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