptMxsN?k!5vUx7@!!_CiyA*~I}LAZ3s2Sc%9o
z5DUo=NXo{ioX@{Sst4G6C4RaiR<-*bwkfAU0~f1bi?6Uh<%}&|8s;V-Z=HOhyDW+{
z7u6mppc!w%&+Wc~WBvz=b;r0vAqeMzrw)QQHUS%S5Q>l{`<4*>)XTo)$@#HzWdN|+
z!aVm2m>f;f%^{iQktVqI%W$${n)9<o#)@{rr+LSn^x7PbqZ~Np^MKz3K~lR69Uh|t
zj8?$%rP>QapC8|bGBL|OsbjpS60<~G+%_0z11}8OC*$;*T%DjNPVoGEVaq7ds|mNT
zU{Bx+sW?<?uD(}H0k53d=0v}*=2xbb2ML}n=PefJXGnwNM+3N4pPW5@1u@oT5^>DF
zDO~1jC2Bm@tVPGT&6+Ns`~+PpscQG#Eu*ta*#fqOmZZu1c87bu?z-Lcum-6k9XvVw
zmlo%SFjTvN`f%otM$3>4j;3(`D<ij=&NzJW(3G-Tw6u<}ltp^mdIH}>n->?ZEK*z@
z;`P@r7yP3(XN6>5g}{W%I5gcvBX7tb+H8tFtoHz+T~O!$HIl`gxbcJ%oVhsLx~Jj)
z6r~<x<#NX7P2+_-ef;16*6+Z!WIW!q5!nF0*KM!f5AH=EI>2VMXxjThJ0B72@1OTC
zmy%Bv{X_d}k5z@ozURzhh;bptzs_t>B`wy)V2Qbvz4S{?ewXWC<FkYBfW+mJ-PqEm
ztCIDD8Qq+Og@uJlC|od5${*RFu>HqozPS5m;y<L!Gg6&@n+a-V2>z<E8lKE-Dj}|r
zY=Rq8F5M$n=ejx*3ZFS}-nC~un9Eg?H5gPiZ&VgKe#~bb3bj>4O|l0~;G+`1@)JBw
zjIn{;F0wI{#WJ^zc?*+~=&h<NPbTH-1w|7y&Z~(zd-4vYqL<f8xn3=+>&3Y*Nctas
z0;CFLRiCaLy`{wkjHtbJ@6|{#^9We)@d{<QE-R}P6DZy>H?OWH6=0DW?~1VwF-wow
z94*S>q0Drb29JmE@zC?$$o-#{+{#@;K{l#cv382qY36)(HpGh7X%#!z5axzF7WpSD
zWJU6MMUCkgw*w2KQEn0XHw7f)j3{24V~yaqPyya6Y2as20jTbsNv<&pRSw|~cVm>a
zSIxr{@Eu65_fUBE3(xsIAH!g1A>(DW<H`dKF>Z_&gBWchkvK~yvqt=WmSP3JUb4A-
zm`(738^(3ma5f~<#Z&*L^X&3<Y#sXTI@++g7Yi$dmUy{}LnMv0X4!VnKF~+5c5Bja
zzeNvh!`w#vUb@{`|A1!uc_?~m5ZZ!Im!g9fE4A^;z0Q#oSQSIZ@h^%Pf2qL}*aRr3
zAYqxD0`?2`O>MF<rpYMv$02Y1)28;R$7bij*hC|t@QU;da_D$1Pkz5s6fkt&_dQv5
z!Moqt#2&$KQXI@j8fZuhTZc07TUCb^D7ox7%E~1{$vXmM8=tBk_MoqmCWM)OJcJpK
zhmsD%k0`<Xy04#8{@TnXE2#5Gehn5S-?b9Y;Nhu^MOj(Rb}n_C%wQ02X3gv>2?5Ti
zLqG7qsR|*Phco5M_SHR!Yvnust^C?1?y{-(Q)i6yu?1$E?}FOB_ASqlC!gH=`SHn~
zu=4I8v*v8ao?RZ(E06ZuxwJ#A=hEi4PfrJ(pG?=pkCiW~RA_f=KsNL^cQ)6>5sr#^
zgBZbcxSG>@)4o20(fyqrLpJjLg6_PxQbQ5^34=986-$MJ*i!9;2zUgjY%?hOA@~Oq
z)B;_G^O-QzB2MQL4OI584bCxn=+S#lgPYohEM1l5SmI(*7jD*1&XAr5N10b0e>e!N
zYWSh({Jyxs9&Ox<H*gLb!<Wy&@qb&Dz*nU8(gAKW^{+_+oup5dNmZ_M%RBt)`JeO~
zysl!}OAZq@)KTA~-5PJ!iBnZm%Y!@cc-jMjb5`_9*}e>qhrho7SqP-MFjet&vFcAQ
z!pY9{r;_S{AH2w~Kp^6LD8bD7m6&sA&)lSt@xc>>*d}SWJY-c+u`8roW~h)6BuipV
zqB%c09;yY{YRSe$xXirED+LUkgUwB%Y1$QkF9j(NG={+G%Q?J&oKgM5x~~HS_BCmy
z?F!KR?Mx$|0eo^~*{L;=Wrd+t3v&>TaQE)1gxHN8H%0fjcVUs|t8hMS%T$wn4A~AS
zFZf`DJYbeTU2C(<eC|H&CByvvRZ(IUJ<Jv}=5IPhk~H9<U^Y3tMMB^R&8|Aev1<>_
z{i5TVeLsoNUy&LfRlufPd@LOA`|2Ic*%FdAIinHC=^p8Av@Q=}k#GJLxO((=yz0?+
z!5U;$1NJz6jQxwu!~=3@RcsI}nYSg+>HAQr**DpSbwC}1rndV@m1%f0MT%RBh2T3s
zg^6p{JIA1%ZoU2T>L;tW0!n@y%shP90)KeLODdf2%h$JOlI_Bj7$D9d@&7M=jpqR0
z#LVjf*Ca2DSE|FVy)RN00ANK9LxpPX0rQB@N>pCnv`hHBxn=|?xrCG5M-{N8_HB$1
zWw_n$?-ec9cswOGH#HPi<+JlJ5#G}?^7M^lg?sL+fE^H1Pdx&s3s@hBh(F+vR3<K#
z%Z84NK1a$skAjiGtRZ+bWl^_>wz*HYF<}$jT$_15NUgwb$Lb4d?Dqxr-l*UO&OZ6u
z#CNYKS~Rc4GQQwXFPUSEvdng0sc%bj&<oaAl!&<mH8B9v9}_z|OlU&6(|_U3zC7`y
zpx)~JE8y9}CEKWh8)(cRSRo|U9>@8SA_$)W`%j{`a7dzi;&oEvfN}+@8`A)AFZ_?)
zcNNb!O69v;4<L6fT?{1;6>P_>LCIHpO4VfA4>gk}7Y?Ev7?;`kW%3UKvPcNN;f;CF
zL&%*Saybi=4I~+-@qjAbH`n;;VwHDc&4CyvZ9k|IP~|p1qDTXJQHeOw`&C5K1@fxE
z@Wt;^i#N9k;bwQ01Xj6peu@M<WO7j7E606lk<OH_LnYC<?Ei^dr%cefXP=%X4RTF<
z)iw&}x8Ah(cz`q@V+{4nQ^iPr*<-B!*BSiR6-_WKEyzPyjO6PP(7{7g`a6t7IxquR
zPMH`bX$xeq1Iy1F`o+sBoc`8VMd7J?rp|>eO%NF?7D!UcU7YPB)jv6PPlYW87V0v7
z(b^x-+`=FecIgTil&lvERgiqjz4I44UU6#y;Jy_UX(tw}3;-uunb*GBzfc@Ml(%G<
z2#4Uv0t2f~g>^aEC^v{$%$D9;KQ16TuvobZ?)JFBjY77bFj=M+Ljmo?U>5no-(w1V
z5|DO#EF^1koB<b$0t%zO^JGyb4rcVk;zCIJug>2ji@7hl&}Jw4l!@;1BVGXZ^2g$+
zY0XZ`qlLSSf~&r{t`!rDI;j;KA#!Q0wvhl|iR**oZA)lTBi0sY;2dX+fiNb8@N1Ih
zp8*+*D+?D<WPO{rQa1>`-|P%9i4r{98D@muC1eP)hhkElkx`1tU9uRl>JV)+hollQ
zDQ7amB*`!bE$Teq0D1$4N<J~Pv*LoHT`Z@h2^3Lb`kaEq>OU^;UFs7;p1%Wa?G|b7
znT{ZJ91-Z<z?WJH5hgEZ;aEc;tVuLbW$S%Ax8R0FEuCJLVmx+#_z7K#ucKwt{Psy4
zpyy|EAgoC@<w04($NErMnRrG%`a%Lh6C%=Jx0T+G%$kmIQGspYa9cKPKBoUrHis`$
zfWt~o@6_?)*z@$gpOVr-pAb@gkTXp1HGOC*nQ2f2j-q!ch42h#XjgZMRKGtp{MzHc
zJke{=KLwB9nBFSIZ&UqsJUtd_+OMykC3Gg~q+Sm19qN9k7{TG|G~MQfq264}6v6y4
zSHrs56xZH*H9OR1NhS{W!g-Wu7r>9Xg{c;}dmy_oS4tl2r%<oeRcN3*UY`F+3h$iQ
z><pA12AG_~l$@z%=eS}c(3}9v+}n9rShK^nw+cH7@>5vV;#kbm1Lltz8r=>L@@yMo
zoFyOB*afdcaZA19Q0*%2ZNN@V$t>6mQz;;VkaXdgz{Vc&U4@u-Oax8?l2@*d*Hp&$
z)l*-9bl3fgM~=KWe-BQEY4d4e(~?Li3mfji8_0KoqPT^?XZvmguaetH;jSM=ti&9r
zQUg?gl)pf;Ijoc8WQ#?4Yp=lgC(Res6>Mq)Tkv@^TEd+b0zi{=+$H6*L_qXs^>Uq?
zs!$ff5_6m;NH+fUzOSE}8`>j<%wL|&SO)p*f5-0k3wU%HM6QGb<Z-!8UaF)3N#-U4
zFz=hrP;(B($aO*!t8JJo+L&Se3<?5ROpN0F-TNtQLWYeRsI4t4`vZ^%s}lax&c}Td
zVVyYB2H6Fi!APV&%41p!9&^U19w-zQNf4=Mv01&745)dIpLNjxNHhqgvV4kELhKVW
zd->r&TQr`aD=@di)_u4$nD*Ag3%$V71xaAL+EF$Xce4w`ZOC%jV`V`lpR7UC`}3M4
zT`mPx?$vu)IQg*F5FM2d^71MZLE1d7SsyRQH`TXTPc?(e2dQNFWxrhT(q=rJyQ5^6
zVQAI0v?lGuhlsH4(fD|kl6vU`>yU2pMNbo0Yc$o1li5Now#j{IA?`0Npmmaz9lvjb
z6EfSTfn93c0}HCK0m04vx)6v=;22`4u;sC0md*OCI+e)?lWN=MxeM3qHa9@>2wRDn
zE0E$6Pz!ryUD6>#!SR5+1(%Ka6na?TZV3eUb0n)d0}@3!6nHfC+s320PfpQO)r^ZQ
zVL?x<IfD1~G2;(Pc0<hu6{7Zo`UKAp9cz*<{5&k6pg7|YjJGU1N)EiPM1Kks61rRR
z<$|JMvii20>`qEP98ze~qBs^m#wK``A1bhL)kra{R=frluSX?@&~tTQM&9DAa*9g0
zFey=<`+R)KvppXFQZQaJLvse^D@k8G8$ZT#?503z__LyY+e?mP+iyqaO_Qc&xna=*
z_N>4HK!YZC%ZJqSNX;?a+P!h5J=%}Tqpa4v{qns{))^5%tp=KNq!1YSFT%|-a@=o7
z9&7?S86QCn9jBUNC^KB_M1IsCJ(bTOaUp46mF=Bg(0w)mEtOG7Q=|wP|4a=Eo`gaT
z8COcc1%VccRIn0V0*2BHqwbT*`V=k|Y#xKUoWL$rI#l^#Zf)PY%Az9Odde~z3~EmM
z?#1jvaWB65=>%A*0k28!V!S5l<q(>A<0%pv8uf)K?sC|}J)w~h8gRe@s*V1=T`i!B
zL>kSF8Ll@=0_tezVO=F8wp4tIcKEh|rY<|9fUkTy`cV%e66sp?%W!h_3vD678u`hU
zjC6mq^N!CK6rU&=P;tVYw?av}6=Uy#gtyPG*FXix$u3SC(_rIcGq0r?y#Qr{67c-P
z{XNF~v4C$tjCCCA!Wv%BXC$ElIQ|3aIiMq|xZHsa<vT0{*cH1prFB$@2!+4nK%`}E
zp!87o7}|g?+{Xhk7x&kbSzt0jL<kqYq{7Au`Z_2HXp{+LBKiUs90kjVycfq^!HGUk
zAUHcyUZ5A2oQ?2fq829nsE<-WR0DE`DmGNQ>wz)axD@1EzL_tITv%e87<MhnfoXM(
z6*zqe(!w9iB@gzLl!+@57x%;{&Gts~Z9sk0PggBZ%;?$+0R~Z0)}XR)t-xY<)MtaL
z;x7$54aANMbbkBPfm<-Y1SG-7Xkg-?7WJqt{F!D~tPja_<i9T<`E7&ot(oDcq==<Y
zb);N=P4pVn{>g+!z$6$dQhqa|T2HM+sHg8a8EtBBK4p;>uh1|BaYlJI?;+4ANLc{*
zuVt_)3z8j;gn@I9m?t8Sn;w8AUacN47YAER)QcZ^VF=Gu!>Z;}<$}gT4(;E7Qj!J)
z5BU$c)6j=f_K9Sz13@)^#FSr&A9lF6ky~hW%vmmn*GdFgHE_Vgm<YQ>TI_+9&OLAn
zwyDy(LLWAOyG)z+9o1C2Y-z2XsBa3@-`Ds{{ISU1cdS$uhoob;l9QK9u(cBHvIdNa
zeLDpw`!`&UAa7|78)rKN8p+2-1Wv|QxlT3l&eUDWSCyfX(UwzohLC><d|$KdEonf+
z<A{UqOemq%0r|((W`sF)c$>8PY$iQ1!QLg`0L}erR4NPVu3)2e2aPudXll2G32lO7
z3urqS;C|5?P=+6VGTO^0hUozBMC+drzOBwmVOx5hK_MR&4WxZ*40w1ThQz7I9GL+Q
z7)!hoWgALCIef`>97BUFz)u0hZ%G0YkMy_rY7%qzU4Mqt-)?3H63a}~O{;Z5{K`?P
zSo*#d3pvJNn??IaA2tD8z3=X}U&I{*4R7{bWB-s(OFdQN0=5+<84TsJF~AX|@Y+rd
zj<a~!H#+qtSY>pT#|Z8EwsuuUMSNFp<E-Tuu}!c36plSB0&(W?n*9DR2CS&;kI_jk
zNZ#q9R&@&8nt^O}czChn{D}GYYm@L~Si0B-FxF<U^WyOF;Hx3k7}!UVL3cX=ac2Jf
zN?4?qkefU5szL-{qZTtB#snGe+fTt5xW-aY+)j5ka}fDs*Kgqzgruj6HIE(B57ngH
zlz(+@So3J*x;Phfk6q>0+y&O$ouwFRmAV|uPWM3s0Oy_`5YRs-oEEP^xd;XA1InRY
zmYQn{cvcB_TX{y#zEzUmYJlXxxYxNri0_rF*D$s1(~4v8n76GreFh;ExamTT{oy(0
z$_CV85T)+OTExFLijh2g?%~$GGE)X_;U@SwJJPp;cve2&laV&F5uza~3q4n`32%3$
zs<Q0?R~Q7j?uXWX9eS2I7>elC&u=w83PF(bqXhR>#NMNz6j=We%7*V~Tv;0zJgFUt
z<6ElQf_B|h9<<Km>h7c54(l%Exh<fn;J=FKZDClN`>bL5u(ZJ??%tqO+d8avZ!`d2
zXU=QYx)n8(2e73Uf?=8VN#ri~(PM=D%{BmFt-cl9CFy>FWIr{u#RB&SxA5x9_kMxm
z8lDl4sdch*jSyRGn=lKhvLRJ2R~}mMJJcE2HzB9>{vXk)a+ivCEPE^%SoM1IZ<F|T
zd5T4iMR7I`mn~I{k#vg-^GkbN(k6nd7T=uZ_=W=@jlNR8*<A446NL>l0LNGc?~N-t
zn@&SYwVL0=2Hkdaey-Ptl+a1=^c{lAyG1m;2R579cxQLJFU`etAo4X8ilYb2fx*2l
zervTKlqaX&HK;gYogF(?eKdA_gtYiI4@b;RxdeV2Iu`WwvsK1DDQ8k({jY%Uy$O^=
zz_f1T8?Z~aBmjcpF@$^pfLss)%4DYWX~4876DOrFDAWL$f_)2hxGI}4B7jQy+-pp>
zoM5P760h3PRdn(P?m5IA4zepbw4%p}#_;K{y!EJ$GXJ>Yt<DVP(z{B;TS9@SU+155
zVeLU~=iePp<_&MKoc4`3NFSquW$kfsi{q(4FWAJBla#h$wOc#2RYNA1=3kwwkmDaW
z1LXO174rNM=#m9um$(s#IirGIdZ~^PjmgMcW1<Q;t^@J~h6<*iNPZ`J6@eVO!=a}q
z2<v68#lP;3H?4$CAQx2Sg26rLZNVq@U5<a<QWNiKQsMj9Xf3LP^B;TIdkbIA?D~6b
zd5E(2nvc{bX2lR-4}b(+_vp{HSaZZ@`Rt*UkBQwh0yrDKG)pc(q6a))MNkiEgmQ*#
zS8}ZA0e=cZx$kjJ-G$yhkcgHp4WGan?c`mH&uqR5m-U*LGh|#dQE&swd*go|a4!7X
zH8lA!c64F>ZB}ehGwftWW+3_uX{CQSp8#81vI)dtG<9aITUpGsLP3}(d_nKEQr-k}
zw#>l?TbPP!M3=%+VU33<_(DjoNh{fDrDpc|sFc0H^Tx8}2x1wfn;Q=N9q7QF`$Oam
zGvW|@*z_RiLpGn|>tj0HfvQoGUo~(tqaS%lEIS1Qs+jk6Dk_H_G2rj<+rBudH@wa(
zNKFzeoR^+7G}UPB-{C8M$Ig)J1jxb&zh(W6dQV6+1kcgUD5oB~)18N+s+SB*l>t&l
z3uwIzsG_G-U_e&n;!k)lSFlZzcogrHO+7?pvA>oU5bI(hD?Cvg1zv!CL;Q-PtHmZG
z-wH9?*KpWzyTx*z;0~`iShX<vHHo)}YfonPO@*##tcB6`_olV49z)HA_(|FH3?14S
zX<+d@SwVFiy9}iXP-T()*7v;Rcy-#Enb6dG8rO@TO$i7o6LXxW#55hY?S8cm)xogp
zC?0wrIBnZk9nNpl{5<OdzQ~V5m974GVbl4t#bypEJ0&`w@er(x<jYI5;UZus5H+g?
zn+15gyxl2T_E4Aw$K`Xa9i?uG>h9+fuGNtLmK<4Zx<zI@fU-E?FSiJ2FhoEbE`eza
z=dxsWc`4?p`MI#L%jKJ+y_%n#V!>*2Z$0|8rNvms?xEW}$5LQbSJ(!>GVz9Od!HFS
zx-}HLS&IF<+tR{R9P`4}e86@Xs#RxkIKObezu<9Vl@i{pB{!!dn2&&9xRpvAq|T{<
zh8hjrVVx8OD}c=;-L`k0sv)j}_8!0h3e=_FFou||uqz2-@{A=M5lEqGQIc`R`UsF?
zn{`K&(Pc5GSikp;If>6V5=+Fo-eUg?)3nDak&)GNuDTs8no!B_=|ifNcd1D+TrR^m
z$&=t8#&LqT4lkhbJir7vAPn_NwBzX%q+XdRj5_gpXf5+j!9zV(&zS3@&uET{u+6%j
zjE~`->Fo_6?ExYK>g)Q;(YLP=Gr}dIp5#K8pJ?BREtPc}{5virUr$xx=G?h{uuzXa
zF!l>v7m&9)uYiQy;M?`uqA3&GRaiTjexn^d@PWS`04^Aife{!rN)L3f@2_4+-j}tl
z3W4bq*M*6iW$rWDebJG2y<5O5Xm)NWuA+UU6ccpkj#wkEcjw*)#$kK#K7hKk_t?e1
zP5e1!&{X9k844*bGoz&XA})79Q};Z(LN;wBKTa9l3NyTR0@NQ;Wzu>n-HV?OhCZF@
zCkYy6r<2V_I}pP#Y-uq~Z`ZPll-cY{rBPDw$VAO{&W>=xV|69%GO!6GPmX@dw{C0t
z;;5jVUb<=E&drFXM_Yl<U#X8Tc;y)7xy3PatR?Mg@qN?6(E?Nmxy#M#1Sg<8xYf;b
z(<AK|Dmb|x@LM0&dviPlpJm4=Wzga}6=h;aPMlV);GBuW<VXuY&^A1>!Ne=8t{!x(
zrBL1UvWS`-AX8y?Tq%zRk9o(()*P$3fiz`K-+^(WT}oGwx@=(8k=*Hvgj4FhK;ZHD
zJ}l*9lHFPoc`|67&ez8$nFyZIOKyuZS7;BfKikoN`sNYmmxdN%nA6S4MI2hs&-_^-
zdc9R1v}lR7^3AI$AYd}`97Zkz#0FD24PiEk2+X4dBaFBSY+PU{$*ofijn;~=(*%0_
z9;-!)saD9eH!V1S+r~2@zj&`oX`WhRXcqt3TGv9XSj8Z_0F;E+n=K+j#_g_dJTcK{
zsS=`9E*2?^;bju>O&XaYVNb4CCdzitJD~j#JpxBTh=U4OgXUb<EXqYiI6-hk9vsiY
zYH1bC51b}NG&v+Vj<tU9*9E>sB}9tSHH78h+{>jNB_{KrOY!P)qb8Btb!lPbo#~6G
zX=KhOxahe-v5>TqXc@f<8L2#62!GtIu)_wKRS>En43oe-{RZtZU-%RH1AUui)>#}v
z8oVQ9-BohzYfGMW6kCF>r<hJ}OI{v%E^5#LyzU>}+a&vqKim(jlC&SZ7QZ#^=@luQ
zc#BIa`SMVkQd8bdiLqOC*}mj-Zkxu3?zI8u+phKQ03Fz*x9anH-Nj8WFs>o|*aOGX
z*$<ROh$>ge)SH1{F3yJoK3e2!3-4Uxrq56EImezae76y_+&8B7s`kxcu&)_1+l{-H
z6_G~YI1cXFQ@^p?zI_vEG3~GIVnDB*T21^`D7l=VmBlFn=^6H#{irEm*U*<8_f6_I
zVH;Jiv(ld%i#Th{cDl9ustX?;FUhoY%|6?JO@PQ8J1=rOQhP>CPPHP$YG?s$OH18l
zVdL%`Dy7|1k<7^@i&sx0_>ZdjLJM2{{On15q^!&|^_%Bdq4h<OK}d)VvC7b?2Lsuo
z!8|RTKP7izQV)IrTLkWnS&bU_rz{?t03nE`GHHHqc2Zyq5DeHW9n=`o`!FcRDsV=G
zW#`7Y%VLkllbB_+XTaNt(0spA;0-Ss{3LM5Kx_|ZRR9Qn?1y)=^3T@EkxVxw7+wWJ
z<cBQ_iPEUizu=5+5??3oSWza~CrI$@xAMC%3l@G198m-8zz6o*MMohW<AizpkDbxQ
z)%lPXL-Le}6p>qzUZyv*=CFegq|f37+znr`e3uP*rtzG=$7r7<Ynk@3=_@>MF4^7J
z2{tO@A@)@#kRV27le=;+H-oD@&PUK$C1K~Ft4GukK?v4lF(c2+j*y~Uj80D91gU-z
zpqgvV-(sZ#8gZ{pD$>7@bV1uh2d$UoreLVd=IGr5jir)JPuC{|2k#)ny1I1zaUP`v
z6foUI;Qh-{_1wQ8><Gs`7PF>IDtQtd>*4(F%fMt4hh!C4$dG!KZXt6<2t-D1p}*Ph
za>==6ldD0OB3!cQ_!tP$vP^0y7_vPVhFYmE*93MpqS*H;yx%5^k3Di*_ZHeKK6+-j
zO`0$l%=frEKKfZS+OdsVqeKkz+Z4^{TCKPQpwd=Nl<i{OEk+hJyZGj)^1K`Er)fSn
z#*Md3+KxW7E(@$m%pS!7<Kj4KLb%i-W_>!-`9oHxpII6pmeGvv=%6a#(s+AvZFTh$
z5FWTcuGPQJ<@He;wK>sB*`Swr>GZaj)h<Olu`#JV`o+}zKu0657a&6TJ+>aVe(#o(
zzBDM5H;)%i<x2f{cg@=M5MAg>{eHWr7YBe>gPnxtT*2*UhhA;rls=cDm7q(CaK46@
z{&r5Bd+AjC`$g!sfTFRUdOM0rZ%v^m;gl}R$g-%N{mnCqIsBBFz2d@}SKG5TOq7RK
zNrvBP)#DJ_veQ)7fw%U8oJK|p*=`0B6<|q2JlGX7O#Ym@%J+7yU-iVM2XhBsG_@^&
z?+!<S`&F(^GBU!a7PWe|t9`EB@K%w_RRb^3cI}~Ek50aGYJ2GCgKvr~H``Tqk7t3r
zU>P^PXty+X4?F9wBS@K1lPT1w>sAv0DV`d~?1*TX&<JsO58q%zF?iv$D+YFFM7lD_
zA6Q*YoN`6WZUgS8BTvb<AglY8{a~Zc=&zJ>$*6VU7?1@7{Mb@*v4*L7?d5`;Yjv$%
zHucl|U(o_bHu(-{^*O%i_#kz%eTK_zx~&C22mK1@Cim1PjdGc#y&o;*mgZAUPDh@Q
z9VysO0(*5{$Cvag=?zQWGu<&^RfFm6n`um3E@$wmQ<+kBOW?S}4T@cPVYW$?=pP|c
zC$NKGkTQ|Dy>a*G+3umN)>|xS0?7yG6Lec{@442R&p8j-2OFfabebV^fu>e1gW{H4
zQ6#`>#vs`*zsOQ^!Cu_ktm@F~j7Zy#kJ|{IVv){3e4wetaqZ^*k1Bk2+DcxQ*x}$B
z4Cbh4S11tvZaU`BSjooHrA(|DYUXv!&hsGK-S7D$Iz#OBpN4I$7!|gQ{%O#e=8vXY
zm&<4iXBAZzMnL-x>=~rV%nI=r>Vnrrg)u3;FY$Anx!qGm=hsi{Xqd1E{2d&rYuf+b
zupKShkn=#s`3+es{rW4O!Q3Nhrj@5Fa(2-}+q;aI=9l)Npt%e`YaLU$$@92<Zy%ab
zJhY)2^ZKzxo6xPIu^BZMj<g5IJM&1gc}A?D#;k^F%M<`Cf;g-D@xgO8Ac&&%USHi$
z0hw4S1&Rfd<9^%s>j|-6FW;Y}(Sk74!$s>9hrRL^Gs%;h6Rk7DSiZ-Bi`F%X!GdQ1
zZ$6Q#pJ~cI?o{6P{_(M~$6foz_J~{t1Gplgu|@l%OU~5yFDLP-SDt4@ieIkD)^mad
zAzCsO?S{(B8tvY&ufB2MCJ-OHHvS=NbTwC`<bi9>=kLZ^<-t>#Py<Bpj~gp0haG_i
zJ!1ycUBBN6S%f5(_Fg7*<t<!5HiM7_rh?G<u1HHX_5IwG@{xF50$%D&W^f1Nr`z3n
zW>{?VOtd*P?E&kYWSD=W9nLwn%M+BkNdDu7IRJdHhZ~jlW<ys`>)j25I_*g25<J6g
z<MWq=i>>?c!^!P2d-hW}BE$+caGH6C(o^TbvvrU%P@8;mH2g|*;C=hH({t*Qd=5Kv
zE~__!5#^UX_WkBL=rn}RE6}=k5jvw@Br-<}y#xZbOk?EkW+{)x6E@!iz(qxfyHA!O
z7(lW2pkqyCU1ey@Ib|!wgflfcg<Bpcy1cGc>p&cu1~0S_s4GgWI?5K1m+S5XYEZn@
zk~}T%Aixo|jLE$OPkpDJSXdKSj?nDUVgXFMK~3W0v95u+jIS@Wm5J~N@R(?^RrNLE
zd>`vB2Yy)F$dzgWIyPDC`uXdED)$OLoT8dBm2avBk_1e(1xnH$N~T~ZCuh+#Q!kgQ
zu%(zS43XH?#k%F5)!8g&kPcsVJ+fz$-CF)B(YF`XH54k<E&W3U-3i}ICRBxFd3C1V
zG(%@p-sJ)R_^Y5Yg$WwvW`oMM_b2J_N|2-P&Ba1yn$tutmPjx4f-}Kys_OX?tPk9H
zc;2!!eC(~FH>Pc3*Hhmt?5kI>v0pgv<?1^3dA&|4uj+BO00%9XVL50|_|{uS>f_qn
zq~5)Gv+AxpV`Js{#@mz9zcFKdjZ09dw$H2jHB*kWT5jUvl)N_%brH~gW;KZ+;7ECi
z7KR7wp)`Y3OMui5Q<~t^#}zl;Ny-h~sQ>vdyq+_`p2lM6ti!6buCKc!WIQeV9A2+M
zJUv;zz58U+S49!<U19AvM%UP*<WH;=lHkl#$6}9#;K#a3flhxGWfy@~3^myV#k66{
zY!D*yCoA8Myp-U2G(9}3`g$!-9K*Mw&_ZRP%5PfVD&k4ZdUKmxZPU0L^oy;ItC7Jq
z-vS<Ch={G4pFXGu2v$<P$Zy)hi!khs3tU+4(1CMQoRwab6RG~rPF0Mai?Aju$|L)q
zjCiZ<J)?~reOf(!S(vn(1@If`rm?GZ9$pq?peHcg<e6F&Ixv0G0^!%RVr=3&CM$2V
zcM%WgF1`bzrDMygJ@<pO^*EO@+}0}5&nwH?=%Uszmp2762X>$#oPU<?X0piaIS6n8
z3>1X@+xFGx=#3U_S0`0XYCY$!yH<zCCVdC7y#pygso<u<g&x+^!n2DUbdYtyv&!s3
zd0$#t>hG@<fd@e)f4|o-1Qps>qs`{>yB^GCbZk(KP&!RW-<&m|L=<mqEiE10DxpXU
zg6l}rG{eR1;73!U@|-frdGc#$S0g|?fsP6Qm=s}qz)H#%c48H4Q3b1g4l6e({%mXl
zPGtd>OKIoaq5yVaTBQ8A=AxBRMea-&J8i5?N}YA&@YX+++%A;q)G!a#@zkAf!eJB6
zCtr;7k)5-w_LJz^z1(C8T|NPg=3?cQr$K^u?2dZOb#@JW_6nR?=3PA;gkPu*f2ZKa
za)Yb<jNT}u*i7`2<P9SYrUYrQrLn|kFLn0oyjIzR6_V;9w|=pP*g~>7Y?xiE(Uv6y
z+SbWcCB;RwEHiAQt^Svz*y<Y-N_<)m8d0?l2UYp;88vIjo0JfnfmGL=p4Foje{v^P
z;k0D(HR`4+)$`?^A;g3(SZAP{m0pM#<>fA0Vn7SSF`&NvQvj6Dj?{bMXYvI!XR1@z
z)r7yGkBLD-H0wQ;q$xLl4lj^=$l<<GM&&IdXNhDwN2Qs3@f5+cHgV4MS=7Njo9GUo
z4ZMHHF(ExRI*IxcSd_=qe@QZH3bKNMgU*vZ=J4kAFk^f6*ZkCEDuX98xZ4}&^_&5t
zZExAj(-R}7j2F<$i#92bmcdY=>LaAc-((;urrHhYLa+h12Eh}$YEGrN><~XQK2zem
zW4&b$ira3bY+2Fse~`FJJ7~^`Te0x6^rC#7FsYs~Z@qn!8t&U%(R5nU+!olSys{EN
z+#8)FEb;0*9XLhO1$7BMP@5^hYiYYUKc-GY8iyf?Yl>)&yUg}HBLP-TCX2bw+R*MD
zVRn^8p_>1Bm;<~gf!&<Zqt=t^W1g+++u7oJc*9k>jazbMwQ?;z$Zw428(_PFC0&KB
z0_lYfGjziKPJ<0I|L0*=cw^lp2|nAI4iU7t;b&maMjWrNO~@WbIsg`thVOdww5H4a
z3YF!?x7s~)GuSOd8czt1OX?(9R&zc}EtiFM4Od{}NDZa_##b+W3Ka!s(U<o>%k&=#
zoyVgDIYxim2JIzjta;PdFl904DGpj=eLAA3$LnXLQ2v6B_&qe|!3;&#8M96=0>(e*
z$y4&1!N-fFZrS5X!U8+Np``;Yu2}8mX7vV3FR`S1Zy-g&<BkwD!!?5vNva=id;AnS
zwnscyIevbqttj`YqA(Vfkgj)HtY*%W0aX#%^G_%#LiElgwj=tr8vE@`zz^p``sm!(
zT?#37vCAA?Gv32T5#1y44uE^^8(FY-k-%_I0?9wS^2H%!Izn)Lj&mC2FNb^UQ6u+O
zP|&i}hT5YiF=0&mHXx-$>|5U~<k-x!MY${3mDWHt3nPOmgO9L3$y_H>!)i&VTbbA=
zX^5%ok6H>+K?6?;n~IHJBjBO%B_DD%bhRK(A0*u%U%we%mthvlZ?HSL9dgZ$rrYI#
z>@m(b{0sN)0pL;=sF!`=BAtrEN$e3uhbYtsob%iM;7&7iU$6zG_9XjmwFgK4Od&i|
zBcWQ^{uzWnMxWw|4tr@cwHEfEu_CrQV^I?8@F^GQSM9GSbnp#sx*W8fEP27>5zC!W
z2DX~lMY81<r%&QvAkVk;6w*+>^r683W%!@L%HyHViSPU2Xig-zuD6+sQz2EU5$!3I
zt(%t5T`Yw6!NW#sc(chq^|;ZvlGE{`&BBfiNGBfMY!7mcIVn~-EEJ5FD^kG^AzOa1
zbf`%&rJmgq{EitS05C&7_^Nnj+o2_NMk9&5SmGM@HMFrBpz!AzZ{>Aqa=Gu5yqJjC
z$mk7s-zykU2mX6o1&VY>lmRW+%ftl{;@iEQxKOzT8?1sB(Aj_%0F!A8rC5iNtIsd+
z({2^|U>Q&zTmO*<P#wNHhZ~>(_F=ijG3k>Bs2UdqUHSofseLiV@vqDK;zdckNsF3z
zfv$ZCA=(Iw2qX<6mxA+fXmz>xBW}qzM}BS9rwI$(j*Ky-Y72#x_}>_C5PfmVjOJtH
z%0toAT?{gz#q%n4DfCt6%V}pJSkw}_%4zOS;KHI;rxXLkTLP#jsKjq5cTR1zKeZf|
znLBC4iLmU8Si?P3XI#`DXdEG9SHdX~ccZ`di>H)iIcMav&aUs-ZSTF5f$qp5CBm2m
zNI;_3YCl67O4Qe}LhO!-FLM)sRB%>dbCSvJiZDY{?{4P>`-R8H|Gv3J3DQFVF}V~w
zlF3^mdAyW+DKpmn=I5mSSKWqWNne{C^zdV)QTugbZ}33O0m{-O!>SWa1<nI^P|82*
z(_;Ebh$%lvd4#uC3<}=StMj+BKtTf!G;^%<uCItrKa#7*cctbmZ7b8S5v2O&(fqUh
zm-E(_v#Q&$Fv);5RBhj6a7Qi$3bcr@*P@!&QjI6-eZ`v(&3wBjgd<K;_X2PO6`X#M
zkNpgk-|N$CUr>T|HQP;S1GZ`*Rk|*zZ#C{-_~P9S(6TcN@r1Z98eLD#ASAIwA!?(Q
z|9^(M=8+m0lAx!y$@j7OwR(k=!e^D}_OIo}McB|jw^Z_*k(pM<F5R4lIauM<S~x2E
z%BKn_Pl!lRO6+q8Ay-3Cg1m(WQy%pBpTqY7(@O8c^1s|!<quW3Q&sNmj{1C<F3~L`
zU90i&qxUu*IB0-YAS40LU;$1v;U6PNe)GNlSWc9so}6VaInR+DYpxm-O;SC5=fmSM
zJ!J4hcWESVk8Z9D41<VA^pL;YmcFrIjVeDEy?&z&i*ZoMH&~%7P9^++Bce4dR>o_-
zpwE%nfRaDG!Y_a$))gA2NZ`Z^s=@^y+TY{WT{i^1lsBNT@Th$?`kn$B{$TEtryZGI
zw<5DmA@zLJm@!6N;27o5;3}{q^U|%onQs=ygCLwjLZjJoBnDSSsQ$s(cju)J^zWK1
z%uZmIdJu*0?sW5dRDjHCln>)e{vQpk`CBait~~^0`Tm)nfiI*^i{8T&^Sygq5?<C!
ziD8p!Gc2Myx`N7K5{hB%xs<{yF-oT^09vD=u}lw}05L4iM-FL({n}DqAcQA-Q^1M8
zZ>5BTaV`G`X82NzP>~Do)?o*LF%70$v_Y;$CT#$^*qY_Go6~79(WM1N<7mH~bh{p=
zLI9^Z(2xmYYr@MLJ{>X7q6I0`=}7^?sc6Jg@DcGz_o%gi&k{xl(NDo|o?~#avx^eZ
zJ&R|JTtlc|vVI?$lke;LjSVh7z#aUT;*c(~?96F<MTts8#B07$yxR4+(G=Gq$8SN8
zeRa2}EX0`jzS)KCqITpsW5P5xnSakr0!6<xbV)G0=AG*xvTN#~a}R7iTbHMtAkDG|
zI3^`+dzB`8Di!h8eI-bFPD(;J7WyO``b`J8gGuIE{F$1mXEAQ1D%quZYZ~JF>nfPn
zJE@oxHC??MyELyu((N3B4lZFoG%r9E&#$)$Ybk1BS#7<YFuaD1RAL4m@6oKG+@LDN
z=RjDKOo228fG(ejD>!@j9Sdd+ciL*22->MZ<jUy)`|Uvro8Y<68jp|dx33JRbEo0-
zu`x9Xdc2gnkpc%qHR&jU&<i1CzsTSM-JA})R7CSCPgR8I$;jl1{yKscG6Y2zY+{%e
z$8HX+IgnZ;XfzBf@vGA|;?bFS`q@7)M4xppo7`Yk>z<yBV`<eCNO<3kq%eI6o6Hln
zpF7+jw8iw-6qZHhmq%)4+L#j7JnjyJ#nG*pm>bH2yGQ2pFr!lZe*&a)cQ_`&{{a7T
z%=i}j_Z>)7vG%_JMz7!wgp;N_1L$Py91L1Qdu?JrNXeO~)+0d&$rJL<p{C2Qbpk{N
z@2F4OexL#k0az9a4D8gB4*2*x09@~<G$Fu{4zn+dKclBM=-TIv<Ttx4Y6ccKzomm!
z7m`NJuD{P>E%Xnp!sjg>1T~eb<an-i8FSZNUK}yCjM<_?>vADKHeoWNb-i_=9}8#a
zof1!}TV-mK(9Vfty-Rmh*by!zn9xY1L6h~Uj`gcB8ltb8bl<N5W78=s(D{MD*2-M4
zl_EYzq>L139VUT!H0NL)I76|e(KWI#e+zq<k1sdRAITFPC4L-I5KR${59BaAY^m$v
z<nkAT(^(w0O)#yBtVO|NXdpabOLLEh9y<FM9)XvX6id6NR);LD(X`eR&WB;1l0fzM
z`SUkalF!Fs7g|r!GT4f-#E?biMRxupOQ4x_-Y?<FzHTI*$i(R&PdD95N3^)Hm=AYH
zk6DTz*(h$e1?91VaFGYtC}{;IzMBk;^j2@&dWJRF!`u7|kj@v!_SXE{ut~ttPD0!i
zWU;HCxe1=H%^S2TEbhlsukC3(I(U~iI-m+^$L+EEHelBHMeLcf&Tt552~TbiXzwn+
z*BW@a$qd7?lf}07iha7)Xu;B=I$ofj^3<eoLpwUq720(}ZT$P4IzzNoLPYo2epZ(e
zb!d!^QUQ3vvpV)lv)?UWp5OFzd43b!z_4#hML)~27Ajmc-HgM0_dNKu;L;I9JXqHc
zk6Bpr<I+OQ61MsJ`%NT7JI9pEh&v2s^Z|bd)RSfIOdRDe7#?+EvH8`7lh^^J)M_wd
zQpZF|Ei&WYWIOWp$LDWgzY9+HCgmO8GmUmQn61@Q--lTcxOFANEZ6F>YR|>+IXkk$
z$T!lY;`Y~D<ThHo>t^hZvWMwXvt8`gcibYt0Ih6j^W_v6olU^zLJyn2s(?eiFcCwa
zYTNfYy%j*#mH7Dy$hv?>pG7+rYXpjenH)RSua&kwz*bRe=tQyljgMELTBLxN99p1Y
z>tZk>7wuhJ5D(C0ca<Jc+`?=!q`ow8y}xdMcZ>Kzce2X$BB#>4S#27RXUT4t2v6Ra
zBRX~scG!X1@cfZpeqVMh(e8D#9Qt)bPEwC&oR2x;-Vecp0R}=oZ;T5#1CQjM7=OC<
zOIP%f0B_zFKrnZH-pIKsss1;q{TA!0sAk&GXab&fprfIx4CfyOLX)>AddRtm!yX(&
zb}A2!=4;?=dn!(i(uIliv~Mkt@l+<JHeUfQ9}_8RcF^&7`v=c5u_fRj(M>g;#(okX
zV5Sv$7K{ePOEX2J+#oeli676ihx>bCwl*G8AN!hgCBD`US}*`r!w4@NJ@QyfL3S#T
zT%Dt!FJ}9;?pM$fdw=(_cN(}R+ZqFaOUPg<gqD`xYu_<TQa%!BBOcHP14E$5jGY>Y
z!;SS>ZCL6rNBbW<`i&82eETNe9=UX7aOxkq7GF|lT>^5L6}EKoqxYOKFs<A}D+v3Z
zl2_B>wuUq>zo#Q}3#3cM!GQ{YK$!7<2<Z{Z24r3Vjsjh35BSacM=T<mvJ-)oCF$BN
zNo)7sTnoCeGj885!H4cI+(RX_UMt*%5a0^)L2mwe5;{{NS_7}=3aV{N7nWiOya1!F
zR>nE}w!xqS{y*l~JRFhD8c_$Rho<g7dF!cL;k{j9D(j$Ig%uvl<@nFxg^*f;*0JWR
z%PpWCKkUg*rHM}2_D(iL`8KEYKur*`4>~5mT9jL<CZ#I;3}0$?sWty5Nw>G8F8|_C
z^ZB@uC}%&D3J)f<Xba^T%$h<vnS0!FWfzX0@Ue_J32kSKD@9-E1us{?G;n@l1_YP{
zM8UuW+York02}cKsd@I`Zi1$Pi&s{UzX7h_svQ|zx3Q*kZrK12!Z&!Rq3Kq6bs`39
z&A(fV?AqBAAd{023wKrjX&a=8v*SYtC^k^~5V7FS$b#Lvi3`z&9abncWOm-qp*D_R
z7&$?A?_d$i=B6ChPyb98A`SpI<91Z@`?&%*63R$3?(ph4T4(OCOoFXD)(DbKtiIy~
zWY8E?SrQ8j*KH6XDR2Ccbo(&8R^H`@IopHjQhHA#j382F>wjYgCoiN5>`Xuofo`Bm
zOS$w3N5o?DhZy@oO2O-8*(G$)O*E#Jao9}74;k+2(ig#D>@9Rt9tNQ-Oyw<wz;8Z<
z4g6N_SBt~XZhaV>mQA;B038-w1!I_u<MaF(E}x=T3L3~z18A>3f^>B<c}!a&hBh1p
z8ZB`2F?rDJT#h`BmE!5JGRNd~QV_xb1473P#97q?*rD6SDVh}gsfwnDN45c*=rN6d
zbsn7Jh^9ybo2N375T`;PjQ2BF@BL}WK2!wlb`nsZbGzk?d|)ThJtJLXGyn6szR2xt
zBlE_MBOOv!&=Reb2vk&@krR)$y@)ofF8w#)|D3;%CqQ|df|9JB*LZ9kOs$_fMd5)2
zn1P?QM;q8eq(S`p>TdFf&~@+-GHT#hxj}6L@;EGDvR#Eh|JcIwvro}f5Oe=baa)*$
z#K4_<<M)z~JFYZFPHq8d-~97Pk|Rth?5J34F<B91o7o3_m@zAjF2A>NdpxKnV}r&&
zafk@%r@ulPr;~ktK0NxpY^hMp=~3p=yOM;6-$$SWX!pOq5z67S&Xp)knAzt?f5Ma)
zkAk<qw_$iN4S;Vgk%5t!Y@{427zh&w(ChzwUKghZ(v=2h{-IkGOwU~XUf#+uf-2}!
z_gJivzwGRD`Zas}&o#qc(C1!yE4PVVWj}s3VD;~84MU8wVSS#v3<Ka|xOcAZ2g<EF
z9(P(+V%2oTVILqaU|JI$ZvvSSw0wTnpaN{cRSBL^<08Kh8~4&5o-PljWw{%2%lhTM
z4tD5P*{~|j&_~&MY(xfF_GrU+)Q<WL>nqUM0=&d;GX$WXlc)FVL9IvAOfjLsz)z3t
z|JikL_a02EH`eb@9e(9shr#~-$o_BMMm`gokYbHslu#lxgvP-D2=1l-^Yw$~=T?#T
z4KU`xDhZ5=kVzqckOq@<en7ZkWV&B~JRr1Cx4KP*5Yd9%)&N1Ol2;6!bv4k8fsB<5
za9_O*#iH&pz&OaQhug$<Af4(^xFg6I?j%5aW#j-t?y!D@VkN>&NAJxwEHZ+jmE&Jm
zM~NF|ZejDrqo2<5<H<_&Q6xjF2Q;j{5V(P@Owj2c?8b58x;z{jRDsyf-F`-4XaD5Y
zN02dMjS#|-1r=bAs3F>50H{a;LYhW}k&5&=uE}0M&iAjdG8)^fGx@ak)rH&O41z9Y
zgf`<JZ}Ep_;vRnbEyp8`$UoBa9VMXC^@X?XbM8+jmCMe(B-?#DoQ70p7D&~H%yzI@
zfIf3bpNJC=B9i>;uL*i!#`NWo(yCYxz4!A1g8wJa!js4MLDUD9=IqluCeSyA7M*i$
z^6iF)#Uo)_fd*JJ0m5o<6$o;s@zV-k9P(r+&+OyyJ&Kuhh7s0ec;~7^fC%1j_i%`i
zDDm)^@g2m1aRD4j%T+D#z8J8m2~z5Oztgz^<k|k3!FwtFJWN)*F>CvNllVs@Ru}t1
zbs1-b3??#zvbP6%*5T{!&&evk*0uP0K1}a@I^Oq5C@)w*s02)ai7+jVKHLOi)lXFT
zYl8Bj_tv!&gTtYm_i6xB^HZQ_13@8|OCv~tV?#hOxYfb}Q(!>W1sRGq(q5zt<4skA
zY|0(%m!chDx)*XK0qG}xDtdrqn!w_WTW+U9ypADwB**Fi$0YzZ&^&i{8ht(+SZ9`B
zx*DVW$LuwjdrQ~(&`qU1h{tgG<-h2%^!J>6FcvOQ@XR9*GSU>h0?FyUIf3?dm%^}g
zpHMxAed7fn_h6$)uV!k&wUqnMfoXsO5pO5VyNL72M*RQuvC;Lg8Ls?zpA|zdbcfGD
z8Hq9b8jqpa4%C0u80mrG7-2U4wyDt70bkxf2c`b6#g6yDGQrM$;}?Yfc*{V%X95Px
zycstG3<zl?r5mUPwLBMDqgkr`kRdX~F<|$PHT*SN^pT*sWZH%I>uJ#bf+KF{RXeWv
zJ&#MmN})m%8fpL~CFqLM5Vs2P<eiOyh^5)&0Mc?5{-u4WZHM5wGr|%QI?$|-O1`Vw
zja)Oz8=0C291Tnsg!#Zw{JKio^<RaaJQ#ni69-yv>7t>1dj@#ymDD1RWAUl(3nk$&
zBmxjd1k(J>6c7$Wo}oTMn(uKGfSEY0m*>tdf5z_s0QoRZKwK_hp$3QqR3@6<hEG?!
z>g?%LlE1<bOB(dpDHH8@GU<d7ya;_{MWEPoq!wl*JalV<+Lt~n+3F;hs!0-XH=jgd
zdNYKj1E7eLjhqN2?uOvs!R1}I0UNpF>?Jub7*wl`#K@KQnBUTnaHCBkV%Emfy_m@G
zuKQ$887Czex<<f9N;{@NUw&lSni)%&j|-ew%BLgHjWpMO0&#*<0=CI8#Ds4&)P-ve
zxbyq6PF%LudV1Oy4I<tDgCppF-x`h}1SRi8SXpd+H+ldF`=e|r-(XM&#2#p$2yKKA
zOJ`a@hXe4m`m8}ckfoKV&j-Vi)v@Mf4`FUwwB<t%7}ExBAi#ZL*AQ#rfghC$>#m<H
z?5_zPFj@CKR!t2k1;h?)W3MmkGX092MYs-<Ji4i=WBb1zRlkQn4&L3L!THym;{O+M
zz%n{A{ru>r32Xy273p!|A6lL(IZ&4h(<MU$bt*KxHQg6yo>40Puj0NuuBmJ7`u1vT
ztyQen(uzP85GSOF7!e4qMMlAjGYZIHK#(v56EFm>Rf>p$L<J!NwIDR0%n(8t>QEzM
zj35Y^hzt^xBow2GcnEyY4sCDmcl+=AzW<=YPjYgy&)(}<&syst5}_^VetGq-d%MpZ
zv7;z2*`xOg_s@3M@+^gfqlsiffcGu<Avjkrh|#{emmPBiehAskt}(#m(|w@W_DtSS
zMxb7rH0|qM=GWZFT&M@X1n9jJuSWua1_8<wo)Hvy0hW<{oxe-4{}O|aT4gAuekS-C
z04ZFxXU+zYk)bq9t4)S_;wpQJX$$m+inp$-aeQ@{`&AtrjyWGy9fMMijuPR!yf*jG
zM%OK3?TA6z;-!Uk<NdI8(UrZiumH9v?<cqnBmrsdrU0*%&5{9B3`463j-a5@NwkGP
zaRPFFw|9^b@@JUhnFZ8;BEveIs-VOG@1mflgt@Q`k<V+cgL4G-45<Hu*W9g!n8I&5
zwdvCU0pO0HyxBHr$A0Zig(DVygQ`B(cJ12~U^EH54NC%Z6pxRCfYcj<MnC+RU>^8L
zXDrDJbdr<IcQ&^yE1vPQ{pErETTp{`n13IEf5t=nFD|>k#cAlW?C)pi-s^H*2&@J4
zVNqWDWp5x(td<0JBf97^nS>?4`8@NnVkmM6<qI+Ql<sbWMF%~TcL&2jHjhNoEfBsU
zk;$Oba0N8=c>M}+{(G09cGSXlZ*OnYY)k+3%x>l`E~G<&BobZ-Y(B-zCLk2hmHf2`
zobjssL+{U8;C~dC!)xonGrEZX+mA`NJ1m3EE$cN9Sh)vfbFk~rRTHL}BxS?{nKe1S
zKYA#9b>wgHo*$#<eH|p$1t<28t{oF__qLC5^)vN9oDCGXw|DHji(*zh7vIux;+V?d
z_wwByo|I)^S_YxR7V!O=a?gEX!t_NN%d_WT?}iNkEq;`A=`BKSVCZIpE~qc=+iDc9
z`<68$2S(nkR{#mJx*&7U1l7y#VW&QrzhO`CB(NIrsm}V~<FEES{n%jBL-764-gFnc
zFH^TvYEBcz=23Tq>i+uK3+#6Dv@{WmXoL6z_pp$w(LcZzgkQ~MYu4UY-Il#Uk^G<w
z01@Y&rwPc;=KT`fTUJXpyaF~Et`r&iVvy%4{?@#T_fl7ggUX(F54O_`4ydD-+Q(HE
zZGv808}w&9!pyHmeGjT*Xp5LZHdCV8O;9-%Kd@DbngWb>@MuZwgozkkwsaVpexYO8
z_Cn<DuIGn{eT&1@(maOd?q6%HnPp-!9(@=%2|5ZL?9%y_(C!(Q3E`GpE+}9YxApi@
zJ$0V8A#k{@X9_HFl-M)pH-E1llUg3-9!1Fs?#NX^7b3`k^aO5-lXHwNoa>6~22&3t
zSM()K)7sE+Z^VNXCP<@u*;4`WVFCZXk#J8nt9$$O+0Etva?J&e$HUze$aZi{+)!1d
z2H&bj3+e|6d;F6u4zP&6Zl|3FRHfSnNDy-ZK?Fz~;g(P7i>JFh0i+DJs_;cgAxW36
zlVp#;rqtAp_jjRZ`^_5gC1l*p($A>42X`1JjyhF@`LO_)=xU)Zz@{b;i+XqQ4p$-7
znUr+eg0mu88Ybo>g&12?A_k{6pS-#6#{T6@2gnJcBc8LX1ykC!iN)6J_#HO{nqT3M
z?K6lTJ@iI}eu)!Db|tqkMu;~K<AUy|Ex^D5Y$h4|R4}%eBiS<wZwFQy(DtQ8B3jei
zfi%y{y+$WSmbZOk;_Mm*^=alhXyX>OYtw&2_1-kZ6a5~!jc1(-Z7r7%`@F^JR$~<I
z@I(2`@=O!=Eruwi%wupm&*TDV8KN&XLu1BF!n?BY(^P(07K5*VW6<m<?yFAuJ?HF0
zF{!52k?4RUYDV)YeVO*q|2C_8Guq=Zylu`?kBaxkO*t7iKYPK=#x}*s2bltXiReAr
zOJ>RTB?t$aN<63Kw5-LM4Usm~u^8zG0?jwXITEi=Lxv#d>0*;w7;aX_Cdu5v#hOgF
z?N9#urD*lQFbO<o!0id>K0vUWsRB*=h}A>He+9Z+O0Q?0GIZpO{FG*DLor>InFr8<
zt}Nb&KzetpVE*=6q)l!#@$<~xXthUu*%Abh?(>&z{;pFJ{1_im8F2VQv-w7<e?t&8
zN20HEEpE1qiP_OmSgC#}0QT4|EGKXJsBsW4Jv<W1{tX@5-l<BT50k>V7(nrr%m{JA
z&T1qWTdE0FBLiDCxH)D<Q?LoVrQp*nj*s?Yp+)9KHa=+4nPI7k7y@qN&hBfnKuRzh
zuCDkaK5_O;8WjBJ%iG-_BpO>U(%dAB`6@+VNoP|ZHFC%w%E06T6w++P9X-cOP4en?
zQ_}5uW2rCxn1c}88+3{D%{@5IEx#yVd<hT)Cprxa;V|lgi-DS<D=B3gFt6Yht05|>
z$f4ND0A&<SMF4LGZrWCL!(1Nm2Hg;-*R0sqK`Ba*qo{sCVSTS4zbw1!*uDl7T$g%R
z^6-A2zCd@=hKBO5ScjxDw<ZmP7Tt^~2qN5$##PlyZM<NY?~3U>envlYswqrOVqD~p
zA|`v{*(nf+)CX-u-hEz+bAy3TGc0gjdF*s1?@Tl<wVL6`Uc5105TLmo{<ZxBWl-6+
zcjM1n&ZC$j5Z2g_JGt4Vma_RO!ID&LZ;fWXCgPD+<~W@hTVf9Q&inxCgv!s{r3P9o
z8cX~0_WTJFoCgM76VKnJD1>`nAvHr6&>_%!@jc$X2Nuq9_7~gEnv<O(e|vU|E(9(A
z_BW9(>C0fdhStiZSnj{XR*D<%fP^-coOkfDQ*3POYo>aHL3r8a1Tf8-)q#a(R}2I_
zK(2n$V4m(a1#9vj%W0VxskezYeiD$R5|sy(vqwsk7%)X>CXS+rcFu-!%(BA?mY0AZ
z;f1eYiDS}+bnGs4e%%}S<7z)L?tYD?P;$jZg+X|g^Q&;vK6E^+Y;_)BM;5j>XBfe(
zn3<r$9Bt^64yS>ZZh3P%jp2a6Epw}5J%Rfa*^i+Urk|?0n@jV*`q%9r5`7M5Wc1dA
zWCS~Z1R?4<-Rrj}9`99jtkRi0z%evu*O5m?Cx?u}hZ3``pFSV1azNQWbLKBKWjg%!
z%dFyeEaZJlZt)l;#>N1a%~>=06pW}7uqYw6(2kO|4jCxgY0DHlPbsbTLH;L<O=3_F
zU1+wfMjMtY=OQ%_BD{+~l8hofN0)d$d8$n^RIY2ps@%YN>3KPBg*LuhF56^Yu#f6=
z8GGBX*l0Q!ccYVt`r?~bw&zd2tfcnaeAzLyFC`D#G_B(qya7I=N)uQzy0YUg`;$M`
zj_v@44Nhcq(M~tJAhhErm|fu7Wd2l+HHn+d{~HEFIL!A5Of(woJ{`nYk#Lmu?XaRm
zBqyCiF#`4|@Qy=yVkWWr5t_D)HEOt3b%k}xpGANJj+Q2oaJ8GkO=T*XAEDFCKhJ=N
z<GarMgG@Gq^sBYzm@n1;->b&(mgDG+8rV(GKEh+iAhn^aq9v^KvGW?WJn*Jd>Y`$I
z``@23<AR<jlM~9GQ5ew`wkFsVRz{H4=F88X_qZmIqou=F4LvE2E<jRPb$3V$j_fm4
z9_00L#H=rBWO?CaPtv_FAgz-e+l+(^9l=rn2()Ox2~TFM7r&eWS^h0J)XmvZ{af44
zT>|}nr{u;e>xu3F*mh-bggJ}ScY1pdOJ`N*J%@Qcu3<#|HE5mG6<oXs$qL>E5RVRV
z0MKEx+B5R=8C{S7FpdDJKt%C8l8M-TxOXTRV&6?4GbR|cAMPIK^)1eAwiGWoPS7O7
z6NTAafMo(Kd+|pRgsg5%s=%LHX6xOl_@`;LYm#4`IDv@Z_zPmuE`$TL4D5I)jvb40
zIx&>#vOW16tP9D^gR?~rK(bx(8;`g~hOY;tP{Lec`N!7VO2YLY$6W~rurY)>cOWr2
z3t0mz#`E{rjHQuO`B(l1+vC%RdR&_vLK=a^rVFpyl5{l03m+B{*|dR%9kLs1GGPj=
z=P%APd=Z12F9c2@xFIu4(<DIyh&rbdEzB9j-lRJ^?~-6Ao+577$%`+o0r$<&o_)S%
zOm+szzUB|i3CETi_7~Y&bIoaNw_k~up&R8}JIx_!(iVuj*}h~cM&>?TbfCzw!iR`w
z>B2uy&V&tCxVirvGB{l$6*#_qHp@+Mc5V4rOE%E`O~(D==DTj3uvx^XF>vyXrMm64
zt1m(2*=7*gv~xqnHng)$-=P@<OR4z~PfyRqgjl}q6S3s(md?MqK~5<S=|lB*h#A+a
z4alL0d5y)T*1!o$SaTgTKx=jMumU9*$YB6mQ9ViK)rO3r-l~a&V)tWeP8pHgo!HZ>
zT`xx+<QIu4TEJKro1p1pI=#9q<ECU`;Wwu~p!-1KZKjLISLiD5Vjp!lPq8%kI4M0Y
z@IQd14j$bf$!`F=k{Q^!Rx#Om?~h*3_M_Lf`ZFM?qlj~jhXgq<jP!#`-UrpbS?UGX
z1i!kd0?`e8{SJpWmx{2+%GRfaE_x6iad?OfX$1SgXie`*uiv>UMj8MKgBmkO?dx4`
zJTJnhtG%7P+uM5}##OX{y4U!iQglB$qX`v|Lm<#t!%U|3+2@9rvz>J|1)sz|)>4g9
z3RLCZ7&L<*mlGep7uF(Vf9Rq}>fjnO<NiRG57*it-2NX$CM-m<=@g1~i^aKDGeX6&
zPdw@6fZd>*3h!(0E9h>c*7QQ<$RsE=O%=nQZ&`Ydlb|Kr$<`%)AT6~V1|6W#1xpWL
zCEAkUG)8;@{0emHO+lA{UJmSpPQrE1RhK}Q`k+s@9%=o=^qE`k!m-qy+LXyi;5v#w
zvIWHu0)T6of@q~qvP3*Rlzz0)@%Hzv?d|;Vy~d)izx>kn@Gt*xQ=svG+Yy$KlTK2J
z;N%N3(?u!XXj8a08B%G(IU%Mt9NUg6uF={T57Kn^H}fsr95E|%FnycL%Y@@pB@GQ0
zteb3#v{6c0ryIV7rV8W|^!JStG*vv_|A!M|dq3F;9R=$>Bb;QN$U-d;krcu@dTw5R
z6wam1LoI#g71iq%jm#aHwtyU^-|)w<+r+cg5MkwZ6IM#`R<HPeRhV6@QssnbyP8HT
zy{0zUaqb(4S>tKgro?Td4px8Gt$(&Df7b&W0ST%5IR8DT?|+XWxL|2>o_X^0Z^+xL
z3qKO<L>7ga=|L!gP-pWC_NHrE^`AmBvJG|S!=SCRamh0ac=DJ-kkGr1iKYux!#q0r
z{T3*MJ*(k=(x*2bf4RHO!?Jnz20N5D&<30eh=oDnG=vJc9Dnz$bwJvEuwdD$csNMi
zhVMd>3uuRz>^l^o%g8o8aBb`RZj&PTup!#bDDiE8&NQ-t<(|FXV&a!sdahx}v&;;9
z(&1MIIE>T=?Kami=zGy?$9BEi`sKn435vQN(>mD1I(EA+S?zsy_djC(U`+qr_W{lK
zTywE&0*X{ca*eigH+1pfpo{Q~fv6I?FlkC<+y<MES7$p!Dz6JL#YciiUjwkryA%}w
zKtF@H2z6#q^sqN{GvaL*MJ7!SAW2Y{c*|#oin@15W|Dvwa2-gaysHnfW9aeyXkJO}
zG(G}e`wv#&U*bQRA_)1sJ+~)-Wf(15&QG5ih=<&wL?}Z#+ea!*vK|NU4IuWS-nv}-
zb})mE;Cz>O!K5RbZ;tYiZ@{3+qP=JWz!rJxT1z|m`2DhqZWN0)1l*%Jn)&wX5Aot(
z27<cUFY+pK8Nd)#`S=VBy%L$)*!}Y*q}j1d{S(Hwx$)AA^H02F(uF^MbIR0`Bj3<=
zu2=P)G41tEHw6R$gK!;=bb2h`6)>{D84D#gZ3}#;M44jDt&C^Ap3$|Sse^q4g+9+D
z+OICT8d$o}ZqrdmF9ig!=u$w62#$CSD7E|@+m?U(1Da%&7uyLVtT^#M8WzxWE^$~&
zzOT?^Ffb**(N!BT#q@fScKkyH?5~-%GVgG*$|BoAB}{A*c1#t3T)_1eY{B#{0$4@a
zNx-2fbkPbx*_hU$z;cMkcMscPKYlv6p>?gfu6SSl22GREd8B-R+clL`cw&*qlMPZ?
zt!k*2Ji=hn-(+s}_W-)+Le~aPcKtCyVCiGqN63B&Z^9o$pLE#MQmB1ZG`V8193T>3
z9^E4kiZrHJh*iKPI}bqFakTVtQ2&$w7M=|hvzQZA#lxAE?PjiEB0<LnF~na@>K@1;
zsAQl4T64V)8k8Q524@{WqM#!qV%a9+kON#%gvEhj6TmIq2U=e<V<mYqmD_NzDZY$<
zULC))hJU_4UmxmrNB~@5WWOpN(I;U_S^#c4yxO%QHRSWSL!xOay<CU#^XEvoPw{$<
z75mijkMVN|cMVfn8NZ@&QZ}4xWwdj3h{i&UR@TEa+UNzG13y7|hHHb<-y<x?!8lB9
z+krO@%Z&4i^}iz@Jx=s5(}w|qFIx1g{0o$_$BC0lRhjl}&ATcHpiiOa(prO)HoB2o
z$zzS9>)Sv;1wIOmkn4-VDP*RgTJ!M6Y{xYnC?X@dSN4e}Xeo-!z$PjSOn8aS9DZF6
zjn^17rLMb6^W6+bP!X-=v0SQ1oI=wIA=270E68}BW(>i-BJAoRgdCHd2C9--zgrOz
z`ZeiyD!tPZ+_q?DXMrb}T_j4a{6RN^RtfyuOmKL;flh77BX63*q|@$U{Vj{_kM&lz
zULPilc0ilJjWsVEcd=S}t2^dN0BhP=6NG5}U<6+3;M4^M5YcNoVp7O=oQCWgkwp&b
zdlT$@(KMnWLMv5H&XETVkSFAnOM1&Te+lqqmYv{PqP~!Ph;J)f=Efs$lg16scZ+yE
z(m~geT6@8FIWs3mNzqtf6EUrc;`O<bb?rwuF3R00ithx|#exM)t?-H5;jmqV5S8>t
z?XKlwZ-Xyu#SMlLqLZZ7!pPP>N#R08*J+U%L^ZG&O9gxe!A_m4wQuy@j=e#GF*n6;
z{ded{*wl55dz*a12Gg+fJVbAfPcIPp)@5+A7+ib}*S994nI^6=Ih3M3rHB7&&(9n=
znV=|g+N@MvYaWvjPY?{%kiwO-=JlZ=@_?B8kenf}r4x+Hq6++3cZek<vD<st<fzx8
zUavf??x?>>^^*X;l2l0Z>ykI?E8{y9n?(E+&hj5c*XxX@O)~6PFa_L69Uv0OzUJZe
zgfm~ULpA(UYTNHftzH)JdyUg{r<}Tlk}<0`<0Q4|nI}#XTzUa0I*-Qbz1Y?4ZrQgy
zytxp*CMt%9CLYK57e?fXdS1dOb*QshBUjPwCW0IjHR0mK$phM6ioAC@Q=r+X>?y;1
z0;ijaF1^HsFTDu8+zxW74Yu?de#a#28Fb|+hvpk9s=ryZ7iEcSRL@&>RQi`FH)d%Q
z1k?L!o-9;qn_-f!n+9Lq%BQs+o<6VKecqSIUhJa`PNjK8;a=48>vS=6^1I1epPm)t
zy~D$!OXL6W2>sUq*JNlgkM+$Nj@voAl}(A-6QG>W!P6RpA*L8WRq8oTRfb_zjLV!m
zRYAFF`j!B~LN9UNJ8#$;i;Jvbylwza&T?0>^BA%&xJ7`>qxb=yBS<x@>Q3MEQ#dX)
z2KRo=^gR$7fGpT4=HV49x)8K$rgtLl4H0)Aak0qQ<f9~>CbSxfJA_kOjPX(`CWR{C
z$)|-v)_++M=aW3FP%q1HXPt>K*KR;Tj13ahluP*6B){ErC=gE>NHVvF>&n3MH$}X6
z8!5A`%H)JC%8^RDr<xr~DFv0Yjf^E|UpANvTiX6t1@gB)*}cT0=2(=$ZMNo|VYDM6
zHGM(qV6`Xobf+PuJ}5=$8bdU~9vV@2c(rn+$AROunQ_<^He(pT&ZFJS)$!ei@B6nT
zu!}fV-jJQfvHb}vT!b3LO^SMvsr5j52FzFS+aQ*;!<Jb1M(Mm8$fJ#W&PXnGN?hBC
z3$yYv-^%egp==uuU#}#wXvA0-P`{_b(iO`Vv}-%oVS^ti3nFk$F)mDn>M((SGMAPf
z?e8L2{fJE*cNy?N{w4gh(3lb<aHOJ9&AA*w&SimX!rlTs8|>-`aaCABVa%(9Q2z=^
z#XRf;TAw!{2QEWOYknYq^DNYux|bioaxA|lzy#XplqiPL4^+Qu$MvzG1#%7R_tTe$
zHe!Pd)^h@WvMY_`zEgzP5x4@0@wc@GL+pyxS=g0Yh{}O#l{fYIb4V0h%Vaxx$Go_n
zoxA2P9+$OtpO<$HV}kAI{>cmOXMMlBJ`w$$etL2F9b)Ujm*gkMN`S(i0+i&rWJ?xT
zON@lN)N@H7=O_>;7rW%qM5VJ=e{Uf}Y|<wGU>DhB=}l<T(24tc68GUvQ1}HTeNBpE
zd#wkJdIpI3!MLnw^ZCc-JW_lqT)@#18wqv?`cIEm@(UdOy&<|QmAO?s7Arar@p2Qf
z)4pmuEwQ8>zZU>QGaSidN|}^+PG;0UK(3RI9mj31F;K82D=`Tf`#ik9P)1B7;D$(!
z#s?f0$U~2rizKcOjcz?Bzb7Yrqx@hCyiO4cIiV|ux30%t5jb(VlI`t^5z&0=F_-=G
zSgU<D*SEhQijUy*NEzV|ctK-Rc&t~X+XO}5JS;6d-V23otQ+fKI4*n(h+N?eonVMk
zSrRkN=vRkQ9ITZGKc#NWA(W(xJ>QFvsgWcpmTgG3oA@g5?uUT3q#-y?r<|LAF-UTI
zu0}j!wC8Anf#k({OguvFRs3*ODO<Hnv-xY$`?2OL<vrz`14T3=dttbH19hX=^pYr`
z^<`<9spJJSO5RhX)#fTbYh>6Fo(Aw=s;&_V7Mr|D2*u5+sp$6E>saAJz4-_R+fCUj
zV^g$mNw2Cx>h2_NRJ-1e;<qYKpU-oR%2+>7V-sQ?B2GOWB{o?W!4f(+KWZ6Uie{D)
z;1>iHu*63*5&lm%z<GI-N=}OBn@qQ9uPAEIa&8?eGCmlm_jmQtBCm$bw+|l$P+Xc|
zP79!;&@MzrF_R74>IxH;Ii2hPmkko$cKOJz7|2EWjJVh=TQYLbQ1g)II*FXZl23@7
zqiJ?6exR{|WFcBKuDgbz$7W0j_<43887bw5*8-@rTeFmS(SSPKOyKgx^MBc3u#W`M
zb{|$z36n_A`hvJD$fXDA^OyqA1$6NYHMPbyoPZ4NyBK4acEfA6gEh)kk&y3NM4c*?
zG(0r4@p6AKp&=I}ymH%>3`NQj7nQuBiGYhBIjW-yGsq@5ja(ch&furpH~N?8ABs9T
zgm`==G%eb8=hPIKYeu>Gdyb9GwZLUGV|7GhD&_QMaZte?7uebc`%tU7h`_xr@jNdd
z3~|iPmGrJEGZ|O1?~{XEDNQtJB?8A!RTOW}HMAfnookDM?Z%m?%-D812-iZIzDYK@
zBR_XHM8ocoeB6%5H8QFNGG~fu-xOZ+X4NvvY|T$;>*+wC)jBR6N`EGl-Flcm%LcO#
zEkIvKTF8wi<7)1r+j&f7wal3lvR{PV&YxRxWYeMo-C-HhU|=hxI+*iQ$h)j5v!yM5
zGIiY+xI*<HrIje>7F^75Fo%Dsp5gt4q+cZ!me`d>O|@YvOcHxOe7rxDKUd9Vi>dsn
z&-Z%uYE~$*i&rbhtR=>$(q0G68|&}TMXb#Lv|tzt7{jTpPm6*+6to%)cEb#KH(k>t
z7B^LC@ME&w(xFhD<H+c8U@M7p1O`^~jG`}PqF!X9@h&1%Pou-+yK)K<>Cl-16V67?
z#Dn=b@t4daPa&M@dX-^z)NSC!cLI8P2I%SiT*c=NE;6>SFllBiLzu9ZStP2fmcC$3
zd)63S7kJLL5k(||N6FMiGulp!8o{gUsgW7gwo66Y?qemO(2zoilI&66Vqu3e?M8Lp
z7RoGmRO1lb2QZzB)qPrik>1UFnhs-^481iC^}6^a5=)xMDZ<`-Uf!O=;Py#+JMn6D
zbWioW-js{o3pkwd>yqyt!$YMyFM7Y$pxf}~9U@K@+xj#@VHE#7ae?CXNy%o<8qH`2
zyk+W`5l-K$Xp39`rxEUYHUGTJXr;)cP`o-h3cYFuQ)E+D&@=PFkKn!f8}o=M5@Mea
zq)xE?$ku2^%Ay$caEJ8F#kxI1(nG(|vg1SUl&$)WYfVKDn})Uxhh^BfY$%8ymZF`W
z8iScV*qdWx7CgM;Rn)o5mE7PdIz=XP6;%WuqMtr`W&evxRVqgiNsyB`82*XTu9tYd
z27Y#by7kB0DLmy#Q&fzq_cryvRC_StDl-a(;*M1_o;M60ATM4?5pNRTXBz&R087Kv
zI*|YDI9J+-Kr-c!C_Rp2aD*N7a~72&8uy?qvxGs&%9RvyEH9lAMwVNfs8xr#D{So4
zGUCVC#_+Ry6d=>G?S--@I$HU97sT*cu&Ej%6vLJ5!glhL)s&!Wuxsq^bl`{$4WYij
zUS#J@<Sv)+TIB3{@+EH$>VQg&d6nXdG(?YAgYt|n1Z#!o<>Tu77?*g3YtUxphh@zy
z@%&%q+#Jx0)swj$3PG3h3uP8IQ9Xz$&oolg>o3Enk5}eGDJlDwWQ@rlyo62cqcGf$
zq*kS(InbrX7d8q#3ZYf<%MHNP^yyDwpo2u!uOKx#qzEoc;q46Pq7NR9MYff=I49m}
zQEPb5dN*v@&jRkI8bHd44!t_O+&I{xbZw&fffD9Yu(NzWho*fZ5C4&KU@t;KC;bor
zp=OA57#X4CL<y(DA&2Hyqw>iU05e|WUt`>=?X7$0r<bm-+JSN>pt}SFa$|^bh-R>+
zqTfZd>IrdGTwlD*ElfT761juAUd5R9wfw-YSfYNjPMnd_EAv)BeV!EyH-nUd$=C*G
z8yV(4>Z%4Lgn%XWY|7_950M2hz7H0+`sZ^f0nQtm=s88yhuM;2GQ<jW$thgPf<4GP
zCYfI*rxZh1bS)Fr(8V8BN&Crm9z;rSA}$V%Bg<8UHZY8iz&2BDaIZm<K0T#rr4zF|
z6@8Mp!Si(G_)#?}?!oF3*RY9>019GoJB@IK0^;|g_-d(y#b^svbNYzcZ9a{$Oy*XD
z1wyZD^$@)1M!8c8bvl3dwXuBBdO88enoAj?LwT<bzatUz5=;6VzJHX+({)R8MbG(b
zL<gd92XrSYXXh1#lFc;|X7C*b)>-26Y8d%!iI0dDn_;{LlFEvxS97#uYH5it^x2C)
zY6J8^_LR%+Nh+10+=wG9%M8ic+GgeJ(+;;Iz^OrB&${y&V6>7i#Ph4=1%qUFNf29}
zL}|@eIRDtc>4&q!#U!*=#tvfQ&;orMOne2J&De<}y3^qIGa*qTl6}KcK^^v3Q7Jn5
zr3SJfstSwjwgvhRiYqFj7;Q)DUmW@!ttKjjvb$I9jeUqX;gmrP=970IMbca%=Z--M
zWSr!MS0k3DlZI#QI_ZPLOhM{LgWmdjrSna-!zFCl(E=67U!lx8ZwaP=b<F2SQY2oC
zE*PEd4F=KtBJ6E%+Z@dVAk#*}SkBz5A_-Y4>s`H;;?v&J(vVa@n?#*8H)zjWH2t@}
zUdIP|n~Z1KeIJS&i{jSE<LWuLE=gu{9Wd-ZSpC%r0lf6Zz&JwoenSmTu|I%ClmJ6k
zUM!df1-S|A2oD6G?6D{d*^v_D@>;y}E}Em(nQwKIZBW+RF#uvT_b~FgcJ2OGRFF0h
zhSJY?f>5cG_Fx@q*4u^UbX!*`1h<s7HOdcLz~Z?V#4RY#N@!g0SX^-}sap1FIGN-`
zxzw5HDcl*!n|k{zh?v$h*@aDl=jk_v{A--lTy2fS>eY1Qn4kCJ4}V(qFTx5hF>`J7
zTtQ0suB*vmO+yQEKcBX^YJGJ1Y<anI-&xI`BjXIeuU_P2z8%p<FUBdY+NcWc?Zp#{
z568`V(rNc-_j{*plsye*iwZ&#SRzkuK>1~}_1gvtg9@Zl>65C$X$$HT$`Gz<vUc;w
zsjjWoi;^ND<XLH5_tJ?aoAB0)q-nXsTZSeKz31$jmC|*~!=}<?ToBSaCaZOQT?hIZ
zivX?W?b=1t(i5ADR+8;}!Ui1Pd_@|+5Zy#6pNcfa%cS$34^KwgY9@EMyrGUiRgmor
zG4`W@P>Fly(;v@CE>M3SOY07^F$7{Zc3J)xsTqmIF&Pw5P^`zE;YxP$&?~u~_G6jw
z%|Fi{b$GGqqFhgE<WRpZ1Hp-Zz5gm1vGAX{ni}=}tg+f5z8Q4L@O<Ob@i_a|cfN|+
zpxlZJp<yoNfMlj-v-1sEo(Zon22)Ngw`%NDO)aTv@bk5|x}Tn6*>=d36ZDI{3qJSt
z)S%=6Jx*To?yj(x<lZ-J9d>xdxP$-Ao>5g9H@7V1+pvMPFZ=CeFRxA)K58E9VeklB
z9@VX1wjf1SChdM=SyyV|#-DdIXhf6L9>S7;AH5~7crc1j`)#D^dGoo?;d0kq@JD&G
zhfhx4M$<Is4b4OH!*v%dkv*XD>lP#y`DGx1ru~OB)qmEv+RroL`~Ps;=H*nr_3-!q
E4@H7~dH?_b

literal 0
HcmV?d00001

diff --git a/src/machine-learning-and-data-mining/main.tex b/src/machine-learning-and-data-mining/main.tex
index 3593190..e25791d 100644
--- a/src/machine-learning-and-data-mining/main.tex
+++ b/src/machine-learning-and-data-mining/main.tex
@@ -29,7 +29,9 @@
     \input{sections/_data_lake.tex}
     \input{sections/_crisp.tex}
     \input{sections/_machine_learning.tex}
+    \input{sections/_data_prepro.tex}
     \input{sections/_classification.tex}
     \input{sections/_regression.tex}
+    \input{sections/_clustering.tex}
 
 \end{document}
\ No newline at end of file
diff --git a/src/machine-learning-and-data-mining/sections/_classification.tex b/src/machine-learning-and-data-mining/sections/_classification.tex
index 01c8909..33310b2 100644
--- a/src/machine-learning-and-data-mining/sections/_classification.tex
+++ b/src/machine-learning-and-data-mining/sections/_classification.tex
@@ -269,14 +269,6 @@ a macro (unweighted) average or a class-weighted average.
         When $\kappa = 1$, there is perfect agreement ($\sum_{i}^{\texttt{classes}} TP_i = 1$), 
         when $\kappa = -1$, there is total disagreement ($\sum_{i}^{\texttt{classes}} TP_i = 0$) and
         when $\kappa = 0$, there is random agreement.
-
-
-    \item[Cost sensitive learning] \marginnote{Cost sensitive learning}
-        Assign a cost to the errors. This can be done by:
-        \begin{itemize}
-            \item Altering the proportions of the dataset by duplicating samples to reduce its misclassification.
-            \item Weighting the classes (possible in some algorithms).
-        \end{itemize}
 \end{description}
 
 
@@ -317,6 +309,35 @@ a macro (unweighted) average or a class-weighted average.
 \end{description}
 
 
+\subsection{Data imbalance}
+A classifier may not perform well when predicting a minority class of the training data.
+Possible solutions are:
+\begin{descriptionlist}
+    \item[Undersampling] \marginnote{Undersampling}
+        Randomly reduce the number of example of the majority classes.
+
+    \item[Oversampling] \marginnote{Oversampling}
+        Increase the examples of the minority classes.
+
+        \begin{description}
+            \item[Synthetic minority oversampling technique (SMOTE)] \marginnote{SMOTE}
+                \begin{enumerate}
+                    \item Randomly select an example $x$ belonging to the minority class.
+                    \item Select a random neighbor $z_i$ among its $k$-nearest neighbors $z_1, \dots, z_k$.
+                    \item Synthetize a new example by selecting a random point of the feature space between $x$ and $z_i$.
+                \end{enumerate}
+        \end{description}
+
+    \item[Cost sensitive learning] \marginnote{Cost sensitive learning}
+        Assign a cost to the errors. Higher weights are assigned to minority classes.
+        This can be done by:
+        \begin{itemize}
+            \item Altering the proportions of the dataset by duplicating samples to reduce its misclassification.
+            \item Weighting the classes (possible in some algorithms).
+        \end{itemize}
+\end{descriptionlist}
+
+
 
 \section{Decision trees}
 
diff --git a/src/machine-learning-and-data-mining/sections/_clustering.tex b/src/machine-learning-and-data-mining/sections/_clustering.tex
new file mode 100644
index 0000000..3ba3d57
--- /dev/null
+++ b/src/machine-learning-and-data-mining/sections/_clustering.tex
@@ -0,0 +1,137 @@
+\chapter{Clustering}
+
+
+\section{Similarity and dissimilarity}
+
+\begin{description}
+    \item[Similarity] \marginnote{Similarity}
+        Measures how alike two objects are.
+        Often defined in the range $[0, 1]$.
+
+    \item[Dissimilarity] \marginnote{Dissimilarity}
+        Measures how two objects differ.
+        0 indicates no difference while the upper-bound varies.
+\end{description}
+
+\begin{table}[ht]
+    \centering
+    \renewcommand{\arraystretch}{2}
+    \begin{tabular}{c | c | c}
+        \textbf{Attribute type} & \textbf{Dissimilarity} & \textbf{Similarity} \\
+        \hline
+        Nominal & $d(p, q) = \begin{cases} 0 & \text{if } p=q \\ 1 & \text{if } p \neq q \end{cases}$ & $s(p, q) = 1 - d(p, q)$ \\
+        \hline
+        Ordinal & $d(p, q) = \frac{\vert p - q \vert}{V}$ with $p, q \in \{ 0, \dots, V \}$ & $s(p, q) = 1 - d(p, q)$ \\
+        \hline
+        Interval or ratio & $d(p, q) = \vert p - q \vert$ & $s(p, q) = \frac{1}{1 + d(p, q)}$
+    \end{tabular}
+    \caption{Similarity and dissimilarity by attribute type}
+\end{table}
+
+\begin{description}
+    \item[Similarity properties] \phantom{}
+        \begin{enumerate}
+            \item $\texttt{sim}(p, q) = 1$ iff $p = q$. 
+            \item $\texttt{sim}(p, q) = \texttt{sim}(q, p)$. 
+        \end{enumerate}
+\end{description}
+
+
+\subsection{Distance}
+
+Given two $D$-dimensional data entries $p$ and $q$, possible distance metrics are:
+\begin{descriptionlist}
+    \item[Minkowski distance ($L_r$)] \marginnote{Minkowski distance}
+        \[ \texttt{dist}(p, q) = \left( \sum_{d=1}^{D} \vert p_d - q_d \vert^r \right)^{\frac{1}{r}} \]
+        where $r$ is a parameter.
+
+        Common values for $r$ are:
+        \begin{descriptionlist}
+            \item[$r = 1$] 
+                Corresponds to the $L_1$ norm.
+                It is useful for discriminating 0 distance and near-0 distance as 
+                an $\varepsilon$ change in the data corresponds to an $\varepsilon$ change in the distance.
+            \item[$r = 2$]
+                Corresponds to the Euclidean distance or $L_2$ norm.
+            \item[$r = \infty$]
+                Corresponds to the $L_\infty$ norm.
+                Considers only the dimensions with the maximum difference.
+        \end{descriptionlist}
+    
+    \item[Mahalanobis distance] \marginnote{Mahalanobis distance}
+        \[ \texttt{dist}(p, q) = \sqrt{ (p-q) \matr{\Sigma}^{-1} (p-q)^T } \]
+        where $\matr{\Sigma}$ is the covariance matrix of the dataset.
+        The Mahalanobis distance of $p$ and $q$ increases when the segment connecting them 
+        points towards a direction of greater variation of the data.
+
+        \begin{figure}[h]
+            \centering
+            \includegraphics[width=0.35\textwidth]{img/mahalanobis.png}
+            \caption{The Mahalanobis distance between $(A, B)$ is greater than $(A, C)$, while the Euclidean distance is the same.}
+        \end{figure}
+\end{descriptionlist}
+
+\subsubsection{Distance properties}
+\begin{descriptionlist}
+    \item[Positive definiteness] 
+        $\texttt{dist}(p, q) \geq 0$ and $\texttt{dist}(p, q) = 0$ iff $p = q$.
+    \item[Symmetry] 
+        $\texttt{dist}(p, q) = \texttt{dist}(q, p)$
+    \item[Triangle inequality] 
+        $\texttt{dist}(p, q) \leq \texttt{dist}(p, r) + \texttt{dist}(r, q)$
+\end{descriptionlist}
+
+
+
+\subsection{Vector similarity}
+
+\begin{description}
+    \item[Binary vectors]
+        Given two examples $p$ and $q$ with binary features, we can compute the following values:
+        \[ 
+            \begin{split}
+                M_{00} &= \text{ number of features that equals to 0 for both $p$ and $q$} \\
+                M_{01} &= \text{ number of features that equals to 0 for $p$ and 1 for $q$} \\
+                M_{10} &= \text{ number of features that equals to 1 for $p$ and 0 for $q$} \\
+                M_{11} &= \text{ number of features that equals to 1 for both $p$ and $q$}
+            \end{split}    
+        \]
+        Possible distance metrics are:
+        \begin{descriptionlist}
+            \item[Simple matching coefficient] \marginnote{Simple matching coefficient}
+                $\texttt{SMC}(p, q) = \frac{M_{00} + M_{11}}{M_{00} + M_{01} + M_{10} + M_{11}}$ 
+            \item[Jaccard coefficient] \marginnote{Jaccard coefficient}
+                $\texttt{JC}(p, q) = \frac{M_{11}}{M_{01} + M_{10} + M_{11}}$ 
+        \end{descriptionlist}
+
+    \item[Cosine similarity] \marginnote{Cosine similarity}
+        Cosine of the angle between two vectors:
+        \[ \texttt{cos}(p, q) = \frac{p \cdot q}{\Vert p \Vert \cdot \Vert q \Vert} \]
+
+    \item[Extended Jaccard coefficient (Tanimoto)] \marginnote{Extended Jaccard coefficient (Tanimoto)}
+        Variation of the Jaccard coefficient for continuous values:
+        \[ \texttt{T}(p, q) = \frac{p \cdot q}{\Vert p \Vert^2 + \Vert q \Vert^2 - p \cdot q} \]
+\end{description}
+
+
+\subsection{Correlation}
+
+\begin{description}
+    \item[Pearson's correlation] \marginnote{Pearson's correlation}
+        Measure of linear relationship between a pair of quantitative attributes $e_1$ and $e_2$.
+        To compute the Pearson's correlation, the values of $e_1$ and $e_2$ are first standardized and then ordered to obtain the vectors $\vec{e}_1$ and $\vec{e}_2$.
+        The correlation is then computed as the dot product between $\vec{e}_1$ and $\vec{e}_2$:
+        \[ \texttt{corr}(e_1, e_2) = \langle \vec{e}_1, \vec{e}_2 \rangle \]
+
+        Pearson's correlation has the following properties:
+        \begin{itemize}
+            \item If the variables are independent, then the correlation is 0 (but not vice versa).
+            \item If the correlation is 0, then there is no linear relationship between the variables.
+            \item $+1$ implies positive linear relationship, $-1$ implies negative linear relationship.
+        \end{itemize}
+
+    \item[Symmetric uncertainty]
+        Measure of correlation for nominal attributes:
+        \[ U(e_1, e_2) = 2 \frac{H(e_1) + H(e_2) - H(e_1, e_2)}{H(e_1) + H(e_2)} \in [0, 1] \]
+        where $H$ is the entropy.
+\end{description}
\ No newline at end of file
diff --git a/src/machine-learning-and-data-mining/sections/_data_prepro.tex b/src/machine-learning-and-data-mining/sections/_data_prepro.tex
new file mode 100644
index 0000000..95a1d88
--- /dev/null
+++ b/src/machine-learning-and-data-mining/sections/_data_prepro.tex
@@ -0,0 +1,163 @@
+\chapter{Data preprocessing}
+
+\section{Aggregation}
+\marginnote{Aggregation}
+
+Combining multiple attributes into a single one.
+Useful for:
+\begin{descriptionlist}
+    \item[Data reduction]
+        Reduce the number of attributes.
+
+    \item[Change of scale] 
+        View the data in a more general level of detail (e.g. from cities and regions to countries).
+
+    \item[Data stability] 
+        Aggregated data tend to have less variability.
+\end{descriptionlist}
+
+
+
+\section{Sampling}
+\marginnote{Sampling}
+Sampling can be used when the full dataset is too expensive to obtain or too expensive to process.
+Obviously a sample has to be representative.
+
+Type of sampling techniques are:
+\begin{descriptionlist}
+    \item[Simple random] \marginnote{Simple random}
+        Extraction of a single element following a given probability distribution.
+    
+    \item[With replacement] \marginnote{With replacement}
+        Multiple extractions with repetitions following a given probability distribution
+        (i.e. multiple simple random extractions).
+
+        If the population is small, the sample may underestimate the actual population.
+
+    \item[Without replacement] \marginnote{Without replacement}
+        Multiple extractions without repetitions following a given probability distribution.
+
+    \item[Stratified] \marginnote{Stratified}
+        Split the data and sample from each partition.
+        Useful when the partitions are homogenous.
+\end{descriptionlist}
+
+\begin{description}
+    \item[Sample size]
+        The sampling size represents a tradeoff between data reduction and precision.
+        In a labeled dataset, it is important to consider the probability of sampling data of all the possible classes.
+\end{description}
+
+
+
+\section{Dimensionality reduction}
+
+\begin{description}
+    \item[Curse of dimensionality] \marginnote{Curse of dimensionality}
+        Data with a high number of dimensions result in a sparse feature space
+        where distance metrics are ineffective. 
+
+    \item[Dimensionality reduction] \marginnote{Dimensionality reduction}
+        Useful to:
+        \begin{itemize}
+            \item Avoid the curse of dimensionality.
+            \item Reduce noise.
+            \item Reduce the time and space complexity of mining and learning algorithms.
+            \item Visualize multi-dimensional data.
+        \end{itemize}
+\end{description}
+
+\subsection{Principal component analysis} \marginnote{PCA} 
+Projection of the data into a lower-dimensional space that maximizes the variance of the data.
+It can be proven that this problem can be solved by finding the eigenvectors of the covariance matrix of the data.
+
+\subsection{Feature subset selection} \marginnote{Feature subset selection} 
+    Local technique to reduce dimensionality by:
+    \begin{itemize}
+        \item Removing redundant attributes.
+        \item Removing irrelevant attributes.
+    \end{itemize}
+
+    This can be achieved by:
+    \begin{descriptionlist}
+        \item[Brute force] 
+            Try all the possible subsets of the dataset.
+
+        \item[Embedded approach]
+            Feature selection is naturally done by the learning algorithm (e.g. decision trees).
+
+        \item[Filter approach]  
+            Features are filtered using domain-specific knowledge.
+
+        \item[Wrapper approaches]  
+            A mining algorithm is used to select the best features.
+    \end{descriptionlist}
+
+
+
+
+\section{Feature creation}
+\marginnote{Feature creation}
+Useful to help a learning algorithm capture data characteristics.
+Possible approaches are:
+\begin{descriptionlist}
+    \item[Feature extraction] 
+        Features extracted from the existing ones (e.g. from a picture of a face, the eye distance can be a new feature).
+
+    \item[Mapping] 
+        Projecting the data into a new feature space.
+
+    \item[New features] 
+        Add new, possibly redundant, features.
+\end{descriptionlist}
+
+
+
+\section{Data type conversion}
+
+\subsection{One-hot encoding} \marginnote{One-hot encoding}
+    A discrete feature $E \in \{ e_1, \dots, e_n \}$ with $n$ unique values is replaced with 
+    $n$ new binary features $H_{e_1}, \dots, H_{e_n}$ each corresponding to a value of $E$.
+    For each entry, if its feature $E$ has value $e_i$, then $H_{e_i} = \texttt{true}$ and the rests are \texttt{false}.
+
+\subsection{Ordinal encoding} \marginnote{Ordinal encoding}
+    A feature whose values have an ordering can be converted in a consecutive sequence of integers
+    (e.g. ["good", "neutral", "bad"] $\mapsto$ [1, 0, -1]).
+
+\subsection{Discretization} \marginnote{Discretization}
+    Convert a continuous feature to a discrete one.
+    \begin{description}
+        \item[Binarization] \marginnote{Binarization}
+            Given a continuous feature and a threshold, 
+            it can be replaced with a new binary feature that is \texttt{true} if the value is above the threshold and \texttt{false} otherwise.
+        
+        \item[Thresholding] \marginnote{Thresholding}
+            Same as binarization but using multiple thresholds.
+
+        \item[K-bins] \marginnote{K-bins}
+            A continuous feature is discretized using $k$ bins each representing an integer from $0$ to $k-1$.
+    \end{description}
+
+
+
+\section{Attribute transformation}
+Useful for normalizing features with different scales and outliers.
+
+\begin{description}
+    \item[Mapping] \marginnote{Mapping}
+        Map the domain of a feature into a new set of values (i.e. apply a function).
+
+    \item[Standardization] \marginnote{Standardization}
+        Transform a feature with Gaussian distribution into a standard distribution.
+        \[ x = \frac{x - \mu}{\sigma} \]
+
+    \item[Rescaling] \marginnote{Rescaling}
+        Map a feature into a fixed range (e.g. scale to $[0, 1]$ or $[-1, 1]$).
+
+    \item[Affine transformation] \marginnote{Affine transformation}
+        Apply a linear transformation on a feature before rescaling it.
+        This method is more robust to outliers.
+
+    \item[Normalization] \marginnote{Normalization}
+        Normalize each data row to unit norm.
+\end{description}