#include <bits/stdc++.h>

using namespace std;

int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n;
    cin >> n;
    vector<int> a(n), b(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    for (int i = 0; i < n; i++) {
        cin >> b[i];
    }
    vector<vector<int>> val(3, vector<int>(2));
    val[0][0] = val[0][1] = a[0];
    val[1][0] = val[1][1] = b[0];
    val[2][0] = val[2][1] = (a[0] + b[0]) / 2;
    for (int i = 1; i < n; i++) {
        for (int j = 0; j < 3; j++) {
            int x = max(a[i], val[j][1]) - min(a[i], val[j][0]);
            int y = max(b[i], val[j][1]) - min(b[i], val[j][0]);
            int z = max(a[i] / 2 + b[i] / 2, val[j][1]) - min(a[i] / 2 + b[i] / 2, val[j][0]);
            if (min({x, y, z}) == x) {
                val[j][0] = min(val[j][0], a[i]);
                val[j][1] = max(val[j][1], a[i]);
            } else if (min({x, y, z}) == y) {
                val[j][0] = min(val[j][0], b[i]);
                val[j][1] = max(val[j][1], b[i]);
            } else {
                val[j][0] = min(val[j][0], a[i] / 2 + b[i] / 2);
                val[j][1] = max(val[j][1], a[i] / 2 + b[i] / 2);
            }
        }
    }
    int ans = 1LL << 30;
    for (int i = 0; i < 3; i++) {
        ans = min(ans, val[i][1] - val[i][0]);
    }
    cout << ans << '\n';
}