iIYVVVVXVVVVVVVVVYVYVYYVYYYYIIIIYYYIYVVVYYYYYYYYYVVYVVVVXVVVVVYI+.
tYVXXXXXXVXXXXVVVYVVVVVVVVVVVVYVVVVVVVVVVVVVVVVVXXXXXVXXXXXXXVVYi.
iYXRXRRRXXXXXXXXXXXVVXVXVVVVVVVVXXXVXVVXXXXXXXXXXXXXXRRRRRRRRRXVi.
tVRRRRRRRRRRRRRRRXRXXXXXXXXXXXXXXRRXXXXRRRRXXXXXXXRRRRRRRRRRRRXV+.
tVRRBBBRMBRRRRRRRRRXXRRRRRXt=+;;;;;==iVXRRRRXXXXRRRRRRRRMMBRRRRXi,
tVRRBMBBMMBBBBBMBBRBBBRBX++=++;;;;;;:;;;IRRRRXXRRRBBBBBBMMBBBRRXi,
iVRMMMMMMMMMMMMMMBRBBMMV==iIVYIi=;;;;:::;;XRRRRRRBBMMMMMMMMBBRRXi.
iVRMMMMMMMMMMMMMMMMMMMY;IBWWWWMMXYi=;:::::;RBBBMMMMMMMMMMMMMMBBXi,
+VRMMRBMMMMMMMMMMMMMMY+;VMMMMMMMRXIi=;:::::=VVXXXRRRMMMMMMMMBBMXi;
=tYYVVVXRRRXXRBMMMMMV+;=RBBMMMXVXXVYt;::::::ttYYVYVVRMMMMMMBXXVI+=
;=tIYYVYYYYYYVVVMMMBt=;;+i=IBi+t==;;i;::::::+iitIIttYRMMMMMRXVVI=;
;=IIIIYYYIIIIttIYItIt;;=VVYXBIVRXVVXI;::::::;+iitttttVMMBRRRVVVI+,
;+++tttIttttiiii+i++==;;RMMMBXXMMMXI+;::::::;+ittttitYVXVYYIYVIi;;
;===iiittiiIitiii++;;;;:IVRVi=iBXVIi;::::::::;==+++++iiittii+++=;;
;;==+iiiiiiiiii+++=;;;;;;VYVIiiiVVt+;::::::::;++++++++++iti++++=;;
;;=++iiii+i+++++iii==;;;::tXYIIYIi+=;:::::,::;+++++++++++++++++=;;
;;;+==+ii+++++iiiiit=;;:::::=====;;;::::::::::+++i+++++++++i+++;;;
;;;==+=+iiiiitttIIII+;;;:,::,;;;;:;=;;;::,::::=++++++++==++++++;;;
:;====+tittiiittttti+;;::::,:=Ytiiiiti=;:::::,:;;==ii+ittItii+==;;
;;+iiittIti+ii;;===;;:;::::;+IVXVVVVVVt;;;;;::::;;===;+IIiiti=;;;;
;=++++iIti+ii+=;;;=;:::;;+VXBMMBBBBBBXY=;=;;:::::;=iYVIIttii++;;;;
;;++iiiItttIi+++=;;:::;=iBMMMMMMMMMMMXI==;;,::;;:;;=+itIttIIti+;;;
;=+++++i+tYIIiii;:,::;itXMMMMMMMMMMMBXti==;:;++=;:::::;=+iittti+;;
;;+ii+ii+iitiIi;::::;iXBMMMMMWWWWWMMBXti+ii=;::::,,,,:::=;==+tI+;;
;;iiiitItttti;:::;::=+itYXXMWWWWWWMBYt+;;::,,,,,,,,,,,,,:==;==;;;;
:;=iIIIttIt+:;:::;;;==;+=+iiittttti+;;:,:,,,,::,,,,,,,,:::;=;==::;
;::=+ittiii=;:::::;;;:;:;=++==;;==;:,,,,,,:;::::,,,,,,,,::;==;;::;
:::;+iiiii=;::::,:;:::::;;:;;::;:::,,,,,,,:::;=;;;:,,,,,:::;;::::;
:;;iIIIIII=;:::,:::::::,::::,:::,,,,,,,,,,,:;;=;:,,,,,,::::;=;:::;
:;==++ii+;;;:::::::::::,,,,,,::,,,,,,,,,,,::::,,,,,,,,,,:,:::::::;
::;;=+=;;;:::;;::,,,,,,,,,,,,,,,,,,,,,,,,,:,,,,,,,,,,,,,,,,,:::::;
::;=;;;:;:::;;;;::,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,::,,::::;
:;;:;::::::,::,,:,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::;
:::::::::::;;;:,,,,,,,,,,,,,...,...,,,.,,,,,,,,,,,,.,,,,,,,,,,,,:;
::::::::;=;;;;;::,,,,,,,,,,,.......,...,,,,,,,,,,,,.,,,,,,,,,,,,,;
:::::,,:;=;;;;;;;iVXXXVt+:,,....,,,,....,.,,,,,,,.,.....,,,,,,,,:;
:,,::,,:::;;;;;;=IVVVXXXXVXVt:,,,,,..,..,,,,.,,,,,..,.,,,,,,,,,,,;
::,::,,,:,:::::,::;=iIYVXVVVVIYIi;,,.,.,,,::,,,,,,,,,,,,,,,,,,,,,.
:,,,,,,,,,,,,,,,,::;+itIIIIIIi:;;i++=;;;;;;;;;::,,,...,,..,,,,,,,.
:,,,,,,,,,,,,,,=iitVYi++iitt==it;;:;;;;::;;::::,,,......,,,,,,,::.
::,,,,,,,,,,,,,++iiIVIi=;;=;+i;:;+:::,,,,,,,,,,,,,.....,,,,,,,,::,
,,,,,,,,,,,,,,,;=+it=:::,,,,,,,,,,.,......,,.,..........,,,,,,,,::
:,,,,,,,,,,,,,,,,:=:,,,,,,,,,,,,,,......................,.,,.,.,,:
:,,,,,,,,,,,,,,,,,:,,,,,,,,,,..,........................,..,...,,:
,,,,,,,,,,,,,,,,,,,.....................................,.......,,
,,,,,,,,,.,,,,,,,...............................................,,
itittiiiii+=++=;;=iiiiiiittiiiiii+iii===;++iiitiiiiiii+=====+ii=+i