#include <bits/stdc++.h>
using namespace std;

struct iofast_t {
    iofast_t() {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
    }
} iofast;

struct uns_t {} uns;
template <typename Element, typename Head, typename ...Args>
auto vec(Element init, Head arg, Args ...args) {
    if constexpr (sizeof...(Args) == 0) return vector(arg, init);
    else return vector(arg, vec(init, args...));
}
template <typename Element, typename Head, typename ...Args>
auto vec(uns_t, Head arg, Args ...args) {
    return vec(Element(), arg, args...);
}

template <typename Container>
auto distance(const Container &c, decltype(begin(c)) iter) {
    return distance(begin(c), iter);
}

template <typename RIter, typename Compare = less<typename iterator_traits<RIter>::value_type>>
auto isort(RIter first, RIter last, Compare comp = Compare()) {
    vector<int> i(distance(first, last));
    iota(begin(i), end(i), 0);
    sort(begin(i), end(i), [&](auto x, auto y) {
        return comp(*(first + x), *(first + y));
    });
    return i;
}

template <typename, template <typename> typename, typename = void_t<>>
struct detect : false_type {};
template <typename T, template <typename> typename Check>
struct detect<T, Check, void_t<Check<T>>> : true_type {};
template <typename T, template <typename> typename Check>
constexpr inline bool detect_v = detect<T, Check>::value;

template <typename T>
using has_member_sort = decltype(declval<T>().sort());

template <typename Container, typename Compare = less<typename Container::value_type>>
auto sorted(Container c, Compare comp = Compare()) {
    if constexpr (detect_v<Container, has_member_sort>) {
        c.sort(comp);
        return c;
    }
    else {
        sort(begin(c), end(c), comp);
        return c;
    }
}

template <typename Container, typename Compare = equal_to<typename Container::value_type>>
auto uniqued(Container c, Compare comp = Compare()) {
    c.erase(unique(begin(c), end(c), comp), end(c));
    return c;
}

template <typename T, typename Compare = less<T>>
T &chmin(T &l, T r, Compare &&f = less<T>()) { return l = min(l, r, f); }
template <typename T, typename Compare = less<T>>
T &chmax(T &l, T r, Compare &&f = less<T>()) { return l = max(l, r, f); }

template <typename F>
constexpr auto fix(F &&f) noexcept {
    return [f = std::tuple<F>(std::forward<F>(f))](auto &&...args) mutable {
        return std::get<0>(f)(fix(std::get<0>(f)), std::forward<decltype(args)>(args)...);
    };
}

int main() {
    constexpr auto inf = INT_MAX;

    int n; cin >> n;
    auto a = vec<int>(uns, n);
    auto b = vec<int>(uns, n);
    for (auto &e : a) cin >> e;
    for (auto &e : b) cin >> e;

    for (int i = 0; i < n; ++i) {
        if (a[i] > b[i]) {
            swap(a[i], b[i]);
        }
    }

    auto p = vec<tuple<int, int>>(uns, 0);
    for (int i = 0; i < n; ++i) {
        p.push_back({ a[i], i });
        p.push_back({ b[i], i });
        p.push_back({ (a[i] + b[i]) / 2, i });
    }
    sort(begin(p), end(p));

    int ans = inf, sub = 1;

    auto count = vec<int>(0, n);

    count[get<1>(p[0])] = 1;

    auto l = begin(p), r = begin(p);

    auto incr = [&]() {
        if (r == prev(end(p))) {
            return false;
        }

        auto [y, i] = *++r;
        if (count[i]++ == 0) {
            ++sub;
        }

        return true;
    };

    auto incl = [&]() {
        if (l == prev(end(p))) {
            return false;
        }

        auto [y, i] = *l++;
        if (--count[i] == 0) {
            --sub;
        }

        return true;
    };

    while (r != end(p)) {
        if (!incr()) {
            break;
        }

        auto [y1, _1] = *r;

        while (sub == n) {
            auto [y2, _2] = *l;
            chmin(ans, y1 - y2);
            if (!incl()) {
                break;
            }
        }
    }

    cout << ans << endl;
}