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2016 FunctionCup 풀이

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  • 2. nnnn nnnnnnnnnnn n nnnnnnnn - - - ss ssssss ssssssss 44 77 7
  • 3. nnnn nnnnnnnnnnn n nnnnnnnn - - - s ssss ssss ; ;;; ; ;; ; ; ;;; ;; ;; ;; ;; ;; ; ;; ; ;; ;; ;V V V VVV V VVVVV ; ;; ;;;; ; ; ;;; ;;;; ; ;; ;; ;; ; ;;; ; ; VVVVV V ;; ;;;; ;; ; ; ; ;; ; ;; ;; ; ; ;; ;; ;V V fVV V Vfff Vfff ;; ;;; ;; ;; ; ;;; ; ; ; ;; V ;22VV22 44
  • 4. nnnn nnnnnnnnnnn n nnnnnnnn - - - s ssss sssss | ; || | ; ;| ; | |; | |;| || | ; ;„„„2„ „2 „„V „„„ „„V „„„ ; ;; ; ŽŽ ; Ž| | Ž7 Ž| Ž Ž Ž Ž| Ž Ž2„„„2„ „2 „„„2 „„ 2f Vff fff 2 „„ 2f Vff fff 2 ;; Ž| Ž| ; Ž| ; 2„f „ „ „„ „‹‹‹‹ „„ „‹‹‹‹ ;; ¡ ¡ ;¡ ¡; ¡ ; ;; ; 222Vf2 2‹ ‹2 2 ‹ fž„‹‹‹‹ ‹ ‹ fž„‹‹‹‹ ‹ 2 2„„„2 ž‹‹‹‹‹‹ ; ; ¡ ; ;;; ;| š; ;‹ ‹ ž f ž‹‹‹‹‹‹ V ž‹‹„V‹‹‹‹ „ ž‹‹‹‹‹„V‹ „ ž‹‹„V‹‹‹„V‹ „ 22„‹‹‹‹ „‹‹‹‹2 2 ; ;ž‹‹‹‹‹‹ V f ;| | || | ; ; ; ;;;„‹‹‹‹ „ † „‹‹‹„V‹ „‹‹‹‹ „ † „‹‹‹„V‹ 2„ „2 „„„ ž‹‹‹‹‹‹ ‹ ‹­ ­ ; ž‹‹‹‹‹‹ ž f 2„‹‹‹„V‹ „ „‹‹‹‹2 „ 2„‹‹‹„V‹ „ „‹‹‹‹2 ¯ ;222Vf2 44 ;°°°;
  • 5. nnnn nnnnnnnnnnn n nnnnnnnn - - - s s s sss ss ss ; ³ ;; ; ¡; ³³ ; ³; ; ;‹œ‹œ2œœ22 œ ‹œ‹œ2œœ22 Vf 44 77 7
  • 6. nnnn nnnnnnnnnnn n nnnnnnnn - - - s ssss ssss ½V ž ¦2„V„¦2½ ¡;; ½ ½ || ; ;°°°; ;½ 7½ ; ;š š|;š šš;; š; ½ ; ; šš ;š; ; ; 2 2 œ ¼¼‹œ‹ ¼¼‹œ‹ V ¼¼‹œ„¦‹ ‹ „ V 2‹ ¦‹ ½œ­ ;‹2 ;°°°; š|;š ½ ; ; šš ;š; ; ; œ ž¼‹œ‹ ž¼‹œ‹ V „‹¼2ž¼‹œ„¦‹ ;‹ „ V2 Ñ ÑÑ ¡; ;š š|;š; °; ¡; ;š š|;š; °;; ³; Ñ4;;; ;Ñ ; ½ ;š š|;š; °; ½ ¦ ž ¦2„V„¦2; ;; ½ ; ;³ ; ½ ½ À ° ¦2½½; ;š ½ š; ¦2½½; ;š „¦2½ ½½ š; ½ ° ; ž ¦2;;; ;š š|;š ; ¦2½½; ;š ; ³; ; ;š š|;š; °; ; Ž 7; ½ À ° ¦2½½; ;š À ½ ;; ° ;š ‹ „¦‹½ ½½ š; ° ; „¦‹ ;;; ;š š|;š ;½ † „¦‹½ À š;; ° ; ¦2 „¦­ ‹;;; „¦‹½ ½½ ° ¦2½½; ;š; ; ;½ šš ;; ½ ½½ ° V ¦2½½; ;š; ; ;½V šš ; Ž 7; ;; V ž ¦2„V„¦2½ ¡;; ½ ;š š|;š; °;; ¡; ;š š|;š; °;; ³ š ; 44 ;š ;°°°;
  • 7. nnnn nnnnnnnnnnn n nnnnnnnn - - - s ssssss sssss ;; š ; ; ; ½ ½ ;; ; ; š ; ;; š ; 7 ; | ;; š ; ; ;; š ; ;; ;; š ; ; ;; ; ;š ;½ š ; ; ; ; š;;; ;½ ; Ž š ; 7 ;| ; š ; ;; Ž f f V f 2 ¦ f ¦õ š ; 7 ; Ê Ê š ; 7 ÊÊ ; Ê š;; ¦ V f ¦„V f ¦„V 2 fõ õ ; ; š ; š ; ;¡;¦„V 2 ¦ V f ¦„Võ õ ; ;š ½ ; ;½ ; 22V2 ! #ý„V ý„V ! # „V f V f 2 ý„V „õ 77 7 77 7 7 7þ „ V ž þ„V „þ „ V ž þ„V 7 7 7 7 # „þ „þ „þ „þ „þ 7 7 „þ „þ „þ „þ 7 7„þ „þ œþ‹‹‹ 77 77 77 #
  • 8. nnnn nnnnnnnnnnn n nnnnnnnn - - - # 7 7 # # # 7 # # ­ 7 7 õ %%% %%% %% %% %%%% %%% %% %% %% %% %% % %% %% %% % %%%% %%%% %% ?% ????? %?%? % ??%III I I I I #% ?%% # ####%% %I I I ???? @
  • 9. nnnn nnnnnnnnnnn n nnnnnnnn - - - s ss ssss % ZZ% ZZ% Z ZZ% Z% % ZZ Z % %% %?%? ZZ Z% Z# Z%% ? %?%% ZZ% I I %% % kk kkkk?k% ? %%Zk% %k% Z` `` `% ``? `% Z %Z% `% ````? ` %%% %`%%` %%% %`%%% `` ?  % %% %Z% Z %Z %? „ %% ?@Z @@%% % @@@ %%% Z ZZ ? ?%% @ I I
  • 10. ­ ­ ­ V % ####%? kk% %# ##% ## % Z ZZ % # % #` ? # ­ ­ % #` ? ?`@ %%@ % %`%% z?z % %z %%% zZ z % zZ? zz%z z% k% ?k% `@ % % ?k% % % @@@ % z z% ¤¤ @ ¤¤%% ¤% ¤¤¤ % ¤`¤ z¤% ¤?k ¤ Z  %# ¤¤ % ¤`¤ z¤ z % Z¤% ¤¤ z¤ % ¤?k ¤ Z # % `®® ®¤ Z%  %Z% %%% %`%%% ¤?k `®® ®
  • 11. nnnn nnnnnnnnnnn n nnnnnnnn - -- - ¤ Z%  %# ¤¤¤ % ¤`¤ z¤% %`% %`%%%  `% % % ?% %%%%% %%% %`%% z % zœ% %%? œz zz% ½ z#% ?% @`%% %% #Z%? `®® ®¤ ½¤%? ½z ?% %`½`? ?% %% !%`! % #`%! ?!! Z  Z !?! ? ?`@ %%% !%`!% ####%% I I I I
  • 12. I I V % kÈ ZÉ zZÉ I
  • 13. nnnn nnnnnnnnnnn n nnnnnnnn - -- - s ss ss % %% % %% ¤Z %²`k% # ²% ²²%% %Z? œ²% % %% #% ²²%% ²%¤²%Ô I Ô Ô ×?% % % Ø Z # % ØØ ? ØØ Ø % %% Ø ØØ`@ %Ô Ô Ô I Ô kÈ
  • 14. nnnn nnnnnnnnnnn n nnnnnnnn - -- - s sssss Z` `Z% ``? %z#`% % #% `! ?%%z `k? `Z% ``? k% á% % `` ? á% @ á`% ##% `` %% `` ½z% %`%%% á%` á %# `` ? @%% á% % #`% %`% `` ? á% @ á`% ##% %% `` ? á% @ á`% ##% I % ` % Z%% %%% #`% á% @ á`% ##% k `` %% !% !% # ! `Z% `` %% I !% !% # ! `Z%% #zì % ìì Z % % #zì% `% % I I ò `k% `Z% ``? %œ z%% ¤ ``? #ZØ % %% %`%%% á%? ¤Z ?% ¤ %á%% % ####% I % ¤¤²? á% @ á`% ##% ?! Z  õ%%` õõ !%`!% %?`% k` ¤¤ õ #% %`%%? ?% õ  ``? Ø % %? ¤¤²? á% @ á`% ##% ú²% % ####%% ZZ? `! Z I kÈ õ%%` õõ !%`! %`%%
  • 15. nnnn nnnnnnnnnnn n nnnnnnnn - -- - s s s s ; ; ; ; ;; ; ; ;II II I III III III II III III II II II # # ;# # #;# ; # ##; ; # ## # #I I ;IIII IIII IIII III # ; ; ; # I _ _I_I ; # ## # _III`_ I I _ _I_I`_I_`II `` _`I`_ I _ `I_I # ; ; I _ ` p qr ;; ; ; s t## l l l ` # # ; # # ## ` I ‚ ; # # # ‚ I †† ˆ ˆˆ# ; ; ## # ‹Œ • ‚ ;#Ž# l`II l`II I I lõ ‚ ; #   # # # ;# ; #
  • 16. nnnn nnnnnnnnnnn n nnnnnnnn - -- - ; # ” ””””” ” ” ” ” ” # ## ” #¡ I I I ¡¡ ¡I_I # ¤ ;# # ; ; #¤ # ¤` ¡I_I ¢ _ ` ` ¢IIII I ¢I¢I Iõ
  • 17. #
  • 18.
  • 19. #; #
  • 20.
  • 21. I _ _`II _`II I I õ ¡I_I I _ ± _ ² I ²`II ² I ²`II I ² I _`II ² ± _õ ³ #¤ # I #¤ # ‚ ; # ;´ ## µµ µ¡I_I I I» ¼ #¤ # ¼ #¤ # ³¼´¼ ;´ ¼ ; À ” ## #‹ • ; ¼” # ¡I_I ¡IlI
  • 22. µ¼ ¡I_I ¢_¢I ” ”##
  • 23. µ¼I ¢_¢I I I Iõ ;#
  • 24. ¢_¢I µ¼ ³² I ²`II ² I ²`II I ² I _`Iõ #¤ # ¤ ² I _`I ² ± _ #¤ # # ; ´ ´ ¼ I ¤ Ȑ” É• ; Ê Ë À Ì Œ”# Í ¼I I
  • 25. # ## # # Ž# ˆ#
  • 27. nnnn nnnnnnnnnnn n nnnnnnnn - -- - s ss s ssss ÒÓ ; ÒÓ Í Ô I _ÕÕÕ`Õ_`Õ ÒÓ ; ‹ _II _II _II I _õ _ ; Ô_ÕÕÕ`Õ_`Õ _I² Õ_Ý _ I _² #II I Õ__ I _² #II I ` III Il_ I l² #II I ` l_ I á² #II I ` á_ I l² #II I ` á_ I á² # II II ;# ; _I ² Õ__ I _² # ## # ;II I III l_ ± l² Ê # #_ ² _ ² ;# #;# ;#Ž#² _ Õ__ ± _² # II I III l_ ` l² Ê #Õ_ ± Õ² _ ² Õ__ ± _² # II I III #I l_ ##I l_ ”# Õ_ ## # Ô ; ÒÓ# # Ô _ ¢_ I ## ; ¢_ Ä`Ä_ kÈ è ‹ #èI I
  • 28. nnnn nnnnnnnnnnn n nnnnnnnn - -- - s ss s ssss s sss | |_ÄI _Ä`II I _õ ` ”   ;  î |_ÄI _Ä`II I _õ ``¢ ”   ;   |î I |_ÄI _Ä`II I _õ ` ”   ;   î |_ÄI _Ä`II I _õ ``¢ ”   ;   î ” ;# ; ”   ;   Ô
  • 29. I Ä ` ``Ä`I ; | |_ÄI _Ä`II I _õ ` ”   ;   î |_Ä`II I _õ ` ”   ;   î # Ô ¼ ” ; ”  Ä ` Ä`I I I ` Ä`I Ô ` ` I _I # | ”   ;   ‹ Ô I ` I _I # Ô I ` I õ ÷ ˆ# ## ;ˆµˆ ³¼ ‹ ¼# ;¢_ |ê
  • 30. «
  • 31. nnnn nnnnnnnnnnn n nnnnnnnn - -- - s sssss sss !I I _ I _ ## # # # # # # O O $ $$ $ $ $ # #V O VVVV VVVVVV # __ $_ $$ $_ __ $ _ # _ _ $ _ _ _ # $$ $_ ; ;$ ;; # # ;; ; ;; _; # $$ $ ;# $ # _ # __ $_ # ; $$ $_ $ __ $_ _ h h
  • 32. nnnn nnnnnnnnnnn n nnnnnnnn - -- - ! ; # # # _ _ _ $$ $_ ;$ ! O h h # # # # … … … … $$ $_O V V ‰ V ‰ ;$ ! h # # # h $ $ ‹ ;‹ # … … ‹‹ O V #   ## # #  $$ $_ _   _  $# h h # # ;‹ $ !  O œ‰œ Vœ‰œ #V h‰œ h‰œ … ‹‹ # _ # $$ $$ #ž ;_ $ $;  ž ž $$ $œ‰œ œ‰œœ œ‰œœ O œœ  __ $_ ž $    ‹ ž ž   _O œ œ  V œ‰œœV V „„ž „ #ž „ „ ž „ „_  „ ; œ‰œV # O „ ;$ ž __ $_ #ž _ $ „„ V V # O h „ # _ ;‹ h # ³ $_ # ž # ³ ³„ $$ $$ #ž¶ ¶ V V œ ¶¶O¶¶¶ #­ — —— _ $$ $ ž # $$ $_½Vœ V½VœV ¶½œ‰ ½Vœ V½VœV ½Vœ V½VœV # ;Á _ $O