+====++++==++++++++++++++=~~:,,:::::::~===++++++++++====~::::,,,,,:====++++==+++
==+==+=~~==++++++++++++++=~~:::~:,,..,,:~=++++++++++==~~~:,,,,,::~===+++++=~===+
====~==~~~==++++++++++++=====~~~:,:::::~~~~=+++++=~~~~:,,,,,,,,::~~~~==~~~~+++++
~====~~~:~=++++++++++++++++===~~~:::::~~~====++===~~~~::,,,,,,,,,,,,:::~~==+++++
~~~~~~~~~~=+++++++++++++++===~:~~:+nd8o888o8o8dd+~~~:::,,,...,,,,,,,,,::~==+++++
::~~~:~~~=++++++++++++++++===~~~8dd8ozzzzzzzoozo8dn=~~:,,,,,,,,,,,,,,,:~~==+++++
::::::~~=++++++++++++++++====ind88oz7z$$$$$$$zzo7$o8dn=:,,,,,,,,,,,:::~~=+++++++
,,,,::~=++++++++++++++====~7dd8oz$7zz$$$7z77$zozzo$7$z8dd,,,,,,::::~~~===+++++++
==~~~++++++++++++++++====idd8oz$7zoz$$7z+=+o+==7zzoddz$$z8n,,,::~~==++++++++++++
====++??++++++++++++++==d88oz77odoz$$7zi~,:+~,,=$zodz,~od8z8~~==++=+++?+++++++++
~=+=++++++++++++++++==$d8o$7$8+dozz$$7$+:..~=..:?oo8n:::~=+++++++++++++++++++=~=
=+++++++++++++++++++++doz7zo~:o8oz$$777+,..:=..,+oood~~===+++++++++++++++==~~~:~
++++++++++++++++++++++z$~~::::n8oz$$777+,..,=..,=zzodi+++++++++++++++===~::,,,,~
+++++++++++++++++++++++==~~:::d8oz$$777+:..:=.=?+zzo8o++++++++++++==~~::::,,,,,:
++++++++++++++++++++++====~~~idozz$$$7$?io8oddo8d8zo8d++++++++?++++==~~::,,,,,,:
+++++++++++++++++++++++===~~~n8ozo8z$7ii=dodzn888i77$oz+++++++++++++=~~~:,,,,,,:
+++++++++++++++++++++====~~~~n8dz7i??++++=====+++++??i7z8++++++=====~::,,,,,,,,:
+++++++++++++++++++++===7ommmn87i++===~~~~~~~~===?=++??i$nn$+++===~::::,,,,,,,,:
+++++++++++++++++==immmmmmmmn87?+=~~~~8zo$~~~~~~zzzz7++?izmmmmmmn7=~:::::,,,,,,:
+++++++++++++++dmmmmmmnmmnnnnzi+=~~~~7z7$oi:~~~=zz$7o++?iznnnmmmmmmmmm7,,,,,,,,~
++++++++++ommmmmmmmnnmnnnnnnnoi?+=~~~o7zo$i~~~~=z$$oi+?i$dnnnnnnnnnnmmmmmm~:,,,:
+++++++mmmmmnnmnnnnnnnnnnnnnnno7??+==ooozz?=====z$ozii7zz$nnnnnnnnnnnnnnmmmmm$,:
++++immmmmnnnnnnnnnnnnnnnnnnnnn8z7i??+$zz7++++??7oo77z8+~~,.innnnnnnnnnnnnnmmmm8
++mmmmmnnnnnnnnnnnnnnnnnnnd7::=+i78z$777iiiii777$zz87i????++~:,?nnn8z$$77777$nm8
Mmmmnnnnnnnnnnnnnnnnnnno:.=+i77$$z++==i7zddddoz?+??7z7iiiii??++=~==~::,,,,,~inno
Mnnnnnnnni~~~==+?ii$o~,=?i7$$zzz?+=~~:::,,:::::~~=+?i$87777iiii7?=~~++?$odnnnnno
Nnnnnnnnnnno?~,,...,:=?$$$zzooi?+=~::,,,,,,,,,::~~=+?7z8$777777iii??7?i$8nnnnnno
Nnnnnnnnnddndddddoozoozzzoooz7?+=~::,,,......,,,::~=+i7o$$$$$$z??ii77,::=iddnnno
Nnnnnnnndddddddz77$$zooo8888$i?=~~:,,,........,,::~=+?7zozzz$$$$$$$$8ddddddddnno
Nnnndddndddnnoi+:..?8:,8ddd8$i+=~::,,..........,,:~~+?i$ddd8o87~=z$7ddddddddddno
Nndndddddddd$+:.,7d7~.?dddd8$i+=~::,,.... .....,,:~=+?i$ddddddddoi=:=zdddnnddndo
Dddddddddddz=~?dddz?,:dddddd$i?=~~:,,.........,,::~=+?7zdddddddddddd88dddddddddo
Dddddddddddddddddd7=,zddddddz7?+=~::,,,......,,,::~=+i7od8dddddddddddddddddddddo
Ddddddddddddddddd8i:odddd8dd8$i?+=~:::,,,,,,,,::~~=+?7zddd888ddddddddddddddddddo
Dddddddddddddddddd7zdd888888do7i?+=~~:::::,::::~==+?i$88dd88dddddddddddddddddddz
Ddddddddddddddddddd8dd8888ddddo$i?++==~~~~~~~~==++?7$888888888888888dddddddddddz
Ddddddddddddddd8d88d8888888888$+z$i??++======++??7$oo8888888888888dddddddddddddz
Ddddddddddddd8888ddd888888888oi7+=i$7ii??????i77$oi7dd888888888888888888dddddddo
Dddddddddddd88888d888888dd8d7???$$ii7ozz$$$$zo8dzo7?7$o888888888888888888d8d8ddz
Ddddddddddd8dd8ddd88888d88z$7iiz88ddd888dd888888z7$7$oi78dd8888888888ddddd8888dz
Dddddddd888dd88d888888888$$z$$oz8888888d88888888z7z$$oz$77d8888888ddd8d888888ddz
Ddddd8dd888888888dd8888dd88nzzd7d8d8888888888888$788oz8d88888888dd8888888888888z
Dd8d8dd88888dd888d8888d8888dd8877d888888d88888887888888888888888888888888888dddz