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160 lines
6.6 KiB
160 lines
6.6 KiB
\begin{cofactors}
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$f$ \= $= (((p \land q) \lor (r \land s)) \lor (\lnot p \land \lnot r))$\\
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\>$f_{s}$ \= $= (((p \land q) \lor r) \lor (\lnot p \land \lnot r))$\\
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\>\>$f_{sr}$ \= $= \true$\\
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\>\>$f_{s\lnot r}$ \= $= ((p \land q) \lor \lnot p)$\\
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\>\>\>$f_{s\lnot rq}$ \= $= \true$\\
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\>\>\>$f_{s\lnot r\lnot q}$ \= $= \lnot p$\\
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\>\>\>\>$f_{s\lnot r\lnot qp}$ \= $= \false$\\
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\>\>\>\>$f_{s\lnot r\lnot q\lnot p}$ \= $= \true$\\
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\>$f_{\lnot s}$ \= $= ((p \land q) \lor (\lnot p \land \lnot r))$\\
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\>\>$f_{\lnot sr}$ \= $= (p \land q)$\\
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\>\>\>$f_{\lnot srq}$ \= $= \lnot f_{s\lnot r\lnot q}$\\
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\>\>\>$f_{\lnot sr\lnot q}$ \= $= \false$\\
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\>\>$f_{\lnot s\lnot r}$ \= $= f_{s\lnot r}$\\
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\end{cofactors}
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The final ROBDD:
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\begin{center}
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\scalebox{0.75}{
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\begin{tikzpicture}[>=latex,line join=bevel,]
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\pgfsetlinewidth{1bp}
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%%
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\pgfsetcolor{black}
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% Edge: f_E -> s0
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\draw [] (123.5bp,268.99bp) .. controls (123.5bp,258.92bp) and (123.5bp,243.47bp) .. (123.5bp,233.3bp);
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% Edge: f_s -> r1
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\draw [] (174.5bp,210.99bp) .. controls (174.5bp,200.92bp) and (174.5bp,185.47bp) .. (174.5bp,175.3bp);
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% Edge: f_s!r -> q2
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\draw [] (123.5bp,152.99bp) .. controls (123.5bp,142.92bp) and (123.5bp,127.47bp) .. (123.5bp,117.3bp);
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% Edge: f_s!r!q -> p3
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\draw [] (72.5bp,94.988bp) .. controls (72.5bp,84.921bp) and (72.5bp,69.474bp) .. (72.5bp,59.304bp);
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (72.5bp,79.304bp) node {\Large$\bullet$};
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% Edge: f_!s -> r4
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\draw [] (72.5bp,210.99bp) .. controls (72.5bp,200.92bp) and (72.5bp,185.47bp) .. (72.5bp,175.3bp);
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% Edge: f_!sr -> q5
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\draw [] (21.5bp,152.99bp) .. controls (21.5bp,142.92bp) and (21.5bp,127.47bp) .. (21.5bp,117.3bp);
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% Edge: s0 -> r4
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\draw [] (116.41bp,213.21bp) .. controls (106.66bp,202.51bp) and (89.243bp,183.38bp) .. (79.531bp,172.72bp);
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\draw (92.998bp,187.51bp) node {\Large$\circ$};
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% Edge: s0 -> r1
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\draw [] (130.59bp,213.21bp) .. controls (140.34bp,202.51bp) and (157.76bp,183.38bp) .. (167.47bp,172.72bp);
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% Edge: r4 -> q5
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\draw [] (65.409bp,155.21bp) .. controls (55.665bp,144.51bp) and (38.243bp,125.38bp) .. (28.531bp,114.72bp);
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% Edge: r4 -> q2
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\draw [] (79.591bp,155.21bp) .. controls (89.335bp,144.51bp) and (106.76bp,125.38bp) .. (116.47bp,114.72bp);
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\draw (103.0bp,129.51bp) node {\Large$\circ$};
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% Edge: q5 -> p3
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\draw [] (28.591bp,97.213bp) .. controls (38.335bp,86.514bp) and (55.757bp,67.385bp) .. (65.469bp,56.72bp);
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% Edge: q5 -> 4
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\draw [] (21.5bp,94.988bp) .. controls (21.5bp,79.384bp) and (21.5bp,50.854bp) .. (21.5bp,49.086bp);
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\draw (21.5bp,69.086bp) node {\Large$\bullet$};
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% Edge: r1 -> q2
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\draw [] (167.41bp,155.21bp) .. controls (157.66bp,144.51bp) and (140.24bp,125.38bp) .. (130.53bp,114.72bp);
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\draw (144.0bp,129.51bp) node {\Large$\circ$};
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% Edge: r1 -> 0
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\draw [] (174.5bp,152.99bp) .. controls (174.5bp,137.38bp) and (174.5bp,108.85bp) .. (174.5bp,107.09bp);
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% Edge: q2 -> p3
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\draw [] (116.41bp,97.213bp) .. controls (106.66bp,86.514bp) and (89.243bp,67.385bp) .. (79.531bp,56.72bp);
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\draw (92.998bp,71.507bp) node {\Large$\bullet$};
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% Edge: q2 -> 1
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\draw [] (123.5bp,94.988bp) .. controls (123.5bp,79.384bp) and (123.5bp,50.854bp) .. (123.5bp,49.086bp);
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% Edge: p3 -> 2
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\draw [] (70.281bp,36.791bp) .. controls (67.427bp,23.663bp) and (62.8bp,2.3815bp) .. (62.514bp,1.0642bp);
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% Edge: p3 -> 3
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\draw [] (74.497bp,36.791bp) .. controls (77.066bp,23.663bp) and (81.23bp,2.3815bp) .. (81.487bp,1.0642bp);
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\draw (77.647bp,20.692bp) node {\Large$\bullet$};
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% Node: f_E
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (145.0bp,291.0bp) -- (102.0bp,291.0bp) -- (102.0bp,269.0bp) -- (145.0bp,269.0bp) -- cycle;
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\draw (123.5bp,280.0bp) node {$f$};
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\end{scope}
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% Node: s0
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (123.5bp,222.0bp) ellipse (11.0bp and 11.0bp);
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\draw (123.5bp,222.0bp) node {$s$};
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\end{scope}
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% Node: f_s
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (196.0bp,233.0bp) -- (153.0bp,233.0bp) -- (153.0bp,211.0bp) -- (196.0bp,211.0bp) -- cycle;
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\draw (174.5bp,222.0bp) node {$f_{s}$};
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\end{scope}
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% Node: r1
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (174.5bp,164.0bp) ellipse (11.0bp and 11.0bp);
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\draw (174.5bp,164.0bp) node {$r$};
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\end{scope}
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% Node: f_s!r
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (145.0bp,175.0bp) -- (102.0bp,175.0bp) -- (102.0bp,153.0bp) -- (145.0bp,153.0bp) -- cycle;
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\draw (123.5bp,164.0bp) node {$f_{s\lnot r}$};
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\end{scope}
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% Node: q2
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (123.5bp,106.0bp) ellipse (11.0bp and 11.0bp);
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\draw (123.5bp,106.0bp) node {$q$};
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\end{scope}
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% Node: f_s!r!q
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (94.0bp,117.0bp) -- (51.0bp,117.0bp) -- (51.0bp,95.0bp) -- (94.0bp,95.0bp) -- cycle;
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\draw (72.5bp,106.0bp) node {$f_{s\lnot r\lnot q}$};
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\end{scope}
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% Node: p3
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (72.5bp,48.0bp) ellipse (11.0bp and 11.0bp);
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\draw (72.5bp,48.0bp) node {$p$};
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\end{scope}
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% Node: f_!s
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (94.0bp,233.0bp) -- (51.0bp,233.0bp) -- (51.0bp,211.0bp) -- (94.0bp,211.0bp) -- cycle;
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\draw (72.5bp,222.0bp) node {$f_{\lnot s}$};
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\end{scope}
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% Node: r4
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (72.5bp,164.0bp) ellipse (11.0bp and 11.0bp);
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\draw (72.5bp,164.0bp) node {$r$};
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\end{scope}
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% Node: f_!sr
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (43.0bp,175.0bp) -- (0.0bp,175.0bp) -- (0.0bp,153.0bp) -- (43.0bp,153.0bp) -- cycle;
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\draw (21.5bp,164.0bp) node {$f_{\lnot sr}$};
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\end{scope}
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% Node: q5
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\begin{scope}
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\definecolor{strokecol}{rgb}{0.0,0.0,0.0};
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\pgfsetstrokecolor{strokecol}
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\draw (21.5bp,106.0bp) ellipse (11.0bp and 11.0bp);
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\draw (21.5bp,106.0bp) node {$q$};
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\end{scope}
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%
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\end{tikzpicture}
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}
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\end{center}
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