#include<cmath>

#include<cstdio>

#include<cstring>

#include<algorithm>

using namespace std;

const int N = 303;

struct Point {

	double x, y;

	Point(double _x = 0, double _y = 0) : x(_x), y(_y) {}

} t[N], p[N];

struct Line {

	Point p, v; double ang;

	Line(Point _p = Point(0, 0), Point _v = Point(0, 0), double _ang = 0) : p(_p), v(_v), ang(_ang) {}

	bool operator < (const Line &x) const {

		return ang < x.ang;

	}

} l[N], q[N];

Point operator + (Point a, Point b) {return Point(a.x + b.x, a.y + b.y);}

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

Point operator * (Point a, double x) {return Point(a.x * x, a.y * x);}

Point operator / (Point a, double x) {return Point(a.x / x, a.y / x);}

int dcmp(double x) {return fabs(x) < 1e-8 ? 0 : (x < 0 ? -1 : 1);}

double Dot(Point a, Point b) {return a.x * b.x + a.y * b.y;}

double Cross(Point a, Point b) {return a.x * b.y - a.y * b.x;}

double sqr(double x) {return x * x;}

double dis(Point a, Point b) {return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y));}

bool onleft(Point a, Line b) {return dcmp(Cross(a - b.p, b.v)) < 0;}

Point intersection(Line a, Line b) {

	Point u; double t;

	u = a.p - b.p;

	t = Cross(b.v, u) / Cross(a.v, b.v);

	return a.p + (a.v * t);

}

int n, head = 1, tail = 2;

double ans;

void mkhalf() {

	q[1] = l[1]; q[2] = l[2];

	p[1] = intersection(q[1], q[2]);

	for(int i = 3; i < n; ++i) {

		while (head < tail && !onleft(p[tail - 1], l[i])) --tail;

		while (head < tail && !onleft(p[head], l[i])) ++head;

		q[++tail] = l[i];

		if (dcmp(Cross(q[tail].v, q[tail - 1].v) == 0)) {

			--tail;

			if (onleft(l[i].p, q[tail])) q[tail] = l[i];

		}

		if (head < tail) p[tail - 1] = intersection(q[tail - 1], q[tail]);

	}

//	while (head < tail + 1 && !onleft(p[tail - 1], q[head])) --tail;

}

double cal(int num) {

	Point j;

	double x = t[num].x, y = t[num].y;

	if (x <= p[head].x) {

		j = intersection(q[head], Line(t[num], Point(0, 1)));

		return j.y - y;

	}

	if (x >= p[tail - 1].x) {

		j = intersection(q[tail], Line(t[num], Point(0, 1)));

		return j.y - y;

	}

	int left = head, right = tail - 1, mid;

	while (left < right) {

		mid = (left + right + 1) >> 1;

		if (p[mid].x > x) right = mid - 1;

		else left = mid;

	}

	j = intersection(q[left + 1], Line(t[num], Point(0, 1)));

	return j.y - y;

}

double cal2(int num) {

	Point j;

	double x = p[num].x, y = p[num].y;

	int left = 1, right = n, mid;

	while (left < right) {

		mid = (left + right + 1) >> 1;

		if (t[mid].x > x) right = mid - 1;

		else left = mid;

	}

	j = intersection(Line(t[left], t[left + 1] - t[left]), Line(p[num], Point(0, -1)));

	return y - j.y;

}

int main() {

	scanf("%d", &n);

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

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

	for(int i = 1; i < n; ++i) l[i] = Line(t[i], t[i + 1] - t[i]), l[i].ang = atan2(l[i].v.y, l[i].v.x);

	sort(l + 1, l + n);

	mkhalf();

	ans = cal(1);

	for(int i = 2; i <= n; ++i)

		ans = min(ans, cal(i));

	for(int i = head; i < tail; ++i)

		if (t[1].x <= p[i].x && p[i].x <= t[n].x)

			ans = min(ans, cal2(i));

//	for(int i = head; i < tail; ++i) printf("%.2lf %.2lf\n", p[i].x, p[i].y);

	printf("%.3lf\n", ans + 1e-8);

	return 0;

}