taks math study guide
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@ X~snca~ `an G`idet Ksdnc
I`~bci`~dhx
Zcwdxcn J`xcn la ^CFX Zcgdacica~x
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Crd~ Ecwce
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@ X~snca~ `an G`idet Ksdnc
X^SNT KSDNC
^cr`x @xxcxxica~ lg Fal{ecnkc `an Xfdeex
Hl}tzdkb~ :==;% ^cr`x Cnsh ~dla @kcaht! @ee zdkb~x zcxczwcn! Zc}zlnsh~dla lg `ee lz }lz~dlax lg ~bdx {lzf dx }zlbdjd~cn
{d~bls~ cr}zcxx {zd~~ca }czidxxdla gzli ~bc cr`x Cnsh`~dla @kcaht!
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Hlwcz }bl~l hzcnd~x? Ecg~ Zlt`e~t)Gzcc,HLZJDX6 Zdkb~ Hb`zecx Ks}~la,HLZJDX6
Jl~~li Zlt`e~t)Gzcc,HLZJDX
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Nc`z X~snca~ `an ]`zca~?
^bc ^cr`x @xxcxxica~ lg Fal{ecnkc `an Xfdeex "^@FX$ dx ` hli}zcbcaxdwc ~cx~dak}zlkz`i glz }sjedh xhblle x~snca~x da kz`ncx 800 ^@FX% dahesndak ^@FX"@hhliiln`~cn$ `an Edaksdx~dh`eet @hhliiln`~cn ^cx~dak "E@^$% b`x zc}e`hcn ~bccr`x @xxcxxica~ lg @h`ncidh Xfdeex "^@@X$ `an dx ncxdkacn ~l ic`xszc ~l {b`~
cr~ca~ ` x~snca~ b`x ec`zacn% sanczx~lln% `an dx `jec ~l `}}et ~bc di}lz~`a~ hlahc}~x`an xfdeex cr}ch~cn `~ c`hb ~cx~cn kz`nc ecwce Da `nnd~dla% ~bc ~cx~ h`a }zlwdncw`es`jec gccnj`hf ~l x~snca~x% }`zca~x% `an xhbllex `jls~ x~snca~ }zlkzcxx gzli kz`nc~l kz`nc
X~snca~x `zc ~cx~cn da i`~bci`~dhx da kz`ncx 8006 zc`ndak da kz`ncx 846 {zd~dak dakz`ncx > `an ;6 Cakedxb e`aks`kc `z~x da kz`ncx 0= `an 006 xhdcahc da kz`ncx 3% 2% 0=%`an 006 `an xlhd`e x~sndcx da kz`ncx 2% 0=% `an 00 Cwczt ^@FX ~cx~ dx ndzch~et edafcn~l ~bc ^cr`x Cxxca~d`e Fal{ecnkc `an Xfdeex "^CFX$ hszzdhsesi ^bc ^CFX dx ~bcx~`~c)i`an`~cn hszzdhsesi glz ^cr`x }sjedh xhblle x~snca~x Cxxca~d`e fal{ecnkc`an xfdeex ~`skb~ `~ c`hb kz`nc jsden s}la ~bc i`~czd`e ec`zacn da }zcwdlsx kz`ncxJt ncwcel}dak ~bc `h`ncidh xfdeex x}chdffcn da ~bc ^CFX% x~snca~x h`a jsden ` x~zlakglsan`~dla glz gs~szc xshhcxx
^bc ^cr`x Cnsh`~dla @kcaht b`x ncwcel}cn ~bdx x~snt ksdnc ~l bce} x~snca~xx~zcak~bca ~bc ^CFX)j`xcn xfdeex ~b`~ `zc ~`skb~ da he`xx `an ~cx~cn la ^@FX ^bcksdnc dx ncxdkacn glz x~snca~x ~l sxc la ~bcdz l{a lz glz x~snca~x `an g`idedcx ~l{lzf ~bzlskb ~lkc~bcz Hlahc}~x `zc }zcxca~cn da ` w`zdc~t lg {`tx ~b`~ {dee bce}x~snca~x zcwdc{ ~bc daglzi`~dla `an xfdeex ~bct accn ~l jc xshhcxxgse la ^@FX Cwcztksdnc dahesncx cr}e`a`~dlax% }z`h~dhc pscx~dlax% nc~`decn `ax{cz fctx% `an x~snca~`h~dwd~dcx @~ ~bc can lg ~bdx x~snt ksdnc dx `a cw`es`~dla glzi glz tls ~l hli}ec~c `ani`de j`hf {bca tls b`wc ffadxbcn ~bc ksdnc Tlsz hliica~x {dee bce} sx di}zlwcgs~szc wczxdlax lg ~bdx ksdnc
^bczc `zc ` asijcz lg zcxlszhcx `w`de`jec glz x~snca~x `an g`idedcx {bl {lsen edfcilzc daglzi`~dla `jls~ ~bc ^@FX ~cx~dak }zlkz`i Daglzi`~dla jllfec~x `zc `w`de`jecglz cwczt ^@FX xsjoch~ `an kz`nc Jzlhbszcx `zc `exl `w`de`jec ~b`~ cr}e`da ~bc X~snca~Xshhcxx Dad~d`~dwc }zlil~dla zcpsdzcica~x `an ~bc ac{ kz`ns`~dla zcpsdzcica~x glzcecwca~b)kz`nc x~snca~x ^l lj~`da hl}dcx lg ~bcxc zcxlszhcx lz ~l ec`za ilzc `jls~~bc ~cx~dak }zlkz`i% }ec`xc hla~`h~ tlsz xhblle lz wdxd~ ~bc ^cr`x Cnsh`~dla @kcaht{cjxd~c `~ {{{~c`x~`~c~rsx,x~snca~`xxcxxica~
^cr`x dx }zlsn lg ~bc }zlkzcxx lsz x~snca~x b`wc i`nc `x ~bct x~zdwc ~l zc`hb ~bcdz`h`ncidh kl`ex [c bl}c ~bc x~snt ksdncx {dee bce} glx~cz x~snca~ ec`zadak% kzl{~b%
`an xshhcxx da `ee lg ~bc ^@FX xsjoch~ `zc`xXdahczcet%
Kelzd` _txfl{xfdNc}s~t @xxlhd`~c Hliidxxdlacz glz X~snca~ @xxcxxica~^cr`x Cnsh`~dla @kcaht
@ Ec~~cz gzli ~bc Nc}s~t @xxlhd`~c Hliidxxdlacz glz X~snca~ @xxcxxica~
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Hla~ca~x
Da~zlnsh~dla ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 3
I`~bci`~dhx Hb`z~! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 2
Ljoch~dwc 0 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 0=
]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 8=
Ljoch~dwc : ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 87
]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 78
Ljoch~dwc 8 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 7;
]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 47
Ljoch~dwc > ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 44
]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 00:
Ljoch~dwc 3 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 007
]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 082
Ljoch~dwc 7 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 0>0
]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 07>
Ljoch~dwc ; ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 072
]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 027
Ljoch~dwc 2 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 04=
]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ::8
Ljoch~dwc 4 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ::2
]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! :3:
Ljoch~dwc 0= ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! :32
]z`h~dhc Pscx~dlax ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! :;>
I`~bci`~dhx @ax{cz Fct! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! :2=
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^bc x~snca~ {dee ncxhzdjc gsah~dla`e zce`~dlaxbd}x da ` w`zdc~t lg {`tx!
Ljoch~dwc 0
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Da ` gsah~dla% ~bct)hllznda`~c dx ncxhzdjcn da ~czix lg ~bcr)hllznda`~c^bc w`esc lg ~bct)hllznda`~c nc}canx la ~bc w`esc lg ~bcr)hllznda`~c
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Ljoch~dwc 0
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^zt D~Glz ` xhdcahc cr}czdica~ I`zd`a` ic`xszcx ~bc z`~c `~ {bdhb `edpsdn hllex Xbc ffanx ~b`~ glz ~bc ffzx~ gc{ idas~cx ~bc edpsdn hllex%d~x ~ci}cz`~szc h`a jc kdwca sxdak ~bc cps`~dla ~ :0; 02i% da{bdhb i zc}zcxca~x ~bc asijcz lg idas~cx ~bc edpsdn b`x jccahlledak `an ~ dx d~x ~ci}cz`~szc da H
[bdhb w`escx `zc ~bc nc}canca~ `an danc}canca~ ps`a~d~dcx da ~bdxgsah~dla`e zce`~dlaxbd}< [bdhb w`escx `zc ~bc hlax~`a~x da ~bdx
gsah~dla`e zce`~dlaxbd}=== ic~czx% ~bc cps`~dla b >=== >4~: ncxhzdjcx b% Xb`aalax`e~d~snc da ic~czx% da ~czix lg~% ~bc asijcz lg xchlanx sa~de xbcl}cax bcz }`z`hbs~c
Dnca~dgt ~bc danc}canca~ `an nc}canca~ ps`a~d~dcx `an ~bchlax~`a~x da ~bdx cps`~dla
^bc asijcz lg xchlanx sa~de Xb`aala l}cax bcz }`z`hbs~c dx~bc danc}canca~ ps`a~d~t
Xb`aalax `e~d~snc nc}canx la ~bc asijcz lg xchlanx xbc b`xjcca g`eedak6 d~ dx ~bc nc}canca~ ps`a~d~t
Xb`aalax x~`z~dak `e~d~snc% >=== ic~czx% `an >4 `zc hlax~`a~xda ~bc gsah~dla jch`sxc ~bct nl al~ hb`akc
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Bl{ H`a Tls Zc}zcxca~ ` Gsah~dla
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Ljoch~dwc 0
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^l sxc gsah~dla al~`~dla ~l ncxhzdjc ` gsah~dla% kdwc ~bc gsah~dla `a`ic% ~t}dh`eet ` ec~~cz xshb `xg% k% lz b ^bca sxc `a `ekcjz`dhcr}zcxxdla ~l ncxhzdjc ~bct)hllznda`~c lg `a lznczcn }`dz
Bczc `zc ~bzcc ic~blnx tls h`a sxc ~l nc~czidac {bc~bcz ~{l ndggczca~zc}zcxca~`~dlax lg ` gsah~dla `zc cpsdw`eca~
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^bdx gsah~dla dx zc`n `x glgrcps`ex 0> ~dicxr}esx 3
Dg tls da}s~r% ~bc ls~}s~ {dee jc 0>r 3
^bct)hllznda`~c lg `at lznczcn }`dz glz ~bdx gsah~dla dx 0>r 3
^bc gsah~dla ncxhzdjcn jtg"r$ 0>r 3 dx ~bc x`ic `x ~bc gsah~dla
ncxhzdjcn jtt 0>r 3 ^bczcglzc% `at lznczcn }`dz
glz ~bdx gsah~dla h`a jc zc}zcxca~cn jt "r% 0>r 3$
Nl tls xcc~b`~ ! ! !
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I`~hb ` edx~ lz ~`jec lg lznczcn}`dzx ~l ` kz`}b!
I`~hb `a cps`~dla ~l ` kz`}b!
I`~hb ` wczj`e ncxhzd}~dla ~l` kz`}b% `a cps`~dla% lz `acr}zcxxdla {zd~~ca da gsah~dlaal~`~dla!
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Xbl{ ~b`~ c`hb lznczcn }`dzedx~cn i`~hbcx ` }lda~ la ~bckz`}b!
Nc~czidac {bc~bcz ~bct `zcjl~b edac`z lz ps`nz`~dhgsah~dlax!
Gdan }lda~x la ~bc kz`}b `anxbl{ ~b`~ ~bcdz hllznda`~cxx`~dxgt ~bc cps`~dla!
Gdan }lda~x ~b`~ x`~dxgt ~bccps`~dla `an xbl{ ~b`~ ~bct`zc la ~bc kz`}b!
Sxc ~bc wczj`e ncxhzd}~dla ~lffan lznczcn }`dzx jcelakdak~l ~bc gsah~dla `an ~bca xbl{~b`~ ~bct x`~dxgt ~bc kz`}b%
cps`~dla% lz gsah~dla zsec! Gdan }lda~x la ~bc kz`}b lz
lznczcn }`dzx x`~dxgtdak ~bccps`~dla lz zsec `an xbl{~b`~ ~bct x`~dxgt ~bc wczj`encxhzd}~dla!
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Ljoch~dwc 0
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@at cps`~dla da ~bc glzit ir j dx ` edac`z gsah~dla D~x kz`}b{dee jc ` edac
@at cps`~dla da ~bc glzit `r: jr h% {bczc ` =% dx `ps`nz`~dh gsah~dla D~x kz`}b {dee jc ` }`z`jle`
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Ljoch~dwc 0
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Nlcx ~bc lznczcn }`dz ":% :=$ jcelak ~l ~bc gsah~dlab"r$ r"r 3$ 7!3 : 7!3= Tcx
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Nlcx ~bc kz`}b jcel{ zc}zcxca~ ~bc cps`~dlat :r: > dx ` ps`nz`~dhgsah~dla jch`sxc ~bczc dx `ar: ~czi da ~bc cps`~dla ^bc kz`}bdx ` }`z`jle` D~ ncxhzdjcx ` ps`nz`~dh gsah~dla Jl~b ~bccps`~dla `an ~bc kz`}b ncxhzdjc ` ps`nz`~dh gsah~dla
Hbchf xcwcz`e }lda~x la ~bc kz`}b ~l xcc {bc~bcz ~bcdzhllznda`~cx x`~dxgt ~bc cps`~dlat :r: > Hbllxc }lda~x{d~b hllznda`~cx ~b`~ `zc c`xdet zc`n gzli ~bc kz`}b Da ~bdxh`xc% hbllxc ~bc }lda~x "8% 0>$% "0% :$% `an ":% >$
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Ljoch~dwc 0
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Tls h`a `exl ffan xcwcz`e lznczcn }`dzx lg asijczx ~b`~ x`~dxgt~bc cps`~dla `an hlaffzi ~b`~ ~bct `zc }lda~x la ~bc kz`}b ]dhfw`escx ~b`~ `zc c`xt ~l xsjx~d~s~c% xshb `xr 0%r =% `an
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^bc lznczcn }`dzx "0% :$% "=% >$% `an ":% >$ x`~dxgt ~bccps`~dla Nc~czidac {bc~bcz ~bcxc lznczcn }`dzx `zc }lda~x la
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Ljoch~dwc 0
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Hbchf `~ ec`x~ ~{l }lda~x la ~bc jlsan`zt lg ~bc kz`}b ~l xcc
{bc~bcz ~bcdz hllznda`~cx x`~dxgt ~bc cps`~dlat :8r 0
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Hbchf `~ ec`x~ lac }lda~ {d~bda ~bc xb`ncn zckdla ~l jc hcz~`da~bc hlzzch~ xdnc lg ~bc edac b`x jcca xb`ncn Tls h`a sxc ~bc}lda~ "7% =$
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l
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a
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7
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$
t
8
:
0
0
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8
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3
=0:8>3 0 : 8 > 3
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Gdan ~{l }lda~x ~b`~ x`~dxgt ~bc cps`~dlat 8r : `an xcc {bc~bcz~bct `zc }lda~x la ~bc kz`}b
Dgr 0% ~bca Dg r 0% ~bca
t 8 \\\\\\\ \\\\\\\ t 8 \\\\\\\ \\\\\\\
t \\\\\\\ \\\\\\\ t \\\\\\\ \\\\\\\
t \\\\\\\ t \\\\\\\
^bc }lda~ "\\\\\\\% \\\\\\\$ ^bc }lda~ "\\\\\\\% \\\\\\\$x`~dxffcx ~bc cps`~dla x`~dxffcx ~bc cps`~dla
^bc }lda~x "\\\\\\\% \\\\\\\$ `an "\\\\\\\% \\\\\\\$ `zc jl~b }lda~xla ~bc kz`}b
^bc kz`}b zc}zcxca~x ~bc gsah~dlat 8r :
^bc cps`~dla dx ` edac`z gsah~dla jch`sxc d~ dx da ~bc glzitirj! D~x kz`}bisx~ jc ` edac! Xdahc ~bc kz`}b dx ` edac% d~ dx ` edac`z gsah~dla!
Dgr = `ant :% Dgr : `ant >%dx ~bc cps`~dlat 8r : ~zsc< dx ~bc cps`~dlat 8r : ~zsc 8 : :
: = : > 7 :
: : > >
Jl~b }lda~x la ~bc kz`}b x`~dxgt ~bc cps`~dla! Gdan ~{l }lda~x ~b`~ x`~dxgt ~bccps`~dlat 8r : `an xcc {bc~bcz ~bct `zc }lda~x la ~bc kz`}b!
Dgr 0% ~bca Dgr 0% ~bca
t 8 0 : t 8 0 :
t 8 : t 8 :
t 0 t 3
^bc }lda~ "0% 0$ ^bc }lda~ "0% 3$x`~dxffcx ~bc cps`~dla! x`~dxffcx ~bc cps`~dla!
^bc }lda~x "0% 0$ `an "0% 3$ `zc jl~b }lda~x la ~bc kz`}b! ^bc kz`}bzc}zcxca~x ~bc gsah~dlat 8r :!
Ljoch~dwc 0
:>
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Bl{ H`a Tls Nz`{ Hlahesxdlax gzli ` Gsah~dla`e Zce`~dlaxbd}=r 0= @ zcgsan {lsenal~ jc `nncn ~l ~bc ~l~`e hlx~6 d~ {lsen jc xsj~z`h~cn$
J ^bc ~l~ e asijcz lg blszx ~z`wcecn%t% `x ` gsah~dla lg ~bc`wcz`kc x}ccn da idecx }cz blsz%r% {bczc >= zc}zcxca~x ~bcasijcz lg idecx ~z`wcecn `an 0= zc}zcxca~x ~bc ndx~`ahc daidecx gzli ~bc x~`z~dak }lda~
"^bdx h`aal~ jc ilncecn jtt >=r 0= ^dic w`zdcx
dawczxcet {d~b x}ccn% `x xbl{a da ~bc cps`~dla ~ $
H ^bc ~l~`e hlx~ lg oldadak ` ff~acxx hesj%t% `x ` gsah~dla lg ~bcasijcz lg ila~bx `~~cancn%r% {bczc >= zc}zcxca~x ~bc hlx~lg c`hb ila~b `an 0= zc}zcxca~x ~bc dad~d`e icijczxbd} gcc
"^bdx h`a jc ilncecn jtt >=r 0=$
N ^bc `zc` lg ` ~z`}cldn%t% `x ` gsah~dla lg lac lg ~bc j`xcx%{bczc ~bc l~bcz j`xc dx >= `an ~bc bcdkb~ lg ~bc ~z`}cldndx 0=
"^bdx h`aal~ jc ilncecn jtt >=r 0= ^bc glzise` glz
~bc `zc` lg ` ~z`}cldn dx @ "j0
j:$b$0
:
n
z
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Ljoch~dwc 0
:4
^zt D~X`i {lzfx `~ `a cech~zladhx x~lzc ^bc kz`}b xbl{x ~bc hliidxxdlabc c`zax la ` x`ec `x ` gsah~dla lg ~bc hlx~ lg ~bc d~ci bc xceex
[b`~ {dee X`ix `}}zlrdi`~c hliidxxdla jc dg bc xceex `a d~ci ~b`~hlx~x .7;3=
2
0:
07
0= := 8= >= 3= 7= ;= 2= 4=
Hliidxxdla
"nlee`zx$
Hlx~ lg D~ci "nlee`zx$
t
r
=
>
2
0:
07
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Hliidxxdla"nlee`zx$
Hlx~ lg D~ci "nlee`zx$
t
r
Al{ }z`h~dhc {b`~ tlswc ec`zacn!
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Ljoch~dwc 0
8=
Pscx~dla 0
^bc j`xfc~j`ee ~c`i dx lznczdak ^)xbdz~x ~l xceeglz ` gsan)z`dxcz! ^bc ~c`i }`dn .:;3 glz ~bcxbdz~x `an {dee xcee ~bci glz .0: c`hb! ^bczce`~dlaxbd} jc~{cca ~bc asijcz lg xbdz~x xlen`an ~bc ~c`ix }zlff~ gzli ~bc x`ec lg ~bc xbdz~xh`a jc zc}zcxca~cn jt ~bc gsah~dlag"a$ 0:a :;3% da {bdhb a zc}zcxca~x ~bcasijcz lg xbdz~x xlen! [b`~ dx ~bc nc}canca~ps`a~d~t da ~bdx gsah~dla`e zce`~dlaxbd} c`hb% {bdhb dacps`ed~t ilncex a% ~bcasijcz lg NWNx Ed`ak dx `jec ~l zca~a 0: 83
J >a 0: 83
H >8a
3 0:
N 83 >a 0:
Pscx~dla 8
[bdhb lg ~bc gleel{dak ~`jecx zc}zcxca~xt `x `gsah~dla lgr :
0 8: >
3 3
r t
: 4
: 7
: 8
: =
@
J
H
N
@ax{cz Fct? }`kc :2=@ax{cz Fct? }`kc :2=
@ax{cz Fct? }`kc :2=
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Ljoch~dwc 0
80
Pscx~dla >
^bc ~l~`e hlx~ lg `a d~ci `~ ` x~lzc dx ~bc }zdhc lg~bc d~ci }esx 7!3# x`ecx ~`r! Dgh% ~bc ~l~`e hlx~ lg~bc d~ci% dx ` gsah~dla lgr% ~bc }zdhc lg ~bc d~ci%{bdhb gsah~dla ilncex ~bdx xd~s`~dla dx ` ps`nz`~dh gsah~dla6 ~bczcglzc% d~x
}`zca~ gsah~dla dx ~bc ps`nz`~dh }`zca~ gsah~dla%t r:
t
r
3
>
7
;
2
4
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0
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0
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8
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37
;
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r:
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v"=% 0$% ":% 7$% "8% 3$y
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v=% :% 8y
Z`akc^bc xc~ lg `ee ~bct)hllznda`~cx da~bc gsah~dlax lznczcn }`dzx
v0% 3% 7y
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v"8% >$% "0% :$% ":% >$% ">% 7$y
^bc nli`da dx ~bc xc~ lgr)hllznda`~cx da ~bc lznczcn }`dzx?v"8% >$% "0% :$% ":% >$% ">% 7$y ^bc nli`da dx v8% 0% :% >y
^bc z`akc dx ~bc xc~ lgt)hllznda`~cx da ~bc lznczcn }`dzx?v"8% >$% "0% :$% ":% >$% ">% 7$y ^bc z`akc dx v7% >% :% >y
Xcc Ljoch~dwc 0%}`kc 0=% glz ilzcdaglzi`~dla `jls~
gsah~dlax!
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Ljoch~dwc :
>=
^zt D~[b`~ `zc ~bc nli`da `an z`akc lg ~bc gsah~dla jcel{
3
0 : 8 > 3r
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Ljoch~dwc :
>8
@ hlax~zsh~dla hli}`at sxcx x~cce e`nncz jc`ix glz xh`gglendak^bc kz`}b jcel{ zc}zcxca~x ~bc zce`~dlaxbd} jc~{ccar% ~bc {cdkb~lg ~bc jc`ix da }lsanx% `ant% ~bcdz ecak~b da gcc~
[b`~ dx ` zc`xla`jec nli`da `an z`akc glz ~bdx gsah~dla=
>3
3=
: > 7
[cdkb~ "}lsanx$
2 0= 0: 0> 07 02 := ::
33
7=
73
Ecak~b"gcc~$
t
r
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Ljoch~dwc :
>>
^zt D~@ zch~`akse`z hlsz~t`zn dx }e`aacn `x }`z~ lg ~bc ncxdka glz ` ac{jsdendak ^bc hlsz~t`zn xblsen jc 8 gcc~ elakcz ~b`a d~ dx {dnc ^bchlsz~t`zn isx~ jc `~ ec`x~ 0: gcc~ {dnc js~ al ilzc ~b`a :3 gcc~
{dnc ^bc gsah~dlag"r$ r:
8rncxhzdjcx ~bc `zc` lg ~bchlsz~t`zn da ~czix lg d~x {dn~b da gcc~% r [b`~ dx ` zc`xla`jec z`akcglz ~bdx gsah~dla> 87
g"r$ 02=
^bc i`rdisi `zc` lg ~bc hlsz~t`zn {dee lhhsz {bcar :3!
g"r$ r: 8r
g"r$ ":3$: 8":3$
g"r$ 7:3 ;3
g"r$ ;==
@ zc`xla`jec z`akc glz ~bdx gsah~dla dx 02= g"r$ ;==!
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Ljoch~dwc :
>3
Bl{ H`a Tls Da~cz}zc~ ` ]zljeci Xd~s`~dla gzli ` Kz`}b{ 7= :{ 7
7{ 77
^bc }czdic~cz lg ~bc acdkbjlzx }lle h`a jc zc}zcxca~cn jt ~bccr}zcxxdla 7{ 77
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Ljoch~dwc :
3:
Bl{ Nl Tls Zc}zcxca~ ]`~~czax da N`~` @ekcjz`dh`eet 8
8 4 2
> 07 03
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Ljoch~dwc :
38
Wczdgt ~b`~ c`hb lg ~bc n`~` }lda~x "lznczcn }`dzx$ x`~dxffcx ~bccps`~dlat r: 0
Zc}e`hct {d~bg"r$ ^bc zsec cr}zcxxcn da gsah~dla al~`~dladxg"r$ r: 0
^bc zsecg"r$ r: 0 zc}zcxca~x ~bdx zce`~dlaxbd}
r g"r$ r: 0 t Tcx,Al
g"0$ "0$: 00 g"0$ 0 0 = Tcx
g"0$ =
g":$ ":$: 0: g":$ > 0 8 Tcx
g":$ 8
g"8$ "8$: 08 g"8$ 4 0 2 Tcx
g"8$ 2
g">$ ">$:
0> g">$ 07 0 03 Tcxg">$ 03
Nl tls xcc
~b`~ ! ! !
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Ljoch~dwc :
3>
Ellf `~ ~bc }`~~cza lg asijczx jcel{
8% ;% 08% :0%
Nlcx ~bc cr}zcxxdla a: a 0 zc}zcxca~ ~bc a~b asijcz da ~bdx}`~~cza : 0 ;
88: 8 0
08 Tcx4 8 0 08
>>: > 0
:0 Tcx07 > 0 :0
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Ljoch~dwc :
33
X~snca~x da ` i`~b he`xx sxcn ` }`~~cza ~l hlax~zsh~ ` xczdcx lgdahzc`xdaket e`zkcz ps`nzde`~cz`ex% `an ~bca ~bct ic`xszcn ~bc}czdic~czx lg ~bc ps`nzde`~cz`ex ^bc }czdic~czx `zc kdwca da ~bc~`jec jcel{
Ps`nzde`~cz`e
Dg ~bc }`~~cza hla~dascx% {b`~ cr}zcxxdla h`a jc sxcn ~l zc}zcxca~~bc }czdic~cz lg ~bc a~b ps`nzde`~cz`e da ~bdx xczdcx ilzc ~b`a ~bc xps`zc lg d~x}lxd~dla asijcz da ~bc xczdcx ^bc }czdic~cz lg ~bc a~bps`nzde`~cz`e xblsen jc a: >
Xcc {bc~bcz ~bdx cr}zcxxdla {lzfx glz ~bc fal{a w`escx
Dg ~bc }`~~cza hla~dascx% ~bc }czdic~cz lg ~bc a~b ps`nzde`~cz`ehlsen jc zc}zcxca~cn jt ~bc cr}zcxxdla a: >
]lxd~dlaXps`zc lg
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: > 2
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> 07 :=
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]lxd~dla a: >]czdic~cz
Tcx,Al"hi$
0 0: > 0 > 3 3 Tcx
: :: > > > 2 2 Tcx
8 8: > 4 > 08 08 Tcx
> >: > 07 > := := Tcx
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Ljoch~dwc :
37
Bl{ Nl Tls Xdi}edgt @ekcjz`dh Cr}zcxxdlax
ecak~b : "{ 3$ : { 4
Gdan ~bc `zc` lg ~bc }lx~cz jl`zn jt ise~d}etdak ~bc ecak~b lg~bc jl`zn jt ~bc {dn~b
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: da!
: da!
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{
: da!
Wl~c glz
Z`ia! : da!
Xcc Ljoch~dwc 3%}`kc 0:4% glz ilzcdaglzi`~dla `jls~~bc GLDE ic~bln!
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Ljoch~dwc :
34
Bl{ Nl Tls Xlewc @ekcjz`dh Cps`~dlax :"r 0$ :8
^bc xles~dla ~l ~bc cps`~dla dxr ;
r > :"r 0$ :8
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8r
:
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7 8i
87
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^bc xles~dla ~l ~bc cps`~dla dx i :
Da ~bc ~czi 7r% 7 dxh`eecn ~bc hlcgffhdca~lgr!
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Ljoch~dwc :
7=
Bl{ i`at ideeded~czx lg {`~cz isx~ jc `nncn ~l ` jc`fczhla~`dadak :== ideeded~czx lg ` xles~dla ~b`~ dx ;3# c~b`ale ~l}zlnshc ` xles~dla ~b`~ dx 3=# c~b`ale
7
;
2
4
8
:
0
=
0
:
8
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3
7
;
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4
0 0:8>37;24 : 8 > 3 7 ; 2 4
@ax{cz Fct? }`kc :2:@ax{cz Fct? }`kc :2:
@ax{cz Fct? }`kc :2:
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Ljoch~dwc :
7>
@
J
H
N
Pscx~dla 03
@x ~bc `kc lg ` h`z dahzc`xcx% d~x w`esc nchzc`xcx! [bdhb xh`~~cz}el~ jcx~ zc}zcxca~x ~bdxzce`~dlaxbd}!:3 }cz }lsan%`an `eilanx hlx~ .3!3= }cz }lsan! Dgr zc}zcxca~x~bc asijcz lg }lsanx lg `eilanx A`aht jlskb~%{bdhb cr}zcxxdla zc}zcxca~x ~bc ~l~`e hlx~ lg ~bcas~x xbc }szhb`xcn2!;3
H 4!;3r >2!;3
N 4!;3r :0!:3
Pscx~dla 02
@ }czxla`e ~z`dacz `~ ` elh`e kti hb`zkcx ~bcgleel{dak gccx glz ` lac)blsz ~z`dadak xcxxdla glz0 ~l > }cl}ec!
[bdhb cps`~dla jcx~ zc}zcxca~x ~bc zce`~dlaxbd}jc~{cca a% ~bc asijcz lg }cl}ec% `an h% ~bc hlx~a 07
N h 3a 0>
Pscx~dla 04
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@ a :
J :a: :
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@ax{cz Fct? }`kc :28@ax{cz Fct? }`kc :2:
@ax{cz Fct? }`kc :2:
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042= .823
0423 .30=
044= .7=3
0443 .;8=
:=== .2:3
:==3 .43=
@ax{cz Fct? }`kc :28
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Ljoch~dwc :
77
Pscx~dla :=
J`zj`z` dx 8 ~dicx `x len `x I`zf! Dg ~bc xsi lg~bcdz `kcx dx 3:% {bdhb cps`~dla h`a jc sxcn ~lffan ~bcdz `kcxr 3:
N 8r > 3:
Pscx~dla :0
[bdhb lg ~bc gleel{dak cr}zcxxdlax dx cpsdw`eca~~l >"a 8$"a :$a: >a :>
J >a: >a :>
H >a: :>
N >a: >a :>
@ax{cz Fct? }`kc :28 @ax{cz Fct? }`kc :28
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7;
^bc x~snca~ {dee ncilax~z`~c `a sanczx~`andak lg edac`z gsah~dlax!
Ljoch~dwc 8
Glz ~bdx ljoch~dwc tls xblsen jc `jec ~l
zc}zcxca~ edac`z gsah~dlax da ndggczca~ {`tx `an ~z`axe`~c `ilak~bcdz w`zdlsx zc}zcxca~`~dlax6 `an
da~cz}zc~ ~bc ic`adak lg xel}c `an da~czhc}~x lg ` edac`z gsah~dla`an ncxhzdjc ~bc cggch~x lg hb`akcx da xel}c `ant)da~czhc}~ dazc`e){lzen `an i`~bci`~dh`e xd~s`~dlax
[b`~ Dx ` Edac`z Gsah~dla
03
8
:
0
=
0
:
8
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3
7
;
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4
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00
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080>
03
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r t
2 08
= 8
0 3
8 4
Xcc Ljoch~dwc 0%
}`kc 0=% glz ilzcdaglzi`~dla `jls~gsah~dlax!
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Ljoch~dwc 8
72
^zt D~^bc ~`jec jcel{ ncxhzdjcx ` edac`z zce`~dlaxbd}
Nlcx ~bc cps`~dlar :t > zc}zcxca~ ~bc x`ic edac`z gsah~dla zc}zcxca~x ~bc x`ic edac`zgsah~dla `x ~bc ~`jec% xsjx~d~s~c ~bc lznczcn }`dzx gzli ~bc ~`jec da~l~bc cps`~dla
^bc ~`jec `an ~bc cps`~dla ncxhzdjc ~bc x`ic gsah~dla
r t
: 8
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2 :
r t Nlcxr :t >< Tcx,Al
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: 8 \\\\\\\\ \\\\\\\\ >
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2 : \\\\\\\\ \\\\\\\\ >
\\\\\\\\ >
r tNlcx
Tcx,Alr :t >> = > = > Tcx
> >
2 :":$ >2 : 2 > > Tcx
> >
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Ljoch~dwc 8
74
[b`~ Dx Xel}c
8
:
0
0
:
8
>
3
=0:8>3 0 : 8 > 3
r 9 :
Sancgdacn xel}c^bc edac dx wcz~dh`e!
t
r
3
>
8
:
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0
:
8
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3
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t 9 :
_czl xel}c^bc edac dx blzdla~`e!
t
r
3
>
8
:
0
0
:
8
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t9r
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t
r
3
>
8
:
0
0
:
8
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3
=0:8>3 0 : 8 > 3
t9r
]lxd~dwc xel}c^bc edac zdxcx gzli ecg~ ~l zdkb~!
Nl tls xcc
~b`~ ! ! !
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Ljoch~dwc 8
;=
Da ~bc kz`}b jcel{ tls h`a ffan ~bc xel}c jt hlsa~dak ~bc hb`akcdat)w`escx `an ~bc hb`akc dar)w`escx jc~{cca `at ~{l }lda~x
^bct)w`esc hb`akcx : sad~x glz cwczt 8 sad~x ~bc r)w`esc hb`akcx@x tls kl gzli ecg~ ~l zdkb~% ~bc edac }lda~x nl{a% xl ~bc xel}c dxack`~dwc ^bc z`~c lg hb`akc dx kdwca jt ~bc z`~dl jcel{
zzdsxac
:8
^bc xel}c lg ~bc kz`}b dx :8
t
r
3
>
8
:
0
0
:
8
>
3
=0:8>3 0 : 8 > 3
8 sad~x
: sad~x
[b`~ dx ~bc xel}c lg ~bc edac }`xxdak ~bzlskb ~bc }lda~x "2% 8$ `an"7% :$
^zt D~Gdan ~bc xel}c `ant)da~czhc}~ lg ~bc kz`}b lg ~bc gsah~dla7r :t 0:
^l nc~czidac ~bc xel}c `ant)da~czhc}~% ~z`axglzi ~bc cps`~dla7r :t 0: da~l xel}c)da~czhc}~ glzi%t ir j
7r :t 0:
\\\\\\\\ \\\\\\\\
:t \\\\\\\\ 0:
:t
7r
0:
t \\\\\\\\ r \\\\\\\\
Zc`n ~bc w`escx lg \\\\\\\\ `an \\\\\\\\ gzli ~bc zcwdxcn cps`~dla
Glz ~bdx gsah~dla% i \\\\\\\\ `an j \\\\\\\\
^bc xel}c lg ~bc kz`}b lg ~bc gsah~dla dx \\\\\\\\
^bct)hllznda`~c lg ~bct)da~czhc}~ lg ~bc kz`}b lg ~bc gsah~dla
dx \\\\\\\\
7r :t 0:
7r 7r
:t 7r 0:
::t
:7r
0::
t 8r 7
Zc`n ~bc w`escx lgi `anj gzli ~bc zcwdxcn cps`~dla! Glz ~bdx gsah~dla%i 8 `anj 7! ^bc xel}c lg ~bc kz`}b lg ~bc gsah~dla dx 8! ^bct)hllznda`~c lg ~bct)da~czhc}~ lg ~bc kz`}b lg ~bc gsah~dla dx 7!
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Ljoch~dwc 8
;3
Gsah~dla 0 Gsah~dla : Cggch~
Xdahc : 08% ~bc kz`}b lg
gsah~dla : dx x~cc}cz ~b`a ~bc kz`}b
lg gsah~dla 0!
Xdahc 0 8% ~bc kz`}b lggsah~dla : dx ecxx x~cc} ~b`a ~bc
kz`}b lg gsah~dla 0!
t
r
3
>
7
;
2
4
8
:
0
=
0
:
8
>
3
7
;
2
4
0 0:8>37;24 : 8 > 3 7 ; 2 4
t98r:
t9r:
t
r
3
>
7
;
2
4
8
:
0
=
0
:
8
>
3
7
;
2
4
0 0:8>37;24 : 8 > 3 7 ; 2 4
t9 r0
8
t9:r
[b`~ @zc ~bc Cggch~x la ~bc Kz`}b lg ` Edac`z Gsah~dla Dg ~bc W`escxlgi`an j@zc Hb`akcn da ~bc Cps`~dla t9 ir& j
3
7
;
2
4
0 0:8>37;24 : 8 > 3 7 ; 2 4
t98r
&3
t9
r&3
Nl tls xcc~b`~ ! ! !
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Ljoch~dwc 8
;;
Hb`akc dat)Da~czhc}~% j
Gsah~dla 0 Gsah~dla : Cggch~
Gsah~dla : hzlxxcx ~bct)`rdx `~ ` }lda~7 sad~x bdkbcz ~b`a gsah~dla 0 jch`sxc3 "0$ 7!
Gsah~dla : hzlxxcx ~bct)`rdx `~ ` }lda~8 sad~x el{cz ~b`a gsah~dla 0 jch`sxc0 > 8!
t
r
3
>
7
;
2
4
8
:
0
=
0
:
8
>
3
7
;
2
4
0 0:8>37;24 : 8 > 3 7 ; 2 4
t 9 r & >0:
t 9 r & 00:
t
r
3
>
7
;
2
4
8
:
0
=
0
:
8
>
3
7
;
2
4
0 0:8>37;24 : 8 > 3 7 ; 2 4
t 9 :r 0
t 9 :r & 3
t :r 0 t :r 3
t 0:r > t
0:r 0
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Ljoch~dwc 8
;2
Dg ~bct)da~czhc}~ lg ~bc gsah~dlat 8:r > {czc nchzc`xcn jt 8%
{b`~ {lsen jc ~bc cps`~dla lg ~bc ac{ gsah~dla
Dg ~bct)da~czhc}~ lg ~bc gsah~dla {czc nchzc`xcn jt 8% d~ {lsenjc > 8 0 ^bc ac{ w`esc glz j {lsen jc 0
^bc cps`~dla lg ~bc ac{ gsah~dla {lsen jc t 8:r 0
^bc gsah~dlat 3r : {`x hb`akcn ~lt 3r : Bl{ {lsen~bc kz`}b lg ~bc ac{ gsah~dla hli}`zc {d~b ~bc kz`}b lg ~bclzdkda`e gsah~dla% ~bc kz`}b lgt 3r : dx > sad~x jcel{ ~bckz`}b lgt 3r :
t
r
3
>
7
;
24
8
:
0
=
0
:
8
>
3
7
;
2
4
0 0:8>37;24 : 8 > 3 7 ; 2 4
t 9 3r & :
t 9 3r :
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Ljoch~dwc 8
;4
Xel}cx lg edacx h`a ~cee tls {bc~bcz ~bc edacx `zc }`z`eece lz }cz}candhse`z
Dg ~{l edacx `zc }`z`eece% ~bca ~bct b`wc ~bc x`ic xel}c% `an ~bcdzcps`~dlax b`wc ~bc x`ic w`esc glz i
Ellf `~ ~bc kz`}bx lg ~bcxc ~{l cps`~dlax?t :r > `ant :r 8
t
r
3
>
7
;
2
4
8
:
0
=
0
:
8
>
3
7
;
2
4
0 0:8>37;24 : 8 > 3 7 ; 2 4
t 9 :r >t 9 :r & 8
]`z`eece edacx
^zt D~Dg ~bc xel}c lg ~bc gsah~dlat =3r > dx dahzc`xcn jt 8% bl{ {dee~bc kz`}b lg ~bc ac{ gsah~dla hli}`zc {d~b ~bc kz`}b lg ~bclzdkda`e gsah~dla! Dg ~bc xel}c dx dahzc`xcn jt 8% ~bc ac{ xel}c jchlicx =!3 8 8!3! ^bcac{ edac {dee b`wc ~bc x`ic t)da~czhc}~ `x ~bc lzdkda`e edac!Xdahc u8!3u u=!3u% ~bc kz`}b lg ~bc ac{ edac {dee jc x~cc}cz ~b`a ~bc lzdkda`eedac!
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Ljoch~dwc 8
2=
Dg ~{l edacx `zc }cz}candhse`z% ~bca ~bct b`wc ack`~dwc zchd}zlh`exel}cx% `an ~bcdz cps`~dlax b`wc ack`~dwc zchd}zlh`e w`escx glz i
Ellf `~ ~bc kz`}bx lg ~bcxc ~{l cps`~dlax?t :8r : `an
t 8:r :
Bl{ Nl Tls [zd~c Edac`z Cps`~dlax
7
;
2
4
8
:
0
=
0
:
8
>
3
7
;
2
4
0 0:8>37;24 : 8 > 3 7 ; 2 4
]cz}candhse`z edacx
t 9 r & :t 9 r & :
8
:
:
8
[b`~ dx ~bc cps`~dla lg ~bc edac {d~b ` xel}c lg > `an ` t)da~czhc}~lg:% ~bca i >
Dg ~bct)da~czhc}~ dx :% ~bca j :
^bc cps`~dla lg ~bc edac dx?
t ir j
t >r :
^{l asijczx `zc ack`~dwczchd}zlh`ex lg c`hb l~bczdg ~bcdz }zlnsh~ dx 0!
Glz cr`i}ec% :8 `an
:8
`zc ack`~dwc zchd}zlh`ex
xdahc :8
:8
770!
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Ljoch~dwc 8
20
Kdwca ~bc xel}c `an ` }lda~ la ~bc kz`}b
Xsjx~d~s~c ~bc kdwca w`escx "~bcr) `ant)hllznda`~cx lg ~bc kdwca}lda~ `an i% ~bc xel}c$ da~l ~bc xel}c)da~czhc}~ glzi lg ~bc
cps`~dla%t ir j Xlewc ~bc cps`~dla glz j
Xsjx~d~s~c ~bc w`escx glz i `an j da~l ~bc xel}c)da~czhc}~ glzi%t ir j
^zt D~[zd~c ~bc cps`~dla lg ~bc edac {d~b ` xel}c lg
03 `an `t)hllznda`~c
lg ~bct)da~czhc}~ lg 2
Dg ~bc xel}c dx 03% ~bca i \\\\\\\\
Dg ~bct)hllznda`~c lg ~bct)da~czhc}~ dx 2% ~bca j \\\\\\\\^bc cps`~dla lg ~bc gsah~dla dx?
t ir j
t \\\\\\\\r \\\\\\\\
Dg ~bc xel}c dx 0
3% ~bcai 0
3! Dg ~bct)hllznda`~c lg ~bct)da~czhc}~ dx 2%~bcaj 2!
^bc cps`~dla lg ~bc gsah~dla dx?
t irj
t 03r 2
[b`~ dx ~bc cps`~dla lg ~bc edac {d~b ` xel}c lg 08 ~b`~ }`xxcx
~bzlskb ~bc }lda~ "8% 7$ 3":$ j
7 0= j 0> 0= j
0= 0= 0= 0=
> j > j
Tls al{ fal{ ~bc w`escx lgi `an j6 xsjx~d~s~c ~bci da~l ~bcxel}c)da~czhc}~ glzi lg ~bc cps`~dla
t ir j
t 3r >
^bc cps`~dla lg ~bc edac }`xxdak ~bzlskb ~bc }lda~x ":% 7$ `an
":% 0>$ dxt 3r >
Kdwca ~{l }lda~x la ~bc kz`}b
Sxc ~bcr)hllznda`~cx `ant)hllznda`~cx lg ~bc ~{l kdwca }lda~x~l ffan ~bc xel}c% i% lg ~bc edac
Xsjx~d~s~c ~bc hllznda`~cx lg lac lg ~bc fal{a }lda~x `an ~bcxel}c tls osx~ glsan da~l ~bc xel}c)da~czhc}~ glzi lg ~bccps`~dla%t ir j
Xlewc ~bc cps`~dla glz j
Xsjx~d~s~c i `an j da~l ~bc xel}c)da~czhc}~ glzi%t ir j!
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Ljoch~dwc 8
23
^zt D~[zd~c ~bc cps`~dla lg ~bc edac`z gsah~dla ~b`~ hla~`dax ~bc }lda~x":% 3$ `an "8% 03$
Jckda jt ffandak ~bc \\\\\\\\\\\\\\\\ lg ~bc kz`}b^bc edac }`xxcx ~bzlskb ~bc }lda~x "\\\\\\\\% \\\\\\\\$ `an
"\\\\\\\\% \\\\\\\\$
i t
r:
:
t
r0
0 \\\\\\\\
^bc xel}c lg ~bc edac dx \\\\\\\\
Acr~% xsjx~d~s~c ~bc hllznda`~cx lg lac lg ~bc kdwca }lda~x%
":% \\\\\\\\$% `an ~bc xel}c tls osx~ glsan% \\\\\\\\% da~l ~bcxel}c)da~czhc}~ glzi lg ~bc cps`~dla lg ` edac ~l ffan ~bc w`esc lgj
t ir j
\\\\\\\\ \\\\\\\\ \\\\\\\\ j
3 \\\\\\\\ j
> >
\\\\\\\\ j
Gda`eet% xsjx~d~s~c ~bc w`escx lgi `an j da~l ~bc xel}c)da~czhc}~
glzi
t \\\\\\\\r \\\\\\\\
Jckda jt ffandak ~bc xel}c lg ~bc kz`}b! ^bc edac }`xxcx ~bzlskb ~bc }lda~x":% 3$ `an "8% 03$!
i t
r:
:
t
r0
0
038
3:
0=3 :
^bc xel}c lg ~bc edac dx :!
Acr~% xsjx~d~s~c ~bc hllznda`~cx lg lac lg ~bc kdwca }lda~x% ":% 3$% `an ~bcxel}c tls osx~ glsan% :% da~l ~bc xel}c)da~czhc}~ glzi lg ~bc cps`~dla lg `edac ~l ffan ~bc w`esc lgj!
t irj
3 : : j
3 > j
> >
4 j
Gda`eet% xsjx~d~s~c ~bc w`escx lgi `anj da~l ~bc xel}c)da~czhc}~ glzi!
t :r 4
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Ljoch~dwc 8
27
Bl{ Nl Tls Gdan ~bc r)Da~czhc}~ `an t)Da~czhc}~ glz ~bc Kz`}b lg `aCps`~dla :r
^bct)da~czhc}~ lg ~bc kz`}b dx : ^bc kz`}b da~czxch~x ~bct)`rdx`~ "=% :$
Gdan ~bcr) `ant)da~czhc}~x lg 8r 7t 0:
^l ffan ~bcr)da~czhc}~% xsjx~d~s~ct = da~l ~bc cps`~dla `anxlewc glzr
8r 7t 0:
8r 7"=$ 0:8r = 0:
8r 0:
r >
^bcr)da~czhc}~ dx > ^bc kz`}b da~czxch~x ~bc r)`rdx `~ ">% =$
Gdan ~bct)da~czhc}~ jt{zd~dak ~bc cps`~dla daxel}c)da~czhc}~ glzi
8r 7t 0:
8r 8r
7t 8r 0:
7
7
t
78r
07:
t 0:r:
^bct)da~czhc}~ dx : ^bckz`}b da~czxch~x ~bct)`rdx `~"=% :$
Lz% ffan ~bct)da~czhc}~ jtxsjx~d~s~dakr = da~l ~bccps`~dla
8r 7t 0:
8"=$ 7t 0:
= 7t 0:
7t 0:
t :
^bct)da~czhc}~ dx : ^bckz`}b da~czxch~x ~bct)`rdx `~"=% :$
[zd~c ~bc cps`~dla da ~bcglzit ir j
;t 0> :r
0> 0>
;t :r0>
;
;
t
:;r
0;>
t :;r :
^bczcglzc% j :
Xsjx~d~s~cr = `an xlewcglzt
;t 0> :r
;t 0> :"=$
;t 0> =
0> 0>
;t 0>
;
;
t
0;>
t :
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Ljoch~dwc 8
22
Zll~x lg Cps`~dlax _czlx lg Gsah~dlax r)Da~czhc}~x lg Kz`}bx
Glz `at cps`~dla% xshb `xt r 2% ` zll~ dx ` w`esc lgr~b`~ i`fcx
t = Glz `at gsah~dla% ` w`esc lgr~b`~ i`fcxg"r$ cps`e ~l czl dx h`eecn
` czl lg ` gsah~dla Jl~b ~bc zll~ lg `a cps`~dla `an ~bc czl lg ` gsah~dla
h`a jc glsan jt elh`~dak ~bcr)hllznda`~c lg ~bcr)da~czhc}~ lg ~bc kz`}b lg
` gsah~dla% ~bc }lda~ `~ {bdhb ~bc kz`}b da~czhc}~x ~bc r)`rdx
>8
t r 2>8
t r 2>8
= r 2
2 2
2 r
" $ "2$ " $ " $r
7 r
r 7
>8
8>
8>
>8
>8
^bc zll~ lg
t r 2
dx 7!
>8
g"r$ r 2>8
^bc czl lg
g"r$ r 2
dx 7!
>8
^bc hllznda`~cx lg ~bcr)da~czhc}~ lg
t r 2
`zc "7% =$!
>8
t
r
3
>
7
;
2
4
0=
8
:
0
=
0
:
8
>
3
7
;
2
4
0=
0 0:8>37;240= : 8 > 3 7 ; 2 4 0=
"7% =$
= r 2
2 2
2 r
" $ "2$ " $ " $r
7 r
r 7
>8
8>
8>
>8
>8
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Ljoch~dwc 8
24
Bl{ Nl Tls Da~cz}zc~ ~bc Ic`adak lg Xel}cx `an Da~czhc}~x=
3=
7=
;=
0 : 8 > 3 7 ; 2 4
t
r
^dic "xchlanx$
Wlesic
"da!8$
=
0%===
:%===
8%===
>%===
3%===
7%===
;%===
2%===
0=%===
4%===
: > 7 2 0= 0: 0> 07 02 := :: :>r
^dic "xchlanx$
@e~d~snc
"gcc~$
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Ljoch~dwc 8
40
^bc nlicx~dh }zlnsh~dla lg hzsnc lde da ~bc Sad~cn X~`~cx gzli0423 ~l :==: h`a jc `}}zlrdi`~cn jt ~bc gleel{dak kz`}b
[b`~ nl ~bc xel}c `ant)da~czhc}~ lg ~bdx kz`}b ~cee tls `jls~ ~bc`wcz`kc SX }zlnsh~dla lg hzsnc lde nszdak ~bdx ~dic }czdln =0>
^bc xel}c lg=0> zc}zcxca~x ` nchedac da `wcz`kc lde }zlnsh~dlalg=0> ideedla j`zzcex }cz n`t }cz tc`z "lz `}}zlrdi`~cet0>=%=== j`zzcex }cz n`t gc{cz c`hb tc`z$
=
2
4
0=
00
: > 7 2 0= 0: 0> 07 02 :=
t
rTc`zx Xdahc 0423
Nlicx~dh ]zlnsh~dla lgHzsnc Lde% 0423:==:
Ideedlax lgJ`zzcex}cz N`t
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Ljoch~dwc 8
4:
^zt D~^bc kz`}b jcel{ ncxhzdjcx ~bc asijcz lg kz`ix lg }l~`xxdsi dlndnc~b`~ {dee ndxxlewc da 0== kz`ix lg {`~cz da ~czix lg ~bc ~ci}cz`~szclg ~bc {`~cz da nckzccx Hcexdsx
[b`~ nlcx ~bc xel}c lg ~bdx kz`}b ~cee tls `jls~ ~bc xlesjded~t lg}l~`xxdsi dlndnc=
7=
2=
0==
0:=
0>=
07=
02=
:==
::=
:>=
0= := 8= >= 3=
Xlesjded~t lg]l~`xxdsi Dlndnc
7= ;= 2= 4= 0==
t
r
^ci}cz`~szc "H$
Xlesjded~t
"kz`ix,0== kz`ixlg {`~cz$
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Ljoch~dwc 8
48
@ h`jec)~cecwdxdla hli}`at hb`zkcx ` .83 dad~d`e dax~`ee`~dla gcc `an~bca .>3 }cz ila~b glz h`jec xczwdhc ^bc kz`}b jcel{ ncxhzdjcx ~bc~l~`e hlx~ lg ~bdx h`jec xczwdhc da ~czix lg ~bc asijcz lg ila~bx d~ dxsxcn
Dg ~bc hli}`at ndxhlsa~cn ~bc hb`zkc ~l .84 }cz ila~b% bl{ {lsen~bdx hb`akc `ggch~ ~bc xel}c `ant)da~czhc}~ lg ~bc kz`}b3 ~l .84 {deenchzc`xc ~bc xel}c lg ~bc kz`}b ^bdx hb`akc {lsen i`fc ~bc kz`}becxx x~cc}
^bc ndxhlsa~ nlcx al~ `ggch~ ~bc dax~`ee`~dla gcc ^bc t)da~czhc}~ lg
~bc kz`}b {lsen zci`da `~ .83
=
3=
0==
03=
:==
:3=
8==
83=
>==
>3=
3==
0 : 8 > 3 7 ; 2 4 0=
t
r
Ila~b
^l~`eHlx~ ".$
Bl{ Nl Tls ]zcndh~ ~bc Cggch~x lg Hb`akdak Xel}cx `an t)Da~czhc}~x da@}}edcn Xd~s`~dlax
Bl{ Nl Tls Xlewc ]zljecix Dawlewdak Ndzch~ W`zd`~dla lz ]zl}lz~dla`eHb`akc37;24 : 8 > 3 7 ; 2 4
r 3 8 = 0 >
t > = 8: 0
0:
@ax{cz Fct? }`kc :28
@ax{cz Fct? }`kc :28
@ax{cz Fct? }`kc :2>
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Ljoch~dwc 8
4;
Pscx~dla :3
^bc kz`}b jcel{ xbl{x ~bc zce`~dlaxbd} jc~{cca~bc asijcz lg ~lax lg cec}b`a~ glln zci`dadak da~bc llx glln x~lz`kc jda `an ~bc asijcz lgn`tx xdahc ~bc glln {`x e`x~ }szhb`xcn!
Bl{ i`at ~lax lg cec}b`a~ glln {czc da ~bc jdadiicnd`~cet `g~cz ~bc e`x~ }szhb`xc lg glln {`x}e`hcn da ~bc jda= ~lax
H 7= ~lax
N 3= ~lax
Pscx~dla :7
^bc osadlz he`xx {dee x}can .3== la nchlz`~dlaxglz ` xhblle }`z~t! ^bc osadlzx {dee }szhb`xcr h`xcx lg j`eellax `ant h`xcx lg x~zc`iczx!J`eellax hlx~ .:3 glz c`hb h`xc% `an x~zc`iczxhlx~ .0:3 glz c`hb h`xc! Dg ~bdx daglzi`~dla dxkz`}bcn `x ` edac`z cps`~dla% {b`~ dx ~bc
r)da~czhc}~ lg ~bc edac37;24 : 8 > 3 7 ; 2 4
=
:=
>=
7=
2=
:= >= 7= 2=
t
r
Asijcz lg N`tx
^laxlg
Glln
@ax{cz Fct? }`kc :2>@ax{cz Fct? }`kc :2>
@ax{cz Fct? }`kc :2>
@ax{cz Fct? }`kc :2>
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Ljoch~dwc 8
42
Pscx~dla :4
[bdhb dx ~bc cps`~dla lg ~bc edac ~b`~ hla~`dax~bc }lda~x "0% 3$ `an ":% 0$r
0:
N t >r 4
Pscx~dla 8=
Olxb ffeex bdx x{diidak }lle `~ ~bc z`~c lg :===k`eelax }cz blsz! ^bczc {czc 8=== k`eelax lg{`~cz da ~bc }lle {bca bc x~`z~cn ffeedak d~! ^bc~l~`e asijcz lg k`eelax lg {`~cz da ~bc }lle `g~czOlxb ffeex d~ glzr blszx h`a jc zc}zcxca~cn jt ~bccps`~dlat :===r 8===! Dg Olxb `nnx `xchlan blxc% bc h`a ffee ~bc }lle ~{dhc `x g`x~!Bl{ {dee ~bdx `ggch~ ~bc kz`}b lg ~bc cps`~dla
@ax{cz Fct? }`kc :2>
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^bc x~snca~ {dee glzise`~c `an sxc edac`z cps`~dlax `an dacps`ed~dcx!
Ljoch~dwc >
44
Glz ~bdx ljoch~dwc tls xblsen jc `jec ~l
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Ljoch~dwc >
0==
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Ljoch~dwc >
0=:
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^zt D~@ zch~`akec b`x ` }czdic~cz lg 3= dahbcx ^bc ecak~b lg ~bc zch~`akecdx xdr dahbcx ecxx ~b`a ~bzcc ~dicx ~bc {dn~b [zd~c ` xtx~ci lgcps`~dlax ~b`~ hlsen jc sxcn ~l ffan ~bc ecak~b `an ~bc {dn~b lg ~bc
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Ljoch~dwc >
0=3
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Xlewc ~bdx xtx~ci lg cps`~dlax sxdak ~bc kz`}bdh`e ic~bln
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0=;
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Ljoch~dwc >
0=2
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Xlewc ~bc x`ic xtx~ci lg cps`~dlax sxdak ~bc cedida`~dla ic~bln
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Ljoch~dwc >
0=4
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Ljoch~dwc >
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Ljoch~dwc >
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Ljoch~dwc 3
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Ljoch~dwc 3
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Ljoch~dwc 3
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^zt D~Dg ~bc kz`}bx lgt r:% t
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Ljoch~dwc 3
0::
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Ljoch~dwc 3
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Ljoch~dwc 3
0:3
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Ljoch~dwc 3
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@ee w`zd`jecx b`wc `acr}laca~! [bca `acr}laca~ dx al~ kdwca% d~dx sanczx~lln ~l jc 0!
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Ljoch~dwc 3
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Ljoch~dwc 3
087
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^zt D~@ zch~`akse`z }zdxi b`x ecak~b :i0:a>% {dn~b 7i8}:% `an bcdkb~>ia3}8 Gdan ~bc wlesic lg ~bc }zdxi
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08;
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Ljoch~dwc 3
082
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Pscx~dla >7
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Pscx~dla 3=
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Ljoch~dwc 3
0>=
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^bc x~snca~ {dee ncilax~z`~c `a sanczx~`andak lg kclic~zdh zce`~dlaxbd}x `an
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Da ~bc nd`kz`i jcel{% GZX dx xdide`z ~l GCN
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Ljoch~dwc 7
0>8
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]lda~ L dx ~bc hca~cz lg ~bc hdzhec jcel{ DgiL@J >=% ffan ~bcic`xszc lg@J
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Ljoch~dwc 7
0>3
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Ljoch~dwc 7
0>7
Bl{ H`a Tls @a`etc `an Ncxhzdjc ]`~~czax da Kclic~zdh Gdkszcx2 hca~dic~czx Dg ~bc }zlhcxxlg glzidak xi`eecz ~zd`akecx da ~bdx {`t hla~dascx% {b`~ dx ~bc}czdic~cz lg ~bc ffg~b ~zd`akec da ~bdx xczdcx2 hi
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Ljoch~dwc 7
0>2
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I`fc ` ~`jec ~l xbl{ ~bc }`~~cza da ~bcxc ffkszcx
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Ljoch~dwc 7
03=
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Ljoch~dwc 7
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Ljoch~dwc 7
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Ljoch~dwc 7
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Ljoch~dwc 7
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