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


exe_bin = "c%1E9eRLaDc7OVCEayW~f)kviY(!S%#6W}<=feiPShkfsfgDV%uz@9+$dVkZktHLIVw+M3E5b6zh<aPjE@!uNIfrw0vxh@rPg@GKfE|Z~rOVbpOKDly94JJ_p_s4>frO~{&b%kjjAxc@yQhEU`AB!}Z|=SCz5Cv~Z|3Rx&R}?p)nXyM*vK~sa(mng-^%bYUquA4CQ<|6Un3WhdBEFMa(a5&qNR>XJ&InFRpIsYkBF99RJ4kim;0A#DIuPU9=6qU5koKXXy|EH@182Ho|Wk}F})@x&#9Z~amxE=XP*ee^|XU%sh!cT_ry3}&s?DJdU^}dQm%Ic=*=U)e__K*wzK-o{BoSNms36tSEQ0Xn>JjLimyv0)A^xwLrt63ZQ9_=Wqj-9Ho2MX)@?gvc^q%6s?D_w!}}X8Kl$R(M{oW5sShV!d8>AEMe8faet@#e$n3bGhb^GVhqd;>h3&cTRdbVb$}#vXF~Col;8kF0wE_OI#aMoaiJj9X^2bf&ziTFMg14LCH75A?O>mzHzQ?4Ue`$iRB7CK2%P|xCwN_)?ZDQvt6Z~<L_B;;tE+)%Kt4GmtvkCiSqTqWjR`5DLkzpR^#CYto%W&>)B7(5DKa&=6Vl*oX0ue%yP9dJiCiW(CVj>&qY)@s<iAc03l~C>(-?@2PcQTs`ZcoaWVslS4my8L?OfD4b7XAKMUo<O-*=SM(AQ;>jOC_S&Alz9mgfcn&h*427lS$=*Xr)_hj3v{Gxh60qfXT#$P&z4g_=Edp0sm$}5c{&3LAVzeqN!9ShBxA=uKhYa|Hj;KIwlMz#Xjh1JedjhC=#1upr6h(3OBCzuZM0$<HJG>?CfhyX9lqvVein8Fp$XRGU;e4DGm$!8<e^?2?De_n~3%c$#gD}6%Bj39k52l8B9795h4vjuzQoxbzOI(kOFJz!G5EDw)1{&h-LC3j@#Z?OvvG|`H8S2J(x_#h3$!4zCVFCV|+Zpm$7|9tZ$#t8%?GNRGUhGBZb&dQ~)mzB}K;cCb3Vqf!_txXLF!G3U1%p-Yzuy8pzggsI6UC@7qwhTJPIP+IQ{@w1ot}uTg<_?gZftK7X@@)o=u(p%o&aP5#DfJM3%ofL6;K?j$yOf?DN23;aE8nO!GcYlat~%$iDEwvyM`{RUiT$>bu8v_7kX<yRzYFyb~<<n3~7<@>;EkMDz>ubOl)`Q+*ETQTxp&v@z1dMoa{yBROm|G5L(mSXn!e!=&@J&P5(R);sR3LA8|hsirUTAcHfs}zcRflamE-%#Oh6@FZWtK&pTg<qh;XH<Bt3O}vFm#T0#YZv-(kqYN=2OlGrsc;^55Wi53GyBzKc5lVfr^3~n+<*$VtMDNeu6{l`pu*M92luM*Y85`J!W}C7K^0!3!XH-Q^HumE6}~`)KcT`Gs_>^&xKo9Xsc@GHe^G@mR^ha8(m_Y67A^G<dT>m%mM3Z9h-0F1zr6A0S`R5-atnOBR<*(v@_l$~>UbH-CEJn5p_rPK`D>BKA($GI`8MQn3Qj#C^H(B|LoxNR%&$ithhS<{<}XDaT|ad|=2s(+&7K;N`4z~ctEcwJ{1W8R#Zz4}KOcE??NqDGTaibXPBqB<7Z(7JuAK77{3+ydN=~_D{sZ89M|uAP-wfR7F9&u6B0IY2T_+y|C{9Q0m#jtKNq2ki1?nFw{q|hBOpjHqUZ!~2<)_c0F&qIY;;oZ9ytSnp0HD$Y^}p~`E8xAZRq!xN{cq9ni8?BMK>gEn{N<H&{2e#-zg8$&^6%23=)Ig4TTVb1!f-uMdJOA{$>{CghOl(1gkgvw9o{ZLsC0}%eU8!%a3?$x2eFZqx2d!FJ@ISdV#^QZfh1w+{jgLn?E-tD!Vx>%&7VZ!E)?F`*?dyG7=+UxthAHKuT#rEKN?v`O4nkOilcZPl8zi>vueyvn-Awdrp1W&vgf=@ZD8QD((^Fvbfm-EKu5yfCffX>xR}P=C>$u*AF$Bo@%%@4zl)BD-km5kK%0+>7eITNT*3Zb5IdTm0fEc?W77-enp&`Oad4#860p_Un@`;_1x~AnIaGSqhBe*}b`F-ss?z;mmdj!3MCl%&2zM#)AY&U8whvhU7#;aXd358n@oIUvT?a3QX-)4sf|KA|y8^cab_I3^gbAo?3|w8h0qTOrUmhNbc)L1^JImOWouTH#qK6hr_OSHo^pcVJBMr20*p7gdJu6Xg)8yb3_O}kCYdd3a;s7+9a=Dk@3Pyo0LfTop&O*oE_k;@n40C9T)*LO|?!BDc@wv<2>-uO6CXGiLqcxMXe&!T)T{?Ekwfk_d%Qx=&&VNB;pU34n-H7YA8Px8W&}bEoS!m5+T7L>P56^1;El&TD)U#&;SEZggn}0!`2cg25vg__c1ZTu)|Er<TJ`PJSQP<;>A!!Wl)1rL=_5VB0>5%kG>i;J?{_~Zg@%P<f|0ggb_Wv4nW>8qu@Hy2FHiu$kp`!iUBktyZ6{Ua_dFHIN_N#h(&qZZrBps!9VXUSsFgL?R`*PMID!s^BM8}WADw~+v&*TSiVakKQ?~F1<VrMi{ByvVGMS{pmzb-v1(~0Sq@oN&l{-YEE3>MAZ%1S7<v@P+-VYakKw$bu47x2ZU&&Xt>SH641G4;+Dpf>9NFeJUQn@aD{!hg<mMZ(3ZYjFw}7rkbcjitawdFhRy`x_;G6kF~BW(O@+4Wq&4(^Ps-Tn-`qQkN3a7wsw^@AdKa?3%z)n&m-1pfu!4*-ZU8(5K_)Y*d<|<E3k;<tTmSoLC12KXxhx7otHkdk0!>SPU^Re+4bH{0J1lB(!HCbo(XXN)JINOBA|rw5lHDEU10}^*)(U;tY!Kn(8gfE(E?CJm*$LTnKEiG+_+3QRz(S{?9S?wEP5HCLN~I+ofO0i0G{bcog7gaOxlJ@K(<+jpHp?WDZ!-in;t+@Vxt56Bu7cs-kG6*m5%x+fZp_&{O!OrSuP=HT_sg1R~GxgP+1yK&3Cc=`r~^fF9fGU{rpd5_iz2%1XJ0N-*b-4sHz>y?;mKC3B**5)55iyxK#hAhh{U-K_trxLKIC<Y(ZP17i&LkH0*9vUKNZa7)G2vVU-YV!Kn}<XSo+I5f_x!#Gw=>nG^=8SB9}@A%{5zH&%93!%Ll9D{qxh2i45y^FBtofaxh`#+>o*z1^H!0HW+*u5hg4uz$UO5;$w|JCN{u=J_xfy21X6kf0dTu;_scyGjeq3r0=E|8(kDX$}c6kT06>uMLcdaWvImR4hDMzQ@N>EEym;o>FF)yPwM-BF<30qM(-^l7;MJ^2}B{7YNu`p>}n!4E}`|4r_Mu=EAAr$hQEP_F$IElj}f@K*i<Tu`dIMrWP&$pm}mVNW^u9^jczwq?joiJY?Kk1e?Q{lLq=z;gB)%Szi-cy=T|t3mY``DTDlA`d+{1l?{uTP~jkIskMC*8uDvC7^DIJ_`YV80ghN@p+{VmN7mj?O_k8{Mp%Z+je3Za$8m|taglAs@;g=S>6n+_shs^F_tI9%jCO0Eth9d!0F!Nth?5=V9;@ZT(jb;OB=nbxjvqu)j=QB&#U;{g8dwYKHP^u!09enJDeWt?)gr4!0G5%KrY9=!RIW<+=Vhhr~5u@z*%>X4Fn5zYiz!=4)ofb4vG(46h2R&UGT?qDBtFE|CzPTS$Ds!&FLxH+nj6fs|q+9?wJ>GHWjKnoO`Sf&v!Nf5^$~s36N})tpyg$o@?IL6_$Hm{lkOvJ!B>Ce-}}Ffc@VLj~VvoHT88E)VI|+X|YvV&1wW6!Dj$$UkyP^KF+<)>E7*ByoNr!562$*meBSsSgDI*T@>r;bhc)V>XF~U{srvdGl%-UrCheGUUMgb_*M0ogS>5_haBV=)~ZJw<T+c}_HH%#E649T);(X&m-FR(IbY6~|JTCLG5NVAKc`gx9;v2JTeSS^?1G<lO|nBWer9-t9YQW=JU>TW$#{OIxq?xCZpxn@_%qLM&y_PsA7q<uWiw?L{OoUx-REa@LyYHVbajlX&pNU2Ggr#a-T2<##rnse<M>%3KjS=5qs6I1+wLZ&&(9Qj{a+(mIe2W8`)6U$ImRDihRclS?VMr!5WD|5<JD)Tf5^gr57w7?%(2TDUBl=mMz=6}Bcr{H?q~EKM!(1Cj~RWE(W8vMu0CY_Ule}M&db*J_A5PWcl6}bV&1dax6#+It}!oj{yY3lzJ?9;3i|ulw!x@18T?X<zk5UsaT^g0aeHNcYw@beyw>9L43h<HFdK)ejc`Y0K56lq%DmO$^DFaPi!Z3Gb1lA*%oyT}$Z>=5vk@nmF~nV!xS_?}WYQ2{T*)8M;!8+Ztr30!>04%m*H+?_7GGM4OIm!H;kvLvbl`DBi^J;o7~!+O=W6j4b1)1icJgsqk7FFQf<Jj2=jkk7S!X#JUhS#qV`((8^9^Qa)UCx^89u4QyBY3Tti_Y8-XUGRL-O@pfBuNs*`u@bs4PEsT+G`4k}SW3#0|#RNd67^d+z+1mhH?P-`~jJwR75EWl?Z_JMnjTi@|*G$-iaRkviSDZ?s^ZhO_dc-dzmux8Xbg-1*Zj=L5{H3m*S_O!5=%HNpShVw@lHnu$E-MJ!RR-_5Mz6DI9f@=u&(fQ|2c49D}8#n!qx@%a*yJc<^;F9v!3`y>xr57|+EZrr%Z#7@oxztyJni|2>&vz+gk$p63u{~OuP+&K9p>#u&?51ZIoWi!tA*km)7-)B?i)topZ&$s2|z-lc%WK(c`d+s)||5N6lF6QS1!=JV(<2%Zfo@4miCU(juIJFz&g55Yz=1)xI|H7`cbBwi<Z=a9Yjq_xlHnH=DNxdgba7&f39kNAe&!oj{G$;CE0|P|Z8os_Q5Eg`7zDEctSs0l75pEKMWG0zTiX@g5b7H=?*B2wR89IX4j~OfJM2-kTJR|H)WqP71AueXJIU$-KBC$;WKq?_7;=awBnwyM;Fcl;zM6=oGu#kX84U^t%v_B!l^Zot9prYagY>Gxy5VmX&bOwdswhl}n61HyJAp|J{X~%XVblkKp&>3ondm81q7Le0VDt@?r%a-n7M2H01!a=Z_h)2aJ%h}nVh(W_c$?j+<84R|s5B6`ruDbzqm#&wyd(uKamx!CD2(`AV^HRPtQAj7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open("./kyomu", 'wb').write(zlib.decompress(base64.b85decode(exe_bin)))
subprocess.run(["chmod +x ./kyomu"], shell=True)
subprocess.run(["./kyomu"], shell=True)

Measured memory_bytes: 10768