# include <iostream>
# include <vector>
const int32_t MAX = 1000000000;
using namespace std;

int main() {
    int32_t n;
    cin >> n;
    vector<int32_t> a(n);
    vector<int32_t> b(n);
    vector<vector<int32_t>> dp(n);
    vector<vector<int32_t>> prev(n);
    vector<vector<pair<int32_t, int32_t>>> count(n);
    for (size_t i = 0; i < n; i++) {
        dp[i].resize(2, MAX);
        count[i].resize(2);
        prev[i].resize(2);
    }
    for (size_t i = 0; i < n; i++) {
        cin >> a[i];
    }
    for (size_t i = 0; i < n; i++) {
        cin >> b[i];
    }
    prev[0][0] = 0;
    prev[0][1] = 0;
    count[0][0].first = 1;
    count[0][0].second = 0;
    count[0][1].first = 0;
    count[0][1].second = 1;
    dp[0][0] = 0;
    dp[0][1] = 0;
    for (size_t i = 0; i < n - 1; i++) {
        if (i % 2 == 0) {
            if (max(dp[i][0], abs(a[i + 1] - a[i])) < dp[i + 1][0]) {
                dp[i + 1][0] = max(dp[i][0], abs(a[i + 1] - a[i]));
                prev[i + 1][0] = 0;
                count[i + 1][0].first = count[i][0].first + 1;
                count[i + 1][0].second = count[i][0].second;
            }
            if (max(dp[i][0], abs(b[i + 1] - a[i])) < dp[i + 1][1]) {
                dp[i + 1][1] = max(dp[i][0], abs(b[i + 1] - a[i]));
                prev[i + 1][1] = 0;
                count[i + 1][1].first = count[i][0].first;
                count[i + 1][1].second = count[i][0].second + 1;
            }

            if (max(dp[i][1], abs(a[i + 1] - b[i])) < dp[i + 1][0]) {
                dp[i + 1][0] = max(dp[i][1], abs(a[i + 1] - b[i]));
                prev[i + 1][0] = 1;
                count[i + 1][0].first = count[i][1].first + 1;
                count[i + 1][0].second = count[i][1].second;
            }
            if (max(dp[i][1], abs(b[i + 1] - b[i])) < dp[i + 1][1]) {
                dp[i + 1][1] = max(dp[i][1], abs(b[i + 1] - b[i]));
                prev[i + 1][1] = 1;
                count[i + 1][1].first = count[i][1].first;
                count[i + 1][1].second = count[i][1].second + 1;
            }
        }
        else {
            int32_t rev = count[i][0].first - count[i][0].second;
            if (rev == 2 || rev == 0) {
                if (max(dp[i][0], abs(b[i + 1] - a[i])) < dp[i + 1][1]) {
                    dp[i + 1][1] = max(dp[i][0], abs(b[i + 1] - a[i]));
                    prev[i + 1][1] = 0;
                    count[i + 1][1].first = count[i][0].first;
                    count[i + 1][1].second = count[i][0].second + 1;
                }
            }
            if (rev == -2 || rev == 0) {
                if (max(dp[i][0], abs(a[i + 1] - a[i])) < dp[i + 1][0]) {
                    dp[i + 1][0] = max(dp[i][0], abs(a[i + 1] - a[i]));
                    prev[i + 1][0] = 0;
                    count[i + 1][0].first = count[i][0].first + 1;
                    count[i + 1][0].second = count[i][0].second;
                }
            }

            rev = count[i][1].first - count[i][1].second;
            if (rev == 2 || rev == 0) {
                if (max(dp[i][1], abs(b[i + 1] - b[i])) < dp[i + 1][1]) {
                    dp[i + 1][1] = max(dp[i][1], abs(b[i + 1] - b[i]));
                    prev[i + 1][1] = 1;
                    count[i + 1][1].first = count[i][1].first;
                    count[i + 1][1].second = count[i][1].second + 1;
                }
            }
            if (rev == -2 || rev == 0) {
                if (max(dp[i][1], abs(a[i + 1] - b[i])) < dp[i + 1][0]) {
                    dp[i + 1][0] = max(dp[i][1], abs(a[i + 1] - b[i]));
                    prev[i + 1][0] = 1;
                    count[i + 1][0].first = count[i][1].first + 1;
                    count[i + 1][0].second = count[i][1].second;
                }
            }
        }
    }
    cout << min(dp[n - 1][0], dp[n - 1][1]);
    return 0;
}