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