\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\providecommand\pbs@newkey[2]{}
\providecommand\pbs@seq@push@cx[2]{}
\providecommand\pbs@at@end@dvi@check{}
\pbs@at@end@dvi@check
\providecommand\mix@newkey[2]{}
\pbs@newkey{pbs@last@page}{1}
\providecommand \oddpage@label [2]{}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {1}{1}}}
\pbs@newkey{pbs@last@page}{2}
\pbs@newkey{pbs@last@page}{3}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{2}{2/3}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {2}{3}}}
\pbs@newkey{pbs@last@page}{4}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{3}{4/4}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {4}{4}}}
\pbs@newkey{pbs@last@page}{5}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{4}{5/5}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {5}{5}}}
\pbs@newkey{pbs@last@page}{6}
\pbs@newkey{pbs@last@page}{7}
\pbs@newkey{pbs@last@page}{8}
\pbs@newkey{pbs@last@page}{9}
\pbs@newkey{pbs@last@page}{10}
\pbs@newkey{pbs@last@page}{11}
\pbs@newkey{pbs@last@page}{12}
\pbs@newkey{pbs@last@page}{13}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{5}{6/13}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {6}{13}}}
\pbs@newkey{pbs@last@page}{14}
\pbs@newkey{pbs@last@page}{15}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{6}{14/15}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {14}{15}}}
\@writefile{nav}{\headcommand {\beamer@partpages {1}{15}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{15}}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{15}}}
\@writefile{nav}{\headcommand {\beamer@documentpages {15}}}
\@writefile{nav}{\headcommand {\gdef \inserttotalframenumber {6}}}