!function(n){var r={};function t(u){if(r[u])return r[u].exports;var e=r[u]={i:u,l:!1,exports:{}};return n[u].call(e.exports,e,e.exports,t),e.l=!0,e.exports}t.m=n,t.c=r,t.d=function(n,r,u){t.o(n,r)||Object.defineProperty(n,r,{enumerable:!0,get:u})},t.r=function(n){"undefined"!=typeof Symbol&&Symbol.toStringTag&&Object.defineProperty(n,Symbol.toStringTag,{value:"Module"}),Object.defineProperty(n,"__esModule",{value:!0})},t.t=function(n,r){if(1&r&&(n=t(n)),8&r)return n;if(4&r&&"object"==typeof n&&n&&n.__esModule)return n;var u=Object.create(null);if(t.r(u),Object.defineProperty(u,"default",{enumerable:!0,value:n}),2&r&&"string"!=typeof n)for(var e in n)t.d(u,e,function(r){return n[r]}.bind(null,e));return u},t.n=function(n){var r=n&&n.__esModule?function(){return n.default}:function(){return n};return t.d(r,"a",r),r},t.o=function(n,r){return Object.prototype.hasOwnProperty.call(n,r)},t.p="",t(t.s=0)}([function(n,r,t){n.exports=t(1)},function(n,r,t){const u=t(2).createInterface(process.stdin,{}),{Elm:e}=t(3),f=e.Worker.init();f.ports.cout.subscribe(n=>{console.log(n)}),u.on("line",n=>{f.ports.cin.send(n)})},function(n,r){n.exports=require("readline")},function(n,r){!function(n){"use strict";function r(n,r,t){return t.a=n,t.f=r,t}function t(n){return r(2,n,function(r){return function(t){return n(r,t)}})}function u(n){return r(3,n,function(r){return function(t){return function(u){return n(r,t,u)}}})}function e(n){return r(4,n,function(r){return function(t){return function(u){return function(e){return n(r,t,u,e)}}}})}function f(n){return r(5,n,function(r){return function(t){return function(u){return function(e){return function(f){return n(r,t,u,e,f)}}}}})}function i(n){return r(6,n,function(r){return function(t){return function(u){return function(e){return function(f){return function(i){return n(r,t,u,e,f,i)}}}}}})}function o(n,r,t){return 2===n.a?n.f(r,t):n(r)(t)}function c(n,r,t,u){return 3===n.a?n.f(r,t,u):n(r)(t)(u)}function a(n,r,t,u,e){return 4===n.a?n.f(r,t,u,e):n(r)(t)(u)(e)}function b(n,r,t,u,e,f){return 5===n.a?n.f(r,t,u,e,f):n(r)(t)(u)(e)(f)}var v={$:0};function l(n,r){return{$:1,a:n,b:r}}var s=t(l);function h(n){for(var r=v,t=n.length;t--;)r=l(n[t],r);return r}function d(n){for(var r=[];n.b;n=n.b)r.push(n.a);return r}var g=u(function(n,r,t){for(var u=[];r.b&&t.b;r=r.b,t=t.b)u.push(o(n,r.a,t.a));return h(u)}),p=(e(function(n,r,t,u){for(var e=[];r.b&&t.b&&u.b;r=r.b,t=t.b,u=u.b)e.push(c(n,r.a,t.a,u.a));return h(e)}),f(function(n,r,t,u,e){for(var f=[];r.b&&t.b&&u.b&&e.b;r=r.b,t=t.b,u=u.b,e=e.b)f.push(a(n,r.a,t.a,u.a,e.a));return h(f)}),i(function(n,r,t,u,e,f){for(var i=[];r.b&&t.b&&u.b&&e.b&&f.b;r=r.b,t=t.b,u=u.b,e=e.b,f=f.b)i.push(b(n,r.a,t.a,u.a,e.a,f.a));return h(i)}),t(function(n,r){return h(d(r).sort(function(r,t){return A(n(r),n(t))}))}));t(function(n,r){return h(d(r).sort(function(r,t){var u=o(n,r,t);return u===On?0:u===mn?-1:1}))});function $(n,r){for(var t,u=[],e=y(n,r,0,u);e&&(t=u.pop());e=y(t.a,t.b,0,u));return e}function y(n,r,t,u){if(t>100)return u.push(j(n,r)),!0;if(n===r)return!0;if("object"!=typeof n||null===n||null===r)return"function"==typeof n&&N(5),!1;for(var e in n.$<0&&(n=Cn(n),r=Cn(r)),n)if(!y(n[e],r[e],t+1,u))return!1;return!0}t($),t(function(n,r){return!$(n,r)});function A(n,r,t){if("object"!=typeof n)return n===r?0:n0}),t(function(n,r){return A(n,r)>=0});var w=t(function(n,r){var t=A(n,r);return t<0?mn:t?jn:On}),O=0;function j(n,r){return{a:n,b:r}}function m(n){return n}function M(n,r){var t={};for(var u in n)t[u]=n[u];for(var u in r)t[u]=r[u];return t}t(function(n,r){if("string"==typeof n)return n+r;if(!n.b)return r;var t=l(n.a,r);n=n.b;for(var u=t;n.b;n=n.b)u=u.b=l(n.a,r);return t});var x=u(function(n,r,t){for(var u=new Array(n),e=0;e=0;u--)r=o(n,t[u],r);return r}));t(function(n,r){for(var t=r.length,u=new Array(t),e=0;et.length&&(e=t.length);for(var f=new Array(u+e),i=0;i"),r});function N(n){throw new Error("https://github.com/elm/core/blob/1.0.0/hints/"+n+".md")}t(function(n,r){return n+r}),t(function(n,r){return n-r}),t(function(n,r){return n*r}),t(function(n,r){return n/r}),t(function(n,r){return n/r|0}),t(Math.pow),t(function(n,r){return r%n}),t(function(n,r){var t=r%n;return 0===n?N(11):t>0&&n<0||t<0&&n>0?t+n:t}),Math.PI,Math.E,Math.cos,Math.sin,Math.tan,Math.acos,Math.asin,Math.atan,t(Math.atan2);var S=Math.ceil,E=Math.floor,k=(Math.round,Math.sqrt,Math.log);isNaN;t(function(n,r){return n&&r}),t(function(n,r){return n||r}),t(function(n,r){return n!==r});t(function(n,r){return n+r});t(function(n,r){return n+r});t(function(n,r){for(var t=r.length,u=new Array(t),e=0;e-1}),t(function(n,r){return 0===r.indexOf(n)}),t(function(n,r){return r.length>=n.length&&r.lastIndexOf(n)===r.length-n.length}),t(function(n,r){var t=n.length;if(t<1)return v;for(var u=0,e=[];(u=r.indexOf(n,u))>-1;)e.push(u),u+=t;return h(e)});function R(n){return{$:2,b:n}}R(function(n){return"number"!=typeof n?G("an INT",n):-2147483647=r.length)return G("a LONGER array. Need index "+e+" but only see "+r.length+" entries",r);u=q(n.b,r[e]);return wn(u)?u:Qn(o(Zn,e,u.a));case 8:if("object"!=typeof r||null===r||D(r))return G("an OBJECT",r);var f=v;for(var i in r)if(r.hasOwnProperty(i)){u=q(n.b,r[i]);if(!wn(u))return Qn(o(Xn,i,u.a));f=l(j(i,u.a),f)}return Un(zn(f));case 9:for(var c=n.f,a=n.g,b=0;b=0&&t.splice(r,1)}}}var gn=t(function(n,r){return function(t){return n(r(t))}});function pn(n,r){var t=v,e=cn[n].r,f=Q(null);return cn[n].b=f,cn[n].c=u(function(n,r,u){return t=r,f}),{send:function(n){var u=o(B,e,H(n));wn(u)||N(4,u.a);for(var f=u.a,i=t;i.b;i=i.b)r(i.a(f))}}}var $n,yn,An,wn=function(n){return!n.$},On=1,jn=2,mn=0,Mn=u(function(n,r,t){for(;;){if(-2===t.$)return r;var u=t.b,e=t.c,f=t.d,i=t.e,o=n,a=c(n,u,e,c(Mn,n,r,i));n=o,r=a,t=f}}),xn=s,Cn=function(n){return c(Mn,u(function(n,r,t){return o(xn,j(n,r),t)}),v,n)},Tn=T,Nn=(u(function(n,r,u){var e=u.c,f=u.d,i=t(function(r,t){if(r.$){var u=r.a;return c(Tn,n,t,u)}var e=r.a;return c(Tn,i,t,e)});return c(Tn,i,c(Tn,n,r,f),e)}),e(function(n,r,t,u){return{$:0,a:n,b:r,c:t,d:u}})),Sn=S,En=t(function(n,r){return k(r)/k(n)}),kn=Sn(o(En,2,32)),Pn=[],Jn=a(Nn,0,kn,Pn,Pn),In=C,Rn=u(function(n,r,t){for(;;){if(!t.b)return r;var u=t.a,e=t.b,f=n,i=o(n,u,r);n=f,r=i,t=e}}),zn=function(n){return c(Rn,xn,v,n)},Ln=t(function(n,r){for(;;){var t=o(In,32,n),u=t.a,e=t.b,f=o(xn,{$:0,a:u},r);if(!e.b)return zn(f);n=e,r=f}}),_n=(t(function(n,r){return r(n)}),t(function(n,r){for(;;){var t=Sn(r/32);if(1===t)return o(In,32,n).a;n=o(Ln,n,v),r=t}})),Bn=(t(function(n,r){return n(r)}),E),qn=t(function(n,r){return A(n,r)>0?n:r}),Fn=function(n){return n.length},Dn=t(function(n,r){if(r.a){var t=32*r.a,u=Bn(o(En,32,t-1)),e=n?zn(r.d):r.d,f=o(_n,e,r.a);return a(Nn,Fn(r.c)+t,o(qn,5,u*kn),f,r.c)}return a(Nn,Fn(r.c),kn,Pn,r.c)}),Yn=x,Gn=f(function(n,r,t,u,e){for(;;){if(r<0)return o(Dn,!1,{d:u,a:t/32|0,c:e});var f={$:1,a:c(Yn,32,r,n)};n=n,r=r-32,t=t,u=o(xn,f,u),e=e}}),Wn=t(function(n,r){if(n<=0)return Jn;var t=n%32,u=c(Yn,t,n-t,r);return b(Gn,r,n-t-32,n,v,u)}),Hn=function(n){return{$:0,a:n}},Kn={$:1},Qn=function(n){return{$:1,a:n}},Un=function(n){return{$:0,a:n}},Vn=t(function(n,r){return{$:3,a:n,b:r}}),Xn=t(function(n,r){return{$:0,a:n,b:r}}),Zn=t(function(n,r){return{$:1,a:n,b:r}}),nr=function(n){return{$:2,a:n}},rr=function(n){var r=n.charCodeAt(0);return 55296<=r&&r<=56319?1024*(r-55296)+n.charCodeAt(1)-56320+65536:r},tr=function(n){var r=rr(n);return 97<=r&&r<=122},ur=function(n){var r=rr(n);return r<=90&&65<=r},er=function(n){return tr(n)||ur(n)},fr=function(n){return tr(n)||ur(n)||function(n){var r=rr(n);return r<=57&&48<=r}(n)},ir=function(n){return c(Rn,t(function(n,r){return r+1}),0,n)},or=g,cr=u(function(n,r,t){for(;;){if(!(A(n,r)<1))return t;var u=n,e=r-1,f=o(xn,r,t);n=u,r=e,t=f}}),ar=t(function(n,r){return c(cr,n,r,v)}),br=t(function(n,r){return c(or,n,o(ar,0,ir(r)-1),r)}),vr=I,lr=function(n){return n+""},sr=t(function(n,r){return o(J,n,d(r))}),hr=function(n){var r=n.charCodeAt(0);return r?Hn(55296<=r&&r<=56319?j(m(n[0]+n[1]),n.slice(2)):j(m(n[0]),n.slice(1))):Kn},dr=t(function(n,r){return h(o(P,n,r))}),gr=function(n){return o(sr,"\n ",o(dr,"\n",n))},pr=W,$r=t(function(n,r){return"\n\n("+lr(n+1)+") "+gr(yr(r))}),yr=function(n){return o(Ar,n,v)},Ar=t(function(n,r){n:for(;;)switch(n.$){case 0:var t=n.a,u=n.b,e=function(){var n=hr(t);if(1===n.$)return!1;var r=n.a,u=r.a,e=r.b;return er(u)&&o(vr,fr,e)}(),f=u,i=o(xn,e?"."+t:"['"+t+"']",r);n=f,r=i;continue n;case 1:var c=n.a,a=(u=n.b,"["+lr(c)+"]");f=u,i=o(xn,a,r);n=f,r=i;continue n;case 2:var b=n.a;if(b.b){if(b.b.b){var v=(r.b?"The Json.Decode.oneOf at json"+o(sr,"",zn(r)):"Json.Decode.oneOf")+" failed in the following "+lr(ir(b))+" ways:";return o(sr,"\n\n",o(xn,v,o(br,$r,b)))}n=f=u=b.a,r=i=r;continue n}return"Ran into a Json.Decode.oneOf with no possibilities"+(r.b?" at json"+o(sr,"",zn(r)):"!");default:var l=n.a,s=n.b;return(v=r.b?"Problem with the value at json"+o(sr,"",zn(r))+":\n\n ":"Problem with the given value:\n\n")+(gr(o(pr,4,s))+"\n\n")+l}}),wr=function(n){return{$:2,m:n}}(v),Or=j({N:"",z:0},wr),jr=t(function(n,r){return{$:0,a:n,b:r}}),mr=(yn=z,sn($n="cin"),cn[$n]={f:gn,r:yn,a:pn},bn($n)),Mr=function(n,r){return sn(n),cn[n]={e:hn,r:r,a:dn},bn(n)}("cout",H),xr=u(function(n,r,t){return n(r(t))}),Cr=function(n){return!n},Tr=t(function(n,r){for(;;){if(!r.b)return!1;var t=r.a,u=r.b;if(n(t))return!0;n=n,r=u}}),Nr=t(function(n,r){return!o(Tr,o(xr,Cr,n),r)}),Sr=function(n){if(n.b){var r=n.a;n.b;return Hn(r)}return Kn},Er=e(function(n,r,t,u){if(u.b){var e=u.a,f=u.b;if(f.b){var i=f.a,b=f.b;if(b.b){var v=b.a,l=b.b;if(l.b){var s=l.a,h=l.b;return o(n,e,o(n,i,o(n,v,o(n,s,t>500?c(Rn,n,r,zn(h)):a(Er,n,r,t+1,h)))))}return o(n,e,o(n,i,o(n,v,r)))}return o(n,e,o(n,i,r))}return o(n,e,r)}return r}),kr=u(function(n,r,t){return a(Er,n,r,0,t)}),Pr=t(function(n,r){return c(kr,t(function(r,t){return o(xn,n(r),t)}),v,r)}),Jr=function(n){return n},Ir=p,Rr=t(function(n,r){return r.$?n:r.a}),zr=function(n){for(var r=0,t=n.charCodeAt(0),u=43==t||45==t?1:0,e=u;e1e3?o(nt,r-4,y):c(rt,n+1,r-4,y)))))}break r}}return t}return h([i=u.b.a])}),tt=t(function(n,r){return c(rt,0,n,r)}),ut=u(function(n,r,t){var u=o(Xr,r,t),e=o(tt,n,t),f=$(n,ir(e));return n>0&&r>0&&f?o(xn,e,c(ut,n,r,u)):v}),et=function(n){return{$:0,a:n}},ft=on({at:function(n){return Or},az:function(n){return mr(jr(n.z))},aB:t(function(n,r){var t,u=n.a,e=n.b;if(u){var f=o(Pr,function(n){return n.$?0:n.a},o(Pr,zr,o(dr," ",e))),i=o(Ir,Jr,f),a=c(ut,2,1,i),b=function(n){return o(Rr,0,function(n){n:for(;;){if(n.b){if(n.b.b){n=n.b;continue n}var r=n.a;return Hn(r)}return Kn}}(n))-o(Rr,0,Sr(n))},v=(t=o(Rr,h([0,0]),Sr(a)),b(t)),l=o(Nr,function(n){return $(b(n),v)},a),s=function(n){return o(Vr,Jr,n)}(f)&&l?"YES":"NO";return j(M(r,{z:u+1}),Mr(s))}return j(M(r,{z:u+1}),wr)})});An={Worker:{init:ft(et(0))(0)}},n.Elm?function n(r,t){for(var u in t)u in r?"init"==u?N(6):n(r[u],t[u]):r[u]=t[u]}(n.Elm,An):n.Elm=An}(this)}]);