From f4dc18852a4660d42d00363b599c3605ff18b0b5 Mon Sep 17 00:00:00 2001
From: Michael Zhang <mail@mzhang.io>
Date: Wed, 3 May 2023 04:14:29 -0500
Subject: [PATCH] Progress

---
 exam-2/1.jpg    | Bin 0 -> 36116 bytes
 exam-2/6aii.jpg | Bin 0 -> 10118 bytes
 exam-2/6bii.jpg | Bin 0 -> 11182 bytes
 exam-2/exam2.md | 169 +++++++++++++++++++++++++++++++-----------------
 exam-2/exam2.py | 161 +++++++++++++++++++++++++++++----------------
 5 files changed, 216 insertions(+), 114 deletions(-)
 create mode 100644 exam-2/1.jpg
 create mode 100644 exam-2/6aii.jpg
 create mode 100644 exam-2/6bii.jpg

diff --git a/exam-2/1.jpg b/exam-2/1.jpg
new file mode 100644
index 0000000000000000000000000000000000000000..7f65d38f3a0c0014dd6abe8ec786d9740518b3d8
GIT binary patch
literal 36116
zcmeFZ2UJtvwl5q+DWV|KYgAOEOBE@JjV3~*h8_U{>C$^5AiYUfK#(R<BPDc*bODjx
zYeH{AsDXs=@;~>UbKf}QzVW^LzWa?g&KTcjti1<2J3DLcxz?P&Ip=Tf^NI5Xz_sVf
zYRUi#3IKqD{0BIn20R5^qP%$VBIPCW?$V`8RMb~!sL2}x9UbizMuzLx85tNEnOM2m
zn3y?P7#Z1bvUBqA0D(Xzwp+Jv@!sa<1@iuN6AJQIsi~;xX=vzqnHiaR|I6F?4*(<0
z1p~?(loYoB7Z@oh87a=&0YGv;FH!t$1N{3&ae?w8xtBDwm+8nCpsoQfP*74{Aorgv
z0Qu?w^5=kyjF+z86n{*`q-9Qh%Y|7YFg}}x?@4(Ji}v8|ZAlB)All2UZ0sDIckc4v
z6A+Y=mU$riQ10n7C1n*=wdXpzdiqcULnF)AR@OFeZ0+3KJv_a<eSCx8hlGZOM?@wh
zCMBn&e*Bb{lbe_SwcuM}QAK4Hs=B7OuD-Rcy`!`1XLrxg@W|-c_{8KC2D`Ylyt2Bs
zzJc4@KR7%(#-E)2B^L#N^54WF@BdA(f0B!lEY}6HS}s!mB^Sj7FLI+~ym;xRIMwyX
zTGZw)Ot&NgX_%kHXP39o@=0p%vRJqdUS_>5g}H<KOSHd9_P-}s(EpKS{}Ajy<eCCp
zp`;)ykCG7p1`tFe?|r%O|F{3-8T8;DL`VUzOw#rF>7j-(mhUA&bXiJfB?0fGby`U>
zy9E({zM=-Cr{xLZP`?f?VvG05JK5W=6nyVgzj?gM@0mhd7Rd^~_*RcA;J<WKvVFYe
z&a7oJ-wvbSFykL!(;RA4_rpw%c_htFInC)_xa?n2Kz-wITS@J?xRc;cIlG<vhF-KF
zBtgu}dVAFhIpdxL?Upk|#~h*~(7Ta%2o@UQQLGN7+Sl@{%MHEH@cYqq8O(&+K5vE_
z%vhiO1!T-(x!39>^EV=1I8%3VJ85QgD^Wu<6`}|4HzljQEO)i_UsUl7p(I7S)YF2F
z82@<_h1Rk4?JxQYD%ZIMzir87xvFj0rw^4KBCc#0IW>HpmCm06%1s&c^KoBOdBSib
zxaDGS3o>u`M<y#i3Wsc$Lv?-xDi4i1iu%`?vK|qD5AUdUw!C}Psd{mhUyj6sw^}gX
zVcwkb*a^d=&8w#|+Hk4g<%4Rp2mDbEaD(v}Q<@os_ehu>q(RIg8c5VTRrqny9}9&T
zLG8q)0yfzxnMyU|fJ2QFMUMeALC$;C4A&px?1b9%CT^-{-4V@=v-o{ENLkLwWIy_f
z1a31IH`m+gn-ysMV)q%9ac^Ba)Yw|}qj9q1gv~1|&A~3&yA6JH@*1GuLh^J5B91v+
zmZ9vew-_Gf2I`CtpBeTuY}u(b?;sBch^}S!&mZP?nZM~2*KT}u7+Dk0<WRllzq&j8
z96z{VD&StqkC_YQOE5itATirH{M>CcJcFJZKoR$Ab*<-Kaod2dWl!GJ{yE^?hsu%-
zpC)HV?IcSPr^UWf!kqSWehIUdl9P9f67x%nf3;?k)e*;}hJjt0nVS;(R5(*HWm`^>
zc;{D^AV7XGrHddv22Gtl2XwgLa@2zfeM~Jsx`4-4Bi#O7^Sx$@>6-=?cSn3I8wL?s
z-MrP1umZW?C@Ww0ajC}bD#Z4>p|8v-k4+ooN*4x5W$-4uvG+Yh;*ZHvuRL)`T=7Jf
z_lF+jihtI1f3vK4V}9WATIA;Dhe0?b5`F`AvTo&Y4)}1ZPW+|rYM9of`Z>TMfk#;B
zg-(ZF(T;%f&UmKq=2}kVLEMddIgx;W)wbL$fX~1~TD;OS=vL;tqwHxOb*Er8uTjir
zx~zTuyo+w5Y&D~+7<%n2u^X&-Fxj1gIf;+h=?9!rm{cOjdif%DN>)oQKcQlS9t;yv
zS!kPUdQxW#-^(o=e1nD_ukR`T@*=R(XI}N!saoAPTY_u(&sFSQUJ`DGMAZkK1Nt>?
zJs{?FcpUx==#PdEy#ap9EbrP;I|l^7HMl>)i;75##9_J9dpS*%zc1g*dG{~bR^a^J
zpZ)n38n(@$zZx#ztO(<fm;v{42F_=y9#GZW?Ge!UGLU44HP|P|Tb6d^5BX_=9`7t8
zL4EOa-`h1hWny=fNC=UB=)E?bV$+clw3mjPdY?${Ilx(7W!3E~UJnzxn-#PzwHdna
zK^sv&a+m+Edc;Flh=0J$>AkX|NFmk7PXxs$xn)Z<Ug+75lZUX({4b#oO(!5x+wF6J
zqEv*=UZV8)_{~!PEM_8Tet+oqGWf<-7i+mE3<TUcU?@SZV%A3btot0WF7i2mS<5VN
z^%AqzqkqN5z1p6|q(rs}uuX>?wOoyqa?87h)5|fBHsBVLu|Gy(@0&SNTj#FSR5e-N
zEp+emDSWPJM1Gq7nRpChLHhRw8fW5fg&ImdP7{0oWOnu(;Ay-HtcL^yi)^`G^$l<x
zK3j%@qLfb2!%Kc2`;UaL+%H}%wCx|7TY|4FlT{{4Hr7xrOo%Hl{|V?e{_#1Wx#k;U
zXW*~rzX(q4Y-UIuT5%_z%|(JGNS6_FVWd>1!JczK?6`OTIY2djd{BvHjrXmV5;Ndm
ztwF&!ruOgNDlJo?P50@?a9A4jYDsA;KeiptAst^zG{Sr3!n!TLdFPBe-EvL1t<^2l
zNqzBp<f9woQm0?DaOzm=Wc$3C(w$I$xu`<Z=U=umw<~UHBI+re32U57g%QDVA_DyU
zIb-L5(Hc-NMS=zMsK1qfax_%ZQ7X-p$!<Kc3Ysq0{~pAd)n;}zRPos->8KM<f=+Vt
z{)}2L<pBo4;JbA%r(U2%Co*!9S6Pfjht14m!<ip}cfK?HlWgfLKMH-o9rq%=HDMYM
zo3n$^`qL%QZDI{CTk5b`4eXb+&q)EHG9Uv%%Qx7Ap37+{gp1q2$SVKh^RMQmsblO&
z(m0jSbHE#WF?zextk0MxL+Dn#6eBX_x6HRWX7To@ST#%t8%P?bi6T7fS~#QBC4j;T
zZa6Bj(#-#wdI0{_WAM77;G#wT**69LLVGiwVd>cmzgIS)L!!aTDT5q$#LGEu>Rx}_
z!tlKhdiIehRx+uA^sa0_dZ3@yT<Wge`^`w;f{mNZ7~tKndHfoZH><`w?$vaK6LfE_
z@z6Ib@3B?Z#Qc=g{iDeA{BA4UT#x5YZz&<|9B|EFWOulQbY)z67SiVH*q%sxTg<g#
zCDVuYre55yymAuvtJg<m500b<QO2h7#$!%=2_kX_9X!pLK%twCzZ65aY{o&!t^Q9&
z{cRS3kq=xp;4EX(O%I+n2%II_UMwp5Bu|&D&*u&J!*|>Lh9&R*Zdk|M4cx^VPS4_9
z(tc}7%1i#q#)+k8PA=t7Zv_Uf8!l{UmqzGB`#8EM*Zi4>JoB{ncJMT9+t1a8kLmeX
z$*g4E*2}PDukoCVsVa3u+Gj?QM@=nUpN#MTEI<9VPaLES5v!RfyK_L{Ie?Q4SMZg4
zcxzhnxooF%03J_1xxWuPmW%s&;F@(jW#2&j-5hxj`Dj1rUoFBYZ*;+OK`!GVTH`x!
zEi2#GzF7PP4-cLxr^J<}?VSVI$*|B7XRN;K>wl^lSfe|74yfNp^wK~`@5#{x%F-<N
zz2fX#)HsQ1wIB&|GrZlbW_KYYpTsge+Mwi9<>=43dpH+?5v#U4adb2MgyK<~a9ipA
z331G&<cYPf&WWsdAC<jV7AEt6O~Lxs-{$|FrN)%rzZrm}zwn;W2YkyO{_-B|WL22q
z91ssB+9S(!up7>Jk79-+K5$Z`eXun22iXu^LErV|P_G8X;d4)Ni*s_T5fXC`NPCp0
zy2&%2M}Je5Y%yyYrX8Vk*ThxsmIm+?{Z!TXkub6OjzY0R$>@7Nn_PmLDDs(}oKEqb
z%eK|0B8CM@uhuffcYmYYMcikNIBdY4GWyESUtUS#^$!L03diCU9}0-B&lFAgR^92<
z7Zt12Cz4~#(ii^<!{AC5hy56wZMQiaIS-sMeDYc-gUu;2c=qEv5bC!->wvQq@^W)=
zN%UsgR+rWYdo+v9vgOg`TJ|kBLteRaK;$siGjSoD6d<NLU9<_CwFYk71Z#US&H(KW
zFE5Af2-dmBMvWs+0#@t7&jA*_i%+*ltMZpwcEvI);3m;z&2A{%&xyPT_^Xw<VO^bf
z>A!>5XR>|<oAQ_wA8C+i#=_1XK1bZSTPMDmPN#+NAgP$aL`_Wj&z4VeRg@5tDiw$w
z<4y!_&}6m4Z`<wpZp+Ale4EqJUSayND&Yf;_~_s^994%=*;f$DLm!u9gYgT+a;PM^
zluvHvvcI5=QjQ0FEU|Z!UnpPd%t%X&jggn1+SGY2Z64NHI1-tpi_$Qa4se$Rvw35&
z^O)w(#p{(NMxoi|EJ4K%=A_CXnhl!uIn>TJH(qpDYy7|kE22FGSYe_O{<Y*p@nkVp
z9&y#D;C-VIRw#>Uy<WMrVD9Uu0+a5$CpXL)TQ0t9e-$bSmOEtNuy4LK=)C<q6*DRA
z#~=O4za$LW|6Rdys!{l^;Mcn`Ci+5Y;+~QEPJJR)y*5YHo@)WT@^mU!^)tC>dzNOt
z&JGRd`BYV>7iSv3{$LMgmcpi)@UrgZ#q?DMh4fT=b3M8;D;|g+ZyJw**^&ft{n74c
zPgWnLE2B_?bT2L^znqTf1sI&Zf>w+}uMQ^(j5^9clu0*fobz0B#fd11y(%lqwP8M~
z^B_4oBVOi23avAw{$Gm^gyO~(B#~c>LFJe%rWvD|7t?u_O}rk(9{@jibiOQE7xBmL
zR6z|CoWGdZTFMdvzDZ6!sN+jI<xbm)y`X3DnN|Qat^UW4Smv|$i%(et8WptD2tTYj
zYqD&}DO&f92`zk6<LkJ@_V$6=%@6laUFN4sp;vOS+jp$Jl%K1oiLTv4vf_J7yc7Dd
z@Cfs4yBhs%g_rN&YxdIBCBGB>vJm^J->v}Rw<vbeUwyFT5Xfw@dCg7?m=>!VM^9kC
zcsr!)r7}3*Z=`~DG@rI8axW^uXm%RG_oLnA%00b8YK_{Kytx$U^si&1dpV7iYft`H
z4yA%<SUQP!Zu1RofKSv^1m>G(u=3@^xxS^YD}BDt5RSkZ5|syul)(P46ON-Ezuc{K
z2p=JYt^~#Ve)`fIvQKAc*P0;ef~`+k!k?EVVKef`mK}w7P_h4J7|)+$X5ek@=w}GS
zXL^UaeVa>o_-KA(@#u1%%S3`uV@_m|?q60rlzqzt_c3BTGZx|$;jZ2-!j?cD7gY~0
z{Jql^jju9o-lN`=4&N`H18$=1MnwV?`lw$*c8q?4al-~!HfaGd{u3_qERi>0>64^J
z8Um3e=fRom6Y%W|)y0{32Lh2g7kKKSb>d=r)h5t?!p@mcyeHk&mCB-p@FAK11@M3V
z<+lH?w%DSzpBo$ouYx3K@^jwF&gx)RJ{&uKTVrDbagRVi9>I>v=Kx=Dy-E!WlwjWl
z;ym#<<575Q(d1l(YX9Ne$WKNYUV)~|ENd$FGg3v|zcwD5CCuY$;#bv0-@~M-*3lwa
zC7vf!B%28P*WQcRg0RE>tBp|46f?+F@>kXTD2M!X@jCjq3@>R)`y(@%#t+dzZ!g_p
zVbGwBwdMZOe!QoJX;<hg2yajW1CzI8Tk{Qs+-ZyUwvT#)+p=as`JCM1{H=0O8(B$L
z_P@?6VM`Se%X5eCp>~R_X3+uDdq|5ED~@{Cwr-_XQ2|ILY0uMnJPB94obbHFh0#@y
z)9EGY&)lX)X}z0&>|W%OJ1ks|WqV>6B?f*va>}Klq>uw42*dSxGnP)FCNz9}@i0Z$
zRVag~QM~=>`pl^udzwM`zIFnl0O|ZuONk}0_CJZYC_ZByE&AI?z~-?->S;$SN)7(P
z9~hN7S<0EnB{=Py;}jBa9S&6Saja1dd=xU~+ZlGI`*iZ<!FFxzXckU5iygnOjQ66Q
zH>WU#nshzA4xD|0m~*%;w@B5bKrVN@q7SOGBuxD_<tyk%&eqKNC8H-Q)`kckO{>e7
zc98_1IY_rs2(y-{O6dPQ+E}ih`lLv9ovls4lcg`dzUIrR4b|s1O|uc({d`PR9AY?=
zG(VBQyde~imxB<6`W`YEOj&`C4>!xogiGfyDUrikaDsfLo`Z+g**e^T>=^&Z{$m3D
zeIotsxZ0?*h@kN{g%EG^@(sHmQ-X9W<D}wVb6Aq$5&Al51Oym9R>?EksQ(rGr{c-Y
zaFXa#2Es~{39HJ-#lyD2q*OoK<0dfE<&SB)%@1$;m9p%K))DmaIqScC8A1*kM7rpX
zKHaWEv^lk8{TMUA2NP8A1)n9xja7l!m4oeXz}wj`&H;;~2QL?{^r@sX-qVK7rJk6=
z`T6?p%?)Ur@@;JhEsEhEp>0jQ(tG=_-PV{|G%*+_;jbf}!|*m@QE91th@$mK2$8s<
z{qT&Xh#Wf#H)r80Iqiq%&H>XOnw#{9Qn00fxI2A~HrFB7fkzpa-!xTP26|C|hA!ht
z;7RqaXYhTq-Knf2tB>b^?VAwiN%hW&#dcm^{@E3B-`o+!pE%C}pAyaiKY-_e+u%|x
zVzr+<tO10p1`?s#G>SA*C|oYQcm8@Qt)Ho7+m;GMaL)={^7Lc~7>ur>ircsKjoD;b
zKT`DS1>^Tifg5E|FlOcDNg3>{7G_#jlXDIL4-h0G@m<^Cs&hbSoe;J#=<t_19Gp0k
zg04bzm|pOx!O<t0zirzQ*^Zj-fu}zYJO}s>`Cp1ILWY!TBJozpW#@J<N&p!v;+wlw
zB(%~`Pa2bx>d<NDWp1w8dR<X#*fnl{v1`SCm?(m)#H5Bt<|88=9r>M4tl(EGDc4h5
z6A$h-zHp{n!Hd|xOm0B>1mNn1AzV)i+U}h2Mkq<pT4b`Maa=c;u`*?6G2fusgdi^!
z^F03lC~tj<$6jUVu=uHM(S-5b6GW&kHSfY9^$hfuKU*mtahyquyZGVBLsH*}TG|9b
zC}0Wr;>^A=r+&@SUMudl>Eh%@^J+oATS7BcjE`Hlk?C06juEk1)<7XZH1*aLe)?(s
zz!LwPhDX*_Zd;qjZfm|?(v$1Q)xIG`rUs^uJt)s6Z@%3?FluWsyFDA!;8f#^mXKSz
ze{f@*3$eQoiCjNqpqrn?JDt?s{k1|3-fo9$D~4Wj^ydi}uS}f>lGG4ObD^xA=11@$
zkf%0*#C8ryIQ?A8(sB-HRaz9I_s`@XP%eFq-oG}ayh1sORfuzyWf}5zZa-xR&)$~`
z(4<SCGP>__E8r!uZLg&GmA!VHVqNa69eTl6UeZYRRNAT=Zs_R?#)FF1Cdl9^dix*P
zDHqG5-~VJ_$0OzmM0D&oYnsmdWy!!lz7!jFhdyB)cR`}K%&6VDnUt#AcD@*$A2l(}
zs&Ry!IF}IV7~j|o(V9u$%vfk}tl0Hjt*Og<iQ6p2C(}x^RZ;U7-HTgt%)HTtaZZ(3
zL(=qpMT@XJaRw_*1h*&hah~4gY+b;YR{&XNlx|_sTP<Y+;_LF-i17r}k!ix<ou%Z2
zJ@R1D4`cr)GfeT*|MrRhEsJwNCN!0n9E>sG$6+RMt>{$M(Ocw`zD+%d#WtdS84@gb
z4siS07{9hMzk`B#&d-rerZ08Ie;7^!aw;P(w2>qKvr2m!s_8wyJj?IbNvF3MKE(~_
zC%qXdmDbEK$vaZl?-00GT$9~o2;#?y24bQZYP^FDDu*3UrpB*_hz2lwSZ+~B?=!TE
zO*xy5i5jcneex9(di-nu6hy0g+yu`=Tj`#80rRc!#tXo9B=3A#&EjY60P(vmwqmmd
z4OR!VSxJ84><36x+pb-kj^4g+&wD@T2Wx1|yt~iPuZQ!ZybArh@@O8?C?`*R!gR~2
z)M;LBpoiy+`)5xAj)11gE2UUi+&O?1W}Q-BVY`>X@V)Cu{-u1d0N>jqVf(c#3V%Ah
z7v@GnSKd{lLmz^EendEU>#K~|$Q8o)*P^0tdK9`>0Mr2exNuho<ZSQ#B3GExSLCSJ
z-tqze#>dF1vCpZm{nIh9Ngd+`a~CX{$!PMAd>WVRuRUOK^#H@d=*Aq!*=G>@n-<PR
z_4={9uoGK^YrD-^`&0prs>w5QPkhEQ!%`~QhGhywPIb@yj`V@^W)7muzUqfyko0S+
zOiBY)eNq&02gbVLBs(g5{YarzLEX=4ZW`6Z-&G0v<dL9z<*!KmuO=weVDDGUNmuM$
z5Yc?#`o#+T(#}ZW>u^0~5DwUa4)xu&^ut`0<KQA085UMMoRYT6Amh@@&4Oo1?p*Ko
z@b>MgV+<ooKAgWl9b9Qp1)7c?1hD*hRhur;f}m<FooqnX&2o?4cNg^6Qt7B9is09G
zhoB9+qaDi~^*kL_ez~`52m{=#rw-EP7~qs&N190g5hCV*9mOELouWFtRddhpkBKAy
zG#$)TpE`=jfq}6Z2V}MTvZUmQhxqWdhl3|wLSa85kH^_CE~G!s@1xHFO+ZiBF8m-C
z_DwUT>h5^rDECg=IUpJiz!k<`ePE<+yt-frv*3t0;E*>VgJccgtNz_Mx+7?HlDf}=
zqtzF9PS;EM4+P;auLIbDrEh(0;y@Bac68JW+*Q=fscZE}^~mECHp(iU3ocz&7St}f
zc$iopQ>I3EBYJh_Ahr9DP`V;kHk$qQ7N?gn(0<TNXSZgtE2z=Qq9SdPzyS4UD4&zP
zyuHqyArwGQdw|qO#&lWXOD;jxnW#B@NS`_PRkAfp1iRAc*T^bbl=_E#`R}abtTd`E
zAm}#}&&uqTtI*T}e%5m@HUhlp3pUf%-;}-?FMMJ$vNXIWUiu{2drvRY{@21U@U=$C
zzQzIX8co=Vjrg^>dq>Xo=YY7oRaHQsH$tb5aH+jwUG4*>1a)!mHT8f^FrJ$L)ibOo
z1?Sq2p{>WHHvN8{1Hyj6J|Sk!dq`9bAk-5yp<VbKkR}IC!^3*!3V@?R17z&{d3>)|
zZ!fjI*?%rH`EQn+9}A<8A<^UL)E%0n`gA{8bmgdmUh~d>Dind==(3bE#P_N;>~8n+
z6iWsFLVY*~R0`rw4i5A7PIRGd-5Q=o<VqyP{Ga-L&R>=qdsvGFLX+h=AW#HE0Q1%6
z<W$vFH`b`9tB04}bV*9!zfz(YzA)^x<FM75-cT#j7BDaKsP5FdaU(%@*v+%Xt?9R*
zLf@KFnVn~vOq@?Ktb2KCvUT|RTx2dkFKM*hpK)01&d?6gu|yfFkCQqF*jp)@S93pR
zKcef$Dhh^m(0wD?U`?4Yzti7V8ku|_kuJRHA5s<5Y|ssye@k6WUFsYCCO)T&v*^}4
zmPbDTo-Dnzf}=hu<*{=}V(Lo2r^c(j(M!1T(UZqu55)8k^dK6h^(H5BQ{mBH*_VH6
zlppXm<jh~II@_@{p(KEQ>aYA~z}^N)C~6q$MJ|^lL1AWaC~1>r>KqVklbc4KL2Ab}
z*bijj{_oWiU1*K|n0~_SoQaa7^X1eOLlePUv3ZF<SbB&Md=v&5miA!!a1%YR$}m}i
zZAn{*?U85Dm!;fe*$b_~ibc#<u|;Sm<{K->={j+3#n%}dTlF(Yo&%Tyd=|FNMh{Ma
zSD?Rga4fG22V(bA=0(o|sh<yIak3MG{_)VnwK!FL6G6k+sA@{3?Wgu1xE4xnSezVU
zeN}~@oC9oYkIegA%&75vIBKkQo`U*fsq(%iD(i}MQ}67HrXXcF_S6R8@=nPwu4O*Z
zjCGf@?c3Zfd%3-L@Nqf+4>e~JPmd9E51qfdn4!!%;CEZBu6g^%e$M=zm%MZ)R?`pp
zbNFyExX^ST3+r}pIS0@;bK>QH=;weL*2VL?O)Jd$2)z-YGG7L(A4g@akwO?8d)h=%
zY^m)-wL_<^gKU}>*A7E+z0ZL8Kb+-%9^bM+^@rWhj9N{>x)n7|RY?}AHqmnTkEtV3
zO0wM@g-VlO>`o<Db|SMXsnY%LjQCS}N^Qm(tRIUSQ6H%+C$71If*Q{OE%U6+cl>XT
zv9*~=4FB0FvG_r_vk#P!TK{OZDzpZ&TBPK$-{x$?A>TJDE{gC}AsN>{%o}GU3E#&(
zIF1h!4Cn|bql~_zozQAMaCFdsj`1lN-$8#`)%$Tr)R!Rz7Wfp?)efZdJ_o21oWnd=
zk_RXiOR|J_fhrJ)%LhNsjm<?^1niQ(&2EG4IpBTG58sgO<&bg-;Q<#9yQbrBm|-4O
z_D<I?(0qUTvmEz%#*b2BoK>9GWfQ7M>RxA8KO2%y9eGqj9Nr38`wP(ycyHyv$Kv#k
zayRPF#`mhTRX9hQK6~_vwPZaak5HUS&i~VM{XhHM#JK}~!nSY@K$7A9m$ZF1|2Bd=
zwE|S^fk;(TjjglIe0g7Vdw|jVO(SB_k-T8+3XSL&KfjNbnQZLdOD}uc2FN@evGD`j
z5`Ss)GMQZ0<7YPj)hx`h7mnGn^`9*@VT|4qQ!CcG4XPKr1!PybmrgnN1y&EI%9=uo
zw4dv*7!{PQzZqIDYl29`+G{r?gDrPl3-1IBpS;m&!23AcxE{}48+9T+bnkLgq1_kB
z18+Z@ftxA{1>snJ7q}FY>uE!NKOu>H$}}&K)Nd52ToIgWQUanxSka`Rout_0R&KB8
zAFHl?{y@X|Yf^{9jW*5&dF2YH4Qh8{>Vb1=RTmb-U`gDoU%}k|$1E%OxtqN=^)t8%
zIM$Anl1sg;{P=Sk5PU0=G>vessaJ*47Z0BkrgmnHguIM1j@!tvA&zO@{<>zW<OWkn
z5=Gz=JqwjD<0kAWG{GCu!dabt|3SpvEGN+Z_x7w^mcwI(0AKwRM7S9TVVydv>X3B1
zoh=-c<w2fs8h+fAL0!6SdZ%s6P?Px7h5%{Qfx6=qTC<=o#oF-wN%3MXKU+_7O1#!{
zfqSLe6>5gYPaAXUvgo~6+oopD0ha0o6(baF6LSTL5;b2LbPn#;+Y#hO1Yf3#s8$jC
zv$MnV%@hvu()KRjLrUP&aSR5#$QY^ZTfGoeV|8uBZTEYf*1}s2FGDH$DLJUqrY{8*
z#}sZAI$M(#g`H$lE+>{6V}@~xGLd`A_)pjvhW4WrUdi3%>d#i*Dk(V7iV{Cp6qVq_
z&z}pU{SoH?Mih+Jy9+Y3UE=6evJ!G9iP=)T_xnwnSCWC9k5?M>m7<bWha(}MWYTO4
z91o4S#Xv2c85?S-pF_4^)0(Fg9r__Tjo9HX_^qJ>vRTBXhK*~~yi+-1xBPwbsn<U*
z!DqoHFxI;)p!p8*QJfNtsTU&;++sBkqi;D%j9&G0$&{>Q*7;ek$F;mXH@>3pSUf4e
zadt@u)T*P_Y+p57XF8-gZZ{<+<C_)H_%s*q)FOr|?ys0`43b8O%nLuhVg6W=qIm4V
zOS8$xes-kSY>Xx4AexyH33>*;;JHRL78dQ`3};`@yj3++B2D8|mJILz_UyI6wEb#`
z`Thl(K40Mb6*gX$A*YMtkM5L*5NksjCEjgoP0$CGx4+`KB5bE7Eoz-PHr(sx0D4u7
z{Vb~{yH_Z}bGSb>FO=r4rQ}oa&6St-#NQaZ)+BZdLD-NZyR_YcZX83W_&ES&y@(4R
zC%ZI5B2~k4#HmS~iWEsMV3FbM*3EybCYwFQZ7w<`?jFq^e7>*r4WIC=rzNAyfk8Qy
zhY-S@iNDAcK~N#OhPBc@2q6kcx#0s-9Xo!s-3bS0Cr*Fa2oMT8%WA%4f{*kjI^wSK
zCro+mZ*Mu#N|+|Nt^9(>Lri#$3m10+njs&|zt>u&S)XbX?h|wn%O^WI^L_0W1rG__
z;EvG)74U8w#wHphvDvrCz_G#hc3lT#_6K%Y^9WdXIX>j^u<Vo^;H}Hy{CncV9B-&n
zn96|Enu9~mT70a*v9+RMoU5z7Hv3}e?NIh1*}*3{H-5a71yBs=6nFP~$1$aMD-n`%
zcUv6LedmDZop^`a_k?!%8^~a?*?aT93@LYkv1Cj&_8F@MLNC-V45M;W(}qKWwvM~r
z%$%ML`7S1!ohkVmnmI=H6c^zQ4G*`*t?QBN?Bm&&am#6-M|crjgUK#E*=y6l+Etyo
zAT@{^YI49T1ICHq-cCiiz+t`%&9%cwM`<p0=MqtiderBO@fu8_Dmnu}a*_M}G2|~+
zfg|J$liq(H|MJ3UzUc5k4M6BVjm@nEKO~Cd1F`*q&G*w=%|t5e0{HsQ&a&mBA7vd5
z@V@7*<$h3(tZZM#gYM-Do0%nv(-{u0i^-k?%<4CYc)h})gb-8n!J|XaSWe*^-?GnT
zwyaati9RgLF+;RB(<GB$A>y|lFY#VAMfUU4KGBrWe{-m#VM=!C+W#nc{S)N+X9)Jc
z^?wNi_gan7pH!C8ybrl~+1*JW#DnB1H;oUVcjYgs^Ms}F*0hO`2p_Tco-_$)XZ9Ja
zG%9^DvjZ`shQ6d+%4FnS@w}-y7#w|tl+0V2WB-7cy>igukH{@L&ivlWnqSmbtp~*7
z!kpU8rCPhaVgcB3gn;4HI+-s6S{1J7k#O8dj}twk7u|2EnCvz8`O<&2sqb5RspPc^
z-^6zT=YY#gaQX-Z4;+ITzR)wf#Nu}hW|toNGn#a2)&FuQgPStu$5_oaUD^DUxBhsm
z9344{CsfO6l_J;0g(yoR2r~6Mk^$0Us~k&MsDgNbH{yjxN($@dMR;joFVNK$QYZbD
zK{We)q4Z-Tk=e3TRF$a$NhLq{hgR>m=lOSRw0mZSYv4%x!^*ls@+|(UmWTykT{F8?
zv*+<yhVBa$%jDa2(k8vig8e66PMlY0=g#HLbHJ3o{jkPpvp>VLBv-{iY(tMwMXVg^
z-kuq5>k#Gz(X)0L`=M1VW^1p0k`lLLd@7$CQH~F@x-?|qjnu5)o!#VSKwTYpcn+}E
z+Kd15R&lc*BsnLGuf#NL%SfX=LTPWRPB4lyi34~u4v=omRjB4_KjY~)POn@-V|A~T
z9#S=?x1(vr*gB4k(7`Li2fc4Dt5^8kc1#H67i>`N(v*-tKsw*;cx8*_Q4>|^8BK3A
z9Y;jKK?Nb7G2(~!W0MfxWhf&x!=uS_z*2MAgT*t8MXXn(djL>r@Q}{U?ic?9@sKyY
zEHefd-WIXdtq!5!f;n+9B&O)-cOqfn!^z?bG6w5{?Vjur?J=wB9t#`3uOuHIS`mJN
z(8(V4yr{fQ&!A1U5s{r+e=OcUCoqlxEsb@5*_rEd-y{7IPtwcx@NqgR#XFf_sm_#~
z>hwVSJz(A8)lc#?sUdnkM8wozIu7@zldewZ(r|N@m=RVVd-NrUx|u!05BhNik2fKT
zLnu|UH^9@N=SIwX%_aiefyXtk+`G&U4@6j2Ub%T=);g1o{5K?4Vyi0&p9eP<_ad-D
z^#?_+4^@)a{g6$DCs|<p>XXLZ;~z1+Z7*S>>nKL4_^butvL|PcIs-PR6v!-sTl!(=
zfLEJ{Ggj13f6ZNJq=HrPQ#)xtE@y_$Uj8KAPr>gV%TD*}#HBa+Qf1k*#Dp{@0m4hM
z1|N7EbOGSU#w*?v(3W9MwZ0y0&vkeh2>LD)$n}67Mbmm;<FE#{(SD$%<c~YBxtYxf
zY$r!97vAztjs6ZuiX5!L6$F<Fmx;Z?SqF=hRtnC%NQ-_E&-$D4zJq|QY=3r1F(MHg
zT8-WxRwMiVySJLH&yt&Y@s?ewnRj4J9nwoO)?#-@op|reEO&kMyr#zWR^HWq2;)$2
zHS&iA&frsRXA-GLquI8%0rsic%S?AuOAERZ4V}Fh5cbuMl`}uVY&~^se5@j%yL8!*
zu{k;~*o>c`;r|9gHKm4ezN(4D3Xu!;0TLNe%zVM;08^SZd3uNg-sV00*1Z3XaRrwz
zZxT>T3{uroh>uTiyWP&$w~zxSD$0GR!;+)>$#jfJf3&m?j;XWzPG5XRpCe1xFXykn
zUm!ETF`OL)gfh$yVodI8X#0eki`reQ4BC_#9kTDOF{{7pPb^2-ldx%3hmeZ$LV}b(
zqy2brSLVYSAOFt%Enz3B7w`A(Ch^v7FduIC*=!iyLq`0rEYWm{@YqBv4GC48!E^@O
zFqp6~VFad?%*MH~_Fwi|e@~cTK$89vgYesU_erym>X9!OC*}p0G0soVmK4Wv?9#J?
zrtB|F9eCc1XNwxD=ngWyw^QnTzD{Ozir~-@Br5N{)mFGrb;dfweS%(X@5TNLSl~+)
zlYj+96`=LH*OBkn&(7c0kHt-mOge9ezL^%>P<~8R2aH71OT}@oOFF^I?FHyW@`;bA
zlu6eXbH6@X*rSkF<(J-1-P*xPYU3TTbtE8uLf!tWba&M8D(Ufl;y9_Ud~@RU{e_IP
z%)3eWqGS_CPOT6-Teo}FGvkJ?d&Sa&{CAIhr$`<T6_}GBHgs$ee1H~Ok8Zqse3AFP
z7L3L>@V~t}z_JRfqK*)&a=!F6Dw`W0*6u}@ZyQN}xiLc_vxSXcF~aDRnv!YSK+dMF
z?&3&0-u4{8a@^79g_S}#4oL+}@rUgn8<S6}en!mkzj0cKpK1y!SD?i-0BO9z>bqkZ
z;K2ieN4U&=)B4IRPYVM=+H}6ALa}L|xQCum=1yysSrqa3Zxyx5kAKf!3MGt#fN$hN
z=8s|``*SudlN*P#dK?IWdo^ed5Nd4D_+|TOwy2#p`Dcxf?;}I=!{bB@zM@MTxPjB4
z8{Rfi1X+J*0g_l#rNuH8rvp?u6$2fjFi1|k7c6n>$g7oW;O&tYU(aXA*WvNqK6kw+
zEbQ_cFJJUkV~tQBz{y=ohr$DwAke1{k2A}wF#N!Bz~X6_b3@Y7Y4zQ(UH)I_6j)vj
z;UuO=D2UXCLx+-_={MEOCXnh^bx8*d&pwh9Fn$1CI0wECqo|`(KZyLZIOO3c@Pf^A
z_(g2Fs$5~bCI$HtM**w-gq1HN<0<C=*_{)lMDE8{v6OoE`OJ9%M|{DO?^WiB+1oL%
zV@3x<^^%qtHv~pkGXp!-_xueT$gF(K*?iIjGOn53cFNZq*qO<n)nQZ<y5l|`DsOvm
z^2unadj-Dm&1$yx+aK{D2w;37)lUbzT`42eog>G6@FP`vPo;e`9TEX%eYJ~d`^@&D
ze5j)<9#D=_y}sP(HPik5$~Ug>ns2|v_i_>-SC$2Y9T`FudbBfBBBNGp=OI4wzNQC~
zSkv!&#(Tx0r_y-lbASyZWS^*tGfz9S(x7U2pSu4#SYYF(&c<xNdFGPMpG|dpKY3M0
z5%X9&@0TjfF5mQ&C;<RDfDj#~|Ghh!691&PElnG~G3zFrXI_wWw$4SS8ohF78H55^
zT$uMuEE9$@+#~n?5a%)FeL=0lit>tc7&36^{ha-eiJ{jx;!aRFt00Zd^Y~9DgFltn
z_w#y-4ucSp?$NQ?qVYe8%!!7-QL_Hp>MKIIxjD6lBoX{2U~ia_Um>{8*;X>~L=<df
zLlh=FtQ~IT$8JAW<m3_FCU&!zfY71qQfJb{kYBM!kqZcn6fU5P7~ITZ7nhl3*AzK_
zvXV;B!J@`b<LKUS!V#+*XZc-c1m@-j4Wb}~G@E)tEg?T86i8s`C`KNh?u1Ga$)x|%
zyo5y(A)oBhpLVf<$^3Gh%sw^V(S0Jj3ri~%VCRg<7i)n#h%I??9xiu&&Y7E^nhL0}
z_cqcEhWFq9_IqYwaj(o0bKK4aWbuB!4@;Y{ZS9_Qx@Ftg7YOzAdgZ}8s!Nnq>mt5r
zv|pr~IaD60zDZs`6N1bnBC@BvRXXHW0`El4gk7F;@8`3Yw!Xpzc-Q3w{osQXy8p|?
zK&`NLN<=DoyrbS%EV=rCRwf};scr{;316AFdFn{YExwZy?CdaYxqo=cCOt@#xhPY1
zJtHx47aWm!E3u<~*gMkxXRAWr)zXg-y<eG_rw`xG>QXE>OUHsk9?<S0)hY+vx$H{=
zG9QXrSw!8uWcbm^^*)8*eFnRQW`Sw%=6=YKW1|u#hVNOBj1`J-z4OZZOTV|vCcAh7
z?0fqPqTaqN%c^s9*qW}c8MH+;PG(7ENN*yElrxSXA-rMfO?7ruj9Q8`J8C%3A;T|F
z8`0V};sjpe+1>9*^yP}udk1V!G|r+g!0~j2lrG^kGFW{>RrfGAkf}ueP$$*nvdHHA
zr;J(xaw*N|t7w@n%|G`R(3m^;7`Jl(Zx+2pwa(xl6gh8pz`{|~1;wXLb(DQ_qYf=G
zTVvG%rc34^wYzT6OU5>i=Rzeh&iGH8^_k5xT@70)VWdw5b9@su;Lkv4^5}-zS?`|e
z{{H1dJ~>^1=R+CIYh8xm%=p6uxmWiA-Jlin+PJpS|I}CRqNfTlf_StNf@Mu+9tR%A
z{wmMe_n{$idwFcg$H(`xA3qlw=&6)DF%y(cV=y@D^MG`Jg647#yp7*4*owdzY|79s
zh`^Vsb8UIuC-W5gFUMMdN`ec>rT>QhK@Z%{_TvS*egJ-G919G2Fl9JvN^8(6ex&~0
z>$R`Y!Us8<w`-4(xy@Jbd;M5oV5#&^85K`-U2`Dh^wSTnFhW5nZ@X7tzys#x5h0yW
zmq1v3F-~kbOK+b@Oq1Q!%V*s^gx}j<i5()tfe6KG{~b}+-|vA0?y3+?fHC!5F|W^7
zA~3H`K~b6d>WSw7pd@nbT`UdXP`y|juVBM&f8gyf<z9TS;U}rSThd_h+SKJM;8_lb
zgP**py4~s4>dec#pkz$Cg2dz_Ry9CZy1<GGxzr%ek1NUF(GZ;<k}rg>(r<XAL=A6)
zhgW__k{PC&|Bxj+Tu-<iK&7Vmt;`sE*w>NOn#DRh#cCYxZd?<NeA&u+BQi2^DLD1D
zsqB8YN*xw->#W4Fv#Hn+&xiS4iQRsna%Frfnu&cehIyeoB!;9(&k?!GfmGdvbeeK?
zlA~x8j2CaL(a=;o{3`kD5c_u4?`Jc&dO`^^=I<W%zgU8HXH_^A;)-AFlFLF@8YwVj
zLil<OG+(UD`48jmIX+-R8-zoUrE=hGu}}U;W8~0L><5Cgxl3WnzxtHRgwOc7Zi__8
z4`!=}7u|vw%=>gxg<ofGJV1XgJJ_E1*la5xQdjDHcN^`t1q&o8jDl`?%W3#QcSBY~
zoUU(gcO;KQ|IyP^^{;yK){AkN91d^(K$|NfOv%N_sC05yHjPrsy`>{^ndVIu_Ab(L
z(A9OzawzzXH;<wCdbXF)d~&WU(0#;5Xb)l+vQ6J*h9^_^m^QNyO`jT#zj)BOf4wAA
zSN#TD*(;^)LrTAb`_7@2KRH2i5lf~C+$=c<Omu@uiN?ChnxgBI$@dC{)J%Ds_}}eF
z*>Wzna321S|GjAW_Qg?bfJ`P7lq(&!h=>3Q?;=9Wvh;U@WJ;jD<(VAEh7f`E+60cb
zlrl5R)r)-J4t;TA)6b_ioP!4;4izj_qp#AeAq%DzH~6RBkXWSvUUmJ4p`chG8_OMm
zJ6`C%;s*gJbaEUYQ;@fvb|$MPtFbe%j=bE+Y2u{61IA9evmxR^g$&@9Ffnebl$ccE
zDiJ$QHn{RGz%9%7U}vHoFQoE)OnTN*zp8RvJ)F_m<jM7!cV5bU@21mlEXJdJU)%gB
zRnTx-rgPM!L2)6}RDOX%o0t~NN-;tZ;MA-=75QO6uBmaZ@3-G(tmBp$qKVg~?9yu4
z4n9p~dVN^9EdBPxk$re&%%o^$Y)@T(+tG33NJ03njlT4vu;am?e0Ayunr~CSKa!WC
zsy`j;C(}jTyDCO{cU9*c5K@V;MJ(}9p$bm}QZ?c$PXdkSm}+-p^X)|aW$JZ0<<8RX
zC_{?gT_)YoKZ8@qvHw)-bk(vi5JHoC^>oX&Pd75@c3Oab!KHHm9i2`sdAXri8=9qe
z&B-xkhHRnL&H=Ri?NM3yL%he;qRcptVlt(8l%wo4GOKvhZxnF{xMyW}tN<n7Ew)+E
zn+`KpyeQxIptab(AiT!7>vq2+#~oF2ShG;eziu=~7l#E$EAZstKj5+B&%^YG7n)UX
z4CTh>8d^dx8^*ol;wYJ)wkK&sb<7`;*C^$GhuZA&lT^droddRvhtUUVa-ag%rgd_s
zru*Rf^x6f)8=SLU#P@JMeA<gcf>1tsk1CbK0tq8K^$)T6SRTmuwoyh*Rxiukc!GZb
zely!&pmz8mG2hIdbYnz$(@|zL=yQH`P+yR;@eM#;0t1T}W!P}q1GFFd_u|VJ>suri
zA{f;Y*QWm)v0jou{@rZx(qb^Jw|+m+YIiQ4mS?EvK0?8|F%cuS&0&e12LdU)i(5{!
zf{4lsC#*FUY}a`js;_Ht7$9%3v>dKy&h21VgG=Eek9V65k<{S@fE+qkixtTmC#L~}
z#%;99tV==Asct$A{~Gz)o1qscuV}TSXO#f(q|<w))%X4Z)8(}Wq(q)?i%IjaX*AYF
z0}>&233BgT0T#5}`$kf_J>n@F3oI)7gH<sm%JtRBmfvV1#G}&PQ_U4!YPt0`?j`9a
z=apT!_ZQCv@PiU1!mLLTwWxj~EJfSgpXl*csi~Gn9Zd;*oQT)krf*dgQ$>A`V-LNb
z7rR<V)YPz;L9|bIX+1tJtqN}(Kad2^0^hCF+l3T6;J$;mWqWGN;?HK_Mt#KPKV(Ib
zBPYGgpZ`Ra`TL47ie&P@VOVb#*d;HW2s?b^KP^A;!j*n==KjH}w~r4mG%MgCWp=QO
zAemV*IpVs*u;^XZ)L-6D-meJ7Z#|$SZQkF6IY9dn)z0sz$}!&ljs-30+qY@{9L2t_
z=0_4KV&TzUsDJ|M6{)7Yy++us{rb9S4BV`G%V*+Lv!@DlkEAm2E{KBq#-Q0l!d?6U
zz5z333ms+~byut&N_l8|v+GaR-X%!=YLg$2|8JXj#i<q>=5{-5&Sw29DEWJ%danw2
z$p{!q`|W=r;NJ!P-#oeixrnCVU?PQwSAjsPVYA2Z!AEFH!Uin){@>OjOXc5T@w9!O
zRMhuGzA|NZhiD=eCl?l;ew@Y-6ue&V<(_iZwX?+Az(#it@Q*iZF{x?IqJ6x80Ib7#
zV%{e{W+fEXe=2ZJQ{gY{Wr{xfv2CiMAzOu-O}E(S^blbPl@n7MUpYJ>^EmZg$-94B
zS^4<e<n#t-Kwrp=g}UFzG>(@CuU|a|#uu*T4JA}^I?CrRiZEeRwi$Or_uJDL+PDHF
zjRvGkO1!j9+7pappZsK1c~TJ~D|@8?u&`iRkJs7-8t($P2#b!_o%vqkydvCB;;}(5
z86io%%r~b28I{+&C`HyJ;E6e*NNToGqcaEEspsmsP4y-?$i(oEIRSjYZsy`s96a?b
z{TrxIy0z^n{Od1=c(P6YC0Drk5ZhE1DY(kd@3oA7^UNZrB&b>M91w)CJ38eFi-NP*
z4ffh%10?m+PW?PNsP2FNfj95!S(Du0QSFyKEoxT9qrZ61w`HOHc^}{*UQ}qL-R=pQ
zNY>_{|Gh-~*~KmH3o+lpvVuPgsL4EUJ3Yt84;)SFMR$IVF|TS(2_At`aa~ad&NQ~g
zUPUkZgi9;NhFInmdyjO@^7bCCNy5ZPBSx!{)<f<qxM$ebMQzW7{-+^()hU}T36@0d
z@*50~fY}QHj0*^IoN8mIfpum!BfBc^9P@os*|XX2WE$C9F(s`G8xDnoZkD}275%v4
zqYTz>eWD4XjUhL7t6#n@r>-W7^X^?fqYGX$x3yR`^c&1&6X-+MDJiD>*@4=>sdD>d
zvG_iJ>uuS7O2&ManAH&Blov^mBQotG$p+OXT*3Iu^oAS?M|f@TR+n%uo!2Po_t?*q
z*ai5JJT&hOf`&+u<2~AF`t^<0w4I@Kv`|eV)BPJ2DxZtqLLLWZ0?JlytL7RkDm{C|
zqNfa?{KC9(@&a*fg}vucu)gBC*YKyQ{;lcqUUk~%8QRN62<Sso#1A8?LXWd-XYMJ@
zuMdr96^WlDH(c7_e4xYhqpWaVcI=-yAnSVXIY7kmM<`CEK46^qP<l?w<n1p(*Kc~y
zUA9HZzG=^MPrNWyXT>dV=FXgAfPVi9a>cEg1BVPlom@rb?<D#bFj%=a>u!+o20GL}
zrv%324Sj^;HurFp;aH+v`gpaXV6cmCeW<Q~3&!njv$9Jnt3L}mC?Dlwx_6)!rb9Zu
zP&|RLC#UaC;;O1o)QLlfeA8I6QaZ!rc6dlGh+KHsd-!nXt+8e?;>!v=#llBxf@1y%
z6m)Zh@72%93yB}tDY>6KG7#@oWqEW-d8hE;s$kcXfvPj67vXJ|1yf!2jvN-#w_={$
z=w4c&=tgqkd9sO8c*g*QBkSjHYw(*R`8Kt+;|2;t0uCp(pbH=O<DPU~{Bwiz_>z^?
zl{|^~504ijmyw~xVV;FtaLC{mNkt#XqH+!S99lEiq`$c$;t#~tA9r*etzY+ss#K00
z_TF?p`(){hF?X%bJ`rA{qO}IzUxLoD?0apC?b>vvb+rd@VUevTrDzP_aJz-QVV(hT
zm_wdN-5heUScow`a%HOI_7UXIzFbX#?BSbTSQKYX`w7|>NU<@0jVSij+YQFXYB8rM
zXZ1njS{>$NNrhWN@5oy@Ei59ena_Ee6G+7nemXE(mi{XW_AARa(1_}TAnDli0x?5&
zaSsXG<!=Q>k{;sMEpbm5?^LJf-%YagGnE^AohZWl!Y-Sm^^1i`LVMyN)|p&Vqk{_>
z!v|S`tRzlbPI#U0+s><~zF#iy<1NKMw9HE6L-ZV0!7<8%NB*<Rex81CqeP+JDdP$h
z0f~2;Z)Wwj(c29RDmmb>>3BdAXbQ{|E1dhYZ*^t)o&4v1z&nuTP<`YooXgCcTn1<{
z@|cfxFV^61mk{FWRfjS#tN2~I{IvF=X~7OJYEVy;_<N~yY=G>t6N3I{p8A&&r=0Td
znR{;GnCON8K;dQ@uJFMzr&pLI|CtO-Vv#3X6SCqGm;d5(e9I?nen@Li9?NnS)aSt)
zWK)jwg{fZFXy>x9Q~m6l^{LZdv%nXY`=zH!6uN@%0PFzI{IAK$G52K+F!y(}+2DHi
z#{sZn-|sn*0-w$Qk*E2mS9H9bpPHUG=(qB@+~?@Rr6lYi!NdM4c<ZsWH1n|SECo(1
z*hv&l10Srgg;q+eJAx<g#`iPW3Q#>{AfWkx#|F@8y?xkr%L2|VXB{qsijtT_PatWy
zKV~Fy0biW}j|QM$;eE}bAaT4#{%pV4rvM93i>F$*7&}1x`1QT6nKZ)O-D>+3^Zjrl
z>=Hz;@`O~#YsPTQQV{0n6sJn21TR2d{vG)Izc~tZZJh(K7$PF=fVAI6x~OweamZ2g
z@qQLUL|O48<s3OZADt-%qQxV=*<a&N|5nRd?{MRFuLu8MZ%CkC;TzPDU)XsM#?asq
z1#6Yybok@C5o`Xt_Jtr@_Dtd~Lr!Fm*+CK<vE=pgtdB!~<BW`GYQPPUPk*hGFKqo!
zX*01s;ieOU-@0!vQ0S5~o-YR63sI&PM?&(l%4TZx)C2T+nLk|Z`^M(m!7LN%{x!bT
zL25n5Hdb@rnxf*5Z-G9a;rY<CfgU*<BmPxmdx!*6Sn9l0;po%L8~hKO4MgVG8qi|R
zKP!v98;o&fxevlfJhG9$@9ymopKX53K2!y-<`NEo;dYyi44A82t(^8o>n`$rlFs!F
zpKAJD&nBk}ce);@jSabP^6+a0YYsbFR8<9fDlw~vXz3S~%P!yZyCSz-fbabcK_*PP
z|JkS(kR=GJrvRh&oew7A{M6)}S_gG2m=@KiEuhd)catDeNS!4E`@s0;3pw-pZu|qh
z4aCYgu?d%`ja&WHnPu1RuGjWcrTi|Lct9a-e6)#UoW<<Wwx4CatTj2aB(qW1rj8*&
z&D^}qcw@{NOYYuk?4VUG`)Xg}s{a{BI8kV0iCkEhHN2CDlQ;)-lSzq}5KCR}&;c=f
zK}5p|GQ(-t=Ih^8p*vdD2iC8$*U;>t`^i=GA~0;kCi}Qdv5}$Z%?s;Y5L!CO20S^Q
z*Kar129^j=*6?zN>Rqw2qe~H+4d5*#W@Z(3hqq{zo#ZtwR~kw08<E23*y5breORYE
zPkB0H+qc=i2TSK>9j7MuXZJUG8hIS1<i1JuWP59BjGj$kBj>(Yq{_R59htvX@LiGk
z{*!MYa?t}Amgeu}{LS0qbhFKCyW3upkoxbmd?7!K(4VG^MpWD^PK=m7(3Z*(Hc3!D
znN;7w!$|5Io=H%06h{k;R(P<7FL**4seqk?uk*S5J1zfo9D?b;{sw-lX8*wPIo)?E
zLuL&5B@qg7?fQD(r3+Ou$KyQ6nWw<Dt-f!TYon=mPOOMXm1B=Xs4|NDt}2^X{|s^e
zmw7c4Ts|>{^J3@x|7h>M<C+SzbWtpbh!_zNK_Dt93IZZUsSy<r5h6A82uSa}6BPla
zg^mJ(f`CYg^iJqV?;xEJIs_7GNb_!I=Da&|X3o5G&YgGvdjGJK{1TGv?A5;YeQVuV
zpO5f&kx33Zr4THD|1L9<oX(1OL?7tr?NDO`yRK^~GUT6Sp{PKjETwPO*2nHvrwcN%
zWy@AQkH{0U&#ysFR|A#YtI}`ZM4cTrV@(gXW+(J9&xTH(B%K|X|L&8&Im;Mk5@K$<
ztgEBkH?y*RuDTI8X#fv7I#qi#Kp+e1YR9|o`z%z*XX=Y~^j+vPO|4vE++g<Mhh<}R
z<q*d1v(?L=zh563vK98PU5#EAc2-W(4Ht$(<5aHd>Mb#v`yWd|o9bpx`&f;eRD}Pg
zYpG1p*|=8be0$5Q!iS&xh4qGMK8(>_d3jnktzRNnTF0f%q>$H9UMK5fT^WEHej{D^
z3nung#}lBAS>E8bAf{1@tZUhIYJO`0;x!?`x#>+ta|4_j5um8>p1`1wH~ms0TKTxA
zSZvAZihvt-Bro7MU6s&A7qJw}?}#5i$P8<Jel>c`zRL4CTi~Mm`;LWXcwfWrTktr(
zsxAlaBsch*jt$Wdt=a{Qs^*i-Mpo&b^`wWE^2RlxtW$b)c??&OhK5A(;r|lj{7cX8
z?>ZL27CIun;32O(A?It}3xvui#b9sPhaFiwkVz}%?08`-6;~_rNm?i6t+yYydOyV&
zGI?CcjNA_*GCu}FsvF>rcaVTP4*UQ%JUFuu#OR~!%;0l;sQbBvNU;wNk^ihiSa<|2
z9_Nn@=_gB0>1eA9)lUpY=5eY&1fTVQ=O5Jqu}<hw%wNX|p^t=>C=V2)(c?-c;jL^B
zF9X}L7LP;G0lKWu{d$nRg<^^Ywl)Lj4UDf5X4NNfUi$d{H=Xiu$KkTsG{VE3bi%vQ
z^kfB|+EX)@??oDa@6<uk%f7#eD858H$#VyiM7MAIVhuB&Z%$gz8Z&i1vRJ8Ittld!
zVUz`P_=*PCss5t!a~jK#FbYS$4^lS_XnJ4Zy0yh8yD6dHw_yZ+*zz^bFFtl3%Nwu6
z-Wk!Z)21rDn$&3%x0$>*yS2H3diTjIt-|Pf$sVnIolR5I)L6;ZR&oSaanr(<n{<;?
zV28aY-sxu}v3ubr015?@jdG$9{`S1t%<oOB!s*Vo>>5C^a9dbAx<t4xosYNy(6rXv
z@J7b7NpcGY#-cm1zv%?Yf(<LtDPQ2ASJ5N3Z2^Gj?2XFDB>%xru!B_K;%H#oYyS6{
z%%9uUNERYT3u&}t%5Y{=^1NH}nCN0p?l|9@pwHt_C41$1!wbu~H!@<Q0^|h=OZjZ$
zADgTffHL!4fJv@s&eb|afDDS>RTxEK(A-3Sqbf3&aeZ{=Io|etxsM4XM|tQ#%33~O
zYdY6Jos#q72A2be{v{aS1p#t_H28H<f58BX;$!fePQrtXEj@BeL+G|X|2M)ryv7KX
zA%;?NLExi_9W97^A^T1F2BPY+da@t>mA^8t8zsBIo0e>wOHAq7Xz>enxv&?s)K9*E
zOhCGaYjv+&?^Vo036B?elZ)y)xZBSMRJ~n8%V&J8Aa7Ct(A+^IuDwKgeYHif%kA|3
zsZXZ9tN&Uu>u^Pl=t;58YPfQXB|Cp+W0h`CGhW<GDrf}YwfB|LnZesewk$`eRVzdd
z<XEq>onG;rKGgbVmpbPoV)#$Ia6z$6J82b>ZFk{vUSMV5;9fgKX0BjFCv$sb=We*d
zIJ4lWUU_Ofv{WxVC{`6Bn|>?DXbx`Y6~vaIpj(ek<_#vIuYgue0ZFI_5wZDot#sP3
z>c#fy-*mc>7E|L@Yer?7m+rTBuKOB5nMS%+bwjwe)4j^lw3i~iqEfwwHgc$(OT2sy
z@$IDENG|0Jm%MY2RIj~`jE!@Rq3bC0D-jvd?Q;=JF%<m5t7I|Ib=P3tUaxg5A1A0=
zK2xomSr7+9{1K|E)cqyY{`HZ4_a1KI3&T*I^n(8I2dlVtz5R2w!#lrz(|rmQH#H&a
z*q+cMUM(`ar)Ifi(t#^(#{zf;2kHyvnMJepCBIMHaY1p12<><t=%m?l9a>mD<5dcV
z0BZV8$84uTUb?8}e5?QZ!i{Ut>RTD@wc&WsFMmBUyd_Xu)w}zbol=4y|GTdUY}fww
zei)0HLT<`<W`&m5o*$|y`E4HVrn0Fbfa!#L(EkMi`A3dcKBZc<gA}nmyD=HWL1OQx
z(te)Y)TNK%Z@fZVUZlA;70R4Gd0ts@UC=5uLetAqF`Iv}sFv3mAGR>|5jz()iHxu+
z=6bk>5}Y+kMap*TsFN!ljo&oPL|FvL5DE`F;9;|Tq4IZEnv;6w%-@hM4@(rZI+<5J
zo_YnVCeM!UTDKbYYGYL1)2;<5{CGds(t2FnL6ICQzHRJBi6o?u&={}e9Eu>3FE^+3
zN@-|wH_k7i!AQ&iyb=@hIsT1n<0`$|P(ChmN&Z@9{Qkxf_)&C|R#TfscwH_(W_+f^
z-*Ys(u>X_Xy?HYHIPKRYM_9r3w)4;p1Fi*J@RQAh%?|!!)8ke4a|9Qfy#6W^dFDjZ
zRZk|`n#gDDAxnlyL=tK1RD(ZZu63Ik2&n3)R{0B?>xPzvKWvOT;~-MH6_$*l&l@=!
z`(&3J5~v>>HpemQIo0f|Bcl6jOC#k%^^rMh$!<JBFF@T<4R7D5oXS0Wl(!=i7k>nQ
zlq;os>!!J#KyT+I0DJ7C%t@ejgH!-?j(s`+xFrAms47dJ{8mFqsD!Vlqtk(`kqz<W
zPTx$Tik`));M(vfgPV#b^>Kpd6Be`By?TY-f2n+<x^?}DS(KVwbd#=*o2tNP)SWuQ
zMKpnH%Tb_lS2f2cNJ?y$_&OmpnVYSGr=J{HU)3#KhB!}weiEhVGPg%yBwrj%-Z77#
zJ@(W8jWpBr722ze=OyJ8C1v45eWwd?nCG!=Tp>D|19UQH_6t>nXNU6-+aX_p3@8qD
zuQD)i{;=$O;5r0Q^3tyi3pLGh3<d~%75SJsdD^^hjo+e1HKVrH(;Pw7XD?S`U((H&
z8Fv4+HH%9VPy4Rg<%9#AlR*r72gPATBN>lugN1wj7+Q$}WyvHk?3$T`_^RM+y&Qv1
zZrGgTT2S)|qyDCQh)|MTTPzD~uy~ldaUa!oY2kXeGPE<@mCRt<<S3_`e`jg2vf|NN
zne08<TXbTeyeTW0W%9Jbh1u!YUE}qgiom4%2|y&Mh2^#D)>nAHOSVd$j-#G+Bko{6
z1648VgY5CYjwpY*pT913(J(P<((Yo6$pc_MfOL#ZM&oGst#+W5w0=uT)gV9XZG5A*
zpInste3TdV3ICRqc>JGa8!D8cnPJD;A(Irk0OGb`we3zr*h~b=XZfcEbnZz@&J4-q
z=czpJQa;UhC45f-jq_;j$mq94%$p!^i~X`>$b@}JvOp36&`A3srV8213e}*aju*Gp
z>)&jhTH_bF6nK9%@cXE14XUO0`qq@@fQU$d?6-^~#}`wY=sD!pkAsEp2qyqSgp0oO
z@EkATD5ND-C4gXWfgVQP8HL=Z6;-ytw6@!22odBqIwsJokXh_b3C(7`ArLm>EM8w^
z-~M)PdTo{`GGlKdpgYnlL>lt3T_Ldt9^g*&w8%HoH(B>~DcFd2JJ339?z|<=(nLDW
z;3kA<^423Alz;aL=S<QM7XF0(e&txS;-b@ZVQ_G-`@#-Ik4x-eZ(66K#%=?(zwENC
zpQ8Wk5u@@`)6t2ExoN}hZPV?7=;8;uXFk)NqT|W4$*e|x{!clfP#d5Tf^!oynkr4f
zyu2epKa)*etDx7U<$81EK%X>Z($mX_0wkToVWwA7wFt4rm4jQ3YE!=&Sv~7Q624hP
zO-$7i-=WM6g!SjMq7oLegeLB7%gRb5R?2f)mh**1-_Q!zs!!ba@|x_(1gsXD{vQU+
z>D`Mi!{ieMOora|Pf2XNqdT<u1zItZ&`bC(qaBH@@g|2{_p}N~B%fZt0bwO3tM+qT
z)HJrBRae8Q`EbMWc6bSr0<>{#{HeEso;z*}i_x&59kfTNQv1!i2RTVD>!OvH(9LsS
zR+gaD^qGH2d-(Sr{^g?l2ajhREt-Qaj(J`x=doxpl*;ly&&1O<8mZOwiu)C3LhKt=
z_Uvy42J2Gd`s){CObs=%ufOqWjs2PX%~FnK)6TDjaQNOK06agV-C6^rqbfftZM{}b
zDX+ehpLnOapJ#VVcGI3i>uVO<R3K!Y_a4eepebFDh|3{DmGRN9ZNCz&Sn}*q_Bk!!
z3~}VNk+d$SaljJv<V)Vftx1j4TwAUH!=U)wN!tTg>+Z_(5c8<Js`qv2&c;Ep#-fcN
zX1Gl{qoa|@Nr0NBU6KD?_ACp3T0u|~3>ZzdzV|d-vjpv)4>sv~8kacYu^$MZ^Y_&U
z^6ruO|9#D%WC@UHNgfz1wK?M)2B@BNA64vX202RL{YyQ(_cYT3U6ee{ToT2!TtmC{
zX5Wk8_Gob<v!T46OE!Bmdup{-Xk>u9874GLqp~ttZ@h?DI)tlEdPH5OE%+7h-S1<z
z^no>wAJ(**-X^|wy_j7n+G}r>Hfh^3$dLtkR=g#Pl|;>hPpr+d8x&32ddfR(FV~N3
z1=;2}%_BSm+5FC~u#b*gJ~NS%Fu5&Y!c9V7rxa7*CK56N??O)3_ypB<=kJ&#FOUv^
z?^GB6>Mv!5P%FYwwGI_*^AX^|eQ(SlZUTh*lJQE|+n^}`e`wD7(Glpx{hMy?WB%%W
zO}KOm;yriO_MtE7GNk0J0<5uDm_V!eGlX$RNR-xXT5qaLz5&4fXINW^H0l@vf5UL!
zu;ty%t^<?^JSqF`kBr8!Ov)dJdFk(BZ9?vO@@VT1)M<X3?0RYS=0G=P67O_5vG37|
zIleUW+PPN^w+QWd1ap7Ua~obHleu>%K1LqUJRmj7o=2*i-*v!#B-p}X6PS_mxLW3G
zuT)|o+i7RVR|+=VATbc=b)z)%t5Ys?-!o3p=xxB~JUhm<b!taF`4~g*B}qnIV?GT3
z*4cT2Qy?eMexCy4eEF-O#yt@-S9O1)eVrta>lz*M+sNtY8S3P@ZCJ=wuNOU|2LCn3
zJ-kKiZ+81lht95|DI<SS{Gqi)#B=aNoCw2?<hle5h<j748&5N6$H0TUz;KN5T}XYp
z$r5cq_0UOyvztaTMJ}mikRJ%l786}X$?+!071JywpaZ`O^vN3$onb#{yX1Zm+7J<+
z;olN;I+@zN7PiZVa0+mR*3ZMws?nAUT8_f^xo*-%bH|yXTghuz4nRk97@A5lq8Uoa
zRyb^?UV|S>?!lLVBI|88_DtY*@N+fV%6r`SQK4TH8^U&A<8AJ5x<ts+*PE7<ZTxRK
zzHT%|miR4WBZzStc_^pk08BAO67@6AYg4_OqF(xKj?DZ0dB?%#dVCCd9kJsepYWS*
z1xtbaJPO8Ijz<N!ep}T7uBlSOjdY2Fm>*(+pA{B9VHv>Q=t4hdim;=b!VRJdHWqob
zVh0HAOJRAMCZ44=?5o;e<nAto;I`HBYd4OjajoWpV=Y5p{N3OtlC|i0UvG*q8F(iX
zeAWU`GPx@QwC_>?DPT&UK#WoD5fedV(lIbu-Y<&1bHC@r9FVESqlp3>rTGAJ?)B0f
zzSct$cr^yh^JoM8$Q3z;B$@`X!1pI%;a`5!A(Ru$>y^V5%9HBxJHW~RO-I(_PDEz_
zC*%$A&Y~G%-Lwi5E3gUa85T^$f$?bCMN!gB&@%XNuNx>u%Qi-AvNkx4W`UrIH~&qy
z<RER2xJyRQr(1wKw%<A*2ABp@H!jCgu=y+$H{zd~uU#*gx@rmT6&hF!y#*P2jHK-Z
z>n;xMO+dzM$B?u=K}0t1xFBL@JrjUWViDvh24Tc99N?0PM<TKJnpf7aCU+2ZJ&+H;
ze>5aoQRSR7L5D>N2$|JI{B{^%)dpYIkhJ|w@S5%-KJ4vR-~mh^%Wt~bAMb#`Ugo|8
z-PC~}?7?Z1Z$`<eYGBIB4x}ly7Dh!arnfH$MaX`FY2WE)J*CR`@>Ak#9>q(jvW<mp
zx~V2>vXy*cf>_f@!<iiwwkPbG51-wko2L`Pagj6>O4~5myk%KOKe1gjM$|UsPd|b9
z=%0sbfUM>{m;etj9iZ{Fk$d?bPZe$u$we(R`FZC&+3-Uxklh~olKmJjF!>IkPpBUN
z(E%ryw)2bo=Ai(cf2=WdbN}<)gpbBbo8gW{E3aUcO!k3_SQa8L;+G&xhk2`>_F>BF
znGov8b(5_!QxvK*NJ<{qD)8?pS>Gg?x=j?i?58%~6&8Nc+UXXe*U_AgA1bM{UMS>f
zmQfw?OwABhojQB-o|^2zW77hJ;v9RMzK^vjG1&K9DR$McMJeiSk^--u97(>Db^{P3
zRtC6%zJxU9wM>l%l#%y?G)>_1HKj$N94QK8`AcCzs7?_S-sH*h2;~vsDXa{?S1H30
ze8^TcdS<g4ed5iJ6Nk_DrV(xS19f7bZF#u{7lu5HZsLTmaSQ&NG%T<1l6mwctxFb9
z7NQ<zUc=~|dj%-N^303-3Us;Dl2RtTcjMP7Bo9^k09YBa^v%+nHBu#j|37U4>d0gN
zVFVXD<~LnMoia4|2LJ{n8J3+zY`<sNN4cQ*sYSS;LA<D5!dYsHzb#_tZZ56Ybo(qc
z{(cK&yDf05LrM$|f+&Ma_%ore4IhGzEakhvWXcL@yl^}$sExxMJ5Rw|-<Z-%k@K_U
zLr_!d+oJ_?JJZZzhl{jBm!?__X7x`DIlcD3BlLea${Hm?nCpO_B&xK=`}p~k2Wo2u
zzh4+GOoHCT-oO4)*~Pcr)#StNQvy8N6PVA7hr^X_f;v(6chx6&vy|K*XBDmz5eqj`
zJp(^8wHm2D*6#2GC9Sqvb6)_>+ZPoS-?yu>D@wGf>U8?>@T;B5pV4ud;f(-%_n#E^
ze=YYqfrW&^*ANwnBf(oy&N>d{lNsQlh8|QT+Dep|8Z=Zn`QfOMW84TmXAYQQ$HwL)
zxd?LTI${enk8h&d(w$(1w-k1Oei*Dd9Z==}`;zeQy=_g5*DuD?UL%U^+>Z3Tq_*XH
z=j<Zq{o)7CEr)L2Z|j_J@<p_j1b7pKS^%H=LUwP;t!DgP@j%n%pygA5egywyBPyr<
z)t|XqX8;E|fmLa6WOz>4s=wIl-Zl=NypXrSTp{Ls{y=9DQ6D|J&i+Xf;kz#@R-$Pa
z=@pue$|vvbJpoSGz`~iEpJPs`Hhw-{1(2<`c+Ty}pLksA=-fK~hzf=R?lT`emxzAN
zVCqLcr>szom4~+(ex-2|oh;m09Y!R_O~ww=^TD?KBv(oYbRK%jmY1a@_V(N4d*cFu
zOVk$U^d(YUkH2*#wBts-kD2X@h41F0iw9wF120oJ>yBaiTboB`69{LvzaoG~jL^b8
zh*Li2Y&^{t(43|s<qI${AC}77ig2Ts7o%?FP6@~_S(^GJw<P(!8s6Hc3eMuwn0%f2
z48&<`(uJBoe-=HnbWrjYOl&YTxIQ6Vxaz(jsGEOXFheAK_Fpg=&c6SIB((<k4fo~Z
z?c2PXyxE6eegOG&0BKnX%vrbG{$@Fk;5IaasyhM#2r)HXI=|^;)|z0Xh8v%pm*Noa
z)$Dxz47@9S@E<{+!H)^b3D7&!O)d=N^)AGoJ}NsOoAImRzy!Q7TZkc}Vv8IsBT-bz
zaHac{x-K$TLl*L;|Lv`>NyD0P<T%Rk{gO_1vp5{E*F!15b@lJUjsiv(=FUoeBxu74
zDlKynrrZPN{_i;@nRqnx2eX`*KxtAsF`yaj$oNosvriVFo^L_0+LhX+jECU1M6Dcm
zdg8lTW&J)yR!eRzN+;f?H>fGx=`_f`)G4oB8d;EXG`-R~<Z0HGY_ty#Uw1{9{HAMl
zbZ+1A3GILfLz8wje0CAm=as5Y)=+-UW1UZ01P|3$6bD?zK+h3X)MdOw_aYpnCQ{uC
z9>n3+d))M?s)gT|`o#1d^zM58_^}vVp4=&_6u4Qz%ayh^y!36W8SpN5rvH*9|E;6Y
zy*9&FLjj`S*9%;3Z{}1944Yr1C1#ttlAqbl0SMs90M$DV@@+MfS7?VR>u(Wrw>$7f
z)3wa|1(t$LI91X5Uwvgqx4KMXG4LPRuanznuZ&798m)Do3OpMJ*w&<SLmleVZ#uI;
zp-mdYxMz~_<r&2n45Q|e=MmCIJE%;dRi70W+-}#{q!io@Msaep{IS%c(gS?lBi6dV
z^`ZZ}$Ax|>NXin2+W{S#x=rik^pDYi2RhWLn;#q_Nxso^2hHiB_1Xp_4ts&ucJ)SX
z=-=L)_g#tE(|N86i9tzH(>*qNmAhfY<ih5`^#<W8^5Z9zRDZT3M=Tf*PUZV1v}T}l
zm=cEgxz!xBezz4;3S=;>Q(L2?U;9r6`JybMbXgvp`F@9vCq$S{FZZ;jl6$%gAqk0L
zI+^<1_eO1%W0IHDMuUIy<~Ovl`#_LxAs4$)uXYYfV30#2VZHO=8C)t?UvBQ|<V#Xg
zo-ccL8dHs`rGp@HJ&<m3{6k-WI>C&`(Gc4*d-h65>}#V!?cwM=M#@hTrP9NhVM9T5
zWS#(S^;Be2U$&)zm1pQHv($lE{`@37gd6mX?k3>l=8u_X=BWtNShe#hQ|%B8Kntud
zSqtpjm+=vOGn6;yQ7?;@Pu5t84eD<YOQMz|Pp`{pBxXUsNR3pMM8!&-5?tJ};s@ph
z$ZZu|Mnufs7z?<EEi|8;Y@Smc$`sRwa%<eUt9s+-uedf<rd{rvE9|{N1B~B%KnsCm
z=&wQR;PY!GEmygjdusVRs*b?x_VxICEuG*4&(xMCJ^4ol755^Ikh2wBcLMLQAEVf>
z7hei!NZ|W067E{CHsRb2<Xu7m{eFeqJd)hTL*+0gUj*bRpzlN@gjquLJcVUU&LHph
zuDwR3c$15jb4)uUT_mQGU7DY@-);{+0c+)`>2Ila*v|3Icvd4tkmb&}`OT8^p!38O
z`?4t~fw~e*<6NIR=LtEt{=P_crO8eXmB6Tc&dohWm5(mC&2MFM3Ue8#4t?mN^iEaQ
zkBBgLH)EN(aA&@^6ayHkHG3}0)9+2@3gtq1IvPophltuG=foCi&x>5BO7FUDW<OtF
z{k`>@ndtipa{tw3Osv&~;8DP85k<GTnu=t712qp#_FqTH0pCIZbRVCT-0{Zsf0nF#
z=K*4Wkge3iY%L^u*;HyaZ2eIsl>k?vh!c(z^D(rr1-hp6gT8yoJSRV!D-!RU5n;2g
zP_mQ3>mHc?j@lSxWt-QE>Cp50&~D8Upj%u02IR8;6K%)8N@9+>4_3$N(QnJZAU@2t
zGw)g>r0D{V^WcW!pRY4mP6)$YcfW^(*yKab7(6i$o}E*BSodmc>Z@~OH3PMa%uC<g
zUg5}9O0*TYx1$G-c(%JMy))oyR1X3S&uZrUDlm>k+F`B2D8k)WAWvK@#+r7#3vvd4
zMEYhgs{tab0scGf#qC*{-y@G5ok?o2;0gDsQ-AijGA)%n(>MA2z(v#KJOFKV>Hp)&
zhvK(cBU@5n8+EgrzOYPPVn__bqIkRG7oGZvr&~XFP|>^U3-t&f=U|jL;zU%u<fs|`
z(i8>_DN&TKtU3ew*5S7wVPjTN89h5I8Gb2--zMu{=Bs^XUxJtJf9k81swTknLa=oN
z39<)q5iHq|!8vt-?9`5p26fqw*$ev31_Cv0=_P80F#Q1_wqu>!np$Mje(4b|6{n)}
znEvC3c{-Um`yNkGwv7h)hSW#Iz*}WQS?)Z)>E3+|(p*o%5~rv|!4>x<SIzEdw^oeB
z8g*{gBOaFrvLu0-1$)agjVeoMwNAaxmwmR><h5xm2u1^D=hmIGA9QHTy@-{sILZ}-
zx3rwc&z^=;cy2%C&$Md<`VISZfhzdy+*1X8;73k!K|R(Sj)uw~Yjf}sYW5Qa6mCD(
zE-tBkIt2LG!^RMAuXQNgEM3f~eAwvn8J(H4H)8!eDL|DCl=YqgQ)}hVo|$o|finFY
zfQWg0>F`fT+v)p%L?wSCM?KMl08-4eU{(sxC^lUF(9ne|q=7*iDNERotfJ(<rG`<S
ziw0c%?xW!=E|uzf5aB66)9)SuWxaut7aGD6FX&H7vzTzRTbjivt}_Q{Vs63bJ8%*t
z&z28m6*W?E;=IgXiDK1|&1EUb77N_JrJJmMz0ESU4^kJ_?SU30`|J=9)vXUJRkCR4
zLS%&vU|xJ9e_yWuS0?n|bo<3A>iLta0P^cuyWCbDQkHzdz4Of1dH=K*uugD^UcBc5
zz@s8%MDAbTRS)m><%^ARvcAo+cNa`Nje0^Y4=|NL9iQ~knlv`vxVxQp;%8;#o1l+@
z=;wtd;LT4MJ`D10MY1=GL;V;WH?-)+@`?qN(|CD(x#3V0K4E;%h;1+Z>W&IU@DKrv
z0YQqOwh6IePwc2r<3B_(<Ud6e6Y6Y$%uH__8gev$610xqXpP?<c^OF=BL%2<6mA+_
zRw+8YZJO^cCsi>tJ^eKH(FKm!X^ifJPJYrcQz)L7u}-_lCwO5ji#6X~D^;G8|I(ec
zK`D+C6$kY1_Bpo=bjAj@k9dAbZXOkbHgPn8${F;}eS0P~dnP9T%lEaI>}`^6S}2A*
zet!Jh0o^fOIn^RtQ|_S~qvff;3UF7!;??W^fJylu>$M;rwv(*iE`-ixB|jhC>YL)Z
z`^zcC3)g{1<%0vPv(0?$o4C@;3zQbn?}n6ozbSj`uW6=Du3^^(7uS-cSH|g(aM0`U
zocsm&Z5f0_U1qI!{Ge|=z1rF8z;bUJ+TA^>X?O3cb(`4&IJ`u-ubgKrc)lkz49Z-x
zp~;h?rLbsSG&sIvw}+GJ>Q^rgZEl_vGSX+`*L?g%mu{0TpG{A{&Y_s`p->W&O<{6I
z>eeh;_$=YlN8P8l4252z3*mpz^s49=f5UwKLz#z4K|5~Krxprm5PH+3<9Z@w7qVyu
zVm%Il!57eYu{HS9G4J<#Mqm~nKcG!DlC>)=`q}0>Por5R@}W%dI=w&VIs4oBU?^J!
z6fUuc2%WW75PXADZNwm~`Y(en2Z;PgUoashrO_vDL3<47CReCSlkOX}L-isJLO|ac
z9>7an^2I>Ut1aozKo6MO<*rEgh*K5JI#-L-1M^Ig9G04m7SpRhR7Rm0hWc~6cZ!pa
z*XBPRA|^!w&f>_T4EXy$vXJW*PvZI7AG(@xs*T5!>fi?z1Ux>sWqDxJdgA-W>(A=B
z%h8}CJKDraz<2q?4%P1TG!$7x<c4I|eFCzoxRI`M{lT0Sk+6{Up<Y7&LF|(&A|#dc
zYs#F>`ps^=IP@|fHIEKeVHSS>>Ju}i==&pr*COfZUeL)4H9;&O$9X_a!^8#}PvztQ
zlXI0@QkM?|FLhMk`~?++%EZbA3RZoacLCtZ&($0#7}03SJzg~XI)fI1tsMBV8}9EN
z{|8$p$HSKtgnU+>5q;;UGFa?1%gFjljt-IRMK>I951@)o{JXCho8-WB_(PmU;L6XG
zmEif0oM8zLP6nJRU(Q{2J){px+_tO}|G4aN9nJ(zxi#fcL@65Gbk}Vg%9do5H(1Xo
z6ZztsXJ`vPTV{|V4{b~4eY_)J1mxRA{17}inW0Euw;tAZqwO=%AK%q{8K=>8veFhr
z@w1KnHhDHu=EsSxXgBGV;NAV?)^~DnLax@RCyy)TmhE@?VPU5g=$xU!t-eNOy&JLB
z)&flNec~B~0oO70mzyUg{Pf;iC5>%#vvmKQnV8BK+lO?O7$6QD_};f`J86%x*k)Uf
zK~X`vOI}IH)eSXJ$Xi?0JPnzugLs;=l4bWsP(QfQl)eN%U20cZdDouzYAt8o$d>X;
z=Y!{n<NhGURWX2S>RT15Zmh1Nm0wFMGl^SGdbg9W_sMp*cLr$x>T~{GRq4O69l-Z#
z6M#79Tz1wY?2O3S8Qb-%Bf2W0r-BR=zH5L={e->1CF8A{Sj6!gpT0qBjRr?wR80rj
zX0`Jr&s}*zjyz=FxR*3`nB;CS(;RQqe_7?W)7_$iJBmC_ry6b$c%n<m3IWbx&xex?
zJU(9PbdGNu%>t)igv^>|JTHt^3JQsTDyNvJcIz7emuT#KozoqIjH@ATEt#`6kL!*%
z?;%#GLAg^SdfuU)g|e-F^hwoUjfLByHXrI6`|)-R1jneDpDyI0&|DIw@2eXWa>+j)
zh5@t=oj>;Ze{7kB-{&T6{T%zUfuX1eNyQSwPgmY5aq`oSHwYFZwW*(j<jZz%53ZeQ
zO0%ZP7g)%N_={W9NN#>-a6q0d`X1`<fo2YX2&uhiFISF;+m6vX7F~7UT;40X6;>G3
z2S3M(*?t`>$_K~Qt2mH?y&oZyt^}TEB__#>!M`jO8{bRlzLS^j*EKS(%UePX+S=T)
zhZMndl3RGF{=D(F&h*&@QWb;zcOFJ?YkqFdeEkaW&+OOPU@L_cTm65!bPxU-M)`lc
z9}q?MVpgNEf<c^I@XeN7bWH9RV_nNK%XVc~KL#$-BoU*!{CLXfq%}K96(H-JwlTer
zA0aWk6AmC71ikdUAIC^1`!Wh05(+Io`Q|h~I89E4d}IBIZk_DHl-eu(Ej6-NgbglK
zeF`}*bYOZO%Uux)Kg%m<92YXy*K4<(Iot=V8^W05ecmm|*K-t+WF`7jE+v`ws0!ps
zk~s0Fc$7iGrWYf0Z4DRoZ&6pTzPa$szCV*49O9eY44%l<z|%5QI-*3cjET(0nobVQ
zxm0N7UQPRPO2c(${@gilYvh;w7HpqDvsG*;2jlk5+G>x<F%!Ra$0T4~l2f+&AL{T?
z@djW-|Jb%Uz&CQyzy<-zcpZ{l+f{Ugxb5L>$mmlBIsl`ZIZg3<ZPLa*__j^ASue^@
zWGJHMr3OnL2d6`SG{OqVnJed*>nuEhwn@7YPGYU-+2dyjZ2QXnK19{@%e~c^yU<^w
z7;rhHnRS6GR%d{jdf`b1;sD}|=)E7Whi8>|WMexH?O6}BiS3f79VsUk@(bXta`kuD
zwQ1EVPxLde;Aa15nb#TBeRz-3P4GcGqoF<VhY5IBRCL&6SZ-QU)yyu?G-u9|7B-}#
zsT368_vLTN2>#y30dm)4ie@Fz6Z42C?H!=PWRGj-3toy2wc?GK8kzTC;DNM(d2HrD
zb+;61^M7)NYK=`8f!syzE75X)EH^wS+G3zA0e-|(&jmQE>Xjk01j)_(#OGNF6%oV8
zpD)v&^#5|{Q+-;JWPuz8L1EMtN<KPcW?bW})eX&ZF8F1NTwm#dD$&w4e?51>`u*Ut
zQeuXN0nIAi;nO&C`e*L>Lx&6uC#m8~aal!i$(yde(>UDcD2wo$<7eJw(H;ABOdA%P
zVXf;P`LdW@!br)>gyZNa72`r^8Ga7G10<pCGXHqU``4w*XZtVOSMYM;XK3i}ve!RF
z3QN=~>%Sg2wyr^UC^<hi#~CDIufSVJD0)55%um!CsTGHcb52T-H&1)^$;P~O@tYqn
z3b4h`tVA?$*f)TOf08YGtL_|k;T%kCUa5GBC7@ygt^#vJpA2U_B_?8=Ii`rwj0Ogd
z4VpLmFX;&?^2mdXcj1U;Und6E;5@yr^4UuK)s8(Q!ZpVDnYCVTr;b!)zSf0sjY02m
z=k^{l69y9P0bHY|%#{T8x1vr4DMAt6j_sT<PUA!FHy{@kjl?n7M_Mn*328QeD|>(f
z$zRp;_8xkgL`n<EdBLuu`t#DsoAWPSN5*qtKbQAx20L_f6(vv3#LxKJ%+409H+N}e
zbKLU+T$69dgMYMEh5=f!a*n3=S?P#(3QUzRV=woQ6kfSxY1Ua4d5-!EbXae{enx1#
z(>+ZY8m=D>>MV-#LX3r8ij)&OzZ45Vt);N`p8;@tP)MDoTdYs$^{JCvE}{t_>Lmuv
zxo=wxb+B%5nRDY*l)^fkn*ynf6T5tL=yh=d#B?G<>b!Kjub_-4w~GvXVi?<tet%)E
zdG>B~^qkS9=&}7DdA_TK6ECTkH=0P#R`^=5_-)B9cFX~03{><9Ej*U$iXn(+i<-fM
zkkxzaY=6cN0o{s!Zm}*vg>MC2vI$}Uobf@u+to_sJFMx;kK}9THW3=CjVDK)->1t1
z{sn*xKnkd$X`FCkMa83!PTZiH;G_7)Z8+al3$}k!e1S7b%h99OBGgH}A%jt#;c)Rj
zshB6hb>A4$g5*sX<q)+F3u_Y??@~aFp&o^?M;w?gvM(PfI)VVvhE4zbWdk)s+oU<)
zP(vPt>GWXokd#7!iY0eo;`}!A8t(=CQcm!f$q0WToyn|x>8(xwV!3!-$}tQxsEPM-
zu;PH@V=02$)^w-%p||`mTH3K!bcLkoYYQM82e$&3+y_5DWk~)mrQXO9bElzwH?=N(
z^G_BY{6Ch3|1&v*(2D3J>p>9Gz?Y&uujVs968*AfIQdL6L!J*=h!h>Q=|{b+<o8k8
zHN4C9Oaqr*AWXSdlInYDyrsEL+6tMVa4KlvUJCabM)duu#WtoRvGogiyM;gRPu!P_
zk#QooH25LE7i<9>CiB{|bfE~}7&*6AOzg<smFUx`JH#nG>;W<2#9T|M8sWGIU;X1F
z%MPVPm06xjPu_X+25)>v1dX3^jKDeIS<5Lf^s)Q$t+Wp}jCc7jAQ(xA#$<Vg<_cIc
zL4ud>cDbDLPR<^*Pn2YWtKG#K7BTPWjmd+LGMqGx5iOASyzIo_9BQs2`V@wZb2F#8
zA2jNZJP1{(_hQHEr%5^p!=9EIzpR8R`^BVLRcCI!3BOrz=I_TPzLTPG>7Ohl559N;
zd5xf{L5|D2h;`L@?MUNKN%MQRVIKk<h}}S2HB1U=lPxJ6IDF@q@^8BJ-N9_WEmWoU
zRJ2NBfF<?o*D7B*2!6u2G~-seUgVa!PwQ!A#QbCH0S`&-`HoFOp1rs20`k41TWlB2
zWq8s3AmWYhjJW4>MC~Cmu%5PYtcC3ko1Uy}GQZ3tT=&xO?zTlweq^G7zuev0?LqF`
z*Ax~k3K=AfxIj!g@bQQtTh?1PhcHmpYdo+!JQ`4jO;H9PYbAi1bt>$$euuT?X$&mM
zYpchvly`9~F(kV%Btc3~YGBIf!Ru?G{6Mt%Oy@$cZmJO2>RGCn*XE{)Y@sjN2e5OI
zFl7!#F0T5Qhku%weLVlPbNFYS%767b16~n)U&ul)mpWgoj04Akn|q037kFFfoNj&7
zsq)qQTs@DRT=lZCUYmgwEj{ZFKmZX$N33lmWl;Fh=bTZ_xWZpQBTghXRFE7yK0szx
zsOkIVctG2nGLto=z-Lg)CVMW|`6AB~>|rrz1V!D2Yr{TKw1~3vXmD2lH-o@19loUz
zVLDZS-REF&4l=tk5Kc~muwmQ<?U~cHS1Q84dZg@cQ%%Hs)6aOo6*#9lH@$**$0ZQw
z*J9WGc(d)lO>`bwzIo815XJ*4Uet>UFhBt;=}J6OJKhK%wLgPPaT_<Z@@D7Bezn4f
zR@U4w32Q-5rUkPjqxT$GcFL)*sD^x`M2J#BaR8@Q;k|cV-v#$5WpVrP;T>*qc8*RH
zH*_N@I(&t484K)`Y#zobTpqu@&wk=|Yy&^^Fb0!MI9_vx*fnDJJT+HO<gN)<DH*AJ
zR|^(V0~kx`rN12kmAu^@tsSqA&a~>`mG8-wROx8`u@BYCmnX|$5tN72tU5+a@%4%*
z{&c<u<5v}7=TB_knnxZ!f`!=yNfNsWB|GXuk1MK?&%CCtSET0%dGN+{LFK%xnl{V#
zKRTbn5}qIYiqQO8nXorJjA-cYnJ@gH6}*J3BlFEE2nGb<t%FZi7zT8s);D4g{8bqe
zFC&IkeNU|34Sayg0ET?g1`NjrI6XdmT@_~zLG1!+I@~?^5I<D&_C%QSP>*3)w9`1O
z7JR3;^136yNh+Hb2bL9O{Td(ey6BY>n5L(9@yF!U!&>uy-EGf62m7`gnQ_Iq+E~8O
z`RGVEnFyoY%NHXx@Ua(Kck_1d%Z<+;Hi@30C_LE?XEri9v5fx2u+{H+!HspJ+aLRf
z;e`tCuprzg^;O(((h7vHP5AN+=00W1>ZX4QWE-w2|45nqf91I@i1Q6BKA?`v%cFZQ
zLxJwe5~=4%d}So&4nUB)@@HR=OH~)~X?P)HRd<coH4m(&;nUS45J1)~6^PgqLg7SD
zY{agcYR+7c$gr$=G-YpXt8fI*w$u+WCl2EmmL!1Tf)mp-&AB#6{qh$*kckg3Do2vo
z527CV+u8>@98^{eOgCadY=dFSyz_Yb&0DVJPw_gXPgzjBI77G}JkB)tWXTdoud;?H
zUXHaHUJeP~ZdO_l7SJ5Dlz)ljxPxppLlcHgfwhG18t4gE6f=qWPitann+iUvi0vse
z^wXsP1N;dL@*UGp38^7#=Og=^F0+n7>3`|jBoLDi)T_02e4N{gRjI!`ncO~*etzty
z?!xwi*g7^ezT$T_0YiozmWeoc3J=ARKklou6MTqpvLaEG_5fy>khJ!j?m;h1EQ4&-
z!w8JSw{2O-#W7(J@%kkr>A;u&92ybQL0%6Bwy{9gRVv5nBeS(vtPkzLlg8-QoWTQ6
zb^<K}SO(U9fkP8N8|E4fN?dM5=-JJbQ49OTyyrC#^%wJ~XW?Vj>-clN%z3x`o<j1K
zIwV>k<<9X6S(yzE$b-_sCqS>SoF1|{dljI3C`qI3<r%=DZzZn<ZfR45QmIe-5vx2@
zfTDF5umP93{-ca1gYdh?L1SZ2K@${a*Q>Z?J4Hx>Rq-~k14G`ii3|!ZBZ8b|a7(nO
z<>d+|`mKT3;J5)4fFDK0TSUu=;u|tTSOMx6+8z5%i-En`o4@e%p&xdEYo;Lr(0kcd
zQgbL4tzm8FRRo^*)wp4&gSNvrj2XhSi$v;W)cOo*dX#6tN5P0<+R(8Fr%DTLNW$nz
z$tb-JjWC*@iScc<qhj{uAVF%T0;i4H5VKyOl_$`C@e81DN6a~XLmannmq1J)I#TL8
zChJren5A0La~6Cv>cr?{z(>d*suL!Q5Lq>ZZUEwj4YzaOhE89D;MtDQ1QKE*K>YPM
zYj`4T@=W*kC}Q!ae8t_|CVH@Te;tgh<&&k8ylD!;?^mS1l(mR+nC|PS7^S<Z&?;#@
zNs%Nj5%iWs<<#Z(%d>cz)lId}2#{lr#S*XZ?(bKI)bU{8Opp2S2d{H&>t58|ImQP%
z$k@KOpzbsr0Ds#kVw}s!<$RRAtwv**9SD4wZDK#-+-ZYkA|lA*KBAArW_-eZDM~(7
zvi!WdRgkR{fROpM7{gF~sYY?humiSaxB$0_GrtsliSP6~`Qy>_`k4(dv0g%T!Vy82
zyWYz*!g5E&QIKslU-1tRv#SndL!bZIlJWoM>(2Ov#%Hge;2=3B{(|hz(j%6I&TM1)
zTgX`-DJ+-{=WT@5L(npZ<j9~2Te0pM;+&(O)O(l6N)-?=!68(OyYh{M8Ex}2B2g^p
z9OVuJUz3aqmIX3aTO*W3hV!DA0A49D>*=Nc8F*I%HoB5%fS*0<fWH?O4MCd$?eEnG
zV{OQ{6yX<&#rUx(JC#Swk*df}d#mvF90<EMHcw!E>Xz1<iL30oY=Yl(xd917c4qj}
W?SCe5|Nmd}e-4oTe{~LjPy8>xc4q(p

literal 0
HcmV?d00001

diff --git a/exam-2/6aii.jpg b/exam-2/6aii.jpg
new file mode 100644
index 0000000000000000000000000000000000000000..936a1087984108b67140b59b5053c4b8a36dd884
GIT binary patch
literal 10118
zcmeI0drVVT9LImRx1}!wUfKd9NTIx{Oo<57X-0Vn3=BGa!Pu~YZCWvEP=U?CS{O{h
zIHu^>Fbk!Epl+Z8l;Pwx9lFH`_&_j3d2B19hO(liLeDNbH?DteUK5t(p5}LN(w^V%
z{yyh?bG~iS4Rjl3MutU%0fqr!<O|SE2mubxX0ve)dEsz4R@@mpE;($3LjDZG#@3dw
zAqbJ3lf6jnC?N<3R|m&gv!qg~$X@0yb9Q%fmO4)s!N^pu71x@_vvw8}V&{K7P!kY5
zRxIv<V=`b77*1g597xGNIoRU?e-4a=v&k-be1VXhP&*S?7>={Z{z(9Gb_V%5unCT>
z>--=qQFH=VmMr$o+*iVL3qIK_S=m19z94a17GGdz@9>hNho_f(_8dR|R~9aMb#chj
z(6I2=BO+I=Ub8kP_RY9=-hFTV2Gz!-?K@IZ)87AJ=f~MOpX}P5o43E<z`@T8zxc99
zceu3dNO{H4W8YTS)SfzB_g#I<59iMR*m~jOPaRjTUc26TqpQ2OuYcf|Uw_jN-Z6~)
zZXA8^&@^VA<iY@df<<1RfIY)SkX$TsTiD!5E{v5%22QX!uJf&IgQB?!$s(C=CQlr^
zujFJi-)+IlVM*e)c7dI{U$2K@674bBKLg8pF0#MC{^sh288}969!`J)9?i>>YgtS%
zYrtrL(Ey_XMgxon7!5EQU^GBS0}aWIro;WJs!CbZ8kYOl#{zz~2a)Ac#w?}to#GKu
zJ%Y;12ud7bNZp%c>bGRIBe?ytay&{pT$`SZAV`H^*v`k|Syv>-Pa()T-k)z4h9l6N
zR2%%%E!PaK6P&{cnqnJGMSUu*^-YUi)u#&mT&ab19>F=XoG_+UYP8EofF&a6+mx%*
zEZJ&`YgmLpTcb7!?GcE=$LA`Y)NOH!an2qDxs{%IaIcZ+=l{Mw{#Vj{3<&aSFFOsI
z*Oyh4Ua#h-X;1InzPoFe3w~8FviM#A55dK#j*kk|`a-QunO>I%@@We1{+?Bq;56lE
z7XqW3G9jk5zI;6Ue&bLz0)3dqJ33ShbR%ZtaJVIMOM&qaf~9AZQ@Ya$1p5z_PIw|{
z_X(6PYkvU`dEO?ezzr=``6(;L_&w^*4G7xy!dhLP9Oy>nmD~B_2YS2)7g}<6_6^mT
z+z@yyj4($b(5=%16w<9vC!fljk@M^k`c0_#4UBHYmp4ntX4kLi*g9c5dcKpQ2gvZD
zTb@q-GrW%k4X<5O40xp=h%ZJE?1#nCajK`eXI5k>Mpo@8F1=;;7}`V81DMx6oi!bI
zDz5(nN&1J!)EAZyS<Wad*(z48I69C+H&Tn)>VYGJiik$zvQGP{VlZOHvvjM|$)5_l
z>FylU!_^2r`>JyyRXxFL<0Q#-8Ufv)oc5LTrYb>?5ALK}o=!dmxAVpt!~LTOT$fat
z?;<c0TEW%mP!Q7$3H7vpJASGd+PED?n)T`QC!qpYoj6W$!$3*J3vgv`>TzFJPZ0!T
z|BU_9v2VJ$jQvx7F*5c))e#x{XY8M*Ju~+IU$*}_Zkx9(kNRHuu<58u%WJr_89{(S
zeT$V}{g(PN^Y(PF$w8M)2j39K6Z&9HQY8JqA?SWrVDgzgU^KvJfYAUg4dAHj4?}nC
AnE(I)

literal 0
HcmV?d00001

diff --git a/exam-2/6bii.jpg b/exam-2/6bii.jpg
new file mode 100644
index 0000000000000000000000000000000000000000..f16cbd1f229b14e5bc0da4fa23655baa724c5185
GIT binary patch
literal 11182
zcmeHLYfw{16yCfD2n8<$f*_;<Dx!i2m5Ps`7+zBcqe4Wf8MVHsl|lpr!8^W+#jz2Q
zs<jp6Ay%uDRtu$r5k)AXB2q-4H6rp5sRY6!A<5k?pp{XlgZ<I^V>fedZjzI;=R5oD
z{q8;R9(({s2l)8=02&Pd8hQa(54-`3!DKQSEOcP8SbA(DeKr~<hK2@4go&vsVL}jQ
z7Gt?)94m8zupDP;Wn;tR@yxh(4tBN<V{Li113_r$uWUWGvA({sEr;OPzVU#U0ijP{
z#(0-OvjcR3#vo|081PV@EZX1z&jyXoV4^Jb4MrIvhl`^DoyK6$QT_-3@=id%117;T
z9p^ev&rG<AZ5P3rz9adhzWw~%BJ;(S3J15<kvk1WS#T}KSdE`B(Q%TK`+GAy-k<5|
zy+GjO>*pV^WNA>aXj#beH6N{Aw|>LMFv*sv=$Ngsal3Z!`7Cko=Sc@s4yAs1_{h<(
z(lau%PGz6|_RJ4IUby&EUjEMoSFRRcD=Gc8?E0Om->UD{+^el?c-Z);skx=~aa(7X
zvb(3ZPo?f3z(oU$Az0`*1nebT1j0o}%fe(2;G)rEkTD1*Yn-c|={zBORfL({^d0(~
z`N=19iwx}D7AwqGM^=uqaBy!J-#Gwn5ZTCp?fh5B{s#5}R~;~7(9q&B2*3v#=Oo7y
zbZoc=m;;ytm;;ytm;;ytm;?V42U@g(#y}(0cHO3^guwQicPtM~Ot#l%9xx8_Yya4T
zvXJf|TW3LVFoo>o&}xOD;o7M@Is~_4AQ(RZf`^U}?8$f_?l*?uQKnog0MScD)({x_
zUY2#+Kv3o{Qzh{mHmJDNE}43g2LyzdO{#eb1Xn5*E;=^ZwK$xzld6`_WkGPFg9=y(
zLGdE?T0w+NaUtFif_ZZ7p<@v2&A_RQtSYzmHOdX1cz*4<`PkXmKFRuWX?xfCPqU;`
zPHfRD2m_AkN&mTZ@#;!KR;f0IRr+=2^=5iI74v!`Ypz4Exe$W1a;c`DEV-1WJBKKA
zqz;06!7e)P)c7p%nBy~Y#SZcJH^}qUcBS<>WJ^~gMWuCS{8=MYsv{sE169>=lS`V{
zAB$e5iR#c&p`^Tua!)Aeqey3d$72Yras*><IG6K=%_PlR2|-0usZPgl3~J3dx~F!{
zuy~cdPvmNCJ_NFCZCD{kGVPZs!^6$}V;cng!@Rz32=<H8zgWjzJ3OB6izLr<3vXO$
z&)Yb=tIeX>KU31|SnfLKN&b10KnSE7vcFAsLli3xx_Ya-rA@kRqRN3I6eJMsERN7?
zq-JxtC{R7A!1r#r&a|idX8cXX5-MPGau3=s3knn5MjU6P^NqyMc8+ER+V-v&A^83~
zali9&b-<-_uP!b3I0S{-WMxRUrnC&jUFq8Ly69$T2|FPOhu}kzI;mswt||x`DLGY;
zqcp!Ss#bI;aPe^QhIR~Q-WyyxUfyiDc({02F#b_7vD#v_#kVTYg#!x)77Q#HSTOM8
z*(+@e{A~MNB!<6Z!N7v?)(D2o+s|m4m;L<|)O_5h7VVRkQF)>|NqrLpOr>i`%v~pm
za>c+0tukHaJsY(H^JS^Fq2%x4>-n<kivCy?Su_)ZT$v1=@MpK?+^%ruKXqyHMV&!z
zSB5SWg6y<J?P#imf}r8Gail#G>iBk^!dqjlfgn+9ro5G;GeQl{ht$$o)Z2_8o%qjY
zGHDO*pm>VF3eU;iZi5*MQTy_m_A~?{{^OQ``206WrN2ro%VSV+sD~!sL_YOs60h0q
z6-kgzQE|1=;vUB`$x14CmSSt**$Fw@(yRwvd`hXt?LoZ@&0D`oEUD*d_N#@ts3`K(
zgcJdY|77Ugdf<Cet@|SO+wD@J2(gS`c*h`^;T8?SDHrhvLIFVSS8TWjm;;ytm;;yt
KZzTsvSo;@69HWN-

literal 0
HcmV?d00001

diff --git a/exam-2/exam2.md b/exam-2/exam2.md
index 002fe96..19bf608 100644
--- a/exam-2/exam2.md
+++ b/exam-2/exam2.md
@@ -11,10 +11,11 @@ author: |
 ---
 
 \renewcommand{\c}[1]{\textcolor{gray}{#1}}
+\renewcommand{\r}[1]{\textcolor{red}{#1}}
 \newcommand{\now}[1]{\textcolor{blue}{#1}}
 \newcommand{\todo}[0]{\textcolor{red}{\textbf{TODO}}}
 
-[ 1 2 3 6 8 9 ]
+[ 2 3 8 9 ]
 
 ## Reflection and Refraction
 
@@ -23,31 +24,44 @@ author: |
    1.0$). If a ray emanating from the point $e = (0, 0, 0)$ intersects $S$ at a
    point $p = (1, 4, 8)$:}
 
+   Legend for the rest of the problem:
+
+   ![](1.jpg){width=50%}
+
    a. \c{(2 points) What is the angle of incidence $\theta_i$?}
 
-   The incoming ray is in the direction $I = p - e = (1, 4, 8)$, and the normal
-   at that point is $N = p - s = (1, 4, 8) - (2, 2, 10) = (1, -2, 2)$. The angle
-   can be found by taking the opposite of the incoming ray $-I$ and using the
-   formula $\cos \theta_i = \frac{-I \cdot N}{|I| |N|} = \frac{(-1, -4, -8)
-   \cdot (1, -2, 2)}{9 \cdot 3} = \frac{-1 + 8 - 16}{27} = -\frac{1}{3}$. So the
-   angle $\boxed{\theta_i = \cos^{-1}(-\frac{1}{3})}$.
+   The incoming ray is in the direction $I = v_0 = p - e = (1, 4, 8)$, and the
+   normal at that point is:
+
+   - $N = p - s = (1, 4, 8) - (2, 2, 10) = (-1, 2, -2)$
+
+   The angle can be found by taking the opposite of the incoming ray $-I$ and
+   using the formula:
+
+   - $\cos \theta_i = \frac{-I \cdot N}{\|I\|_2 \|N\|_2} 
+     = \frac{(-1, -4, -8) \cdot (-1, 2, -2)}{9 \cdot 3} = \frac{1 - 8 + 16}{27} = \frac{1}{3}$.
+
+   So the angle $\boxed{\theta_i = \cos^{-1}\left(\frac{1}{3}\right)}$.
 
    b. \c{(1 points) What is the angle of reflection $\theta_r$?}
 
    The angle of reflection always equals the angle of incidence, $\theta_r =
-   \theta_i = \boxed{\cos^{-1}(-\frac{1}{3})}$.
+   \theta_i = \boxed{\cos^{-1}\left(\frac{1}{3}\right)}$.
 
    c. \c{(3 points) What is the direction of the reflected ray?}
 
-   The reflected ray can be found by first projecting the incident ray $-I$ onto
-   the normalized normal $N$, which is $v = N \times |-I|\cos(\theta_i) =
-   (\frac{1}{3}, -\frac{2}{3}, \frac{2}{3}) \times 9 \times \frac{1}{3} = (-1,
-   2, -2)$. Then, we know the point on N where this happened is $p' = p + v =
-   (1, 4, 8) + (-1, 2, -2) = (0, 6, 6)$.
+   The reflected ray can be found by first projecting the incident ray $v_0$ onto
+   the normalized normal $n$, which is:
+
+   - $proj = n \times |v_0|\cos(\theta_i) = \left(\frac{1}{3}, -\frac{2}{3}, \frac{2}{3}\right) \times 9 \times \frac{1}{3} = (-1, 2, -2)$
+
+   Then, we know the point on N where this happened is:
+
+   - $nx = p + proj = (1, 4, 8) + (-1, 2, -2) = (0, 6, 6)$.
 
    Now, we can subtract this point from where the ray originated to know the
    direction to add in the other direction, which is still $(0, 6, 6)$ in this
-   case since the ray starts at the origin. Adding this to the point $p'$ gets
+   case since the ray starts at the origin. Adding this to the point $nx$ gets
    us $(0, 12, 12)$, which means a point from the origin will get reflected to
    $(0, 12, 12)$.
 
@@ -56,34 +70,45 @@ author: |
 
    d. \c{(3 points) What is the angle of transmission $\theta_t$?}
 
-   Using Snell's law, we know that $\eta_i \sin \theta_i = \eta_t \sin \theta_t
-   = 1.0 \times \sin(\cos^{-1}(-\frac{1}{3})) = 1.5 \times \sin(\theta_t)$. To
-   find the angle $\theta_t$ we can just solve: $\theta_t =
-   \sin^{-1}(\frac{2}{3} \times \sin(\cos^{-1}(-\frac{1}{3}))) \approx
-   \boxed{0.6796}$ (in radians).
+   Using Snell's law, we know that
+
+   \begin{align}
+   \eta_i \sin \theta_i &= \eta_t \sin \theta_t \\
+   \r{1.0} \times \sin \theta_i &= \r{1.5} \times \sin \theta_t \\
+   1.0 \times \sin(\r{ \cos^{-1}(-\frac{1}{3}) }) &= 1.5 \times \sin \theta_t \\
+   1.0 \times \r{ \frac{2\sqrt{2}}{3} } &= 1.5 \times \sin \theta_t \\
+   \r{ \frac{1.0}{1.5} } \times \frac{2\sqrt{2}}{3} &= \sin \theta_t \\
+   \r{ \frac{4}{9} } \sqrt{2} &= \sin \theta_t \\
+   \theta_t &= \sin^{-1} \left(\frac{4}{9}\sqrt{2}\right) \approx
+   \boxed{0.67967 \ldots}
+   \end{align}
 
    e. \c{(4 points) What is the direction of the transmitted ray?}
 
-   We can just add the angle obtained above to the inverse of the normal $n' =
-   (-1, 2, -2)$ (since that will be transmitted through the material). For the
-   tangent direction, we can use the vector from the ray's origin to the
-   incident ray projected onto the normal, which we'll call $v = (0, 6, 6)$.
+   We can just add together $s - p$ and $v_5$ in the diagram above, these two
+   make up the orthogonal basis of the transmitted ray $v_4$. The lengths of
+   these two are not important, but related through the angle $\theta_t$.
 
-   Now we know that the relationship between the coefficients of $n'$ and $v$ is
-   $\tan(\theta_t)$. We can add these to obtain a point along the transmitted
-   ray (it doesn't actually matter where this occurs since we're going to
-   normalize this anyway, the proportion stays consistent regardless). So using
-   the unit length for the inverse normal which is $\frac{n'}{||n'||} =
-   (\frac{1}{3}, -\frac{2}{3}, \frac{2}{3})$ we know that the perpendicular
-   vector will be $\tan(\theta_t) \times (0, \frac{1}{\sqrt{2}},
-   \frac{1}{\sqrt{2}})$.
+   Also note that in the diagram, the sphere is drawn as a 2D circle. But in
+   reality, the number of vectors perpendicular to $s - p$ is infinite. The
+   $v_5$ we're looking for is parallel with $v_1$, so we can just use
+   $\frac{v_1}{\|v_1\|_2}$ as our unit vector for $v_5$.
 
-   The final step is then adding these vectors together and subtracting the
-   interersection point: $(\frac{1}{3}, -\frac{2}{3}, \frac{2}{3}) +
-   \tan(\theta_t) \times (0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}) - (1, 4,
-   8)$.
+   \begin{align}
+   v_4 &= (s - p) + \tan \theta_t \times \|s - p\|_2 \times \frac{v_1}{\|v_1\|_2} \\
+   v_4 &= (\r{ (2, 2, 10) - (1, 4, 8) }) + \tan \theta_t \times \|s - p\|_2 \times \frac{v_1}{\|v_1\|_2} \\
+   v_4 &= \r{ (1, -2, 2) } + \tan \theta_t \times \|\r{(1, -2, 2)}\|_2 \times \frac{v_1}{\|v_1\|_2} \\
+   v_4 &= (1, -2, 2) + \tan \theta_t \times \r{3} \times \frac{v_1}{\|v_1\|_2} \\
+   v_4 &= (1, -2, 2) + \tan \theta_t \times 3 \times \frac{\r{(0, 6, 6)}}{\|\r{(0, 6, 6)}\|_2} \\
+   v_4 &= (1, -2, 2) + \tan \theta_t \times 3 \times \r{\left(0, \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)} \\
+   v_4 &= (1, -2, 2) + \tan \theta_t \times \left(0, \r{\frac{3}{2}\sqrt{2}}, \r{\frac{3}{2}\sqrt{2}} \right) \\
+   v_4 &= (1, -2, 2) + \r{\frac{4}{7}\sqrt{2}} \times \left(0, \frac{3}{2}\sqrt{2}, \frac{3}{2}\sqrt{2} \right) \\
+   v_4 &= (1, -2, 2) + \r{\left(0, \frac{12}{7}, \frac{12}{7} \right)} \\
+   v_4 &= \r{\left(1, \frac{-2}{7}, \frac{26}{7} \right)} \\
+   \end{align}
 
-   \todo all the numbers are wrong
+   This can be normalized into $\boxed{\left(\frac{7}{27}, -\frac{2}{27},
+   \frac{26}{27}\right)}$.
 
 ## Geometric Transformations
 
@@ -380,14 +405,14 @@ author: |
    i) \c{(2 points) Where will the six vertex locations be after such a
    projection, omitting the normalization step?}
 
-   - $[\begin{matrix}-1.732 & -1.732 & -6.928\end{matrix}]$ $\rightarrow$ $[\begin{matrix}-1.0 & -1.0 & 7.0\end{matrix}]$
-   - $[\begin{matrix}-1.732 & -1.732 & -3.464\end{matrix}]$ $\rightarrow$ $[\begin{matrix}-1.0 & -1.0 & 5.0\end{matrix}]$
-   - $[\begin{matrix}-1.732 & 1.732 & -6.928\end{matrix}]$ $\rightarrow$ $[\begin{matrix}-1.0 & 1.0 & 7.0\end{matrix}]$
-   - $[\begin{matrix}-1.732 & 1.732 & -3.464\end{matrix}]$ $\rightarrow$ $[\begin{matrix}-1.0 & 1.0 & 5.0\end{matrix}]$
-   - $[\begin{matrix}1.732 & -1.732 & -6.928\end{matrix}]$ $\rightarrow$ $[\begin{matrix}1.0 & -1.0 & 7.0\end{matrix}]$
-   - $[\begin{matrix}1.732 & -1.732 & -3.464\end{matrix}]$ $\rightarrow$ $[\begin{matrix}1.0 & -1.0 & 5.0\end{matrix}]$
-   - $[\begin{matrix}1.732 & 1.732 & -6.928\end{matrix}]$ $\rightarrow$ $[\begin{matrix}1.0 & 1.0 & 7.0\end{matrix}]$
-   - $[\begin{matrix}1.732 & 1.732 & -3.464\end{matrix}]$ $\rightarrow$ $[\begin{matrix}1.0 & 1.0 & 5.0\end{matrix}]$
+   - $[\begin{matrix}- \sqrt{3} & - \sqrt{3} & - 4 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}-1 & -1 & 7\end{matrix}]$
+   - $[\begin{matrix}- \sqrt{3} & \sqrt{3} & - 4 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}-1 & 1 & 7\end{matrix}]$
+   - $[\begin{matrix}\sqrt{3} & - \sqrt{3} & - 4 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}1 & -1 & 7\end{matrix}]$
+   - $[\begin{matrix}\sqrt{3} & \sqrt{3} & - 4 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}1 & 1 & 7\end{matrix}]$
+   - $[\begin{matrix}- \sqrt{3} & - \sqrt{3} & - 2 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}-1 & -1 & 5\end{matrix}]$
+   - $[\begin{matrix}- \sqrt{3} & \sqrt{3} & - 2 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}-1 & 1 & 5\end{matrix}]$
+   - $[\begin{matrix}\sqrt{3} & - \sqrt{3} & - 2 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}1 & -1 & 5\end{matrix}]$
+   - $[\begin{matrix}\sqrt{3} & \sqrt{3} & - 2 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}1 & 1 & 5\end{matrix}]$
 
    ii) \c{(1 points) Sketch the result, being as accurate as possible and
    labeling the colors of each of the visible faces.}
@@ -396,6 +421,8 @@ author: |
    sides are not visible because the cube is parallel to the axis, and when you
    do an orthographic projection, those faces are lost.
 
+   ![](6aii.jpg){width=40%}
+
    iii) \c{(2 points) Show how you could achieve this transformation using one or
    more matrix multiplication operations. Specify the matrix entries you would
    use, and, if using multiple matrices, the order in which they would be
@@ -405,14 +432,7 @@ author: |
    in this Python script:
 
    ```py
-   def ortho(points):
-     left = min(map(lambda p: p[0], points))
-     right = max(map(lambda p: p[0], points))
-     bottom = min(map(lambda p: p[1], points))
-     top = max(map(lambda p: p[1], points))
-     near = min(map(lambda p: p[2], points))
-     far = max(map(lambda p: p[2], points))
-
+   def ortho_transform(left, right, bottom, top, near, far):
      step_1 = np.array([
        [1, 0, 0, 0],
        [0, 1, 0, 0],
@@ -421,20 +441,20 @@ author: |
      ])
 
      step_2 = np.array([
-       [1, 0, 0, -(left + right) / 2.0],
-       [0, 1, 0, -(bottom + top) / 2.0],
-       [0, 0, 1, -(near + far) / 2.0],
+       [1, 0, 0, -((left + right) / 2)],
+       [0, 1, 0, -((bottom + top) / 2)],
+       [0, 0, 1, -((near + far) / 2)],
        [0, 0, 0, 1],
      ])
 
      step_3 = np.array([
-       [2.0 / (right - left), 0, 0, 0],
-       [0, 2.0 / (top - bottom), 0, 0],
-       [0, 0, 2.0 / (far - near), 0],
+       [(2 / (right - left)), 0, 0, 0],
+       [0, (2 / (top - bottom)), 0, 0],
+       [0, 0, (2 / (far - near)), 0],
        [0, 0, 0, 1],
      ])
 
-     M_ortho = step_3 @ step_2 @ step_1
+     return step_3 @ step_2 @ step_1
    ```
 
    b. \c{Show how you could project the vertices of this cube to the plane $z =
@@ -444,14 +464,45 @@ author: |
    i) \c{(3 points) Where will the six vertex locations be after such a
    projection, omitting the normalization step?}
 
+   - $[\begin{matrix}- \sqrt{3} & - \sqrt{3} & - 4 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}- \frac{4 \sqrt{3}}{3} - 1 & -1 & 7\end{matrix}]$
+   - $[\begin{matrix}- \sqrt{3} & \sqrt{3} & - 4 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}- \frac{4 \sqrt{3}}{3} - 1 & 1 & 7\end{matrix}]$
+   - $[\begin{matrix}\sqrt{3} & - \sqrt{3} & - 4 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}1 - \frac{4 \sqrt{3}}{3} & -1 & 7\end{matrix}]$
+   - $[\begin{matrix}\sqrt{3} & \sqrt{3} & - 4 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}1 - \frac{4 \sqrt{3}}{3} & 1 & 7\end{matrix}]$
+   - $[\begin{matrix}- \sqrt{3} & - \sqrt{3} & - 2 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}- \frac{2 \sqrt{3}}{3} - 1 & -1 & 5\end{matrix}]$
+   - $[\begin{matrix}- \sqrt{3} & \sqrt{3} & - 2 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}- \frac{2 \sqrt{3}}{3} - 1 & 1 & 5\end{matrix}]$
+   - $[\begin{matrix}\sqrt{3} & - \sqrt{3} & - 2 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}1 - \frac{2 \sqrt{3}}{3} & -1 & 5\end{matrix}]$
+   - $[\begin{matrix}\sqrt{3} & \sqrt{3} & - 2 \sqrt{3}\end{matrix}]$ $\rightarrow$ $[\begin{matrix}1 - \frac{2 \sqrt{3}}{3} & 1 & 5\end{matrix}]$
+
    ii) \c{(2 points) Sketch the result, being as accurate as possible and
    labeling the colors of each of the visible faces.}
 
+   ![](6bii.jpg){width=40%}
+
+   Excuse the poor sketch but the point is the transformation exposes the green
+   face to the left by doing a shear first.
+
    iii) \c{(4 points) Show how you could achieve this transformation using one
    or more matrix multiplication operations. Specify the matrix entries you
    would use, and, if using multiple matrices, the order in which they would be
    multiplied.}
 
+   It's the same as the ortho, except it uses an extra matrix that is applied
+   before any of the other transformations:
+
+   ```py
+   def oblique_transform(left, right, bottom, top, near, far):
+     step_0 = np.array([
+       [1, 0, (1 / sqrt3), 0],
+       [0, 1, 0, 0],
+       [0, 0, 1, 0],
+       [0, 0, 0, 1],
+     ])
+
+     M_ortho = ortho_transform(left, right, bottom, top, near, far)
+
+     return M_ortho @ step_0
+   ```
+
 7. \c{Consider the simple scene shown in the image below, where two cubes, one
    of height 1 and one of height 2, are both resting on a horizontal groundplane
    ($y = -\frac{1}{2}$), with the smaller cube’s front face aligned with $z =
diff --git a/exam-2/exam2.py b/exam-2/exam2.py
index 2acc6ef..cf29637 100644
--- a/exam-2/exam2.py
+++ b/exam-2/exam2.py
@@ -1,7 +1,12 @@
 import itertools
 import numpy as np
-from sympy import *
 import math
+from sympy import N, Number, Rational, init_printing, latex, simplify, Expr
+from sympy.vector import CoordSys3D, Vector
+
+init_printing()
+
+import sympy
 
 unit = lambda v: v/np.linalg.norm(v)
 
@@ -57,45 +62,65 @@ def print_bmatrix(arr):
     print("\\\\")
 
 def problem_1():
-  p = np.array([1, 4, 8])
-  e = np.array([0, 0, 0])
-  s = np.array([2, 2, 10])
+  C = CoordSys3D('C')
+  p = 1 * C.i + 4 * C.j + 8 * C.k
+  e = 0 * C.i + 0 * C.j + 0 * C.k
+  s = 2 * C.i + 2 * C.j + 10 * C.k
+  radius = 3
 
-  i = p - e
-  print("incoming", i)
-  print("|I| =", np.linalg.norm(i))
-  n = s - p
-  print("normal", n)
+  v0 = p - e
+  print("v0 (incoming ray) =", v0)
+  print(" - |v0| =", v0.magnitude())
+  print()
 
-  n_norm = unit(n)
-  print("normal_norm", n_norm)
-  cos_theta_i = np.dot(-i, n) / (np.linalg.norm(i) * np.linalg.norm(n))
-  print("part a = cos^{-1} of ", cos_theta_i)
-  print(np.arccos(cos_theta_i))
+  n = p - s
+  print("n (normal) =", n)
+  n_norm = n.normalize()
+  print(" - n_norm (normalized) =", n_norm)
+  print()
 
-  proj = n_norm * np.linalg.norm(i) * cos_theta_i
-  print("proj", proj)
+  cos_theta_i = (-v0).dot(n) / (v0.magnitude() * n.magnitude())
+  theta_i = sympy.acos(cos_theta_i)
+  print("[1a] theta_i (angle of incidence) =", theta_i)
+  print()
 
-  p_ = p + proj
-  print("proj point", p_)
+  proj_len = cos_theta_i * v0.magnitude()
+  proj = n_norm * proj_len
+  print("projection of v0 onto n =", proj)
 
-  v2 = p_ - e
-  print("v2", v2)
+  nx = p + proj
+  print("nx (proj point) =", nx)
+  print()
 
-  sin_theta_i = np.sin(np.arccos(cos_theta_i))
-  print("sin theta_i =", sin_theta_i)
+  v1 = nx - e
+  print("v1 (from e to nx) =", v1)
 
-  theta_t = np.arcsin(1.0 / 1.5 * sin_theta_i)
-  print("approx answer for part d", theta_t)
+  z = e + 2 * v1
+  print("z =", z)
 
-  uin = unit(n_norm)
-  print("unit inv normal", uin)
+  v3 = z - p
+  print("v3 =", v3)
+  print()
 
-  uperp = unit(v2)
-  print("uperp", uperp)
+  sin_theta_i = sympy.sin(theta_i)
+  print("sin(theta_i) =", sin_theta_i)
 
-  answer_1e = uin + math.tan(theta_t) * uperp - p
-  print("1e answer", unit(answer_1e))
+  theta_t = sympy.asin(Rational(2, 3) * sin_theta_i)
+  print("[1d] theta_t (angle of transmission) =", theta_t)
+  print(" - approx =", theta_t.evalf())
+  print()
+
+  v5_len = sympy.tan(theta_t) * (s - p).magnitude()
+  print("v5 len =", v5_len)
+  v4 = (s - p) + v1.normalize() * v5_len
+  print("v4 =", v4)
+  print(" - [1e] normalized =", v4.normalize())
+  print()
+
+  print("s - p =", s - p)
+  print("|s - p| =", (s - p).magnitude())
+  print("|v1| =", v1.normalize())
+  print("tan(theta_t) =", sympy.tan(theta_t))
 
 def problem_4():
   camera_pos = np.array([2, 3, 5])
@@ -229,14 +254,11 @@ def problem_7():
   solve(camera_pos, angle)
 
 def problem_6():
-  def calculate(points):
-    left = min(map(lambda p: p[0], points))
-    right = max(map(lambda p: p[0], points))
-    bottom = min(map(lambda p: p[1], points))
-    top = max(map(lambda p: p[1], points))
-    near = min(map(lambda p: p[2], points))
-    far = max(map(lambda p: p[2], points))
+  # sqrt3 = math.sqrt(3)
+  sqrt3 = sympy.sqrt(3)
+  width = 2 * sqrt3
 
+  def ortho_transform(left, right, bottom, top, near, far):
     step_1 = np.array([
       [1, 0, 0, 0],
       [0, 1, 0, 0],
@@ -245,46 +267,75 @@ def problem_6():
     ])
 
     step_2 = np.array([
-      [1, 0, 0, -(left + right) / 2.0],
-      [0, 1, 0, -(bottom + top) / 2.0],
-      [0, 0, 1, -(near + far) / 2.0],
+      [1, 0, 0, -((left + right) / 2)],
+      [0, 1, 0, -((bottom + top) / 2)],
+      [0, 0, 1, -((near + far) / 2)],
       [0, 0, 0, 1],
     ])
 
     step_3 = np.array([
-      [2.0 / (right - left), 0, 0, 0],
-      [0, 2.0 / (top - bottom), 0, 0],
-      [0, 0, 2.0 / (far - near), 0],
+      [(2 / (right - left)), 0, 0, 0],
+      [0, (2 / (top - bottom)), 0, 0],
+      [0, 0, (2 / (far - near)), 0],
       [0, 0, 0, 1],
     ])
 
-    M_ortho = step_3 @ step_2 @ step_1
+    return step_3 @ step_2 @ step_1
+
+  def oblique_transform(left, right, bottom, top, near, far):
+    step_0 = np.array([
+      [1, 0, (1 / sqrt3), 0],
+      [0, 1, 0, 0],
+      [0, 0, 1, 0],
+      [0, 0, 0, 1],
+    ])
+
+    M_ortho = ortho_transform(left, right, bottom, top, near, far)
+
+    return M_ortho @ step_0
+
+  def calculate(M, points):
+    left = min(map(lambda p: p[0], points))
+    right = max(map(lambda p: p[0], points))
+    bottom = min(map(lambda p: p[1], points))
+    top = max(map(lambda p: p[1], points))
+    near = min(map(lambda p: p[2], points))
+    far = max(map(lambda p: p[2], points))
 
     for point in points:
       point_ = np.r_[point, [1]]
-      trans_ = M_ortho @ point_
+      trans_ = M(left, right, bottom, top, near, far) @ point_
       trans = trans_[:3]
-      print("-", print_trans(np.around(point, 3), np.around(trans, 3)))
+      v = np.vectorize(lambda x: float(x.evalf()))
+      l = np.vectorize(lambda x: latex(simplify(x)))
+      point = l(point)
+      trans = l(trans)
+      print("-", print_trans(point, trans))
 
-  sqrt3 = math.sqrt(3)
-  width = 2.0 * sqrt3
-  cube_center = np.array([0, 0, -3.0 * sqrt3])
-  print("HELLOSU")
+  cube_center = np.array([0, 0, -3 * sqrt3])
 
   points = []
-  for (dx, dy, dz) in itertools.product([-1, 1], [-1, 1], [-1, 1]):
-    point = cube_center + np.array([dx * width / 2, dy * width / 2, dz * width / 2])
+  for (dz, dx, dy) in itertools.product([-1, 1], [-1, 1], [-1, 1]):
+    point = cube_center + np.array([
+      dx * width / 2,
+      dy * width / 2,
+      dz * width / 2,
+    ])
     points.append(point)
 
-  calculate(points)
+  print("Helosu Ortho")
+  calculate(ortho_transform, points)
+
+  print("Helosu Oblique")
+  calculate(oblique_transform, points)
 
 def problem_9():
   pass
 
 print("\nPROBLEM 8 -------------------------"); problem_8()
-print("\nPROBLEM 1 -------------------------"); problem_1()
 print("\nPROBLEM 5 -------------------------"); problem_5()
 print("\nPROBLEM 9 -------------------------"); problem_9()
 print("\nPROBLEM 7 -------------------------"); problem_7()
-print("\nPROBLEM 6 -------------------------"); problem_6()
 print("\nPROBLEM 4 -------------------------"); problem_4()
+print("\nPROBLEM 6 -------------------------"); problem_6()
+print("\nPROBLEM 1 -------------------------"); problem_1()