/* Ternary Search */
#include <iostream>
#include <iomanip>
#include <cmath>
#define esp 1e-16
#define maxn 100100
using namespace std;
long double l,r,m1,m2;
int a[maxn];
int v[maxn];
int n;
long double get(long double time)
{
long double ll = a[1]+v[1]*time;
long double rr = a[1]+v[1]*time;
for (int i=2; i<=n; i++)
{
ll = min(ll,a[i]+v[i]*time);
rr = max(rr,a[i]+v[i]*time);
}
return ((rr-ll)/2);
}
int main()
{
ios::sync_with_stdio(false);
cin>>n;
for (int i=1; i<=n; i++) cin>>a[i];
for (int i=1; i<=n; i++) cin>>v[i];
l = 0;
r = 1e9 + 1;
while (l<=r-esp)
{
m1 = l + (r-l)/3;
m2 = r - (r-l)/3;
long double res1 = get(m1);
long double res2 = get(m2);
if (res1<=res2) r = m2;
else
l = m1;
}
long double res = get(l);
int nm;
if (res==0) nm = 0;
else
nm = log10(res)+1;
nm+=3;
cout.precision(nm);
cout<<res;
return 0;
}
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