CS4248_Tutorial_2

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School

National University of Singapore *

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Course

4248

Subject

Computer Science

Date

Nov 24, 2024

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pdf

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8ofc¤G<l|mm®G<l|A69v ZQN*nkk¬oo°neb£*VM UL*[ROIn~oo°*In~@5u aXUuneb£_VSs9@5ugd¥gd¥PG[ROIn~ mj«oo°nkk¬_VSsneb£PG*VM mm®:/ UL*[ROIn~oo°*In~@5u XOL_VSs=2@5uVMgd¥ *[RO=2 mj«@5uv}nkk¬ 8VM*gd¥gd¥PG´9*nkk¬PG_VSs[RO BBBCBBBBFTf@NONNNR`rL jjjjh@@@A@@@DRd>CCDCCCCGUgAdcccca jjjjhnnnjjjjhRSRRqVdvPbaaaa_CCDCCCCGUgA±IJIIIIM[mG....ER2 ss33334W7WǶIJIIIIM[mGIJIIIIM[mG UVUUtYgtySbaaaa_±,,,P0jjjjhCCDCCCCGUgA,,,P033334W7W 88889986<\6RSRRqVdvPnnnbaaaa_ jjjjh33334W7W,,,P0@@@A@@@DRd>NONNNR`rLCCDCCCCGUgA,,,P0±IJIIIIM[mG jjjjhRSRRqVdvPUVUUtYgtySCCDCCCCGUgA,,,P0dcccca 88889986<\6baaaa_RSRRqVdvPLMLLP^pJ RSRRqVdvPnnnbaaaa_ rrr33334W7W33334W7WGHGGGGGKYkE …kkkki ±NONNNR`rL00001T4T …::::;:8>^8 IJIIIIM[mG33334W7W,,,P0jjjjhnnnbaaaa_33334W7Wdcccca----DQ1 HIHHHHHLZlF±NONNNR`rL<<<=<<@`:nnn±<<<=<<@`:33334W7W KLKKO]oIRSRRqVdvP00001T4T33334W7WIJIIIIM[mGdcccca....ER2 TUTTsXfsxR33334W7Wbaaaa_UVUUtYgtySIJIIIIM[mG33334W7WuCCDCCCCGUgAjjjjh„....ER2 jjjjh88889986<\6 × CCDCCCCGUgA00001T4T88889986<\6 ±NONNNR`rL00001T4T MNMMMQ_qK±qqq33334W7W ##G±„33334W7WdccccaYZYY]kx}W TUTTsXfsxRIJIIIIM[mG33334W7W±dcccca33334W7W ,,,P0RSRRqVdvPLMLLP^pJ33334W7W jjjjhRSRRqVdvP „RSRRqVdvPnnnbaaaa_ jjjjhnnnjjjjhRSRRqVdvPbaaaa_CCDCCCCGUgA±IJIIIIM[mG dcccca33334W7WdccccadccccaCCDCCCCGUgARSRRqVdvPNONNNR`rL....ER2 ssCCDCCCCGUgAjjjjh@@@A@@@DRd> „RSRRqVdvPnnnbaaaa_ ±jjjjhjjjjh33334W7WLMLLP^pJUVUUtYgtySjjjjhdcccca jjjjhRSRRqVdvP jjjjh@@@A@@@DRd>33334W7Wdcccca33334W7W \]\\\n{Znnn33334W7WdccccajjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rLdccccaYZYY]kx}W BBBCBBBBFTf@jjjjhǶdcccca ´NONNNR`rL33334W7W jjjjhRSRRqVdvP ,,,P0RSRRqVdvPLMLLP^pJ33334W7W ssCCDCCCCGUgAjjjjh@@@A@@@DRd>RSRRqVdvPnnnjjjjh ± ssRSRRqVdvPbaaaa_GHGGGGGKYkECCDCCCCGUgANONNNR`rL<<<=<<@`: dccccaRSRRqVdvPIJIIIIM[mGnnnjjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rL $$Hnnnjjjjh jjjjhRSRRqVdvP <<<=<<@`:33334W7Wjjjjh jjjjh@@@A@@@DRd>33334W7W LMLLP^pJRSRRqVdvPdccccajjjjh RSRRqVdvPnnnjjjjh RSRRqVdvP88889986<\6 jjjjhnnnjjjjhRSRRqVdvPbaaaa_CCDCCCCGUgA±IJIIIIM[mG....ER2 „RSRRqVdvPnnn dcccca@@@A@@@DRd>RSRRqVdvPnnnIJIIIIM[mG00001T4T ±jjjjhjjjjh33334W7WLMLLP^pJUVUUtYgtySjjjjh jjjjh@@@A@@@DRd>33334W7WLMLLP^pJ dccccaRSRRqVdvP jjjjh@@@A@@@DRd>±jjjjh „RSRRqVdvPnnn @@@A@@@DRd>±qqq33334W7W UVUUtYgtySbaaaa_±,,,P0jjjjhCCDCCCCGUgA,,,P033334W7W $$H33334W7W88889986<\6RSRRqVdvPbaaaa_33334W7W dccccaRSRRqVdvPIJIIIIM[mGnnnjjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rLdcccca ,,,P0±NONNNR`rL $$H33334W7W dcccca@@@A@@@DRd>±baaaa_33334W7W00001T4TYZYY]kx}W 22223V6Vujjjjh33334W7WNONNNR`rLdccccaCCDCCCCGUgARSRRqVdvPNONNNR`rL 33334W7Wu33334W7Wbaaaa_,,,P0CCDCCCCGUgAdcccca33334W7Wdcccca LMLLP^pJ±baaaa_GHGGGGGKYkE33334W7W00001T4T ssCCDCCCCGUgAjjjjh@@@A@@@DRd> ± ǳ!!Ǵ RSRRqVdvPbaaaa_ ǳ!!!Ǵ ±baaaa_33334W7W dccccaIJIIIIM[mGCCDCCCCGUgA<<<=<<@`:@@@A@@@DRd>jjjjhIJIIIIM[mG„ LMLLP^pJRSRRqVdvPbaaaa_33334W7W ±00001T4Tqqq±NONNNR`rL,,,P033334W7W00001T4T ±NONNNR`rL00001T4T „RSRRqVdvPnnn VWVVZhuzT±NONNNR`rL00001T4T „RSRRqVdvPnnnbaaaa_ jjjjhnnnjjjjhRSRRqVdvPbaaaa_CCDCCCCGUgA±IJIIIIM[mG IJIIIIM[mG33334W7W±00001T4T33334W7Wbaaaa_WXWW[iv{U LMLLP^pJ±„ NONNNR`rLRSRRqVdvPjjjjh @@@A@@@DRd>±qqq33334W7W jjjjhCCDCCCCGUgALMLLP^pJ33334W7W jjjjhRSRRqVdvP <<<=<<@`:RSRRqVdvP RSRRqVdvPqqq33334W7Wbaaaa_ jjjjh@@@A@@@DRd>33334W7WLMLLP^pJYZYY]kx}W ‚RSRRqVdvPnnnǶbaaaa_33334W7W ss33334W7WIJIIIIM[mG,,,P0RSRRqVdvPLMLLP^pJ33334W7W00001T4T jjjjhRSRRqVdvP 00001T4TCCDCCCCGUgAdcccca,,,P0nnndccccadcccca jjjjh@@@A@@@DRd>33334W7Wdcccca33334W7W RSRRqVdvPNONNNR`rL jjjjh@@@A@@@DRd>33334W7W 88889986<\6RSRRqVdvPbaaaa_nnnLMLLP^pJ ±LMLLP^pJRSRRqVdvPNONNNR`rL<<<=<<@`: „RSRRqVdvPnnnbaaaa_dcccca33334W7WIJIIIIM[mGqqq33334W7Wdcccca VWVVZhuzTHIHHHHHLZlF33334W7WjjjjhǶdcccca GHGGGGGKYkE33334W7W33334W7WUVUUtYgtyS ±NONNNR`rL ±,,,P0jjjjhCCDCCCCGUgAqqq33334W7W 88889986<\6RSRRqVdvPbaaaa_nnnLMLLP^pJ666677Z4:Z4WXWW[iv{U STSSrWewQYZYY]kx}W t@D@D@@r±ljj GCGCECuggecc <@<@<VVTRRGCGCECuRRPNN<@<@< )-)OOMKK}²ffdbbJJFHFx*.*aa_]] ZZXVVVLLHJHHz±RRPNN<@<@<nnp±<@<@<37373 OOMKK}VVTRR040037373MMIKII{ggecc ±RRPNN0400 ffdbbPPNLLL~VVTRRVVTRRljj@D@D@@rGCGCECuRRPNN<@<@<[[YWWW STSSrWewQYZYY]kx}W HIHHHHHLZlF33334W7WjjjjhǶdcccca CCDCCCCGUgALMLLP^pJ±<<<=<<@`:CCDCCCCGUgANONNNR`rL33334W7W „RSRRqVdvPnnnbaaaa_ $$Hbaaaa_±CCDCCCCGUgANONNNR`rL ±dcccca ± dccccannnUVUUtYgtyS33334W7Wbaaaa_ IJIIIIM[mG±NONNNR`rL<<<=<<@`:nnn±<<<=<<@`:33334W7W LMLLP^pJRSRRqVdvP00001T4T33334W7WIJIIIIM[mG VWVVZhuzTssCCDCCCCGUgAjjjjh@@@A@@@DRd> nnnNONNNR`rLIJIIIIM[mGCCDCCCCGUgALMLLP^pJCCDCCCCGUgAjjjjh33334W7W00001T4T ,,,P0±UVUUtYgtyS±,,,P0CCDCCCCGUgAjjjjh„ 88889986<\6RSRRqVdvPbaaaa_ qqqRSRRqVdvP,,,P0±$$HnnnIJIIIIM[mG±baaaa_„ ±NONNNR`rL00001T4T ±,,,P0,,,P0RSRRqVdvPLMLLP^pJUVUUtYgtyS±NONNNR`rL„CCDCCCCGUgANONNNR`rL<<<=<<@`: UVUUtYgtySbaaaa_RSRRqVdvP$$H±$$HCCDCCCCGUgAIJIIIIM[mGCCDCCCCGUgAjjjjhCCDCCCCGUgA33334W7WdccccaWXWW[iv{UYZYY]kx}W +++O/RSRRqVdvPLMLLP^pJ33334W7W nnnUVUUtYgtyS ssCCDCCCCGUgAjjjjh@@@A@@@DRd> jjjjh@@@A@@@DRd>baaaa_33334W7W33334W7W UVUUtYgtySbaaaa_33334W7W00001T4TCCDCCCCGUgA,,,P0jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rLdcccca 88889986<\6RSRRqVdvPbaaaa_ ǳ rt@FCB>±mmjh IFEFAifeffa <B?>~:XUTUUPIFEFATQPQNQL<B?>~: ))MKLKKO]oI²cbbbb`FGFFFFJXjD***N.Ǵ ±NONNNR`rL00001T4T baaaa_±NONNNR`rLGHGGGGGKYkE $$H„ jjjjh@@@A@@@DRd>33334W7WCCDCCCCGUgAbaaaa_ ±UVUUtYgtySUVUUtYgtySbaaaa_RSRRqVdvPuCCDCCCCGUgALMLLP^pJ±jjjjh33334W7W IJIIIIM[mGCCDCCCCGUgAGHGGGGGKYkE33334W7WIJIIIIM[mGCCDCCCCGUgA@@@A@@@DRd>RSRRqVdvPRSRRqVdvP00001T4TYZYY]kx}W lllljYZYY]kx}W ;;;;<;;?_9CCDCCCCGUgAqqq33334W7WNONNNR`rL jjjjh@@@A@@@DRd>33334W7W ,,,P0RSRRqVdvPbaaaa_UVUUtYgtySnnndcccca $$H33334W7WIJIIIIM[mGRSRRqVdvPss....ER2 ,,,P0±IJIIIIM[mG,,,P0nnnIJIIIIM[mG±jjjjh33334W7W jjjjh@@@A@@@DRd>33334W7W $$HCCDCCCCGUgA<<<=<<@`:baaaa_±LMLLP^pJ KLKKO]oIHIHHHHHLZlF22223V6V P ( w | go ) 88889986<\6RSRRqVdvPbaaaa_ ±IJIIIIM[mGIJIIIIM[mG UVUUtYgtySRSRRqVdvPdccccadccccaCCDCCCCGUgA$$HIJIIIIM[mG33334W7W ssRSRRqVdvPbaaaa_00001T4Tdcccca w YZYY]kx}W 777788[5;[5RSRRqVdvPbaaaa_ jjjjh@@@A@@@DRd>CCDCCCCGUgAdcccca 33334W7Wu33334W7Wbaaaa_,,,P0CCDCCCCGUgAdcccca33334W7W RSRRqVdvPNONNNR`rLIJIIIIM[mG„....ER2 00001T4TRSRRqVdvP dccccaRSRRqVdvPLMLLP^pJ33334W7W UVUUtYgtySbaaaa_33334W7WAAABAAAESe?UVUUtYgtySbaaaa_RSRRqVdvP,,,P033334W7WdccccadccccaCCDCCCCGUgANONNNR`rL<<<=<<@`: ±NONNNR`rL00001T4T IJIIIIM[mG33334W7WLMLLP^pJLMLLP^pJ±jjjjhCCDCCCCGUgA»33334W7W jjjjh@@@A@@@DRd>33334W7W ssRSRRqVdvPbaaaa_00001T4Tdcccca $$H33334W7W88889986<\6RSRRqVdvPbaaaa_33334W7W ,,,P0RSRRqVdvPNONNNR`rLdccccajjjjhbaaaa_nnn,,,P0jjjjhCCDCCCCGUgANONNNR`rL<<<=<<@`: jjjjh@@@A@@@DRd>33334W7W jjjjhRSRRqVdvPGHGGGGGKYkE33334W7WNONNNR`rLdcccca ±NONNNR`rL00001T4T UVUUtYgtySbaaaa_RSRRqVdvP$$H±$$HCCDCCCCGUgAIJIIIIM[mGCCDCCCCGUgAjjjjhCCDCCCCGUgA33334W7Wdcccca VWVVZhuzTss33334W7W 00001T4TRSRRqVdvP jjjjh@@@A@@@DRd>CCDCCCCGUgAdcccca @@@A@@@DRd>33334W7Wbaaaa_33334W7W jjjjhRSRRqVdvP 00001T4T33334W7WNONNNR`rLdccccaCCDCCCCGUgA88889986<\6„ jjjjh@@@A@@@DRd>33334W7W UVUUtYgtySbaaaa_RSRRqVdvP$$H±$$HCCDCCCCGUgAIJIIIIM[mGCCDCCCCGUgAjjjjhCCDCCCCGUgA33334W7Wdcccca ± $$HCCDCCCCGUgAjjjjhWXWW[iv{UYZYY]kx}W !! llgXUTUUP mmjh@FCB>IFEFATQPQNQLMJIJE ±$*XUTUUPqnpmmjh-3-d BBBCBBBBFTf@NONNNR`rL UVUUtYgtySbaaaa_±,,,P0jjjjhCCDCCCCGUgA,,,P033334W7W....ER2 HIHHHHHLZlFKLKKO]oIdcccca nnndccccannn±IJIIIIM[mGIJIIIIM[mG„ 00001T4TRSRRqVdvP qqq33334W7Wbaaaa_„ IJIIIIM[mGCCDCCCCGUgAjjjjhjjjjhIJIIIIM[mG33334W7W RSRRqVdvPbaaaa_ NONNNR`rLRSRRqVdvP UVUUtYgtySbaaaa_33334W7WUVUUtYgtySbaaaa_RSRRqVdvP,,,P033334W7WdccccadccccaCCDCCCCGUgANONNNR`rL<<<=<<@`: RSRRqVdvPnnnjjjjhdccccaCCDCCCCGUgA00001T4T33334W7W RSRRqVdvP88889986<\6 jjjjhRSRRqVdvPGHGGGGGKYkE33334W7WNONNNR`rLCCDCCCCGUgA»±jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rLYZYY]kx}W rrr@@@A@@@DRd>„ 00001T4TRSRRqVdvP „RSRRqVdvPnnn jjjjh@@@A@@@DRd>CCDCCCCGUgANONNNR`rLGHGGGGGKYkE jjjjh@@@A@@@DRd>±jjjjh CCDCCCCGUgAdcccca]^]]]o|[ ²OLKLGIFEFA,23936u IFEFAifeffa <B?>~:XUTUUPIFEFATQPQNQL<B?>~: mmjhXUTUUP mmjh@FCB>3936u ifeffa,2@FCB>XUTUUPXUTUUPOLKLG_\[\\xW llg@FCB>3936u mmjhgdcdd_±¿,2 IFEFAifeffa <B?>~:XUTUUPIFEFATQPQNQL<B?>~: ifeffaRONOLJXUTUUPXUTUUPmmjh@FCB>OLKLGx_\[\\xW hedee`@FCB>3936u IFEFAifeffa <B?>~:XUTUUPIFEFATQPQNQL<B?>~: mmjhXUTUUP @FCB>±qs3936u ± RONOLJ3936u3936ummjhIFEFATQPQNQL<B?>~: sutIFEFAmmjh@FCB> @FCB>3936ugdcdd_ ±060grqsIFEFAifeffaXUTUUPgdcdd_.4.e ZWVWWsRgdcdd_XUTUUP8>8;z6 hedee`RONOLJIFEFAmmjh@FCB>_\[\\xW fcbcc^3936u,23936uTQPQNQLmmjhOLKLGx @FCB>3936ugdcdd_ gdcdd_3936uifeffa3936u±gdcdd_,2@FCB> IFEFAifeffa <B?>~:XUTUUPIFEFATQPQNQL<B?>~: XUTUUPTQPQNQL qs3936ugdcdd_x sut3936uOLKLGOLKLG_\[\\xW rt@FCB>3936uTQPQNQL ZWVWWsRgdcdd_XUTUUP8>8;z6 hedee`RONOLJIFEFAmmjh@FCB> ±ifeffaMJIJEifeffa Ǵ@FCB>XUTUUPsutǷifeffa IFEFAmmjh <B?>~:XUTUUPIFEFATQPQNQL<B?>~: sutIFEFAmmjh@FCB> xXUTUUPqnpgdcdd_ gdcdd_3936uifeffa3936u±gdcdd_,2@FCB>c`_``|[ǵ.4.e ²OLKLGIFEFA,23936uǷifeffa @FCB>3936u±gdcdd_mmjh $*3936u±mmjh 060grXUTUUP3936uifeffa TQPQNQLXUTUUPmmjh <B?>~:XUTUUP qnp[XWXXtS ±TQPQNQL060gr ifeffa@FCB>3936u <B?>~:XUTUUP3936uifeffa XUTUUPTQPQNQL sutIFEFAmmjh@FCB> ± ,2OLKLG3936u±gdcdd_ qnp[XWXXtS060gr±mmjh3936u_\[\\xW ²8>8;z6mmjh3936ugdcdd_ mmjh@FCB>3936u RONOLJ3936u3936ummjhIFEFATQPQNQL<B?>~:.4.e mmjh@FCB>3936ux <B?>~:XUTUUP 8>8;z6XUTUUPgdcdd_ ± ,2XUTUUP‰3936u3936u 060grXUTUUPsutTQPQNQLifeffammjh±IFEFAgdcdd_ifeffa mmjhXUTUUP<B?>~:3936ummjh@FCB>3936ugdcdd__\[\\xW kkkkiYZYY]kx}W HIHHHHHLZlF33334W7WjjjjhǶdcccca ±dccccadccccannnLMLLP^pJ33334W7W | V | = 100 YZYY]kx}W +++O/±IJIIIIM[mG,,,P0nnnIJIIIIM[mG±jjjjh33334W7W P ( smoothly | go ) 00001T4TCCDCCCCGUgAbaaaa_33334W7W,,,P0jjjjhIJIIIIM[mG„ nnndccccaCCDCCCCGUgANONNNR`rL<<<=<<@`: „RSRRqVdvPnnnbaaaa_ IJIIIIM[mG±NONNNR`rL<<<=<<@`:nnn±<<<=<<@`:33334W7W LMLLP^pJRSRRqVdvP00001T4T33334W7WIJIIIIM[mG RSRRqVdvP$$Hjjjjh±CCDCCCCGUgANONNNR`rL33334W7W00001T4T CCDCCCCGUgANONNNR`rL IJIIIIM[mG±dccccajjjjh dccccajjjjh33334W7WUVUUtYgtyS]^]]]o|[ BBBCBBBBFTf@88889986<\6 jjjjh@@@A@@@DRd>CCDCCCCGUgAdcccca CCDCCCCGUgAdccccaNONNNR`rLǶjjjjh UVUUtYgtySRSRRqVdvPdccccadccccaCCDCCCCGUgA$$HIJIIIIM[mG33334W7W....ER2 dccccajjjjh±jjjjh33334W7W ss@@@A@@@DRd>„ ±NONNNR`rL00001T4T @@@A@@@DRd>RSRRqVdvPss „RSRRqVdvPnnn ,,,P0RSRRqVdvPnnnIJIIIIM[mG00001T4T baaaa_33334W7WdccccaRSRRqVdvPIJIIIIM[mGqqq33334W7W CCDCCCCGUgAjjjjh....ER2 ±NONNNR`rL00001T4T „RSRRqVdvPnnnbaaaa_ 33334W7W\]\\\n{ZnnnCCDCCCCGUgAqqq±IJIIIIM[mG33334W7WNONNNR`rLjjjjh UVUUtYgtySbaaaa_RSRRqVdvP$$H±$$HCCDCCCCGUgAIJIIIIM[mGCCDCCCCGUgAjjjjh„YZYY]kx}W !! llgXUTUUP mmjh@FCB>IFEFATQPQNQLMJIJE ±$*XUTUUPqnpmmjh-3-d rrr@@@A@@@DRd>±jjjjh ±baaaa_33334W7W IJIIIIM[mGCCDCCCCGUgALMLLP^pJCCDCCCCGUgAjjjjh±jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rLdcccca RSRRqVdvP88889986<\6 ± $$HCCDCCCCGUgA<<<=<<@`:baaaa_±LMLLP^pJ VWVVZhuzTRSRRqVdvPbaaaa_ 33334W7Wqqq33334W7WNONNNR`rL ±NONNNR`rL„ KLKKO]oI±baaaa_GHGGGGGKYkERSRRqVdvPqqq ±dccccadccccannnLMLLP^pJUVUUtYgtySjjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rLWXWW[iv{U]^]]]o|[ HIHHHHHLZlF33334W7WjjjjhǶdcccca ,,,P0RSRRqVdvPNONNNR`rLdccccaCCDCCCCGUgA00001T4T33334W7Wbaaaa_ dccccaRSRRqVdvPLMLLP^pJ33334W7W NONNNR`rL33334W7Wss ,,,P0RSRRqVdvPNONNNR`rLjjjjh33334W7Wujjjjhdcccca----DQ1 ?EBA=IFEFA ²OLKLGIFEFA,23936u.4.e sut@FCB>±mmjh IFEFAifeffa <B?>~:XUTUUPIFEFATQPQNQL<B?>~: ))MKLKKO]oI²cbbbb`FGFFFFJXjD***N.]^]]]o|[ llg@FCB>3936u RONOLJIFEFA,2gdcdd_XUTUUPsut±qs3936u IFEFAifeffa TQPQNQLXUTUUPmmjh @FCB>3936u±mmjhIFEFATQPQNQL<B?>~: qnp[XWXXtS.4.e sut@FCB>±mmjh IFEFAifeffa <B?>~:XUTUUPIFEFATQPQNQL<B?>~: ))MKLKKO]oI²cbbbb`FGFFFFJXjD***N.]^]]]o|[ llg@FCB>3936u mmjh±uwv IFEFAifeffa <B?>~:XUTUUPIFEFATQPQNQL<B?>~: ))MKLKKO]oI²cbbbb`FGFFFFJXjD***N. $*x mmjh3936uTQPQNQL [XWXXtS3936ugdcdd_,23936uTQPQNQLmmjh YZYY]kx}W +++O/±NONNNR`rL ss33334W7W <<<=<<@`:33334W7Wjjjjh dcccca±jjjjhCCDCCCCGUgAdcccca88889986<\6±,,,P0jjjjhRSRRqVdvPbaaaa_„ UVUUtYgtySbaaaa_33334W7W00001T4TCCDCCCCGUgA,,,P0jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rLdcccca ssCCDCCCCGUgAjjjjh@@@A@@@DRd> ± $$HCCDCCCCGUgA<<<=<<@`:baaaa_±LMLLP^pJ HIHHHHHLZlFKLKKO]oI]^]]]o|[ ???@???Cc=RSRRqVdvPss ssRSRRqVdvPnnnIJIIIIM[mG00001T4T „RSRRqVdvPnnn dccccaRSRRqVdvPIJIIIIM[mGqqq33334W7W „RSRRqVdvPnnnbaaaa_ CCDCCCCGUgA00001T4T33334W7WNONNNR`rLjjjjhCCDCCCCGUgA´33334W7W00001T4T IJIIIIM[mGCCDCCCCGUgALMLLP^pJCCDCCCCGUgAjjjjh±jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rLdcccca]^]]]o|[ ?C?C??GCGCECuRRPNNljj-1-- TUTTsXfsxRIJIIIIM[mG±„ ±baaaa_RSRRqVdvPnnnNONNNR`rL00001T4T jjjjh@@@A@@@DRd>33334W7W CCDCCCCGUgANONNNR`rLjjjjh33334W7Wbaaaa_±,,,P0jjjjhCCDCCCCGUgAqqq33334W7W HIHHHHHLZlFKLKKO]oI 00001T4T33334W7WLMLLP^pJRSRRqVdvP @@@A@@@DRd>33334W7Wbaaaa_33334W7W----DQ1 @@@A@@@DRd>jjjjhjjjjhUVUUtYgtySdcccca----DQ1ggggegggge00001T4T33334W7WLMLLP^pJRSRRqVdvPYZYY]kx}W±IJIIIIM[mGIJIIIIM[mG33334W7WNONNNR`rLNONNNR`rLIJIIIIM[mGUVUUtYgtySYZYY]kx}WRSRRqVdvPbaaaa_<<<=<<@`:ggggeLMLLP^pJ±dccccaGHGGGGGKYkE33334W7W00001T4TAAABAAAESe?IJIIIIM[mGLMLLP^pJYZYY]kx}W MNMMMQ_qKRSRRqVdvPjjjjh33334W7W jjjjh@@@A@@@DRd>±jjjjh jjjjh@@@A@@@DRd>CCDCCCCGUgAdcccca CCDCCCCGUgAdcccca LMLLP^pJRSRRqVdvPbaaaa_33334W7W <<<=<<@`:33334W7WNONNNR`rL33334W7Wbaaaa_±IJIIIIM[mG IJIIIIM[mG±NONNNR`rL<<<=<<@`:nnn±<<<=<<@`:33334W7W LMLLP^pJRSRRqVdvP00001T4T33334W7WIJIIIIM[mG ±NONNNR`rL00001T4T NONNNR`rLRSRRqVdvPjjjjh RSRRqVdvPNONNNR`rL33334W7W $$H±dcccca33334W7W00001T4T dccccajjjjhbaaaa_CCDCCCCGUgA,,,P0jjjjhIJIIIIM[mG„ RSRRqVdvPNONNNR`rL $$HCCDCCCCGUgA<<<=<<@`:baaaa_±LMLLP^pJdccccaYZYY]kx}W BBBCBBBBFTf@jjjjh nnndcccca33334W7Wdcccca ± jjjjhbaaaa_±NONNNR`rLdcccca88889986<\6RSRRqVdvPbaaaa_LMLLP^pJ33334W7Wbaaaa_ ±baaaa_,,,P0@@@A@@@DRd>CCDCCCCGUgAjjjjh33334W7W,,,P0jjjjhnnnbaaaa_33334W7W jjjjh@@@A@@@DRd>±jjjjh CCDCCCCGUgAdcccca ±jjjjh jjjjh@@@A@@@DRd>33334W7W IJIIIIM[mGCCDCCCCGUgALMLLP^pJCCDCCCCGUgAjjjjh RSRRqVdvP88889986<\6 RSRRqVdvPnnnbaaaa_ dcccca„IJIIIIM[mGIJIIIIM[mG±$$Hnnndccccaeddddb ss33334W7WǶIJIIIIM[mGIJIIIIM[mG jjjjhRSRRqVdvPnnn,,,P0@@@A@@@DRd> nnnUVUUtYgtySRSRRqVdvPNONNNR`rL CCDCCCCGUgAjjjjh dccccajjjjh±baaaa_jjjjhCCDCCCCGUgANONNNR`rL<<<=<<@`: CCDCCCCGUgANONNNR`rL rrr33334W7W33334W7WGHGGGGGKYkE …444455X8X2YZYY]kx}W lllljYZYY]kx}W /3//VVTRRRRPNNǶljj $(37373 YYWUUU37373eecaaYYWUUUMMIKII{37373wv373730400 TUTTsXfsxR±<<<=<<@`:33334W7W STSSrWewQ RSRRqVdvP88889986<\6 ::::;:8>^8

w i JKJJJN\nHdcccca>>>?>>Bb< BBBCBBBBFTf@ ±LMLLP^pJ @@@A@@@DRd>33334W7Wbaaaa_33334W7W JKJJJN\nHggggedcccca>>>?>>Bb< w i - 1 JKJJJN\nHdcccca>>>?>>Bb< … …YZYY]kx}WSTSSrWewQ …YZYY]kx}W………llllj …YZYY]kx}W…STSSrWewQ … BBBCBBBBFTf@ … …YZYY]kx}W………kkkki …YZYY]kx}W9999::97=]7 …YZYY]kx}W………STSSrWewQ …YZYY]kx}W………llllj ±LMLLP^pJ … …YZYY]kx}W……9999::97=]7 …YZYY]kx}W………STSSrWewQ …YZYY]kx}W…kkkki …YZYY]kx}W………9999::97=]7 @@@A@@@DRd>33334W7Wbaaaa_33334W7W … …YZYY]kx}W…llllj …YZYY]kx}W………STSSrWewQ …YZYY]kx}W……kkkki …YZYY]kx}W……STSSrWewQ JKJJJN\nHggggedcccca>>>?>>Bb< … … … … … STSSrWewQYZYY]kx}W HIHHHHHLZlF33334W7WjjjjhǶdcccca dccccajjjjh±baaaa_jjjjh dccccaCCDCCCCGUgALMLLP^pJUVUUtYgtySIJIIIIM[mG„YZYY]kx}W /3//37373jRRPNNGCGCECuljjGCGCECuVVTRRRRPNN-1-- rrr@@@A@@@DRd>±jjjjh CCDCCCCGUgAdcccca TUTTsXfsxR33334W7Wbaaaa_UVUUtYgtySIJIIIIM[mG33334W7WuCCDCCCCGUgAjjjjh„]^]]]o|[ rrr@@@A@@@DRd>„ 00001T4TRSRRqVdvP ss33334W7W NONNNR`rL33334W7W33334W7W00001T4T jjjjh@@@A@@@DRd>33334W7W 88889986<\6baaaa_±,,,P0jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rL 1 N CCDCCCCGUgANONNNR`rL jjjjh@@@A@@@DRd>33334W7W 00001T4T33334W7W´NONNNR`rLCCDCCCCGUgAjjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rL RSRRqVdvP88889986<\6 UVUUtYgtyS33334W7Wbaaaa_UVUUtYgtySIJIIIIM[mG33334W7WuCCDCCCCGUgAjjjjh„]^]]]o|[ lllljYZYY]kx}W BFBFBBtRRPNNljjnnpGCGCECuljjGCGCECuVVTRRRRPNN-1-- rrr@@@A@@@DRd>„ 00001T4TRSRRqVdvP ss33334W7W NONNNR`rL33334W7W33334W7W00001T4T jjjjh@@@A@@@DRd>CCDCCCCGUgAdcccca LMLLP^pJ33334W7W±dccccannnbaaaa_33334W7W RSRRqVdvP88889986<\6 UVUUtYgtyS33334W7Wbaaaa_UVUUtYgtySIJIIIIM[mG33334W7WuCCDCCCCGUgAjjjjh„]^]]]o|[ kkkkiYZYY]kx}W qsggecc XXVTTeecaaVVTRR$(±$(GCGCECuMMIKII{GCGCECuljjx-1-- ;;;;<;;?_9CCDCCCCGUgAqqq33334W7WNONNNR`rL ± jjjjh33334W7Wdccccajjjjh dcccca33334W7Wjjjjh rrr....ER2 @@@A@@@DRd>RSRRqVdvPss 00001T4TRSRRqVdvP33334W7Wdcccca jjjjh@@@A@@@DRd>33334W7W UVUUtYgtySbaaaa_RSRRqVdvP$$H±$$HCCDCCCCGUgAIJIIIIM[mGCCDCCCCGUgAjjjjh„ P ( W ) ,,,P0@@@A@@@DRd>±NONNNR`rL<<<=<<@`:33334W7W ss@@@A@@@DRd>33334W7WNONNNR`rL ss33334W7W LMLLP^pJCCDCCCCGUgANONNNR`rLCCDCCCCGUgALMLLP^pJCCDCCCCGUgA»33334W7W UVUUtYgtyS33334W7Wbaaaa_UVUUtYgtySIJIIIIM[mG33334W7WuCCDCCCCGUgAjjjjh„]^]]]o|[ ::::;:8>^8YZYY]kx}W XXVTTeecaa±,0,,ljjGCGCECu,0,,37373-1-- ²dccccadccccannnLMLLP^pJ33334W7W ss33334W7W ±baaaa_33334W7W nnndccccaCCDCCCCGUgANONNNR`rL<<<=<<@`: $$HCCDCCCCGUgA<<<=<<@`:baaaa_±LMLLP^pJ LMLLP^pJRSRRqVdvP00001T4T33334W7WIJIIIIM[mGYZYY]kx}W ;;;;<;;?_9CCDCCCCGUgAqqq33334W7WNONNNR`rL W = ǳBBBCBBBBFTf@ ±LMLLP^pJ @@@A@@@DRd>33334W7Wbaaaa_33334W7WǴ ±NONNNR`rL00001T4T jjjjh@@@A@@@DRd>33334W7W 88889986<\6RSRRqVdvPIJIIIIM[mGIJIIIIM[mGRSRRqVdvPssCCDCCCCGUgANONNNR`rL<<<=<<@`: jjjjh±$$HIJIIIIM[mG33334W7W....ER2 ,,,P0RSRRqVdvPLMLLP^pJUVUUtYgtySnnnjjjjh33334W7W PP ( w ) YZYY]kx}W !! rtXUTUUPgdcdd_060gr ifeffa,2gdcdd_±RONOLJ$*OLKLG3936u ----DQ1 rrr@@@A@@@DRd>±jjjjh @@@A@@@DRd>±UVUUtYgtySUVUUtYgtyS33334W7WNONNNR`rLdcccca ssCCDCCCCGUgAjjjjh@@@A@@@DRd> jjjjh@@@A@@@DRd>33334W7W CCDCCCCGUgANONNNR`rLUVUUtYgtySnnnjjjjh W = ǴBBBCBBBBFTf@ @@@A@@@DRd>33334W7Wbaaaa_33334W7W ±LMLLP^pJǴ]^]]]o|[ rrrRSRRqVdvPnnnIJIIIIM[mG00001T4T ss33334W7W RSRRqVdvP$$Hjjjjh±CCDCCCCGUgANONNNR`rL ± dccccaLMLLP^pJ±IJIIIIM[mGIJIIIIM[mG33334W7Wbaaaa_ RSRRqVdvPbaaaa_ IJIIIIM[mG±baaaa_<<<=<<@`:33334W7Wbaaaa_ UVUUtYgtyS33334W7Wbaaaa_UVUUtYgtySIJIIIIM[mG33334W7WuCCDCCCCGUgAjjjjh„]^]]]o|[ rrr@@@A@@@DRd>„]^]]]o|[ kkkkiYZYY]kx}W t@D@D@@rGCGCECu,0,,@D@D@@r GCGCECuggecc $(37373ljjljj37373eecaaaa_]] ZZXVVV±]][YYKKGIGy]][YY±]][YY #UUSQQt qsggecc ljj8<8<8 × GCGCECu04008<8<8 ±RRPNN0400 +/++VVTRRggeccGCGCECuRRPNN37373 ffdbbGCGCECuPPNLLL~GCGCECuMMIKII{±eecaaGCGCECuljjx[[YWWW +++O/RSRRqVdvPNONNNR`rLdccccaCCDCCCCGUgA00001T4T33334W7Wbaaaa_ 88889986<\6RSRRqVdvPIJIIIIM[mGIJIIIIM[mGRSRRqVdvPssCCDCCCCGUgANONNNR`rL<<<=<<@`: \]\\\n{Znnn33334W7Wbaaaa_„VWVVZhuzT b_^__{Z WXWW[iv{U ±NONNNR`rL00001T4T 00001T4TRSRRqVdvP,,,P0nnnLMLLP^pJ33334W7WNONNNR`rLjjjjhdcccca VWVVZhuzT 060grYVUVVrQ AAABAAAESe? 060grnki WXWW[iv{U----DQ1 b_^__{Z ----DQ1 ²[XWXXtS[XWXXtSOLKLG3936u ifeffa@FCB>IFEFA[XWXXtSifeffa TQPQNQL3936usut QNMNKI±,2$*XUTUUPXUTUUPMJIJE_\[\\xW 060grYVUVVrQ ----DQ1 llghedee`QNMNKI+1 IFEFAifeffa $*qnpifeffax [XWXXtSgdcdd_XUTUUP060grqnp,2IFEFATQPQNQL<B?>~: TQPQNQL3936usut QNMNKI±,2$*XUTUUPXUTUUPMJIJE_\[\\xW 060grolj ----DQ1 ²[XWXXtS[XWXXtSOLKLG3936u hedee`mmjhXUTUUPgdcdd_3936uifeffa ±gdcdd_3936u $*qnpifeffax @FCB>XUTUUPifeffammjhIFEFATQPQNQL<B?>~: QNMNKI±,2$*XUTUUPXUTUUPMJIJE 8>8;z6±TQPQNQLifeffa_\[\\xW 060grnki ----DQ1 SPOPMK3936usut OLKLG±[XWXXtSmmjhXUTUUP[XWXXtS ±gdcdd_3936u ±TQPQNQLTQPQNQLXUTUUPqnpTQPQNQL,23936u060gr $*x llgIFEFARONOLJ +1XUTUUPXUTUUPMJIJE_\[\\xW STSSrWewQYZYY]kx}W cbbbb`@@@A@@@DRd>RSRRqVdvPss ± ##G±<<<=<<@`: RSRRqVdvP88889986<\6 rrrRSRRqVdvPbaaaa_00001T4Tdcccca VWVVZhuzT##GRSRRqVdvPrrrWXWW[iv{U baaaa_33334W7WUVUUtYgtySbaaaa_33334W7Wdcccca33334W7WNONNNR`rLjjjjh±jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rL ±NONNNR`rL00001T4T jjjjh88889986<\6 × CCDCCCCGUgA00001T4T88889986<\6 baaaa_33334W7WUVUUtYgtySbaaaa_33334W7Wdcccca33334W7WNONNNR`rLjjjjh±jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rL RSRRqVdvP88889986<\6 ±IJIIIIM[mGIJIIIIM[mG jjjjh@@@A@@@DRd>33334W7W 00001T4TRSRRqVdvP,,,P0nnnLMLLP^pJ33334W7WNONNNR`rLjjjjhdccccaYZYY]kx}W TUTTsXfsxRbaaaa_33334W7WUVUUtYgtySbaaaa_RSRRqVdvPAAABAAAESe? ,,,P033334W7Wdccccadcccca ´baaaa_dccccajjjjh $$H„ baaaa_33334W7WLMLLP^pJRSRRqVdvPqqqCCDCCCCGUgANONNNR`rL<<<=<<@`: dccccajjjjhRSRRqVdvPUVUUtYgtyS ssRSRRqVdvPbaaaa_00001T4Tdcccca 88889986<\6baaaa_RSRRqVdvPLMLLP^pJ UVUUtYgtySbaaaa_33334W7Wdcccca33334W7WNONNNR`rLjjjjh RSRRqVdvPNONNNR`rL jjjjh@@@A@@@DRd>33334W7W MNMMMQ_qKHIHHHHHLZlFiiigFGFFFFJXjD IJIIIIM[mGCCDCCCCGUgAdccccajjjjh----DQ1 VWVVZhuzT@@@A@@@DRd>jjjjhjjjjhUVUUtYgtySdcccca----DQ1ggggegggge<<<=<<@`:CCDCCCCGUgAdccccajjjjhYZYY]kx}W<<<=<<@`:CCDCCCCGUgAjjjjh@@@A@@@DRd>nnn$$HYZYY]kx}W,,,P0RSRRqVdvPLMLLP^pJggggedcccca33334W7W$$HIJIIIIM[mG33334W7WCCDCCCCGUgA33334W7Wbaaaa_gggge9999::97=]79999::97=]7::::;:8>^8llllj444455X8X2…WXWW[iv{UYZYY]kx}W lllljYZYY]kx}W TUTTsXfsxRIJIIIIM[mG33334W7W±dcccca33334W7W ,,,P0±IJIIIIM[mG,,,P0nnnIJIIIIM[mG±jjjjh33334W7W jjjjh@@@A@@@DRd>33334W7W +++O/RSRRqVdvPdccccaCCDCCCCGUgANONNNR`rL33334W7W dccccaCCDCCCCGUgALMLLP^pJCCDCCCCGUgAIJIIIIM[mG±baaaa_CCDCCCCGUgAjjjjh„ $$H33334W7Wjjjjhss33334W7W33334W7WNONNNR`rL JKJJJN\nH b_^__{Z.4.e 060grYVUVVrQ >>>?>>Bb<....ER2 JKJJJN\nH b_^__{Z.4.e 060grolj >>>?>>Bb<....ER2 JKJJJN\nH b_^__{Z.4.e 060grnki >>>?>>Bb< nnndccccaCCDCCCCGUgANONNNR`rL<<<=<<@`: $$HRSRRqVdvPjjjjh@@@A@@@DRd> ##GRSRRqVdvPrrr ±NONNNR`rL00001T4T jjjjh88889986<\6 × CCDCCCCGUgA00001T4T88889986<\6 baaaa_33334W7WUVUUtYgtySbaaaa_33334W7Wdcccca33334W7WNONNNR`rLjjjjh±jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rLYZYY]kx}W kkkkiYZYY]kx}W rrr@@@A@@@DRd>CCDCCCCGUgA,,,P0@@@A@@@DRd> 00001T4TRSRRqVdvP,,,P0nnnLMLLP^pJ33334W7WNONNNR`rLjjjjh dcccca@@@A@@@DRd>±baaaa_33334W7Wdcccca jjjjh@@@A@@@DRd>33334W7W @@@A@@@DRd>CCDCCCCGUgA<<<=<<@`:@@@A@@@DRd>33334W7Wdccccajjjjh dcccca33334W7WLMLLP^pJ±NONNNR`rLjjjjhCCDCCCCGUgA,,,P0 dccccaCCDCCCCGUgALMLLP^pJCCDCCCCGUgAIJIIIIM[mG±baaaa_CCDCCCCGUgAjjjjh„ ssCCDCCCCGUgAjjjjh@@@A@@@DRd> jjjjh@@@A@@@DRd>33334W7W \]\\\n{Znnn33334W7Wbaaaa_„]^]]]o|[ ???@???Cc=±dcccca CCDCCCCGUgAjjjjh $$H33334W7W33334W7WNONNNR`rL baaaa_±NONNNR`rLGHGGGGGKYkE33334W7W00001T4T ±jjjjh jjjjh@@@A@@@DRd>33334W7W @@@A@@@DRd>CCDCCCCGUgA<<<=<<@`:@@@A@@@DRd>33334W7Wdccccajjjjh UVUUtYgtySIJIIIIM[mG±,,,P033334W7W]^]]]o|[ BBBCBBBBFTf@88889986<\6 NONNNR`rLRSRRqVdvPjjjjh....ER2 ±NONNNR`rL„ baaaa_33334W7W,,,P0RSRRqVdvPLMLLP^pJLMLLP^pJ33334W7WNONNNR`rL00001T4T±jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rL jjjjhRSRRqVdvP ±00001T4T00001T4Tbaaaa_33334W7Wdccccadcccca jjjjh@@@A@@@DRd>CCDCCCCGUgAdcccca UVUUtYgtySbaaaa_RSRRqVdvP$$HIJIIIIM[mG33334W7WLMLLP^pJ]^]]]o|[ ?C?C??GCGCECuRRPNNljj-1-- ǳcbbbb`33334W7WLMLLP^pJ±NONNNR`rLjjjjhCCDCCCCGUgA,,,P0 dccccaCCDCCCCGUgALMLLP^pJCCDCCCCGUgAIJIIIIM[mG±baaaa_CCDCCCCGUgAjjjjh„Ǵ ±IJIIIIM[mGdccccaRSRRqVdvP LMLLP^pJ33334W7W±dccccannnbaaaa_33334W7Wdcccca @@@A@@@DRd>RSRRqVdvPss dccccaCCDCCCCGUgALMLLP^pJCCDCCCCGUgAIJIIIIM[mG±baaaa_ ± dcccca33334W7Wjjjjh RSRRqVdvP88889986<\6 00001T4TRSRRqVdvP,,,P0nnnLMLLP^pJ33334W7WNONNNR`rLjjjjhdcccca ±baaaa_33334W7WYZYY]kx}W ##Gnnnjjjjh CCDCCCCGUgAjjjjh CCDCCCCGUgAdcccca $$H±dcccca33334W7W00001T4T RSRRqVdvPNONNNR`rL jjjjh@@@A@@@DRd>33334W7W IJIIIIM[mGCCDCCCCGUgAGHGGGGGKYkE33334W7WNONNNR`rL33334W7Wdccccadcccca RSRRqVdvP88889986<\6 jjjjh@@@A@@@DRd>33334W7WCCDCCCCGUgAbaaaa_ LMLLP^pJ33334W7W±NONNNR`rLCCDCCCCGUgANONNNR`rL<<<=<<@`: RSRRqVdvPbaaaa_ dcccca33334W7WLMLLP^pJ±NONNNR`rLjjjjhCCDCCCCGUgA,,,P0 ,,,P0RSRRqVdvPNONNNR`rLjjjjh33334W7WNONNNR`rLjjjjh hhhfª ±dcccca RSRRqVdvPUVUUtYgtySUVUUtYgtySRSRRqVdvPdcccca33334W7W00001T4T jjjjhRSRRqVdvP IJIIIIM[mG33334W7WuCCDCCCCGUgA,,,P0RSRRqVdvP<<<=<<@`:baaaa_±UVUUtYgtyS@@@A@@@DRd>CCDCCCCGUgA,,,P0±IJIIIIM[mG dccccaCCDCCCCGUgALMLLP^pJCCDCCCCGUgAIJIIIIM[mG±baaaa_CCDCCCCGUgAjjjjh„ VWVVZhuzTss@@@A@@@DRd>CCDCCCCGUgA,,,P0@@@A@@@DRd> jjjjh88889986<\6 × CCDCCCCGUgA00001T4T88889986<\6 CCDCCCCGUgAdcccca 00001T4T33334W7WdccccaCCDCCCCGUgA<<<=<<@`:NONNNR`rL33334W7W00001T4T 88889986<\6RSRRqVdvPbaaaa_WXWW[iv{UYZYY]kx}W !!! 7=7:y5gdcdd_XUTUUPRONOLJ ± 060grIFEFA‰3936ugdcdd_3936uTQPQNQLmmjh [XWXXtS3936ugdcdd_ifeffa[XWXXtS3936u,2mmjhIFEFAqs3936u \YXYYuT±TQPQNQL<B?>~:OLKLG3936u]ZYZZvU ----DQ1 ##G33334W7WdccccaCCDCCCCGUgA00001T4T33334W7Wdcccca +++O/RSRRqVdvPdccccaCCDCCCCGUgANONNNR`rL33334W7W ////FS3CCDCCCCGUgAdccccajjjjh±NONNNR`rL,,,P033334W7W....ER2 ss@@@A@@@DRd>±jjjjh RSRRqVdvPjjjjh@@@A@@@DRd>33334W7Wbaaaa_ 00001T4TCCDCCCCGUgAdccccajjjjh±NONNNR`rL,,,P033334W7W LMLLP^pJ33334W7Wjjjjhbaaaa_CCDCCCCGUgA,,,P0dcccca ±baaaa_33334W7W CCDCCCCGUgANONNNR`rL „RSRRqVdvPnnnbaaaa_ baaaa_±00001T4T±baaaa_]^]]]o|[ ////FS3RSRRqVdvP „RSRRqVdvPnnn jjjjh@@@A@@@DRd>CCDCCCCGUgANONNNR`rLGHGGGGGKYkE jjjjh@@@A@@@DRd>33334W7Wbaaaa_33334W7W ssCCDCCCCGUgAIJIIIIM[mGIJIIIIM[mG $$H33334W7W ± $$HCCDCCCCGUgA<<<=<<@`: CCDCCCCGUgALMLLP^pJUVUUtYgtyS±,,,P0jjjjh jjjjhRSRRqVdvP jjjjh@@@A@@@DRd>33334W7W baaaa_±NONNNR`rLGHGGGGGKYkECCDCCCCGUgANONNNR`rL<<<=<<@`: $$H„ ,,,P0@@@A@@@DRd>±NONNNR`rL<<<=<<@`:CCDCCCCGUgANONNNR`rL<<<=<<@`: jjjjh@@@A@@@DRd>33334W7W 00001T4TCCDCCCCGUgAdccccajjjjh±NONNNR`rL,,,P033334W7W LMLLP^pJ33334W7Wjjjjhbaaaa_CCDCCCCGUgA,,,P0]^]]]o|[ ::::;:8>^8YZYY]kx}W ffdbbljj±x ffdbbGCGCECuPPNLLL~YYWUUUMMIKII{37373.2.. ffdbbljj±x QQOMMM±qs37373.2.. ZZXVVV±]][YYKKGIGy]][YY±]][YY QQOMMM±qs37373 #±x37373ggecc[[YWWW ƒ NBBllj®llj®cWWWWteeeec§;iiig«iiig«A5w\PPPg[[[[xsQEEUIIQEEcWWWWtA5w>2tQEE+g[[[[x`TTTTocccca¥J>iiig«sQEEUIIQEEiiig«pddddb¦A5wZNNN+\PPPllj®QEE:qoeeeec§QEEZNNNQEEWKKK+occcca¥QEEllj®„ TUTTsXfsxR±<<<=<<@`:33334W7W llllj RSRRqVdvP88889986<\6 ::::;:8>^8

00001T4TRSRRqVdvP,,,P0 33334W7Wu,,,P0CCDCCCCGUgAjjjjhCCDCCCCGUgANONNNR`rL<<<=<<@`: @@@A@@@DRd>±UVUUtYgtySUVUUtYgtyS„ nnnUVUUtYgtySdcccca33334W7Wjjjjh 88889986<\6nnnbaaaa_CCDCCCCGUgARSRRqVdvPnnndcccca ,,,P0IJIIIIM[mG±dccccadcccca d 1 … STSSrWewQ llllj STSSrWewQ TQPQNQL3936u<B?>~: d 2 llllj STSSrWewQ llllj kkkki TQPQNQL3936u<B?>~: d 3 … … STSSrWewQ STSSrWewQ TQPQNQL3936u<B?>~: d 4 kkkki kkkki … … [XWXXtSXUTUUPifeffa d 5 llllj … STSSrWewQ … [XWXXtSXUTUUPifeffa iiig±$$HIJIIIIM[mG33334W7W STSSrWewQSTSSrWewQ----DQ1 +++O/RSRRqVdvPnnnNONNNR`rLjjjjhdcccca RSRRqVdvP88889986<\6 GHGGGGGKYkE33334W7W„ dcccca33334W7WNONNNR`rLjjjjhCCDCCCCGUgALMLLP^pJ33334W7WNONNNR`rLjjjjh ssRSRRqVdvPbaaaa_00001T4Tdcccca 88889986<\6RSRRqVdvPbaaaa_ 33334W7W±,,,P0@@@A@@@DRd> 00001T4TRSRRqVdvP,,,P0nnnLMLLP^pJ33334W7WNONNNR`rLjjjjhYZYY]kx}W iiig@@@A@@@DRd>33334W7W ±dccccadccccaCCDCCCCGUgA<<<=<<@`:NONNNR`rL33334W7W00001T4T ,,,P0IJIIIIM[mG±dccccadcccca33334W7Wdcccca ±baaaa_33334W7W <<<=<<@`:CCDCCCCGUgAqqq33334W7WNONNNR`rL CCDCCCCGUgANONNNR`rL jjjjh@@@A@@@DRd>33334W7W IJIIIIM[mG±dccccajjjjh ,,,P0RSRRqVdvPIJIIIIM[mGnnnLMLLP^pJNONNNR`rL VWVVZhuzT [XWXXtSXUTUUPifeffa 88889986<\6RSRRqVdvPbaaaa_ UVUUtYgtySRSRRqVdvPdccccaCCDCCCCGUgAjjjjhCCDCCCCGUgAqqq33334W7W ±NONNNR`rL00001T4T TQPQNQL3936u<B?>~: 88889986<\6RSRRqVdvPbaaaa_ NONNNR`rL33334W7W<<<=<<@`:±jjjjhCCDCCCCGUgAqqq33334W7WWXWW[iv{UYZYY]kx}W 00001T4TRSRRqVdvP,,,P0 jjjjh33334W7Wujjjjh ,,,P0IJIIIIM[mG±dccccadcccca d 6 AAABAAAESe? BBBCBBBBFTf@ ±LMLLP^pJ @@@A@@@DRd>±UVUUtYgtySUVUUtYgtyS„....ER2 @@@A@@@DRd>±UVUUtYgtySUVUUtYgtyS„ ssCCDCCCCGUgAjjjjh@@@A@@@DRd> jjjjh@@@A@@@DRd>33334W7W 33334W7Wu,,,P0CCDCCCCGUgAjjjjhCCDCCCCGUgANONNNR`rL<<<=<<@`: baaaa_33334W7WdccccannnIJIIIIM[mGjjjjh....ER2 $$Hnnnjjjjh 88889986<\6nnnbaaaa_CCDCCCCGUgARSRRqVdvPnnndcccca ±jjjjh „RSRRqVdvPnnnbaaaa_ ±jjjjhjjjjhCCDCCCCGUgAjjjjhnnn00001T4T33334W7WYZYY]kx}W TQPQNQL3936u<B?>~: d 7 AAABAAAESe? BBBCBBBBFTf@ 00001T4TRSRRqVdvPNONNNR`rLǶjjjjh jjjjh@@@A@@@DRd>CCDCCCCGUgANONNNR`rLGHGGGGGKYkE jjjjh@@@A@@@DRd>33334W7W„ǶIJIIIIM[mGIJIIIIM[mG $$H33334W7W @@@A@@@DRd>±UVUUtYgtySUVUUtYgtyS„ ssCCDCCCCGUgAjjjjh@@@A@@@DRd> jjjjh@@@A@@@DRd>33334W7W dcccca33334W7W33334W7WLMLLP^pJIJIIIIM[mG„ @@@A@@@DRd>±UVUUtYgtySUVUUtYgtyS„ NONNNR`rL33334W7Wssdcccca....ER2 ss@@@A@@@DRd>CCDCCCCGUgA,,,P0@@@A@@@DRd> LMLLP^pJ±GHGGGGGKYkE33334W7Wdcccca TQPQNQL3936u<B?>~: LMLLP^pJ33334W7W nnnUVUUtYgtySdcccca33334W7Wjjjjh baaaa_±jjjjh@@@A@@@DRd>33334W7Wbaaaa_ jjjjh@@@A@@@DRd>±NONNNR`rL @@@A@@@DRd>±UVUUtYgtySUVUUtYgtyS„YZYY]kx}W d 8 AAABAAAESe? iiig@@@A@@@DRd>33334W7W 33334W7Wu,,,P0CCDCCCCGUgAjjjjhCCDCCCCGUgANONNNR`rL<<<=<<@`: NONNNR`rL33334W7Wssdcccca CCDCCCCGUgAdcccca IJIIIIM[mGCCDCCCCGUgAGHGGGGGKYkE33334W7W ±NONNNR`rL 33334W7Wu,,,P0CCDCCCCGUgAjjjjhCCDCCCCGUgANONNNR`rL<<<=<<@`: <<<=<<@`:CCDCCCCGUgA88889986<\6jjjjh....ER2 00001T4TCCDCCCCGUgAdccccaUVUUtYgtyS33334W7WIJIIIIM[mGIJIIIIM[mGCCDCCCCGUgANONNNR`rL<<<=<<@`: LMLLP^pJ„ nnnUVUUtYgtySdcccca33334W7Wjjjjh LMLLP^pJRSRRqVdvPRSRRqVdvP00001T4TYZYY]kx}W [XWXXtSXUTUUPifeffa iiig±$$HIJIIIIM[mG33334W7W STSSrWewQllllj----DQ1 iiig33334W7Wujjjjh RSRRqVdvP88889986<\6 jjjjh33334W7WdccccajjjjhCCDCCCCGUgANONNNR`rL<<<=<<@`: 00001T4TRSRRqVdvP,,,P0nnnLMLLP^pJ33334W7WNONNNR`rLjjjjhdcccca....ER2 ss@@@A@@@DRd>33334W7Wbaaaa_33334W7W jjjjh@@@A@@@DRd>33334W7W <<<=<<@`:baaaa_RSRRqVdvPnnnNONNNR`rL00001T4TAAABAAAESe?jjjjhbaaaa_nnnjjjjh@@@A@@@DRd> ,,,P0IJIIIIM[mG±dccccadcccca33334W7Wdcccca ±baaaa_33334W7W 00001T4TCCDCCCCGUgAdccccaUVUUtYgtySIJIIIIM[mG±„33334W7W00001T4T CCDCCCCGUgANONNNR`rL jjjjh@@@A@@@DRd>33334W7W IJIIIIM[mG±dccccajjjjh ,,,P0RSRRqVdvPIJIIIIM[mGnnnLMLLP^pJNONNNR`rLYZYY]kx}W MNMMMQ_qK±qqq33334W7W ##G±„33334W7Wdcccca ±IJIIIIM[mGIJIIIIM[mGRSRRqVdvPssdcccca nnndcccca jjjjhRSRRqVdvP 00001T4T33334W7W´NONNNR`rL33334W7W jjjjh@@@A@@@DRd>33334W7W 88889986<\633334W7W±jjjjhnnnbaaaa_33334W7Wdcccca ss33334W7W ss±NONNNR`rLjjjjh CCDCCCCGUgANONNNR`rL jjjjh33334W7Wujjjjh ,,,P0IJIIIIM[mG±dccccadccccaCCDCCCCGUgA´,,,P0±jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rLYZYY]kx}W BBBCBBBBFTf@NONNNR`rL jjjjh@@@A@@@DRd>CCDCCCCGUgAdcccca \]\\\n{Znnn33334W7WdccccajjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rL....ER2 „RSRRqVdvPnnn ssCCDCCCCGUgAIJIIIIM[mGIJIIIIM[mG nnnjjjjhCCDCCCCGUgAIJIIIIM[mGCCDCCCCGUgA»33334W7W MNMMMQ_qK±qqq33334W7W ##G±„33334W7Wdcccca VWVVZhuzT±NONNNR`rL00001T4T CCDCCCCGUgAjjjjhdcccca qqq±baaaa_CCDCCCCGUgA±NONNNR`rLjjjjhdccccaWXWW[iv{U jjjjhRSRRqVdvP 00001T4TRSRRqVdvP dcccca33334W7WNONNNR`rLjjjjhCCDCCCCGUgALMLLP^pJ33334W7WNONNNR`rLjjjjh ±NONNNR`rL±IJIIIIM[mG„dccccaCCDCCCCGUgAdccccaYZYY]kx}W iiigRSRRqVdvP dccccaCCDCCCCGUgALMLLP^pJUVUUtYgtySIJIIIIM[mGCCDCCCCGUgA88889986<\6„....ER2 ss33334W7W ´u jjjjh@@@A@@@DRd>33334W7W dcccca33334W7Wjjjjh RSRRqVdvP88889986<\6 GHGGGGGKYkE33334W7W„ dcccca33334W7WNONNNR`rLjjjjhCCDCCCCGUgALMLLP^pJ33334W7WNONNNR`rLjjjjh ssRSRRqVdvPbaaaa_00001T4Tdcccca ±dcccca 0<4kx5-LDFMtumLDFMWOQXE=?7/f IAC&^VX_`^VX_`„7/f yq^VX_`dfmn<4ktum7/f A9;yqjbdklLDFM[SU\yqdfmn1 YZYY]kx}W ²NONNNR`rL00001T4T jjjjh@@@A@@@DRd>33334W7W ssRSRRqVdvPbaaaa_00001T4T ,,,P0RSRRqVdvPnnnNONNNR`rLjjjjhdcccca RSRRqVdvP88889986<\6 33334W7W±,,,P0@@@A@@@DRd> 00001T4TRSRRqVdvP,,,P0nnnLMLLP^pJ33334W7WNONNNR`rLjjjjh ±baaaa_33334W7W UVUUtYgtySbaaaa_RSRRqVdvPqqqCCDCCCCGUgA00001T4T33334W7W00001T4T CCDCCCCGUgANONNNR`rL iiig±$$HIJIIIIM[mG33334W7W STSSrWewQSTSSrWewQ ssCCDCCCCGUgAjjjjh@@@A@@@DRd> jjjjh@@@A@@@DRd>33334W7W dcccca33334W7WNONNNR`rLjjjjhCCDCCCCGUgALMLLP^pJ33334W7WNONNNR`rLjjjjh ,,,P0IJIIIIM[mG±dccccadcccca ±dcccca jjjjh@@@A@@@DRd>33334W7W jjjjhbaaaa_±CCDCCCCGUgANONNNR`rLCCDCCCCGUgANONNNR`rL<<<=<<@`: ,,,P0RSRRqVdvPbaaaa_UVUUtYgtySnnndccccaYZYY]kx}W BBBCBBBBFTf@NONNNR`rL jjjjh@@@A@@@DRd>33334W7W 88889986<\6RSRRqVdvPIJIIIIM[mGIJIIIIM[mGRSRRqVdvPssCCDCCCCGUgANONNNR`rL<<<=<<@`: jjjjh±dccccaGHGGGGGKYkEdcccca....ER2 „RSRRqVdvPnnn NONNNR`rL33334W7W33334W7W00001T4T jjjjhRSRRqVdvP jjjjhbaaaa_±CCDCCCCGUgANONNNR`rL MNMMMQ_qK±qqq33334W7W ##G±„33334W7Wdcccca VWVVZhuzT±NONNNR`rL00001T4T CCDCCCCGUgAjjjjhdcccca qqq±baaaa_CCDCCCCGUgA±NONNNR`rLjjjjhdccccaWXWW[iv{U RSRRqVdvPNONNNR`rL CCDCCCCGUgAjjjjh jjjjhRSRRqVdvP UVUUtYgtySbaaaa_33334W7W00001T4TCCDCCCCGUgA,,,P0jjjjh jjjjh@@@A@@@DRd>33334W7W ,,,P0IJIIIIM[mG±dccccadcccca RSRRqVdvP88889986<\6 jjjjh@@@A@@@DRd>33334W7W jjjjh33334W7WdccccajjjjhCCDCCCCGUgANONNNR`rL<<<=<<@`: dcccca±LMLLP^pJUVUUtYgtySIJIIIIM[mG33334W7Wdcccca CCDCCCCGUgANONNNR`rL iiig±$$HIJIIIIM[mG33334W7W STSSrWewQlllljYZYY]kx}W STSSrWewQYZYY]kx}W iiigbaaaa_±CCDCCCCGUgANONNNR`rL ± LMLLP^pJnnnIJIIIIM[mGjjjjhCCDCCCCGUgANONNNR`rLRSRRqVdvPLMLLP^pJCCDCCCCGUgA±IJIIIIM[mG MNMMMQ_qK±qqq33334W7W ##G±„33334W7Wdcccca LMLLP^pJRSRRqVdvP00001T4T33334W7WIJIIIIM[mG ssCCDCCCCGUgAjjjjh@@@A@@@DRd> ±00001T4T00001T4TAAABAAAESe?STSSrWewQ dccccaLMLLP^pJRSRRqVdvPRSRRqVdvPjjjjh@@@A@@@DRd>CCDCCCCGUgANONNNR`rL<<<=<<@`:YZYY]kx}W mmmdcccca33334W7W jjjjh@@@A@@@DRd>CCDCCCCGUgAdcccca LMLLP^pJRSRRqVdvP00001T4T33334W7WIJIIIIM[mG jjjjhRSRRqVdvP ±dccccadccccaCCDCCCCGUgA<<<=<<@`:NONNNR`rL ± ,,,P0IJIIIIM[mG±dccccadcccca VWVVZhuzT [XWXXtSXUTUUPifeffa RSRRqVdvPbaaaa_ TQPQNQL3936u<B?>~: WXWW[iv{U jjjjhRSRRqVdvP 33334W7W±,,,P0@@@A@@@DRd> RSRRqVdvP88889986<\6 jjjjh@@@A@@@DRd>33334W7W 00001T4TRSRRqVdvP,,,P0nnnLMLLP^pJ33334W7WNONNNR`rLjjjjh CCDCCCCGUgANONNNR`rL jjjjh33334W7WdccccajjjjhCCDCCCCGUgANONNNR`rL<<<=<<@`: dcccca33334W7WjjjjhYZYY]kx}W lllljYZYY]kx}W BBBCBBBBFTf@NONNNR`rL UVUUtYgtySbaaaa_±,,,P0jjjjhCCDCCCCGUgA,,,P033334W7W....ER2 ss@@@A@@@DRd>33334W7Wjjjjh@@@A@@@DRd>33334W7Wbaaaa_ ± ssRSRRqVdvPbaaaa_00001T4T RSRRqVdvP,,,P0,,,P0nnnbaaaa_dcccca RSRRqVdvPbaaaa_ NONNNR`rLRSRRqVdvPjjjjh nnndccccannn±IJIIIIM[mGIJIIIIM[mG„ LMLLP^pJ±jjjjhjjjjh33334W7Wbaaaa_dcccca LMLLP^pJRSRRqVdvPbaaaa_33334W7W jjjjh@@@A@@@DRd>±NONNNR`rL CCDCCCCGUgAjjjjhdcccca 88889986<\6baaaa_33334W7W\]\\\n{Znnn33334W7WNONNNR`rL,,,P0„....ER2 ss@@@A@@@DRd>CCDCCCCGUgA,,,P0@@@A@@@DRd> LMLLP^pJRSRRqVdvPjjjjhCCDCCCCGUgAqqq±jjjjh33334W7Wdcccca ± IJIIIIM[mGRSRRqVdvPjjjjh RSRRqVdvP88889986<\6 ssRSRRqVdvPbaaaa_GHGGGGGKYkEdcccca jjjjhRSRRqVdvP ,,,P0IJIIIIM[mGCCDCCCCGUgAUVUUtYgtyS jjjjh@@@A@@@DRd>33334W7W ssRSRRqVdvPbaaaa_00001T4T ,,,P0RSRRqVdvPnnnNONNNR`rLjjjjhdcccca VWVVZhuzT IFEFA_\[\\xW3936u_\[\\xW ....ER2 baaaa_33334W7WLMLLP^pJRSRRqVdvPqqq33334W7W ±IJIIIIM[mGIJIIIIM[mG 00001T4TnnnUVUUtYgtySIJIIIIM[mGCCDCCCCGUgA,,,P0±jjjjh33334W7W ssRSRRqVdvPbaaaa_00001T4TdccccaWXWW[iv{U CCDCCCCGUgANONNNR`rL 33334W7W±,,,P0@@@A@@@DRd> 00001T4TRSRRqVdvP,,,P0nnnLMLLP^pJ33334W7WNONNNR`rLjjjjhYZYY]kx}W ²NONNNR`rL00001T4T jjjjh@@@A@@@DRd>CCDCCCCGUgAdcccca qqq±baaaa_CCDCCCCGUgA±NONNNR`rLjjjjh CCDCCCCGUgAdcccca ,,,P0±IJIIIIM[mGIJIIIIM[mG33334W7W00001T4T $(GCGCECuRRPNN±eecaax PPNLLL~nnpMMIKII{ljjGCGCECuRRPNNVVTRRPPNLLL~GCGCECu±MMIKII{ QQOMMM±qs37373 #±x37373ggecc YZYY]kx}W +++O/RSRRqVdvPNONNNR`rLdccccajjjjhbaaaa_nnn,,,P0jjjjh ± $$HCCDCCCCGUgANONNNR`rL±baaaa_„ LMLLP^pJnnnIJIIIIM[mGjjjjhCCDCCCCGUgANONNNR`rLRSRRqVdvPLMLLP^pJCCDCCCCGUgA±IJIIIIM[mG MNMMMQ_qK±qqq33334W7W ##G±„33334W7Wdcccca LMLLP^pJRSRRqVdvP00001T4T33334W7WIJIIIIM[mG jjjjhbaaaa_±CCDCCCCGUgANONNNR`rL33334W7W00001T4T RSRRqVdvPNONNNR`rL jjjjh@@@A@@@DRd>33334W7W dcccca±LMLLP^pJ33334W7W ,,,P0RSRRqVdvPbaaaa_UVUUtYgtySnnndcccca....ER2 ±NONNNR`rL00001T4T nnndcccca33334W7W CCDCCCCGUgAjjjjh jjjjhRSRRqVdvP UVUUtYgtySbaaaa_33334W7W00001T4TCCDCCCCGUgA,,,P0jjjjh jjjjh@@@A@@@DRd>33334W7W IJIIIIM[mG±$$H33334W7WIJIIIIM[mGdcccca RSRRqVdvP88889986<\6 jjjjh@@@A@@@DRd>33334W7W jjjjh33334W7WdccccajjjjhCCDCCCCGUgANONNNR`rL<<<=<<@`: dcccca33334W7WjjjjhYZYY]kx}W kkkkiYZYY]kx}W mmmdcccca33334W7W jjjjh@@@A@@@DRd>33334W7W LMLLP^pJ33334W7Wjjjjhbaaaa_CCDCCCCGUgA,,,P0dcccca ss33334W7WǶqqq33334W7W IJIIIIM[mG33334W7W±baaaa_NONNNR`rL33334W7W00001T4T 88889986<\6baaaa_RSRRqVdvPLMLLP^pJ ,,,P0IJIIIIM[mG±dccccadcccca jjjjhRSRRqVdvP 33334W7Wqqq±IJIIIIM[mGnnn±jjjjh33334W7W jjjjh@@@A@@@DRd>33334W7W baaaa_33334W7WdccccannnIJIIIIM[mGjjjjhdccccaYZYY]kx}W +++O/±NONNNR`rL „RSRRqVdvPnnn dcccca33334W7W33334W7W dccccaRSRRqVdvPLMLLP^pJ33334W7W 00001T4TCCDCCCCGUgA‰33334W7Wbaaaa_33334W7WNONNNR`rL,,,P033334W7W CCDCCCCGUgANONNNR`rL jjjjh@@@A@@@DRd>33334W7W UVUUtYgtySbaaaa_33334W7W00001T4TCCDCCCCGUgA,,,P0jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rLdcccca RSRRqVdvP88889986<\6 jjjjh@@@A@@@DRd>33334W7W jjjjhssRSRRqVdvP LMLLP^pJRSRRqVdvP00001T4T33334W7WIJIIIIM[mGdcccca]^]]]o|[ rrr@@@A@@@DRd>CCDCCCCGUgA,,,P0@@@A@@@DRd> LMLLP^pJ33334W7Wjjjjhbaaaa_CCDCCCCGUgA,,,P0 00001T4TRSRRqVdvP „RSRRqVdvPnnn jjjjh@@@A@@@DRd>CCDCCCCGUgANONNNR`rLGHGGGGGKYkE $$H33334W7Wjjjjhjjjjh33334W7Wbaaaa_ baaaa_33334W7Wˆ33334W7W,,,P0jjjjhdcccca jjjjh@@@A@@@DRd>33334W7W LMLLP^pJRSRRqVdvP00001T4T33334W7WIJIIIIM[mGdccccaǶ UVUUtYgtyS33334W7Wbaaaa_88889986<\6RSRRqVdvPbaaaa_LMLLP^pJ±NONNNR`rL,,,P033334W7W]^]]]o|[ ::::;:8>^8YZYY]kx}W MNMMMQ_qK33334W7W<<<=<<@`:±jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rL CCDCCCCGUgAdcccca ±NONNNR`rL CCDCCCCGUgALMLLP^pJUVUUtYgtySRSRRqVdvPbaaaa_jjjjh±NONNNR`rLjjjjh CCDCCCCGUgAdccccadccccannn33334W7W CCDCCCCGUgANONNNR`rL dcccca33334W7WNONNNR`rLjjjjhCCDCCCCGUgALMLLP^pJ33334W7WNONNNR`rLjjjjh ±NONNNR`rL±IJIIIIM[mG„dccccaCCDCCCCGUgAdccccaYZYY]kx}W 777788[5;[5RSRRqVdvPbaaaa_ 33334W7Wu±LMLLP^pJUVUUtYgtySIJIIIIM[mG33334W7W....ER2 CCDCCCCGUgANONNNR`rL d 6 ....ER2 CCDCCCCGUgAjjjjh ,,,P0@@@A@@@DRd>±NONNNR`rL<<<=<<@`:33334W7Wdcccca jjjjh@@@A@@@DRd>33334W7W dcccca33334W7WNONNNR`rLjjjjhCCDCCCCGUgALMLLP^pJ33334W7WNONNNR`rLjjjjh UVUUtYgtySRSRRqVdvPIJIIIIM[mG±baaaa_CCDCCCCGUgAjjjjhCCDCCCCGUgA33334W7Wdcccca RSRRqVdvP88889986<\6 jjjjh@@@A@@@DRd>33334W7W GHGGGGGKYkE33334W7W„ ssRSRRqVdvPbaaaa_00001T4TdccccaYZYY]kx}W +++O/±NONNNR`rL „RSRRqVdvPnnn jjjjh@@@A@@@DRd>CCDCCCCGUgANONNNR`rLGHGGGGGKYkE RSRRqVdvP88889986<\6 ±NONNNR`rL CCDCCCCGUgA00001T4T33334W7W± jjjjhRSRRqVdvP ±00001T4T00001T4Tbaaaa_33334W7Wdccccadcccca jjjjh@@@A@@@DRd>33334W7W CCDCCCCGUgANONNNR`rLˆnnn33334W7WNONNNR`rL,,,P033334W7W RSRRqVdvP88889986<\6 NONNNR`rL33334W7W<<<=<<@`:±jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rL @@@A@@@DRd>33334W7Wbaaaa_33334W7W]^]]]o|[ ?C?C??GCGCECuRRPNNljjggecc YZYY]kx}W ‚RSRRqVdvPnnn ,,,P0±NONNNR`rL nnnjjjjhCCDCCCCGUgAIJIIIIM[mGCCDCCCCGUgA»33334W7W jjjjh@@@A@@@DRd>33334W7W IJIIIIM[mGRSRRqVdvP<<<=<<@`:UVUUtYgtySbaaaa_CCDCCCCGUgARSRRqVdvPbaaaa_dcccca ±NONNNR`rL00001T4T IJIIIIM[mGRSRRqVdvP<<<=<<@`:IJIIIIM[mGCCDCCCCGUgAGHGGGGGKYkE33334W7WIJIIIIM[mGCCDCCCCGUgA@@@A@@@DRd>RSRRqVdvPRSRRqVdvP00001T4Tdcccca $$H33334W7WIJIIIIM[mGRSRRqVdvPss 88889986<\6RSRRqVdvPbaaaa_ „RSRRqVdvPnnnbaaaa_ ,,,P0±IJIIIIM[mG,,,P0nnnIJIIIIM[mG±jjjjhCCDCCCCGUgARSRRqVdvPNONNNR`rLYZYY]kx}W a```r^33334W7W,,,P0±IJIIIIM[mGIJIIIIM[mG jjjjh@@@A@@@DRd>33334W7W 88889986<\6RSRRqVdvPbaaaa_LMLLP^pJnnnIJIIIIM[mG±dcccca jjjjhRSRRqVdvP ,,,P0±IJIIIIM[mG,,,P0nnnIJIIIIM[mG±jjjjh33334W7W jjjjh@@@A@@@DRd>33334W7W IJIIIIM[mGRSRRqVdvP<<<=<<@`:AAABAAAESe?UVUUtYgtySbaaaa_CCDCCCCGUgARSRRqVdvPbaaaa_ 88889986<\6RSRRqVdvPbaaaa_ ± ,,,P0IJIIIIM[mG±dccccadcccca c VWVVZhuzT STSSrWewQSTSSrWewQWXWW[iv{U ±NONNNR`rL00001T4T jjjjh@@@A@@@DRd>33334W7W VWVVZhuzT±00001T4T00001T4TAAABAAAESe?RSRRqVdvPNONNNR`rL33334W7WWXWW[iv{U IJIIIIM[mGRSRRqVdvP<<<=<<@`:AAABAAAESe?IJIIIIM[mGCCDCCCCGUgAGHGGGGGKYkE33334W7WIJIIIIM[mGCCDCCCCGUgA@@@A@@@DRd>RSRRqVdvPRSRRqVdvP00001T4T 88889986<\6RSRRqVdvPbaaaa_ ± ssRSRRqVdvPbaaaa_00001T4T w ssYZYY]kx}Wbaaaa_YZYY]kx}Wjjjjh ± ,,,P0IJIIIIM[mG±dccccadcccca c VWVVZhuzT STSSrWewQlllljWXWW[iv{U----DQ1 logprior [ c ] ← log N c N doc VWVVZhuzTSTSSrWewQSTSSrWewQWXWW[iv{U loglikelihood [ w , c ] ← log count ( w , c ) + 1 ∑ w 0 ∈ V ( count ( w 0 , c ) + 1 ) VWVVZhuzTSTSSrWewQlllljWXWW[iv{U iiig@@@A@@@DRd>33334W7WNONNNR`rL 88889986<\6RSRRqVdvPbaaaa_ LMLLP^pJnnnIJIIIIM[mGjjjjhCCDCCCCGUgANONNNR`rLRSRRqVdvPLMLLP^pJCCDCCCCGUgA±IJIIIIM[mG MNMMMQ_qK##G....ER2 ss33334W7W @@@A@@@DRd>±qqq33334W7W jjjjh@@@A@@@DRd>33334W7W baaaa_33334W7WdccccannnIJIIIIM[mGjjjjhdcccca ±dcccca 88889986<\6RSRRqVdvPIJIIIIM[mGIJIIIIM[mGRSRRqVdvPssdcccca----DQ1 logprior [ pos ] = log 2 5 , logprior [ neg ] = log 3 5 TUTTsXfsxR±<<<=<<@`:33334W7W kkkki RSRRqVdvP88889986<\6 ::::;:8>^8

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loglikelihood [ exciting , pos ] = log 5 + 1 9 + 4 = log 6 13 , loglikelihood [ exciting , neg ] = log 2 + 1 14 + 4 = log 1 6 loglikelihood [ happy , pos ] = log 3 + 1 9 + 4 = log 4 13 , loglikelihood [ happy , neg ] = log 2 + 1 14 + 4 = log 1 6 loglikelihood [ upset , pos ] = log 1 + 1 9 + 4 = log 2 13 , loglikelihood [ upset , neg ] = log 5 + 1 14 + 4 = log 1 3 loglikelihood [ f urious , pos ] = log 0 + 1 9 + 4 = log 1 13 , loglikelihood [ f urious , neg ] = log 5 + 1 14 + 4 = log 1 3 777788[5;[5RSRRqVdvPbaaaa_ $$HCCDCCCCGUgANONNNR`rL±baaaa_„ MNMMMQ_qK##G....ER2 ss33334W7W @@@A@@@DRd>±qqq33334W7W jjjjh@@@A@@@DRd>33334W7W baaaa_33334W7WdccccannnIJIIIIM[mGjjjjhdcccca ±dcccca 88889986<\6RSRRqVdvPIJIIIIM[mGIJIIIIM[mGRSRRqVdvPssdcccca----DQ1 logprior [ pos ] = log 2 5 , logprior [ neg ] = log 3 5 loglikelihood [ exciting , pos ] = log 2 + 1 4 + 4 = log 3 8 , loglikelihood [ exciting , neg ] = log 1 + 1 9 + 4 = log 2 13 loglikelihood [ happy , pos ] = log 1 + 1 4 + 4 = log 1 4 , loglikelihood [ happy , neg ] = log 2 + 1 9 + 4 = log 3 13 loglikelihood [ upset , pos ] = log 1 + 1 4 + 4 = log 1 4 , loglikelihood [ upset , neg ] = log 3 + 1 9 + 4 = log 4 13 loglikelihood [ f urious , pos ] = log 0 + 1 4 + 4 = log 1 8 , loglikelihood [ f urious , neg ] = log 3 + 1 9 + 4 = log 4 13 TUTTsXfsxR±<<<=<<@`:33334W7W ::::;:8>^8 RSRRqVdvP88889986<\6 ::::;:8>^8

CS4248_Tutorial_2

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