#include <cstdio>#include <cstring>#include <cmath>#include <string>#include <iostream>#include <algorithm>#include <queue>#include <set>#include <map>#include <sstream>using namespace std;typedef long long ll;#define pb push_back#define rep(i, n) for(int i=0; i<(n); ++i)#define for1(i,a,n) for(int i=(a);i<=(n);++i)#define for2(i,a,n) for(int i=(a);i<(n);++i)#define for3(i,a,n) for(int i=(a);i>=(n);--i)#define for4(i,a,n) for(int i=(a);i>(n);--i)#define CC(i,a) memset(i,a,sizeof(i))#define read(a) a=getint()#define print(a) printf("%d", a)#define dbg(x) cout << (#x) << " = " << (x) << endl#define error(x) (!(x)?puts("error"):0)#define rdm(x, i) for(int i=ihead[x]; i; i=e[i].next)inline int getint() { static int r, k; r=0,k=1; static char c; c=getchar(); for(; c<‘0‘||c>‘9‘; c=getchar()) if(c==‘-‘) k=-1; for(; c>=‘0‘&&c<=‘9‘; c=getchar()) r=r*10+c-‘0‘; return k*r; }const double eps=1e-6, oo=1e60;const int N=1005;int dcmp(double x) { return abs(x)<eps?0:(x<0?-1:1); }struct iP { double x, y; iP(double _x=0, double _y=0) : x(_x), y(_y) {} };typedef iP iV;iV operator-(iP a, iP b) { return iV(a.x-b.x, a.y-b.y); }iP operator+(iP a, iV b) { return iP(a.x+b.x, a.y+b.y); }iV operator*(iV a, double x) { return iV(a.x*x, a.y*x); }double cross(iV a, iV b) { return a.x*b.y-a.y*b.x; }double angle(iV &a) { return atan2(a.y, a.x); }struct iL {	iP p; iV v; double ang;	iL() {}	iL(iP a, iP b) { set(a, b); }	void set(iP a, iP b) { p=a; v=b-a; ang=angle(v); }	bool operator< (const iL &b) const { return ang<b.ang; }};iP LLi(iL &a, iL &b) {	static iV u;	static double t;	u=a.p-b.p;	t=cross(b.v, u)/cross(a.v, b.v);	return a.p+a.v*t;}bool OnLeft(iP &p, iL &l) { return dcmp(cross(l.v, p-l.p))>0; }bool half(iL *line, int ln, iP *s, int &cnt) {	static iL a[N], q[N];	static iP b[N];	memcpy(a, line, sizeof(iL)*(ln+1));	sort(a+1, a+1+ln);	int front=0, tail=0;	q[0]=a[1];	for1(i, 2, ln) {		while(front!=tail && !OnLeft(b[tail-1], a[i])) --tail;		while(front!=tail && !OnLeft(b[front], a[i])) ++front;		q[++tail]=a[i];		if(dcmp(cross(q[tail].v, q[tail-1].v))==0) {			--tail;			if(OnLeft(a[i].p, q[tail])) q[tail]=a[i];		}		if(front!=tail) b[tail-1]=LLi(q[tail-1], q[tail]);	}	while(front!=tail && !OnLeft(b[tail-1], q[front])) --tail;	if(tail-front<=1) return 0;	b[tail]=LLi(q[front], q[tail]);	cnt=0;	for1(i, front, tail) s[++cnt]=b[i];	return 1;}iL line[N];iP p[N], pp[N], a[N];int n, ln, num;void build() {	iP t1, t2;	for1(i, 1, n-1) line[i].set(a[i], a[i+1]);	ln=n-1;	++ln; line[ln].set(iP(oo, oo), iP(-oo, oo));	++ln; line[ln].set(iP(-oo, -oo), iP(oo, -oo));	++ln; line[ln].set(iP(-oo, oo), iP(-oo, -oo));	++ln; line[ln].set(iP(oo, -oo), iP(oo, oo));}double cal(iP &a, iP &b, double x) {	double k=(b.y-a.y)/(b.x-a.x), B=a.y-k*a.x;	return k*x+B;}int main() {	read(n);	for1(i, 1, n) a[i].x=getint();	for1(i, 1, n) a[i].y=getint();	build();	half(line, ln, pp, num);	double ans=oo;	double mnx=oo, mny=oo; int pos=1;	for1(i, 1, num) if(dcmp(mnx-pp[i].x)>0 || (dcmp(mnx-pp[i].x)==0 && dcmp(mny-pp[i].y)>0)) { mnx=pp[i].x; mny=pp[i].y; pos=i; }	for1(i, 1, num) p[i]=pp[pos], pos=pos%num+1;	int now=2;	for1(i, 1, n) {		while(now<num && dcmp(p[now].x-a[i].x)<0) ++now;		if(dcmp(a[i].x-p[now-1].x)>=0 && dcmp(p[now].x-a[i].x)>=0)			ans=min(ans, cal(p[now], p[now-1], a[i].x)-a[i].y);	}	now=2;	for1(i, 1, num) {		while(now<n && dcmp(a[now].x-p[i].x)<0) ++now;		if(dcmp(p[i].x-a[now-1].x)>=0 && dcmp(a[now].x-p[i].x)>=0)			ans=min(ans, p[i].y-cal(a[now], a[now-1], p[i].x));	}	printf("%.3f\n", ans+eps);	return 0;}