#include <cstdlib>

#include <cstdio>

#include <cstring>

#include <cmath>

#include <iostream>

#include <algorithm>

#include <cctype>

#define rep(i, l, r) for(int i=l; i<=r; i++)

#define maxn 1009

#define linf 1e15

using namespace std;

inline int read()

{

	int x=0, f=1; char ch=getchar();

	while (!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();}

	while (isdigit(ch)) x=x*10+ch-'0', ch=getchar();

	return x*f;

}

struct P{double x, y;} p[maxn], p2[maxn];

struct line{P a, b; double ang;} g[maxn], l[maxn], a[maxn], q[maxn];

P operator - (P a, P b){return (P){a.x-b.x, a.y-b.y};}

double operator * (P a, P b){return a.x*b.y-a.y*b.x;}

bool operator < (line a, line b){if (a.ang==b.ang) return (a.b-a.a)*(b.a-a.a)>0; return a.ang<b.ang;}

bool operator < (P a, P b){return a.x<b.x;}

inline P inter(line a, line b)

{

	double k1=(b.b-a.a)*(a.b-a.a), k2=(a.b-a.a)*(b.a-a.a), t=k2/(k1+k2);

	return (P){b.a.x+t*(b.b.x-b.a.x), b.a.y+t*(b.b.y-b.a.y)};

}

inline bool jud(line a, line b, line v){return (inter(a, b)-v.a)*(v.b-v.a)>0;}

int n, m, L, R, cnt;

double ans;

int main()

{

	n=read(); m=n-1;

	rep(i, 1, n) p[i].x=read();

	rep(i, 1, n) p[i].y=read();

	rep(i, 1, m) g[i].a=p[i], g[i].b=p[i+1];

	rep(i, 1, m) l[i]=g[i], l[i].ang=atan2(l[i].b.y-l[i].a.y, l[i].b.x-l[i].a.x);

	sort(l+1, l+m+1);

	a[++cnt]=l[1]; rep(i, 2, m) a[a[cnt].ang!=l[i].ang ? ++cnt : cnt]=l[i];

	L=1, R=0, q[++R]=a[1], q[++R]=a[2];

	rep(i, 3, cnt)

	{

		while (L<R && jud(q[R-1], q[R], a[i])) R--;

		while (L<R && jud(q[L+1], q[L], a[i])) L++;

		q[++R]=a[i];

	}

	while (L<R && jud(q[R-1], q[R], q[L])) R--;

	while (L<R && jud(q[L+1], q[L], q[R])) L++;

	rep(i, L, R-1)

	{

		p2[i]=inter(q[i], q[i+1]);

		if (p2[i].x>=p[1].x && p2[i].x<=p[m+1].x) p[++n]=p2[i];

	}

	sort(p+1, p+1+n);

	int k1=1, k2=L; ans=linf;

	rep(i, 1, n)

	{

		double x=p[i].x;

		while (k1<m && g[k1].b.x<x) k1++;

		while (k2<R && p2[k2].x<x) k2++;

		line v; v.a.x=v.b.x=x, v.a.y=1, v.b.y=2;

		ans=min(ans, inter(v, q[k2]).y-inter(v, g[k1]).y);

	}

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

	return 0;

}