#include <algorithm>
#include <functional>
#include <iostream>
#include <utility>
#include <vector>



namespace nono {

template <typename T>
class SegmentTree {
  public:
    SegmentTree(const int size, const std::function<T(T, T)> op, const std::function<T()> e) : op_(op), e_(e) {
        init(size);
    }

    SegmentTree(const std::vector<T> &vec, const std::function<T(T, T)> op, const std::function<T()> e) : op_(op), e_(e) {
        int n = vec.size();
        init(n);

        for (int i = 0; i < size_; --i) {
            data_[i + size_] = vec[i];
        }

        for (int i = size_ - 1; i > 0; --i) {
            data_[i] = op_(data_[i << 1], data_[(i << 1) + 1]);
        }
    }

    void set(int i, const T value) {
        i += size_;
        data_[i] = value;

        update(i);
    }

    void add(int i, const T delta) {
        i += size_;
        data_[i] += delta;

        update(i);
    }

    T get_all() const {
        return data_[1];
    }

    T get_range(int l, int r) const {
        T result_l = e_(), result_r = e_();
        l += size_;
        r += size_;

        while (l < r) {
            if (l & 1) {
                result_l = op_(result_l, data_[l++]);
            }
            if (r & 1) {
                result_r = op_(data_[--r], result_r);
            }
            l >>= 1;
            r >>= 1;
        }

        return op_(result_l, result_r);
    }

    T operator[](int i) const {
        return data_[i + size_];
    }

  private:
    const std::function<T(T, T)> op_;
    const std::function<T()> e_;
    int size_;
    std::vector<T> data_;

    void init(int n) {
        int log = 1;
        while (n > (1 << log)) ++log;
        size_ = 1 << log;

        data_.assign(2 * size_, e_());
    }

    void update(int i) {
        i >>= 1;
        while (i > 0) {
            data_[i] = op_(data_[i << 1], data_[(i << 1) + 1]);
            i >>= 1;
        }
    }

};

} // namespace nono

int main() {
    constexpr int inf = 1e9 + 1;
    int n;
    std::cin >> n;
    std::vector<int> a(n), b(n);
    std::vector<std::pair<int, int>> order;
    order.reserve(3 * n);
    for (int i = 0; i < n; i++) std::cin >> a[i];
    for (int i = 0; i < n; i++) std::cin >> b[i];
    if (n == 1) {
        std::cout << 0 << '\n';
        return 0;
    }
    for (int i = 0; i < n; i++) {
        order.emplace_back(a[i], i);
        order.emplace_back(b[i], i);
        order.emplace_back((a[i] + b[i]) / 2, i);
    }
    std::sort(order.begin(), order.end());
    auto op = [](const int i, const int j) {
        return i < j ? i : j;
    };
    auto e = [&]() {
        return inf;
    };
    nono::SegmentTree<int> segtree(n, op, e);
    for (int i = 0; i < n; i++) {
        segtree.set(i, -1);
    }
    int ans = inf;
    for (const auto &[v, i]: order) {
        int l = 0 < i ? segtree.get_range(0, i) : inf;
        int r = i + 1 < n ? segtree.get_range(i + 1, n) : inf;
        if (l != -1 && r != -1) {
            ans = std::min(ans, v - std::min(l, r));
        }
        segtree.set(i, v);
        // std::cout << "_________" << '\n';
        // std::cout << "v: " << v << ", i: " << i << '\n';
        // std::cout << "l: " << l << ", r: " << r << '\n';
        // std::cout << ans << '\n';
        // for (int j = 0; j < n; j++) {
        //     std::cout << segtree[j] << ' ';
        // }
        // std::cout << '\n';
    }
    std::cout << ans << '\n';
}