#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
using ll=long long;
using ld=long double;
ld pie=3.14159265359;
ll inf=1001000000000;
ll mod=1000000007;
int main(){
    ll n;
    cin >> n;
    vector<ll>a(n),b(n);
    for (ll i = 0; i < n; i++)
    {
        cin >> a[i];
    }
    for (ll i = 0; i < n; i++)
    {
        cin >> b[i];
    }
    vector<pair<ll,ll>>c;
    for (ll i = 0; i < n; i++)
    {
        c.push_back({a[i],i});
        c.push_back({b[i],i});
        c.push_back({(a[i]+b[i])/2,i});
    }
    sort(c.begin(),c.end());
    vector<ll>memo(n,0);
    ll mi=c[0].first;
    ll now=0;
    ll ans=inf;
    ll st=0;
    for (ll i = 0; i < c.size(); i++)
    {
        if (memo[c[i].second]==0)
        {
            now+=1;
        }
        memo[c[i].second]+=1;
        if (now==n)
        {
            for (ll j = st; j < i; j++)
            {
                if (memo[c[j].second]==1)
                {
                    mi=c[j].first;
                    st=j;
                    break;
                }else{
                    memo[c[j].second]-=1;
                }
            }
            ans=min(ans,c[i].first-mi);
        }
    }
    cout << ans << endl;
}