================;;;:::::::::;;;::::;;;;:;;;=+++=;;;=;::;;;:::;;;;=+itti+++++++++++++++=++ii++iittIIIIIItttttiitttttttiii+++++iiiiiii+++++++++==;;;;:;;==;;=+iti=;::,:;==++ii======++=++++itIYIIi
ii+++++i+++++++++===;;;;;=;;===;;;=====;==++iii+==++=;;;;==;;====+iIYItiiiiiiitiiiiiii+iittiitIIYYYYYYYYYIIIitIYIIIItttttiiiitttttttiiiiiiiii++====;;=+++++iIYIi+=;:;==+iiti+===++ii=+++itIYYYYI
IIIttttttttiiii+++===;;=================++++ii+===++=;;;;===;==++iitIItittiiiiiiiiiiiiiiiittttIVVVVVVVVVVYYYttYYIIIIttttttiiiittttttiiiiiiiii+++=======+++iiIYItii+;====++ii==+iitti+++iitIIYYII
IIIttttttttiiii++=======++==============++++++=====++=;:;;;;;===+itttttttttiiii++iiiiiiiiiittIIYVYYYYVVVVYYYttYIIIIItttttttiiitiittiiiiiiiiiii+++++++==++iiitYIttti+=========+iittti==+++iitIItI
ii+++ii++++++=====;;;;;===;;;;;;;;;;;;;;====;;;;;;===;;;;;;;;;;==++iittttiii+++++ii++iiii++itIIIYYIIYYYYYYYttttIIIIItttttiii+ii+iii++++++iii++===+++===+++iitttiiiti=;=;;;;;==+iiit+===++++++iii
============;;;;:::::::::::::::::::::::::::::::::;;;;::::;;;;;;;;===+++i++++=====+++++++++++iitttttIIIIIIIItiittttttiiiii++++++++=============;;=====;;====+++++++ii+;;:::::;;;===+=;;;=======++
:::::::::::::::,,,,...,,,,....,,,,,,,,,,,,,,,,:::::::::,:::::::::;;;;;;;;===;;;;;;=====++===+++i++iiitttttti++++iii+++++===+=====;;;;==;;;;;=;;;;;;;;;;;;;;;;;;;;;=+=;,,..,,,,,,,:::,,,::::::::;
,,,,,,,,,,,,,,,,.....................,,,,,,,,,,,,,,,,,:,::::::::::;;;;;;;;;=;;;;;;;;;=========++++++iiiiiii+++==+++++++=========;;;====;;;;;;;;;;;;;;;;;:::::::::::;;:,..  ....................,
,,,,,,,,,,,,,,,......................,,,,,,,,,,,,,,,,:::::::::::::;;;;;;;==;;;;;==;;;========+++++++iiiiii+======+++++==========;:;======;;;;;;;;;;;;;::::::::::::,::::,.         .   .       ..
:::::::::,,,,,,,...................,,,,,,,,,,,,,,,,,,,,:::::::::::;;;;;;=====;;=====;;====++++++++++iiiiiii+++==++++++=++======;;;=+=====;==;;;;;;;;;;;;:::::::::::::;;::.....   ..... .........
;;;;;;;;;;;:::::::::,,,::,,,,,,::::::::::::,,:::::::::::::::;;;;;;;;;;===++++==++++++++++++iiiiiiiiiittttttiiii+iii+i+++++++++=;;=++===============;;;;;;;;;;;;;;;;;=====;:,,,...,,,:,,,,,,,,,,,
+++================;:;;;;;;;;;;====;;;;::;;::;;;;==;;;;;;;;;===;====;==+iiiii++tiiiitttittttttIIIIIIttIYIYYItttttttittiiiiii+++=++i+=++===++==++++=======;=;;==++==+ii+iii=;::,::::;===;;;;;;:::
ttiiiiiiiii+++++++++==+++=++++iii++++==;;=;;;;====++=====;=======++===+itIYIttiIIIIIIYYIIIIIIIIYYYYYYIIYVVYYIIIIItIItttItIItti++iti++ii+++iiii+iii++=++======+++iiiitti+ti+==;:;;;;=ii++====;;=;
IIItttttttiiiiiii+i+++++iiiiitttii+++=;;;;;========+++++====+++++++++++tIYYYIIIYYYYYYVVIIIIIYYIYYVVVVYYVVVYYYYIIYIIIIYIIIYYIIi+iittiiiiiiiiiiiittii+++++++++++iittttttii+i+;;=;;;;;=iii+========
tttttttttiiiiiii+++i+++iItttIYItti++==;;;;;======;=++++++===+++++=+++++ttIIIIIIYYYYVVXXYYYYYYYIYYYVVVVVVVVYYYIitYItIYYIIYVYYIii++itiittittttiitttti++==++++++iittIIItiii+i+=:;;;;;;=+ii+=;;=====
tttttttiiiiiiii+++++++++ttiitttti+====;;::;;;;;==;==+++++++=++++=;=++++ittItttIIYYYVVXXYYYYYYYYYYYYYYYVVYVYYYI+tIIttIYIIYYYYIii+=+iiiitttttiiiittii++++++++++iitIYYItii+iii+;:::;;;;=+==;;;;;;;;
tttiiiiiiiii++++++++++++i++++++++=;;;;;;::;;;;===;;====+++++++++=;=+++itttIIIIIIIIYYVVVYYYYYYYYYYYYYYYYYYYYYVYttYItIYYIIIYIIIiii+iitiiitiiii++iiii+++++++++++iitIIItii++iii+=::::;;;;;;:::::::::
++=======================;==;;;=;;;;;;;;:::::;;==;;;;;===+++++++=;=++++iittIIIIttttIIIIIIIIIIIIIIYYYYYYYYYIIYYIIYIIIIIttttttIiii+iittiiiiiii+++++++++++=+++++++itti+++====+;=;,,,::::,,,,,,,,,,,
;;;;;;;;;;;;;;;;;:::::::::::,:::::::::::::::::;;;;;;;;;=============++++++iiiii+++iitttittttttttttIIIItIItttIIttttttiiititiiti++++iiii+++++++++======================;;;;;=:::,,................
:::::::::::::::,,,,,,,..,,,,,,,,,,::::,::::::::;;;;;;;;;============++=+++++++++++++i++++iiiiiiiiitttttttiittti+iiii=+iiiiiii+=+++i+ii++++++++================;;::;;;;;:;;:;:,,..     ..        
,,,,,,,,,,,,,,,,,,........,,,,,,,,,,,,,,::::;:::::;;;;;===;;===;=========+=+=+====+++++++iiiiiiiiiiiittttttttii+iiii==+iiiiit+++++++ii+ii++=++++=============;;;;;;;;;;;;::::::.  .             
,,,,,,,,,,,,,,,,,,........,,.,,,,,,,,:::::::;;:::;;;;;;;;;;;;;;;;===========+======+++++iiiiiiiiiiittttttttttttiiiii++iiiiiit++++iiiiiiii+++++++++=============;;;;;;;;;;;;;;;;,               .
,,,,,,,,,,,,,,,,,,,...,,,,,,,,,,,,,,,:::::::::::::::::;:;;;;;;;;============+=+===++++i+iiiiiiiiiiittttttttttttiiiitiittttttt+++iiiiiiiii++++++++++====+=====;=====;;;;;;;;;;;=:,.       .    ..
::::::::::::::::::,,,,,,,,,,,,,,,::,:::::;;;;:::::::::;:;;;;;============+=+=+++++++++++iiiiitttttttttIIIIIIIttiiiitttttIttttiiiiiiiiiiiiiii++++++++++=++++====++++====;;;;;;;;;;:,.. ..........
;;;;;;;======;;;;;::::::::::::::::::::::;====;:;;;;;;;;=;;;;;==++==;;==+++++++++iiiiiiiiittttIIIIIIIIIIIIYYYYIItiitIIIIYYItttiitttttttttiiiii++iiiiii++iiiii++itiiii+++++==;;;====;:,.,..,,,,,,,
+++++++ii++++++++==;;;;;;;;;;::::;;;;;;;;=+++=;;;======+==;;;++i+++===++iitii+i+iitttIItttIIIIYYYIYYYYYYYYYVVVVYIIYYYYYVVYItttttIttttttttiii+++iiiiiii+itttiiittttttiii++++====+++=;;,,,,,:::,,,
iiiiiiittiiiiiii++=====;;;;;;::::;;;;;=;==+++=;;;==+++++====+iitiiiiiiiittIttittttIIIIIIIIIIIYYYYYYYYYYVVVVVVVVVYYYYYVYVXYIItttIIItttttttiiiiiiiiiiiiiiittiitttttttiiiiii++++++++++;;:,,,,::::::
tiiiitttttttiiii++==+++==;;;;::::;;;====;==++=;;;==++++===++iiitiitttiittItItIIYIIIIIYYIIIIIYYYYYYYYYYVVVVVVVVVVVVYYVVYVVYYItIttIItttttttiiiiitttti+iiiiiiiittttiiii+++ii+++i++++i+;;;::,,::::::
iiiittttttttiiii+====++==;;;;::::;;========++======+++++==++iittiitttttIItttttttIYVYYYVYYIYYYYYYYYYYYVVVVVVVVVVVVVYYYVVVVVYIIIIIIIItttIttiiiiitItititiii+iiitttiiii++++++++iii+++ti+::,::,,:::::
i++iiiiiiiiiiiii+=;;;===;;;;:::::;;;===;;==+++=+====+++++++iitttiiittttttttttttttIIYIYVYYYYYYYYYYYYYYVVVVVVVVVVVVVYYYYYVVVYYIIIIIIItttIttiiiiitttiiii++iiiittiiiiii++++=+++iii+++it=:,,,::,:::::
====++++++++++++=;::::;;;;::::::::;;;;;;;=========;===++==++iitii++itttiiiittttttttIIIIYYIIIIYYIIYYYYYVVVYYYYYVVVVYYYYYYYYYYIIIIIIIttttttiiiiiiiiiiii++++iiii++++++++=====++++==++i=;,..,,,,,,,,
:::;;;;;;;;;;;;;::,,,::,:::::::::::::::;;;;;;;;;;;;;;=======++++++++ii+i++iiiiiiitttttttttttttIIIIIYYYYYYYYYYYYYYYIIIIIIIIIIIIIIIIIttttttttttiiiiiii+++++++++=+==++==========;;=;;+==:..........
,,,::::::::::::,,,,,,,,,,,,,,,:::::::::::;:::;;;;;;;;;;;==========+++++++++iiiiiiii+iiiiiitiitttIIIIIIIIIIIIIIIIIIIIttttttIIIIIIIItttttttttttiiiiiii+++++++++=+============;;;;;:;;==;.         
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:,:::::::::::::;;;;;;;;;;;==========++++i+iiiiiiiiii+++it+iiiiiitttIIIIIIIIIIIIIIIIIIIItttttttIIIIIIttttttttttttiiiii+++i++++++===============;;;;:;:;;;,         
,,,,,,:::::::,,:,,,,,,,,,,,,::::::::::::;;;;;;;;;==============++++++i++iiiitttttiiiittiitttittttIIIIIIIIIIIIIIIIYYIIIttttttIIIIIIIIIIItttttttiiiiii+it++++++++++============;;;;;;;;;;,        
::::::::;;;;;::::,,,,,:,,::;;;::::;;;;;;;======+++++===+++++++++ii+iii++iitttttttttttttttttttttttIIIIYYYYYIIIIIIIYYYIIIIIIIIIIIIIIIIIIItttttttitiiii+iti+i++++++++++i+++========;;=;;;=;,   ....
;;;========;;==;;:,::::::;;==;;:;;=++===++ii++iiittiiiiiiii+ii+iiiittitttttIItIIIIIIIIIIIIIItttttIIYYYYYYYYYYYYYYYYYIIIIIIIIIYYIIYYIIIIItIIItiiitttiiitttiiiiitiiiittiiii+i+++=+++===;==;,..,.,,
==++++++++++++++=;::::;;;========+ittiiiiiiiiittIIIIIttttttiiiiittIYYIIItIIIIIIIYYYVVVYYYIIItttIIIIYYYYYYYYYYYYYVVYYYYYIIIIIYYIYYYYYYYIIIIIItiittIItttttttttitIIIIIIItIttitt+++iii+==;=++;,.,,,,
iiiitttiiiiiiiii+;;::;;==+++++++iiIIYYItiittttttYVYVVYtttttttttIIYYVYIIIIIIIYYYYVVVVVVVVVYYIIIIIIIYVVVVVYVYYVYVVVVYYYYYYYIYYYYIYYVVVVYYYIIIIIIIIIIIIItttttIttIYYVYYYIIIIttItiiititi++==+i=:,,,,,
ttttttttttttttti+;;;;;=++++++itiitIYVVYIitttttttIYYVVYItittttttttttIIttIIYYVVYVVXXVVVVVVVVYYYIIIIIYYYVVVVVVVVVVYYYYYYYYYYIIIIIYYYYVVVYYYYIYYYYYYYYIIItttIttIYVYYVVVYIItttttt+iiiittii=++ii;,,,,,
ittttttttiiiiiii+;;;;==+++++itIiitIYVYYIttItttiitIIYVYItiittIttItttIIIIYIYVVVYYYVVVVVVVVVVVYYYYYYIIIIYVVYVVVVVVVYYYYYYYYIIIIIYYYYYVVYYYYIIIYYYYYYYIItttIIItIVVYYVVVYIttitiii+iiiittti+i+ii=:..,,
+iiiiiiiiiiiii+++;;;;;=+++++itItitIIIIttttItiiiiittIIIIttitIIIIttttIIIIYIYYYYIIIYYYYYYYVVVVVYYYYYYIIIIYVYYYYVVVVVYYIIIIIYYYYYYYIYYYYYYYYIIIYYYYIIYIIIttIIIIYYYYYYYYItiiiii+++ii++itttii++=;,...,
=+++++++++++++++=;;;;;;====++iiiiitttiiiitti++++iiittttttitttttttttIIttttIIIIIIIIIIIIYIYYVVVYYYYYYYYIIYYYYYYYYVVYYIIIIIIYYIIYYYtIYYYYYYYIIYYYYIIIIIIIIIIIIIIIIIIIIIti+++i++++iii+iiti++=;:,.....
=================;:;:;;;;;;=++++++ii+++=iii++===+++iiittiiiiiiiiiiiti++iitttIIItIIIYYIttIYYYYIIYYIIYIIIYYYYYYYYYYYIIIIIIYYItIYIttYYVYYYYYYYYYIIIIIIIIttttIIIIIttIIIti++++++++iii++iii++=;,.  ...
::::::;;;:::::;:::::::::::;;;;;;=========+=====;=++++iti++i++i+++iiiiititttttttttIIIIYIIIYYIIYYYYYYIIIIIIYYIIIYYYIIIIIIIIYYIYYIIIYYYYYYYYYYYYIIIIIIIItIiitIttttiiiii++++++++++++======;;::.     
,,,,,,:::::::::::::::::::::::;;;;;;;;;=========;==++++i+=++++++=++iiittttttttttttIIIIYIIIYYIIYYYYYIIIIYIIYYIIIYYIIItIIYYIYYYIIIIIIIYYYYIYYYIIIIIIIIItttiiittitiiiiii++++++++====;;;;;;:;;:.     
,,,,,,,::::::::::::::::::::::;;;;;;;;======;;=====++++++++++++++iittttttttttIttttIIIYItIIYYYYYYYYYYYYYYIIYYYYYYIIIItIYYYIYYYIIYIIIIYYYIIYYYIIIIIIIIttttiitttttiiiiii+++++++++====;;;;;:;;;,     
,,,,::::::::::::::::::::::;;;;;;;====++=========+++++++ii++++iitttIItttIItIIIIItIIYYYYIIYYYYYYYYYYYYYYIIYYYVVYYIYYIIYYIYYYYYYYIYIIIIIYYYYIIYYYYIIIItIItttttttttiiiiiiiiiii++++++===;;;;;;;:..   
::::::;;;;;;;;;;;:::;;;;;;;========++++++++====+++++++iii+++iitIttIItttIIIIIIIIIIIIYVYIYYYYYYYYYVVVYYYYIYYYYVYYYYYYYYYIYYYYYYItIIIIIIYYYYIIIYYIIIIIIIIIIIItIttttttttttiiiiiiii++++++==;;;;;:,...
;;;;;;;==========;;;========++i++++iiiiiiii++==++++++iiiiittttIIttIItIIYYIIIIYYYIIIIYVYVVVVYYYYVVVVYYYYYYYYYVYYVYYYYYYYYYYYYItttIIYIYYYYYIYYYYIIYIIIIIIIIIIIIIttttIItttttiitttiiiiiiii+==;=;:,,,
====++++++++++++++==++i+iii++itttiitttttiitii+++ii++iitiitYYIIIIYYIIIIYYYYYYYYYYYYIIYVVVVVVVYYYVVVVVVYYYYVYYYYVVYIYVYYYVYYYVYttIIYYYYYIIIYYYYYYIYIIVYIYYYYYIIIIIIIIIIIttttttItttttttItii+=;=;::,
++++iiiiiiiiiiiiii+++iiitti++itIttiitttttttttii+iiiitttiiIVYYYYIYVYIIYIIYYVVVVYVVYItIYVYYVVVYYYVVVVXXVIIIVVYYYVVIIYYIIIVVVYVVYYYYYIIYIItIYYYYYYIYIYVYIVVYYYIIIIIIIIIIIIttttIIIttttttIItii+;=;:::
iiitttttttiiiiiiiii+++ittti++itIti+iittttttttiiitttittttYVXYttIIYVYYYYYYVVVVVVVVVVYYIYYYYVVVVYVYVXVVXXVYIYVYYVVYYVYVYYVVVVYYYYYYYYIIIYYIIYYYYYYIYYYYYYYIYYYYIYYIIIIIIIIIIIIIIYIIIIttYItii=;;;:::
+iiitiiiiiiiiiiiiii+=++itii++iii++==++iitttttti+ittttIIIIYIi+itIYVYYVYYVVXXVVVVVVVYYYYYYYYVVVVVVVXVVVXVVYYYYYVVVVXVVVVXVVYYYYYYYVVIIIVRVYIYYYIIIIIIIIIIIIIYYYYYYIIItIIIIIIIIIIIttttIYYItt+:::;;:
++++i++iiiiiiiiiii+=;=+iii++++++=====++iittttii+itttIIYIIttiitIYYVVVVYYVVXXVVVVVYYYYYYYIYYYVVYYYVVVVVXXVVVVYYYYYYVYYYVVVYYYYYYYIYYIIIVRXIIIIIIIIIIIIIIIIIIIYYYYIIItttIIIIIIIIIItttttYYIIIi::::::
=======+++++++++===;:;=+++=+++=======++iiiittii+itttIIItttttIYYYYYYYYYYYVVVYYVVYIIYYYYYIYYYYYYYYYVVVVVXVVVVYVVYIIYYtIYIYYYYIIIItIItttIIItttttttIIIIIIIIttIIYYYIIIIIttttIIIItIttttttttttIYt;,,,,:
;;;;;;=========;;;;::;;==============++iiiiiii+++ittttttittIIYYYYYYYIYYVVVYYYYYYIIIYYYYIYYYVVVVVYVVVVVVVVVYYYVYYYYYtYYIIYIIIttttttttttiiitiitttttIIIItttttIIIIItIIIttttiittttttiitiiiiiit+;...,.
:::::;;;;;;;;;;;;:::;;;;;;===========++++++++++++iittiiiitIIYYIIIIIIIYYYYYYYYYYYYYYYYYYYYYYYYYVVYYYYVVXVVVVYYYYYYVYYYYIIItttttttiiititttiiiiiitttttttttttttttttttttttttiiiiiiiii+i+++++++=;.  . 
,,,,:::::::::::::::;;;;;;======;=====+++++++++++iiiiiiiitIIYYIIIIIIIIIIIYYYYYYYYYYYYYYVYYYYYIIYYYYYYVVVVVVVYYYYYYYIYIttti++++iiiii+iiittiiiiiiittttttttttttttttttttttttiiiiiiiii+++++==;;;;:    
,,,,::::::::::::::::;;;;;===;==;=====+++++++++++iiiiiiittIIIIIIIIIIIIItIYYYYYYIIYYYYYVVVVYVYIIYVYYYYVVYYYYVYYYYVVYtYt+=++==;;=+++++i+iiiii++iiiiittttttIItttttttttttttiiiiiiiiii++++===;,:::    
,:::;;:;;;;;;;;;;:;;;;;;;;=======+++++++++++++iiiiiiiitttIIIIIItIIttIYItIYYYYYYVVYYYYYYVVVVYYVVYVYIIYYIIIYtYYYXXYItii++++======+==+++++++ii+++iiitttttIIIIIItttttttttttttiiiiii+i+++ii+=;,::,.  
:;;;=;;;;========;;;;;;;;======+++++iii+iiiiiiitiiiiittIIIIIIYIIIIItIIItIIIIIYYVVVYYYYYYYVYYYYYYYYIIYYIIYYIIYIYYtii+==================++++++++++iittttIIIIIIItIIIIIIttttttttttiiiiiittii=:,::,..
;==+++=+++++++++=;;;;;;;====;==+iiiittiiiitttttItttttIIYIIIIIYIIttttttIIIIIIYYYYVVVVYYYYYYVVVVVVVYYIIIIYIIIIYIIt+++=;;=======;;;;;=====++++++++++ittttIIIIIIIIttIIIItIIIIttttttiiittIYtIt;,::::,
=++++++iiiiiiiii+;;;;==;======+iittttttiittttttIIttIIYYYYIYYYYItiittttIIIIIYYYYYYYYYYYYYVYYVVYYVYYIIIIIIIIItIIt+;;=;:;;;;;;;;;;;;;;====++++++++++ittIIIIYIIIIIIIIIIItIYYIIttttIttiitYYtYI=,,,::,
+++iiiiiiiiiiiii+;;;;========++ittttttttttttttIIIIIIIYYYYYYYIIttttttIIIIIIIYVVYYYYYYYYYYVYYVVYVXVYIIIItIIItitt+=:;==;;;;;::;;;;:::;;===========++ittIIIYYYIYYYIIIIIIIIIIIttttIIIttttIIttt=,,,,,,
++iittttttttttti+;;;;========++itttttIIIttttttIIIYIIIYVVYYYItItttttIYYYIIIIYYYYYYYYYYYYIYYYVVVVXVVYIIttttItit+=;::===;;;:,,:;;;;;::;;===========++itIIIIYYIYYYIYYIYYYYYYIIIttIIItttIIItii=:,,,,,
+++iiiiiittiiiii+=;;;========++iitttIIIItttttttIYYYYYYYVVYYItttttIIIYYIIIIIYYYYYYVYYYYIYYYYYIIIIIIttttttttii++==;;===;;::,:::;;;;;;;;;;;==++==+=+++itIIYYIYYYYYYIIIYYYYYYYIIttttIttIItti+=;,,,,,
==++ii++iiii+iii+=;=;=======++i+iittIIIItttttttIYYYYYYYYYYYItttttIIIIItttIYYYYYVVVYYIIIYYVVYYIIIIIttttttii++===;;;;;;::::::::::;;;;;;;;;;=+++++++++itIIYYYYVVYYYItttIIIIIYYItttttttItitt+;:,.,,,
;;=++++++++++ii++=;;;=======+++++iittttttt++tttIIIIYYIIIYIttttttttttttttttIItIIYVYIIIIIYYYItttttttiiittii++==;;;;::::::::::::::::;;;;;;;;;===;;;=++itttIYYYYYYIIIIIIIIIIIIIItiiitttttiii=:,.....
::;==========+++============++++++iiiiiiitiitttttIIIIIItItttttttttttttttttttttItIIttttttttiiiiiiiiiiiii++==;;;;:::::::::::::::::::;;;;;::;;;;::;;==+ittIIYYYYYYYIIIIIIIIIIIttiiiiiiiiii+;,..    
,,:;;;;;;;;;=============+++++++++++i++++iittiiittttttttttttttttttttttttttttttItttttittiii++++++++++++++=;;;;;:::::::::::::::::::::::::::::::::;;;=+itttIIYYIIYYIIIIIIIIIItttiiiii+++i+;,,.     
,,,:;:;;;;;;;;;;;========++++++++++++++++iittiittttitttttttttttttttitttttttttttItttiittiii++++++++++======;;;:::::::::,::,,:::,::::::::::::::;;;;;==+itttIYYYYYYIIIIIIIIIItttiiiiii+++=:..      
..,:;:;;;;;;;;;;;==========++++++++++++iiiiiiiitttiittttttttttttttittttttttttittiiiiiti++===++=======;;;;==;::,,,::::,,,,,,,,,,,::::::::::::::;;;;;=+itttIYYYYYYYIIIIIIItttttiii+i+++i;.        
..:;;;;;;;;;===============+++++++++++iiiiiiiititttttttttttttttttttttttttttiiiiiii+iii+============;;;;;;;;:,,:,,:::,,,,,,,,,,,,:::::::,,:::,:::::;;=+itIIYYIYYYYYIIIttItttttttiiiii+t+         
,,:=+========+++=======+==+++++++++iiiiiitiiiitttttttttttttIIItttttttttttiiii+++i+iii+========;;===;;;:;::::,,,,,,::,,,,,,,,,,,,::::::,:::::,::;;;;;==+tIYYYYYYYYYYYYIIIIItIIttttttiiYt,    . ..
::;+i++++++++iii+===+==+=++++++i++iiiiiittiiiitttttttttttttYYIttttttttttiii++++ii++i+====;;;;;::;;;=;;:;:::,,,,.,,,,,,,,,,,,,,,,,:::,,,::,,,,:::::;;=++tIYYYYYYYYYYYVYIIYYIIIIIIIIttiYY;.  ...,,
::=+ii+iiiiiiiiii+======++++++++++iiiiiiiiiiiiiitIIttttttItttttttttttttiii+++++++ii+=;;;;;;;;::::;==;:,:::::,,...,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::;:;;=+itIYIYVVVYYYVXVYYYYVYYIIIIItIItt=,  ....,
:;+iiiiiiiiitttii+====+=++++++++++iiiiiiiiiiiiitIIIIttttttttItttttttttti++++++++iii+=;;:;;;;;;::;;==;:,,::::,,...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::::;==itYYYYYVYYYYYVVYYYYYIIIIIIIIYY+=+;.  .,,,
:;++iiiiiiittttti+====+++++++++++iiiiiiiiiiittitttIItttttttttttttttttiii+++++++++i+=;;;;;:::;;:;;;==;:,,,,,,,....,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::;;;==itIIIYYYYYYYYYVVYIYIIIItIitXX=,;:,  ...,
:;+++iiiiiiitttti+====+++++++++++iiiiiiiiiiittttttttttttttIttttitttttii+++++==++++=;;::;;::::::;;;:::,,,,,,,.....,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::;;;+itIIIYYYYYYYVVVYYYIIIItIiiVX; ... .....
:;===+i++++iiiiii+=++=++++++++++iiiiiiiiiitttttttttttttttttttttitttiii+++++=;==+==;;:::::,,:::::::::,,,,,,......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::;;;;==+itIIIIIYYYYVYYYYIYIIIttIiitY;  .     ..
,:;;==+===++++++++=++=+++++ii++iiiiiiiiiiitiiittttIIItttttttttttttiii++========+=;;::::,,,,::::::::,,,,,,,......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::;;=+itIIIIYYYIYYYIIIIYIIttiIi=+t;          
,,::;;=;======++++++++++++iii++iiiiiiiiiiiiiiiitttIYIttttttttiitttiii++=========;:::::::,,,:::,,,:,,,,,,,......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::::::;===+ttIIIYYIIIYYIIItIttttiY+,:=:          
.,::;;;;;=======++++++++++iii+++iiitttitiiiiiiitIIIItitttttttttitttii++========;;:,,,,,,,,,:;;:,,,,,,,,,,.....,,,,,,...,,,,,...,,,,,,,,,,,,,,,,,,,:::;;=+ittIIIVYIIIIIIIItIttttiV+  .           
..,:;;;;;========+++++++++++iii+iittttiitiiiitttIIItttiittttitttttiii++==+=====;::,,,,,,,,::;:,,,,,,::,,,.....,,,..............,,,,,,,,,,,,,,,,,,,:::;;==+iIYIIIIYIIYYYYIttIIttiY+  .           
...:;;;;;========+++++++++iiiiiiiitittiiiiiittttIIItttitttttiiiittii++++++====;::,,,,,,,,,,,,,.,,,,,,,,,......,,..............,,,,,....,,,,,,,,,,,::::;;==+tIItIIIIIIIIIIttItttiVi.             
...:==;;=====++++++++++=++ii+++iiiiiiiiiiiitttIIIIttttttItttttttItii+++++====;:::,,,,,,,,,,,,...,,,,,,,.......................,.,,.......,,,,,,,,,::::;;==+itttIIIIIItIIIItItttiVt,             
..,:=+=====+++++++++++++++i++++iiiiiiiiiiittttIIIItttttIIttttttIIItiii+++====;:::,,,,,,,,,,,.,,,,,,,,,...................................,,,,,,,,,,::::;;==+ittIIIIIItIIIIIItttiYI;             
,,:;+i++++++iiiii++++++i+iiii+iiiiiiiiiiittttIIIIItIIItIYtttitttttiiii++++==;;:,,,,,,,,,,,,,.,,.,,,,,....................................,,,,,,,,,::::::;;=++ittIYIIIIIIIIIItttiIY+             
::;=+iiiiiiiiitti++++++++iiii+iiiiiiiiiiittttIIIIItIItitItiiiiiiti++ii+=+++=;::,,,,,,,,,,.,,.....,,,,,................................,..,,,,,,,,,,,:::::;;=+ittIYIIIIIIIIIIttttIYi            .
::;=itiiiitttttti+++++++++ii++iiiiiiiiiiitttttIIIIttttiitiititttii++++==+i+=;:,,,,,,,,,,..........,,,....................................,,,,,,,,,,,,::::;;;=iIIIYIIIttIIIIIttttIYi             
::;=iiiiittttttti+++++++++i+++itttiiiiiittttttIIIItttiitttttttiii+++++++iti=:,,.,,,,,,,........,..........................................,,,,,,,,,,,,::::;;;+IItIIIItItIIIItttItYi             
,:;;+ii++iiittiti+++++++++++++itii+iii+iiitttIIIIttttiiiitttIti++++++++=+i=;.,.,,,,,,,.....,,.............................................,,,,,,,,,,,,,,:::;;+YYIIIIIIIttIttttitIY+             
,,:;+i++++iiiiiii+++ii+++ii+++iiiiiiii+ittiittIIIttiiiiiiiiiiiii++++++==+i=;,:,,,,,,,....................................................,,,,,,,,,,,,,,::::::+VVIYIIIItttIttttttIY+             
.,:;=+====+++++++++iii++iii++++ii+iiiiitttiittIIIIt++iiii++iiiii+==++=;===;;,:,:,,,,.....................................................,,,,,,,,,,,,,,::::::iVXYIIIIIIttttttttIIt=             
..,:;=======++++++iiiii+ii+++iiiiiiiiiiittitttIIIIti+ii+++++i+++======;==;;:,:::,,,,...................... ...............................,,,,,,,,,,,,,,:::::+VVIIIIIYYIttttttIVt=:             
...,:;=======++++++iiiiiii++iiiiiit+iitittiittIttttiiiiii+iiti++=========:;:::::,,,....................... ................................,,,,,,,,,,,,,,::::+YYIIIIYYYIttttttYVi,.             
  .,:;+======++++++iiiiii++++ii+iii++itittittitttttiiii++=++i++=====;====:::,:,,,,,............................   ........  ..............,,,,,,,,,,,,,,,::::+YYIYIIIIIIttttitYV+               
. .,:;++=====++++++iiiiii++++ii+iii++iittttiiitttttiii+++++++++=+++=====;:::,,,,..,............................    .....     .........,.,,,,,,,,,,,,,,,,,::::+VVIIIIIIttttttiiIV=               
...,::=+===++++++iiiiiiiii++++iiitiiiiittitiiiittttii++++++++++++ii+===;;:,:,,,,..............................         ..   ........,,,,,,,,,,,,,,,,,,,,,,:::iXXIIIIIIItttttiiIY=               
..,,:;;+i+++++iiiiiiitttiii=;++tiItitiitttiiiiiitIti+++++=;;=++++++==+;;:::,,,,............................   .     .. .....  ....,,,::,,,,,,,,,,,,,,,,,:,,,;+YYYYIIIItIttttiiVR:               
,,,:::;ii+iiiitiiiiittttiii+;=+tittittttttiiiiiitIti++====;==========+;:::,,,..........................        ..         .. ....,,,,::,,,,,,,,,,,,,,,,,:,,,;+YIIIItIIIItIttitVY.               
,,::,::+iiiiittttiitttttiii+==+iiiiittitttiiiiiiitti++===========;==++;::,,,,.......................                   .. ....,.,:::::::::,,,,::,,,,,,,,,,::;+VYIIIIIIIttItttIV+                
,,,,,,,;=+itiiittiitttttitii=;+iiittttitttiiii+iiitii+==+=======;;;=++;::,,,.........  ........                       .    ...,,,:;;;;:;:::::::::,,,,,,,,,:,;+VVIIIIIIItttttttV;                
,,,,,,,,;+itiiiiiiiittttttii+==ittttti+itttiii+iiiti++=======;;=;;;=+=::,,,,........                              .   .    .,,:;;;;;;;;;;;;;:::::,,,,,,,,,,,;iVItIIIIttttttIiiI;                
,,,,,,,,:;+i+iiiiiiitttittii+==+tttii+=+ttttii+iiii+++======;;;;;:;+=;,,,,,,.......                                    ...,::;;=====;;;;;::;;:::,,,,,,,,,,,.;iYtttIIIIIttttI++t:                
,,,,,...,:;==+iiiiiiittiitii+=;+itiii==+iittiii+++++++======;;;;;:;+=:..,,,........                                   ..,,:;;;===+=;;;=;;;;;;:::,,,,,,,,,,,,;+YttIIIIItttttt+=+,                
..........,;;=+iii++iiiiiiii==;=+i+ii=++iittttiiii+i++=====;;::;;:;==:  .,,........                          ..      .,:;;=======++===+======;::,,,,,,,,.,,,:+YttIItItttttii+;=.                
       ....:;;=i++++iiiiiii++=;++iiiii++iitttttiiii+++==;=+;:::::;==;:..,,.......                .       ..       .,:;==+++++ii=+===+=;:;;;;;:::::,,.,,,,,,,:+tttttItttttiiIi;;                 
       .   .:;;+++++ii+iitti+++++itii+++iitttttttiiiii+==+=,,,,..:;=;:,.,,.......               ...      .....  .,:;+tIIttttIti++==;;;;;::::::::::,,,,,.,,::;+ttitttttttiiiIi;,                 
           .,:;==+++i+++itIi+++=+iti++i+iittttttttttiiiii++;;;:::;=;;:,,,,........          .....        ...,,.:=itIVXXIIttti+;;;;::,,::,,,,,,::::,,,,,.,,::;+ttttttttttiitt+,                  
           .,,:=+++iii++iit++=+;=+ii++iiiiiiittttttttttttii=;;:::;;;::::,,,.......       ........ ..........,:;iIVYYYIttti+=:,..,,,,:,,..,,,,,,,,,,,,,,,,,,:;+tItttttttiiiIi=                   
            .,,=+++iiii+iitii+=;;=+++i+ii+iitiitttttttYYYIItiiii+==;::::,,,,.......    ..................,,:;++tYYtttti=;:,.   .....,,...,,,,,,,,,,,,,.,,,,:;=itttittttiiit+:                   
              .;++++i+++iiiit+=;==++ii+++iitttittttttIYVVVVYVIii+==;;;:::,,,........   ..................:;+itttti=;::.        ....   ..,,,,,,,,,,,,,,,.,,::;=++itiiitttii++.                   
           .   :+i++++iiiiiii+;;;;++ii+++iitttiiitttIIYVXVXXRXYIti+===::::,,,..........................,,;=+ii+=;:,,..    ........,.........,,,.,,.,,,,,,,::;==+itiiitttii=:                    
.........  .   :+t++++iiiiti+=::,:=+++++++++i++iiiiiiiiitttittIItt++++;:;::,,,.......................,,::==;:::,.        .   .......,,.........,,,,,,,,,,,,:;==+iItiiiiiii=                     
.............  .+titiiiiiiiii=:,;;;++=+===+++++++++++++=;;;;==;=======;:;;:,,,......................,,,,::,,:,....., .,..,.,,.........................,,,,:::;==+i+iiii+tt+                     
.............  .+ittiiiiiiiit=:,;:;=+==========;====;;;;::,,,,,,:::;;;;:;;:,,,........................,,,,,,,..,,,,,:,,,......,,.,....................,,,,,::;===++++iitIt=                     
.............  .;+itiiiiiittI+::;;;==================;=;;::,,,,:::;;;::::::,,,.........................,,,,,.,,,:::,:,,,,........,,...................,.,,,::;;+=++++iiYYI;                     
........   .    :;=ii++iiittY+;,:;:;==;;;;;;;==;;;::;;;;:,:::::::::::,,:::,,,,.........................,,,,,,,,::::,:::;;:;::;::,::. ...................,,,::;;+===++iiIYI:                     
                .:;++++iiiiiI+;,:::;=;;:;;;;;;;=;;;;;;;;:,::::,::::::::::,,,,,,.........................,,,,,,,::::=itttt++iYVt+=++=;:,,,,,.............,,,::;;++=;=+++tIt:                     
                .,:=+++iiii+i=;,,::;;;;;;;;;;;;;;;;;;::;::::,,.,,,,::::::,,,,,,,.......................,,,,,,,,:;;;tXMBII+;iBMY==iYYI+:,,,,.............,,,:::;;=;;=+++tIi:                     
                 ,:=+++ii+++=;;,,,,,:::;:::;;;;;===;;,,,,,,....,.,,,:::::,,,,,,,,......................,,,,,,,:;=;;=YWBIti;+XX+,,=tYYt=::,,,,,...........,,,::;;;;;=++iII+:                     
                 ,:=+++iii++;;::,,,,,::::::::;;;;;;;:,..,,,,:;:;::,,,,::::::,,,,,,....................,,,,:,,,:==:: =XVXVXIIVt,  .;=ii+;;:,,,............,,,,:;;;;;+=+iYI=:.                    
                 .:=+=++iIi=:,:,,,,,,,::::,,::;;=====;++=+i+I+iit=;;:::::,,,:,,,,,.....................,,,,,,::;;:  ,=XRWBRXX=   .:;+i+;::,,,............,,,:::;=;;===+tti:                     
                  ,=i+++tI+:,,,,,,,,,,::;:,,,::;==iIIYtXR#YYYi+tMY===:,:::,,,,,,,,.....................,,,,,,,:;:.  .:tVMMBVt,   .,:;=;::,,,.............,,,::::;;;;==+iI=,                     
..                ,;++iiIt=...,,,,,,,,::;::::::==iYItt+IR#Xtt=iVRi;=+;;::::,,,,,,,.....................,,,,,,:==:,    :=iti=:  ..,,,::::,,,..............,,,,::;;;;:=+=IV=,                     
......           .,;++tIIi;   ,,,,,,,,,::,:;;;;=iVRi+;=+VXIiYItYY;,,;=;::,:::,,,,,,.......     .........,,,,.:+i;:,.      .    .,,,,,,::,,...............,,,,::::::,;=+IY=.                     
..........       .,:=+tIYt;   ,,,,,,,,,::::;;;=+IVV++,:=IIVYRBYIt. ,;i=;:::::,,,,,,......      .........,..,.,=+;;:,.          .,,,,,,,,,..... ..........,,,,::::,..:=tIYi.                     
...........       ,:==itYY;   .,,,,,,,,:,::;=;++IIi=;;,:=+VYXXYt; .;=Ii=;,,,,,,,,,,....         .......,...,..,,,,,,,,.,.......,,,,,,..,..................,,,::::,..:+IYVt.                     
.........         .,;=ttIV;   .,,,,.,,,::::;===+t+==;=:;;+=iII+=:;;:=t+;:,,,,,,,,,.....         ............... ...,,,,,,..,,,,,,.........................,,,:::.   :+IIVi                      
.......            .:=IttY;   .,,,,.,,,,:::;;;;i+==;;;;;;;===;=;:;:::.::,..,,,,,,,.....         .............,..,,,,,,,,,,,,..............................,,,,::.   ;itYRi                      
..                  :ittIY=    .,,..,,,,,::::;;;;;;;;;;;;;;;;;;:::,,,,,,,..,,,,,,,,.....        ...............,,,,,,,,,,...................   ...........,,,,,.    =ItIX=                      
                    :+ttII=.   .,,..,,,,,,,::::;;;:::::::;;;::::::,,,,,,,..,,,,,,,,.....        .................,,,,,,,...................    ............,,,..   .+t+IX+                      
                    .=ttII;    .,,..,,,,,,,,,::::::,,,:::::::::::,,:::,,,,,,,,,,,,,....         ..................,,,.....................      ...........,:,     :=+=IY;                      
                     ;iiYI;     .......,,,,,,,::::,,,,,,,,:,,,,,,,,,:,,,,,,,,,,,,,,,...         .............................  ..      ..        .........,,:.    .;=;+YY;                      
                     :iiYI;     ........,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...         ............................                      ........,,,.    .;:;iIi:                      
                     :itYt:     ........,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...,,,,,,,,....        ..........................                        .........,,.    .,,;t+;.                      
                     :+tYt:     ........,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,....,,,,,,,,....        ............... .........                         ........,,,.   .,,:+t;,.                      
                     :+tYI:     .........,,,,,,,,,,,,,,,,,,,,,,,,..,,,......,,,,,,,,....        ...............     .....                          .......,,,.   .,.:+=,.                       
..                   :=iVY:      .............,,,,,,,,,,,,..................,,,,,,,,...         ......   ......                                    .......,,,.  .,,,;;:..                       
.....                ,=iXV,      .............,,,,..........................,,,,,,,....         .......  ......                                    .......,,.    .,:=;..                        
.......              ,;iXV,      ...........................................,,,,,,,....         .......  .....                                     ........,.    ,:;=,                          
......               .:+YV;       ,.........................................,,,,,,,....         .......  ....                                      ..........    ;=;:                           
...                  .,;IVi       ..........................................,,,,,,.....          ......  ...                                     . .........    .;;,.                           
                      .:iVY       ..........................................,,,,,,....           ...... .....                                      .........    ,:,                             
                       ,;IY,      ..........................................,,,,,.....           ...... ......                                     ..........  .,,                              
                        ,iY;.     .........................    .............,,,,,.....           ...... .......                                    ............::.                              
                        .;t=       ......................         ............,,,,....           ............                                   .. .........,:;+;.                              
                         ,+=.      ................... .         ..............,,,....           ............                                   ..  .........:++:.                              
                         .==,      ..................            ..............,,,....           .............                                  ..  .......  ,=:.                               
                         .;=:.     .................             ..............,,,....           ..............                                 ..  ..  ..    .                                 
                          :;,      ..................             .............,,,....           ..............                                 ..  .. ...  ..                                  
..                        ,,.      ............... .               ...........,,,,....           ..............                                 ..  .........                                   
....                      ,...     ................                  ........,,,,,....           .............                                  ..  ......,.                                    
....                      .  .     .............. .                   .......,,,,,....           .............                                  .. ..........                                   
..                          .        .........  ..                   ........,,,,....             ............                                   ...........                                    
                            ..       .......... ..                   .......,,,,,....             .............                                 ....... ....                                    
                            ..       .......... ..                    .....,,,,,,....             .............                                ........  ...                                    
                                    ........... ..                  .......,,,,,,...              .......,,.....                               ......... ..                                     
                                     .......... ..                 .,,....,,,,,,,...              .......,,,....                               ........ ...                                     
                                     .......... ..                 .,,....,,,,,,....              .......,,,,...                               ........ .,,.                                    
                                     .......... ..                 .......,,,,,,....               ........,,,...                             ...........,,.                                    
                                     .............                   ....,,,,,,.....               ........,,,,..                             .......... ..                                     
                                      . ..........                  .....,,,,......                .........,,,                                ......                                           
                                      . ...........                 .....,,,.......               ..........,,,.                               .....                                            
                                        ...........                 ......,.........               .........,,,.                               .....   .                                        
..                                      ...........                 ................              ...........,,.                               ......  ..                                       
..                                       ..........                 .................            ...............                               .....   .                                        
                                         ..........                 ..................           ..............                                                                                 
                                          .........                 ...................         ......... .....                                                                                 
                                          ........                  ...................     ............. ....                                                                                  
                                         ..........                 ........,,,.,,,.......  ......,,,,,,,.....                                . ..                                              
                                         ..........            .............,,,:::,..............,:::::::,,...                                . ..  ..                                          
                                         ..........            .............,,,::;:,,............,::,,:::,,..                                .. ......                                          
                                          .........          ...............,,,,:;;;:,...........,,,,,,:,,..                                 .....  .                                           
                                           ........         .................,,,:;;;:,........,,,,,,,,,....                              .   .....                                              
                                           .........  .   .....................,,,,,,,,,.......,,,..,,,....                            ...   .....                                              
                                           ........................................,,,,,...................                            ....  ....   .                                           
                                            ......................................,,,...,,,,,,,...........                             ....  ....  ...                                          
.  .                                        .. ......................,,.,,..............,,,,,,..............                        ...     .. .   ..                                           
.                                            ...........................,...,,,,,........,,,...................                     ... ......    ...                                           
.                                            .................,.,,,,,,,,,,,,,,.,......................................           ...... .......  ...                                            
                                              ...............,,...,,::,,,,,,,,..............................................   ........ ....... ....                                            
                                              ...............,,,,,:;=;;;::,,,,,,,,,..........................................       ...........                                                 
                                               ..............,,,,:;+++=+=;::,,,.,,.............................................     ..... ......                                                
     .                                         ..............,,,:==++======;:::,,,,,,,..........................,,...,,,................  ......                                                
     ,...                                       .............,,:;=;:,,,:::;====;::,,,,..........................,,...,,,,......................,.                                               
   .,.                                           ............,,,::,,,,...,,:;===+i+;;:,,,......,,,,,,,,,,,,,.. .,,,.,,,,,.....................,,,                                               
    ..                                            .............,,,,,,.......,,:;=++==;;:,,.....,,,,,,,:,,:,,,,,,:::,,,.,,....................,,,,.                                              
      .                                           ..............................,:;;;==;::,,::,::,::::::;;======++=;:,,,.....................,,,,,.                                             
      .                                            ..................   ....    ..,,:;===;;;;=======++;==++=======;;:,,.....................,,,,,:,.                                            
      .                                              ................  ..............,:;;;=======+++=====;::::,,,,,,,,.....................,,,,,,::,.                                           
                                                     ..........................      .. .,,,,,,:::::,,,,,,..,.......,......................,,,,,,:;:,.                                          
                                                      ......................... ..........,,....,...,,....,,..............................,,,,,,,:;=;,.                                         
                                                       .........,.................   .   ...   .      ..................................,,,,,,,,,:;=;,.                                         
                                                       .,....,............................              ...............................,,,,,,,,,,,:i+=..                                        
                                                        ...................................             ...............................,,,,,,,,,,,:iti..                                        
                                                       ......................................           ..............................,,,,,,,,,,,,,+YI:.                                        
                                                      .,:,.........................................    ..............................,,,,,,,,,,,,,,=VV=.                                        
                                                    .,:==:........................................................................,,,,,,,,,,,,,,,,,;YV+.                                        
                                                    .,;ii;,......................................................................,,,,,,,,,,,,,,,,,,;IVt,                                        
                                                  ..,:=ti;,,...........,,......,,...............................................,,,,,,,,,,,,,,,,,,,;iVI,                                        
                                                  .,:=it+:::..,........,,....,,,,,,,............................................,,,,,,,,,,,,,,,,:,:;iVY:                                        
                                                 ..,:+ii=:::,,,..,,,..,.....,,,,,,,,,,...,,,,,,..............................,,,,,,,,,,,,,,,,,,,:::;+YV:                                        
                                                 .,,:it+;::,,,,..,,,.,,..,,,,,,,,,,,,,.,,,,,,,,,,,..........................,,,,,,,,,,,,,,,,,,,,:::;+YY:                                        
                                                .,,:;tI=;::,,,,,,,.,,,,.,,,,,,,,,,,,,,,,,,,,,,,,,,,........................,,,,,,,,,,,,,,,,,,,,,,::;iYI,                                        
                                               ..,,:+tt;;:::::,,,,..,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,......................,,,,,,,,,,,,,,,,,,,,,,,:;;iYt,                                        
                                              ....,;tIi;;:::,::,,,,,,,.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...................,,,,,,,,,,,,,,,,,,,,,,,,::;;iY+.                                        
                                              ....:=It+;::::,::,,,,,,..,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,................,,,,,,,,,,,,,,,,,,,,,,,,,::;;iI;                                         
                                              ...,=iIi=;::::,::,,,,,,,.,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,................,,,,,,,,,,,,,,,,,,,,,,,,,::;=iI:                                         
                                             ..  :itI+;;::::::::::,,,,.,,...,,,,,,,,,,,::,,,,,,,,,,,,,,...............,,,,,,,,,,,,,,,,,,,,,,,,,,;:;=tI:                                         
                                             .. .=Yti=;:::::::::::,,,,,,,..,,,,,,,,,,,,,,,,,,,,,,,,,,...............,,,,,,,,,,,,,,,,,,,,,,,,,,,:;;;+Ii,                                         
                                            ..  :iIt+=;::::::::::::,,,,,,...,,,,,,,,,,,,,,,,,,,,,,,,...............,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::;+I+,                                         
                                            ..,:+Iti;;;::::::::,:::,,,,,,,...,,,,,,,,,,,,,,,,,,,,,,,..............,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::;=+I=,.                                        
                                             .,=tI++;;:::::::::,,,::,,,,,,,...,,,,,,,,,,,,,,,,,,,,,..............,,,,,,,,,,,......,,,,,,,,,,,:::;;=+I=,.                                        
                                            ,;+tti==;;;:::::::,,,,,,,,,,,,,,,,.,,,,,,,,,,,,,,,,,,,,.............,,,,,,,,,,,....,,.,,,,,,,,,,::::;;;+I=,.                                        
                                           ,+IYti==;=;;:::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...........,,,,,,,,,,,,,....,,..,,,,,,,,,::::;;;+I=,.                                        
                                          ,=IYIi+==;;;;::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.......,....,,,,,,,,,,,,.....,...,,,,,,,,,:::;;;=tI=.                                         
                                         .:+YYt+===;;;:::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.........,,,..,,,,,,,,,,,..........,,,,,,,,,:::;;=iYt;                                          
                                         ,:;it+====;;;:::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,........,,.........,,,,,,,,,,,,,,::;;=+Yi:                                          
                                         .,:=i+====;;;:::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,........,,.........,,,,,,,,,,,,,,::;;=tt=.                                          
                                        ...,;+i+=;=;;;:::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,....................,,,,,,,,,,,,::;;==It:                                           
                                        ,...,=i+=;;;;::::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.....................,,,,,,,,,,,,::;;=iYt,                                           
.                                       ,....:++=;;;;::::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.....................,,,,,,,,,,,,:::;;=iVi.                                           
.                                       ...  ,;++=;;;::::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,..........................,,,,,,,,,,,,,:;;;=iV=                                            
.                                        ..   :=++;;;:::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,................,.........,,,,,,,,,,,,::;=;+IY:                                            
.                                        ..   ,;++;;;:::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...............,,.........,,,,,,,,,,,:::;;=iVI.                                            
.                                        ..    :=i+;;;::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,........................,,,,,,,,,,,,:::;;;;tt;                                             
.                                        ..    .:++=::::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,........................,,,,,,,,,,,,,:::;iit+,                                             
.                                        ..     .=i+;:::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,........................,,,,,,,,,,,:,,:;=+ti:                                              
.                                                :+i=::::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,......................,,,,,,,,,,,:,,;;,=ti:                                               
.                                                .;++;:::::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.....................,,,,,,,,,,,,,:,,=tt:.                                               
..                                                ,=+=:::::,,,,,,,,,,,,,,,,,,,,,,,,,....,,,,,,,,,,,,,.......................,,,,,,,,,,,,,::;;i=                                                 
..                                                 ,==:::::,,,,,,,,,,,.,,..,,,,,,,,.........,,,,,,..........................,,,,,,,,,,,,:,:+=;                                                  
..                                                 .;=;::::,,,,,,,,,,,.,,...,,,,,,,.........................................,,,,,,,,,,,,::;i:.                                                  
.                                                   .,;::::,,,,,,,,,..........,,,,,,........................................,,,,::,,,,:,:;=:                                                    
.                                                    .::,:,,,,,,,,,............,,,,,........................................,,,,,,,::,::;;:.                                                    
..                                                    ,,:,,::,,,,,..........................................................,,,:,,::,,:;;:.                                                     
..                                                     ,::::,,,,,............................................................,,:,::,,::=:.                                                      
..                                                     .:;::,,,.............................................................,,:::::,:;;:.                                                       
...                                                     ,:;:,,,.............................................................,,::::,:;;:                                                         
...                                                      ,::,,,.............................................................,::::,:::,.                                                     ..  
...                                                      .:::,.,........................... ...............................,,,::::::,                                                       ,,  
...                                                       .,,,,,,..............................   .........................,,::;;::.                                                            
....                                                       .,,,...............................     ........................,,:;=;,.                                                             
....                                                       .,:,..............................          ...................,,:;=;:.                                                        ,