\s{Definice:} {\I Sí»} je uspoøádaná pìtice $(V,E,z,s,c)$, pro ní¾ platí:
\itemize\ibull
\:$(V,E)$ je orientovaný graf.
-\:$c:E\to{\bb R}_{0}^{+}$ je {\I kapacita} hran.
+\:$c:E\to{\bb R}_{0}^{+}$ je funkce pøiøazující hranám jejich {\I kapacity.}
\:$z,s \in V$ jsou dva vrcholy grafu, kterým øíkáme {\I zdroj} a~{\I stok} (spotøebiè).
\:Graf je symetrický, tedy $\forall u,v \in V: uv \in E \Leftrightarrow vu \in E$\foot{%
Nebude-li hrozit nedorozumìní, budeme hranu z~vrcholu~$u$ do vrcholu~$v$
-znaèit $uv$ namísto formálnìj¹ího, ale ménì pøehledného $(u,v)$. Podobnì pro neorientovaný
-pí¹eme $uv$ namísto $\{u,v\}$.}
+znaèit $uv$ namísto formálnìj¹ího, ale ménì pøehledného $(u,v)$. Podobnì u~neorientovaných
+hran pí¹eme $uv$ namísto $\{u,v\}$.}
(tuto podmínku si~mù¾eme zvolit bez~újmy na~obecnosti, nebo» v¾dy mù¾eme
do~grafu pøidat hranu, která v~nìm je¹tì nebyla, a~dát jí nulovou kapacitu).
%% \figure{tok.eps}{Pøíklad toku. Èísla pøedstavují toky po~hranách, v~závorkách jsou kapacity.}{4in}
-\s{Definice:} Pro libovolnou funkci $f:E \to {\bb R}$ se nám bude hodit následující znaèení:
+Sumy podobné tìm v~Kirchhoffovì zákonì budeme psát èasto, zavedeme si pro nì tedy
+¹ikovné znaèení:
+
+\s{Definice:} Pro libovolnou funkci $f:E \to {\bb R}$ definujeme:
\itemize\ibull
-\:$f^+(v) = \sum_{u: uv \in E}{f(uv)}$ (celkový {\I pøítok} do vrcholu)
-\:$f^-(v) = \sum_{u: vu \in E}{f(vu)}$ (celkový {\I odtok} z~vrcholu)
-\:$f^\Delta(v) = f^+(v) - f^-(v)$ ({\I pøebytek} ve~vrcholu)
+\:$f^+(v) := \sum_{u: uv \in E}{f(uv)}$ (celkový {\I pøítok} do vrcholu)
+\:$f^-(v) := \sum_{u: vu \in E}{f(vu)}$ (celkový {\I odtok} z~vrcholu)
+\:$f^\Delta(v) := f^+(v) - f^-(v)$ ({\I pøebytek} ve~vrcholu)
\endlist
\>(Kirchhoffùv zákon pak øíká prostì to, ¾e $f^\Delta(v)=0$ pro v¹echna $v\ne z,s$.)
-\s{Pozorování:} Nìjaký tok v¾dy existuje. V libovolné síti mù¾eme v¾dy zvolit
-konstantnì nulovou funkci (po~¾ádné hranì nic nepoteèe). To je korektní tok,
-ale sotva u¾iteèný. Budeme chtít najít tok, který pøepraví co nejvíce tekutiny
-ze~zdroje do~spotøebièe.
+\s{Pozorování:} V~ka¾dé síti nìjaký tok existuje: tøeba funkce, která je v¹ude
+nulová (po~¾ádné hranì nic neteèe). To je korektní tok, ale sotva u¾iteèný. Budeme
+chtít najít tok, který pøepraví co nejvíce tekutiny ze~zdroje do~spotøebièe.
\s{Definice:} {\I Velikost toku} $f$ budeme znaèit $\vert f\vert$ a polo¾íme ji
rovnu souètu velikostí toku na hranách vedoucích do spotøebièe minus souèet
\s{Pozorování:} Jeliko¾ sí» tìsní, mìlo by být jedno, zda velikost toku mìøíme
u~spotøebièe nebo u~zdroje. Vskutku, krátkým výpoètem ovìøíme, ¾e tomu tak je:
$$
-f^\Delta(z) - f^\Delta(s) = \sum_v f^\Delta(v) = 0.
+f^\Delta(z) + f^\Delta(s) = \sum_v f^\Delta(v) = 0.
$$
První rovnost platí proto, ¾e podle Kirchhoffova zákona jsou zdroj a spotøebiè jediné
dva vrcholy, jejich¾ pøebytek mù¾e být nenulový. Druhou rovnost získáme tak, ¾e si
\s{První pokus:} Hledejme cestu $P$ ze~$z$ do~$s$ takovou, ¾e~$\forall e \in
P: f(e) < c(e)$ (po~v¹ech jejích hranách teèe ostøe ménì, ne¾ jim dovolují
jejich kapacity). Pak zjevnì mù¾eme tok upravit tak, aby se~jeho velikost
-zvìt¹ila. Zvolme $$\varepsilon := \min_{e \in P} \left(c(e) - f(e)\right).$$ Nový tok $f'$
-pak definujme jako $f'(e):=f(e) + \varepsilon$. Kapacity nepøekroèíme ($\varepsilon$
-je nejvìt¹í mo¾ná hodnota, abychom tok zvìt¹ili, ale nepøekroèili kapacitu ani
-jedné z~hran cesty $P$) a~Kirchhoffovy zákony zùstanou neporu¹eny, nebo» zdroj
-a~stok neomezují a~ka¾dému jinému vrcholu na~cestì $P$ se~pøítok $f^+(v)$
-i~odtok $f^-(v)$ zvìt¹í pøesnì o~$\varepsilon$.
-
-Opakujme tento proces tak dlouho, dokud existují zlep¹ující cesty. A¾ se algoritmus
-zastaví (co¾ by obecnì nemusel, ale nás je¹tì chvíli trápit nemusí), získáme maximální tok?
-Pøekvapivì nemusíme. Napø. na~obrázku je vidìt, ¾e~kdy¾ najdeme nejdøíve cestu
-pøes hranu s~kapacitou 1 (na obrázku tuènì) a~u¾ hodnotu toku na~této hranì
-nesní¾íme, tak dosáhneme velikost toku nejvý¹e 19. Ale maximální tok této sítì
-má velikost 20.
+zvìt¹ila. Zvolme
+$$\varepsilon := \min_{e \in P} \left(c(e) - f(e)\right).$$
+Po ka¾dé hranì zvý¹íme prùtok o~$\varepsilon$, èili definujeme nový tok~$f'$ takto:
+$$
+f'(e) := \cases{
+ f(e) + \varepsilon &\hbox{pro $e\in P$} \cr
+ f(e) &\hbox{pro $e\not\in P$} \cr
+ }
+$$
+To je opìt korektní tok: kapacity nepøekroèíme ($\varepsilon$~jsme zvolili
+nejvy¹¹í mo¾né, aby se to je¹tì nestalo) a~Kirchhoffovy zákony zùstanou
+neporu¹eny, nebo» zdroj a~stok neomezují a~ka¾dému jinému vrcholu na~cestì $P$
+se~pøítok $f^+(v)$ i~odtok $f^-(v)$ zvìt¹í pøesnì o~$\varepsilon$.
+
+Opakujme tento proces tak dlouho, dokud existují cesty, po nich¾ mù¾eme tok
+zlep¹ovat. A¾ se algoritmus zastaví (co¾ by obecnì nemusel, ale to nás je¹tì chvíli
+trápit nemusí), získáme maximální tok?
+Pøekvapivì ne v¾dy. Uva¾ujme napøíklad síti nakreslenou pod tímto odstavcem.
+Najdeme-li nejdøíve cestu pøes svislou hranu (na obrázku tuènì, zlep¹ujeme o~1),
+potom jednu cestu po horní dvojici hran (zlep¹ujeme o~9) a jednu po spodní
+dvojici (zlep¹ujeme také o~9), dostaneme tok o~velikosti 19 a ¾ádná dal¹í cesta
+ho u¾ nemù¾e zlep¹it. Ov¹em maximální tok v~této síti má evidentnì velikost~20.
\figure{toky02.eps}{Èísla pøedstavují kapacity jednotlivých hran.}{1.5in}
\s{Definice:} {\I Rezerva hrany} $uv$ je $r(uv):=c(uv) - f(uv) + f(vu).$
+\s{Definice:} Hranì budeme øíkat {\I nasycená,} pokud má nulovou rezervu.
+Nenasycená cesta je taková, její¾ v¹echny hrany mají nenulovou rezervu.
+
\smallskip
-Algoritmus bude vypadat následovnì. Postupnì doká¾eme, ¾e je koneèný a ¾e v~ka¾dé
-síti najde maximální tok.
+Budeme tedy opakovanì hledat nenasycené cesty a tok po~nich zlep¹ovat.
+Postupnì doká¾eme, ¾e tento postup je koneèný a v~ka¾dé síti najde maximální tok.
\s{Algoritmus (Fordùv-Fulkersonùv)}
\algo
\:$f \leftarrow$ libovolný tok, napø. v¹ude nulový.
-\:Dokud $\exists P$ cesta ze $z$ do $s$ taková, ¾e~$\forall e \in P: r(e) > 0$, opakujeme:
+\:Dokud existuje nenasycená cesta~$P$ ze $z$ do $s$, opakujeme:
\::$\varepsilon \leftarrow \min \{r(e) \mid e \in P\}$.
\::Pro v¹echny hrany $uv \in P$:
\:::$\delta \leftarrow \min \{f(vu),\varepsilon\}$
\:Pro~celoèíselné kapacity se~v~ka¾dém kroku zvìt¹í velikost toku alespoò o~1.
Algoritmus se~tedy zastaví po~nejvíce tolika krocích, kolik je nìjaká horní
-závora pro~velikost maximálního toku -- napø. souèet kapacit v¹ech hran
+mez pro~velikost maximálního toku -- napø. souèet kapacit v¹ech hran
vedoucích do~stoku (tedy $c^+(s)$).
\:Pro~racionální kapacity vyu¾ijeme jednoduchý trik. Nech» $M$ je nejmen¹í
\endlist
\s{Definice:} {\I Øez} je uspoøádaná dvojice mno¾in vrcholù ($A,B$) taková, ¾e
-$A$ a $B$ jsou disjunktní, pokrývají v¹echny vrcholy, $A$ obsahuje zdroj a $B$
-obsahuje stok. Neboli $A \cap B = \emptyset$, $A \cup B = V$, $z \in A$, $s \in B$.
-Mno¾inì~$A$ budeme øíkat {\I levá mno¾ina,} mno¾inì~$B$ {\I pravá.}
-
-\>{\I Kapacitu øezu} definujeme jako souèet kapacit hran zleva doprava, tedy $c(A,B)$.
+$A$ a $B$ jsou disjunktní, dohromady obsahují v¹echny vrcholy, $A$ obsahuje zdroj a $B$
+obsahuje stok.
+Mno¾inì~$A$ budeme øíkat {\I levá mno¾ina øezu,} mno¾inì~$B$ {\I pravá.}
+{\I Kapacitu øezu} definujeme jako souèet kapacit hran zleva doprava, tedy $c(A,B)$.
-\s{Poznámka:} Øezy se~dají definovat více zpùsoby. Jiná obvyklá definice øezu øíká,
+\s{Poznámka:} Jiná obvyklá definice øezu øíká,
¾e øez je mno¾ina hran grafu, po~jejím¾ odebrání se~graf rozpadne na~více
komponent. Tuto vlastnost mají i na¹e øezy, ale opaènì to nemusí platit.
-\s{Lemma:} Pro ka¾dý øez $(A,B)$ a ka¾dý tok~$f$ platí, ¾e $f^\Delta(A,B)
-= \vert f\vert$. (Jinými slovy velikost toku mù¾eme mìøit na libovolném øezu,
-nejen na triviálních øezech kolem zdroje nebo kolem spotøebièe.)
+\s{Lemma:} Pro ka¾dý øez $(A,B)$ a ka¾dý tok~$f$ platí $f^\Delta(A,B)
+= \vert f\vert$.
\proof
Opìt ¹ikovným seètením pøebytkù vrcholù:
do~jiného vrcholu v~$B$ pøispìje jednou kladnì a jednou zápornì; hrany le¾ící
celé mimo~$B$ nepøispìjí vùbec; hrany s~jedním koncem v~$B$ a druhým mimo pøispìjí
jednou, pøièem¾ znaménko se bude li¹it podle toho, který konec je v~$B$. Druhá
-rovnost je snadná: v¹echny vrcholy v~$B$ mimo spotøebièe mají podle Kirchhoffova
-zákona nulový pøebytek.
+rovnost je snadná: v¹echny vrcholy v~$B$ mimo spotøebiè mají podle Kirchhoffova
+zákona nulový pøebytek (zdroj toti¾ v~$B$ nele¾í).
\qed
+\s{Poznámka:} Pùvodní definice velikosti toku coby pøebytku spotøebièe je speciálním
+pøípadem pøedchozího lemmatu -- mìøí toti¾ prùtok pøes øez $(V\setminus\{s\},\{s\})$.
+
\s{Dùsledek:} Pro ka¾dý tok~$f$ a ka¾dý øez $(A,B)$ platí $\vert f \vert \le c(A,B)$.
(Velikost ka¾dého toku je shora omezena kapacitou ka¾dého øezu.)
\s{Dùsledek:} Pokud $\vert f\vert = c(A,B)$, pak je tok~$f$ maximální a øez~$(A,B)$
minimální. Jinými slovy pokud najdeme dvojici tok a stejnì velký øez, mù¾eme øez pou¾ít
-jako certifikát maximality toku. Následující vìta nám zaruèí, ¾e je to mo¾né v¾dy:
+jako certifikát maximality toku. Následující vìta nám zaruèí, ¾e je to v¾dy mo¾né:
\s{Vìta:} Pokud se~Fordùv-Fulkersonùv algoritmus zastaví, tak vydá maximální tok.
\proof
-Nech» se~Fordùv-Fulkersonùv algoritmus zastaví. Definujme mno¾inu vrcholù $A
-:= \{v \in V \mid \hbox{existuje cesta ze~$z$ do~$v$ jdoucí po~hranách s~$r
-> 0$}\}$ a~$B := V \setminus A$.
+Nech» se~Fordùv-Fulkersonùv algoritmus zastaví. Definujme mno¾iny vrcholù $A
+:= \{v \in V \mid \hbox{existuje nenasycená cesta ze~$z$ do~$v$}\}$ a~$B := V \setminus A$.
Dvojice $(A,B)$ je øez, nebo» $z \in A$ (ze~$z$ do~$z$ existuje cesta délky 0)
-a~$s \in B$ (kdyby $s \not\in B$, tak by musela existovat cesta ze~$z$ do~$s$
-s~kladnou rezervou, tudí¾ by algoritmus neskonèil, nýbr¾ tuto cestu vzal
-a~stávající tok vylep¹il).
-
-Dále víme, ¾e~v¹echny hrany øezu mají nulovou rezervu, èili $\forall uv \in
-E(A,B) : r(uv) = 0$ (kdyby mìla hrana $uv$ rezervu nenulovou, tedy kladnou,
-tak by vrchol $v$ patøil do~$A$). Proto po~v¹ech hranách øezu vedoucích z~$A$
-do~$B$ teèe tolik, kolik jsou kapacity tìchto hran, a~po~hranách vedoucích
-z~$B$ do~$A$ neteèe nic, tedy $f(uv) = c(uv)$ a $f(vu) = 0$. Máme øez $(A,B)$
-takový, ¾e~$f^\Delta(A,B) = c(A,B)$. To znamená, ¾e~jsme na¹li maximální tok
-a~minimální øez. \qed
+a~$s \in B$ (kdyby $s \not\in B$, musela by existovat nenasycená cesta ze~$z$ do~$s$,
+tudí¾ by algoritmus neskonèil, nýbr¾ by po této cestì stávající tok vylep¹il).
+
+Dále víme, ¾e~v¹echny hrany øezu mají nulovou rezervu: kdyby toti¾ pro nìjaké $u\in A$
+a $v\in B$ mìla hrana $uv$ rezervu nenulovou (nebyla nasycená), spojením nenasycené
+cesty ze zdroje do~$u$ s~touto hranou by vznikla nenasycená cesta ze~zdroje do~$v$, tak¾e
+vrchol~$v$ by také musel le¾et v~$A$, co¾ není mo¾né.
+
+Proto po~v¹ech hranách øezu vedoucích z~$A$ do~$B$ teèe tolik, kolik jsou
+kapacity tìchto hran, a~po~hranách vedoucích z~$B$ do~$A$ neteèe nic. Nalezli
+jsme tedy øez $(A,B)$ pro nìj¾ $f^\Delta(A,B) = c(A,B)$. To znamená, ¾e~tento
+øez je minimální a tok~$f$ maximální.
+\qed
-Dokázali jsme tedy následující:
+Nyní ji¾ mù¾eme vyslovit vìtu o~chování Fordova-Fulkersonova algoritmu:
-\s{Vìta:} Pro~sí» s~racionálními kapacitami se~Fordùv-Fulkersonùv algoritmus
+\s{Vìta:} Pro ka¾dou sí» s~racionálními kapacitami se~Fordùv-Fulkersonùv algoritmus
zastaví a~vydá maximální tok a~minimální øez.
-\s{Vìta:} Sí» s~celoèíselnými kapacitami má aspoò jeden z~maximálních tokù
+\s{Dùsledek:} Sí» s~celoèíselnými kapacitami má aspoò jeden z~maximálních tokù
celoèíselný a~Fordùv-Fulkersonùv algoritmus takový tok najde.
\proof
-Kdy¾ dostane Fordùv-Fulkersonùv algoritmus celoèíselnou sí», tak najde maximální tok a~ten bude zase celoèíselný (algoritmus nikde nedìlí).
+Kdy¾ dostane Fordùv-Fulkersonùv algoritmus celoèíselnou sí», najde v~ní maximální tok
+a~ten bude zase celoèíselný (algoritmus nikde nevytváøí z~celých èísel necelá).
\qed
-To, ¾e~umíme najít celoèíselné øe¹ení není úplnì samozøejmé. (U~jiných problémù takové ¹tìstí mít nebudeme.) Uka¾me si rovnou jednu aplikaci, která právì celoèíselný tok vyu¾ije.
+To, ¾e~umíme najít celoèíselné øe¹ení, není vùbec samozøejmé.
+(U~jiných problémù takové ¹tìstí mít nebudeme.)
+Uka¾me si rovnou jednu aplikaci, která celoèíselnost vyu¾ije.
\h{Hledání nejvìt¹ího párování v~bipartitních grafech}
hran.
Chceme-li v~daném bipartitním grafu $(V,E)$ nalézt nejmen¹í párování,
-pøetvoøíme jej nejprve na sí» $(V',E',c,z,s)$ takto:
+pøetvoøíme graf nejprve na sí» $(V',E',c,z,s)$ takto:
\itemize\ibull
\:Nalezneme partity grafu, budeme jim øíkat {\I levá} a {\I pravá.}
\>Nyní v~této síti najdeme maximální celoèíselný tok. Jeliko¾ v¹echny hrany
mají kapacitu~1, musí po ka¾dé hranì téci buï~0 nebo~1. Do~výsledného párování
-dáme právì ty hrany pùvodního grafu, po~kterých teèe~1.
+vlo¾íme právì ty hrany pùvodního grafu, po~kterých teèe~1.
Dostaneme opravdu párování? Kdybychom nedostali, znamenalo by to, ¾e nìjaké
-dvì hrany mají spoleèný vrchol. Ov¹em kdyby se setkaly ve~vrcholu v~pravé
-partitì, pøitekly by do tohoto vrcholu alespoò 2 jednotky toku a ty by nemìly
+dvì hrany mají spoleèný vrchol. Ov¹em kdyby se setkaly ve~vrcholu z~pravé
+partity, pøitekly by do tohoto vrcholu alespoò 2 jednotky toku a ty by nemìly
kam odtéci. Analogicky pokud by se setkaly nalevo, musely by z~vrcholu odtéci
alespoò 2 jednotky, ale ty se tam nemají kudy dostat.
-Zbývá nahlédnout, ¾e párování je nejvìt¹í mo¾né. K~tomu si staèí v¹imnout,
+Zbývá nahlédnout, ¾e nalezené párování je nejvìt¹í mo¾né. K~tomu si staèí v¹imnout,
¾e z~toku vytvoøíme párování o~tolika hranách, kolik je velikost toku, a naopak
z~ka¾dého párování umíme vytvoøit celoèíselný tok odpovídající velikosti.
Jinými slovy nalezli jsme bijekci mezi mno¾inou v¹ech celoèíselných tokù
a mno¾inou v¹ech párování a tato bijekce zachovává velikost. Nejvìt¹í
tok tedy musí odpovídat nejvìt¹ímu párování.
-Snadno tak získáme následující vìtu:
+Navíc doká¾eme, ¾e Fordùv-Fulkersonùv algoritmus na sítích tohoto druhu
+pracuje pøekvapivì rychle:
+
+\s{Vìta:} Pro sí», její¾ v¹echny kapacity jsou jednotkové, nalezne Fordùv-Fulkersonùv
+algoritmus maximální tok v~èase $\O(nm)$.
+
+\proof
+Jedna iterace algoritmu bì¾í v~èase $\O(m)$: nenasycenou cestu najdeme prohledáním
+grafu do ¹íøky, samotné zlep¹ení toku zvládneme v~èase lineárním s~délkou cesty.
+Jeliko¾ ka¾dá iterace zlep¹í tok alespoò o~1,\foot{Mimochodem, mù¾e i o~2, proto¾e
+pøi jednotkových kapacitách mohou rezervy být a¾ dvojky.}
+poèet iterací je omezen velikostí maximálního toku, co¾ je nejvý¹e~$n$
+(uva¾ujte øez tvoøený hranami okolo zdroje).
+\qed
-\s{Vìta:} Nejvìt¹í párování v~bipartitním grafu lze nalézt v~èase $\O(mn)$.
+\s{Dùsledek:} Nejvìt¹í párování v~bipartitním grafu lze nalézt v~èase $\O(mn)$.
\proof
Pøedvedená konstrukce vytvoøí z~grafu sí» o~$n'=n+2$ vrcholech a~$m'=m+2n$
%!PS-Adobe-3.0 EPSF-3.0
-%%Creator: inkscape 0.46
+%%Creator: cairo 1.8.10 (http://cairographics.org)
+%%CreationDate: Mon Nov 7 16:15:56 2011
%%Pages: 1
-%%Orientation: Portrait
-%%BoundingBox: 2 1 239 159
-%%HiResBoundingBox: 2.6998657 1.3954594 238.79938 158.58773
+%%BoundingBox: 0 0 236 162
+%%DocumentData: Clean7Bit
+%%LanguageLevel: 2
%%EndComments
+%%BeginProlog
+/cairo_eps_state save def
+/dict_count countdictstack def
+/op_count count 1 sub def
+userdict begin
+/q { gsave } bind def
+/Q { grestore } bind def
+/cm { 6 array astore concat } bind def
+/w { setlinewidth } bind def
+/J { setlinecap } bind def
+/j { setlinejoin } bind def
+/M { setmiterlimit } bind def
+/d { setdash } bind def
+/m { moveto } bind def
+/l { lineto } bind def
+/c { curveto } bind def
+/h { closepath } bind def
+/re { exch dup neg 3 1 roll 5 3 roll moveto 0 rlineto
+ 0 exch rlineto 0 rlineto closepath } bind def
+/S { stroke } bind def
+/f { fill } bind def
+/f* { eofill } bind def
+/B { fill stroke } bind def
+/B* { eofill stroke } bind def
+/n { newpath } bind def
+/W { clip } bind def
+/W* { eoclip } bind def
+/BT { } bind def
+/ET { } bind def
+/pdfmark where { pop globaldict /?pdfmark /exec load put }
+ { globaldict begin /?pdfmark /pop load def /pdfmark
+ /cleartomark load def end } ifelse
+/BDC { mark 3 1 roll /BDC pdfmark } bind def
+/EMC { mark /EMC pdfmark } bind def
+/cairo_store_point { /cairo_point_y exch def /cairo_point_x exch def } def
+/Tj { show currentpoint cairo_store_point } bind def
+/TJ {
+ {
+ dup
+ type /stringtype eq
+ { show } { -0.001 mul 0 cairo_font_matrix dtransform rmoveto } ifelse
+ } forall
+ currentpoint cairo_store_point
+} bind def
+/cairo_selectfont { cairo_font_matrix aload pop pop pop 0 0 6 array astore
+ cairo_font exch selectfont cairo_point_x cairo_point_y moveto } bind def
+/Tf { pop /cairo_font exch def /cairo_font_matrix where
+ { pop cairo_selectfont } if } bind def
+/Td { matrix translate cairo_font_matrix matrix concatmatrix dup
+ /cairo_font_matrix exch def dup 4 get exch 5 get cairo_store_point
+ /cairo_font where { pop cairo_selectfont } if } bind def
+/Tm { 2 copy 8 2 roll 6 array astore /cairo_font_matrix exch def
+ cairo_store_point /cairo_font where { pop cairo_selectfont } if } bind def
+/g { setgray } bind def
+/rg { setrgbcolor } bind def
+/d1 { setcachedevice } bind def
+%%EndProlog
+11 dict begin
+/FontType 42 def
+/FontName /f-0-0 def
+/PaintType 0 def
+/FontMatrix [ 1 0 0 1 0 0 ] def
+/FontBBox [ 0 0 0 0 ] def
+/Encoding 256 array def
+0 1 255 { Encoding exch /.notdef put } for
+Encoding 1 /uni007A put
+Encoding 2 /uni0073 put
+Encoding 3 /uni0031 put
+Encoding 4 /uni0030 put
+/CharStrings 5 dict dup begin
+/.notdef 0 def
+/uni007A 1 def
+/uni0073 2 def
+/uni0031 3 def
+/uni0030 4 def
+end readonly def
+/sfnts [
+<00010000000a008000030020636d6170001bf08d000002640000004863767420078304240000
+02ac000000326670676d058b8542000002e0000000c6676c7966e0eebc34000000ac000001b8
+68656164f4d8164e000003a800000036686865610759031d000003e000000024686d74780895
+00f600000404000000146c6f63610000053000000418000000186d61787001b0086800000430
+000000207072657021912aa40000045000000147000200210000012a029a00030007002eb101
+002f3cb2070417ed32b10605dc3cb2030217ed3200b103002f3cb2050417ed32b2070618fc3c
+b2010217ed323311211127331123210109e8c7c7029afd66210258000001001b000001a201c2
+0013000025323e023717072135012322060723372115010110272e1a0a07120efe87010a8a2d
+20071203015bfef31e0a221e2304870f01952137760ffe6b00010033fff6015c01cb002e0000
+0132373317232e0123220615141f011e0115140623222623220723353316171633323635342f
+012e01353436333216011c010f0b040f11322b222b2b6c2d27533a19540a0f080d1010162039
+262d343a40354d3b213a01b80a884338261e2b19401b3725344c120c9c461d2927212d1e2124
+422a3645130000000001006f0000018a02a400110000132207353717111416171521353e0135
+1134b71236b408243bfeec38270251160e5b02fda82416010f0f021d2f01c52f000000020018
+fff201dc02a400100018000017222e0335343637363332161514060322111020113426fa3452
+30200c352b374f627c7c65830104420e304a61582b589e2a34c09a98c00298febdfec5013c9d
+a500000000000002000300000000001400010000000000340004002000000004000400010000
+f004ffff0000f000ffff10000001000000000006001400000000000500000001000200030004
+000001c20296001e0002000600260026002b0035003c0049005500020006004e00550055005b
+00670067006d0073002102790000b0002cb000134bb02a5058b04a7659b000233f18b0062b58
+3d594bb02a50587d5920d4b001132e182db0012c2020da2fb0072b5c582020472346616a2058
+206462381b2121591b21592db0022c4b5258452359212db0032c691820b040505821b040592d
+b0042cb0062b582123217a58dd1bcd591b4b525858fd1bed591b21b0052b58b046765958dd1b
+cd595959182db0052c0d5c5a2db0062cb12201885058b020885c5c1bb000592db0072cb12401
+885058b040885c5c1bb000592db0082c121120392f2d00000001000000015ba56d22450c5f0f
+3cf5028b03e800000000c7e13c1f00000000c7e13c1ffc91fddf06e703a60000000800000001
+00000000000100000384fed4005a06d8fc91fd6b06e700010000000000000000000000000000
+0005016c002101bc001b0185003301f4006f01f4001800000000000000540000009c00000124
+00000164000001b800010000000501d90040065a0053000200010000000900000100002e000d
+0005b801ff85004bb0085058b101018e59b146062b5821b010594bb014525821b080591db006
+2b5c5800b0032045b0032b44b0052045b20332022bb0032b44b0042045b205f9022bb0032b44
+b0062045b2034f022bb0032b44b0072045ba00067fff00022bb0032b44b0082045b2072f022b
+b0032b44b0092045b20826022bb0032b44b00a2045b20922022bb0032b44b00b2045b20a1c02
+2bb0032b4401b00c2045b0032b44b00f2045b20c4d022bb10346762b44b00e2045b20f12022b
+b10346762b44b00d2045ba000e012300022bb10346762b44b0102045ba000c7fff00022bb103
+46762b44b0112045ba00107fff00022bb10346762b44b0122045b21158022bb10346762b44b0
+132045b21227022bb10346762b44b0142045ba00137fff00022bb10346762b44b0152045b214
+1c022bb10346762b44b0162045b2151b022bb10346762b44590000>
+] def
+FontName currentdict end definefont pop
%%Page: 1 1
-0 160 translate
-0.8 -0.8 scale
-0 0 0 setrgbcolor
-[] 0 setdash
-1 setlinewidth
-0 setlinejoin
-0 setlinecap
-gsave [1 0 0 1 0 0] concat
-gsave [1 0 0 1 65.357439 42.656501] concat
-gsave [1 0 0 1 0 -1.0592059] concat
-gsave [0.5423082 0 0 0.5423082 -77.973242 -183.75924] concat
-gsave
-0 0 0 setrgbcolor
-newpath
-39.28625 459.74622 moveto
-40.326238 459.74622 41.152904 459.67956 41.76625 459.54622 curveto
-42.379569 459.41289 42.859569 459.11956 43.20625 458.66622 curveto
-43.552902 458.21289 43.792901 457.78622 43.92625 457.38622 curveto
-44.059568 456.98622 44.219568 456.31956 44.40625 455.38622 curveto
-45.12625 455.54622 lineto
-44.56625 460.94622 lineto
-29.48625 460.94622 lineto
-29.48625 460.34622 lineto
-40.12625 444.14622 lineto
-34.60625 444.14622 lineto
-33.406245 444.14624 32.592912 444.3729 32.16625 444.82622 curveto
-31.73958 445.2529 31.432914 446.19957 31.24625 447.66622 curveto
-30.52625 447.66622 lineto
-30.64625 442.94622 lineto
-44.52625 442.94622 lineto
-44.52625 443.54622 lineto
-33.76625 459.74622 lineto
-39.28625 459.74622 lineto
-fill
-grestore
-grestore
-gsave [3.701096 0 0 3.701096 -485.99687 -362.02608] concat
-0 0 0 setrgbcolor
-[] 0 setdash
-0.5615024 setlinewidth
-0 setlinejoin
-0 setlinecap
-newpath
-154.48447 87.582116 moveto
-154.34819 139.61237 lineto
-stroke
-gsave [-0.001176566 0.44920038 -0.44920038 -0.001176566 154.46976 93.197121] concat
-gsave
-0 0 0 setrgbcolor
-newpath
-0 0 moveto
-5 -5 lineto
--12.5 0 lineto
-5 5 lineto
-0 0 lineto
-closepath
-eofill
-grestore
-0 0 0 setrgbcolor
-[] 0 setdash
-1.25 setlinewidth
-0 setlinejoin
-0 setlinecap
-newpath
-0 0 moveto
-5 -5 lineto
--12.5 0 lineto
-5 5 lineto
-0 0 lineto
-closepath
-stroke
-grestore
-gsave [0.1548257 0 0 0.1548257 99.409066 44.19146] concat
-gsave
-0 0 0 setrgbcolor
-newpath
-136.33842 442.38977 moveto
-136.33842 447.48542 132.20282 451.62102 127.10717 451.62102 curveto
-122.01152 451.62102 117.87592 447.48542 117.87592 442.38977 curveto
-117.87592 437.29412 122.01152 433.15852 127.10717 433.15852 curveto
-132.20282 433.15852 136.33842 437.29412 136.33842 442.38977 curveto
-closepath
-fill
-grestore
-grestore
-gsave [0.1548257 0 0 0.1548257 170.23357 45.708194] concat
-gsave
-0 0 0 setrgbcolor
-newpath
-136.33842 442.38977 moveto
-136.33842 447.48542 132.20282 451.62102 127.10717 451.62102 curveto
-122.01152 451.62102 117.87592 447.48542 117.87592 442.38977 curveto
-117.87592 437.29412 122.01152 433.15852 127.10717 433.15852 curveto
-132.20282 433.15852 136.33842 437.29412 136.33842 442.38977 curveto
-closepath
-fill
-grestore
-grestore
-gsave [0.1548257 0 0 0.1548257 187.75105 44.864973] concat
-gsave
-0 0 0 setrgbcolor
-newpath
-39.76625 443.34622 moveto
-39.792905 443.34624 40.006238 443.21291 40.40625 442.94622 curveto
-40.84625 442.94622 lineto
-41.00625 448.38622 lineto
-40.40625 448.38622 lineto
-39.952905 446.59957 39.392906 445.3329 38.72625 444.58622 curveto
-38.059574 443.83957 37.152908 443.46624 36.00625 443.46622 curveto
-35.099577 443.46624 34.352911 443.71957 33.76625 444.22622 curveto
-33.206245 444.7329 32.926245 445.38624 32.92625 446.18622 curveto
-32.926245 447.3329 33.499578 448.23957 34.64625 448.90622 curveto
-38.96625 451.46622 lineto
-40.166238 452.18623 41.019571 452.91956 41.52625 453.66622 curveto
-42.05957 454.38623 42.326236 455.23956 42.32625 456.22622 curveto
-42.326236 457.61289 41.766237 458.81289 40.64625 459.82622 curveto
-39.552906 460.83955 38.232907 461.34622 36.68625 461.34622 curveto
-36.019576 461.34622 35.126243 461.22622 34.00625 460.98622 curveto
-32.886246 460.74622 32.192913 460.62622 31.92625 460.62622 curveto
-31.526247 460.62622 31.219581 460.78622 31.00625 461.10622 curveto
-30.48625 461.10622 lineto
-30.48625 454.86622 lineto
-31.12625 454.86622 lineto
-31.152914 455.13289 31.219581 455.46623 31.32625 455.86622 curveto
-31.45958 456.23956 31.57958 456.63956 31.68625 457.06622 curveto
-31.81958 457.46622 32.01958 457.86622 32.28625 458.26622 curveto
-32.552913 458.66622 32.846246 459.03956 33.16625 459.38622 curveto
-33.486245 459.70622 33.912911 459.97289 34.44625 460.18622 curveto
-34.979577 460.37289 35.566243 460.46622 36.20625 460.46622 curveto
-37.219575 460.46622 38.019574 460.21289 38.60625 459.70622 curveto
-39.219573 459.17289 39.526239 458.46622 39.52625 457.58622 curveto
-39.526239 456.38623 38.832906 455.38623 37.44625 454.58622 curveto
-35.12625 453.26622 lineto
-33.419578 452.30623 32.206246 451.38623 31.48625 450.50622 curveto
-30.792914 449.62623 30.446248 448.62623 30.44625 447.50622 curveto
-30.446248 446.06624 30.952914 444.8929 31.96625 443.98622 curveto
-33.006245 443.05291 34.312911 442.58624 35.88625 442.58622 curveto
-36.766242 442.58624 37.592907 442.71957 38.36625 442.98622 curveto
-39.139573 443.22624 39.606239 443.34624 39.76625 443.34622 curveto
-fill
-grestore
-grestore
-gsave
-0 0 0 setrgbcolor
-newpath
-128.9072 127.81223 moveto
-128.83288 127.81223 128.68425 127.85765 128.4613 127.94848 curveto
-128.4613 127.86177 lineto
-129.57604 127.29821 lineto
-129.62559 127.31059 lineto
-129.62559 131.02641 lineto
-129.62559 131.17504 129.66274 131.27207 129.73706 131.31748 curveto
-129.81138 131.3629 129.97033 131.38767 130.21393 131.3918 curveto
-130.21393 131.4847 lineto
-128.50465 131.4847 lineto
-128.50465 131.3918 lineto
-128.73586 131.38354 128.89068 131.35051 128.96913 131.29271 curveto
-129.0517 131.23078 129.09299 131.10279 129.09299 130.90874 curveto
-129.09299 128.1033 lineto
-129.09299 127.90926 129.03106 127.81223 128.9072 127.81223 curveto
-fill
-grestore
-gsave
-0 0 0 setrgbcolor
-newpath
-132.41864 131.5714 moveto
-132.20395 131.5714 132.01197 131.52185 131.84269 131.42277 curveto
-131.67341 131.32368 131.53923 131.19775 131.44014 131.04499 curveto
-131.34106 130.89223 131.25848 130.71676 131.19242 130.51858 curveto
-131.12636 130.31628 131.08095 130.12429 131.05618 129.94263 curveto
-131.0314 129.76097 131.01902 129.58137 131.01902 129.40384 curveto
-131.01902 129.04052 131.07269 128.69577 131.18004 128.3696 curveto
-131.29151 128.04344 131.43602 127.79365 131.61355 127.62025 curveto
-131.84063 127.40556 132.11725 127.29821 132.44342 127.29821 curveto
-132.84802 127.29821 133.17832 127.49639 133.4343 127.89274 curveto
-133.69028 128.2891 133.81826 128.80518 133.81827 129.441 curveto
-133.81826 130.06856 133.69028 130.58051 133.4343 130.97687 curveto
-133.17832 131.37322 132.83977 131.5714 132.41864 131.5714 curveto
-132.42484 127.45923 moveto
-131.88398 127.45923 131.61355 128.12601 131.61355 129.45958 curveto
-131.61355 130.76011 131.88191 131.41038 132.41864 131.41038 curveto
-132.95537 131.41038 133.22373 130.75805 133.22374 129.45338 curveto
-133.22373 128.80518 133.15561 128.3118 133.01937 127.97325 curveto
-132.88312 127.63057 132.68494 127.45923 132.42484 127.45923 curveto
-fill
-grestore
-gsave
-0 0 0 setrgbcolor
-newpath
-157.05212 109.78189 moveto
-156.9778 109.78189 156.82917 109.82731 156.60622 109.91813 curveto
-156.60622 109.83143 lineto
-157.72096 109.26787 lineto
-157.77051 109.28025 lineto
-157.77051 112.99607 lineto
-157.77051 113.1447 157.80766 113.24173 157.88198 113.28714 curveto
-157.9563 113.33256 158.11525 113.35733 158.35885 113.36146 curveto
-158.35885 113.45435 lineto
-156.64957 113.45435 lineto
-156.64957 113.36146 lineto
-156.88078 113.3532 157.0356 113.32017 157.11405 113.26237 curveto
-157.19662 113.20044 157.23791 113.07245 157.23791 112.8784 curveto
-157.23791 110.07296 lineto
-157.23791 109.87892 157.17598 109.78189 157.05212 109.78189 curveto
-fill
-grestore
-gsave
-0 0 0 setrgbcolor
-newpath
-173.91537 127.66329 moveto
-173.84105 127.66329 173.69242 127.70871 173.46947 127.79954 curveto
-173.46947 127.71283 lineto
-174.58421 127.14927 lineto
-174.63376 127.16165 lineto
-174.63376 130.87747 lineto
-174.63376 131.0261 174.67092 131.12313 174.74523 131.16854 curveto
-174.81955 131.21396 174.9785 131.23873 175.2221 131.24286 curveto
-175.2221 131.33575 lineto
-173.51282 131.33575 lineto
-173.51282 131.24286 lineto
-173.74403 131.2346 173.89885 131.20157 173.9773 131.14377 curveto
-174.05987 131.08184 174.10116 130.95385 174.10116 130.7598 curveto
-174.10116 127.95436 lineto
-174.10116 127.76032 174.03923 127.66329 173.91537 127.66329 curveto
-fill
-grestore
-gsave
-0 0 0 setrgbcolor
-newpath
-177.42681 131.42246 moveto
-177.21212 131.42246 177.02014 131.37291 176.85086 131.27382 curveto
-176.68159 131.17474 176.5474 131.04881 176.44832 130.89605 curveto
-176.34923 130.74329 176.26665 130.56782 176.20059 130.36964 curveto
-176.13454 130.16734 176.08912 129.97535 176.06435 129.79369 curveto
-176.03958 129.61203 176.02719 129.43243 176.02719 129.2549 curveto
-176.02719 128.89158 176.08086 128.54683 176.18821 128.22066 curveto
-176.29968 127.8945 176.44419 127.64471 176.62172 127.4713 curveto
-176.8488 127.25662 177.12542 127.14927 177.45159 127.14927 curveto
-177.8562 127.14927 178.18649 127.34745 178.44247 127.7438 curveto
-178.69845 128.14016 178.82644 128.65624 178.82644 129.29206 curveto
-178.82644 129.91962 178.69845 130.43157 178.44247 130.82793 curveto
-178.18649 131.22428 177.84794 131.42246 177.42681 131.42246 curveto
-177.43301 127.31029 moveto
-176.89215 127.31029 176.62172 127.97707 176.62172 129.31063 curveto
-176.62172 130.61117 176.89008 131.26144 177.42681 131.26144 curveto
-177.96354 131.26144 178.23191 130.60911 178.23191 129.30444 curveto
-178.23191 128.65624 178.16378 128.16286 178.02754 127.82431 curveto
-177.89129 127.48163 177.69311 127.31029 177.43301 127.31029 curveto
-fill
-grestore
-gsave
-0 0 0 setrgbcolor
-newpath
-172.59608 93.801434 moveto
-172.52176 93.801438 172.37313 93.846853 172.15018 93.937681 curveto
-172.15018 93.850978 lineto
-173.26492 93.287413 lineto
-173.31447 93.299799 lineto
-173.31447 97.015616 lineto
-173.31447 97.164249 173.35162 97.261273 173.42594 97.306688 curveto
-173.50026 97.352104 173.65921 97.376876 173.90281 97.381004 curveto
-173.90281 97.4739 lineto
-172.19353 97.4739 lineto
-172.19353 97.381004 lineto
-172.42474 97.372747 172.57956 97.339718 172.65801 97.281916 curveto
-172.74058 97.219986 172.78187 97.091997 172.78187 96.897948 curveto
-172.78187 94.092507 lineto
-172.78187 93.898462 172.71994 93.801438 172.59608 93.801434 curveto
-fill
-grestore
-gsave
-0 0 0 setrgbcolor
-newpath
-176.10752 97.560602 moveto
-175.89283 97.560602 175.70085 97.511058 175.53157 97.41197 curveto
-175.3623 97.312881 175.22811 97.186956 175.12903 97.034195 curveto
-175.02994 96.881434 174.94736 96.705965 174.8813 96.507787 curveto
-174.81525 96.305483 174.76983 96.113499 174.74506 95.931836 curveto
-174.72029 95.750175 174.7079 95.570578 174.7079 95.393042 curveto
-174.7079 95.029721 174.76157 94.684976 174.86892 94.358807 curveto
-174.98039 94.032644 175.1249 93.782859 175.30243 93.60945 curveto
-175.52951 93.394763 175.80613 93.287417 176.1323 93.287413 curveto
-176.53691 93.287417 176.8672 93.485594 177.12318 93.881944 curveto
-177.37916 94.278301 177.50715 94.794386 177.50715 95.430201 curveto
-177.50715 96.057762 177.37916 96.569719 177.12318 96.966072 curveto
-176.8672 97.362425 176.52865 97.560602 176.10752 97.560602 curveto
-176.11372 93.448432 moveto
-175.57286 93.448436 175.30243 94.115218 175.30243 95.44878 curveto
-175.30243 96.749316 175.57079 97.399584 176.10752 97.399584 curveto
-176.64425 97.399584 176.91262 96.747252 176.91262 95.442587 curveto
-176.91262 94.794386 176.84449 94.301008 176.70825 93.962453 curveto
-176.572 93.619776 176.37382 93.448436 176.11372 93.448432 curveto
-fill
-grestore
-gsave
-0 0 0 setrgbcolor
-newpath
-129.49917 94.680966 moveto
-129.42485 94.68097 129.27622 94.726385 129.05327 94.817213 curveto
-129.05327 94.73051 lineto
-130.16802 94.166945 lineto
-130.21756 94.179331 lineto
-130.21756 97.895148 lineto
-130.21756 98.043781 130.25472 98.140805 130.32903 98.18622 curveto
-130.40335 98.231636 130.5623 98.256408 130.8059 98.260536 curveto
-130.8059 98.353432 lineto
-129.09662 98.353432 lineto
-129.09662 98.260536 lineto
-129.32783 98.252279 129.48265 98.21925 129.5611 98.161448 curveto
-129.64367 98.099518 129.68496 97.971529 129.68496 97.77748 curveto
-129.68496 94.972038 lineto
-129.68496 94.777994 129.62303 94.68097 129.49917 94.680966 curveto
-fill
-grestore
-gsave
-0 0 0 setrgbcolor
-newpath
-133.01062 98.440134 moveto
-132.79592 98.440134 132.60394 98.39059 132.43466 98.291501 curveto
-132.26539 98.192413 132.13121 98.066488 132.03212 97.913727 curveto
-131.93303 97.760966 131.85045 97.585497 131.7844 97.387319 curveto
-131.71834 97.185015 131.67292 96.993031 131.64815 96.811368 curveto
-131.62338 96.629707 131.61099 96.45011 131.61099 96.272574 curveto
-131.61099 95.909252 131.66466 95.564508 131.77201 95.238339 curveto
-131.88348 94.912176 132.02799 94.662391 132.20552 94.488982 curveto
-132.4326 94.274295 132.70922 94.166949 133.03539 94.166945 curveto
-133.44 94.166949 133.77029 94.365126 134.02627 94.761475 curveto
-134.28225 95.157832 134.41024 95.673918 134.41024 96.309732 curveto
-134.41024 96.937294 134.28225 97.449251 134.02627 97.845603 curveto
-133.77029 98.241957 133.43174 98.440134 133.01062 98.440134 curveto
-133.01681 94.327964 moveto
-132.47595 94.327968 132.20552 94.99475 132.20552 96.328312 curveto
-132.20552 97.628848 132.47389 98.279115 133.01062 98.279115 curveto
-133.54734 98.279115 133.81571 97.626784 133.81571 96.322119 curveto
-133.81571 95.673918 133.74758 95.18054 133.61134 94.841985 curveto
-133.47509 94.499308 133.27691 94.327968 133.01681 94.327964 curveto
-fill
-grestore
-0 0 0 setrgbcolor
-[] 0 setdash
-0.55861318 setlinewidth
-0 setlinejoin
-0 setlinecap
-newpath
-121.42177 114.59451 moveto
-152.90305 139.86417 lineto
-stroke
-gsave [-0.34850538 -0.27974124 0.27974124 -0.34850538 148.54673 136.3674] concat
-gsave
-0 0 0 setrgbcolor
-newpath
-0 0 moveto
-5 -5 lineto
--12.5 0 lineto
-5 5 lineto
-0 0 lineto
-closepath
-eofill
-grestore
-0 0 0 setrgbcolor
-[] 0 setdash
-1.25 setlinewidth
-0 setlinejoin
-0 setlinecap
-newpath
-0 0 moveto
-5 -5 lineto
--12.5 0 lineto
-5 5 lineto
-0 0 lineto
-closepath
-stroke
-grestore
-0 0 0 setrgbcolor
-[] 0 setdash
-0.24528226 setlinewidth
-0 setlinejoin
-0 setlinecap
-newpath
-120.71887 111.30893 moveto
-153.48798 87.176346 lineto
-stroke
-gsave [-0.15800284 0.1163601 -0.1163601 -0.15800284 151.51294 88.630847] concat
-gsave
-0 0 0 setrgbcolor
-newpath
-0 0 moveto
-5 -5 lineto
--12.5 0 lineto
-5 5 lineto
-0 0 lineto
-closepath
-eofill
-grestore
-0 0 0 setrgbcolor
-[] 0 setdash
-1.25 setlinewidth
-0 setlinejoin
-0 setlinecap
-newpath
-0 0 moveto
-5 -5 lineto
--12.5 0 lineto
-5 5 lineto
-0 0 lineto
-closepath
-stroke
-grestore
-0 0 0 setrgbcolor
-[] 0 setdash
-0.24740434 setlinewidth
-0 setlinejoin
-0 setlinecap
-newpath
-155.04488 139.88563 moveto
-188.09749 115.54426 lineto
-stroke
-gsave [-0.1593698 0.11736681 -0.11736681 -0.1593698 186.10537 117.01135] concat
-gsave
-0 0 0 setrgbcolor
-newpath
-0 0 moveto
-5 -5 lineto
--12.5 0 lineto
-5 5 lineto
-0 0 lineto
-closepath
-eofill
-grestore
-0 0 0 setrgbcolor
-[] 0 setdash
-1.25 setlinewidth
-0 setlinejoin
-0 setlinecap
-newpath
-0 0 moveto
-5 -5 lineto
--12.5 0 lineto
-5 5 lineto
-0 0 lineto
-closepath
-stroke
-grestore
-0 0 0 setrgbcolor
-[] 0 setdash
-0.55861318 setlinewidth
-0 setlinejoin
-0 setlinecap
-newpath
-155.81693 87.632824 moveto
-187.25073 112.96152 lineto
-stroke
-gsave [-0.34797977 -0.28039479 0.28039479 -0.34797977 182.90098 109.45659] concat
-gsave
-0 0 0 setrgbcolor
-newpath
-0 0 moveto
-5 -5 lineto
--12.5 0 lineto
-5 5 lineto
-0 0 lineto
-closepath
-eofill
-grestore
-0 0 0 setrgbcolor
-[] 0 setdash
-1.25 setlinewidth
-0 setlinejoin
-0 setlinecap
-newpath
-0 0 moveto
-5 -5 lineto
--12.5 0 lineto
-5 5 lineto
-0 0 lineto
-closepath
-stroke
-grestore
-grestore
-grestore
-grestore
-grestore
+%%BeginPageSetup
+%%PageBoundingBox: 0 0 236 162
+%%EndPageSetup
+q
+0 g
+BT
+17.353862 0 0 17.353862 -0.468554 73.959624 Tm
+/f-0-0 1 Tf
+<01>Tj
+ET
+2.960877 w
+0 J
+0 j
+[] 0.0 d
+1 M q 1 0 0 -1 0 161.154541 cm
+118.199 3.922 m 117.793 157.977 l S Q
+110.992 141.764 m 118.18 161.155 l 125.266 141.725 l 121.062 144.838
+115.297 144.834 110.992 141.764 c h
+110.992 141.764 m f*
+17.625 82.908 m 17.625 80.569 15.73 78.674 13.395 78.674 c 11.059
+78.674 9.164 80.569 9.164 82.908 c 9.164 85.244 11.059 87.139 13.395
+87.139 c 15.73 87.139 17.625 85.244 17.625 82.908 c h
+17.625 82.908 m f
+227.328 78.416 m 227.328 76.08 225.434 74.186 223.098 74.186 c 220.762
+74.186 218.867 76.08 218.867 78.416 c 218.867 80.752 220.762 82.647
+223.098 82.647 c 225.434 82.647 227.328 80.752 227.328 78.416 c h
+227.328 78.416 m f
+BT
+18.336793 0 0 18.336793 229.718306 72.406485 Tm
+/f-0-0 1 Tf
+<02>Tj
+18.336793 0 0 18.336793 39.111284 27.243044 Tm
+<0304>Tj
+4.544614 2.911394 Td
+<03>Tj
+2.722941 -2.887344 Td
+<0304>Tj
+-0.213028 5.467738 Td
+<0304>Tj
+-6.95894 -0.14202 Td
+<0304>Tj
+ET
+q 1 0 0 -1 0 161.154541 cm
+20.305 83.902 m 113.516 158.723 l S Q
+105.922 17.717 m 116.59 -0.002 l 96.988 6.584 l 102.043 7.928 105.637
+12.436 105.922 17.717 c h
+105.922 17.717 m f*
+0.726251 w
+q 1 0 0 -1 0 161.154541 cm
+18.223 74.172 m 115.246 2.719 l S Q
+109.398 154.127 m 108.785 150.065 l 115.246 158.436 l 105.34 154.744 l
+109.398 154.127 l h
+109.398 154.127 m f*
+0.584784 w
+4 M q -1 -0.736443 -0.736443 1 0 161.154541 cm
+-67.574 -56.792 m -65.237 -59.133 l -73.423 -56.791 l -65.238 -54.454 l
+-67.574 -56.792 l h
+-67.574 -56.792 m S Q
+0.732534 w
+1 M q 1 0 0 -1 0 161.154541 cm
+119.855 158.785 m 217.723 86.715 l S Q
+211.824 70.096 m 211.203 65.998 l 217.723 74.44 l 207.727 70.717 l
+211.824 70.096 l h
+211.824 70.096 m f*
+0.589843 w
+4 M q -1 -0.736443 -0.736443 1 0 161.154541 cm
+-93.86 -160.181 m -91.501 -162.541 l -99.758 -160.181 l -91.5 -157.822
+l -93.86 -160.181 l h
+-93.86 -160.181 m S Q
+2.960877 w
+1 M q 1 0 0 -1 0 161.154541 cm
+122.145 4.07 m 215.215 79.066 l S Q
+207.652 97.385 m 218.285 79.651 l 198.695 86.272 l 203.754 87.608
+207.355 92.108 207.652 97.385 c h
+207.652 97.385 m f*
+Q
showpage
+%%Trailer
+count op_count sub {pop} repeat
+countdictstack dict_count sub {end} repeat
+cairo_eps_state restore
%%EOF
<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
<svg
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:cc="http://creativecommons.org/ns#"
xmlns="http://www.w3.org/2000/svg"
xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
- width="300"
- height="200"
+ width="295.12439"
+ height="201.44318"
id="svg2"
inkscape:label="Pozadí"
sodipodi:version="0.32"
- inkscape:version="0.46"
- sodipodi:docname="toky012copy.svg"
+ inkscape:version="0.47 r22583"
+ sodipodi:docname="toky02.svg"
inkscape:output_extension="org.inkscape.output.svg.inkscape"
version="1.0">
<defs
id="defs5013">
+ <marker
+ inkscape:stockid="Arrow2Mend"
+ orient="auto"
+ refY="0"
+ refX="0"
+ id="Arrow2Mend"
+ style="overflow:visible">
+ <path
+ id="path3858"
+ style="font-size:12px;fill-rule:evenodd;stroke-width:0.625;stroke-linejoin:round"
+ d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
+ transform="scale(-0.6,-0.6)" />
+ </marker>
+ <marker
+ inkscape:stockid="Arrow2Mstart"
+ orient="auto"
+ refY="0"
+ refX="0"
+ id="Arrow2Mstart"
+ style="overflow:visible">
+ <path
+ id="path3855"
+ style="font-size:12px;fill-rule:evenodd;stroke-width:0.625;stroke-linejoin:round"
+ d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
+ transform="scale(0.6,0.6)" />
+ </marker>
<marker
inkscape:stockid="Arrow1Lend"
orient="auto"
style="overflow:visible">
<path
id="path3196"
- d="M 0,0 L 5,-5 L -12.5,0 L 5,5 L 0,0 z"
+ d="M 0,0 5,-5 -12.5,0 5,5 0,0 z"
style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;marker-start:none"
transform="matrix(-0.8,0,0,-0.8,-10,0)" />
</marker>
style="overflow:visible">
<path
id="path3193"
- d="M 0,0 L 5,-5 L -12.5,0 L 5,5 L 0,0 z"
+ d="M 0,0 5,-5 -12.5,0 5,5 0,0 z"
style="fill-rule:evenodd;stroke:#000000;stroke-width:1pt;marker-start:none"
transform="matrix(0.8,0,0,0.8,10,0)" />
</marker>
<path
id="path3214"
style="font-size:12px;fill-rule:evenodd;stroke-width:0.625;stroke-linejoin:round"
- d="M 8.7185878,4.0337352 L -2.2072895,0.016013256 L 8.7185884,-4.0017078 C 6.97309,-1.6296469 6.9831476,1.6157441 8.7185878,4.0337352 z"
+ d="M 8.7185878,4.0337352 -2.2072895,0.01601326 8.7185884,-4.0017078 c -1.7454984,2.3720609 -1.7354408,5.6174519 -6e-7,8.035443 z"
transform="matrix(-1.1,0,0,-1.1,-1.1,0)" />
</marker>
<inkscape:perspective
inkscape:pageopacity="0.49019608"
inkscape:pageshadow="2"
inkscape:zoom="2.8323106"
- inkscape:cx="179.88601"
- inkscape:cy="111.07186"
+ inkscape:cx="176.51118"
+ inkscape:cy="111.33435"
inkscape:document-units="px"
inkscape:current-layer="layer1"
showgrid="false"
- inkscape:window-width="1400"
+ inkscape:window-width="1280"
inkscape:window-height="973"
inkscape:window-x="0"
- inkscape:window-y="27" />
+ inkscape:window-y="27"
+ inkscape:window-maximized="0" />
<metadata
id="metadata5016">
<rdf:RDF>
inkscape:label="Vrstva 1"
inkscape:groupmode="layer"
id="layer1"
- transform="translate(65.357439,42.656501)">
+ transform="translate(61.982607,43.837177)">
<flowRoot
xml:space="preserve"
id="flowRoot7653"
- style="font-size:40px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:FreeSerif;-inkscape-font-specification:FreeSerif"><flowRegion
+ style="font-size:40px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;fill:#000000;fill-opacity:1;stroke:none;font-family:FreeSerif;-inkscape-font-specification:FreeSerif"><flowRegion
id="flowRegion7655"><rect
id="rect7657"
width="251.37396"
x="41.185566"
y="519.79022"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:FreeSerif;-inkscape-font-specification:FreeSerif" /></flowRegion><flowPara
- id="flowPara7659"></flowPara></flowRoot> <g
+ id="flowPara7659" /></flowRoot> <g
id="g12524"
transform="translate(0,-1.0592059)">
<flowRoot
transform="matrix(0.5423082,0,0,0.5423082,-77.973242,-183.75924)"
- style="font-size:40px;font-style:normal;font-weight:normal;opacity:1;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ style="font-size:40px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;font-family:Bitstream Vera Sans"
id="flowRoot7637"
xml:space="preserve"><flowRegion
id="flowRegion7639"><rect
transform="matrix(3.701096,0,0,3.701096,-485.99687,-362.02608)"
id="g12500">
<path
- style="opacity:1;fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.5615024;stroke-linecap:butt;stroke-linejoin:miter;marker-start:url(#Arrow1Lstart);marker-end:none;stroke-miterlimit:0.30000001;stroke-dasharray:none;stroke-opacity:1;display:inline"
- d="M 154.48447,87.582116 L 154.34819,139.61237"
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:0.30000001;stroke-opacity:1;stroke-dasharray:none;marker-start:url(#Arrow2Mstart);marker-end:none;display:inline"
+ d="m 154.48447,87.582116 -0.13628,52.030254"
id="path6064"
inkscape:connector-type="polyline" />
<path
sodipodi:type="arc"
- style="opacity:1;fill:#000000;stroke-width:0.977;stroke-miterlimit:5;stroke-dasharray:none"
+ style="fill:#000000;stroke-width:0.977;stroke-miterlimit:5;stroke-dasharray:none"
id="path7633"
sodipodi:cx="127.10717"
sodipodi:cy="442.38977"
sodipodi:rx="9.2312469"
sodipodi:ry="9.2312469"
- d="M 136.33842,442.38977 A 9.2312469,9.2312469 0 1 1 117.87592,442.38977 A 9.2312469,9.2312469 0 1 1 136.33842,442.38977 z"
+ d="m 136.33842,442.38977 c 0,5.09828 -4.13297,9.23125 -9.23125,9.23125 -5.09828,0 -9.23125,-4.13297 -9.23125,-9.23125 0,-5.09828 4.13297,-9.23125 9.23125,-9.23125 5.09828,0 9.23125,4.13297 9.23125,9.23125 z"
transform="matrix(0.1548257,0,0,0.1548257,99.409066,44.19146)" />
<path
sodipodi:type="arc"
- style="opacity:1;fill:#000000;stroke-width:0.977;stroke-miterlimit:5;stroke-dasharray:none"
+ style="fill:#000000;stroke-width:0.977;stroke-miterlimit:5;stroke-dasharray:none"
id="path7635"
sodipodi:cx="127.10717"
sodipodi:cy="442.38977"
sodipodi:rx="9.2312469"
sodipodi:ry="9.2312469"
- d="M 136.33842,442.38977 A 9.2312469,9.2312469 0 1 1 117.87592,442.38977 A 9.2312469,9.2312469 0 1 1 136.33842,442.38977 z"
+ d="m 136.33842,442.38977 c 0,5.09828 -4.13297,9.23125 -9.23125,9.23125 -5.09828,0 -9.23125,-4.13297 -9.23125,-9.23125 0,-5.09828 4.13297,-9.23125 9.23125,-9.23125 5.09828,0 9.23125,4.13297 9.23125,9.23125 z"
transform="matrix(0.1548257,0,0,0.1548257,170.23357,45.708194)" />
<flowRoot
xml:space="preserve"
id="flowRoot7645"
- style="font-size:40px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;opacity:1;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:FreeSerif;-inkscape-font-specification:FreeSerif"
+ style="font-size:40px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;fill:#000000;fill-opacity:1;stroke:none;font-family:FreeSerif;-inkscape-font-specification:FreeSerif"
transform="matrix(0.1548257,0,0,0.1548257,187.75105,44.864973)"><flowRegion
id="flowRegion7647"><rect
id="rect7649"
id="flowPara7651"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:FreeSerif;-inkscape-font-specification:FreeSerif">s</flowPara></flowRoot> <text
xml:space="preserve"
- style="font-size:6.19302797px;font-style:normal;font-weight:normal;opacity:1;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ style="font-size:6.19302797px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;font-family:Bitstream Vera Sans"
x="127.77387"
y="131.4847"
id="text7661"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:FreeSerif;-inkscape-font-specification:FreeSerif">10</tspan></text>
<text
xml:space="preserve"
- style="font-size:6.19302797px;font-style:normal;font-weight:normal;opacity:1;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ style="font-size:6.19302797px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;font-family:Bitstream Vera Sans"
x="155.91879"
y="113.45435"
id="text7665"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:FreeSerif;-inkscape-font-specification:FreeSerif">1</tspan></text>
<text
xml:space="preserve"
- style="font-size:6.19302797px;font-style:normal;font-weight:normal;opacity:1;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ style="font-size:6.19302797px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;font-family:Bitstream Vera Sans"
x="172.78204"
y="131.33575"
id="text7669"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:FreeSerif;-inkscape-font-specification:FreeSerif">10</tspan></text>
<text
xml:space="preserve"
- style="font-size:6.19302797px;font-style:normal;font-weight:normal;opacity:1;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ style="font-size:6.19302797px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;font-family:Bitstream Vera Sans"
x="171.46275"
y="97.4739"
id="text7673"><tspan
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:FreeSerif;-inkscape-font-specification:FreeSerif">10</tspan></text>
<text
xml:space="preserve"
- style="font-size:6.19302797px;font-style:normal;font-weight:normal;opacity:1;fill:#000000;fill-opacity:1;stroke:none;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1;font-family:Bitstream Vera Sans"
+ style="font-size:6.19302797px;font-style:normal;font-weight:normal;fill:#000000;fill-opacity:1;stroke:none;font-family:Bitstream Vera Sans"
x="128.36584"
y="98.353432"
id="text7677"><tspan
y="98.353432"
style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-family:FreeSerif;-inkscape-font-specification:FreeSerif">10</tspan></text>
<path
- style="opacity:1;fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.55861318;stroke-linecap:butt;stroke-linejoin:miter;marker-start:none;marker-end:url(#Arrow1Lend);stroke-miterlimit:0.30000001;stroke-dasharray:none;stroke-opacity:1;display:inline"
- d="M 121.42177,114.59451 L 152.90305,139.86417"
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:0.30000001;stroke-opacity:1;stroke-dasharray:none;marker-start:none;marker-end:url(#Arrow2Mend);display:inline"
+ d="m 121.42177,114.59451 31.48128,25.26966"
id="path8716"
inkscape:connector-type="polyline" />
<g
<path
inkscape:connector-type="polyline"
id="path8720"
- d="M 120.71887,111.30893 L 153.48798,87.176346"
- style="opacity:1;fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.24528226;stroke-linecap:butt;stroke-linejoin:miter;marker-start:none;marker-end:url(#Arrow1Lend);stroke-miterlimit:0.30000001;stroke-dasharray:none;stroke-opacity:1;display:inline" />
+ d="M 120.71887,111.30893 153.48798,87.176346"
+ style="fill:none;stroke:#000000;stroke-width:0.24528226;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:0.30000001;stroke-opacity:1;stroke-dasharray:none;marker-start:none;marker-end:url(#Arrow1Lend);display:inline" />
</g>
<path
- style="opacity:1;fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.24740434;stroke-linecap:butt;stroke-linejoin:miter;marker-start:none;marker-end:url(#Arrow1Lend);stroke-miterlimit:0.30000001;stroke-dasharray:none;stroke-opacity:1;display:inline"
- d="M 155.04488,139.88563 L 188.09749,115.54426"
+ style="fill:none;stroke:#000000;stroke-width:0.24740434;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:0.30000001;stroke-opacity:1;stroke-dasharray:none;marker-start:none;marker-end:url(#Arrow1Lend);display:inline"
+ d="m 155.04488,139.88563 33.05261,-24.34137"
id="path8724"
inkscape:connector-type="polyline" />
<path
- style="opacity:1;fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.55861318;stroke-linecap:butt;stroke-linejoin:miter;marker-start:none;marker-end:url(#Arrow1Lend);stroke-miterlimit:0.30000001;stroke-dasharray:none;stroke-opacity:1;display:inline"
- d="M 155.81693,87.632824 L 187.25073,112.96152"
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:0.30000001;stroke-opacity:1;stroke-dasharray:none;marker-start:none;marker-end:url(#Arrow2Mend);display:inline"
+ d="m 155.81693,87.632824 31.4338,25.328696"
id="path8726"
inkscape:connector-type="polyline" />
</g>
projects / ads2.git / commitdiff
