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

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int N; cin >> N;
    vector<int> A(N), B(N);
    for (auto &x : A) cin >> x;
    for (auto &x : B) cin >> x;
    vector<pair<int, int>> V;
    for (int i = 0; i < N; i++) {
        V.emplace_back(A[i], i);
        V.emplace_back(B[i], i);
        V.emplace_back(A[i] / 2 + B[i] / 2, i);
    }
    sort(V.begin(), V.end());
    vector<int> M(N, 0); int cnt = 0;
    int Ans = 2e9;
    for (int l = 0, r = 0; r < 3 * N; l++) {
        // [l, r)
        while (cnt != N && r < 3 * N) {
            auto &[u, v] = V[r++];
            if (M[v]++ == 0) cnt++;
            if (cnt == N) {
                Ans = min(Ans, u - V[l].first);
                break;
            }
        }
        while (cnt == N) {
            auto &[u, v] = V[l];
            if (M[v]-- > 1) {
                l++;
                Ans = min(Ans, V[r - 1].first - V[l].first);
            } else {
                cnt--;
            }
        }
    }
    cout << Ans << "\n";
    return 0;
}