DDDDDNNNNNNMMMNNMMMMMMMMNMMMMMMMMMMMMMMMNND88OZZ$77IIIII?????+?+++++++?????+???I77$ZZZZ$$$$$777IIII???+++++++++++++++=++++++++++++?++++??++?++?++++++++++++++===
DDNNNNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNDD8OZZ$$7777IIIIIIII??????+++????I77$$$ZZZZZZZ$$$$777III????+++++++++++++++++++++++++++++????????++++++++++++++++====
NNNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNDD8OOZ7$Z$$7I777I7II??+I7I7II7$7?IIIII7$ZZOZZZZZ$$$77IIII?????+++++++++++++++++++++?++???????????+??????+++++++++++=
NNNNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNDD888O$$$7Z$$777I777+?+I777III+=?+++===?I777ZZZZZ$$$77IIII?????++++++++++++++++++++?+???????????????????+????+++++++=
NNNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNDD8$OZOOZZ$7$$7I?+?+==II777I=~~?+~~====+???+??777$Z$$77IIII?????+?++++++++++++++++++++?++?????????????+???+++++??+++=
NNNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNNDZ8ZOOOZO$7I?+~:~~~===+7I?:~?7I?7I~=~~~~~~::~+??I7Z$$777IIII????+??++++++++++++++??????????????????+???++++??+++++++=
NNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNN8D8D888O$II7+~:,~==777$7$?+IO$7I?+=II=+++~===~==++?III$7777IIIII??????+++++++++++++++???????????????????++++++??+++++++
NNNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNOOZ$$7?=:,~:,,,:++=:=7+:?7$7I?=~~==+?=~:,,:~=++==+?I+?777I7IIII?????+++++++++++++??+???????????????????+++++++??++++++
NNNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNDNO8$?+::,,.,~==~:~~~?II?I++?=~~::,,:,,:::~:~~~,,~+++=+???$7IIII?I???????++?+++++++??+?????????????????????++++++?++++++
NNNNNNMNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMD$$I?+=~=::~~:~~===+7OZOI7?IZ?======::,,,,,,,,,,,,:~=~,=+?+=+7$7I7II????????????+??+?+++??????????????????????????++++++++
DNNNNNNDNMMMMMMMMMMMMMMMMMMMMMMMMMNN88$7I+I=:,,,,,,,::~+$$777=7$77?++==::,,,,.......,,:,,:=~++:,+I?=I$$IIII??I?????????????++?????????I??????????????++?++?+++++
88888DDNNMMMMMMMMMMMMMMMMMMMMMMMNNNMO7I?+~:::,::,:,:~+==ZO7OZ8Z?$+$I+===???+=~~~:,..,,:::::~~:+???=??+II7?III???????????+????????????I???I??I????????++?+?++++++
8D88DDDDNMMMMMMMMMMMMMMMMMMMMMMNMNN7$7?~:~::~~:~::,::~~~+:??Z7$=77$II?I777O88OZ7IIII?+=,,~~=~=?+=?+7=?+I?77IIIIIIII????+??????????II?IIIIIIIII????????+++++++++=
OOO888DDNNMMMMMMMMMMMMMMMMMMMMMMNO7$Z?+=:~=~~:,.::,++?7+7?$+7I$7I?I77ZOOONNOZ+$I????I$$7?7+===~=+I+=+7??=7I$??I?II????????????????II??IIIIIIIII?I????+??++++++++
OOOO888DNNNNNMMMMMMMMMMMMMMMMMNNDI$77~+=:~~,.,:::=I$Z7Z$$+$I?$$7$7I7OZODDM88OZ7~:~?=I7+Z?I$I~:~=?I++?++I$?+7$I?????I?????????????I??IIIIIIIIIII?I??????+++++++++
OO888DDDDNNNNMMMMMMMMMMMMMMMMDOO7$$==~~~::,::,=?Z8NN$Z8OOZ8$$7?$$$7$Z$88D88NNDN8$+::+++IOI=I??=:,,,+II+????7+?7+???????+?+????????III?IIIIIIIIIII???I??+++++++++
OO88DDDDDNNNNNMMMMMMMMMMNNNNNM8OI++=I~=:~,::=I$7NMNDMMD87+7$II7I$O7$7$ZZ8O88DO8DD$=~::=+78I+7II+=::,,+Z?I?7?+7+?+?I????+???????????I?IIIIIIIIIIII?????????+++++=
OOO8DDDNNNNNMMMMMMMMMMMNNMMMN8D$?O+7~~~~::,~?$Z$8DDNMDOZ7I++++77?77?I$$O7ZZOZZ7$7DI+~~=+=+O$I$ZZ+?~~,,~+7I+I?I??I?+?II??????????????IIIIIIIIIIIIIII???????++++++
ZO88DDNNNNNNMMMMMMMMMNMMNNNN8N$$$?I~:=~,,:=IZOZONDMNO$?+~::::~~=+?++++++=?+?I??=+I$?7==~=+7Z?+I$7$Z7~~:~~7$7ZZI?I$7??????+????????????IIIIIIIIII?II??I?????+++++
OO88DDDDNNNNMMMMMMMMMMMNMNMDD$$O$I~=+=:,~~+7I$DDD8Z$I+~::::,,,,:,:~=~::~~~::~~====7$?I+=~==IZ+++?+OD$=~~~~Z$O$Z$?IIZ???+?++?????????IIIIIIIIIIIIIIIII?I????+++++
88DDDDDNNNMNMNMMMMMMMNMMNN8DOZ$O7:===::??I$IZ8Z88ZI+=~:,,,,,,,,,,,,,,,,,,,,,:::::~~+7??=+:==?I?++=?+78=+==?$O$O$O77777+I???+?+??????I?IIIIIIIIIIIIIIIII????+?++=
DDDNNNNNMNNNMMMMMMMMMNMNNNNONO87?=?+:=~=?+$8N8Z8$I=~:::,,,,.,,,,,,,,,,.,,,,,,,,,:,::==+?~~~==?+==+=??8N=?+=?$O$Z$7OOI$7+??+????????IIIIIIIIIIII7IIIIIII??????+++
NNNNMNNMMMNMMMMMMMMMMNMNNNONDO$I~?+~~?=??7OOOZ$7+~::::,,..,,,,,,,,.,,........,,,.,,:,~:?++=:~=+==~:+II$N=?++7$787IZ8$7?++++?+??????IIIIII7I7IIIIIIIIIIIII??????+
NNNMMMMMMMMMMMMMMMMMMMMNNDZD87=+I+=~~=?IZ$87$Z$?~::::,,..,..,,,,,,,,..............,,,:~~++~~~~==~=~==I?O8~+?I7Z7D$?7$7I?++++++??????IIIIIIIIIIIIIII7IIIIII?????+
NNMMMMMMMMMMMMMMMMMMMNMNDDODDI+=+==~=??+I$ON77+=::::,,,,,,..,,.,..................,,,,:,:==+:~~=~~~~==?IOI?I+7I?8$$7+?I?I===++?+????IIIIIIIIIIIIIIIIIIIIII?I???+
NMMMMMMMMMMMMMMMMMMMMNNNNO8OZ?===~:=+?ZDNNDOI+=~::::,,,,,,,,,,.....................,,,,:,:~==~~:=~~::~==?8=?$?Z7Z8DNO877I???+?+????I?IIIIIIIIIIIIIIIIIIIIIIII??+
NMMMMMMMMMMMMMMMMMMNNNNNND8O?=~:?~==78DD8DD$?+=:::::,,,,,,,,,........................,.,,,:~==~:~=~:::~~+7=+IZ$IO?O8MDZ$O7?==+++?+???IIIIIIIIIIIIIIIIIIIIIIII??$
MMMMMMMMMMMMMMMMMNNNNNNNDDO7=+=+:+?7+8O8N8$7==~::::::,,,,,,.,,..........................,,,:=~==~==~,,:~==Z+I$Z$$?O+$ODD$I$??=??++???I?IIIIIIIIIIIIIIIIIIIIII???
MMMMMMMMMMMMMMMNNNNNNDNND87++~+:~?=I$7DM8Z$I+=~::,,::,,,,,,.,,.,,.......................,,.,:====~=~:,,:~~$+?7ZZZZ7ODOZZO8Z7??+++=~+??IIIIIIIIIIIIIIIIIIIIIIII??
MMMMMMMMMMMMMNNNNDDDNND8$7+I~:=~=?7788ZOO$I?=~=~:::~:,,,,.,..,...........................,.,,:===+==:,,,,:~$=?OD$ZO7IODO8$I$$7===~~=++?IIIIIIIIIIIIIIIIII?IIII??
NMMMMMMMMMMMNNDDDDDDDD8DZII?,:,=?=7$Z$OO7I+?~~~::::::,,,,.,,,.............................,.,:~=~====:,,:,~I77ZD88Z7O+8Z$Z8OOZ7I=+I+??????IIIIIIIIIIIIIIIIIIII??
NMMMMMMMMNNNDDDDDDD88D8Z7I=:,::+???ZZ7ZO??===:~::::::::,,,,,,...,,,,,,,...................,,.,:=,~~=+~::,:~~7?7I8O8OI?I8ZZZOO8ZZ77+I?IIIIIIIIIIIIIIIIIIIIIIIIII?
NMMMMMMMNNNDDDD8D88N8OZZ7=:~,~?7+=ZII77I??+=~=:~::::::::,,.,,,..,,,,,,,,...................,.,:=:::~=+=:::::+I?IOZ8OOZ7?D7I$Z888Z?II?IIIIIIIIIIIIIII7II7IIIIIII?
NNMMMMMNNNNDDDDDDDD8DDO$~+=~=I?=I7+IIII??+?=~:=~::::::::,,,,,,,,,,,,,,,,....................,.,~::,:~=++::::~7=ZI8D8Z8$7IZ$7$ZZOZ7+?I??IIII7III7II7777IIIII7IIII
NNMNMMNNNDDDDDDDDDDD8Z+I7?~=++=I=I++77+I+?~=~=::~:::::::,,,,,.,,,,,,,,,,,....................,.,~:,,,:~=+=~~:~7$$$OD$O$Z77I=?ZZ7I$I++?II777777777777777IIIIIIII?
NMMMMMMNNNNNNNDDDDDDIZ7?+I=??I+==?==I+?+=+=~~::~~::~~::::,,,,.,,,,,,.,,.,....................,,,:,,,,,::~~:::,??D$ZO8DO$II?+?7+??I~=+??I77777777777777777777IIII
NMMMMMMNNNDNNDDDDNDO8D777++IZI?~=+:I~=+:+=~~=~~=~~:::::::,,,,,,,,,:,,,,,......................,,,,,...,.,:::::,??87$O8ND$Z77??+I?+====+?77777777777$77$$777777II
NMMMMMMMNNNNNNNDDNONNNI?=+$7+$=I:=I=+~:?=~==~+===~::::::::,,,,,,,,,,,,,,........................,.....,,,,,,:,:~?I8$DDZZ8ZZ$Z7?7?7I???7$$$$$$$$$7$7$$$7$$$777777
NMMMMMMMNNNNNNNNNDNMD$++$O$7$==,+~~+~~?+~:==+===~~~::::::,,,,,,,,,,,,.....................................,,,,,:~+IZOO88DOOOO$II+?I=I777$$$$$$$$$$$$$$$$$$$$$777
MMMMMMMMMMNNNNNNDNMO77?$ZZI77+++=:~::I=~~==+=+?==~~:::::::,,,,,,,,,,......................................,,,,,,::??I8OZOZ8ZZIO?$I==??I$$$$$$Z$$$$$$Z$$$$$$$$$$7
MMMMMMMMMMNNNNNDDNNOZ$$Z8?7Z?$I=:===I~:=+++??+===~~~:::::,,,,,,..,,,,.....................................,,,,,,,::??ZZ$$O$OZ$OZ?+??+=7I7$$ZZZZZZZZZZZ$$$$$Z$$$7
MMMMMMMMMMNNNNNN8ODDO?ZZ$$O7I==+?~==+:+=:?7I7?+=~~~~~::::,,,.,,..,.,.......................................,,,,,,,:~?7?$OZO$IZZO8$I?I??7ZZZZZZZ$Z$ZZZZ$$Z$$Z$Z$$
MMMMMMMMMMMMMMMNNMNO+IDI$O7O?++?+====:++?I7$7?+=~~::~::::,,,,......,,...,................................,.,,,,,,,,:+??I7$ZZ$7OZ$$I???II?$OZOZZZZZZZZZZZZ$$ZZZZ$
MMMMMMMMMMMMMNMNNDN7ZZZD8IIII$+:I=:~?~:$7O$7I+==~~~:~~::::,......,.,,,,,,.,,,,,..........,........,...,,,,::::::::::=III+77I$77?$ZI+?II77$Z$ZZZZZZ$$$$ZZZZZ$$$$$
MMMMMMMMMMMMNNNNMNMZDONZ$I?I+=?+~=~=777IZO??I+=~~:~~~::::,,.,.,,::::::::::~~~::,,,,,,...,,......,,,,,::~~~====~+~==~~?I7+7$77$77II$777$$ZZZZZZZZZZZ$$$$$$ZZZZZZ$
MMMMMMMMMMMNNNMNNNNI$ZZZI?+?=7?~+=7O7?$O$I7$I=~~~:~~~=~~:::::~==+==++???I?+++=+==:,,.,..,,,..,,,,,:~~=?7$77II?7ZZZ$77I$OII7I7$IZ$?I=I??77$Z$$ZZ$$$$$$Z$$$$$$$ZZZ
MMMMMMMMMMNNNNNNNNN7OZ8II+I+7=?$:$I7I$8D7$ZI?+:~::::~~~~==~~=~===+?II$Z$7$I??+==~~:,,,,,,,,,.,,,::~=+?IZZZZ$II?+=?7$$II777?$8$7IZO$?I+?77$$$$$$$$$$$$$$$$$$$$ZZZ
NMMMMMMNMMMNNNNNNND78ZI7++=+?I?+Z+$Z$ZDIZ8??+=~~::,:~~==+?+==++==~~~~~~==+??++++~~:~~::,,,,.,::~~=+??I=+==~~::::~=??$7?OOO$7ZODO7IZ$77I$$$$$7$7$$$$$7$$$$$$$$$ZZ
MMMMMMMMNNNNNNNDNDZO$7$=+I++$??$ZOZDOND7O$II+~~~:,,:~~=+III+=~~~:::,,,,,,::~~~====~~~::,.,,.,~~~++==:~,,~:::::~::~??I+=?Z?Z$?ZZO8$I77I??I$77$7777$$777777777$$$7
MMMMMNMMNNNNNNDDDN+O7==I=+7III7ZNO888DOZ$ZII=~~~::::~~=++??+=~::,,:,,,::::::::~~~~==~~:,,.,.,:~=~~,,,::~=~=+?II?==+++==OZZ?$Z?$ZO$$7I$I?III7777777777777777777$$
NNNNNNNNNNNNNNNNN7=I$I?I???$+ZZDZ8ONN8N$8OZI+~~::::,~===+++=~~~~=I7I?I$OO887?=~~~~=~~~:,..,..:~=~:,:~=+=.:78NO8Z8Z?+~=~?87IO+7Z77OD$?I+++++?IIIIIIIIIII7777777$7
NNNNNNNNNNNNNNNOO7O$?II+?77?$O88DDD88O87DO$I=~~:,,,::~~~===~~+Z$7I~,,,?~D77?$~=~===~~:,,.....,:~~~:=+:,.,,7ZZZ$7II?+~::+$$78$ZZZ$7OZ7I?~==++??I?I?IIIIIII7777777
NNNNNNNNNNNNNNDDDZ??$+?I8Z$OZODDND8DNN?8IO??=:=::::,,::~~=+??+?+~=~~:.~+I++++++,:~:~~:,,.....,,:::~,:::::~~,,::~~=~~:~~~OZDDD888OO$II??=++===?????????IIII777777
DDNNDNNNNNNDNNNNO$=7?II78Z$8DDON$DN8NO887$7+~~:::::,,,,,:~=+=~=:::,,,,,,:::::,:,,,::::,,......,,:::,:::,,,,,,,,~:~:,,::~ZOZDN8DD8DOI++++?+++++++++?+????III77777
DDDDDDDNDDDNNMZ8D7$7++$87ZOMD?~OO?I7ODD=N7$?~~::::,,,,,,,:~::::::,,,,.,,:::,,,,,,,,:,,:,.......,:,,,,,,,,,,,:,:,,::,,,:~OD$ODDNMNNZ?==~========+++++++??II7777$$
888DDDDDDD8ND$DNN8?+I?$ZODDN7O+?~==7DDZ78O$+=~~~~:,:,,,,,,::,,,:::::,,,,::::,,,,,,,:,::,........::,,.,,,,,,,,,,,,,,,,,::8DZO88DDND7+=~===========+++++???I777$77
888DD8DDDDDDDDDDNDZ++$O8O88D7ZI~:~~=$DON8Z$I+~~~:::,,,,,..,,:,,..,,,,,,,,,,,,,,,,,:,,::,........,::,,.,,,..,,,,,,,,,,,::ODZOOZD8O7?=~=~~~==~=====+++????II777$$$
8DD88888DDDDNNNMND87I$8O$OI8?8?:,::~$7IM$Z77++~~~~:,,,....,,,,,,.,......,,,.,,,.,:::::::,,.....,,~:,,,,,.,,....,,,,,,::~O8Z$7I$ZI+=~~~~~~~~~====++?????II77$$$ZZ
88D88OO88DDDNNNNNDN7$$8Z7Z?Z7D=,,,,=$?IZ8$ZZ7++==~:,,,,,.....,,,......,,..,,,,,,,:::,::::,,.....,~~:,,,,.......,,,,,,:::ZO$$7+Z7+=~~~~~~~~~~~===++??I?I7777$$ZZZ
8888OOOOO88DDDDNNDN8IZ$OI$II7D=...,:+?~IZ$NO$7++=~~:,,,,,.................,,,,,,:~:::,:::,,,...,,~~:,,,,........,,,,,,:=$Z7I+?+===~~~~~~~~~~===+++??II77$$$ZZOOO
88D8OO8888D8DDDNNDDDOOZO7ZI7IZ7,,,,,=+:+7Z$NZI?++~~:,,,,,,,....,..........,,,,,,,:::::~::,,,,,.,:~~~,,,,,...,..,,,,,:::~$7????==~~~~~~~~~~~~===++?III77$$ZZOOOOO
888888OO8888DDDNNNNNNNNDOZII7?M~,,:~~==:+$ZOD7??+=~~:::,,,,,.,,,..........,,,,,,,,::::~::,,,,..,,::~,,,,,...,..,,,,,::~+Z?+++==~~~~~~~~~~=====++??II77$$O888DDD8
8O88D888888888NNNNNNNMNN8OO77?ZD:,,:::=~,?78O7I??==~::,,,,,,,,,..............,,,,:,~~~~:,,,,,...,,:::,,,,....,.,,,,,::=I7++++==~~~~~~~~==~==+++??II7$$O88DDDNNNN
O8888888D888DDDNNNNNNNMNNN8$I?7DZ~~::,,:::?I7I++++=~~:::,,,,,,,.............,,,,::~~~=~,,,,,,,..,,:::,,,,,,.,.,.,,,:::=?I++++=====~~~===+++++??II7$$ZO8DDNNMMMMN
88888DDDD8DDDDDNNNNNMMNNNMOO7IIDM~~~~,,,~:+I?I++?++=~:::,,,,,,,....,.,,...,,,,::~~~~::~:,,,..,,,,,,:::,,,,,,,,,,,::::~==I+?+++=========++++??II77$$ZO8DNMMMMMMMM
888DDDDDDDDDDNNNNNNNNMNNNMD8$?IZM?::::,,:~=????++++===~::,,,,,,,...,..,,.,,,,:~~=~::::~::,,,,,,,,,,::~::::,,,,,,,::::~==??++++=======+++???III77$ZO88DNMMMMMMMMM
DDNDDDDDDDNDDNNNNNNNMNNNMNNO$7$7NN~,,,,,,:~I????+++===~~~:::,,,,,,,,,,,,,,,::::~=:::::::,,,,,,,,,,,:~::~~:::,,,,,:::~~=+??++++++++++++??III7$$ZZO8DNNMMMMMMMMMMM
DNNDDDDDNDDNDNNNNNNNNNMMMMNZZ$Z$NM+::,,,,,:I????+++==~~~~:::,:,,,,,,,,,,,::::::,=~:::::::::,...,,,:~=::~=~~:::::,:~:~==I++?+??+++++???III777ZZO8DNNMMMMMMMMMMMMM
NNNDDDDNDDNDDNNNNNNNNNMNNMD8OZ87ZNM+::,,:,,=7?II?++===~~~~::::::,,,::,::~~::,,,,,++==~===~~:,,,,,,~=~:::~~=~~:::::~~~=++?+??+???????III7$$$Z8DDNNMMMMMMMMMMMMMMM
NNNNNNNNNNNNNNNMMMNNMNMMNNOO8D$IZMNN?~,:,,,:$II7??+==~~~~=~:::::,::::::~~:,,,,,,::==+?I77+==~:::::=~~::::~~++~~:::~~==++II????????IIII7$$ZO8DNNMMMMMMMMMMMMMMMMM
NNNMMNNNNNNNNMMMMMMNNNNMMNNNM$DZ8MMMNN$+=~=8D$77??+++~~=~~~~~~::::::~==~:,,,,:::::~~=+?+++$7+++++++=~~~~=~~=+I+~~~~~==?II?I?IIIIIII77$$ZO8DNMMMMMMMMMMMMMMMMMMMM
NNMMMNNMMNNNNMMNNNNNMMMMNNNMNOM$8DNMNMMNNNNNNO$7I??++=~=~~~~~~::~~~===~:,,,,,::,:::~~===+=?=?I??I+==~~~~~~~~++?=~~~~==?II?II?IIIIII7$ZZ88DNNMMMMMMMMMMMMMMMMMMMM
NMMMMMMMNMNNNNMMMMMMMMMMMMMMMNNODDDNMMMNMMMMMDO$II??+=~~~~~~::::::~==~~:::::::::::~~~===~=+++=+++++==~~=~~~~+==::::~==?I7?II??I7777$$ZO8NNMMMMMMMMMMMMMMMMMMMMMM
NMMMMMMMMMMMMMMMMMMMMMMMMMMMMN8ZZODNDMODMMMMMMOZ$I??+=~~~~~~~:::~~===~~::::~~:~:::~~~~~==++++++=+=~=~~~=====~::::::~==?III7777I77$$ZOO8NNMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMNMNNZ$Z8NDMZNMMMMMM8O$7+?+==~~~~:::::~====~~:~~~~~~~~~::~:~~===+=~==~==~~~~~~++~~:::,,::~+=?II77I77$7$$ZO8DDNMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMDD7IOZ8DD8NNMMMMMZZO$7?+==~~~:::::::~~~==+==~~~~~~:::,:::::~~~~~~~:~~==~=??=:~:,,,,,::==IIII7777$$$ZZ88DDNMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMDZ$8O8ONZDNDMNMMMZ$OZ7II==~~~~~:::,,:::~=+++==~~=~:~::::~:::::~:::~??II77+=~~::,,,:::~=?O7II7$Z$ZZOO88DNNMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNDNMMNDMDNDMMMMD7ZOO77+==~~~~::::,:::~===I7II77777III?+?+???I?I$$77I?+=~~~:::,:,::~=+ONZ77$ZZZZOO8DDNNMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNNNNDMOMNNNNNNMN$7$O$$I+=~~~~:::,:,:::~~====?IIIIIIIIIIII777II??++=++=~~~~~~:::::~=++NNOZI$OOO888DDNNMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMN88$DMN8NMD8DDNMMZI77OZ$I+=~~~~::,::::::~::::~~~~==+~~~~~~~~~~~~~~===~==~~~~::~:~===+8NND8ZZ8DDDDNNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNO88NMDMNDD8DNMMD?I77ZZ$?===~~~::~::::::::::~~~~~~~~~~::::~~:~=~~~~===~~~~~:~~~==++$MMNN8$ODDDDNNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNN8ON8DN8NNODNMMMIIIII8Z7+===~~~::::::::::::::~===~~~~~~~~~~~==+?+=~==~~~~~~~~=+++INMMNDDZ8NNNNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMND8888DNDNDDNMMM77I?I$OZ$++===~=~:::::~::::::~:~~~=~~=++??+??+++====~~~~~~~~=+??7MNMMMMD8NMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNND$8$88NMNNNMMMZ7I??I7OZ$?+++=+~~~:~::::::::~~~~=~===+===+++++===+~~~~~=~~=++?I8NNMMMMMNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
NMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNO8OZNNMMNMMMMMD7I?III7ZZI??++====~::::,,:~:~::~~==+++=+++++++=+=~~~~~:~~==??I?ODNMM8Z8MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
NMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNM8ODNMMNMMMMMMZ7I?I?7$Z$I???++==~~:::::,:::::~~~~=+=+==++==~~=~~:~:::~~=+??I:$8DMNOZOZMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
NMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM8ZDNMMMMMMMMMD$I??II77ZZ7??++==~~~~:,,:,:,,,,:::,:,,,:,::::::::::::~~=+?I?::IODND888O$ONMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
NMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMND8O8NMMMMMMNNMN$7I?I?I7$$Z7I?++==~~~~:,::,,,,,,,:,,,,,,,,::::::::::~~~+II+~,,IO8D8DD8ZZ$$8MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNNNMMNMMNNMN87I??II77$Z$$I?I?++==~::,:,,,,,,,,,,,,,,,,,::::::::~:==?I+=,,:7O8DDDD8Z$$$7OMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNMMMMMNMN8$I?III?777$$$7II?++==~~::::,,,,,,,,,,,:::::::::~~~~~+?I=~,.,:$Z8NNNDOZZZ$$$7NMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNNDDDNNDDI7OIIIIIII7777$$$7I7I?==~::::::~::::::::~~:::~:~~~~==+?I==.,,,=ZODNDD8Z$Z$$$777$DMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNNNDNDDNDZ:,Z7I?IIIIIII7I77$7$7II+==~~~~~~:~~~~~~~~~~:~~~~=++++I~~~....,7O8NNNN8Z$$$$$$$7III?I??$DMMMMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNNDDD8DDDDD8$,:?7I?IIII?II77II77$$$$I?==+=====~~~~~~~====~=++?+??+:~~,,.,.,ZONNNN8ZZ$ZOZ$$77II7777IIII7DMMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNNDDDD88888888$,,:I????II????IIIII77777$7???+++++++++++=++++??III=:~=,...,,.?O8NNNDOZZZZZOZ$$7777$$$$77777II7$Z8DNMMMMMNMNNMMM
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNDDD8OO8OOOOOOZ~,,=????????????IIIIIII7777$IIIII7I??II??IIII7?=:~~~:.....,,:7ODNNNDOZ$$ZZZZ$$$777ZZZ$$$$777777II7I?I$ZODDDDDD8
NMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNNNDD88OOZZ$$$$$$Z?,.,I++++?+?++???????????II777I77777II?I??++=~~~~~~,......,,IO8NMNNOOZ$ZZZZZ$$$777ZOOZZZ$777777$7777II?????????
MMMMMMMMMMMMMMMMMMMNMMMMMMMMMNNNNDD8OZZZ$$$77777$Z:,,+?==++?++++?+++??++++??????+==++==++=~~~:~~~=,.......,,+ZONNNNDOZZ$ZZZZZ$$$$$7O8OOZZZ$$$77$Z$777I77IIIII???
MMMMMMMMMMMMMMMMMMNNNMMMMNNNNNNND88OOZZ$$7777I7778=,..~+===+++++=+++++++++++++==~~===~=~~~~~~~~~:........,,~$O8NNND8OZ$O$OZZ$$Z$$77$88OOZZ$7$$$$Z$$$$777777IIIII
MMMMMMMMMMMMMMMMMNNNMNNNNNNNNNNND88OOZ$77777IIII$D?:,,..~====+++++++++++===~=~~~~~~=~~:~~~~:~~:.........,,:$O8DNND8OZZZZZZZZZZZ$$$77OOOO88OO$$$$ZOZZ$$$$777IIII?
MMMMMMMNMMMMMMMNNNNNNNNNNNNNNNNND8OOOZZ7777IIII7ON7~:,...,~~=~==+==++++++=====~~~~~~~~=~~~~~:..........,,,7ZO8DDD8OZ$ZZZZZZZZZ$$$77$OOOO8OOOO$$$$OZZZ$$$$777$77I
MMMMMMMMMMMMMMMNNNNNNNNNNNNNNNNND8OOOZ$777IIII7ZND8=:,,....,:~=~=====++====~==~~~~~~~~~~~:,...........,,,~OODDN88OZZZZ$$Z$$Z$$Z$$$$$ZOOOO8OZZOZ$ZZOOZ$$$$777$77I
MMMMMMMMMMMMMMNNNNNNNNNNNNNNNNNNND88OZZ$$$777$Z8NDD?:,....,...:~~~~=======+====~~~~~=~:,.............,,,:$8ODND8OOZZZ$ZZZZZ$$$$$$$77ZOOO888OOOZ$ZZ$ZZO$$$$777777
NMMMMMMMMMNNMMNNNNNNNNNNNNNNNNNNNDD8OOZ77II7$ZZDMNDZ=:,..........,:~~~~~=~~~=~~~~~~::................,,,7OO8D88OZZZZ$7$$$$$$$$$$$777ZZZOZOOOOOZZZZZZOZ$ZZ$$7$$7I
NMMMMMMMMMNNNMNNNNNMNNNNNNNNNNNNNNND8O7I77$OZ$ONMNDO?~,............,::~~~=====~~~:,.................,,.?ZO8D88OZZZ$Z$7$$$$$$$7$$7777Z$ZOOOOOOOZZZZZZZZZZZZ$$$$$$
NNMMMMMMMMMMMMNNMMMMNNMNNNNNNNNNNNN8$II7$ZOOZZODNNN87~:,...............,~=====~,...................,.,=OOO888ZZZZ$Z$$$$$$$7$$7$$$777Z$ZOZZOOZOZOOOZZZZZ$Z$$$$$77
NMMMMMMMMMMMMMMMMNNMMMNNNNNNNNNNN$III$ZOOO8ZZO888DND8=~:,...............,,,,,,,,.....................=OOZOO8OOOZZZ$Z$$$$$$$$$7$$$$77Z$$$$ZZZOOZZOOZZZZZZZZZZ$$$7
MMMMMMMMMMMMMMMMMMNMNMNNNMMMNNNOI?I7$ZZO888ZO88888ND8?=:,,.............,::,,,::+:...................,ZOZOOZOOZO$$O$Z$$$$$$Z$7$$$$$77$$$Z$$ZZ$OZOOOZZZZZZOZZ$$Z$$
MMMMMMMMMMMMMMMMMMMMMMMMMMMMN$?II$ZZO888D8ZZO88888NN8$=~:.............I8DNNNNNNMM$,.................=OOOZOZZ$ZZZ$$$$$$$$Z$$$$Z$$$$$7ZZZZZZZOZOZOZOOOOZZZZZZ$$$$$
MMMMMMMMMMMMMMMMMMMMMMMMMMN87?77$OO888DDDO$ZO8O888DNDO?~~:..........,I7Z8DD88NNNMN~................:$OOOOZZZ$$ZZ$$$$$7$$Z$$Z$Z$Z$$$7$$$$ZOZOOZOOOOZOZOZZZZZ$$$77
NMMMMMMMMMMMNMMMMMMMMMMMNZ??I$Z$$OO88D8D8ZZOOOOO8DDNN8$+::,........,OOOO88888OZOO87+.,...........,.IZOOZOZZZZZ$$$$$7Z$$Z$ZZZZZ$$$$$$$ZZZZOOOZOOOZZOOOZ$ZZZZ$$7$$
NMMMMNMNMNMNNMMMMMMMMMN8I?II$$ZZZ888D8D8ZZOOOO88DDDMN8O?::,,.....,.ODNNDD8O$$$7??7$7~.............=ZOOOOZOZZZZZ$$ZZZZ$$$$ZZZ$$$$$$$$$Z$OOOOOZOOO$ZZZZZZZZZ$$Z$$$
NNMMNNNNMNNNNNNMMNNZI??I77$ZZ88O88DDD8DZZZOO88O8DDNMN88O+~:,......,MNNNNDD88O7:=~?I8D:...........:ZOZOOZZZOOZZ$$$$$$$$$$$ZZ$$$$$7$$$$Z$ZOOOOOOOOOZ$ZZZZZZZZZ$Z$$
NNNNNNNMNNNNNNND$I???II7$ZZZOOO8888OO8O$ZZZO8888DNNNMOO8I~::,....,=MMMNNND8Z$$I~==7I8O..........,IOO8OZZZZ$ZZZ$$$$$Z$$$$$$$$$$$$7$$$$ZZZZZZOOOZZZZZZZ$$ZZZ$ZZ$$7
NNMNNMMMNNNNDZ??++?II77$ZOOOOOO8O8OOO8OZO$OZO8DDDDDNNOZ8O=::,,...,8MMMNND88Z7III778D8.+.......,.~ZOOZOZZO$ZZ$ZZ7$$$7$7$$$$$$$$$$$$$$$8$ZZOOOOOOOZOZZOZZ$ZZZ$$$$7
NNNMNNMMNZ7??????I7$$$ZOOOOO888888OZ8OZ$OZOO8DDDD8DD8OZO87:::,,..=MMMMMND8ZZIII77ZMD...,........7$ZOOZOZZZ$$$$$$$$$$777$$$7$$Z$$$7ONDZ$ZZ$ZOO888OZZZ$ZZOZZZ$$7$7
NNNNMDD$I??????II77ZZZZOOOOO8888OOOO8ZOZOO888888D8NOOOZZOO,::,,..7MMMMMMD8Z7II77$DM~.,.~.......,ZZZOZZZZZZ$$Z$$ZZ$77777$$$$$$$$$7ODOZZ$$$$OO8OOOOZZ$ZZZOOZZ$$$$7
NDZI++?+?????I777Z$ZZOOOOO888OOO8OZOOZOOOOOOOO8DNNN8OOOZ$O=,,,,.,,ZMMMMND8OIII77ZNO.....~......?OOZOZZ$$$$$$$7$$$$$$7$777777$$7ON8ZZ$7$$$OZOOOO$ZZ$ZZ$OZOZ$$$$$7
I+++++??IIIII77$Z$$ZO8O888888OOOO$ZDZOOOOOOOOODDNN8888OOO$7,,,,.,:=DMMNMD8$7?I77OM=.....,:....~Z$ZOZOZZ$$$$$7Z$Z$$$$$$$77$$$77NDZZ$$$77$$ZOOOOZZ$$$Z$OZOZZZ$$777
++???I??II7777$Z$ZOO888888O88OOOOZ8OZOOZZZOZODDNMD8OOO8Z$Z$I,,,.,,:?=NMMNO$I?I7$MM........:..,$$ZZZZZZZ$ZZZZ$$Z$$$$$ZZ$$$$7$DNOZZZZ$$$$ZZOOOOOZ$$$$$ZZZZZZZ$$777
+????I?I777Z$$ZZOZOOOO88DOOOOOOOOO8ZOOZ$ZOOO8NNNDOOOO8OOOZZ$:,,.,,,:ZNMMN8$??778MN.........:.=Z$ZZZZZ$ZZ$Z$$$$$$$$$$$Z$$7$8MDZ$ZZZZZ$$$ZZOOOOZ$Z$$ZZZZ$$$$$$777+
??III777$$$ZZZZOOOO888888888OOOOO8DOOOOZZOZ8DDNNZOOOOOOOOZ$$?.,.,,,:=OMMND$??77NM8.........::ZZOZ$Z7ZZ$$$Z$$$$$$77$$Z7$7ZMMDZZ$ZZZ$Z$$ZOOO8OZ$$$$ZZZZ$$$$Z$$7$7?
II777$ZZZZZZOOOOO888D888888OO8OOOD8888OOOO8DDND8ZZOOOOO88OZZ$,......,$OMN87??7ZMMI.........:IZZZZ$$ZZZ$$$$$$$$$$$$$$$$$7ZD8Z$Z$ZZZZZZZZOOOZZZZZ$$$$Z$ZZ$Z$$7777+
7777$ZZ$$ZZOOO8OO888D888O8OOO8OOOD8888D8D8NNNNOZZ$O88OO88OZ$Z:.,....,+$MN8III$DMM+.........:ZZZZOZZZZZZ$$$$$$$$$$$$Z$$$$$$$$ZZOOOZOZOOOOOOZ$$$$$$$ZOZZO$Z$$77$7+
7$$ZOOZZOOZOO888888DD888888OO8OOODOO88DNNNND8$ZZZOOOOOO8OZZ$O:.,,...,?OD87?++ZDMMI........:=Z$ZZ$$ZZZ$$$$$$$$$$$$$$Z$$$$$$7$ZZZZZZOOOOOOOOZZ$7$$7$$ZZ$ZZ$$$$III+
7$$OOOOOOOOO8O88888D888888888OOOZNND888DNDD8Z$Z$ZZZZO8OOOOZ$Z?.,....:=DNM$I?+7O8N$........,7$$$$$$$$Z$$$Z$$$$$$$$$$$Z$$$$$7777$$$ZZ$ZZZZZZ$$777$$$$$$$$$$$$IIII=
ZZOOOO8O8OO888DD888D88888OZOOOOO88MMMDDDND87$7$$OZZOOOOZOOOZ$O:,,...,=?MN$III?ODNNI......,+Z$$$$$$$$$$Z$$$$$$77$$$$Z$$777$7Z$777ZZOZOZOZZZ$$77$7$$$$7$$$$$$IIII+
ZO8O8888O888D8DD888888888OOOOOOOO8DMMMN88DZ777IZZZZOOZZOOOZ$$Z=......~+MNOII7+ONNN8I.....:$$$$$$$$$7$$$Z$$7$7777777$7777$777$77II7OOZO8ZZZZ$77$7$$7$Z$$$$77IIII=
NNNNMMMMMMMMMMMMNNNNNNNNDNNNNNDDDDDDDDDNDD$IO888DD7+7I?7I+=+7I7ZI7I+?+~:===+=:~I=~==I?+~:=+?==~~=~~==~~~====~~~:::::::::::::::,,,,,,,,,,,,,,,,,,,,,::,,,,,,,,,,,