#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n - 1); i >= 0; i--)
#define all(x) (x).begin(), (x).end()
#define sz(x) int(x.size())
using namespace std;
using ll = long long;
constexpr int INF = 1e9;
constexpr ll LINF = 1e18;
string YesNo(bool cond) {
    return cond ? "Yes" : "No";
}
string YESNO(bool cond) {
    return cond ? "YES" : "NO";
}
template <class T>
bool chmax(T& a, const T& b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
template <class T>
bool chmin(T& a, const T& b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}
template <typename T, class F>
T bisect(T ok, T ng, const F& f) {
    while (abs(ok - ng) > 1) {
        T mid = min(ok, ng) + (abs(ok - ng) >> 1);
        (f(mid) ? ok : ng) = mid;
    }
    return ok;
}
template <typename T, class F>
T bisect_double(T ok, T ng, const F& f, int iter = 100) {
    while (iter--) {
        T mid = (ok + ng) / 2;
        (f(mid) ? ok : ng) = mid;
    }
    return ok;
}
template <class T>
vector<T> make_vec(size_t a) {
    return vector<T>(a);
}
template <class T, class... Ts>
auto make_vec(size_t a, Ts... ts) {
    return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}
template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
    for (int i = 0; i < int(v.size()); i++) {
        is >> v[i];
    }
    return is;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    for (int i = 0; i < int(v.size()); i++) {
        os << v[i];
        if (i < sz(v) - 1) os << ' ';
    }
    return os;
}
#include <atcoder/segtree>
using S = ll;
S op(S a, S b) {
    return min(a, b);
}
S e() {
    return LINF;
}
int main() {
    int n;
    cin >> n;
    vector a(2, vector<ll>(n));
    cin >> a;

    map<ll, vector<int>> mp;
    rep(i, n) {
        mp[a[0][i]].push_back(i);
        mp[a[1][i]].push_back(i);
        mp[(a[0][i] + a[1][i]) / 2].push_back(i);
    }

    ll ans = LINF;
    atcoder::segtree<S, op, e> segt(n);
    rep(i, n) segt.set(i, -LINF);
    for (auto [max_c, id] : mp) {
        for (int i : id) {
            ll min_c = min(segt.prod(0, i), segt.prod(i + 1, n));
            chmin(ans, max_c - min_c);
            segt.set(i, max_c);
        }
    }
    cout << ans << '\n';
}