##((((((#%%%####(((((((###%%%%#((#%&&&&&&&&%%########%&&&%%&&&&%%%#%%%%%%%#(((//(((((((((////////(((
((###(((((##(((((((#####%%%%%&%%%%%&&%###((((#(((((#######(##%%%%%%%%%%%%%%##########(((((((((////((
(((((((###%%%%#####(((((##%%%&&@&&&&&%######%###((#%#((((//((#%%%####((/(((#%&%%&&%%%####((####(///(
#(((((#######%%%%%#(/////((######%%%%#(((//((#((/((((///((((((((////(////((###%%%%%%##(#(((((#######
%#((((##%##(((###(/****/(((##%%#%%%%##(,(/./***//(../*, .( (#%%#(////(/////(((#%%%%%##((##%###(#%%%%
(#&@@@@&&%#(/////******/(####%###/*///*(((((/*/(((,(/(((..#(*//**,((#%%#((//(#&@@@&&&%%%%&&&%#%&@@&%
//((#####(////(//*****/(%&& /**/((((((#(/# ,(###(#(#(#((( (*(#//, /,*(((///(&@@@&&&@&&&&&@@&&&%%%%#
****/////////(((#(/((%&/**(*/////#(/#(#(####/ .#/(. (/(.(/(((((#(#//(/(*/*#%%%%%&%%##%%%&&&&%%#(//((
///****////(#####%%#,/(( ,(///.#((/**/.. /,,*//(//(((((((((#/((/*(.(, *****/(#####///(((((((((#####
((((/(((#%%&%%%%#** ,/*/*(**,(/,,//,.//////(((#(#((((////////*/////(( ((( //%(*,(##(//*/////(%&&&&&&
%%%&&@&&&&&&&&&%%((/*.***#%((,/.,,//. ,( ** *((/.((/ (((//(#((.(..///((((*(/(** .#####(((#%&&&&&&@
&%&&@&#/*/(##/ #/(## /,///// ,/(*/*(((///,((/,( .(((((((, .//*/(/*((##(/(////(*(,* *%&&&&&%%%%%%%&%
&&%%%%%#//(#(/ ( ,#%#//(##(* ,//#/((#( .( ,*/(*(/*** *** .,//////(((/( ####(#..** ,..////(((#%%%##
%&%%#%%%%#((((((*#(* /(.##.. ###.##. ##( /.*//,*,**,*******//*# , (#((#..*%##..#%##%//(###(//(#%%###
###((//(#((((((#%%%%##%%%##%%#/##(##/*#%. ,####,.....*./ ####., .*#(#.#.#%(%%%%%%%%,*.%#%#(((#%#((#&
**(/*/(#(/(/((((((///(##(/*/#(#&(/***,*(&####%%%##%/#&%##/*..,.#.%.#(%.# ,/.*%&/%%%/#,.*%&&%%%%&&@@@
/*,,,/%&&&%(//%&%%#((((#(#%##//#((//(##(/*///((((((((#####%%%&%&#/********//(#%&@&%(//(///(((######(
##((#(%/(#//*/#&@@@@@&###((/*&&&%(****/%,,****////////////%%#%%#&%#//((%%(%&&&@&&%#//(&&&%#((///***(
/*#/#*&(#(,#%#&&%%%###(#(//(@&#((%(((&%,,,,******/*******/#((#(//&&%%%#((((%&&%%%((#(%@@@@@@@@@&%(((
#(((((#@@@&&&%(##&@@&(#%(////(&&@%@@@@,.(,,,,,,,,*,,,,,,,#*/*(#(**/&&#(#(#%##%&%&&%#%%%######(((((%%
(*&#(*###%(#&%%*#%%#(@%/#/&(#@@@@&%&@@/&#//#(,*,.,,.......//*#******/*##&&%#(%&&&#%###(/(/(#####(((/
(/&&(%#%#%#@#&&&%#&##%#(&&@@@@@@@@@@%##&@@/#(///*##**#(///////,,,,,#*&((####%&@@@&&((//**/*/##%@%///
%#&#%%*(#@###&/%&%((&@#@@@@@&%&&&%%(#@@@@@@@&#,,.,......*#(*/*,,*/(&##%&#%%&&&&&%%&%%%*,,,,.***(&&%%
#/&&(&/&*%#%@@@@@@@@@@@&&&&@&&/(#%,,*((#&%@@@&.,,.......,,../#/,(#%%%##%%#%&@@%%%%###&@/*&#(#(*/#&@#
%/&&@@@@@&(%#((&%%@&&@@@&%&##@@*#(/,/*/#%&@&#%*.( . . ... .*%&##%&&&#(#((%@&%%%%%%%%#%(#((%#(#(/@@@
@%#@%%(/&@(@&@@&&%(@(#/(*(/(%#/@@%(*@&&**#@@(#, . , . ,,,**%&@#((##(#(#(/(#%@(@@##&#%#%//,//((##&%
%%%@&&@@@@/@@@@@@%**//,*///&&&&//&&&&@%(%%#%/@, , . (..,@@%@@//(*#/%(#&#######(%(#%/((//@@#%%%(
#@@@#&&@@&&@@@@&%*((%%/((,/*(&&&&@@@&@&&@@%###,/(..#,.,/#/ ..*@@/((%#%((#%#/#&&&%###(@&#/#/##%#%@((&
&%&&@@@@#&&&@@/&&&%&###%&&&&&&&@@@/&&(/@&&%##(%%## ./*,...,/@*/%&%%%(/(#%%##%&%&%/((#(#((@@&&%*/@
%//((((#(@(((#//(*/#/#//(###(%*%@@@@@@&@@@@@@@@@&&/.... //.#%#((((%(#((&@@(#&&@%&%%%%#(%&%/&(#(@@%(%
#((/*/(///#(((/%/(#///#((((#(#(((&@%((&(#@@@((/(*/&,&&*%#%%%&%(%##&&@@(#%/(%#(@%@(#%#/@&&%%@@@@@&%*%
*//*/*//*/*//%////#(&&&*%@(#((*/&/#*#@%&@%&(#///////(((((#%(#&%#&@@#&(/(*/#&%@&&(&%%(/(//(((#%##&#%%