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

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);

    int n;
    cin >> n;

    vector<pair<int, int>> p(n * 3);
    for (int i = 0; i < n; i++) {
        int a;
        cin >> a;
        p[i] = { a, i };
    }
    for (int i = 0; i < n; i++) {
        int b;
        cin >> b;
        p[n + i] = { b, i };
        p[n * 2 + i] = { (p[i].first + b) / 2, i };
    }
    sort(p.begin(), p.end());

    vector<int> c(n, 0);
    int r = 1 << 30;
    int k = 0;
    int a1 = 0;
    int i1 = 0;
    for (int i0 = 0; i0 < n * 3; i0++) {
        while (k < n && i1 < n * 3) {
            auto [a, i] = p[i1++];
            a1 = max(a1, a);
            k += c[i]++ == 0;
        }
        if (k < n) break;
        auto [a, i] = p[i0];
        r = min(r, a1 - a);
        k -= --c[i] == 0;
    }
    cout << r << endl;

    return 0;
}