^^^```````````````..........................................`........```.............```````....````````^':''^```````````````.````````````````````````````````````^````````^`^`^^`^'^^^^^^^^'^^^^^:':''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^''''^^''''''
`````````````.````....................................................`...............``........````````^''''^``````````.`````````````````````````^````````````````````````````^`^^:^^^^^^^^^^^^^'^':'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^'''':':
``^^``````````````.```....`.........................`....`....`......```...``....`......`````.`````````^'::''^````````````````````````````````````.```.`````^^^^^`^```^^````^^^^^`^'^^^^^^'^^^^^^^~':'''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^''''^''::
^^^^``````````````.``.....```...............................`.......````.`.``..```.`......```.`````````^':''^^````.``````````````````````````:;TwZZOED4DE2I^```^^`^`^``^``^^`^`^^^^:^^^^^^^^^^^^^''''''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'''''''':
`````````````.````````.....................................```.......``````.........````..`````````````^^''^^```````````````````````````^"LCV2ZOGEDDDD44DDDBD4Z:````````^``````^`^^''^^^^^^^^^^^^^^'''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^''^^'''
^^^````````````````````............````....`....``.``..``````.``...`````.``````..`.````````````````````^^::'^^```````````````````````:=LtVPD444BBBBBBBBBBBBB4DBBBt.`^^`^````^^^^^`^'^^^^^^^^^^^^^':':'^^^^^'^^^'^^^^^^^^^^^^^^^^^^^^^''^^^^^^^^^^^^^^^^^'^^^''''
`````````````.````....``.``...........``````..................````.``````````.``````````.````````^`````^'::''^`````.`````````````^^_=)2O44B4BD4BB4BBBBBBBBBBWWBBB4BZ^`^`^`^```^^^^^'^^^^^^^^^^^^^^^''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'''''
`````````````.``````````.``.............```...................````.``````````.``````````.````````^``````':'''^```````````````````_=ctPD4B44D4B44BBBWWWWWBWNWBBBWBB44C```^^^`````^^^'^^^^^'''^^^^^^^^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^''^'
^^^```````````````````````........`...........````.``````````.``````````.````````````````````````^^```^^^::''^`````````````````_=)ZZ4BBED444BBBBWBBWWNNNNNWWWWWWWWB4DC``^^^`````^^^'^^^^^^^'^^^^^:~:'^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^^^^^'^^'^''
`````````````.``````````.`....................``````````.`````````.``````````.``````````.````````^`````^':'^^^```````````````:;)2OB4EGD4B4BBBBBBBBWWWWNNWNNWWWWWBBBBBBDC;`^^```^^^^^^^^^^^^^^^^^^^^''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^''''
^^^^``````````````.``````````.`````...``.````````````````````.````````````````````````````````````^```^^^'::'^`````````````~IcVPGDOE4DD4BBBBBWWWWWWWWWNNNWNNNNWBWNWWWBWBBt^`^^^^^^^:^^^^^^^^^^^^^'''''^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^^^^^''^^^^^^^^^^^^^^''
^^^^``````````````....```````.`````..```.````````````````````````````````````````````````````````^^```^^'::''^``````````^^:+TwwOGGD4D44WBBBBBBBWWWWWNN%%%%%NNWNWWNWNNWNWNBL^^^^^^^^:'^^^^^^^^^^^^^''''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'''''^''
``````````````````.......................```........````.````````````````````.``````````.````````^`````^::':'^``````````^_=LVwOE4DDGEBBWBBBBBBBNWBBBWWNNWNNNN%NNNNWWNWNWWB4C`^`^^^''^^^^^^^^^^^^^^^'^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'
^`^```````````````.```.....``.`.....````.````````````````````````````````````````````````````````^````^'~~::'^`````````:=TtVGD4BEGODNWWBWWBWBBBBBBBB44BBWWNWWWWWNNNBBNNNWWWB)^^^^^'''^^^^^^^^^^^^':''^^'^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^^^^^^'^^'^^^^^^''^^^^^^'
^````````````.``````````.``............`````````````````.````````````````````````````````````````^````^^':~:'^````````~=)VZ44BDDOEWWWBWWWBBBDEOPZZZwZZZPPG4BBBB4DBBBWNNWWWBW4T'^^^'''^^^^^^^''^^^^^:^'^^^^^^`^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^''^^^^^
^`````````````````.``````````.``````````.````````````````````````````````````````````````````````^````^^':::'^```````:=VZGBBBE4G4NWWWWWB4DGZ2wVCTLLtVV2w2ZOEDEOE4WNNNNWNBNBBBBc`^^^'^^^^^^^^^^^^^''''^^^^^^^^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^'^^''
^^^```````````````.``````````.```````````````````````````````````````````````````````````````````^````^:~:::'^``````'1CZD4BB4BG4NWBBBBWBDZwtLLTc))TLtVV2PPPOOPODBWNNNNWWBWBBBBZ^^'':''^^^^^^^^^^^^'''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'''''^^^^^''
^^``````````````````````.`````````.``````````.``````````.````````````````````````````````````````^````^'':'''^`````^+LwDDBBBGG4WWBDGPZZD4PT)==c==cc))TLC2wPOPPODBNWWWBWBWWWBWBBc^^''^^^^^^^^^^`^^^^'^^^^^^`^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^'^^
``^```````````````.```````````````````````````````.```````````````````````````````````````````````````':'~:::^``^`^+TPEBBBBEED4BBGDBZVV22Zt)c======cc)))TtwwPOG4WWNNWWWWWNWBWWBO_'''^^^^^^^^^^^^'^^''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^'
`````````````.``````````.`````````.``````````.``..```````````````````````````````````````````````^````^'~:''^^^``:I)wDBBD4OGGwwwZPNBWOttVCTc=========cc))TCVwOGBWBWNWWWWNWNBNWWBT^''^^^^^^^'^^^^^^^''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^'^
`````````````.``````````.````````````````````.``..```````````````````````````````````````````````^````'^:::':^```"=tO4BDEGPEw2Vtt2DWWDVttL)c===ccc==c))))LLt2wO4NNBNNNNN%NWWNWNWt'''^^^^^^^^^^^^^^^''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^'^^^^'
^`^```````````````.````````````````````````````.``.``````````````````````````````````````````````^^```^':~::::`^~TCG4B4P22POtLLTLCV22PtVC))c=ccTttT))c)cTTLLtwGBNNWNNNNNWNNW%%NND_^'^^^^'^^^^^`^^^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^''
`````````````.``````````.`````````.``````````.``..```````````````````````````````````````````````^````^^::::'^`')TPD4BPC)VOtLTc)c)))TLCLTc===))TtZODOtT))TTCVPEWNNWNNNNNNNNWNNNWB+^'^^^^^^^^^^^^^^^^^^^^^^^^`^^^^^^^^`^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^^^''^'
^`^`````````````````````````````````````...```````.``````````````````````````````````````````````^^```^^~~:::^^I)w44BOt)LtwCT))))))TTT))c==cTLLLCtVVG4EVtTLLVP4NNNNN%N%NNNNWN%NNBT~'^^^^^^^^^'^^^^:^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^^^^^^^^^^^^^''
`^^`````````````````````````````````````...```````.``````````````````````````````````````````````^^```^''~~:'':t)GDBBV)TLVVT)c)))T))LT)c==c)LtCCCtttCtGE2tLC2PBN%%%%%NN%NNNNN%NNWC~'^^^^^^^^`^^^^^^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^'^^^'^^^
`^^``````````.``````````.`````````.``````...`.```````````````````````````````````````````````````^````^'~~:^'^)cVEDBw)c)ctLT))ccLLLLT)ccccc)TVGOPw2CLTLCwPCt2P4N%%NN%%NN%NNNNNNWBt1'^^^^^^^^^^^^^^^^^^^^^^^^^^^^`^^`^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^^^^^'^
`^^`````````````````````````````````````.`````````.``````````````````````````````````````````````^^```:'~_:~~_t)ZDBDLcc))tT)))TL))))ccc)))ccLtwPW4BZVLLTTV22ZPB%%%N%%%NNN%NN%%NWBTc'^^^^^^^^^^^^^^^^''^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^'^^''^^^
`````````````.``````````.`````````.``````````.```````````````````````````````````````````````````^````^'~~::_c=TG4B2c=ccTT)))TLT2====cc)))c=cLCVBWEPPtLLLC2wPEB%%%W%N%WN%%%N%NNWB)I^^^^^^^^`^^^^^^^^^^^^^`^`^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^
^^^```````````````.```````````````````````````````.```````````````````````````````````````````````````^^:~::;=T2GWP)==c)T)))))LCC)T))))TT)ccc)TTLtZPDwCtttwPE4W%%%%%%%N%N%NN%%WWBTI'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^'^^^
^`^^````````````````````````````````````.```````.`.``````````````````````````````````````````````^^`^`^':~:_+cC24Btc=cc))))))))TTLLVt))LL)c=cc))TTLV22ttt2wPDB%%%%%N%%N%%%%NN%WWB)":'^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^':''
`^``````````````````````.````````````````````.``..```````````````````````````````````````````````^``^`^'__~~1L2wWET==ccTLLTLLLTTTT)LZTTLT)c=c=ccc)))TLLLtVwGB%%%%NN%%NWN%NN%NWBBD)~'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^`^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^'
^^^`^```````````````````````````````````.`````````.`````````````````````````````````````````````^^^^^`^:____ctZDWZ==c))CPP2VtVtCCTTTtVCTT)cccccccc)))TTL2wGB%%%%%NN%%NNNNNW%NNWBVc:'^^^^^^^^^^^^^^^^'^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^'^'^:':
^^````````````````````````````````.``````````.```````````````````````````````````````````````````^^```^'_~::c2OBWw==ccc)VtwEVwtVtL))ccc))))))c)))))))TC2wOB%%%%N%%%%%WNN%NW%WBWET;''^`'^``^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^:'''
^^`^``````````````````````````````.``````````.```````````````````````````````````````````````````^````^:~:'~)ZEWWw==cc))Ltt2EBZ22C))c))))))))))c))TTTCVZPDN%%%%%N%%%NWNN%NN%WBBL1"'^^`^^^^^^^^^^^^^^^^^^^^^^`^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'''^^^^''^'
^^^^^^^^````````````````````````````````.```````````````````````````````````````````````````````^^^^^^:~___"cGBWNOI=))))TCttCVGBGwtTT)))T)T)))T)TTTLtwO4W%@%%%%%%%%%NN%N%N%NBBG_=~^^'^^^''^^^^''^^''^^^^^^^''^^^^'^^^'^^^^^^^^'^^^'^^^^'^^^^^^^^^^^''::^:'^^'^''
`^``````^`````````````````````````.``````````.```````````````````````````````````````````````````^````^'__~_IEDBWB+1=c))TTVVttCtVZOVT))TTTTT)))TLLtVZG4NN%%%%%%%@%%%NN%N%WNBBOc'=':^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^^^'^^^^^^^^^^^^^^^^^^'^^^^''^^^'^^^
^^^^`^``````````````````````````````````````````````````````````````````````````````````````````^^^^^'^:__~~;PGB4NP1=cc)TTCtVVVV2ww2LTTTTTTLLLCCCVwODBN%@%%%%%%%@%%%N%%NWBB4O)::"^^^^^^^^^^^^^^^^^'^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^^^^^^^^'^^'
^^^^^^^^^^``````````````````````````````````````````````````````````````````````````````````````^^^^^^':__~~_PO4DWWc=c))TTTLCtVVVtCCLT))TTTLCCtV2PODBBNN%%%%@%@%%%%%N%%NBB4Dt:'_^^':^^^^^^^^^^^^^^^^^^^'^^^^^^^^^^^^'''^^^^'^^^^^^^^^^^^^^^^'^'^^^^^^^^^^^^^^^':
^^^^````^`````````````````````````.``````````.`````````````````````````````````````````````````````^^^':~_'::TwEOBBB=c)))TTTTTLCtCLCT)TTLLLCttVZOE4BBDBNN%%%%%%%%%%%NNNBB4GZL^:~^^''^^^^^^^^^^`^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'
^^^^````````````````````````````````````.```````````````````````````````````````````````````````^^^`^^'~~_:::+wEPDBNWT)TLTTTT)TLLLCCCCttCtt2wPOED4B%#@%@@%%@%%@@%N%N%NWBDEPw=^"'^^^:^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^''^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^'^^^'^^^
``````````````````````````````````.``````````.```````````````````````````````````````````````````^`^^^^:__'::+VPOE4WWB2TTTTTTLLCtttVVVwwwZPOEEDBB@M@#@@%%%@@%@%%N%WWNNWEDZw2)'^``^~^`^^^`^^^^^^^^^^^^^^^^`^^^^'^^^^^^^`^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^`^^``````````````````````````````````````````````````````````````````````````````````````````^^``^^':__~:"1I2PE4WW4GGPVttVV2wwwwwZPPOOGDDBBW%@####@@%%%@@%@%%NNNN%WBEPGPw"^'^^^'^`^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^''^^^^^^^^^
^^^^^^``````````````````````````````````````````````````````````````````````````````````````````^^^^^^':~_:~;"c2w44WBDOGOPPwwZZwPPPPOOGEDD4BW%%%@#@##@@%%@#%%%%%NNWWNWDOZ2VC1_'^^^:'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^^^^^^^^'^'^^^^^
`````````````````````````````````````````````.```````````````````````````````````````````````````^``^^::__~~;twVDOEB4EPPZZww2wZPOOOGGED4BBWN%NN%#@@@@%@%%#@%%%%NNWBNWBOwVCL)c===I"~'^^^`^^^^`^^^^^^^^^^^^^`^`^^`^^^^^^^^^^``^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^''
`^^^`^``````````````````````````````````````````````````````````````````````````````````````````^^^^^^':___Iw4t2OZ14BGZZPZw2wwZPOGEEDD44BD4BN%@###@@@@%@@@%@%%NNNN%NWDZVCLT))c===111I"'^^^^^^^^^^^^^'^^^^^^^^^^^^^^^^^^^'^^^`^^^^^^^^^^^^^^^^^'^^^'^''^'^'''::''
^````````````````````````````^```````````````````````````````````````````````````````````````````^^^`^''__=w4)VPG_;DEPw222w22ZZZPPPOGGEEDDB%@%@@@@@@%%@#%%%%N%NWN%NWBPtCT))c===1111=1II+;_'^^^^^^^^^^^^^'^`^^^^^^^^^^^^^^``^^^^^^^^^^^^^^^^^^^^^^^''^''^^'^'^'':
^````````````````````````````^```````````````````````````````````````````````````````````````````^``^^'~_=VOVtPG)'2GPZ22VVVV222wZPZPPGGDBN@@#%@@@@%%%@#@%N%%N%WWW%WWDwCTT)===1=11===111II+;_^^^^^^^^^^'^^^^^^^^^^^^^^^^^`^^^^^^^^^^^^^^^^^^^^^^^^^'^^'^^^^^^^:^^
^^^^````^```````````````````````````````````````````````````````````````````````````````````````^^^^^:;=VVPGPPGP1cVwwwVVVV2V22wwZZZPGDW%@@@@###@@@%%@#@%%%%%%W%N%NN4ZtTTc===1111111111111III+_'^^^^^^^^^^`^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^'^^^^'^^^^''''^^'
`````````````````````````````^```````````````````````````````````````````````````````````````````^`^`_CTwPPPO4Z_IcCV2VttCttVV22wZwPGB%%@@@@@@%%%%%@#@@%%%@%NN%WNNWDPVLTcc==111111111111111III++"'^^^^^^`^^^`^^^^^^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^''^^''''':
``^`````````````````````````````````````````````````````````````````````````````````````````````^^^:)I)VtOCGE=~")=VtV2VtttCt2VwwPO4%%@@@%@%%%%%%@@@@@@%@%%%N%WN%WGPwtT)cc======11111111111IIIII++;_:^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^':^^^'^''':~_
``^````````````````````````````````````````````````````````````````````````````````````````````^^^~="1TL2tCO1~_II))CwVVVCCCCtVwPDN%@%%@%%%%%%%@%%%%%@%%%%%N%NNNWEwwVCT)c========111111==111II+II+II+"~'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^''''::__;
```````````````````````````````````````````````````````````````````````````````````````````````^_"^'_;c;:=w"_~;I+I=CttVZPwZEGDBNNNNN%N%%%%%%NWWW%%%%%%%%%%NWNNDOwVVCL)cc=========1=11==1111111IIII+I+I++;__:^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'::~_"=
^^^````````````````````````````````````````````````````````````````````````````````````````^^^^^'^':_I:~LV"__;+""+cLCCtt22OB%%N%%%%%%%%%WB444BBNNBB%%%%%%NWNGGZ2VVCLTTcc))ccc)=)==========111=11II1IIIIIIIII++;"~^^^^^^^^^^^^^^^^^'^^^^^^^^^^^^^'^^^^''::::~_"+L
```````````````````````````````````````````````````````````````````````````````````````^^':~__~:'::__'_tc~:~___~_1CVwPG4EDBGDW%N%%%%%W4EEEGGEDGGEN%%%%NN%N4VVPwVtLLLT))TT)))cc)c))=c)=========111111II1I1II1II+II+I;_'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'''::~~_;=w
``^``````````````````````````````````````````````````````````````````````````````````^:_;;+""___""_::"C+__~~___"1LtVwwVCLLVE%%%%%%%NBDEGGOOPPPGEW%%%%%NNBZLc+C2CCCLTTTT)))TTTT)TT)T)c)cccc======11=1=1111111I1I111IIII+_:^^^^^^^^^^^^^^^^'^^^'''^^'^'''':::_"ILZ
``^^`^`^````````````````````````````````````````````````````````````````````````````'_"+++;;+++II++""T)I++;";+I=cTTTTLLCVtDW%%%%%NWBEGPZZZPZPPGWN%%NNNN4C11"_cVttLLLTLTT))TT)TT)TLLT)c))cc=c=c======111=111=111111IIIII+I":^^^^''^^^^^^^^^^^''^'^^^^^^''~~~_+1Cw
```^````^````````````````````^```````````````````````````````````````````````````^'~_;+I++++I11=1III)L)c====T)c))TLTTLCPDDBNN%%%N4GOPw2VVV22ZDWN%WBBNBD4==_1T_CLLLTTTT))LLTTT))T))TT))))ccccc=c====c===1=1=1111=1111II11II++"~''^'^^''^^''''^^'^^''^^'':~~__+=Lw
^`^``^``^````^``````````````````````````````````````````````````````````````````'_"+I111=111===1=I+=L1===c))TT)))TTTLwZGGEBNN%%WEGPwVVtVtCVGWN%B4BWBOOGO':;c_:cTTTTTTTTTTTTTTTTTTTTTTTT)TT)))ccccccc===c============11111I1II++;_''^^'^'^^^^^^^'^^''''':___"I1Lw
^```````^````````````````````^````````````````````````````````````````````````^:;I1===c==ccc=c==1I=)II11=cc))c))))TLCLC2GBWNNNBGG2tVttttwENNBDDBBO2wwwwL^1_:'^_LTT)))T)TLTTTTTTLLLTTTT)))T))))))))cccccccc===========111=11111IIII;_'^^^^^^^^^^^'''^^'':~~__+=Lw
````````^````````````````````^````````````````````````````````````````````````^_I1==cccc=c=====1I1==III1==cc)c))))TLTLCPDBWNWNDGwVVVtVwDBBB4ED4G2V222VV"'"_::1;LT))TT)TTTTLLLTLCLLLLT)TT)))))))ccccc))ccc=c====c============1111II++":^^^^^^'^^'^^^'^''~~__"+1Tw
^^^`````````````````````````````````````````````````````````````````````````^'_I===ccccc)cccc=1111II1I1===c)c)))c)TTLLO4BBNWBEPOVVwPPOOZVVVw2VCtVCtLLLc'^'_=_^:=))))))))TTLCCCttttCtCLLTTTT))c))))))))))c)c=ccc=c=======cc====1====I++":^^^^'^''':'::::~___"+1Lw
`````````````````````````````````````````````.``````````````````````````````^:;1===c)ccccccc==1111III11==c=ccc)c))L)LV44BWWBGPP2ttCCCLLLCCtCLLLLT)cccL"~:"~:'^^_=c=ccc)TTLLCwwww2tCttLLLTLTL)L))T)c))))))c)cc==c=ccc=ccccccccc=====1II+"_'^^^^'^''^^'':~__";+=L2
`^^`````````````````````````````````````````````````````````````````````````'_I==c=ccc)))cc===111=1=11=====cc)cc))TLLEDBNBBDZPwVCCCCLCLLTL)T)T))cccc)+~:^:_:c=_~c))cc))TTtPwwwwwV1':_cLCLLLLLTLTLLLTTLLT)))c)T))))c))))))))))))ccc=c=1I+;"'^^^^^^''''::~_"";I=Tt
^^^`````````````````````````````````````````````````````````````````````````'"I====cccc)ccc===11111111====cccccccc=TwEDBWB4PwZVtCLTLTLT)))ccccc=====)_'^^':':_'~1c)))))TV2w2w22Vt:^^'''_+=)LLLLLTTLTTLTLTTLLTTLLT))))TTT))TTTT)))=====II+;~^^^^'''^^:::__"";I=cL
^^``````````````````````````````````````````````````````````````````````^``^~+I1===ccc==ccc=1=111111111========ccc)LPDEB44PVVCCLTL)))))cccc========c;^^_1~~'_::+;=c)T)LtVCLCCCtL:^'^^^^^^^^^^'''~+=))LLTLLTLLLCLLTLLLTLLLLt22tLT)c==111II+_^^^^^^^'^'''_";";+11=
^^^````````````````````````````````````````````````````````````````````````^_+===ccccc)))cc====111111111=====cc=c)TZOEB4BGVtt)T)T))))ccc=c==cc====1+':1'':;_"^^^:==c)CtCCCCCLL)'^:^^^^^^'^^^^:''':::':~"+=)LLCCtttCttVZGwCTT))))c===11I1I+_^^'''''^'^''~"++;++I+
^^``````````````````````````````````````````````````````````````````````^``^_+1====cc)))c)c===1111111111=1==1==cc)2wGO44P2CLTL))))ccccc))==c=c1+:^^^^''_''^:^:":_=ccLLLCCLCTTI^^^^'^^`^^`^^^`^`^^^^':^':~:__:^~IC2wZDZCLT))ccc======11111I:^^^^'^'^^^'':_+1+;+++
^^^^^`````````````````````````^````````````````````````````````````````````^_I=====c)))TT)cc=1=1=11=11111=======ctVwGOBGZtTLTc))ccc))cccc=cI__''+~I:__'":'_"'^"__+=c)TTLTLLT_^^^^^^^^^^^^^^^^^^'^'''''''^^''^^^^':+)LLT)))c=====1==11111I_'^^^^^^^^^:^':_;11+++;
^^^^``````````````````````````^`````````````````````````````````````````^``^_I1==ccc))TL)))cc==1111111111=======cVtZPE4ZVLT))cccccccccc)T1_'''^'''_:_'^^~"''_:''^;=c)T)TLT)I'^^^^^'^^^^^^''^'^'''':~'^'^''^^^^^^^:;=LL))ccccc======1111I_:^^^^^'''^^''''~_I=I++;
^^^^`````````.``````````````````````````````````````````````````````````^``^"I====cc))LC)))cc==111111111====1==ccLtZZEOtL)c)))ccc==c=c+~:^';~~~1"::1":+':^^'"::":"=c))TT)T1:^^^'^^^^^^'^^^^^^^^^^^^''^^'^^^^^^^^^_+=))))=======1=11II++~'^^^^^^^^^^^'^'''~;1c=I;
^^^^^^``````````````````````````````````````````````````````````````````^`^^"1=====ccTCtLT)))====1=11111111=====cTLZtEwLLT)cccc===c)":;_::~~_'':^'^'''''^'""'''';;=cc)))cc_^^^^^^^^^^^^^^^^^^^^^^'^^'^^^^^^^^^^'~+c)))cc=====111111I+_'^^^^^^^^^^'^'^^^^':_+==;~
^^^^^```````````````````````````````````````````````````````````````````^``^"I1=====c)LV)))))c==1111==11=11111==))t2tGt)Tc)c)cc==I;_^:::~_+_:~~^^""';:'^:I~''~"~^~_Ic=))c;'^^^^^^^'^^^`^^^^^`^^^^^^^^^^'^^^^^^^:;=c)ccc=1=11111I1I+;~^^^^^^^^^^^'^'^^^^^^^:_+1":
`^``````````````````````````````````````````````````````````````````````^``^"I1=====c)L2T)TT)c=1=11===111111111=ccVVVGt)c)ccccc)I~"~:+_:_~:_="'^^::^_:1_^'':'''_:"+:_=)c)"^^`^^^^^^'^^^^^^^^^^^^^^'''^'^'^'^^^'"1c)cc==11111==11II;~^^^^^^^^^^^^^'^^^^^'^':_;+;:
````````````````````````````````````````````````````````````````````````^``^"I1======cTVC)LC)I;_+I+I==11cc=1==1==cCtVwtccc==c)c;:_~:'~)=_:;":'^_:":^^^:_''':;_'_~~_":"~_:'^^^^^^^^^^^^^^'^^^^^^^^^:'^^^^^^^^^~"=)cccc==========I+_''^^^^^^^^^^^^^^^^^^'''^':__~:
```````````````````````````````````````````````````````````````````````^^``^"I1==1====ctwV2+II^''''^'_"_""";II11ccCLLCTc====)c_;~~_)"^_::I=~+'^___:'''''^;"^':":_;~~+_~~~'`^^^^^^^^^^^^^^^^`^^`^^^^'^^^^^^^'_+=)c======11===11I":^^^^^^^^^^^^^^^^^^:'^^^^^''''^^
``````````````````.`````````````````````````````````````````````^`^``^```^^^_11==11===)+'^^'^^_=~;'"+::__::+_:_::~"_+))cccc=;_:__"_~__1:':'''+=:^'^:+'~+_'''"^:":;I__~"+_'^^^'^^^^^^^^^^^^^^^^^^^^^''^^^^^~+=ccc====1==1=111I+_'^^^^^^^^^^^^'^^^^^^^^^^^^'^'^^^^
``````````````````````````````````````````````````````````````````^`^^```^^^_I=======c);^:'I:___:~^':~1:^__:__="'++~~+:~_"_:::T+_+~~)I~:_;_~~'_'I;^^''':''__":^_:I__c"__:'^^^^^^^^^^^^^''^`^^`^^^^:''^^^'~+cccc========11111;~^^^^^^^^^^^^^^^^^^^^^^^'^^^^^^^^^:
``````````````````````````````````````````````````````````````````````^`````:+1=====1_^`^^'^^^^':_=_^1+''':_+:''':+_:1;'^_;__+~+_:~~::"I_~:;~^^^:~'^;I~I+''_':+:+1_cI_::+'^^^`^^^^^^^^^^^^^'''^^^'^''^^_;1=====1=====1==11I_'^^^^^^^^^^^^^^^^^^^^^^^^''^^'^^^^'~
^^^^^^^^^^`````````````````````````````````````````````````````````````````^:+I=111+'^+"~_"="1:1~^':_::~"I"~~~"1:~c;::'^^^':"~:_~"1_:~::~+_~':I"';1:'~':::_''^'~_~__~I_;'^^^^^^^^^^^^^^^^^^'^^^'^'::^:"I=c==1==1==1===111_'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^:_
````````````````````````````````````````````````````````````````````````````'"I11"''~~_T2PC=I=^^~_~I__=_:__~_:~_;_~_+~^_1:^^':~I"~::~I_:_1_;+~:''++:=_''^:'+~^_=;__"~_::_^^'^^^^^^^^'^^^^^^`^^^^^^':_I=c===11111====11I_^^^`^^^^^```^^^^^^^^^^^^^^^^^^^^^^^^^'~_
````````````````````````````````````````````````````````````````````````````^_II:~'~__Cw2Pt_"=1L"_^~'^':+1:~+;_:~;:^^'"^''^~;^^~_:_I+~~:+c"':~_1___:''"":'^'"LIII)))+_I_:^^^^^^^^^^^^^^^^^^^^^^^^'_+======111=1=1111+_'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^::
````````````````````````````````````````````````````````````````````````````^~;:^^_;+V2wwwt~_:~"'~_::^_:'::':~:'+:^``~"''"':^`:;_~___;;__I"1_~_"~1"_1_~~~1_:"Cc==)L)Tc+~~^^^^^^^^^^^^`^^^^''^'^^~;1=c==1111111=111I+:^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^'^''^''':
````````````````````````````````````````````````````````````````````````````^''_tVwttLLLCV2__;:)'~::I"^':I=_;I+_^`^":^`^^^^:_'`^:~1I_+_~~++~~IT1::::~:_^:":__+LTLTTTT)=1====_~''^^^^^^^^^^^^^''"1===111111==1111I_'^^^^^^^^^^^^^^^`^^^^^^^^^^^^^^^^^^^^''^'^':^'
```````````````````````````````````````````````````````````````````````````^^~;wtCTL)))TCVPI:_"__=~+~_~;;_~';"^^_'^^':_~^~~:^^^'"^^'+~_I="_____=T__++++~~~~"I__=ttCCLL)cccc===1=1=1;:'^^^^^^:_+=c==1111=11==11+~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^'^^^^^:~_";;__~~:'
````````````````````````````````````````````````````````````````````````````^_tVL)))c=)))LVZ~+~"~_:_:II_:^^`^`^`^'`^^_^^^^^``~_:`^;~::'_":"=I'_"'^_+~^^'':~~"Ic)C22wVVCLLT)c===1I1=1I1+_:~"+=c==111111=11=1I_^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^:"+)L)I++;:'
````````````````````````````````````````````````````````````````````````^``^^"2CT))ccccc)TtPL:":+~'":'::~^_'^++''__~::''''_:'^'^^^'_^^'':'''~^'^::__'^";__;+I==cTCVwwV2tCTT))c===111111==cc)=1=11111111I1I"'^^^^'^^^^^^^^^^^^^`^^^^^^^^^^^^^^^^^^^^^:_ITLTI;I+~_
``^`````````````````````````````````````````````````````^`````````^`````^^^^^"VT)))cccccLTtwDL"_~:_;~+"::~;"I+II1=TTCtV22VVVVttL)==I1I"_""+_^'"_:__:_;++III11=c)TLCVwVV2VCLTTL))cc====1c))c==1======11II_:''''^''^'^^^^::~+I_~~_+'^^^^^^^^^^^^^^^^^^_+1LCCI+1cII
``````````````````````````````````````````````````````````````````````````^^^:C)ccccc=cc=TCVOwLLVZtC2ZC)I+I+++++II1=c)TTLLLLLLLTcc111IIIIII+++++++++++IIII11==cc)TTtw2VLL)))T))))))c===ccc=========1I+~'^^'^^^^^^^^^^^^::_c="~__I~^^^^^^^^^^^^^^^^''_+1TLLI"+"':
``^``````````^````````````````````````````````````````````````````^``````^^^^^1ccc===cc)c)LVT1=LttVVC=1IIIII++IIIII1==cccc=c))TTT)c==111I11IIIIIII11II11=1====cc)TCZtLL)))c)c)))))))))))T))))cccc=11_:''^^^^^^^^^^^^^^'~;GW2;~:_+:^^^^^'^^^^^^^^^^^'_+1LCL+";_::
`````````````^`````````````^^^^^^^^``````````````````````````^````^``````^^^^^_1=c=====cc)Lt==cLCttL)=11IIII+IIIII1==ccccccccc)TT))cc===1=111111111111====cccc=ccTVwTLT))))))TTT))))))))T))))))==1;~:''^^^^'^''^^^^^'^`'+wPT;::~;:^^^^^^^'^^^^^^^^^'_;1TCT+;;_::
`````````````````````````````````````````````````````````````^``````````^`^^^^:I==c===c==cLC===)TT)c=11IIIIIIIIII11===cccc==cc))TTT))cc===============ccccccc==c)T2tTTT)T))TT)))))))))))))))))=1I_'::^^^^^^^^^^^^'+c+;""_+)T;::~;'^^^^^^^^^^^^^^^^:'_+cCC)+;;_:'
``^`````````````````````````````````````````````````````^``^^^^^^^^``^^^`^^^`^'I====c=cc))Tt===c)c)c=111I1111111===ccc)ccccccc))TTLTTT)))))))cc))))))))))cccc=c))LZLT)CtCLLLTLTTLLLTT))TTTTc=1I_':~:'^^^^^^^^^^^^^^'^^'"_1Vc"^::;'^^^^^^^^^^^^^^^^^'"+cCC=;"+"__
```````````````````````````````````````````````````````````^``````````^^^`^``^'+=======c))TtL===cccc==1==111111==c)))T)c=cc=ccc))))TLTTT))T)))))))T)))))ccccc)))cLZT)TtLLTTLLLCLLLLTLT)))c=+_'':^'~'^^^^^^^^^^^^^^^^^``_~_);_'''"'^^^^^^^^^^^^^^^^^'_;=LTI__+=I+
`````````````````````````````````````````````````````````````^````^``^^^^``^^^^;===c===c))TCZL)c)cc))=======ccc)))TTT)))cccccc)cc)T))TTTTTTT))))))))))cc)))c)))TTtZ))))tTTVVLVL=;__~:~:'::''^^^^^'::'^^^^^^^^^^^^^^^^^`___c;_^::;^^^^^^^^^^^^'^^^^^:__=TT+__"_~:
````````````````````````````````````````````````````````````^````^^``^^`^``^^^^"======ccc)TCwGtc)ccc)ccc=c=cc)))TTLTT)))cc)c==ccc)))))TTTTT)))))))cccc)))c)c)))))V2T)))t)TLLc+'^^^^^^`^:'^^^^'^^^^^^^^^^^^^^^^^^^^^^^^^___);_^':"^^^^^^^^^^^^^^^^^^:_'+I+____^^:
`````````````````````````````````````````````````````````````^`````^`````````^^_1======ccc)LVZGP)))))))cc)))TTTLLLT)Tccccccccccccccc))))))))))cccc)cccccc=cc))))TwCLT))CTTTT"^^`^`^``^``````````````````^``^``````^^^^`:^^+"_'~'_``^`^^`^^^^^^^^^^^'_:^^^:_~_:''
`````````````````````````````````````````````````````````````^````^`^^```^^^^^^:1===c==cc))LtwPDw"TCC)LLLLLLCCCLLLTT))c=c=ccccccccccccc)cc))ccccc)ccccccccccc))TTZtCLLLLT)))~^^````````^^^``````````````````````````^^'~^^~_~^_''`^``````^^`^^^^^^^^_:~'~:___^^'
`````````````````````````````````````````````````````````````^``````````^`^`^^^:1======cc))TCtZOw:')w2VV2VtttCLLLTT)cc==1====cc=cc=cc======c==c==cccc==cc=cccc))CZTLTLtL))=1^^`^``````^``````^``````````^```````^~:^~";I;"__^^~:```````````````````````^`^'':^^^
````````````````````````````````````````````````````````````````````````^`^`^^^:I====c=ccc)))t2PP:'1222w2ttLCLLTT)))c=========c====================c==ccccccc)))tV)TL)wTT)=+^`^`^`^```^^`````^``````````^``^^``^'_~'_~'^::::'^~'^````````````````````````````^``
``````````````````````````````````````````````````````````````````^`````^^^`^^^'I====ccc))))TCVZG;_+wVtLCCCLLTTT))ccc==========c=================c=ccccccccccc)TZCTTTtZCLL)'^^`^^^^```````````````^````````^`^``__^:'^'~::__:^~:^```````````````````````````````
````````````````````````````````````````````````````````````````````````^^`^^^^~I=====))))))TLC2P"'~ZVCLLLTTTT))cccc===============11==1=1=========ccccc=cccc))CZCTT)CwtLL"^^^`^^`^``````````^`````````````````:_^^```^'^^:^^^:'````````````````````````````````
````````````````````````````````````````````````````````^`````^^^^^^^^^'^'^''::~I==c==))TTTTTTCVP;^'tVtLLLLTT)c)cc==================1==1============cccccc=ccc)wCLLL)TtTTI'^^^^^^^^^^^^`^^```````````````````_1c~'^`^``^^::^`^:'^```````````````````````````````
````````````````````````````````````````````````````````^``^^^^^''^'^^^'^^^^^^^_I==ccc))TTLTTTLtwI^^c2tCLLLTTT)ccc==================11==============c=cccccccc)2LLLT)LtT=;^`^^`^^````^`^^```````````````````^'1wV~``^``^'__^`^::^```````````````````````````````
`````````````````````````````````````````````````````^```^```^^^^^^^^^^^^^^^^^^_=ccccc)))TTTTTLtw1`^;2tCLLLT)ccc================111111=1==1================c)))V)c)ccLt)1:````^````````````````````````````````````````^';~'^^:'````````````````````````````````
```````````````````````````````````````````````````````^^`^^^``^^`^^^^```````^'+=ccc))TCLLLTTLCt2c^^~wtLLLLT)c)cc===============111===1=1=======ccc===cccccccc)VT)ccctCT1'```^^``````^``^`````````^`````````````````^`^^':'^^^:^^```````````````````````````````
`````````````````````````````````````````````````````````````^````````````````:I=====c)TLLLTTLLC2)^^^VVtLLLT)cccc==============1==1=1==========cccccccccccccc)c======CL)"^```^```````````````````````````````````````````^'^`^'^````````````````````````````````
`````````````````````````````````````````````````````````````````````````````^~I=====)))LLLTTTTt2T^^^)2ttCCLT))ccc===========1==11===========cccccc))))c)ccccccc==cc=CT+^^``^^`^^```````^`````````^`````````````````````^^^`^^~'^```````````````````````^``^^^^^
`````````````^``^^^^^```^````````````````````````````````````````````````````^_1======))TTLTT)TL2L^`^=wVVtCLTT)cc===============1=========cc=cccc)c)T)))c)c)cccc===c=LL_^```^^```^````^^^`````^``````````````````````````':'^^_:^````````````^````````^`^`^^^^^^
``````````````^^^^'^^^^^^^```````````````````````````````````````````````````^"1======c)))T)TTTLVT`^^I2VVVCTTT)cccc===========111=1===========ccc)))))cc=ccccc=c==1=1I'^^^^```````^^`^^`^`^`^^````^''^`````````````````````^^^'^^`````````````^^``^````^^```^^^^
``^``````````^^^^''^^^^^^^^^````````````````````````````````````````````````^^+======cc)))))TTLCV=^^^IVVVVtCLT))cccc=========================ccc)cc)))cccccccccc==1==+::'''''^^^^^^^^^^^'^''^^'^^^^^^^^^^^^^^^^^^````````````^^^``^```````^``^`^^^^^^^^^^^^^^^^^
``````````````^^^^^^^^^^^^^``````````````````````````^^^^^^^^^```````````````'+1======cc=c)))TTC2"``^=VVtVtLL))))cc===1========1==============cccc))ccccccc=cc======1+_~_~_~~__~______~__~_____~~~::::~'::'''^'^^`^`^```````````````````^`````^```^^^```^^`^^^^^
`````````````^^^'^'^^^^^^^^`````````````````````````^^'^''^'^''''^^^^^^^^^^`^:I11=====cccc)))TTC2'``^)VVVtCCLTTT))ccc========cc=c======1====ccccccccccccc)cc=c=====11;::::''''':''''::''':::~~:~:~~::~~~_~_______~_:::'^^^^^^^``````````^`````````^`````^^`^`^`^
``^```^``^^^^'^'''^^'^^''^^`````````````````````````^''''':''''':'::'':::::::_I=======cccc))))LCL^^^'CVVVVCCCLLTT)c))c=c=====cccccccc=======cccccccccc)ccccccc======1"'^''^''^'''^^''^'''''''^''''''''''^''':':::::::::::~~:~~~~~:'^^^^^^^`````````````^^````^^^
````````^````^^^'''^^^^'^^^``^``````````````````````^^^^^''''''''''''::::::::"1==1=======c)c)LLtT""";CVtVttCLLLT))))cccc====cccccc==========ccccccc=ccccc)cc=c=====11+'^^^^^^^^^^^^^^^^^^^^^^'''^'^^^^^^^^^^^^^'^^^^^^^^^^^^^^^^^^^''''''''^^^```````````````^``
````````^^^`^^^^'^^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^''^':'''^'''''''''''':':~+1===11===ccc)))TLtc;;;1tVVtttCCLLTTTT)))cccccc)cccccccccc===cccccccccc)c)c)ccc==c=c===1I'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^`^`````````^``^^^^^^^^^^^^```````````````
`````````^^^^^^^^^''^'^^^^^^^^^^^^^^^^^^^^^^^'^^^^^'''''''':'''''':'':::::::~I==========cc)))TCV=;;;)2VVtttCCLLTTTT)))cccc))cc))cccccccccccccccc=cccc))))c)cccc======I:^^^^`^^^^^^^^^^'^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^````^^```^`^`````^^^^^^````````````````
`````^^^^^^^^^^^'^^^^^^^^^^^^^^^^^^^^''^'''''''''''''''''':'':'''':'''::::::_I1====11===cccc)LLVI++ICVVttCCLLLLTTTTTT)))cccc)c))ccc)c)cccc====c=cccccccccccccc=c==1==I:^^`````````^```````^`^^^^^^^^^``````^`^^```^````````^````````````````````````````````````
``^`^^^^^^^^^^^^'^'^^^'^'''^^^^^^^'''''''''''''''''''''':'':::::::~:::::::::"1==========cc)))LCV+;")VVVVCCCLLLLTTTTT)))))c))))))cccccccc=ccc=c=ccccccccccccc=cc=======I"_~~~::'''^^^^^^^^^^^`^`^^^^^``^```^^`^^^``^```^```^^`^^^````````````````````````````````
^````^^^^^^^^^^^'''^''''^^^^^^^^'^^^'''''''''''''''^'''''::'':'''::::':::'::;1=====1======))TLCL;"cCVttCCLLLLLLTTTLT))))c)))))))))ccccccc=cc==cccccc=cc==c=============++"_"_~_~~~~:~~::':''^^^^^^^^^^^'^^'`^^':'`^````````^`^^`````````^```````````````````````
^^^^^^^^^^^^^^^^^''^^^^''^'^^''''':'''::':::::::::'':''':''':'':::'''::::::~+==c========cc)TLLtc"1VVVttCCCLLLLLLLTTT))))))))T))))))))))c==ccccccc)cccccc)cc===c=c=====cI"""_________~~~~_~:::::::::::::::''^^''^^^^^^^^^^^^^`^^```^````^`^``'^````````^`^```````
^^^^^^^^^^^^^^^'''''^'^^'''''''''':'''''''':':::'':''::::::'':':::~:''::::~~+1==========cc)TTLt="LVVVtCCCLLLLLTTTTTT))))))))TT)))))))c)ccccccccc)ccccccc)cc====cccc===cI++""_______~~____~~_~~~:::~:~:~:~::~:~~:':'::'''''^^^^^^^^^^`^^^^^^^`^````````^^^```````
^^^^^^^^^^^^^^^^^^''^^^^^'^^^'^^'^':'''''':''''''''':':''''''~:'''::''':~::~+1==========cc))TCt"1VVVtCLLLLLTTTTTT)))))))c))TTT)))cccccccccc=c=====cccccc=c========1===cI+"""_______~~~~~_~~::~~~::::::::~::~::::::~:::~::''::::'''''^^^^^^^^^^^^^`^```^^^^`^^^``
^^^^^^^^^^^^^^^^''''^''^'''^^^'''''''''''::'':'::''::'::::':''''::::::::::~~+==========cc))TLCC"t2VttCCLLLLTTTTT)))))c))T)TTLLT))c)))))ccccc)ccccccccccccccc==c======c)I;;""______~___~~__~~~_~::~~:~:::::~::_~:::::::::::::::'::::'''''':':'''^'''''^^^^^^^^^^^
^^^^^^^^^^^^^^^'^:''''^'^'''''^^''':':'''''':':::'::::::'::':::::::::::::~~~+1=cc======cc))TLC=c2tCtCLLCLLTTTT))))))ccc)))TLZVT)))ccc))cccc=cc=cc=cc=cccccc=cc=======c)I++"""_________~~~~~~_~~~~~~~~~~:~:~~::~:::::::::::~::::::::::':'''':::'''''''''''''':'^'
^^^^^^^^^^^^^^^''^^^^^^^^'^'''^'''''':'''''':':''::'':'':::::~:'::':':~::::~+==c=======ccc)TL2=V2VCCTLLTLTT)))))))cc=c)))TLCZ4T)c)c=ccc=c===c=======cccc==cc========cc)=+;";_______~_~~~~_~~~__~::~::~_:~~~:::::::~~:~::':':::::::::'':::'':'':::'::'''':''''~':
^^^^^^^^^^^^^''':''''''^'^'^'^^'':::::::':::::':''':''::::::::::::~::::~~:~~+cc========cc))LCwtw2VCLTTTTTTTTTT)))cccc))))TTCwZT)))c===c======c==cc==ccc=ccccc=======c))1+;;"_"________~~~~_~~~~~~~~~~:::~~:~~~~:~:::::::~::::':::::::::::':'::'::'':''::::::::::
^^^^^^^^^^^^^^^^'^'^^^^^^^^^^^^^''''':'::::':::':'''''''''''':':':'::'':~:~~+=c==========c)TCVZwtCLTTTTTTT)T)))cccc===cccc)TLT))cc=c==c==========cc=c====c==========ccc1I"""______~~~~~~:~~~~~~::::::~::~::::::::~~~::':':::::::':'':::':'::'':::'''''::''':''::
^^^^^^^^^^^^^^^^''^''''''''^^^^^''''''::':::::::':''':::'''::'''':~::::::::~+=ccc======c)))L2OPZtCTLTTTTTTTT)))cccc=c===cc)))c)cccc==c========ccccc=c=ccccc========c)c)=+;"_"_______~~~~_~~~~~~~~_~~_~~~:::::::::::::~:::::::'::':'::::::::::::'::::::''::::::::
^^^^^^^^^^^^^^^':____~::^''^^^^^^^''''''''::'':':'''''''''''::':::'::'::~:::+====c===1=cc)TLwGZVCLTT))))T))))cc=c=========c=cc======================================ccc1+;""_______~~~~~~~:::~:::~~::::::':::::::'::':::''''''':'''''''::':::'':'':''''':'''':::
^^^^^^^^^^'^^''::_+==)c=II;"_~::''''''''''':':::''''''''''''::''':::::'':::~;==cc====1==c)TLPOwVLTTT)))))))))cc=c===================================================ccc=+;"________~~~~~~:~~~~:::::::::~~::::':::::::'''^''''::':'''':'':':::'::'''::'''''''''''
^^'''^'^^'^^^'^'::~_;I==c======I;___"__"I_:~:::::::::''''''''':'::::::::::~~;ccc=======)))TtEZ2VCLTT))))))))))ccc============================cc=====================ccc=I;""______~_~~_~~~:~~:~::~~:::~::::~::~:::':::':::::''::':'::'::':':::'::''''':'::::''''
^^^^^^^^^'^^''':::~~_"+I++++++++;"""=;c;+;+I1I11====1I;"__~~:~:::::::::::~~_;==c====1=ccc)T2P2VtLLTTTT)))))cc=ccc=ccc============1====1=============11===1=1=========c)c1+;;"__""______~~~~~~~::::::::::::':::::::'::::::::::'::::':::::'::::':''''':'''''''''''
^^'^^^^^'^':'::~::~~___""__~_~__~________";1ccc))cccc)cccc)c)c))c==1+"______;=cccc====cc))LZwVtLLTTTTTT))))cccccccccccccc=============================11=11=========ccc=+;;"""_______~~__~~~~:~::~_~:::::::::::::''''':'::'::::::::::::'':::':'''''''''''''^^^''
^^^^''^''''':::~::~~~~____~~:~~_~~__~_____"I=)))))))))))T)))cc))))))))))))))==cccc====ccT)LZ2CCLLTLT))T)))))cccccc=cccccccc===c=======1================1============ccc)I+;";;___________~~_~~~~~:~:::::::~~~~~~::::::':::':::::::':::::'''''''''''''''^^^^^^^'^
^^^'^^'^'''':'::::~::_~~~~::::~~:~~~~~____"+ccc)T)Tc))))cc))c))T))c))c))T))T)=cc==c===cc))CwCCLLLTTTT)T)))c)c=c==cccc)c)cccccc===============111=1=1=11=============cccc1+;"""_________~__~~~~~~:::~:::::::::::::::::::':::::::::'::::'':''''^'''''''''^^^^^^^^^
:''':''''''::~:~~:~~~__~~~:::~~~:~~~~~~___"+=)c)TT)))))))))))T)TT)T)))))TT)T)1=====1==ccTT22CLLLLLLTTT))))cccccccc=ccc))ccccc===================11111111=1=========c)c))1++;_"________~~~~_~~~~~~~~~~:::~::::~:::::::::::::::::::::::::''::'''''''^':''^^'^^^^^^
''^''''':':::':~~:~~~~~~~::::~:~:~~~~~_____;==c)T)cc))))c)))))))))cccc)))T)))==========c)TwVCLTTTLTTTTT)T)cccccccccccccc)cc=======1======1====1111==1=1111===cccccc)))))=I+;""""_______~_~~~~~~~~~~~:_:~_~:::::~:::::::::::::~:::::::::':::':''''':':'''^'^^'''^
^''''''':::::::~~:~~:~~~~:::::~~:::::~~:~__;===cT))ccc)cccc=ccc))c=c)))))))))=======1==))LZVCCLTTTTTTT))T)ccc=ccccccc)cc===============1===1==11111=11=========c))ccc))c1+;;""_________~___~__~~~~:~~:::::::~:::::::::::'::::~::::':::'':'''''''''''''''^''^''^'
''''':''::::~~:~~~~~~~~~~::::~~~::~~~~~~~__;Iccc))c))c))cccc)c)T)))))))))TLLL==cc=====cTLCZtCLLLLTLT)))))))cc=cccccc=cc==)c================11=111111======ccccccc)))))))=++"";"_____~__~~_~~~~~:~:~~:::::::~:::::~:::::::::'::':::'':::''::''''''''''''''''''^^'
''^''':':::::~:~::~~~~~_~::::~~~::::~~~~~__;I1=c)cc==c)cccc=ccc)))))TTTTL)T))1========cTTVwCLLLLTTTTT))))))cccc=cccccccc=c======1=1======1=11111=1=====c===cccccc)c))))c=I+;""________~~~~~~~~~:::~~~::::::::::''::'::::'::::::'::'::':':':''''''''''^''''''''''
'':':::':::::~:~~~~~:~~~~~:::~~~::~:~~~~~__;I11cc=====c))TT)TLTTTT)cccc)c)))c==ccc====)TCw2CLLLLLTTT)T))))ccccccccc)ccccccc=cc=======1==11111=111======ccccccccc)ccc)))T=cI1++;"""____~___~~_~~~:~~~::::~:::::::::':::::~::::''::':'':''':':''''''^''''':''''^''
^:'::':::':::::~::~~~~~~~::::::_::~~:~~____"+I1=)))cTT)T))cc=cc)=cccc=ccc)c)c1==ccc===cTCwVLLLLLTLTTT))))cccccccc))ccccc=cc=======111==1==111111=1==c=cc=c)cccccccccc)))c1=c===c=====111I+"___~~~~:~~~~:~::~~:::::::':::::::::':::'':''::::'''''''''''''''''':::
''''':':~:::~::~::~::~~~~::::~:~~~~~~~_____;I1cccc)ccccc=ccc==ccccccccc)c)))=1==cccc=c)TCwtLLLLLLLTLT)))))))cccccc)cc)cccc=c=============111=1=11====c)cccccccccccc)))))======================))11I+___~~::::::~:~~:::~:::::::::::':::'':::'''''''''''''''':''::
^':''':::~:::~~:::~:~~~~~:~:~~~~~__~~~_~~__"I1I1==1=1==c======cc)ccccccc)))c===ccc=ccc)L2ZVCLLCLLLLLLT)))))))ccc))c))))cccccc====cc=====1=======cccccccc)ccccccc))))))T)=====c===c=c=cccc==ccc)PO2CCtLTLLLLCZPT1I_~:~:::::''::::~~::::::::::::::::::'':::::':::~
'''^'''::::::::~~:~~::~~~~:~:_~~:::::::~~~_"+++11I11111========c==1=c=cc=ccc==ccc)cccc)TtwtCLLLLLTTLLTTT)))c)ccccccc)))cccc=cccc============c=cccc)ccccc=cccccccccc)))T)======c===cc=====c=c==c=)V2ZP2VwZZP2c==cc=c=========I1"__~~~::'::':::':::'~':::''::::~::
':::''::::::~~~~~~~~~~~~_~~~:~~~::::~~~~~___"+++1+1I111==1===1=cc=c==cc)=cc)cc)))cc)cc)LCwtCCCCLLLLLCLLTT)))))cc)cc))c)))ccc)cc=======cc====ccccc)c))c)c)cccccc=c)))TTL)==cccccc=c===c=c==cccccccV44DOPOD4GT=c=c)c=ccccc==c===cc=========11I;++_::::::::~:::~:::
':::':::'::~~~~__~~~~~~~~~::~~~~:~~_~~~~_~__;+++1+III11====111=c=c========cccc)))))))))TL2tCCCLCLLLLCCLTTT)))))ccccc)ccc)cccccccc=c=cc====ccccc)))c))))))ccccccc))))TTLc=============c=c=c=cc=c=CDWWWBBBBBBP)cccc)=ccccc=======c========1=1==cTL2T=1=I;___~:~~::
':::::~:~~~:~:~~~:~::~:::::::::~~::::__~_~__";;+III+I+II11111==1=1===c===c===c)))))cccc))LtCCCLLLLLLLtLTLTT))))))c)))c)cc))cc==ccc===c===cccccccc))))))ccc)cc)cc)))))TLc=1==c=========cc=ccc===cTZZVwVT))ZPwLVZPVcccccc==cccccc=1===c==111===1cTTV)========1====
~::::::::::~~~~~:::::~~:~:::::~~:~_~~~~_~~___;++++++III1111I11===1=11=====cc=)))c)c)c=cc))LVCLLLLLLLLVVCTLVVLTLTLTT)))))))))ccc)cc))cccc))))))cc)))))))))cccc)))))TTTLL==============c1===c====cctT=GT1I1VCwEDEGEPtVV2wwZZZPZwZt===============)TtCccccc)c======
::''::::::::::~~::~~~~~~~::::::_::~::~~:~~____";++++I+IIIIIII1I1111111=1=====c))c)ccc===cc))CCLLLLTLTCwtttVVZw2CtVVCLT)T))))))ccc))))c))))))))cc))))))cc=cccc)))T)))LLL1=====1=========c1=====c=cC=1Gc1I12t2Z22wZZVCCLT)ccc==========11===1=1I1c))C)1=====cc====
:':'':::::::~:'~~:~~:~~~:~~:::~~:::::~~:_~____"+;;++I+++++II1=I11111I11===1==c)))cccc===ccc)TCLLLTTLLL2wttVwOOPwZZGZVCtLTT)T))))))))))))T)))cc))))T))ccc=ccc))))TT)TLLT1=11=1==11===1===1=====1=ct==G=1I=Vt2w2VZZCc===============1=1==1=1====1c)=TT==c==c=1=c11
::~::':::::::~:~~:~~~~~~~:~::~~:::~~:~~~~~~___";;;";++++I11III11111I11=11====)))))ccccc)c)))TLCLLTLTTTLPPw2ZEDBB44BWB4PwVVtTT)))))T)))))))))))))))))))c))ccc)TTTTTLTLCc==================c=c====cC==P=111VtVtVtT)=ccc===c================1====1=)c=Lc===========
'''''::::::::~:~~:::::~::::::~:~::~:~:~~~~_____""";;";+;+II++IIIII+11I11111=cc))c))ccc=ccc)))LCLTT)))TLtOO2PDBWWWBWWNBGGwV22tLTTT))T)T))T))))))))))))ccccc)))TTTTT)LLL=1=11=11==11====1=1=1====1cC1cP=I+=VCC======c=============1=111111=1=111=1))=)c1==1=======
':::::::::~~~~~:~~:~~_~~~~~::~~~::~::~~~~~_____";"";;++++++II11III1+1111I1==c)T)))ccccc))))))TCCTTTTTTLLVDGG4B%%%%WBW4DPwZ2tCLLLLLLTLTTT)T)))T)))))))c))))))))TTLLLCC)11==111========1=c===c1===cTTctI_=T)L)1==c========cc==============1cc1=c=1c)=))==c====c===
'::::::':::::::~::~::~~~::::::~~~::~~~:~~~_____""_;_""";";;;+++I+++1111=====c)))))))ccccc)TT)TLtTT)))TTLVOBBBN%%%%%%WDOw2tLCttLLLLTLTTTTTT)))T))))))))ccc)))TTTTTTLLL==111=11=11=111=1111==11=1=1=L)Ct))CCC==1==1=====1=11==1==11I111=11==1111===T==)=11=1====11
':'::::::::::::~::~~:~:~'::::::~::::~~~~~:~____"__""""""";;++++I+I111=1===1=))))))))ccc)))TTT)Lt))))))LCVPWWN%%@%%%NBGPZt2ZVCLCCCLLLTTT)TTT)))))))))))c))))))TTTTLLLC=1==1=1I111=11=111=11=1111=1=L1LLIIVCL==1=====11=1=I1====11=11==11111=====1=T)cT1=1==1=111I
:::''::::::::~:~::~:::~:~::::'::::::::~:~~~____"___"_;;;;;++1II1IIIIIIII1I1)TT)))TT))))))TLTL)TtLTTTTTLLVPW%%@@@@%%N4DOZP2VtVtVtttLLLLTTTTT)))))c)))))c)))))T)TTCLLCL=1=I==1I11I11111=11=11==1===cL1LTIIVCT=================c=====1========11==1=)))C====11==11I
'::':':::::::::~~:~:::~:::'''::::'':::::::~____"__;";;++";;;+++I+++++I+I11cTTTTTTTLT)))TTTCLLLL2tTTTTTTCVw4%%%@@#@%NBDEPPZZww22tCLLLT)T))))))))))cccc)c))))))TTLLLLC)I=1=111111111=111111111==111=T1L)1IVCT11===1=======1===111=======1==1111111=)L)C=111111I1II
'':::::::':::::~~::::::::'':'::::::::~~~~____"""______";;";;;+++++++II+IIIcLTTTTTTTLTTTLLLPLCCCtVLLTTLt2wEDN%@@@@@%%BBDDEGGGZ2VCCLTTc====c)))cccccc)cc))T))TTTLLLCtC1111I11111111=11==11=111=111=cL1L)11VCT========c========111======11111111=1=1c)cC=11==1III+I
''::::::^::'::'::::::::~::::::~~:~~~~~______""";_____""__"""++;+;"++I+II1IcCTLTLTTTTLTTLLLV2CLLCwtLLLtVwVOBN%%@@#@%%NBBBBBG2T1+;;;;;";"""_""+Tcc)cc)))))T)TTTTLLLCCT111I11111111111111=11==111==1=L=L=I1VCL1=====11=1=====111111====11=1=11=1==11cc)Cc11=I1IIII+
^'^''''''':''::::':::::::::::~~::::~~::~~:~~______________"";+;+;;";;+;+II)LTTTLTTTTTTTLLL44wtLT22ttCVVVZPEBBBBBB2="+I+;""___________"__"__"""";1))c)cc))))TTTTLCLC=IIIII1IIII1I111II1111III11I11=TIL=I1tLT11I11II=11I11111II=1I11+11II1=1II1II11=TcL1IIIIII+I++
'''''''':'':::::::::~~~~~~::::::::~::~~::~~~_____________"""""";"+++;;+++ITLTTLLLTTLLLTLLtcI;""_"""""_"""""__"______"_"___________________________"+c)))))))TTTLLCTI1III11II11III1III11111111I1I1=TIt1+1tL)I11111=11111111111I111I1III111=11==1I1cTcL=II=1I++I+I
^''''^^':::::::::~~~~~~::::'::::::::::~:~:~~____________"_""";;;";;;;;+++ICTTTLLTTLLLLTTTC)I;;"";;;"";"";++;+;+II+;;"""""";+I=I;__"__________________"=T)T)TLTTTLL++II1IIIIIIIIIII111IIII1II1IIII=TIL1+1VL)I1II111=1I111I1IIIIIIIIIII1I111II1IIII=TcT=11III+II++
''''^'':''':::~~::::~~~:::'::::~::~:::~~~:_~_______________"_+""";""";;++ILT)TLTTTLLLLTTLCt)c1IIIIII1==1)twwVLTc====c)CtCCL)I++II11II=1II"______"_____"+cTTTLLLTC)+IIIIIIII+IIIIII1IIIIII11II1III=cICI+1VL)1111111=1IIII11II1IIIII++IIIIIII+II11I=TcL=IIII+IIII+
'''::::::::::::::::::~~:~::::~::::~:~~_~~~___________"__""_""_""";+;;;;;;+LT)LtLTTTVVTTTLLTI+++;;;+ctCcI++;;;;;;;I+II+;";"";"_________""""""I1cc+___""""""ITLLLCL1II11IIIIIII1II111II11111II1IIII=LIC1+=VLcI1111111111111111IIIII1I11II111I11==I1=TcL=I1III11III
::::::'''''''':::'::'::::::':~:~:::::::~_~~~_________""_____"__";;"""+;";+)LLLVTTTLVG)TT)LtLC2wt=+;;;+++++++;;;+;"""=)I"________________""""""""";+1I+"";""";";c=I++IIIIIIIII+IIII1IIIII1IIIII1I1c)ItI+cVLcI1I1111111111I1I11111111I11IIIIIII1111cL)L=1IIIIIIII+
:::::::::::::::~~:~~~~::::::::::::~:::~:~:~__""_____"__"""""";;;;";;;;+++I1CttwTTLCVGtLLLCC)==11===1III+++;;;""+CtT+;"_____"__"___""_"_"_""""""""";;"+==1II+++;+III111III1I1I==1I111IIII11I1111IIcT1tIIcVLc1111111I1I1I1111111111111111II11111===cLTC)=1===11111
':':::::::'::'::::~~:~:::':::::::::'::::~~~_______________"_""";"_""";";";ITLtZLLLt2PVCCCLtCc==1=11I1I+++;+)VGEC1;;"""_____________"_"_"""__"""""_;"""";;+11++++II++III1IIII+II1I111+III++II+II+I))It+IcVTcIII11I11II1I1III+11III++III1111111111I=LTC=1I1IIIIIII
''''''''''::'::::::::::::::'':''::::::::~~~_______________"_";""""""";;;;;ITLtwCCCVwPVCtCCLTc=111III1111=cTC2GV1;"___________"___"___""""""""""""""";"";""+==II++III+IIIIIIII+IIII1+IIII+II+I1IITw2)V1IL2ww)IIIIIII1IIIIIIIII1IIII+IIIIIIIIIIIIIIcLTL=1II1IIIIII
''''''''''::::::::::::~:::::::~::::::~~~~~______________"__"__";""""";;"+++TCtZtttt2TLVCCCCCc111IIIII1===TLtt=I+;"_"_______"______"""""""""""""""""";""";";+cc=I+++III+I+++IIII+++++++I++++I++II=";IC_+II1LLIIIIIIIIII1I1I1++III+IIIIIIIIII+I1IIIcTTC=1IIII1I+II
''''':'':'''::::~::::::::::::::~:::::~~:_~~__________________;"""""";+;+I++TtCwLCCttc1cLLCCL1II+;++++II1===tT1+;;""_"_"____"""__""_"""""_"""__"""""""_""";;;1L1II++++++++++I++++++;+++;+;+++++++1=+=C=I1==c1++IIIIIII+I11+III1+II+++++III++IIII1I)LTt=1IIIIII1II
''::'':::::::::::::::::~~:::::~~::~:~~~~~_______________""""";;;;;+;;";";;+=tVwVLCC2ZtVVtLCCT=I+++++IIII1I=L++;""""__"______"""""_"""""""""_"""""__""";;;;++=I+++I1+III+I++I+;+;;+;++;+++++;++++I)==CII=VLc+IIII++IIIIII11IIIIII+III+++++IIIIIIII)LTC11I1IIIII++
':':''::::::::::::::::~:::::~~~~~~__~~~~~~~____"______"""";;;";""__"_""";;;ITtw2LCtw2LTCVCCLC)=I1I111I1111)))T)c=I+;;;;;+;"______"";""""""""""""";""";;;+++II+II++I+++I+++++++++++;+++++;;+++;+++)==C+IcVLc+++II+I++I+I11I+++III+IIIII+I++IIIIIII)LTC11I1IIII+I+
^':':''':''::::~~::::~:~:::~~~~~_~~_~~~~___________"""""_"_____"____""""""";)LLLCLV2t)T)LtCCtL)TLCLtVVtCCVZP)cT))ccc=====I;"";"""_____"""""""""_"""";"""+;II+++II+;+++I++;+++;+;+++;;++;;;;;;;;+I)1=C++=V)c;+;++++++++IIIIII+++++I+++I++I+++++III)LTLIIII+I++I;;
'::::::''::::~:::::~:~~~~~~~___~~~___~~_____";"""""_"__________"__""""";_";"++cTCLC2tT))TLLTtT)TTTTTLLCt2PDtT))))cccc====1====)=;""";""_"_""""""""""";;;++II+++++II+I+++++++;+;+++++;;;";;+;+;++TVccC++)Vtt1;+++++++++I1c)))=II++++++++++;++II+II)TTLIIII+++++;"
'''::''':::':::~:'::~::~::~~:~::_~_~____"_"_______"__________________"""+""";+=)TLCwLT))))LCLT)TTTTTLLCVwZw)T))c)cccc=============c=;"""+"_______"""";;;++++++++++++;+++++++;;++;;;;;;;;;";;;;;1TL)VP=))TLtc+;;;;++++I1=1II1LtT1++++;+++I++++;+++)LTTIII+I++++;;
':'':''':':'':::'':::::::~~:~~~~~:~__________________~_____________"___"_"_";;1)TLVVT))cc)cT)T))TTTTLLV2ZPC))))cccc)c=============1=cc;_""";""___";""";+++++;+++++++;+++++;++";+;;;;"""";+;;;+++cT==)_+IIIc1;";;++I++Ic1+I++1LC)I+;+++++II++++++ITLTL+I1I1==1I++
'':::::'':::'::::''::~~~~~~~___________~~___"_~:::~~________________"_""_;"""+1)TTTTT))ccccc))))LTLLLCtwwZT)))cccc====c================cc)+""";""""";+++I+;++;+++;+++;;++;++;+;;+;""";";;";"";;;+c)cC==TL)I+;+;+++;+I1ccc)VwT==T=++;++++++++++;+ILTLLI=Tt2ww2tT1
''''::::'::''':~:::::::~~______~~~~~~~_________"_~___________________"__""""""I)))T)))cc=ccc))))TLLLCtVwPtT))cccccc=cc================ccccc));;"";+;;;++++++;;++;+;;;;+;+;+;+;+;;;"";";;";;";;;;+=c1T++)L)+";+;+;;++++1=II)ttTcTc+++;+;++;;++;;IC2VVZCCww2PGOOZC
''~:':::::::::::~:~~__~~~:~~_~___~_~~________""_______________""___""_"__"""";Ic))))TTcc)cc)))))TLCLCt2Z2)))cccccc===============c===cc))))))T)T;+";++++;;+;;++I+;+;;;+;++++;;;;;";"";;;+;;"""+++==1T++TT)I;;+";;;;"++=c==)CT=cL)I+++;;;+;+++++I=LcVWZtc+=2PwT=2
':':::::::~~:~~~:~~~~~~~~~~~:~~~_~~~___________"____________________"""""""";+Ic)))))))c=c)))TTTLLLCtVwZL))ccccccc=================cccc))cc)))))T)+++++;;;;;;+;;;;;;;;;;;;;;;""""";"""""""""";";;11=T+;)T)+;;;;;;;+;;++1I1==1=))I++;++++I;I++;+ItZPwZVTLP4BGVI_I
':'::::~~:~~:~::::~:::~~::~~:~~__~~~~_~~_"_____"_______________"_____"_;;""""_I)))T)))))c))))TTLLLLCVwZ2))))c=ccc====c===========c=ccccc)cc))))LTLVI+I;;;;;;;I+++;;;++;;;;";;";"";+;"""""""""";";111T+;TTT+;;;;;"";;;"+++I1I=)T=++++++++I+++++IT2w2cTVCtVPOVVT=I
:~~~~:::::':::::~:::::::::~~~:~__~~~~____________________"_____"____""_";"""";I))))LT)c))))))TTLLCtVVwZL)))cc)ccc========c======cccc)c))))))TTTTTTLVI1;;+++;;;;;;;;;;+;;+;++;+;;;""";""""_"";;;;;1c=T+IT))+;"+;;;;;;;";;++I=c1I++++++IIIII+++1))+T=1LCtLT)V2PL==
:''''':':'::::::::::::::~::~:~~~~~~~___~__~~_______"_~______________"____""";;I)))))))ccc)))TTTLCCCV2ZV)))cc=cc=========1===c)ccccccc)))))))TTTTTLLV=+;;;;+;;;;;+;;;;;;;;+;;;"";"""""""__""""+";+===L+ITTc+"""";""+;;";"";;;++;++I++I1=c)c==)TC11;;L)TTTc)wOZLIc
':::::''':':::::::::::~:~:~~~~~_~~~~~~~___~~~__________________"__"_""_"_";;;II)))))))))))))TTLLCtV2ZZ))))ccc)c==c=c========c=cc)c))c)))))TTTLTTLLLI;++;;+;;;;;;;;;;;;;;;;;+;;"";"_"__""""";""";+c==LIILT)+;;+;";;"";;;""";;;++++I1c)CV2w2CTVwVII'~=T)c)CVVVVCCt
'::::'::'':'::::::::::~::~::~~~~_~~~~___~___~___________"__"___"_"_"_";"_+;+;+1))))))))))))TTTLLLtV2Z2)T))cccc=cccc=====cccccc)ccc))))))T)TTTTTLLL++;;;+;;;;;";;+;";;";;;;++;+;"""""_""";"";"_;;;===LIIT))I+""";;"""";;;";"";++IITVwww2L=1ctPwLIcc1c)c1=TLCtCLT=
'''''''::''::':::::~::::::::~~~_~::::~~~~~_______~___________"";""""_";__""";++c)))))))))))TTTTLtVV2wT)))ccccc==c=========c=ccccccc))))TTTTLTTLLL++";";;;;;;;;;";"";;;;;+;;;;_"_""__"_""_""""";""1==L+I)Tc;;;_;;""""";""""""";;1CwVCtZPtT)LCwVLIcT)1I+;;;++I++""
'::'':'::::::::::'::::~:~~~~~:~__~~~~~~~~~~~__________________"""";_"__"__"";+I)))))TTTTTT)TTLLCtV2wC)))cccccc==cc=c====c=ccccc)c))))TTTTTTTLLLL+;"";";;;;;;;+""+;+;;;"";;""""""""_"_"""""""""";"1c=L++T)c+""""";;;;"""""";;;;1TT+;+c2OPVC2wwwV=Ic=1I+;";______"
'::'''::'':::'::~'::::::~:~~:~~:~~:~~:~~~~~~~~___~________"_""""____"___"""""++)))))))))TTT)TLLCtV2V)))cccccc====cc===c=c=cc)))))))))TTTLTTLTTL;;;+;;";"";;"";;""""";""";""""__"_""_"__"___"_""""1=cL++)T=+_"_"__";"_""";;";+Ic)I)wEBBBET_1t2CtL+1cI;;"_________
''''':''''':::::~::::::::::::::~~~::~~~~_~~~~~_~~_____________________"_""_"_"Ic)cc)))))T)))TLLCV2wL))ccccccccc==========cccc)))))c)TTTTLTTLLLI""""";"";";;;;"";""_""""""""""_____"_"________"__"1c=T+;))=;"__""___"___"__;;;Ic)cVPG4DOG2c;"tCCCII=++"__________
''''''::^^'':''::::::::::::::::~~~~~:~~_~~~~~~_____"______________"_______"";+I)))))))TTTTTTTLCVV2C)))c)c))cccccc=====ccc)))))))))TT)TTLTTLC)+;;;;";;";"""";"""""""""""""__"""__"_______________"1==T;+)c1;"""__"__"_"""_";+=LtCCCVVw2tEEt=+1TTtL=+;;"""__"_____
''''':'':''':::::'':':::':::::::~::::~~~_________~_~________________________""+c))))))TTTTTTLLLtVtc)))ccccccc=cc=======c=ccc)))))TTTTTTLLTT);"";"""""""""""""""""__""""""________________________111T"+))1"____________;+cCttttt2VLLLCtG4VI+c))T)I;;"___________
''''':''':'':::::'':::::::~::::~__~~____~_~_______~________________"_____;"_"+Ic)))))TTTTTTTLLttV))))))cccc)))cc====cc)c))))))))T))TTTTLLLT;;+""";;;;""";""""""""""_"""_"______________________;LwVCCIICtVC1_____"_"+=LttVttwww2CTT))C2DGt+1=c)T);;""___________
'''^^^'^'^'^'':''''''::''::::~~_~:~~~:::~::~:~~~~:_~~______~_~______________""+c)c)))))T)T)TLLtVT)c)))cccc=cccc===c==cccccc)))))TT)TTTTLTT"""_""""""_"""_""_""__"_______________________________c+;It"'=1;+I_____"=C2VttCV2VL)==c=I=LwPVC="===));""_______~____~
:'''''''''''^''::'''''::::~~~~~~~:~::::~~:~::~~:~~~_~~_~___~~________________"Ic))))))TTTTTTLtCt))c)ccc))cccc=cc=c=cc)))c))))))T)T)TTTTLLI"_"""""""""_"__""""""_"____________________~__________=I_+wV_;+;I;____"L2ZZwVVCC)====11=c)LCCCC)=c=ccI_______~~~~___~_
''''''''''^':::::'':::::~::::::::':::~~:~~~~~~:~~::~~~~______________________"I))T))TTTTLTLLLCtT))))))ccc)ccccccccccc)))))))T))))TTTTTT)";""";"""""""""""___"_""_""_____________________________"cLLV))T)=;____+tOOGOV)==11111III=)TCLLLT)111+___________~~_~~~~
''''''''''''''':::~::::''::::::'::'::::~~::_~~:~~:~~_~_~~~___________________"1)))TTTTTTTTTLCtC)))c))c)cccccc==cccccccccc)))T)T)TT)TTTc";""""""_"""""_"""_"__"_"___________________~__~___~______1=)CI+ccI;___"CPZPZVT=I1II;";;++++++IIII+;"________~~~~~~~~~_~~
'':'''::'':::::::'':''::::::'':::'::::~~:~~:~~:~~~~~~~~__~___________________"=)))TLLTLTLLLCtL)))))))))cc)ccccccccc))c)))TTTT)TTTTTLT);"";""""""_"_""_"""""""_""______________________~__________1=)L;+)=I;__;cPEZw2t=I";"""";";;;;;"""_"_____~_____~~~~_~_~~~~~
'':''':::::::''::'''':::::::::::~::::~~:::~::~~:_~~~~~_~_~~_________________";=)TTTLLLLLLLLCCT))))))))))c)ccc)cccccc)c))TT)TTTTTTTTT);"""""_""""""____"____"_"___________________________________1=cL;+)=I;_";LZGPO2L=;____"";;;""________~~~~__~__~~~~~~~~~~~~~
:::::''''^'''''':''''':::'''':''::'::::::~::~:~:~~~~:~~~~~~_______________"_"+cTTTLLLLLLLLCCTT))))))))))))cc==cccc)cc))T))))TTTLTL));"_""""""__"__"____________________________~_~__~~~__________I1))_;==+___I1"~^_Vc+___"""";"_____~~~:~~~::::~~~~~~:~~:::~~~~~
:::'''''''''':'::''::::::::::~:::::::~~:~~~~~~::~~~~_~~___~____________"""__"IcTLLLLLCLCCCCL)))))TT)))))ccccccccccc))))T)TTTTTTTLL=;""""_""""_"________________________________~__~~~~_~___~_____1=)L";=1;__"=++'^_=I"_""""""______~~~~~:::~:::~::::::~:~:~~::~_
'''^''^''''^^''':''''':'''::':::::::::::~::::::__~~~~~__~_~~_________________I)TTLLLCCCtCttT))))T)))))))cccccccc)cc))T)))T)TTTTTL+"""_"""______"_____________________________~_~~~_~~~~~~~~______1IcL"+c1;__+=+=+_~+I____"""_____~:~~:::~:::::::::::::~::::~~~:_
'^''''^''':''''::''''''''''''~:'::::::::~:::~::~:~_~_~~_____________________"1)TLLCCCtCtttC))))))))))))))cccccc))))))TTT)TTTTLLL1"_"""""""___"___""________________________~_~~~~~_~~~~~~~~_~____II)T;;c1;"_+=1)I_"=+"_____"____~~~~::::~:::::::::::~::~::~~::::
''''^''''''''':':''''::'::':::::::::::~~:~~:~~~~_~~~__~______""_____________"=)TLCCCtttttVT)))))T)TT))))c)))))c))))TTTTTLTTTTTCI"";"__""_"""_"_______________________~__~_____~~___~~~~~~~_~~~___1c)T"+=1+"ItC)T;+cLCT;_________~~~:~:::::::::::::::::::~::~:::~
''''''''''''^''':''''':'''':::::::':~:::~~:~:::~~:~~________________________"=)TLLCtCtCCCL)T)TT))T)T))))))c)cc))T)TTTTTTTTTLLLI""_"""_"_"_____________________________~___~~~~~~~~~:~~~~~~~:__~~_1c)T"+=1++=LtwV:_TL=1"_____~_~~~~'::::'::::'':::::':::''':::'':
'''^^''''''':''''''':''':'::::::::::~~~::~::~~:~_~_____~__________"_______"";cTLLLCCttttC)TTTTTTTTLTTTT))))))TT)TTTTTLTLTLTLc;""_";""__";"_"_"_"____________________~_~~~~~~~_~~~~~~~_:~_~~~~~~~_cTTT;+=I+"+)Lw2=Ic=I;__"___~~~~::::::::::::::'':::::':'::::''':
''^'''':'^'''^'^'''''''''''':::::::::::::::~~~~_~~_~~~~_~~__________________+)TTLLCCCtttT)TTTTTTTTT))))TT))))))TTTLTTTTLTLT)""_";"___________"____________________~___~~~~~~~~~::~~~:::~~_~~~~~~_IccT"I=1;__I))TI=cc;______~~~:::::::::::'':''::'''':'''^'''''''
'''^^''''''''''''^':'':'''''':'::'':::~:~~~~~:::~~~~:~~~_~_______________"__I)TLLLCCCCtt)TTTTTTTTTTT))))TT))))TTTTLTTLLLLTL+"""____"""____________________________~___~~_~~~~~::::~~~::~~:~~~~~~~+))L"1c="__1=Ic""+c"____~~~~:::'''::'':''':''::':''''''^'''''''
''''''''''''':':::::::::~:::::::::::~~~~~~:::~~:~~~~~~~~~~_________________"=TLLLCCCCCVCTLLLLLLLLLTTTTTTTTTTTTTLLLLLLLTLLC=_""""_"""_____""__""____________________~____~~~~~~:~~~~~:~:~_~::~____I)=c+=c+;_;TTc:`:II___~~~~~''::::::::::::::':''''':'''''''''^''
''''''^^'^^''''::'''''''''':'::~::~::~:::::::::~::~:~~_~~~__~______________")TTLLLCCCtVCTLLLTLLLLLLLTTTTTTTTTTLTLTLLLLLLTL"__"__"__________________________~_______~_~~~_~~~~::~::~::~:~~~~~~_~:~"==c;Ic=+;=ZOOPwt="___~~~::::'':''::':::'''''''''':''''''':''''
'':'''''''^''::':'':''::~:_~~_~~::::::::'::~::::~:~~~~_~____~~_____________+)TLLLCCtttVCLLLLLLLLLLLLLLLLTLLLLLTLLLLLLTLLC1"""_""_";;"_""__"________"_____________~_~_~_~_~~~:~~:~~::~:::~:~~~_~~~"TLC;+)=IcVOOZZVc;"~__~~~:::::''''':'''':::::::::'''':''':'''''
'^'^':'''''::'''''':::~~~~~~~~::~::'::::~:~~:~~~_~:~_~~~___________________ITLTLCCtVtV2tLLLLLLLLLLLCLCLLLLLLLLLLLLLLTTLCt+"""_"_";;""""_"""__"_"___"________~____~__~~~~_~~~~_~~~:::~::~_~~~~~~~~"Ttt1ITc1LE4PwVL1;____~:::::''::'':'':'^:':::::::'':'':'':'''''
''^''''''''''^''''::~::::''':::::''':~:::::::~:~~~~:~~~_~~~~____~__________cTTTLCtttVV2VTLLCCCLLLLLLCLLLLLLLLLLLTLLLTTLLL;"""""_""""_""__"_______________~__~_~~~~:~~~~~_~~:~~~:~~~:::~~~~~~~~~~~_ICtC)LT1+c)==1+;_~_~~~::::''''''''''::':''''''''''''''^'':''''
''''':'''''::~::::''::':::::::::::::::::::~:~~~_~~_:~_:~_~________________;)TTTLLCttV2wZCLLLCLCLLLLLLLCCLLLLLLLLLLLTLLLL2L;""__"""""_"_________________________~_~~~~~~~:::::~:~:~:~::::~:~~~:~~~__1tttCL=;;+I+;"____~~~::':''''''''':'::::''':::::':'::':'':'::
''''':::::~~:'':'^^'''''''':'''~:::::'':::::~::~~::~_~~~_~~:~___~~________I)TTTLLCCCtV2w2CLLLLLLLLTLLCCLLLLLLLLTLTLLLLLCCtVtI_"_________"_____________________~~__~~__~~~~~~:':::~~::::~:::~~~~~____ILtttL=;_";"____~:::::''''^'''''''''''''''''''''''''''''::::
'''::~::~:''''''''''''':''':::::::'':'::::~:::~~~~~~~~~~~~~~_____~_______"=)TTTLLCCtVV22ZLLLLLLCLLLLLLCLLLLLLLTLLLLLLLLLLCCCtL;"____"______________"______________~~~_~~_~~~:::::~:::~::::::~~:~_~___ITttCT1++"_____~:~:':'''''':''''''^'^''^^''^^'''':'''':''''
:~~:'::'''^^'''':''''::''':::'::~::::::~:::::~~~:~~_~~~~__~~_~_______";Ic)TTTTTLLCLCtVV2ZVLCCLCLCCCCLCCCLLLLTLTTLLLLLTLLLTLLCLCc"""""""__""______________________~_~~__~_~~~::::~~~:~:~~:~~~~:~~~~_____;+;;"________~~~:::'''''''''''''^''''''':::'''''^'''''':'
:'''''''''''''':''''::'':'':::::::::~:::~::::::~~~~~~~_~~________;+I=TC2ZZ))TTTLLLLCttt2VwtLCCCLCCLCCCLLLLLTLTTLTLLTLTTTTTLLLLTLT"__""________________________~__~~_~~~~_~~~~~~:~::~~~::::~:~~~::~~~________________~::::'''''^''''''''''''''^'^^^'''^''^'''''^'
'''''''''^::':''''''''''::''::::~::::::::~:~~_:__~~~~~______";I11TVwwPPPOw)TTTTTLLLCCttV22ZVLCtCCttCCCCLLLLLLLLLLLTTTLTTLLTTLTTTLL;"_""_____________________________~~~~~~~~~~~~_~~:~~~:~~::::~~~~_____"_____"____~~~:::::'''^'''''''''''''''''''^^^'^''''''''''
'''':'::~::''''':':'''::':''::::::::::~~~~~:~~~~~~_~~____"+=TCVC)tPGGGZwwC)TTTTTTLLLLCtV22wZ2LtttttttCLLCLLLLLLLLLTTTLLTLLTLTLTTLLLI________________________~____~~_~:~~_~~:::::~:::::~':::::~~~~~~_~______________~~~:::'''''''''^'::'^'''''^'^^''^''^'^^''''^'
''':::'':'''''''::'''''':'::::::~:':::::~:~~:~~~~~__~_"I=cLVZZP2CtwZOP2CCT)TTTTTTTLLLLCVV2wZPPtttVtttCCCCCCLLLLLLTLTLLTTTTLLTLTTLLLT"__"____________________~_~~~~~~___~~~~:~::::~~::~::'::::~:~~~~________________~~:::^'''''''''^'''''''''^^^''''^^'^'^^^^^'''
:::::::''':::''::::::::::''''::::::::~~~~~~~~__~~_;+=LVwPZZOOOG2LCVtC)1++)TTTTTTLTTLLLCt22ZPPPOZVtVVttCCCCCCLLLLLLLLLLLLLTTTLLLLLLLL)_"______________________~_~_~_~~~~~~~~~~~:::::::':::'::':~:~~~_______________~~~~~:'''''^''''^''''^^'^'^''''^^''^''^^'''^'^
'''''''':''''''''^:'':''''''::::':::::::::~___+1cCVwwOEEGOPZPPwC=I+"____+)T)))TT))T)TLLtt22wPPOOO2VVtttttCCCCLLLLTLLTLTTTTTTTLLTTTTLC="____________~______~~~__~~~~~~:~:~~::::::::::::::'::::::::~~~~___________~~~~::''^'''^^'^^^^'^'^'^''''^'^^^^^'^^'^^^^^^''
:':':':::'':':':~''::'::::::::::::~::::~__;=)LtPOOPOPPOGOPVL)I+"___~____+TTTTTTTTT)TTLCtVVV2ZPPPPPPwVVVtCttCCCLLTLLLTTLTTTTTLLLLLLLLTL;_____________~__________~~~~~~:::~::::~::::::::'::::::::~~~~____________~~~~~:::::''''^''^^^''^'^^''''^''''^^'^^^'^^^^^^'
'':::'':::'':':::'::'::::::::'::::~::~_+1TC2wwwOGEGPZww2tT=+"___________I)TTTTTT))TTTLCCtt22ZZPPOOPtLVtVCCCCCCCLLLLLLLTLLTTTTTTLLLLLLLc_______________~__~~_~_~~~~_~~~~::::~:~::::'::::':::::':~~~~~~__________~~~~~~:::'''''''''^''''''^'^^^''^^'^^^'^''^'^^^^^
:''''''':'::'''':':'':::'':'::::~__+=)tV2PPGGZwZZPZVTc1;___~~___:~______=)T)))))T)))TLLCLtV222wPZZwL"=VtVtCCCLLLLLLTTTTTTTTTTTLLTTLTLLT;____________~__~______~~~~~~~:::~::::::::::':'':':'':':::~~~~________~__~~~::::''''':'^'^'^':'^'''^'^^'^''^^^^''^^^^^^''
:':'':::':''':':::'''':::::~__;I=)VwZZPPOPPGO2ttL=I;___~_~_____~________1T)TTTTTT)))TTLCCtV2VVwZPZZL;;+VVVVtCCCCLLLLLLTLLLTTLLLLLLLLLLLT"____________~~~_~__~~~~~~_~~~~~::::::::::'':'''':':::::::~~~_~~~_~_~_~~~~::::::''''''^'''^''^''^^''''''^'^^^^^^^^^^^^^^
:'''':'':::''':':::::::~__"1TLtwwPOGGGPwZZVL)1+"___~_~~~~~_~____~______"=)TTTTTT)))))TLLLCCVtV2wwwwT;;"IVttttCCLLLLLLLTTTTTTLCLLTLTLLLLLT"___________~~~~~~~__~~~~:::~::~::':'::::::''''''''::'::~:~~~~~~~~_~~~~::~::':'^'''''^^''^^'^'^'^^^^^^^^^^^'^'^^^^^^^^^
:'''::':~:::::::':'::_"I==ICZPZPZw2wZPwtLL1"_~__~__~~~~~_~~~~____~______=TTTT))))))))TLLLCttttVwww2);;;"=VVttCLLCLLLLTTLTTTTLCLLLLLTTLLTC1___~_________~_~~~~~~~~::::::::::::''':::'::''':''::::::::~~:~~~_~::~~:::::'::''^'''''''^''^'^''^^^^'^^^'^^^'^^^'^^^^^
':::::::'':::~::~__+)tV2wLctZPGGZVttLcI"___~_____~~~_~~____~____________1T)TTTTT))))TLLCtttttVV2wwwc;;"""1VttLLCCLLLLLTLLLLLLTLLLLCLLCLLL)________~~~~_~__~~~~~~~~~:::::::::::'':'''':'':''::::'::::~:~~:~~::~::~:::::''''''^'''''^'''''^'^''''''''^^''^^^^^^^^^
'''::'''::::__;cLVVtZOPOPt1LVVVt)I;__~::~~~~~:~__~~~~~~~~~____~~__~_____I)TTTTT)))T))LLCLCCCCtt22wV1++;;+;1VttVtCCCLLLLLTTTTLLTTLLLLLLLLLC1_~____~____~~_~~~~~~::~:::~:::::::':'':''''''':::''::'''::::::::::''::::'''''^''^^''^^''^''^''''^'^''^^''^^^^^^^^^^'^
''::~:~~_;1)C2POOPPPPZZOZLI==;__~::::~~~_~~~~__~__~_~_~~~~_~~___________+TTTTTTT)T))TLLCCCCCtCtV22V1;;;+;;+=VCtVtCCCLLLLLTTTLTLLLLCLCLLLLL)___________~__~~~~~:~~~~::~::'::::::::''::'''''':''':'':':~::::::::::::''''''^''^''''''':''''^''^'^^^''^'''^^^^^'^^^^
~:::_;cCVVPPPGGEEGwww2L)+"~~::'::::::::~~~::~~~~~~~~~~~~_~__~___________;)T))))TT)T))TLLLCCtCtttV2LI11I++++;=LVttCCCCLLTTTTTTLLTLLLCCCCLLLL+____~~_~~~~~_~~~:~~::::::::::::::''':'''''''''''''''''''::::':::''::''''''''^^'''''''^^''''''''''^'^'^^''^^^^^^^^^''
~_"ITLwGEOGOwwZPOP2L)1"_::::::::::'::::~_~~~~~~~~~~~___~~~~______~~____";)TTTTTTT)T))TLLLLLLCtttV2LI=====1II+1tttttCCLLLTTTTTLLTLLLTLTLTTTTI_~~~~~_~_~~__~~~~~:::::::::':::':''::'''''''^''''''''''''''':'':'':::''''''''''''^'^''^'^^^^'''''''''^^^''''^^'''^^'
VwPOZZZZOGEPttVC=;__~~::::':':::~:~~~:~~~~~~___~~~_~~~~______~_~_______""=TTTLTTT))TTTLLLLLCtCtVVVT=)))c=)cc===CVVVVttLLLLLLLCLTLLLLLTLLLLT)____~_____~~_~~~~~~~::::::::::::::'':''::::''^':''''''''':''':::''''''''''''^'''''''^:':'''^'''''''^^^^^'''''''''^''
GOPEOwww22t)1__~::::''':'::''::~~:::~:::~~~~~~~~~~~~~~~~~~__~_~~________;=TTTTTT))T))TTLLLLLLLttVVc=cc=cccc=ccc)CVVtttCCCCLLLLLTTLLLTLLLCLLL;_~~~__~~~~~~~~:~~~::::::::':'::'''^''''''''^'''^''^''^'':''':::'^::''''''^'^''''^'^''^'''''''''''''^''''^^^^^^^^'^^
OwwOZCTc+"_~::::~:':::::~::::'::~:::~:~:~~_~__~~~~~_~_~___~_______"______1)TTLTTTT))TTLLLLLCCCtVVL==cccc=cccc)cccLVVVttCCLLLLLLLLLLLLLLLLTLL=____~_~~~~~_~~~~~:~:::::::'''::::':''''''''''''''''^'''''''''':''''''^'^'^''^'''^'''^'''''^^''''''''''''^''^^''''''
Z2VtcI"_~~:~::::::'::~::::::::::::::~~~~~~~~~_~_~~~_~~___~~_______"_____"1TLLLTTTTT))LLLLLCLCCttVL==cc===c=c)))ccc)t2tttCCCLLLLLLLLLLLLLLTLL);______~~_~~~::~:::::~:::::'':':''::''^''^^'''''''''''''^^'^''''^''^^^'''^''^'''^^'^^^'''''^'^'^''^''^'^'''^^^'^^''
1"_~~~:::::::::::::''::::::::::'::::~::~~~~~~:~~~~_~~__~~~___________~___I)TTTTTT))))TTLLLLLLCttV)11=============ccct2VVttCLLLLLTTTTLLLLLLTLLI_________~~~~~~~::::'::::''''''':''''^^^^^^''''^^'^'^^'^^^'^'^'^^^'^^^^^^'^^^^^^^^^'^'^^'^'^^''^^^'^^^^^^^^^^'^''^
~~~::~:~:~::::::::''::::::::::::::::::~:~~~~~____~__~______~_~___________+)TLTTTTTT))TTLLLLLCCtVC1===c=======cc=cc=ccL2VVVttCLLLLLLLLLLLLLLCT)I;;"_________~~~~~~~~::::::::''''''''''''''^^^^'''^':'''^'^''''''''^^^''^'^'^'^^'^'^^'''''^^'''^''''''^'^''''^'^''
::::::::~:::'::::::::::::::::~::::::~~~~~:~~~~_~_~______~________~______"+)TTTLTT)T))TTLLLLLLLttC=1=======cc======cc==)VVVttLLLLLTTTLLLLLLLLLL=IIII++;;""_____~~~~:::~::::::'^''''''''''^''^'''''^^'''^^^''^'^'^'^^^^''^^^^^^'^^''^''^'''''''^^'^^'''':^^^^'^^''
:::::::~~::::::::::::::':::::~::~:~~::~~~~:~~~________~____~~_________"";I)TTTTTTTTTTTTLLCLLCttV)=1==========1=========)VVVtCCCLLTLLLLLLLLLLT))IIIIII+++++;;""____::::::::::''':'':''''''''''''''''''^''''''^^^^^^^^^^^^^^'^'^^'''^'''''^'^^'^'''''''^^^^^'''^''
:~~~~~:~:~~::~~:~:::::::~~::::~~~~~:~__~~~_______________________"";++III1)TTTTTTTTTTLTLLLLCCtCtccccc=====ccc=c=c=)c===c=LVVVttCLLLLLLLLLLLLCLTII1IIIIII+IIII+I++;;""___~~::::::::::::::'::':':''':'''^''''''^^^^^^^^^'^'^''''':''''^'''^'''''''''''''''''''''''
~:~::~~:::::::::::~:::'':::::::~~~:~~~~_____~~~~___~__~_~~____";+I+III+IIITTTTTTT)T)TTTLLLLLLtVt==========1===============)VVVtCLLLLLLLLLLLLLLT=+IIII+I+++++++++++;++;+;;""____~:::'::::'':':':'''^''^'^^^^'^^^^^^''''''^''^'^'^^'^''''''''''^''^'^'''''^'''''::
~~~:~~~~:::::~~~:::::::::::~:::~~~_~~___~~~~_________~____"";+II+I++++IIIITLLLTTTTTTTLTTLLLLCtVT=====11=1========c==cc=====ctVVtCLLLLLLLLLLLTLL)IIIII+I+II+++++++++++;;;;++;;;;;"_____~~:::::''''':::''''''':''''''''''''''^'^''''^'''''^''''''^^'^^''''''''''::
~~::::::~:::::::~:~~::::::::~::~~~__:~::~_~~~:~_~_____";";++++++++++++++II)))TTTT)T))TTLLLLLLCC=111111=1c=======c==========1=tVVtCLLLLLLLTLLLTLTII++II+I++++++++;+++++;;++++;;;;+;;;";;;;""____~~:::''::::''::'''''''''''''''''''''^'''''^'''^''''''''''':''''''
~:::~:~:~:::::::::~~::::::::~~~~~~:::::~~~~~_~_______;+I+++++++;++++++++++=)))T)T)T))TTTTLLLLCC1==11====c=c==11=====1=========CVttLLLLLLLLLLLLCL=+++I+I++++++++;+;;;+++;+;;;;;;;+++++;;;;++;;;;"_"__~~~::::''':::::'''''''''''''''^'''''''''''''''^'''^'''''''''
::~~~~~~:~~:~:::~::~~~~~_~_~~~~~~~~::~~~~______";++++II++++++++++++++III+I=TTTTTT))TTTTTTLLCttt1========1======================tVtCLCLLLLLLTLLLLc++III++++++++++;;;++;;;;;;";;;;;;;;;;;;+++++++++++;+;"____~~:::::::''''''':'':'''''''''^':''':''''''''':::::'::
~~:~~:::~~:::~::::::~~_~~~:::~::~~:~:~~~____"";+++I++++++++++++++++I++I+II1)TTTTT))))TTT)LLCtt)=====cc=))c==ccc======1=11111===cVtLCCLLLLLTLLTLTLVVTII+++++++++++;;;;;;;+;;;;";";;;;;;;;;;;;;+;;;+++++++++;;"___~~~~~:::::::''''''''''''''''''''''''''''''::::::
~:~~~~:~~~~:~~~::~~~~~~:~~~~~:~__~_~_____";++++++++I+I++++1+I++II+I+IIIIII1TTLTT)))))TTTLCCCttc==1==c===11==1==c=======1===1====L2VtCLCLLTTLLLLLLCCtt=+I+++++++++++;++;+;;;;;;;+;;;;;;;++;;;;;;;+++;;;;+;;;;++;;;""""___~::::::::'''::::::::::::::''::'':'::::::
~~~~~~~~~~~~~~~~_~:~:~~:~~~~~~~_______";;+++++++++++++++++I+;+++++++II+++IIcTLTT))))))TTTTTLtCc=========1======1=======1=11111==cVVtLCCLLLLLLLLLLCCtVC1+++++++++++++++++;;;;;;+++;;+;;;;++;;;;++;;;;;;++;;;+++;+;;;;;;;""____~~:::::::::::::::::::~::'::'':'::::
~~:~~_~:_~~__~~~_~~~~:~~_~:~______";;+++++++++++++++;;++++++++;+++++I++III+=LTTT))))))TTTTLCtCcccc=c====cc=1===111c=1=1111111=111LVVtCLLLLLLLLTTTTLCttL1++++++++++;;+;+;;;;;++++;++;+;;;;+;;;;;+;;;;;;;;;;;;;;;+;+++;;+;;+++;;;"""___~:~~::::':~~~~:~~:::::::::~
~~~~~~__~~~::~~~~~~_~~~~~____"";++++++I+++++++++++++++++++I+I+++IIIIIIIIII1=TLTT)))))TTTLTLCtT==ccccc====ccc=======c=c=======1==1cVVtCLLLLLLLLLLLLLtttC)I+++++++++++++++;;+;+++++++++;+;++;;;;;+;;;;;;;;;;;;;;;;;;;;;+;;+;++++++++I+++;;;"__:::::::::::~::::::::
_~___~~~~~:~:~:::::~~~~_~_"";++++++;;;++++;;;;;++;+;++++++++;++++++;+++++++I)TT))))))))))TTLC)11=========1111==1=1=1111111III1I111TVtCLLLLLTTTTTTTLCtCLT1+++++++++;;;;;;;;;;;;;;;;;;;;;;;;;;;;";;;;;;;;;;;;;;;;;;;;;;;;;;;;;;+;;;;;++++++++++""""__~~~:::::::~~:
___~~~::~~~~::::::~:___""";+;+;+++;;;++;+++++++++++++++++++++++++++I++I+I+II)TT))))))cc)TTLCC)====1=c====111111=1111111111111=1111cVVtCLLLLLLLLLLLLLtCLT=++I++++++;++;;;+;;;;;;;;;+;;;;;;;;;++;;;;;;;;;;;;;;;;;+;;+;;;;;";+;;;;+;++++++++++++++++++""___~~_~~~~~
___~~~______~_~~___";++++++++++I++++++++++++++++++++++++++++++I+I+++IIII+III=LLT))))))))TTLCt===c===cc===cc============1====111=11)V2VCLLCLLLLTLLLLLttLL)I++++++I++++;;++;;;;;;+;;;;;;;;;++++;++++++;+;+;++++++++;++;;+++;++++++++++++++++++I+++++++++I+I+++;"""
inserted by FC2 system