#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pll = pair<ll, ll>;
#define drep(i, cc, n) for (ll i = (cc); i <= (n); ++i)
#define rep(i, n) drep(i, 0, n - 1)
#define all(a) (a).begin(), (a).end()
#define pb push_back
#define fi first
#define se second

const ll MOD = 1000000007;
const ll MOD2 = 998244353;
const ll INF = 1LL << 60;
const ll MAX_N = 2e5;

ll n;
vector<ll> a, b;
ll solve(ll base){
    vector<ll> c(n, 0);
    c[0] = base;
    for(ll i=1; i<n; i++){
        ll diff = INF, v = INF;
        if(abs(a[i]-base) < diff){
            diff = abs(a[i]-base);
            v = a[i];
        }
        if(abs(b[i]-base) < diff){
            diff = abs(b[i]-base);
            v = b[i];
        }
        if(abs((a[i]+b[i])/2-base) < diff){
            diff = abs((a[i]+b[i])/2-base);
            v = (a[i]+b[i])/2;
        }

        c[i] = v;
    }

    ll c_max = -INF, c_min = INF;
    rep(i, n){
        c_max = max(c_max, c[i]);
        c_min = min(c_min, c[i]);
    }

    return c_max-c_min;
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    
    cin >> n;
    a.resize(n);
    b.resize(n);
    rep(i, n) cin >> a[i];
    rep(i, n) cin >> b[i];

    ll ans = INF;
    ans = min(ans, solve(a[0]));
    ans = min(ans, solve(b[0]));
    ans = min(ans, solve((a[0]+b[0])/2));

    cout << ans << endl;
}