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