\relax 
\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]{}
\@writefile{toc}{\beamer@endinputifotherversion {3.10pt}}
\@writefile{nav}{\beamer@endinputifotherversion {3.10pt}}
\select@language{english}
\@writefile{toc}{\select@language{english}}
\@writefile{lof}{\select@language{english}}
\@writefile{lot}{\select@language{english}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{1}{1/1}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {1}{1}}}
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\@writefile{nav}{\headcommand {\beamer@framepages {6}{6}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{7}{7/7}{}{0}}}
\@writefile{nav}{\headcommand {\beamer@framepages {7}{7}}}
\@writefile{nav}{\headcommand {\slideentry {0}{0}{8}{8/8}{}{0}}}
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\@writefile{nav}{\headcommand {\beamer@partpages {1}{16}}}
\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{16}}}
\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{16}}}
\@writefile{nav}{\headcommand {\beamer@documentpages {16}}}
\@writefile{nav}{\headcommand {\def \inserttotalframenumber {16}}}