# Original solution
import base64
import subprocess


exe_bin = "e??420s#R400000000000{}h%0RR91&<Owl00000KmY&$00000s2czP0000000000Kma%Z2>?I<9RM5v1^@s61ONa4KmY&$00000KmY&$00000KmY&$00000_yGU_00000_yGU_000002mk;8000000{{R31ONa4I066w00000I066w00000I066w000008~^|S000008~^|S000000RR91000000RR911poj5000000000000000000000000000000*bD#w00000*bD#w00000001BW000000RR911^@s6Xbk`W00000Xbm6$00000Xbm6$00000r~&{0000007zF?T00000001BW000000ssI21^@s6fDHfu00000fDIr300000fDIr30000000IC20000000IC2000002mk;8000001ONa41ONa4R004100000R004100000R004100000L;wH)00000L;wH)000001ONa400000P~~)F1ONa4YzqJY00000YzqJY00000YzqJY00000L;wH)00000L;wH)000001ONa400000QRQ@G1^@s6000000000000000000000000000000000000000000000000005C8xG00000Qss1H1ONa4Xbk`W00000Xbm6$00000Xbm6$00000m;wL*00000m;wL*000000RR9100000FKlUIHZ(76WG!rIZgqGqcsMpKHZ(4CZ!R(b1ONa45C8xG0RR91M^04$000000{{R30ssI2000001ONa46aWAK0{{R3M^04$66o;Pv0SFPAbMN%YxTqg6IY|L0ssI24gdfE0RR911^@s6000mI0RRL54gdfE000006qpP{bCw4J000000000000000000000000000000fdBvi5&!@I00000000000000000000LID5(A^-pY00000000000000000000E&%`l5&!@I00000000000000000000RR9105&!@I00000000000000000000H30ws5&!@I000000000000000000009RUCU5&!@I00000000000000000000qW}N^5&!@I00000000000000000000@c;k-5&!@I000000000000000000009{>OVAOHXW00000000000000000000Q2_t|5&!@I000000000000000000005C8xGAOHXW00000000000000000000I{*LxAOHXW00000000000000000000X#fBK5&!@I000000000000000000002>}2A5datfKoB4R000005CH%H00000U;qFB5datfU=bhy000007y$qP000000BmVub97{5D=RK@Z!R_fUtec!Z*E_6bYXIIUta)UNmNZ=WMy(?XK8bEWpY$aLu_wuWmI8eY-IpnNmNZ=a%E>}b97~LR82!{Z*FB&VPb4$0AE^8Q)zN@MN(-1Us_XiGh=CP0AE^8Q*=0KZ*yN_VRL0PNp5L$L@`Bn0AE^8Q*=0KZ*yN_VRL0MHFJ4xV_$b^bZB35bYy97MPdM7T2pi}HeX+Fb98cLVQpV&ZgXXFbV*}VbTKhwXkl_+baG*7baP2#MMY9mbTKnxVRLC?UvG1Ca%Ev{NmO4{FkeMeHeXOnQ!`&|0AE^8Q*=0KZ*yN_VRL0PNp5L$Lor2m0AE^DbTngcb#wr1X<}n8b8jv-0AF8obYWv_Ut?%%UuI!xYyfj~a%^R80AF8Ycwt{*bY*yHbO2vpV|Za-W@&C=Y-xIB0AF8hX<}nvb97;HbYE>@X>I^VOi4mRUotK<07pzoLPK9NE;24P07pzoLPJ<sUo$Q=E;#^4Oi4mRSXf^(E;IlD000620{{a60ssR51ONp90ssI20{{R3000620ssO4000000RRF369E7K5C8xGFaQ7m6lrM<000C4V*vmF5C8xGbsA|200093Z2<rP000000RRF30RR915C8xG00000iGL{q000F5c>w?b5C8xGbSaVu00062hXDWp00000Xbm6$000002mk;800000&<X$m00000a19^;000002mk;800000pa}o~00000cnu%`000002mk;800000kO}|*000002oN9u000002mk;8000002oN9u00000&<`L0000001^@s60ssI20000000000*bg88000001^@s62><{90000000000;13`G000001^@s63IG5A0000000000=no(O000001^@s63jhEB0000000000@DCsW000001^@s63;+NC0000000000_zxfe000001^@s64FCWD0000000000KoB4R000001poj54gdfE0000000000U=bhy000001poj54*&oF0000000000m=7QT000002LJ#70RR910000000000pbsDb000002LJ#70{{R30000000000s1G0j000002LJ#71ONa40000000000un!;r000002LJ#71poj50000000000xDOxz000002LJ#71^@s60000000000zz-k*000002LJ#72LJ#70000000000$PXX@000002LJ#72mk;80000000000NQ3MMNQ(u%2Ot1Qg}`(I|IkQ-#0bLx0000000000|20AfAOQa*L<b-M4<A4P|0O~PAOL6p0002#;Q#;s|0OyHAOL6q0002#(EtDc|0Oa9AOL6r0002#!2kdM|0OC1AOL6s0002#u>b%6|0N;^AOL6t0002#p#T5>|0Nm+AOL6u0002#kpKVx|0NO!AOL6v0002#fdBvh|0N0sAOL2N0000000000Q!)QYjU9~w002mX>>y-Fiv%So0000;i9{qAF~I0u|Ns9;jdUaoNR2&V2p|AR#|1tKAOHXW008J=|Ns9;jdUasNQuYjRR90~NR4zP6iA83=tuwm|BFN<6iAIVFaiJo53fWd5IaO93`h@5-bjhx=okP0|45BJ@CG0NNQuHoiQec%|Ns9;jdUanNR2(&1|R^s0RR91#zZ6w3g{~T|NlsfOe7d&NHYv2C;$KebqGj<#2_)iTf^x6{{R0E9{^@94<Cd800000NR2(x2p|ARgX{?C0RR90NQ*r|1|R@PjTK4;AOJ{>HM9sI07!$x2<fu^|Nmx?G3`l-(OyW2;z)z!@K97tjRk4}002mh4f6m107#8J-2VUn{}tv1AOQ3aA4C8ENR2%S1|R@cNR0&n1|R@PIrvD4<#ZWHiv_v`AOJ{(z;q2=|KMgW4<Cd800000UBeF_KmcYg4<Cd800000NR2(o1t0)OjWxmrAOKZJDgH=_<w(K)14xPRNWthoNCC!3(f)K8NQ(u51t0)Og}`(SUH{-_4<Cd800000UBeF_KmcYg4<Cd800000fIZ;{AOHY$FGzzuF9jd~098nd<#Y^4i#=KeAOPqM{{R2zNdN!;#s#?tAOHbf!w(;T00000^TTEjA4C8ERY-~DUFl~3|NmwWA4C8EL03UmNr~4%RY6otjU{#hAOKZJjV*oxAOKTAiTz25_Dm_|NQ3MMNWuLB=nwt>|44=HbRaR?4<Cd800000Oo{qTiS|T^??L|*+(?7N0Z2LBb?Qii#0XnmL0myyL0&;$!;oe!4<Cd800000^TPlDNQ3MMNQ1-(!vFvP0RRF3PHzBNWpe-k0UHB5KmY&$2LJ#7)cpVdi~s-tRQ><|v;Y7AWc~mD%m4rYH2(kp@Bjb+Wd8sETmS$7bpQYV3;_TD<p2NwQ~>}06aWAK000000eVsZ0eBDr8w>{skO2n}6aWAK8~^|S0RI2~D*ylh00000000006aWAK000000eVsZ0eBDr8w>{skO2SyBme*a8~^|SK>YvzfB*mh01gmF4j4)g3wH>B06!W#Dl;S^000006aWAKL;wH)nEe0$2mk;80000000000AOHXWTmS$7ko^Du!vFvP06`8Ag91$sFaoR!4iG~Q2tf+~7ytkOfB*mhJpKRwE&u=k080)KUJeKV00000L;wH)oB#j-VE+IAWdHyG074EBj{-st7>)x)4j_#LLJla51xOAsh6YFuID-dG4nT4aI6)3DK@KQF4j@7f7(xyZLJkN35C8xG<NyEwi2nco0ssI20000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000&<X$m00000pa}o~00000kO}|*000000RR91000000RR91000000RR910000069E7K000003;+NC00000AP4{e000004FCWD00000R0{wA0000082|tP00000Xbm6$000008vp<R000005C8xG000008UO$Q00000cnu%`000008~^|S000002mk;800000_5S~F00000m;wL*000001poj500000Km-5)000001^@s600000zybgO000003IG5A00000lK}t#000003jhEB000007ytkO000006#xJL0000000000000000{{R300000fDa%5000000ssI200000r~m)}000006aWAK000002LJ#7000007XSbN00000cn1Ig000002LJ#700000SOx$9000002mk;800000AOQdX000002><{9000007ytkO000009smFU000002mk;800000`~UxM000000RR9900000{{R1P00000_yqs}00000|NsAQ000000ssI200000@c;jB00000)CB+l00000`TzfK000001ONa4000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000fDIr30000000000000000000000000RtNw90000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open("./kyomu", 'wb').write(base64.b85decode(exe_bin))
subprocess.run(["chmod +x ./kyomu"], shell=True)
subprocess.run(["./kyomu"], shell=True)

# Optimized solution
# This code is generated by [Atcoder_base64](https://github.com/kyomukyomupurin/AtCoder_base64)
import base64
import subprocess
import zlib


exe_bin = "c%02yeQaCR6~DIg;WUZkrY#MHt`<wT7M9nf`5>hWvy-@e0Vgeu%XfS0*iQ3S$L{Rsl2jUm1sGNdi^hcd2a}LMs7R9r6PpIoL`oP8X@7)?2__gTQ<)q#v>;Yiwl&_l@7?qK-t~I}A^zBv>~qiWo^$TK=YF4ePdKv2?Q#)J9&$Zl+)|y+2RVM`3PS|2UQ!4Do5_`=2KXwIoJcRatki4NqwDp$bzY=b5-W9?Xf<(8Z#7scApt{=wRNIVM<*Hs7J7!)+fr@Sb922Jt~bNwkrJ+l6#G}je^HK$bdXqS6{q{(R}(Css@HjuI_cd6dNt(pCqJhLczsTOInCRP6vtslN*U|v+L21MrId7js%@&br>&<;%4MXTTATb_cJIhRO`eT6x{8&r=NKz*F0Q=!?43_NA2@l(g<}_9u3C4?6VEbPA1RL;SaiEU)5mSBKix2pd$bl!R-}93*KC9LgTbq8aLHvaf6&2Bw}bp<2mA>KJ0CgVTL{iTYr4t7zTZK9w*#&?)LRGk*OC?z^y^xFKHx`)jvra8<1IK5U>@YuMEsg-*x2_FN{>!v(ln>WvMQy74n>D)BAHDdRdQ-F8yy}<WzxxLY%G=3%j`>T9~o7$x$pr6vZHEeTuEz~+N)%8bS#!jb`7N!b+99RLclw^bJOWKy-QIipbZHn6CTq{bo5Y~$*I|7Y?3PJTr#T;#R2VzPsFlR&BhcpHxv(t4*=E)c9b|u4@GITorXty=>8i=J88<U9RqqhM%Au(Ca*G&#L*exhxjoXpEyRxV@isE%~TTlLgQ008dH-~iprUBB^^sCC!z0@>2n88#-QhWBSZZIbf?s1<aSEkdj8g1X{XdB?J{$0P~5P#JlcO1?3Qeic!-X>`6_e)UFXv0O*{P7D@r3<nQ@NgHz{>YYm$#MlXsEwzEQYmyPNIA(_CKN{zEUb|9vix`v>laOKWs`T)-da=ggFV&vSXN--;u@)TGlIQr=fsddq~@necNae2ob&n(%rPzGA`~O!!3;-e|&cy|ClMXTov4FucixpXPRINqJ9Y>2VY8G2v%Sc$Eo%#)O;C#b26m^SQ8K!fQ?VZ%nw?gv+yk^U9~He^nbG^8E{{yR;<FzU*Bz%1hn-P*mDF2>(r6f{<hU1S?uTSAw+lI>xguE-z{PPR6q#TVBxks~OL_y8MjBU&VOV#pTB}eiP$a*OuoszM1i?OUpAFzXtg6d2G*UM@gRBJm=P09!SWis<v)p-6#yUwsb5M4}pd}r?xi8bA2%{^y$^=>+AHM7h}B4FBe`dMme*dF?)eIH3<2+?sl-;^wYss|L#FB(iC}DF8ryuQ4{W4sR4t9m*m2`#V}W|2lx*FzrY;u%3y2#n&Q>0=v1V&B_Ve<XpPHz!KZ<ag*z6DmsU%qrY&S#YT9z2?*F;I-?4VWFcgWV*%xBf%x$<qBi+wwr7wGze+H`K^Bo@!6<$9q7yc~Io?qD?jm%Yl+r_LjeykgN2c$|H{!$$v|7hAWs6lmL=%74T?P3OZU6c#&tCz!&zfi3YdE=qdxpI3BEwWLzwC}ZQtsyT}Gc(&)L0>+*>X8d8^4a3IWY;V5>#J%D7`&GoY+weR?9KGO2jfZdJLK8E9iRXvp*;=I?c0GXHbV1@GIZgU>gPeu#nfk*-p7mMT7Q`Mq2+Oq(D~3Up__*aZ-x$rz!zIjxV5gf-3@d!RJb%$_$0FZeQl1Pz2qr2T>=N+|DhV_cpKXjDf}x^_++r~_fTp5JM!$JOWyUz{0Ge8cN_}c89Ed?9HNW!<@SHP$kz;CC2Zdu$&lNUImln(*&XC-?2Z4FN)G{zLY2<}O#uBZ&@SlU3gdy^2~>riG{6X+2O4$h_a>HHCl3(Ul;3qlL#=n-RqJQCc2@?yYfS6cUY?LvE+2$;Xb$xG_xM_FXsW-<J43#;Y4_EgtyiHwyK9~XIrF~2)(mUkJmA`H5c2tF-NU|i_fOXN`~yC3s2*+$FrM)HCiG2WGB^7Chkd#gX7e%l9f9^H8PM<Z|G?evYkAlc_66pu`hD9Ts+N8257fxM-r3q=Uoh+I4f)zbzHR-!0LX!SKiFbt&w2Pg2zDGVgZ~E!&p$lx@O(4BYs_>V&*0e;;LgW0C&~}2%Q=tdEk4umoZiGKp0D_x!m+%tTFNkr_j^1;g8Y!dvtxmm<JtKLZy%nSEu3y3)`Vx+3_o9RjLvY1^Apdajo98=D}HN@wcP<;Kc4Ye|5u1r?%yT7e=ZKKa{eOkXo>UKt`*L|!OK78y!p)iGL!L+6w=MS1LK^Y;Pe4bALaBZPJdxuoL?Z}y=w2kz;%Ib2gmYhH6OTE>XzEuI`bOWad$_r)ZVpSM?a5E4|u)TW>K=6Y19_?5Y-m1GUlfhuQukT6|XVouNAK~#?^{@jrm~3>x_A4#n%|~(~8#{>(q)jkf1HzNEU2yA6c@+n~ZgD#r@=nExy)>8(8sX@{BFM&e%t+_<Cdiu;LqR=dXucW~_HB4y)U5hnL@*R{Zh`j4k^r@=-~|**@R~zv2EWaeT9;(?X`31BO0J-*B*VEw^KNBtY85@t}Z5I6g1nW4zueq2BLk`AUDD=603@J5OrzmE+>ne*MnTOx|b^OYG%e*ZwQ#$$8CA<@kQ6{jaNN|0>7DcCK|XJC*a{>)N|<Bk>F4KJ8|Ai^_Q-X>p12JjdnT=MWD`ImCG$bdYD~N3&_&;S1+6R<C=bu|HyZ+QH6W-3+f>r)M4Hzw74p@_CDQx3?YSU)1C)_nCk4c8dP=xb5v6aofjv?sDtnBKrSRCIj*_%~t$Aw~mYT&O6lmbKc)`e4Zyc{%f~=oa#L;zn}XPxBHLW_VK7%kA1yg^Vr+(cEI;J*dZ(=BgNx{?v3p04@D@=<;Uod9;sn5phz#JN=8X5Dv4*+oSGjWm*S)x0;B3Ajk8c!j!>G&(4(o$SS&>oY9^bbvHTQ?XC{xQl4>#`UE8y(*ItN)ixe8mW@FPdnO3vYWIP+2OwvSta&j6}OdMrRv4~Q-=RjyUOv59CEJ8>3jvS<6nS=7+0YV3F8wm{$4M3SiIbj8~5S8JFeS7wdhNCnZ>W_rMYBCX1V}uUv)536Rn$IN@pB<|U2F-yiYh;X<@$i=(NwZ?$s$7On#L@{%4AIW09(xnjt<k!2DbtD$51_}s%y^=uani1G7*T9B^C!BTj^%Qgw+}~(+FDF8p37_F_rIgEWmz`Ki~y{y#d4HVbY*1}*fG*;6V<g=Mx@;Iq#7Fos%CXMfjK1&CXW*-ol%ogsDG$UjUDCO(R5xK%PXlwo01?JHxbKC5GgU8275YHvwF#iWHzT{(iVn7SvHx9F+rX?o>Ezr;6j#_j%FYOGYS4RUrE`FHtnV41Yd#^iENqERrS@QYhWH~h)pVS$Y|;?yhMV1U=kLr-5&G>5_=c2EfV)nr|)f;Tmt`9qQAvZU;LgG5ah+{cZZ;l_k5(SpP|p<1)soM4E4qDQrkF=*Ld;zJVNxhD(d6A0qG3yFuU%%O#1k)yqQ?PVd47%=_7)}ME@No`dbtA@g0IRAhcijtVoU#{q2f8zE_YQA?5bFNoD^}65Xe$kMA0!_?{O1hyA~g>-TdW-#<w4J<s$nv(bN;n7`$f;~7Zt-H%Be|AL^8?<u4+g1ld#KN9ru-Gx;2msg-a7WDC+i1d5HJJfGwweNpseY_tctrO(M{y$Bu>lg3ANX6%zsQ;{>@AO^SN&iJbAK#Biw+Rzo^yh0t|1N^@pz?QSofrKj`v3Pt|9*n{`2Lt`w69Ope~;+CH{wyocYF@;j@1Zy*e>=ybCJq;)(rosGxHhse<0`^_iMkk9#J3D3dd02xVLk~pfLY}g8l_wzZked{p|v77nih)uLimP3U?ekXWB^R`mZy!-JII_!dHbtasOQFp#LNfaIOltsQ+L3Oq3M"

open("./kyomu", 'wb').write(zlib.decompress(base64.b85decode(exe_bin)))
subprocess.run(["chmod +x ./kyomu"], shell=True)
subprocess.run(["./kyomu"], shell=True)