` ````...`..````..```````````` ``````````````````,z;znnxxn*ii;i#+*;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;*#+i;i#zzz#:,,,,,,,:;i::::,.`..`````...```.,,:::
 ` ````......````.``````` ````` ``````````````````,zz#xzxn#*ii*#+;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;*z#ii*zzzz+:,:i;,::;i:;;;;......`````````..,:::
````````......````````````````` `  ```````````````.#xnxnnz*i*#+*;:;;;:;;;;;;;;;;;;;;;;;;;;;;:;;;;;;;;;;;*z#*i#zzz#**#+,,::::::,:i,........`````....,,,
```   `.,,,...```````` ```````` ``````````````````.inxxxn+**z#i;;:;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;*z#*+zzzzzz#;,,,,,::,.,,............``.......
```` ``.,:,,..````.````````````````` `````````  ``.,#xxxz+#z#i;;;:;;:;;;;;;;;;;;;;;;;;;;;;;;;:;;;;;;;;;;;;*zz+#zzz##*i;:,,,,,,................`...,...
````  `.,,:,,..`..,``````````````````````` ```  ``.inxxxnnnz*;:;;:;;:;;;;;;;;;;:;;;;;;:;;;;;;;:;;;;;;;;;;;;*zz#zz####+*i;,,,,..................``....`
```   `..,,,,...,...`````  `` ````````````````````.zxxxxnnz*i;:;;:;:;;;;;;:;;;;;:;;;;;;;;;;;;;;:;;;;;;;;;;;;*#z###+*;,,.......................`````.``
```   ``..,,,.......```````  `````````````````` ``:nxxxnnz*i;;:;;:;:;;;;;;:;;;;;:;;;;;;:;;;;;;;;::::;;:;;:;;;*######*,...```...........`....,.````````
```` ```........``..`````` ````.....``````````` ``:nxxnz#*i;;;:;;:::;;;;;;::;;;;;:;;;;;:;;;;;;;;:::::::::::;;;*####+#;.````...........``....,.````````
`````````...`..````..``````````....```````` ``  ``,zxxz**i;;;;::;:::;;;;;;;::;;;;::;;;;;:;;;;;;;;:::::::::::;;;*###*++,.````..........``............``
`````````````..````.``````````....````````     ```.+xxn+ii;;;;::;;::;;;;;;;:::;;;:::;;;;::::;;;;;;::::::::::::;;+##+:+:.````...........``.``..,,.,,.``
```````````````````...```````.``````````` ```````.,#xxnz*i;;::::::::;:::;;;:::::;:::::;;;::::::::::::,,::;::::::i##+;:i`````,,.,,..,.......`..,,,,:,.`
````...`````````````.````...````````````````;....,+xxxnn+;;;::::::::;::::;:::::,:;:,,,::;;::;;;;;;:::::::::::::::*+#i,:`````.,,,,.......,,.`.,:,,::,,.
````,,,.```.`````````````...````````````````i#ii*zxxxnn#i;;;;::,::::;:::::;::::,,:::::::::;::::;;;:::::::::::::::i+#+..`````.,,,,.........``..,,::;:,,
````.::,````````````````````````` ``````````.+nnxxxxnz+*i;;;:;::::;;;:::::::::,.,:::::::::::,:::::::::::::::::::;i+#+,``````.,,,,,,,.......`....,::::,
``...,,,````````````````````````````````````.,+nxxxxnnz*i;;;:;;i+*i;;:;;:::::,..::::,::::::::,::;;::::::::,:::::i*+++,``````.,,,,.,,.......``..`..,:,,
``...,..``...````````.````````````.....``````..*zznnnn+i;;;;:;;*xnn#*;;;;:::,..,::::,::,:::::::::::::::,,,,:::::;++++,``````.,.....,..,....`.,.....,,,
```..,,.``.....````...```````````.....````````.:+znnnz*i;;:;;:;+xxxxz*++*;::..,:::::,,.:;;:::::,,::,::,,::,::::::*++*.``````..``....,,...```.,,,,,..,.
```.`..,```..`........```````..`.....``````````.:znnnz++;;::;:;+xnnxx+#nz#;:,,::::::i::;;;::::::::,:::,:::,::::::*++i.``````..``.```.,.....``.,::,....
``````..```````.,.....```````....``.```````````.*n+znzz*;;::;;;+xnnxxn#n*i;:;i;::i#xx;;;;;;;:::::,,::,,,,,:,:::::i++;.``````..```````.....,```..,.``..
``````..````````....,...........```````````````.z+*nnnz*;;;::;i#xxzxxnz+ii;:;;i#nxWWz+*ii;;;:::::,,::,::,,,,::,::i++,.``````````.````....,.```........
`````````````````....,::::::,,,,.``````````````,#:+nnnz*;;;:;;*#xxnxxnz*i*+i:nWn*+xMxxxz#*i;:::::,,::,,::,,,,:,::*+i..````.`````````..............````
`````````````````....,,:::::,:,:,,.``..````````,;,+nnnz*;:;;;:;i+#zxxn#*#xnzixWn*+#nxxxxxn#i;::::,,:::,,,,,,,:,::**,,..``..````````.,,...,,.......````
`````````````````......,,,,,,,,,::,....````````...*nnnn*;:;::+iiii*xxn##xnnnizzz#*zxxxxxxxn+;::::,:::,,,,,,,,:,:;+;,,,..``.``````...,,...,,,...```````
 ````````````````..,,,,,,...`...,:,,....`````````.;nnzn+;:::izz+i;i+xxxnnnxznnnnnnxxxxxxxxn+;::::,:::,,,,,,,,,,:ii::,:;:``.``  ```.,::..,,,:::.```````
 `````````.````.``....,,,,..``.......,,,``````````.+nzn#;:::*z+*i;:i#xxnznxxxxxxxxxxxxxxxxn+;::::::::,,,,,,,,,,:;****+;....``` ```..::,,,,,:;:.```````
``````````````.```````...```````````.,,,.`````````.:+z#*;:;;i*:*#+#++xxxnxxxxxxxxxxxxxxxxxn#;::::::::,,,,,,::,,:**++*;,....```  ```..,.,::::;:..``````
`````````````````````````````````````.,...```````..,iz#*;:;;;*ixnizxzxMxxxxxxxxxxxxxxxxxxxn#;:::::::,,,,,,:,,,,:**i;:,,....```````````.,,:,,,,....````
`````.````````````````````````````````.,..``````.,,izz#i;;;;;*zn#*#xnxxxxxxxxxxxxxxxxxxxxxn+;:::::::,,,,,::,,,,:i+i::,,,,..````````````,::,,,,,,..````
`````.```````````` ````````````````````....````.;*#nn++;;;;;;*x#*#xxnnxxxxxxxxxxxxxxxxxxxxn+;::::::,,,,,,::,,,:i;*+i:,,,,..```````` ```.:,,,::;:,.````
``````````````````  ````````````````````....````,;**;:+::;:;;*xxxxxxnnxxxxxxxxxxxxxxxxxxxxn*;::::::,,,,,::,,,,:***++;,,,:,.```````   ```,,,,,,::..````
`````````.``.```` ```````````````````````...``.......,*,,::;;inMxxxxnzxnxxxxxxxxxxxxxxxxxnn*;::::::,,,::::,,,,:**:i+*:,,,..```````   ```.......,.`````
````````..``.````` ```````````````````...`````..`````.*,.:::;izMxxxnzz+***+zxxxxxxxxxxxxxnn*;:::::,,,,::::,,,,:**,.:*:.....`.````   ``.....```...`````
````````..`..`````````````````````.```...`.`...```````i,.,,,;i+Mxxxn+*i;;i*#xxxxxxxxxxxxxnni:::::,,,,,,:::,,,,:i+:.`,;```````````````.,,....```..`````
````````.....`````````````````````.``...``.....```````,,.....:ixxxxxz*i;;izxxxxxxxxxxn#xnnni:::::,,,,,,:::,,,,,;+;.``.```````````````......`````.````.
`````````..,...````````````````````............``````.`.`..``.,nMxxxxz+ii#xxxxxxxxxxn+zxnnz;::::,,,,,,,,:,,,,,,:**.``````````````````......````.`````.
````.```..,:,..``..````````````````.```..`......```....``````..+Mxxxxxx#+nxxxxxxnnnz+*nxnn#;::::,,,,,,,,,,,,,,,,i+:`````````````` ```......````.``````
```..``...:i:,.`...````````````````.```.``.......``.,..``````.,;xxxxxxxnxxxxnnnzznn+i+nxnn#;:::,,,,,,,,,,,,,,,,,:*i.``````````     ```.,...```....````
``...``..,;i:,.`..`````````````````````...........`..,,.....`..,#Mxxxxnnnnzznnxxnnzii#xxnn+;:::,,,,,,,,,,,,,,,,::;*;.````` ``       ```,.``````..`````
``..``...,::,,....`````````````````````...```....````.,.....`...;xMxxxnnnxnxnz#*i;:::zxxnn*::::,,,,,,,,,,,,,,,,:i;i*;,.``` ``       ``````````````````
``..``.,,,:,,...,..``````````````````````````````````....,,.....,+Mxxxxnznz*;:::::::innnnzi::,,,,,,,,,,,,,,,,,,,i*+++**;,`  ```      ``````  `````````
`..```.,,::,.,,,,..``````````````````````````````````...,,,,.....:nMxxxxzi;::,::;;;;*nnnn#;::,,,,,,,,,,,,,,,,,,,:i*iiii:.`  ````      ````````````````
`..```.,,:,..,:,,.````````````````````````````````````...,..,.....;xMxxxx+:::;*+++++#xnnn+;::,,,,,,,,,,,,,,,,,,,,:*+i:..`` ```````     `````` ````````
`.```..,:;,.,:::,.``````````````````````````````````````.......``.,*MMxxxni;i++++++#nxnnn*;::,,,,,,,,,,,,,,,,,,,,,:*+*,.`` `````````   ``````````````.
..```..,:i,,:;;:,.````````````````````````````````````````....```..,+MMxxx#z+#####nznnnnzi::,,,,,,,,,,,,,,,,,,,,,,,:*+*,``` ``...```` ```  ```````````
......,:;i:,:i;:.```````````````````````````````````````````.`````..,#Mxxxnz####znznnnnn#;::,,,,,,,,,,...,,,,,,,,,,:;++*,``````...```````  ```````````
.``.,,:;ii::;ii:.````````````````````````````````````````````````....,zMxxnzxnnnnznxnnnn+::,,,,,,,,,,..,,,,,......,;ii++*,`````.....`````  ```````````
...,:,:;i;::;ii:.``.`````````````````````````````````````````````````.:zMxxnznnznnxnnnnzi::,,,,,,,,,,,,,,,,,.......,i*i++i.``````..```````````````````
...::,:;;;;;iii:.`````````````````````````...```````````````   ``.````.:nxxxxnnxxnn+znnz;:,,,,,,,,,,,,,,,,,,........,;*:*+:.``````````````````````````
..,:,,,;;;;;i**:.```````````````````````..,;*;.`````````````   ``.`````.ixxxnnz###*#nnn#;,,,,,,,,,,,,,,,,,,...,,,,...:+;,i*..``````````````````..`````
..,:,,:;;;;i*++:.`````````````````````.,;+nxxx;`` ```````````````.``````.+Mxn+iiii#nnnn*:,,,,,,,,,,,,,,,,,....,,,,...;+i..;,```````````````````.``````
.,,,,,;;;;i**#+,.``````.````.````````.:zxxxzxx#.````..`````````.````` ```,zxxn+*+znnnn#;::,,,,,,,,,,,,,,,,.....,,....i+*.``.`    `````````````````````
.,,.,:;;;;i**+*,``````.....,,.``````.:+xMMxzxx+.```.,,::,,.````.`` ``````.iMxxnnnnnnn#;::,,,,,,,,,,,,,,,,,.....,....,;++:`````   `````````````````.```
.,,,,;ii;;*+*+*,`````...,,::,.```..,:;#Mxxxnx#i,``.::::::::,.````` ```````,nMxnnnnnz*;::,,,,,,,,,,,,,,,,..........,,,:*+;``` ````````````````.````````
.,,,:;**;;*+*+*,.`````...,:,.`...,,::;+xxxxx#i;:`.,:::::::::,`````````````.inxnnnn#i::::,,,,,,,,,,,,,,,..........,,,,:*+i`````..``````````````````````
,,,::;+*:;*+*+*,.```````..,,...,,,::;*+znnz#i;;:..::::::,,,,.``````.```````.:i+++i::::,,,,,,,,,,,,,,,,........,,,,,,,,*+i.````````````````````````````
,.,::i+i::i**+*,.```````.,:,,,,,,::izxxxxx#i;;::,:::::,,,..````````.```````.,,:::::::,,,,,,,,,,,,,,........,,,,,,,,,,,i+*.```````````` ```````````````
,.,,:ii:,,;*i*i,.```..``.:,,,,,,::inxxxxxzi;::::,::::,,,.````````````````.,,::::::,,,,,,,,,,,,..........,,,,,,,,,,,,.,i+i.```.````````````````````````
,.,,:;;:,,;iii;......,....,,,,,,:;#xxxxxn*;;::::,::,,,,..````````..``...,,::;;::::,,,,,,,,,..........,,,,,,,,,,,,,,,,,i+i.```.````````````````````````
,..,:ii:,,:;;;:...,,,,...,,,,,,::;zxxxxx+;;:::::,,,,,,.``````````..`.;,,:;;;;:::,:,,,,,,.......,,,,,,,,,,,,,,,,,,,,,,,i+i`````````````````````````````
,..,:ii:,,:;;;:...,:::,,,,,,,,::;*zznnn+i:;::::,,,,,,.````````....``,#i:::::::::,,,,,,,.....,,,,,,,,,,,,,,,,,,,,,,,,,.,:,`````  ``````````````````````
,..,:;;:,;i::i:,,,,;;:,,,,,,,,:;*nxxxn+i;;:::::,..,,,,.````.`.,:,.``.*#;::::::::,,,,,,...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,`````  ``````````````  ``````
,..,:;;:,;*;;;::,,:;;:,,,,:::::;zxxxn#i;;:::::,.``.,:,.......,:;:.``.:nni::,,,:::,,,,..,,,,,,,,,,,,,,.,,,,,,,,,,,,,,,.,,,...````````.`````````````````
,..,:;;,,;i;;;;:::;;;:,,,::::i##nxxx#;:::::,:,.````,:,,::,.,,:;;;:.,::*xzi;:,,,::,,,..,,,,,,,,,,,,,,,.,,,,,,,,,,,,,,..,,,,..````````.`````````````````
....:;:,:;;;;;;;;;;;;::,,,::*nxxnzxni;:::::,..`````.::::;:,::;;;;:::;;inx#;;:,,,:,,..,,,,,,,,,,,,,,,,.,,,,,,,,,,,,,..,,,,,,,,........`````````````````
....,,,,,:;;;;;;;;;;:,:,,,:;nxxxxnz*;:::::,.``````.:;;;;;::;;;;;;;;;;;inzn*;:,,,:,..,,,,,,,,,,,,,,,,,.,,,,,,,,,,,,..,,,,,,,,,,,,,,,,,,.........```````
....,:,,,:;;;;;;;;;;:,,,,,:ixxxnnn*;;:::::.``````.:;;;;;;;;;;;;;;;;;;ii#+z+*::,.,,.,,,,,,,,,,,,,,,,,,.,,,,,,,,,,,,.,,,,,,,,,,,,,,,,,,,,,,,,,,,,..`````
....:;:,,:i;;;;;;;;;,,,,:::ixxxzz+;;::::::.``````:;;;;;;;;;;;;;;;;;;;i+#z#+z;,,....,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...`
`...:;:,,:i;;;;;;;;:,:,,::i*zxxn#;;::::::,``````.;;;;;;;;;;;;;;;;;;;i*nzx##n+::,..,:,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.....
.`..,::::ii;;;;;;;;,,:,,::#znxxzi::::::,.```````,;;;;;;;;;;;;;;;;;;ii#Mnxnnxzi;,..:::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,......
`..,,,:::iii;;;;;;:,,,,,,:#nznzi;::::,..````````:;;::::;;;;;;;iiiiii+xMxxnxxnz#;,,::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,........
`..,,,::;iiii;;;;:,:,,,,,:inzz*;::::,``````````.:::,,,,::;iiiii**+#nxxnxxxxxxnn*:::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.,,,,,......,,,.
`.,,,,:::i;i;;;;;:,:,,,,,::+n*;:,,,..``````````.,,,,,,,::;*+#nnxxMMMMxxnxxxxxxn#i;:::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,....,,.,..,,,
..::,,:::i;;;;;;:,,:,,,,,,,:;::,.``````````````..,,,,::i+zxMMMMMMMMxxxxxnnxxxxn+++;:::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.......,,,,,,,
,:;:,,;:;*i;;;;:,,,,,,,,,,,.....``````````````..,,::i+nxMMMMMMMMMMMxxxxxxznxxxn+#n+;::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,..,,........,,,,,,,,
i*i:.,;;i*iii;;:,,,,,,,,,,.`.````````````````..,,;*zxMMMMMMMMMMxMxxxxxxxxnzxnn###zz*::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.........,,,,,,,,,
#+;,,::;*+*i;;;,,,,,,,,,,.`````````````````..,,;+nMMMMMMMMMMxxxxxxxxxxxxxn###+###znn+;::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,....,..,,,,,,,,,,,
*i;,,::i*+ii;;;,,,,,,,,,.`````````````````.,:i#xMMMMMMMMMMxxxxxxxxxxxxxxn##++#znxnnnn*;:,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,..,,..,,..,,,,,,,,,,,,,
;;:,:;:i+*ii;;:,,,,,,,,..````````````````.iznxxMMMMMMMMxxxxxxxxxxxxxxxxn###znxxnnnnnnn*;:,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.,,,...,,,,,,,,,,,,,,,,,
;;:,;i;*#*ii;:,,,,,,,,..```````````````..;nxxxxxMMMMMxxxxxxxxxxxxxxxxxx###nxxxxnnnnnnnz*::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...,.,,,,,,,,,,,,,,,,
;:,,;ii+#*ii;,.,,,,,,,.```````````````..;nxxnxxMxxxxxxxxxxxxxxxxxxxxxxz##nxxxxnnnnnnnnnz*::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.....,,,,,,,,,,,,,,,,,
;:,,i;i++*i;,,..,,,,,.```````````````.,inxxxnxxxxxxxxxxxxxxxxxxxxnnxxz#+nxxxxxnnnnnnnnnnzi::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.,,,..,.,,,,,,,,,,,,,,,,,,,