#include<cstdio>

#include<algorithm>

#include<cstring>

#include<cmath>

#define eps 1e-7

using namespace std;

const int maxn = 300 + 10;

struct Point {

    double x,y;

}p[maxn],t;

struct Line {

    double k,b;

    void init(Point p1,Point p2) {

        k=(p1.y-p2.y)/(p1.x-p2.x);

        b=p2.y-k*p2.x;

    }

}l[maxn],s[maxn];

int n,sp;

double res=1e11;

bool cmp(Line x,Line y) {

    if(abs(x.k-y.k)<eps) return x.b<y.b;

    return x.k<y.k;

}

Point inter(Line l1,Line l2) {

    Point res;

    res.x=(l2.b-l1.b)/(l1.k-l2.k);

    res.y=l1.k*res.x+l1.b;

    return res;

}

void push(Line l) {

    while(sp>=2 && inter(s[sp],l).x < inter(s[sp-1],s[sp]).x) sp--;

    s[++sp]=l;

}

double f(double x) {

    double res=0;

    for(int i=1;i<=sp;i++) res=max(res,s[i].k*x+s[i].b);

    return res;

}

double g(double x) {

    int i;

    for(i=n;i&&x<p[i].x;i--);

    return p[i].y+(x-p[i].x)/(p[i+1].x-p[i].x)*(p[i+1].y-p[i].y);

}

int main() {

    scanf("%d",&n);

    for(int i=1;i<=n;i++) scanf("%lf",&p[i].x);

    for(int i=1;i<=n;i++) scanf("%lf",&p[i].y);

    for(int i=1;i<n;i++) l[i].init(p[i],p[i+1]);

    sort(l+1,l+n,cmp);

    for(int i=1;i<n;i++) if(i==n-1 || abs(l[i].k-l[i+1].k)>eps) push(l[i]);

    for(int i=1;i<=n;i++) res=min(res,f(p[i].x)-p[i].y);

    for(int i=1;i<sp;i++) {

        t=inter(s[i],s[i+1]);

        res=min(res,t.y-g(t.x));

    }

    printf("%.3lf\n",res);

    return 0;

}