C++ :

#include<cstdio>
#include<iostream>
#include<cstring>
#include<cmath>
#include<cstdlib>
#define d double
#define ld long double
using namespace std;
const int maxn=323;
const d eps=1e-7;
struct poi{
    int x,y;
}a[maxn];
d ansx,ansaddy,nowx,nowy;int posl,posr;
int i,j,k,n,m;

int ra,fh;char rx;
inline int read(){
    rx=getchar(),ra=0,fh=1;
    while((rx<'0'||rx>'9')&&rx!='-')rx=getchar();
    if(rx=='-')fh=-1,rx=getchar();
    while(rx>='0'&&rx<='9')ra*=10,ra+=rx-48,rx=getchar();return ra*fh;
}

inline d randlf(){
    return rand()%10000/10000.0;
}
bool judge(){
    int i;
    for(i=1;i<posl;i++)if((nowy-a[i].y)*(nowx-a[i+1].x)>(nowy-a[i+1].y)*(nowx-a[i].x))
        return 0;
    for(i=posr;i<n;i++)if((a[i].y-nowy)*(a[i+1].x-nowx)>(a[i+1].y-nowy)*(a[i].x-nowx))
        return 0;
    return 1;
}
inline d geth(){
    int L=1,R=n,MID;ld sy,l,r,mid;
    while(L<R)
        if(a[(MID=(L+R+1)>>1)].x<=nowx)L=MID;else R=MID-1;
    posl=L,posr=L+1;
    if(a[L].x==nowx)posl--,sy=a[L].y;else sy=a[posl].y+(a[posr].y-a[posl].y)*(nowx-a[posl].x)/(a[posr].x-a[posl].x);
    l=0,r=1e11;//printf("geth:  x:%.8lf   l r:%d %d   sy:%.3lf\n",nowx,a[posl].x,a[posr].x,sy);
    while(l+1e-7<r){
        mid=(l+r)/2;nowy=sy+mid;
        if(judge())r=mid;//,printf("success:  %.2lf %.2lf   %.9lf\n",nowx,(d)sy,(d)mid);
        else l=mid;//,printf("failed:  %.2lf %.2lf   %.9lf  %.9lf %.9lf\n",nowx,(d)sy,(d)mid,(d)l,(d)r);
    }
    if(l<ansaddy)ansaddy=l,ansx=nowx;
    return l;
}//<n*64
inline void SA(){
    d T=a[n].x-a[1].x,prex,tmpaddy,nowaddy;
    nowx=ansx=(a[n].x+a[1].x)/2.0;nowaddy=geth();//printf("   %.2lf\n",nowx);
    while(T>1e-5){
        T*=0.99;//printf("!  %d\n",fabs(nowaddy-geth())<=eps);
        prex=nowx,nowx+=T*(randlf()*2-1);
    //    printf("try:%.3lf\n",nowx);
        if(nowx<a[1].x||nowx>a[n].x){nowx=prex;T/=0.991;continue;}
        tmpaddy=geth();
        
        if(tmpaddy>nowaddy&&exp((nowaddy-tmpaddy)/T)<randlf())
            nowx=prex;
        else nowaddy=tmpaddy;
    }
    for(int i=1;i<=1023;i++){
        nowx=ansx+T*(randlf()*2-1);//printf("try1:%.3lf\n",nowx);
        if(nowx<a[1].x||nowx>a[n].x)continue;
        geth();
    }
}
int main(){
    n=read();srand(233);
//    srand(19980406);
    for(i=1;i<=n;i++)a[i].x=read();
    for(i=1;i<=n;i++)a[i].y=read();ansaddy=1e11;
    SA();
    printf("%.3lf\n",ansaddy+eps);//printf("ansx:  %.3lf\n",ansx);
    return 0;
}