import zlib, base64;exec(zlib.decompress(base64.b85decode('c$}42?{3>R5dW^HAk?9;8%MH|wkwhuL)N(ck_1Ek02}H+qb1sAOOYx`#c`7Wdxw49i|q5>WKXg?QnKVE?JzZ!#Jl6&kEh=qXs#lGrVS;6LKrFj~d#2=!>!JygsimQ-W@M^qsa3|z8iXEZElKM0aoPo$c#uIL)Lf0WwzdNJzwJcQ+d$`{`)7f_vvclVG6GKO2v~p|0HpR{^BKWSW=QwAz@xHSSq>yNT<=@aq0&%^^)zk!z+6OeDL}FnYC1)Qs2#BmeyV=eebGE{LSpd`{7~OYBFkDQN#7CrtkR7kN%D7OY@q0-Y*cM-0)$j0<*33r0!`U6)yCQrwX1N=T;ZR4@!q$s|1D8k(zuZhN6AqM>3E0tjm1D^?;W6gf+%B-C2y6X2&CNkP}Axr=59fW**-X>de7Nwws1jv}rBhFwH{W`FRXDN3&Hp8$p{pzAeo!R^W;br{VC$Oc&lEY(wPHEt|V!F7%xfUcxO*yyY*1H*AA08a@?{4b|i`eCJndznh{mPqAW)C1|DRSG9(&$>5vTztjj%LWWFN0W{>tJkc1N%V#Nf7%2}E%6o)-?P2O-UkuQ`OfP++_dd@7lJUfP%prIKe7OT*I$naP}qFWE&J|hntj5Z9Rp8V21g0#{CV&Gw+S1$y=a%T-a7R{ppSy)@{$FWcu6$@qT{+r>OVO)x8&ZUWw6>u(yjr{nwGFBBw%<#EHryf1iX6zRk!kiS6(zV8XDvF+w&{i6!|M9qNeF!STjIEx5wzWVFVN5h8nI9|Bl%yFdoX-Z~0&1ReGXHO_h4fj6=cqu>%%JAS6^5nq)$mwd$N@JMWmy7CS(g7T#m^2~Zf-Qtf2W@*W$U!}f><20rGF(i~_R2KP|2>cL*KKC>c|Ho9ZubbP}t7GmH_=7|!N#Cydmto?Tju$eddRgwhsY+cY-K-O=N0d;}eQw*C+^3Jc0zs-RWuliL>TefZ=rllpgzqXp1BilVUpFA$e8QU')).decode())