`````````````````````````````````````````````````````````````````````````````````````````````````````...................................................................................................
```````````````````````````````````````````````````````````````````````````````````````````````````````.................................................................................................
``````````````````````````````````````````````````````````````````````````````````````````````````````````..............................................................................................
````````````````````````````````````````````````````````````````````````````````````````````````````````````````........................................................................................
``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````..............................................................................
````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````....................................................................
`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````.......................................................
`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````...............................................
`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````...........................................
``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````......................................
```````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````.................................
```````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````.............................
````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````........................
`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````...................
``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````..............
````````````````````````````````````````````````...```````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````..........
``````````````````````````````````````````````+@@@@@+, ````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````.....
```````````````````````````````````````````@@,,:::,,,.+@@@```````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````...
````````````````````````````````````````.@',::::::::::::;,:'@+.`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
```````````````````````````````````````#;:::::::,,;'#####+:,;,:@'```````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
``````````````````````````````````````@,:::::#+,:::::::::,,.'#,,,@;`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
`````````````````````````````````````@,:::#,::::::::::,::::,::,#::,@````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
````````````````````````````````````@,;;#,:#',,::,'##+;;;;;;##:;,#:,+;``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
```````````````````````````````````:,;:'::@::::##,:::::,,,,,:,:@,:,#:,@`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
`````````````````````````````````.`#;:'::@:::#,:::::#@#+''#@#:::'#::,@.@````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
``````````````````````````````````',;'::',::::::'+@','+::::::+'::,@::;;:+'.`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
``````````````````````````````````@;:+::#::;::;::+:::,':::::,,,+::,#:::,',@`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
``````````````````````````````````';;+::#::;;;;;@,@@@,:,:::::,,,+:::#,::,,,@,```````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
``````````````````````````````````;;;;;;#;;;;#;';@:;;#:'+#@::::,:;::,#,::',,;+``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
``````````````````````````````````#,;;';;;;;@:;@;::;+,+::::;':::,+;:,,#:::#,,,#`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
```````````````````````````````````#,;';;;'#;:@++:;;+,+::::::+::,,@;:,,#:::,,,,'````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
````````````````````````````````````@.;;:@##@@@@+:;@,#:::::::::::,:;;,,:;::@:,,+````````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
`````````````````````````````````````@:##...:::,#;@,,+::::::::+;:,,@;;,,@:,:;:,,+```````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
`````````````````````````````````````+#,,,,,,,,,,'.,#@@;:;,::::#;,,:';:,,+,:#:,,#```````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
`````````````````````````````````````#,;,:,,,,:,:',,+:::+;:;:::';:,:#;;,,#,,;::,:```````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
````````````````````````````````````.';:,,,,,,,,,;;@:;;:,+;,,:::+;,,;;;:,,;,:+:,,.``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
```````````````````````````````````.@.@.,,,,,,,,,,,''::+;;;;+:::#;,,:#;:,:#:,#::,'``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
```````````````````````````````````.:::,,,,,,,,,,,;#,#::';#;::::+;:,:@;;:,#:,;::,#``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
``````````````````````````````````.@,,,:,,:':.::,,:+';;::;:#;+:::;;,,+;;:,,:,:,::#.`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
``````````````````````````````````'.#'',,:,,,::,,,:'@;#::+;';::::';,,:;;::,#,:+::+``````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
``````````````````````````````````#.,'.@;:,,,+,,,,;;@::+:+;,':+::+;,,:#;;:,@,,#::,.`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
`````````````````````````````````@..@+`@,,,,,,,,,,;;##;'::;;+:;::#;;,,@;;:,+:,#::.'`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
````````````````````````````````.;.,@'@,,,,,,,,::,:;+#;:#;+:#:,::+;;,,#;;:,,:,;::#@`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
`````````````````````````````.``@..+.,,,,,,,,:,,,:;#++;:#:#:#,:+:;;;,,+;;::,+,::::+`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
```````````````````````````````@..,,,,,:,,,,,,,,,::++;;:::#:#,:#:,;;,,:;;::,#,,';::`````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
``````````````````````````````@..;,,:,,,,,,,,,,,:;':#;;:::;:#,:'::+;:,,+;::,@,,+#+,;````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
````````````````````````````:#..',,,,:,,,,,,,,,:::#;#;;::'::#,:;::#;:,,+;::,@,,#@#:#.```````````````````````````````````````````````````````````````````````````````````````````````````````````````````
```````````````````````````#:,,#,,,,,,,,,,,,,,:;;+:;+;;::+::#,::::#;;,,+;;:,#,,@+,+#````````````````````````````````````````````````````````````````````````````````````````````````````````````````````
`````````````````````````.@`,:#,,,,,,,,,,,,,,,;::';;;;;::'::#,::,:+;;,,#;;:,#,,#+,+:.```````````````````````````````````````````````````````````````````````````````````````````````````````````````````
````````````````````````#;:,:+,,,,,,,,,:,,,,,:;;@:;#;+;::+::@,:::::;;,,#;;::@:,#;,,#@.`````````````````````````````````````````````````````````````````