$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#>-~~~~~~~~~~~~~~~~~~~~~~:+%%&&$$$$########### $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&*:~~~~~~~~~~~~~~~~~~~~~--;?%&&$$$$$########## $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$=:;!---~~~~~~~~~~~-::-~~---!=&&$$$$$########## $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$>-;!!;!;-:-~~~~-:!)!;-~-----)&&$$$$$$######### $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+~;---;!!!!!;;!!;!*---------;=&&$$$$########## $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$####$+-;-~~~~---::----:;--------~-+&&&$$$$######### $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######?-;!+!-~~~~~~~~~~::~---------)&&&$$$$$######## $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######=:*)+=>:~~--;**:-:;-~--------!&&&$$$$$######## $$$$$$$$$$$$$$$$$$$$$$$$$&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######=-!::!+!-;>==?+*;-:;---------!%&&$$$$$######## $$$$$$$$$$$$$$$$$$$$$&?+***)>=&$$&==??=&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#$####=:;;*!!;--;;;:-----;!--------!%&&$$$$$$####### $$$$$$$$$$$$$$$$$$$%+;~^^^^^~-:*?>:~^^~-*?&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$####$#&)!;?);!~~~:*!!-~~-:;:--:;---*&&&$$$$$$####### $$$$$$$$$$$$$$$$$&>;~^^^^^^^^^^^~;**;:-^^~:!>%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##$$$$&)~;;;:~~~!?!::-~--;-~-!*!--+&&$$$$$$######## $$$$$$$$$$$$$$$$&+~^^^^^^^^^^^^^^^~:)+!;-~^^^-)%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#$$$$$&!~~;;-~~~:*:~-~~--;-~:***::=&&&$$$$$$####### $$$$$$$$$$&$$$$&)~^^^^^^^^^^^^^^^^^^~!*::;-~~^^:?$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%:~-!-~~~~~~~~~~~~-:-:!);!:;%$&$$$$$$$####### $$$$$$$$$$&&&$&?-^^^^^^^^^^^^^^^^^^^~-*);;!;;-^^~)&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$?-~-;-::-~~~~~~~~~~:!!!*;!:!%&&&$$$$$$$$##$$$ $$$$$$$$$$&&&&%!^^^^^^^^^^^^^^^^^^^^;;;:-~^^^^^^^^;=$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$>~~~----~~~~~~~~~~~-:-:;!!-!%&&&&$$$$$$$$$$$$ $$$$$$$$$$$&&&?~^^^^^^^^^^^^^^^^^^^^::-~^-:-~^^^^^^-+&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$?~~~~~~~~~~~~~~~~~~~~--;*:-!%&&&&$$$$$$$$$$$$ $$$$$$$$$$$$&&*^^^^^^^^^^^^^^^^^^^^,^-:::;+!;;-^^^^^~!=$$$$$$$$$$$$$$$$$$$$$$$&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$=-~-::--~~~~~~~~~~~~--;*;--!%&&&&$$$$$$$$$$$$ $$$$$$$$$$&&&%:^^^^^^^^^^^^^^^^^^^^^^^^^^^;)~~;;~^^^^^:>$$$$$$$$$$$$$$$$$$$$$&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&;~-;;;;;:;!-~~~~~~-:!);:--*&&&&&$$$$$$$$$$$$ $$$$$$$$$$&&&?-^^^^^^^^^^^^^^^^^^^^^^^^^^^~)):^~~^^^^^^~*%$$$$$$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&*~-;;:-----~~~~~~~-!;!:;::>&&&&$$$$$$$$$$$$$ $$$$$$$$$$&&&>~^^^^^^^^^^^^^^^^^^^^^^^^^~^^-?%>)!-^,^^^^^:+=$$$$$&$$$&&&&$$&&$&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$>-~:::-~~~~~~~~~~~;;:*!!:+&&&$$$$$$$$$$$$$$$ $$$$$$$$$$&&&+~^^~~^^^^^^^^^^^^^^^^^^^^-!;;~;&$$&=*~,^^^^-~^)%$$$&&&&&&&&$$&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$=:~~~~~~~~~~~~~~~:!-:*!;+&$&$$$$$$$$$$$$$$$$ $$$$$$$$$$&&&+~^^--^^^^^^^^^^^^^^^~;)!~~>$&)-+$$$$&>-^^^^:,'.->&&&&&&&&&&$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!~~~~~~~~~~~~~~;*:-:*)=&$$$$$$$$$$$$$$$$$$# $$$$$$$$$$&$&+~^^;-^^^^^^^^^^^^^^~+&#&*~+##$+;%$$$&&?:^,~;.''',;?&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$>-~~~~~~~~~~~-!*:--;?&$$$$$$$$$$$$$$$$$$#$$ $$$$$$$$$$&$&+~^~!-^^^^^^^^^^^^^~)$@@@%::%##$*)&$$&&&=:,--''''''^!=$$&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&*~~~~~~~~-:!*!----;=&&&$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$&$$+~^~!~^^^^^^^^^^^^^-%@@@@$!^!&##>-=$$&&&$=::,''''''''~)%&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&?*!:::;;**;-~----*=%&&&$$$$$$$$$$$$$$$$$$ $$$$$$$$$$&$&)~^:!~^^^^^^^^^^^^^;$@@@@#*^~*&#)^*$$&&&&%)-''''''''''.->&&$&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#$%*!;::--~~~~--*???%&&&$$$$$$$$$$$$$$$$$ $$$$$$$&&&&$&!^^;;~^^^^^^^^^^^^^!#@@@@#*^^^*%;^:&$&&&&%)^'''''''''''',;?&$&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&=:~~~~~~~~~~:)=?>>?%&&$$$$$$$$$$$$$$$$$ $$$$$$&&&&&$%;~~!-^^^^^^^^^^^^^^!&#@@@%:^^^~*-^~=$&&&&&%!,''''''''''''',!=&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&%===+-~~~~~~~~-!?=>>+>>=&&&$$$$$$$$$$$$$$$$ $$$$$&&&&&&&=-^-;~^^^^^^^^^^^^^^~:+%&?;^^^^^:;^^+$&&&&&&%),''''''''''''''^*=&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&%=?>?!~~~~~~~:*?=?>>+++>>%&&$$$$$$$$$$$$$$$$ $$$$$&&&&&&&)~^::^^^^^^^^^^^^^^^^^^--~^^^^^^~!~^)&&&&&&&&%+^'''''''''''''''~)=&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&%???>?:~~~~~-)==?>>++++++>?%&&$$$$$$$$$$$$$$$ $$$$$&&&&&&>;~^~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^!-^!&&&&&&&&&&>~'''''''''''''''.~)%&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&%?+>?>?!-~~~-+==?>++++++++>>%&&&$$$$$$$$$$$$$$ $$$$&&&&&&+;:-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^-:^!&&&&&&&&&&&?-.'''''''''''''''.~*>>%&$$$$$$$$$$$$$$$$$$$$$$$$$$$&&?>++>??=?)!)==>>>>>+++++++>>?%&&$$$$$$$$$$$$$$ $$$&&&&&&)~~:;~^^^^^^^^^^^^^^^^^^^^^^^^^,,,^,~:^!&&&&&&&&&&&&=;,''''''''''''''''.-~:)*)+>?==%%%%%&&&&%%====??>++==>+++))+))?=?=>++++>+++++++>)::)=&&&$$$$$$$$$$$ $$$&$&&$=-^^^:;-^^^^^^^^^^^^^^^^^^^^^^^^^,,^,^^^!&&&&&&&&&&&&&%)^'''''''''''''''',-'^^...,,^^~^~----~~^,,,,,...~>?++!~^!!!)>>>>++++++>+++++++:^^^-!>=&&&$$$$$$$$ $$$$&%=?>*!;-~-!;~~^^^^^^^^^^^^^^^^^^,,^^^,^,^^^;%&&&&&&&&&&&&&&>-.''''''''''''''.-''~,''''''''''''''''''''''',*?+!~,,:+)+>>??++++++++++++++;^^^^,,^-!>%&$$$$$$$ $$&?):~~~:))*!:-:!;-^^^^^^^^^^^^^^^^^^^^^,,,,,,^;>>=&&&&&&&&&&&&&=:.''''''''''''''~.'.,''`'``````'````'''''''.;+)-,.^!+>)>>*??+++++++++++++;^^,,,,,,,,^-*=&$$$$$ $%)-^^^^^^-!*!**:-:;-^^^^^^^^^^^^^^^^^^^^^^^,,^^;!~;?&&&&&&&&&&&&&%*,'''''''''''''-.''''````````````````'''''-;;^,,-*)+*)++*)>>++++++*:)++*~,,,,,,,....,,~*=&$$$ >:~^^^^^^^^~:*;;*;~~~^^^^^^^^^^^^^^^^^^^^^^^,^^^;!^^-+&&&&&&&&&&&&&&+~''''''''''''~.''''````'``````````'''''^;,..,:**+**+*+)!>>+++++!^,-))-,,,,,,,,,......,->&&$ -^^^^^^^^^^^^:*!:**:~^^^^^^^^^^^^^^^^^^^^^^^,^^^:!^^^~+&&&&&&&&&&&&&&=:.'''''''''''''''''```````````````'''.;^..,;*!))!*+*)+!)?>++):,,,,--,,,,,,,,,.........~+&& ^^^^^^^^^^^^^^-;!:!);~^^^^^^^^^^^^^^^^^^,,^,,^^^:*^^^^;%&&&&&&&&&&&&&&%)~.'''''''''''''''```````````````'''~-,..:*;*+*!))!)+!*>?+;^,.,,,,,,,,,,,,,...........^+& ^^^^^^^^^^^^^^^~;*::*!~^^^^^^^^^^^^^^^^^,,,,,^^^:*^^^^~?&&&&&&&&&&&&&&&&=*~.'''''''''''''''`````````````''.:^..^*;;**!!))!*+!!)+-,,.....,..,,,,,,.............^+ ^^^^^^^^~;:~^^^^~:*:-!*-^^^^^^^^^^^^^^^^^,,^,^^^-*~^^^^+&&&&&&&&&&&&&&&&&&=*^.''''''''''''''```````````'''~-...-!;!!!!!+*!*+!!*)~,,...........,,,..............~ ^^^^^^^^^-!*:~^^^^-!:~;*:^^^^^^^^^^^^^^^^^^^^^^^-)~^,^^*&&&&&&&&&&&&&&&&&&$&=!~,.''''''''''''```````'''''.:^..,;!!!!!!*+*!!)!!!)-,.........,,..,,.............., ^^^^^^^^^^~:!!-^^^~~;:~:*;~^^^^^^^^^^^^^^^^^^^^^-)-,,,^!%&&&&&&&&&&&&&&&&&&&&&%?)!:~^,.'''''''''''''''''',:,..,!!;!!!*+>!!!!!!!);,.............................. ^^^^^^^^^^^^~;*-^^^^~::~-*!~^^^^^^^^^^^^^^^^^^^^~+:^^^^:%&&&&&&&&&&&&&&&&&&&&&&&&&&%%?>*;-~,..'''''''''''~-...,!!;;!))!)!!!!!!!*;,.............................. ^^^^^^^^^^^^^^:!~^^^^~-~~~!*-^^^^^^^^^^^^^^^^^^^~+!--^^:=&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%=?+*;:~^^,,.'.-~...,!;;!+;^~*!!!!!!!*;,.............................. ^^^^^^^^^^^^^^~;:^^^^^^^^^~;*-^^^^^^^^^^^^^^^^^^^*)!-^^:=&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$&&&%==?>++*^...,!;!):,.,!!!!!!!!*-,.............................. ^^^^^^^^^^^^^^^-!~^^^^^^^^^~;*:~^^^^^^^^^^^^^^^^^;>)~^^:%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$&&&&&&&!....,!!*~....:*!!!!!!*~............................... ^^^^^^^^^^^^^^^~;:^^^^^^^^^^^:);~^^^^^^^^^^^^^^^^->)~^^;%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$&&$&;....,;!^.....~*!!!!!**^...........,,,,,,,............. ^^^^^^^^^^^^^^^^-;~^^^^^^^^^^^-!*!-~^^^-!)*:~^^^~;?!^^^*&&&&&&&&&&&&&&&&&&&&&&&&$&&&&&&$$$$$$$$$$$$$$$&&%-.....,,......,;*!!!!):,...........,,,,,,,............. ^^^^^^^^^^^^^^^^~:~^^^^^^^^^^^^^-!)*!;!**::**!*!)>>-^^~>&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$&%-........'.....-)!!!!)~,..........,,,,,^-^,............ ^^^^^^^^^^^^^^^^^:-^^^^^^^^^^^^^^^~-:::-~^^^-;);-;*^^^-=&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$&=-..............^**!!*!,...........,,,,,,-:^,,.......... ^^^^^^^^^^^^^^^^^:;~^^^^^^^^^^^^^^^^^^^^^^^^^~*-~*:^^^!&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$&=-......'........:*;!)-..........,,,,^-^^^-;^,,......... ^^^^^^^^^^^^^^^^^~;~^^^^^^^^^^^^^^^^^^^^^^^^^~)::)~^^~+&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&%-......''''.....,!!!*^..........,,,,,~--^^-:^,,........ ^^^^^^^^^^^^^^^^^~;-~~^^^^^^^^^^^^^^^^^^^^^^^~):!;^^^:=$&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&;......'''.......-**:...........,,,,,,^-::~-;~,........ ^^^^^^^^^^^^^^^^^^;;-:~^^^^^^^^^^^^^^^^^^^^^^~);)-^^^*$$&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&*................,;)^...........,,,,,,,,^-;::!~,....... ^^~~^^^^^^^^^^^^^^:!:;-^^^^^^^^^^^^^^^^^^^^^^-+)*^^^:=$$&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&>,................,~...........,,,,,,,,,,,^~;**-,...... ~~~:~^^^^^^^^^^^^^-*:;:^^^^^^^^^^^^^^^^^^^^^^->+:^~;?&$$$&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$=~.............................,,,,,,,,,,,,,^-!)-,..... ~~~!~^^^^^^^^^^^^^~)!:;^^^^^^^^^^^^^^^^^^^^^^:>+-~!=&&$$$&&&$&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%:.............................,,,,,,,,,,,,,,,^*>:,.... ~~-!-^^^^^^^^^^^^^^!*:!~~:~^^^^^^^^^^^^^^^^^~!?):+%&$$&$$$$$&&&&$&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&*,............................,,,,,,,,,,,,,,,^)%?:,... ~~~*:~^^^^^^^^^^^^^:*:*-~!-^^^^^^^^^^^^^^^^^~)++=&&$$&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&>^............................,,,,,,,,,,,,,,,^+%%?:,.. ~~~!:^^^^^^^^^^^^^^-*:*-~!:^^^^^^^^^^^^^^^^~:?=&&&$$$&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&=-............................,,,,,,,,,,,,,,,~>%%%=;,. -~~!!~^^^^^^^^^^^^^~*;):~;:^^^^^^^^^^^^^^~-!?&$$$$&&$$#$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&!,...........................,,,,,,,,,,,,,,,-?%%%%=!, ;~~!*~~~~~^^^^^^^^^~*)+:~:;~^^^^^^^^^^^~-!?%&&$$$&&$?=$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+,...........................,,,,,,,,,,,,,,,-=%%%&&=; *-~;*~~~~~~~^^^^^^^~!>+:~:!~^^^^^^^^~~:*?&&&$$&&$$%)-)$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$=~...........................,,,,,,,,,,,,,,,-=%%%%&%+ );~:*~~~~~~~~^^^^^^~;?+;~:*~^^^^^^~~:)=&$$$$&&&$$=+~^)$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&;...........................,,,,,,,,,,,,,,,:=%%%%&&) **--*-~~~~~~~^^^^^^~:>+;~:*-^~~~~:*>=&&$$$$&&&&?!;*~^)$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&),..........................,,,,,,,,,,,,,,^*%%%%&&%) *);-);~~~~~~~~^~~~~~-++!~-)-~~:!>%&&&$$$&$$&&?!:~:*~~+$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&>^.........................,,,,,,,,,,,,,^~!=%%%&&%)^ !)):*!~~~~~~~~~~~~~~-))!~-*;!+=&$$$$$$&&&$%>!-~!::)--=$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&$&=-.........................,,,,,,,,,,,,,^!=%&&&&&+~, :*+!;)-~~~~~~~~~~~~~-))):!>=&$$$$$$$$&&%?*:~~~-)--)-!&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&;,........................,,,,,,,,,,,,^-)=%&&&&>-,, *;*);)-~~~~~~~~~~---;>?%%&$$$$&&&&&$&=);-~:~~-**~-)!=$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&*,.......................,,,,,,,,,,,,,,^~)%%%%=:,,, %+!)*);-~----:;!*+>=%$$$$$$$$&&&&%=+!-~^^-*-;!+--!%&$&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&+,......................,,,,,,,,,,,,,,^~!>%&%=!,,,, $&=>+>>)))+>?%&$$$$$#$&&&&&$$%=>)!-~~~^~~!;;)+**>%$$$$##$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&>^......................,,,,,,,,,,,^^~:)=%%%%*^,,,, $$#$$$$$$$&&&$$&&&&$$&&&&%=+*;--~~~~~~~~:);+=%&$&&$$####$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&?^......................,,,,,,,,,,^^-!*?%%%%>~..,,, ##$$$$$#$$$$$$$&&&%%=>)!;:--~~~~~~~~~-:!>==&$$$&$$###$$#$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&=;-^...........^~-~....,,,,,,,,,,^~;!:-?%%%?:,.,,,, $$$$$$$$$####$=>+)!!;:::)>>*:-:;;!)+?=%&$&&&$$$$##$$$$$####&%###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&$$&&$$==*,,;*!^.....;==+,..,,,,,,,,,,,~::~^-?%%=;,,,,,,, $$$$$$$#$$$$>$$&&&&&&&&%$==$%%&&&$$$$$$#$$$$#####$$#$$#####=)#########$$$##$$$###$$$$$$$$$$$$$$$$$$$$#>?#$$$$#+>+~->>=!~~~^.!?)?-~~~~^~~~------~^^^~?%=!^,,,,,,, %%&$$$$$###$*$$$#$%%$$+)=>?#%=%####%=&##%%$##&=&#$#$&##%##%?*%=&##&=%$####$==&$%=&#&$#$%$&==$$%=%##&==+>#$&)>%++=?%$?&&=?=?~*?)=?%$==*??&%?>>=)^,^^~+=*^,,,,,,,, );)?&$$$$##$*$##$)++)&**=&$=*??$$#?*>?&+++*&=*>*?##&*$=;?$*+;>>*%?*>)>###&*+>&%>+*&)%#&*=*>>%?*>*=&)>>;>#$&!)=)!>+)&)%?*>>?~*>;>>*%+?>=*%)++:?+^^^^^!*~,,,,,,,,, +---!+=&$$$$*$$#=:>>!%>?###%*>%###=)>%%;+>;=**>*)#$#)?)))=)?*$#+?*=#&!$##?)###&=?!%)%#&*%)+=&!)>*+>)##)>#$#)=#+>&&*%*%=*+%&:*?)&&++)??%*%!??!%!~^^^-!~,,,,,,,,,, %);:---;*+=&*$##=;=%%$>>####$=*%###$=*>!?%%$))%%&###=**&**?=)##+>*?#%*$##=)$#&*?=!=)=#=*$$%)+*+%%&?)$$)>#&$)=#+>?%*=*%#$=!=;*>*&&)>+>&%!&+*>%#==!^-!-,,,,,,,,,,^ $&%=+!;::-!%*)+>&>)+>#%*>$#%++)&##=++)&>)+>$%)++%#&?&!?#>;&=+##>=%)+)?###$+)+=)++!%?*+)*%++)==)++%$+)+*?#&#?*?>?>=)%)%=++)%;!?*++)&=*+)!%)*)>%+?):);^,,,,,,,,,-) $$$$$&&=?>+&&&%%&&%%%%%%%&=%%%&%?%$$$$##$&#@##&%%+)*==&#$&##$##$$#$&$##$$##$$#$$$$##$$$$#$&$##$$$###$$$$$&$$$$&?*>?=??%===+~:>====>?==%%=)%%++&%+*!!-^^,,^^^~!?$ ##$$$&$$&$$$$&%==???>>>>>>>?==%%&&&&&$$&&&$$=+;--~!!-~!&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&)^^^^^^,^^^^,.,,^^^^,^^~~*%)))+%=!:--:!;~^^^~;?&$$ $$$$$$$$$$$$&&&&&$$$$$&&&&&$$$&&&&&&$$&&%?+!-^^^^^;*~^~>&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&%),,,,,,,,,,,,,,,,,,,,,,,^-)??=%?!------!*:-;?&$$$$ $$$$$$##$$$$$$$$$$$$&&&&&&$$$&&&&&$$$&?*:-~^^^^^^^:)~^^!&&&&&&&&&&$$$$$$$$$&$$$&&&$$$$$$$$$$$$&&&&$&&&&&&&&&&&)^,,,,,,,,,,,,,,,,,,,,,,^^^-!)*-~~-----;?%%&$#$$$$ #$$$$$$&&&&&$$$$$$$$&&&$$$$$$$$$&%?+!:-~^^^^^^^^^^:)~^^:=&&&&&&&&&&$$$$$$$$$$&$&&$$$$$$$$$$&&&&&&&&&&&&&&&&&&&+^,,,,,,,,,,,,,,,,,,,,,^^-!+>*:~~~----:>%$$$$$$$$$ $?>&%%%&&&&&&$$$$&&&&&&&&&&=?+*!;-~~^^^^^^^^^^^^^^:)~^^~+&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&$$$$$&&&&&&&&+^,,,,,,,,,,,,,,,,,^^~-;)>??*:-~~~----*?%$$$$$$$## $==&==%&&&&$$$$$$$$$$$$$$&&=??>>>>>>>>>>>>>>>>>>>>?=>>>>=&&&$&$$&%%&=++++++=$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%>>>>>>>>>>>>>>>>>>>?=%&&&&%=?????????%&&$$$$$#### $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&$$$$$$$$$$$$$&=>)-:)-,,,,,,;&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########################################$######## $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&$$$$=)*;^-!-,,,,,,,~?$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################## $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$=!::!!:~,,,,,,^,^?$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################## $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&$$$&$&$$$$%*;;-;:,,,,,~^--,~?&$$$$$$$$$$$$$$$$$$$$$$$$$$$####################################################### $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&%=??>>>>>>>>>>>>>>+*:-~~~^,,,,,:::^,:;!%$$$$$$$$$$$$$$$$$$$$$$$$$######################################################## $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&=>)*:--~^^^^^,,,,,,,,,,,,,,,,,~-~,,,,~!;~,~!~,:=$$$$$$$$$$$$$$$$$$$$$$$$#################################$$$###################$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$&=+;~^,,,,,,,,,,,...........,,,^-~~^,,:;:!*:^,;:,,,;&$$$$$$$$$$$$$$$$$$$$$$#################################$$$$###################$ $$$$$$$$$$$$$$$$$$$$$$$$$&=+!~^,,,,,,,,,,,,,,,........,^~---~,,,,~!~^~--:;!^,^,~%$$$$$$$$$$$$$$$$$$$$$$################################$$$$$$##################$ $$$$$$$$$$$$$$$$$$$$$$$&?*-^,,,,,,,,,,,,,,,,,,,,,,....,,^,,,,,,,--:;~^^^~;;;:~^~=$$$$$$$$$$$$$$$$$$$$$################################$$$$$$$##################$ $$$$$$$$$$$$$$$$$$$$$&?;^,,,,,,,,,,,,^~~--:::-~^,,.....,,,,,,^-;:^,-;:-~^^~:;-^~=$$$$$$$$$$$$$$$$$$$$$################################$$$$$$$##################$ $$$$$$$$$$$$$$$$$$$&>;^,,,,,,,,,,,~-:;:~^,^^,,,,,,,,..,,,,,~:;-^,,,,^~-;!-^,^:--%$$$$$$$$$$$$$$$$$$$$$################################$$$$$$$#################$$ $$$$$$$$$$$$$$$$$$&)^,,,,,,,,,,^-:-~^,,,,,,,,,,,,,,,,,,^~-:-~^,,.,~;~,~:;*-^,^^-%$$$$$$$$$$$$$$$$$$$$$$############################$$$$$$$$$$#################$$ $$$$$$$$$$$$$$$$$&*!:^,,,,,,^~::~^,,,,,,,,,,,,,,,,,,,^--~^,,,,..,:?=~,:-::~^,^^-%$$$$$$$$$$$$$$$$$$$$$$#########################$#$$$$$$$$$$$$###############$$$ $$$$$$$$$$$$$$$$$&;~:;~,,,,~::~,,,,,,,,,,,,,,,,,,,,,,,,,..,,,,,-+&$>^~;^;~,,^^^-%$$$$$$$$$$$$$$$$$$$$$$###########&%===&$$#####$$#$$$$$$$$$$$$################$$ $$$$$$$$$$$$$$$$$&+~^-!-^^:;~,,,,,,,,,,,,,,,,,,,,,,,,,,,,.,^~-)&##%:^;:^;^,,^^,-%$$&$$$$$$$$$$$$$$$$$$$$#####$$#&+:~~~~-:*=$#$$###$$$$$$$$$$$$$$##############$$ $$$$$$$$$$$$$$$$$$%;^,^-::;;:-^,,,,,,,,,,,,,,,,,,,,,,,,,,^:!*=$#%+-^-?>;:^,,^^^;&$$&&&$$$$$$$$$$$$$$$$$$$$$$$$$&!~^^^^^^^^~;)>?==%&&$$$&&&&&$$$$$$$############# $$$$$$$$$$$$$$$$$$$=:,,,,^^^^-;-^,,,,,,,,,,,,,,,,,,,,,,~::-^-*)!-^,^)&%)-,,,^^^!&$$&&&&$$$$$$$$$$$$$$$$$$$$$$$$>~^^~^^~~~^^^~~-:--:;)?%&&&&&&$$$$$$$############ $$$$$$$$$$$$$$$$$$$$=:,,,,,,,^~;;-~~~~^,,,,,,,,,,,,,^-::~,,,,,,,,,^)&$>)~,,^^^^*$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$*^^~~~~~~~~^~~^^~^^^^~~;)?%%%&&&$$$$$$########### $$$$$$$$$$$$$$$$$$$$$=:^^^^^~----:-~^^^^^,,,,,,,^~-::-^,,,,,,,,,,^!&#=)?:,,^^^^*$$$&&&&&$$$$$$$$$$$$$$$$$$$$$$$*^^^~~~~~~~~~~~^~~~~~~~~~:+=%%&&&&$$$$$########## $$$$$$$$$$$$$$$$$$$$$&?;:;;:-~^^^^~~^^,^~~,,,^~-:;-^,,,,,,,,,,,,^!%$?;)%*,,^^~:+$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$&*-^^~~~~~^~^~^~~~~~~~~~~~~-)=%%&&&$$$$$$######### $$$$$$$$$$$$$$$$$%?)!:--:;-~^^^^^^^^^^^^^~~~---~^,,,,,,,,,,,,,,~;**;~;>+!--;;:^;&$&&&&&&&$$$$$$$$$$$$$$$$$$$$$=-:-~~~~~~^~^^^^~~~~~~~~~~~~-+%&&&&$$$$$$######### $$$$$$$$$$$$$$&=*:~~^^^^~~^^~~~~~~^^^^^^^:;:~^,,,,,,,,,,,,,,,,~:~,,,-?+---~^,.'~=&&&&&&&&&&$$&$$&$$$$$$$$$$$$$)~;*;:;---~~~~~~~~-:;;-~~~~~~:?&&&&&$$$$$######### $$$$$$$$$$$$$%*-~~~~~~~~~~~~~~~~~~~~^^^^^:~,,,,,,,,,,,,,,,,,^--^..,^+&)..'''''',>&&&&&&&&&&&$$$&$$$$$$$$$$$$$$!^;--:;*!;;;---:;!!):~~~~~~~~~!%&&&&$$$$########## $$$$$$$$$$$$=!~~~~~~~~~~~~~~~~~~~~~~~^^^~*:^,,,,,,,,,,,,,,,,~-,,..^*%&).'''''''.)&$&&&&&&&&&&&&$$$$$$$$$$$$$$$!~;~~~--:::;;;::--:;~~~~~~~~~~-?&&&&$$$$$######### $$$$$$$$$$$%!~~~~~~~~~~~~~~~~~~~~~~~~~~-::):^,,,,,,,,,,,,,,,,,...,*%&&+.'''''''.!&$&&&&&&&&&&&&$$$$$$$$$$$$$$$)-;:!:~~~~~~~~~~~~::~~~~~~~~~~-)&&&&$$$$$######### $$$$$$$$$$$)~~~~~~~:;:-~~~~~~~~~~-~-:-:*:^!*:,,,,,,,,,,,,,,,,,..,*%&&&).'''''''':&&&&&&&&&&&&&&$$$$$$$$$$$$$$$+-!)>?+:~~~~-:!;-~:;-~~~~~~~~~~!%&&&$$$$$$######## $$$$$$$$$$?-~~~~~~~-:!)!:--~~~~-::;*!;;;;^::!~,,,,,,,,,,,,,,,,.^!%&&&&*.''''''''^=&$&&&&&&&&&&&&$$$$$$$$$$$$$$+~!--!>!~-!+?=?+!:-::~~~~~~~~~~;%&&&$$$$$$######## $$$$$$$$$$*~~~~~~~~~~-!::;;;;;!!!!!:--~-;^-~;-,,,,,,,,,,,,,,,,~+%$&&&&!''''''''',>$$&&&&&&&&&&&&$$$$$$$$$$$$$$+~;;*!;;-~;**!:--:--;!-~~~~~~~~!%&&&$$$$$$$####### $$$$$$$$$%:~~~~~~~~~~~::~~~~---~~~~~~~--;~-~;:,,,,,,,,,,,,,,^;?&&&&&&&!'''''''''.*&&&&&&&&&&&&&&&$$$$$$$$$$$$$%!!;>):!-~~~!*;;--~--;:~~~::~~~*%&&&$$$$$$$#####$$ $$$$$$$$$=-~~~~~~~~~~~::~~~~~~~~~~~~;>>*;~:~;:^,,,,,,,,,,,,~)%&&&&&&&&!.'''''''''-&&&&&&&&&&&&&$$$$$$$$$$$$$$$$&!-;;::~~~-+>-::~~--;-~~:*!;-->&&&&$$$$$$$#$$##$$ $$$$$$$$$>-~~~~~~~~~~-;--:)>+!:-~~-+=>!!!~:~-!-^^,,,,,,,,~!=&&&&&&&&&&*.''''''''',?$&&&&&&&&&&$$$$$$$$$$$$$$$$$&;~~:;-~~~-!*-~~~~~-:-~-;!!!-:?&&&&$$$$$$$$$##$$$ $$$$$$$$$+~~~~~~~~~~:;--:;!)>==>;~-!!;:-;~:~^:;^^^,,,,,~!?&$$&&&&&&&&&*.''''''''''*$&&&&&&&&&&&$$$$$$$$$$$$$$$$=-~-;-~~~~~~~~~~~~~~:--;**;!-;%&&&&&$$$$$$$$$$$$$ $$$$$$$$$+~~~~-~~~~;!:---~~-;;:-~~;!;!);;~!~^*;^^^^^^-!?&$$$$$$$&&&&&$+.'''''''''':&&&&&&&&&&&&$$$$$$$$$$$$$$$$>~~-;::;-~~~~~~~~~~~:;!!!!;!-!%&&&&&$$$$$$$$$$$$$ $$$$$$$$$>-~-:!;~~-:;--~~-;;!)-~~~:!:>+:!+%;-)-^^^~!>%&$$$$$$$$$$&&&&&>.''''''''''^=$&&&&&&&&&&$$$$$$$$$$$$$$$&)~~~-----~~~~~~~~~~~----:!!:-*&&&&&&$$$$$$$$$$$$$ $$$$$$$$$%:~:*!!-~~:;-~~~-:-+=;~~~-;::-~*$$=):^^-*=&$$$$$$$$$$$$$$$&&$?,''''''''''.>$$&&&&&&&&&&$$$$$$$$$$$$$$&+~~~~-~~~~~~~~~~~~~~~~--:!;--!&&&&&&$$$$$$$$$$$$$ $$$$$$$$$$!-;***;~~::--~~~~~:;-~~~~-!:~^!&$$?:-)%$$$$$$$$$$$$$$$$$$&&&=,'''''''''''*&$&&&&&&&&&&&$$$$$$$$$$$$$$?-~-;;;:-----~~~~~~~~--;*;---*&&&&&&&$$$$$$$$$$$$ $$$$$$$$$$)-;;;**;-:--~~~~~~~~~~~~-~-!~^-%$$$%%$$$$$$$$$$$$$$$$$$$$$$&%^'''''''''''-%$&&$&$$&&&&&$$$$$$$$$$$$$$%;~-;;::;;;;;-~~~~~~~:!*!----+&&&&&$$$$$$$$$$$$$$ $$$$$$$$$$>-;!;!!!!!-~~~~~~~~~~~~:;-;:~~-?$$$$$$$$$$$$$$$$$$$$$$$$$$$$&-''''''''''',>$$$$$$$$&&&&$$$$$$$$$$$$$$&*~-;!;;-~~~~~~~~~~~-!:;;:!-!=&&&&&$$$$$$$$$$$$$$ $$$$$$$$$$>--!!;:---~~~~~~~~~~~~~-~~-~~~~>$$$$$$$$$$$$$$$$$$$$$$$$$$$$&:'''''''''''.)&$$$$$$&$&&$$$$$$$$$$$$$$$$>-~~---~~~~~~~~~~~-!;-!*!:!=&&&&&$$$$$$$$$$$###$ $$$$$$$$$$>--:*;--~~~~~~~~~~~~~~~~~~~~~~-?$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!.'''''''''',*?&$$$$&$$&$$$$$$$$$$$$$$$$$%:~~~~~~~~~~~~~~~-!*:-!!;)=&&&&&$$$$$$$$$$####$$ $$$$$$$$$$>-~-:*!--~~~~~~~~~--~~--:;::-~:%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$>.''''''''''--;=&$$$$&&$$$$$$$$$$$$$$$$$$$)~~~~~~~~~~~~~~:**:--*?=&&&&&&$$$$$$$$$$$#$$#$$ $$$$$$$$$$?----:**!-~~~~~~~~;!;;;;;;::-~!&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$=^'''''''''^;,---*?&&$$$$$$$$$$$$$$$$$$$$$=:~~~~~~~~~~-:!*;----+&&&&&&&&$$$$$$$$$$$$$$$$$ $$$$$$$$$$&)-:!:!;;;-~~~~~~~~~----;!!;-~)$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&:''''''''.;^'-,'',~!+=&$$$$$$$$$$$$&&&&&&$=*:-~~~--:!**;--~~-:>%%&&&&&&&&$$$$$$$$$$$$$$$ $$$$$$$$$$$%!-!**;:*;-~~~~~~~~~~~--:--~-?$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!.'''''''~^''-.'''`'',-!+=%&$$$$$$&&&&&&&$$&%=)!!!!;:--~~~~~-)??=%&&&&&&&$$$$$$$$$$$$$$$ $$$$$$$$$$$$%+;;*;-;):-~~~~~~~~~~~~~~~~;&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+.'''''''.''','''`````''',^:*>?%&&&&&&&&&$$$$&!----~~~~~~~-;+?>>>=&&&&&&&$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$=+);--;*;-~~~~~~~~~~~~~~~+$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%~''''''''''''''``````'```'''',^:*+=&&&&&%==?>-~~~~~~~~~~:)?>++++>%&&&&&&&$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$%!---:**:-~~~~~~~~~~~~:%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$+,''''''''''''````````''````'''''.^-*>%%?>>?)~~~~~~~~-;)??>++++++?%&&&&&&$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$&!-----;**;--~~~~~~~~:>$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&+~.''''''''''```````````````''''''''->>>?+?;~~~~~~-)?=?>++++++++>=%&&&&&&&$$$$$$$$$$$$ $$$$$$$$$$$$$$&%?+-------:!)*!;;:;!)>&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%)^'''''''`````````````````''''''',)>++>+?!:-~~~:>==>+++++++++++>%&&&&&&&$$$$$$$$$$$$ $$$$$$$$$$$$$&%?>?>:-~~~~~~~--:;;!=##$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$=*~.'''''``````````'```````''''.*>+++>>>??+!!+%=>>>>+++++++++>??%%&&&&&&$$$$$$$$$$$ $$$$$$$$$$$$$%?++>?>*:~~~~~~~~~~~~+&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%+-.''''````````````````''''.!>++++**+**)=?==>++++>++++++++>*-:)?%&&&&&$$$$$$$$$$ $$$$$$$$$$$&&?+++++>?>*-~~~~~~~~~~!???=%&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%>:,'''``````````````''''.!?>+);~^!!;*>>+?>++++++>+++++++*~^^^~;)?%&&&$$$$$$$$$ $$$$$$$$$$&&=++++++++>??+;-~~~~~~~->?+?==%?=&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&?!^.''````````````'''';??):,.,:+++>+>?>++++++++>+++++*~^^^,,,,~:*>%&$$$$$$$$ $$$$$$$$$&&%>++++++++++>==>;~~~~~~~+?+?>>>;-!+%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%)-.'''``'``'''`''.-++;^..~!+>)>?)+?>++++++++)++)+*-^,,,,,,...,,-*=&&$$$$$ $$$$&%?>>))>>+++++++++++>?=?*-~~~-;>>>>+++*^,^-!>%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&%+:,'''..'''''''~*;~..^;))+*)+++*>>+++++++*-;++)-^,,,,,,,......,~!?&&&&& $$&?!-^^^~;)>++++++++++>>>>?%?)*)>??>?+++++!^,,,^:+%$$$&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&?*^..^,'''''^!~...-**)+**+)*>**?>++++):^,^;);,,,,,,,,..........~+%&&& &=!^,,,,,,^;++++++++++>+++++?=>=?*!*>==>+++>!,,,,,^;?&$&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%)-,-,'''.::,..-**!+***+**+*!+?++);~,,,,^-^,,,,,,,............^*%&& +-,,,,,,,,,,:++++++++>+++++++>>+?+!!*%&+:!)+>:,,,,,,~)&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$&>::,''-;,..-*!!))!*)+**+)!*?>;^,..,,,,,,,,,,,...............,;=& ^,,,,,,,,,,,,-)+++++>++++++++>??>>>++%=-,,~!>)^,,,,,,^+&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$=*!,,!~..,;!!!)***+)*!+)!!)!,................................:? ,,,,,,,,,,,,,,-)+)++++++++++++??)+?++?+;^,,,-!~,,,,,,,:%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$&);;,..^*!!!!!!*+)*!))!!*)^.................................: ,,,,,,,,,,,,,.,:)+)-;++++++++>>))>)+*)+)!-^,.,,,,,,,,,^?$$&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$?~...-)!!!!!!)>)!!**!!*)~................................., ,,,,,,,,^:-^,,,^!)!-^-*++++++>+!)+*+)!)+**;^..,,,,,,,,,+&$&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$!....-)!!!!*++>*!!!!!!*)-.................................. ,,,,,,,,,~;!:^,,^~^:-^~;)+++>>*!++!)+!!++!!!~,,,,,,,,,,*&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$%-....-);!!+*--)*!!!!!!!)-.................................. ,,,,,,,,,,,~;!~,,,,^:-,,-*)>?)!!+)**>*!*+*;!!~,,,,,,,,,;&$&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$?^....:*;*+;^.,!*!!!!!!!)~.................................. ,,,,,,,,,,,,,-!~,..,^-~,,~;!+!!!+)!*+)!!*)!;!:,,,,,,,,,:%$&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$&),....-***-....:*!!!!!!**^.................................. ,,,,,,,,,,,,,,-:,,,,,,^,,,^;)!!*+*!!++!!!!!!!!~,,,,-^,,-%&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$&&;.....-)!^.....~*!!!!!!);,.................................. ,,,,,,,,,,,,,,,:-,,,,..,,,,!*!!*)!!!++!!!!!!!*-,,,^;~,,-=&&&&&&&&&&&&&&&&&$&&$$$$$$$$$$$$$$$$$$$$$&%:.....,~,.''''.,;*!!!!!)~.................,,,............... ,,,,,,,,,,,,,,,~:^,,,...,.,!!!!!!!!!)?)*!!!!!*-,,,~!^,,-%&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$&&=-.......''''''..~)!!!!**,................,^-^,.............. ,,,,,,,,,,,,,,,,:~,,....,,^!!!!!!!!!*!:!)*!!!*-,,,-;,,,;%&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$&=-.....''''''''..,!*!!!):..............,,,,,-:^,............. ,,,,,,,,,,,,,,,,~:,,....,,^!!!!!!!!!*;,^:)*!;!-,,,;:,,,*&&&&&&&&&&&&&&&&&&$&&$$$$$$$$$$$$$$$$$$$$$&=-.....'''''''....~*!!**^..............,^~^,,~:~,............