thys2/Journal/Paper.tex
changeset 389 d4b3b0f942f4
parent 387 b257b9ba8a25
equal deleted inserted replaced
388:e4cfa64271ed 389:d4b3b0f942f4
   141   \isa{\mbox{}\inferrule{\mbox{r\isactrlsub {\isadigit{1}}\ {\isasymleadsto}\ r\isactrlsub {\isadigit{2}}}}{\mbox{ASEQ\ bs\ r\isactrlsub {\isadigit{1}}\ r\isactrlsub {\isadigit{3}}\ {\isasymleadsto}\ ASEQ\ bs\ r\isactrlsub {\isadigit{2}}\ r\isactrlsub {\isadigit{3}}}}}\\
   141   \isa{\mbox{}\inferrule{\mbox{r\isactrlsub {\isadigit{1}}\ {\isasymleadsto}\ r\isactrlsub {\isadigit{2}}}}{\mbox{ASEQ\ bs\ r\isactrlsub {\isadigit{1}}\ r\isactrlsub {\isadigit{3}}\ {\isasymleadsto}\ ASEQ\ bs\ r\isactrlsub {\isadigit{2}}\ r\isactrlsub {\isadigit{3}}}}}\\
   142   \isa{\mbox{}\inferrule{\mbox{r\isactrlsub {\isadigit{3}}\ {\isasymleadsto}\ r\isactrlsub {\isadigit{4}}}}{\mbox{ASEQ\ bs\ r\isactrlsub {\isadigit{1}}\ r\isactrlsub {\isadigit{3}}\ {\isasymleadsto}\ ASEQ\ bs\ r\isactrlsub {\isadigit{1}}\ r\isactrlsub {\isadigit{4}}}}}\\
   142   \isa{\mbox{}\inferrule{\mbox{r\isactrlsub {\isadigit{3}}\ {\isasymleadsto}\ r\isactrlsub {\isadigit{4}}}}{\mbox{ASEQ\ bs\ r\isactrlsub {\isadigit{1}}\ r\isactrlsub {\isadigit{3}}\ {\isasymleadsto}\ ASEQ\ bs\ r\isactrlsub {\isadigit{1}}\ r\isactrlsub {\isadigit{4}}}}}\\
   143   \isa{\mbox{}\inferrule{\mbox{r\ {\isasymleadsto}\ r{\isacharprime}{\kern0pt}}}{\mbox{AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub {\isadigit{1}}\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}r{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub {\isadigit{2}}{\isacharparenright}{\kern0pt}\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub {\isadigit{1}}\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}r{\isacharprime}{\kern0pt}{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub {\isadigit{2}}{\isacharparenright}{\kern0pt}}}}\\
   143   \isa{\mbox{}\inferrule{\mbox{r\ {\isasymleadsto}\ r{\isacharprime}{\kern0pt}}}{\mbox{AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub {\isadigit{1}}\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}r{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub {\isadigit{2}}{\isacharparenright}{\kern0pt}\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub {\isadigit{1}}\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}r{\isacharprime}{\kern0pt}{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub {\isadigit{2}}{\isacharparenright}{\kern0pt}}}}\\
   144   \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}AZERO{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub b{\isacharparenright}{\kern0pt}\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ rs\isactrlsub b{\isacharparenright}{\kern0pt}}}}\\
   144   \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}AZERO{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub b{\isacharparenright}{\kern0pt}\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ rs\isactrlsub b{\isacharparenright}{\kern0pt}}}}\\
   145   \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}AALTs\ bs\isactrlsub {\isadigit{1}}\ rs\isactrlsub {\isadigit{1}}{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub b{\isacharparenright}{\kern0pt}\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ map\ {\isacharparenleft}{\kern0pt}fuse\ bs\isactrlsub {\isadigit{1}}{\isacharparenright}{\kern0pt}\ rs\isactrlsub {\isadigit{1}}\ {\isacharat}{\kern0pt}\ rs\isactrlsub b{\isacharparenright}{\kern0pt}}}}\\
   145   \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}AALTs\ bs\isactrlsub {\isadigit{1}}\ rs\isactrlsub {\isadigit{1}}{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub b{\isacharparenright}{\kern0pt}\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ map\ {\isacharparenleft}{\kern0pt}fuse\ bs\isactrlsub {\isadigit{1}}{\isacharparenright}{\kern0pt}\ rs\isactrlsub {\isadigit{1}}\ {\isacharat}{\kern0pt}\ rs\isactrlsub b{\isacharparenright}{\kern0pt}}}}\\
   146   \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ {\isacharparenleft}{\kern0pt}bs\ {\isacharat}{\kern0pt}\ bs\isactrlsub {\isadigit{1}}{\isacharparenright}{\kern0pt}\ rs\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}map\ {\isacharparenleft}{\kern0pt}fuse\ bs\isactrlsub {\isadigit{1}}{\isacharparenright}{\kern0pt}\ rs{\isacharparenright}{\kern0pt}}}}\\
       
   147   \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ bs\ {\isacharbrackleft}{\kern0pt}{\isacharbrackright}{\kern0pt}\ {\isasymleadsto}\ AZERO}}}\\
       
   148   \isa{\mbox{}\inferrule{\mbox{}}{\mbox{AALTs\ bs\ {\isacharbrackleft}{\kern0pt}r\isactrlsub {\isadigit{1}}{\isacharbrackright}{\kern0pt}\ {\isasymleadsto}\ fuse\ bs\ r\isactrlsub {\isadigit{1}}}}}\\
       
   149   \isa{\mbox{}\inferrule{\mbox{a\isactrlsub {\isadigit{1}}\mbox{$^\downarrow$}\ {\isacharequal}{\kern0pt}\ a\isactrlsub {\isadigit{2}}\mbox{$^\downarrow$}}}{\mbox{AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}a\isactrlsub {\isadigit{1}}{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub b\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}a\isactrlsub {\isadigit{2}}{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub c{\isacharparenright}{\kern0pt}\ {\isasymleadsto}\ AALTs\ bs\ {\isacharparenleft}{\kern0pt}rs\isactrlsub a\ {\isacharat}{\kern0pt}\ {\isacharbrackleft}{\kern0pt}a\isactrlsub {\isadigit{1}}{\isacharbrackright}{\kern0pt}\ {\isacharat}{\kern0pt}\ rs\isactrlsub b\ {\isacharat}{\kern0pt}\ rs\isactrlsub c{\isacharparenright}{\kern0pt}}}}\\
       
   150 
       
   151   \end{tabular}
   146   \end{tabular}
   152 \end{center}
   147 \end{center}
   153 
   148 
   154 
   149 
   155 And these can be made compact by the following simplification function:
   150 And these can be made compact by the following simplification function:
   226 \end{center}
   221 \end{center}
   227 
   222 
   228 This rule allows us to simplify \mbox{\isa{{\isacharparenleft}{\kern0pt}a\ {\isacharplus}{\kern0pt}\ b{\isacharparenright}{\kern0pt}\ {\isasymcdot}\ c\ {\isacharplus}{\kern0pt}\ a\ {\isasymcdot}\ c}}
   223 This rule allows us to simplify \mbox{\isa{{\isacharparenleft}{\kern0pt}a\ {\isacharplus}{\kern0pt}\ b{\isacharparenright}{\kern0pt}\ {\isasymcdot}\ c\ {\isacharplus}{\kern0pt}\ a\ {\isasymcdot}\ c}}
   229  into  \mbox{\isa{a\ {\isasymcdot}\ c\ {\isacharplus}{\kern0pt}\ b\ {\isasymcdot}\ c}},
   224  into  \mbox{\isa{a\ {\isasymcdot}\ c\ {\isacharplus}{\kern0pt}\ b\ {\isasymcdot}\ c}},
   230 which  cannot be done under the rrewrite rule because only alternatives which are
   225 which  cannot be done under the rrewrite rule because only alternatives which are
   231 children of another alternative can be spilled out.%
   226 children of another alternative can be spilled out.
       
   227 
       
   228 Now with this rule we have some examples where we get
       
   229 even smaller intermediate derivatives than not having this
       
   230 rule:
       
   231 $\textit{(a+aa)}^* \rightarrow \textit{(1+1a)(a+aa)}^* \rightarrow
       
   232  \textit{(1+a)(a+aa)}^* $%
   232 \end{isamarkuptext}\isamarkuptrue%
   233 \end{isamarkuptext}\isamarkuptrue%
   233 %
   234 %
   234 \isadelimdocument
   235 \isadelimdocument
   235 %
   236 %
   236 \endisadelimdocument
   237 \endisadelimdocument
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  2104 %:%453=501%:%
  2104 %:%454=498%:%
  2105 %:%454=502%:%
  2105 %:%455=499%:%
  2106 %:%455=503%:%
  2106 %:%456=500%:%
  2107 %:%456=504%:%
  2107 %:%457=501%:%
  2108 %:%457=505%:%
  2108 %:%458=502%:%
  2109 %:%458=506%:%
  2109 %:%459=503%:%
  2110 %:%459=507%:%
  2110 %:%460=504%:%
  2111 %:%460=508%:%
  2111 %:%461=505%:%
  2112 %:%461=509%:%
  2112 %:%462=506%:%
  2113 %:%462=510%:%
  2113 %:%463=507%:%
  2114 %:%463=511%:%
  2114 %:%464=508%:%
  2115 %:%464=512%:%
  2115 %:%465=509%:%
  2116 %:%465=513%:%
  2116 %:%466=510%:%
  2117 %:%466=514%:%
  2117 %:%467=511%:%
  2118 %:%467=515%:%
  2118 %:%468=512%:%
  2119 %:%468=516%:%
  2119 %:%469=513%:%
  2120 %:%469=517%:%
  2120 %:%470=514%:%
  2121 %:%470=518%:%
  2121 %:%471=515%:%
  2122 %:%471=519%:%
  2122 %:%472=516%:%
  2123 %:%472=520%:%
  2123 %:%473=517%:%
  2124 %:%473=521%:%
  2124 %:%474=518%:%
  2125 %:%474=522%:%
  2125 %:%475=519%:%
  2126 %:%475=523%:%
  2126 %:%476=520%:%
  2127 %:%476=524%:%
  2127 %:%477=521%:%
  2128 %:%477=525%:%
  2128 %:%478=522%:%
  2129 %:%478=526%:%
  2129 %:%479=523%:%
  2130 %:%479=527%:%
  2130 %:%480=524%:%
  2131 %:%480=528%:%
  2131 %:%481=525%:%
  2132 %:%481=529%:%
  2132 %:%482=526%:%
  2133 %:%482=530%:%
  2133 %:%483=527%:%
  2134 %:%483=531%:%
  2134 %:%484=528%:%
  2135 %:%484=532%:%
  2135 %:%485=529%:%
  2136 %:%485=533%:%
  2136 %:%485=530%:%
  2137 %:%486=534%:%
  2137 %:%486=531%:%
  2138 %:%486=535%:%
  2138 %:%487=532%:%
  2139 %:%487=536%:%
  2139 %:%488=533%:%
  2140 %:%488=537%:%
  2140 %:%489=534%:%
  2141 %:%489=538%:%
  2141 %:%490=535%:%
  2142 %:%490=539%:%
  2142 %:%490=536%:%
  2143 %:%491=540%:%
  2143 %:%491=537%:%
  2144 %:%491=541%:%
  2144 %:%492=538%:%
  2145 %:%492=542%:%
  2145 %:%493=539%:%
  2146 %:%493=543%:%
  2146 %:%494=540%:%
  2147 %:%494=544%:%
  2147 %:%495=541%:%
  2148 %:%495=545%:%
  2148 %:%496=542%:%
  2149 %:%496=546%:%
  2149 %:%497=543%:%
  2150 %:%497=547%:%
  2150 %:%498=544%:%
  2151 %:%498=548%:%
  2151 %:%499=545%:%
  2152 %:%499=549%:%
  2152 %:%500=546%:%
  2153 %:%500=550%:%
  2153 %:%501=547%:%
  2154 %:%501=551%:%
  2154 %:%502=548%:%
  2155 %:%502=552%:%
  2155 %:%503=549%:%
  2156 %:%503=553%:%
  2156 %:%504=550%:%
  2157 %:%504=554%:%
  2157 %:%505=551%:%
  2158 %:%505=555%:%
  2158 %:%506=552%:%
  2159 %:%506=556%:%
  2159 %:%507=553%:%
  2160 %:%507=557%:%
  2160 %:%508=554%:%
  2161 %:%508=558%:%
  2161 %:%509=555%:%
  2162 %:%509=559%:%
  2162 %:%510=556%:%
  2163 %:%510=560%:%
  2163 %:%511=557%:%
  2164 %:%511=561%:%
  2164 %:%512=558%:%
  2165 %:%512=562%:%
  2165 %:%513=559%:%
  2166 %:%513=563%:%
  2166 %:%514=560%:%
  2167 %:%514=564%:%
  2167 %:%515=561%:%
  2168 %:%515=565%:%
  2168 %:%516=562%:%
  2169 %:%516=566%:%
  2169 %:%517=563%:%
  2170 %:%517=567%:%
  2170 %:%518=564%:%
  2171 %:%518=568%:%
  2171 %:%519=565%:%
  2172 %:%519=569%:%
  2172 %:%520=566%:%
  2173 %:%520=570%:%
  2173 %:%521=567%:%
  2174 %:%521=571%:%
  2174 %:%522=568%:%
  2175 %:%522=572%:%
  2175 %:%523=569%:%
  2176 %:%523=573%:%
  2176 %:%524=570%:%
  2177 %:%524=574%:%
  2177 %:%525=571%:%
  2178 %:%525=575%:%
  2178 %:%526=572%:%
  2179 %:%526=576%:%
  2179 %:%527=573%:%
  2180 %:%527=577%:%
  2180 %:%528=574%:%
  2181 %:%528=578%:%
  2181 %:%529=575%:%
  2182 %:%529=579%:%
  2182 %:%530=576%:%
  2183 %:%530=580%:%
  2183 %:%531=577%:%
  2184 %:%531=581%:%
  2184 %:%532=578%:%
  2185 %:%532=582%:%
  2185 %:%533=579%:%
  2186 %:%533=583%:%
  2186 %:%534=580%:%
  2187 %:%534=584%:%
  2187 %:%535=581%:%
  2188 %:%535=585%:%
  2188 %:%536=582%:%
  2189 %:%536=586%:%
  2189 %:%537=583%:%
  2190 %:%537=587%:%
  2190 %:%538=584%:%
  2191 %:%538=588%:%
  2191 %:%539=585%:%
  2192 %:%539=589%:%
  2192 %:%540=586%:%
  2193 %:%540=590%:%
  2193 %:%541=587%:%
  2194 %:%541=591%:%
  2194 %:%542=588%:%
  2195 %:%542=592%:%
  2195 %:%543=589%:%
  2196 %:%543=593%:%
  2196 %:%544=590%:%
  2197 %:%544=594%:%
  2197 %:%545=591%:%
  2198 %:%545=595%:%
  2198 %:%546=592%:%
  2199 %:%546=596%:%
  2199 %:%547=593%:%
  2200 %:%547=597%:%
  2200 %:%548=594%:%
  2201 %:%548=598%:%
  2201 %:%549=595%:%
  2202 %:%549=599%:%
  2202 %:%550=596%:%
  2203 %:%550=600%:%
  2203 %:%551=597%:%
  2204 %:%551=601%:%
  2204 %:%552=598%:%
  2205 %:%552=602%:%
  2205 %:%553=599%:%
  2206 %:%553=603%:%
  2206 %:%554=600%:%
  2207 %:%554=604%:%
  2207 %:%555=601%:%
  2208 %:%555=605%:%
  2208 %:%556=602%:%
  2209 %:%556=606%:%
  2209 %:%557=603%:%
  2210 %:%557=607%:%
  2210 %:%558=604%:%
  2211 %:%558=608%:%
  2211 %:%559=605%:%
  2212 %:%559=609%:%
  2212 %:%560=606%:%
  2213 %:%560=610%:%
  2213 %:%561=607%:%
  2214 %:%561=611%:%
  2214 %:%562=608%:%
  2215 %:%562=612%:%
  2215 %:%563=609%:%
  2216 %:%563=613%:%
  2216 %:%564=610%:%
  2217 %:%564=614%:%
  2217 %:%565=611%:%
  2218 %:%565=615%:%
  2218 %:%566=612%:%
  2219 %:%566=616%:%
  2219 %:%567=613%:%
  2220 %:%567=617%:%
  2220 %:%568=614%:%
  2221 %:%568=618%:%
  2221 %:%569=615%:%
  2222 %:%569=619%:%
  2222 %:%570=616%:%
  2223 %:%570=620%:%
  2223 %:%571=617%:%
  2224 %:%571=621%:%
  2224 %:%572=618%:%
  2225 %:%572=622%:%
  2225 %:%573=619%:%
  2226 %:%573=623%:%
  2226 %:%574=620%:%
  2227 %:%574=624%:%
  2227 %:%575=621%:%
  2228 %:%575=625%:%
  2228 %:%576=622%:%
  2229 %:%576=626%:%
  2229 %:%577=623%:%
  2230 %:%577=627%:%
  2230 %:%578=624%:%
  2231 %:%578=628%:%
  2231 %:%579=625%:%
  2232 %:%579=629%:%
  2232 %:%588=629%:%
  2233 %:%580=630%:%
  2233 %:%600=633%:%
  2234 %:%589=634%:%
  2234 %:%601=634%:%
  2235 %:%601=638%:%
  2235 %:%602=635%:%
  2236 %:%602=639%:%
  2236 %:%603=636%:%
  2237 %:%603=640%:%
  2237 %:%604=637%:%
  2238 %:%604=641%:%
  2238 %:%605=638%:%
  2239 %:%605=642%:%
  2239 %:%606=639%:%
  2240 %:%606=643%:%
  2240 %:%607=640%:%
  2241 %:%607=644%:%
  2241 %:%608=641%:%
  2242 %:%608=645%:%
  2242 %:%609=642%:%
  2243 %:%609=646%:%
  2243 %:%610=643%:%
  2244 %:%610=647%:%
  2244 %:%611=644%:%
  2245 %:%611=648%:%
  2245 %:%612=645%:%
  2246 %:%612=649%:%
  2246 %:%613=646%:%
  2247 %:%613=650%:%
  2247 %:%614=647%:%
  2248 %:%614=651%:%
  2248 %:%615=648%:%
  2249 %:%615=652%:%
  2249 %:%616=649%:%
  2250 %:%616=653%:%
  2250 %:%617=650%:%
  2251 %:%617=654%:%
  2251 %:%618=651%:%
  2252 %:%618=655%:%
  2252 %:%619=652%:%
  2253 %:%619=656%:%
  2253 %:%620=653%:%
  2254 %:%620=657%:%
  2254 %:%621=654%:%
  2255 %:%621=658%:%
  2255 %:%622=655%:%
  2256 %:%622=659%:%
  2256 %:%623=656%:%
  2257 %:%623=660%:%
  2257 %:%624=657%:%
  2258 %:%624=661%:%
  2258 %:%625=658%:%
  2259 %:%625=662%:%
  2259 %:%626=659%:%
  2260 %:%626=663%:%
  2260 %:%627=660%:%
  2261 %:%627=664%:%
  2261 %:%628=661%:%
  2262 %:%628=665%:%
  2262 %:%629=662%:%
  2263 %:%629=666%:%
  2263 %:%630=663%:%
  2264 %:%630=667%:%
  2264 %:%631=664%:%
  2265 %:%631=668%:%
  2265 %:%632=665%:%
  2266 %:%632=669%:%
  2266 %:%633=666%:%
  2267 %:%633=670%:%
  2267 %:%634=667%:%
  2268 %:%634=671%:%
  2268 %:%635=668%:%
  2269 %:%635=672%:%
  2269 %:%636=669%:%
  2270 %:%636=673%:%
  2270 %:%637=670%:%
  2271 %:%637=674%:%
  2271 %:%638=671%:%
  2272 %:%638=675%:%
  2272 %:%639=672%:%
  2273 %:%639=676%:%
  2273 %:%640=673%:%
  2274 %:%640=677%:%
  2274 %:%641=674%:%
  2275 %:%641=678%:%
  2275 %:%642=675%:%
  2276 %:%642=679%:%
  2276 %:%643=676%:%
  2277 %:%643=680%:%
  2277 %:%644=677%:%
  2278 %:%644=681%:%
  2278 %:%645=678%:%
  2279 %:%645=682%:%
  2279 %:%646=679%:%
  2280 %:%646=683%:%
  2280 %:%647=680%:%
  2281 %:%647=684%:%
  2281 %:%648=681%:%
  2282 %:%648=685%:%
  2282 %:%649=682%:%
  2283 %:%649=686%:%
  2283 %:%650=683%:%
  2284 %:%650=687%:%
  2284 %:%651=684%:%
  2285 %:%651=688%:%
  2285 %:%652=685%:%
  2286 %:%652=689%:%
  2286 %:%653=686%:%
  2287 %:%653=690%:%
  2287 %:%654=687%:%
  2288 %:%654=691%:%
  2288 %:%655=688%:%
  2289 %:%655=692%:%
  2289 %:%656=689%:%
  2290 %:%656=693%:%
  2290 %:%657=690%:%
  2291 %:%657=694%:%
  2291 %:%658=691%:%
  2292 %:%658=695%:%
  2292 %:%659=692%:%
  2293 %:%659=696%:%
  2293 %:%660=693%:%
  2294 %:%660=697%:%
  2294 %:%661=694%:%
  2295 %:%661=698%:%
  2295 %:%662=695%:%
  2296 %:%662=699%:%
  2296 %:%663=696%:%
  2297 %:%663=700%:%
  2297 %:%664=697%:%
  2298 %:%664=701%:%
  2298 %:%665=698%:%
  2299 %:%665=702%:%
  2299 %:%666=699%:%
  2300 %:%666=703%:%
  2300 %:%667=700%:%
  2301 %:%667=704%:%
  2301 %:%668=701%:%
  2302 %:%668=705%:%
  2302 %:%669=702%:%
  2303 %:%669=706%:%
  2303 %:%670=703%:%
  2304 %:%670=707%:%
  2304 %:%671=704%:%
  2305 %:%671=708%:%
  2305 %:%672=705%:%
  2306 %:%672=709%:%
  2306 %:%673=706%:%
  2307 %:%673=710%:%
  2307 %:%674=707%:%
  2308 %:%674=711%:%
  2308 %:%675=708%:%
  2309 %:%675=712%:%
  2309 %:%676=709%:%
  2310 %:%676=713%:%
  2310 %:%677=710%:%
  2311 %:%677=714%:%
  2311 %:%678=711%:%
  2312 %:%678=715%:%
  2312 %:%679=712%:%
  2313 %:%679=716%:%
  2313 %:%680=713%:%
  2314 %:%680=717%:%
  2314 %:%681=714%:%
  2315 %:%681=718%:%
  2315 %:%682=715%:%
  2316 %:%682=719%:%
  2316 %:%683=716%:%
  2317 %:%683=720%:%
  2317 %:%684=717%:%
  2318 %:%684=721%:%
  2318 %:%685=718%:%
  2319 %:%685=722%:%
  2319 %:%686=719%:%
  2320 %:%686=723%:%
  2320 %:%687=720%:%
  2321 %:%687=724%:%
  2321 %:%688=721%:%
  2322 %:%688=725%:%
  2322 %:%689=722%:%
  2323 %:%689=726%:%
  2323 %:%690=723%:%
  2324 %:%690=727%:%
  2324 %:%691=724%:%
  2325 %:%691=728%:%
  2325 %:%692=725%:%
  2326 %:%692=729%:%
  2326 %:%693=726%:%
  2327 %:%693=730%:%
  2327 %:%694=727%:%
  2328 %:%694=731%:%
  2328 %:%695=728%:%
  2329 %:%695=732%:%
  2329 %:%696=729%:%
  2330 %:%696=733%:%
  2330 %:%697=730%:%
  2331 %:%697=734%:%
  2331 %:%698=731%:%
  2332 %:%698=735%:%
  2332 %:%699=732%:%
  2333 %:%699=736%:%
  2333 %:%700=733%:%
  2334 %:%700=737%:%
  2334 %:%701=734%:%
  2335 %:%701=738%:%
  2335 %:%702=735%:%
  2336 %:%702=739%:%
  2336 %:%703=736%:%
  2337 %:%703=740%:%
  2337 %:%704=737%:%
  2338 %:%704=741%:%
  2338 %:%705=738%:%
  2339 %:%705=742%:%
  2339 %:%706=739%:%
  2340 %:%706=743%:%
  2340 %:%707=740%:%
  2341 %:%707=744%:%
  2341 %:%708=741%:%
  2342 %:%708=745%:%
  2342 %:%709=742%:%
  2343 %:%709=746%:%
  2343 %:%710=743%:%
  2344 %:%710=747%:%
  2344 %:%711=744%:%
  2345 %:%711=748%:%
  2345 %:%712=745%:%
  2346 %:%712=749%:%
  2346 %:%713=746%:%
  2347 %:%713=750%:%
  2347 %:%714=747%:%
  2348 %:%714=751%:%
  2348 %:%714=748%:%
  2349 %:%715=752%:%
  2349 %:%715=749%:%
  2350 %:%715=753%:%
  2350 %:%715=750%:%
  2351 %:%716=754%:%
  2351 %:%716=751%:%
  2352 %:%716=755%:%
  2352 %:%717=752%:%
  2353 %:%717=756%:%
  2353 %:%717=753%:%
  2354 %:%718=757%:%
  2354 %:%718=754%:%
  2355 %:%718=758%:%
  2355 %:%719=755%:%
  2356 %:%719=759%:%
  2356 %:%720=756%:%
  2357 %:%720=760%:%
  2357 %:%721=757%:%
  2358 %:%721=761%:%
  2358 %:%722=758%:%
  2359 %:%722=762%:%
  2359 %:%723=759%:%
  2360 %:%723=763%:%
  2360 %:%724=760%:%
  2361 %:%724=764%:%
  2361 %:%725=761%:%
  2362 %:%725=765%:%
  2362 %:%726=762%:%
  2363 %:%726=766%:%
  2363 %:%727=763%:%
  2364 %:%727=767%:%
  2364 %:%728=764%:%
  2365 %:%728=768%:%
  2365 %:%729=765%:%
  2366 %:%729=769%:%
  2366 %:%730=766%:%
  2367 %:%730=770%:%
  2367 %:%731=767%:%
  2368 %:%731=771%:%
  2368 %:%732=768%:%
  2369 %:%732=772%:%
  2369 %:%733=769%:%
  2370 %:%733=773%:%
  2370 %:%734=770%:%
  2371 %:%734=774%:%
  2371 %:%735=771%:%
  2372 %:%735=775%:%
  2372 %:%736=772%:%
  2373 %:%736=776%:%
  2373 %:%737=773%:%
  2374 %:%737=777%:%
  2374 %:%738=774%:%
  2375 %:%738=778%:%
  2375 %:%739=775%:%
  2376 %:%739=779%:%
  2376 %:%740=776%:%
  2377 %:%740=780%:%
  2377 %:%741=777%:%
  2378 %:%741=781%:%
  2378 %:%742=778%:%
  2379 %:%742=782%:%
  2379 %:%743=779%:%
  2380 %:%743=783%:%
  2380 %:%744=780%:%
  2381 %:%744=784%:%
  2381 %:%745=781%:%
  2382 %:%745=785%:%
  2382 %:%746=782%:%
  2383 %:%746=786%:%
  2383 %:%747=783%:%
  2384 %:%747=787%:%
  2384 %:%748=784%:%
  2385 %:%748=788%:%
  2385 %:%749=785%:%
  2386 %:%749=789%:%
  2386 %:%750=786%:%
  2387 %:%750=790%:%
  2387 %:%751=787%:%
  2388 %:%751=791%:%
  2388 %:%752=788%:%
  2389 %:%752=792%:%
  2389 %:%753=789%:%
  2390 %:%753=793%:%
  2390 %:%754=790%:%
  2391 %:%754=794%:%
  2391 %:%755=791%:%
  2392 %:%755=795%:%
  2392 %:%756=792%:%
  2393 %:%756=796%:%
  2393 %:%757=793%:%
  2394 %:%757=797%:%
  2394 %:%758=794%:%
  2395 %:%758=798%:%
  2395 %:%759=795%:%
  2396 %:%759=799%:%
  2396 %:%760=796%:%
  2397 %:%760=800%:%
  2397 %:%761=797%:%
  2398 %:%761=801%:%
  2398 %:%762=798%:%
  2399 %:%762=802%:%
  2399 %:%763=799%:%
  2400 %:%763=803%:%
  2400 %:%764=800%:%
  2401 %:%764=804%:%
  2401 %:%765=801%:%
  2402 %:%765=805%:%
  2402 %:%766=802%:%
  2403 %:%766=806%:%
  2403 %:%767=803%:%
  2404 %:%767=807%:%
  2404 %:%768=804%:%
  2405 %:%768=808%:%
  2405 %:%769=805%:%
  2406 %:%769=809%:%
  2406 %:%770=806%:%
  2407 %:%770=810%:%
  2407 %:%771=807%:%
  2408 %:%771=811%:%
  2408 %:%772=808%:%
  2409 %:%772=812%:%
  2409 %:%773=809%:%
  2410 %:%773=813%:%
  2410 %:%773=810%:%
  2411 %:%774=814%:%
  2411 %:%773=811%:%
  2412 %:%774=815%:%
  2412 %:%774=812%:%
  2413 %:%774=816%:%
  2413 %:%775=813%:%
  2414 %:%775=817%:%
  2414 %:%776=814%:%
  2415 %:%776=818%:%
  2415 %:%777=815%:%
  2416 %:%777=819%:%
  2416 %:%778=816%:%
  2417 %:%778=820%:%
  2417 %:%779=817%:%
  2418 %:%779=821%:%
  2418 %:%780=818%:%
  2419 %:%780=822%:%
  2419 %:%781=819%:%
  2420 %:%781=823%:%
  2420 %:%782=820%:%
  2421 %:%782=824%:%
  2421 %:%782=821%:%
  2422 %:%783=825%:%
  2422 %:%783=822%:%
  2423 %:%783=826%:%
  2423 %:%784=823%:%
  2424 %:%784=827%:%
  2424 %:%785=824%:%
  2425 %:%785=828%:%
  2425 %:%786=825%:%
  2426 %:%786=829%:%
  2426 %:%787=826%:%
  2427 %:%787=830%:%
  2427 %:%788=827%:%
  2428 %:%788=831%:%
  2428 %:%789=828%:%
  2429 %:%789=832%:%
  2429 %:%790=829%:%
  2430 %:%790=833%:%
  2430 %:%791=830%:%
  2431 %:%791=834%:%
  2431 %:%792=831%:%
  2432 %:%792=835%:%
  2432 %:%793=832%:%
  2433 %:%793=836%:%
  2433 %:%794=833%:%
  2434 %:%794=837%:%
  2434 %:%795=834%:%
  2435 %:%795=838%:%
  2435 %:%796=835%:%
  2436 %:%796=839%:%
  2436 %:%797=836%:%
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