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