ZZZuuuzzvrrttOll=1<<<<<<<<<~~___.....```````````````` ````````........_.1?MMMMMMMMMMMMMMMMMMMMMMMMMM
uuzzvrrttlll==??>;;:::~~~~~~.......`.`.`````````````````.`...------___~?_.(TMMMMMMMMMMMMMMMMMMMMMMMM
uuuzzzvrrrtttlll===??>>>;;::::::::~~~~~~~~~~~~~..........~.~.~.~~~~~~~~~~__...TMMMMMMMMMMMMMMMMMMMMM
Zuuuzzzvvrrrtttttlllll===?????>>>;>;;;;::::::~_~~.~~~~~~~~~~~~_((JJ+JeZTYYOTN+_.UMMMMMMMMMMMMMMMMMMM
ZZuuuuzzzvvrrrrtttttlllll======??????>>>>;;;<~..--(((JJ&ggkWY"""<<-..... XIC<;<MMMMMMMMMMMMMMMMMMM
NMNNNNMMMMMMNNNNNNNNNNNNNNNNNNNNNNNNMMMMMHHHHHHHNNNM"=<(-JuuAywwXdkWXkAA+- Oj>::<JMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMHHQmmsMNNMMNMMNMNNNMMNMMMNNNMMMMMMMHHHHHHMMNMMMdHHH@HHr Ay>(<(JMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMNMMMNHHM@MX@dMNNMMMMMNNMMMMMMMMMMMMMMH##MMNMHMH#NMMMM##MMMY""=<:<:+=dMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMNMHQmyX#dMMMMMMMMMMMMMMMHMMMMMHMMMMMMMMMMMMHB""7<___.....~~~<+lldMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMNNNNNNNMMMMMMMMMMNMHHHNNNH&ZWWMMMMB"=<_.__``````````````..~(+zrwMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMM#MMMMMHMN#MMMMMNkAAAsY=<___````````````````````` __+zwuXMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMHHHHH9UUUYYYYT>~~~...```````````````. _(?THMHMhwXZXMMMMMMMMMMMMMMMMMM
ffVVVVVVyWNNNNNNHNHHHHHHHHHHHHHHH===????>>>;;_____ ` ....------(((++zzwwwXHHMKZZXMMMMMMMMMMMMMMMMMM
MMNMMMNMMMMMMMMMMMMMMMMMMMMMMMMMMMMNMMMNMMMNMMMMMMMNNmggxzzOwwwwXXXXyyyyyyVg#N#yyWMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMHH#NM##@MMMMNMM#MMMMMMMMMMMMNMMMMNNMNNNMNkWfpppppfppppppffg#NNVVWMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMNMMMMM#NMMMMMMMMMMMMMMNMMMMNMMNWMHqkkkkbHHbbbbbppgHMMVfWMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMWNdNWamdMMMMNMMMMM#NMMMMMNMMMMMMMMNMNMNNMMMMMMNmqqqqqqqqkqkbp@HMMppMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM#MMMMMMMNMMMMMMMMNMMMMMMMMMMMNmmgmmmqqqkHWUMMMWHpMMMNMMNMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNMMMMMMMMMMMMMMMMMNMMMNMMMNMMMMNmmgmqHHUVC<<zMMWHbMNMNNMMNMNNMNNMNNMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNMMMMMMMMMNNMMMNNMMMHNMMMMNMNHHUXw&dQQkHMN#VWWMNNNNNNNNNNNNNNNNNN
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNMMNMMMMNNMMMHHM#MMMMMMMMNNMMMMMMMHM0zXWMNNNNNNNNNNNNNNNNNN
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNMMMMMMMMMMMMNMMNMM#HMMMMMMMMMNMMMMMWVT71>+&&ggMM#########NNNNNNNN#
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNNMMMNMMMMMMMMMMNWkHMMMMMNNNMMMNggNNMMMMMMMMMMMHHHHHHHHHHHHHHHHHH
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMH@@@@@@@@@@@@@@H@@
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM@@@@@@@@@@@@@@@@@@@
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM@gggggmgggggggggggg