Description：

Solution：

Code：

#include<algorithm>

#include<iostream>

#include<cstdlib>

#include<cstdio>

#include<cctype>

#include<cstring>

using namespace std;

int n;

#define MAXN 310

struct point

{

	double x,y;

}p[MAXN];

bool cmp_x(point a,point b){return a.x < b.x;}

struct line

{

	double k,b;

}l[MAXN];

double calc(double x1,double y1,double x2,double y2,double x)

{

    double slope = (y2 - y1) / (x2 - x1);

    return x * slope + y1 - x1 * slope;

}

double fabs(double k){return (k < 0 ? -k : k);}

bool equal(double a,double b){return fabs(a - b) <= 1e-8;}

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);

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

	for(int i = 1;i < n;++i)

	{

		l[i].k = (p[i + 1].y - p[i].y) / (p[i + 1].x - p[i].x);

		l[i].b = p[i].y - l[i].k * p[i].x;

	}

	double ans = 1000000000000;

	for(int i = 1;i < n;++i)

	{

		for(int j = 1;j < n;++j)

		{

			if(equal(l[i].k,l[j].k))continue;

			double x = (l[i].b - l[j].b) / (l[j].k - l[i].k);

			if(x < p[1].x || x > p[n].x)continue;

			double top = x * l[i].k + l[i].b;

			int s;

			for(s = 1;s < n;++s)

			{

				if(p[s].x <= x && x <= p[s + 1].x)break;

			}

			for(int w = 1;w < n;++w)

      		{

            	top = max(top,calc(p[w].x,p[w].y,p[w + 1].x,p[w + 1].y,x)); 

        	}

			double bot = calc(p[s].x,p[s].y,p[s + 1].x,p[s + 1].y,x);

			ans = min(ans,top - bot);

		}

	}

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

	return 0;

}