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