#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <deque>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>

#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

using namespace std;
typedef long long ll;

template<typename T>
vector<vector<T>> vec2d(int n, int m, T v){
    return vector<vector<T>>(n, vector<T>(m, v));
}

template<typename T>
vector<vector<vector<T>>> vec3d(int n, int m, int k, T v){
    return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
}

template<typename T>
void print_vector(vector<T> v, char delimiter=' '){
    if(v.empty()) {
        cout << endl;
        return;
    }
    for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter;
    cout << v.back() << endl;
}

template<typename T>
class Compress{
    public:
    vector<T> data;
    int offset;
    Compress(vector<T> data_, int offset=0): offset(offset){
        data = data_;
        sort(begin(data), end(data));
        data.erase(unique(begin(data), end(data)), end(data));
    };
    int operator[](T x) {
        auto p = lower_bound(data.begin(), data.end(), x);
        assert(x == *p);
        return offset+(p-data.begin());
	}
    T inv(int x){
        return data[x-offset];
    }
    int size(){
        return data.size();
    }
};

const ll inf = 1e18;

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    int n; cin >> n;
    vector<ll> 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<ll> v;
    for(int i = 0; i < n; i++){
        if(a[i] > b[i]) swap(a[i], b[i]);
        v.push_back(a[i]);
        v.push_back(b[i]);
        v.push_back((a[i]+b[i])/2);
    }
    auto cp = Compress<ll>(v);
    int m = cp.size();
    auto indices = vec2d(3, m, vector<int>());
    for(int i = 0; i < n; i++){
        indices[0][cp[a[i]]].push_back(i);
        indices[1][cp[(a[i]+b[i])/2]].push_back(i);
        indices[2][cp[b[i]]].push_back(i);
    }
    ll ans = inf;
    ll mx = *max_element(a.begin(), a.end());
    for(int i = 0; i < m; i++){
        int x = cp.data[i];
        chmin(ans, mx-x);
        for(int idx: indices[0][i]){
            chmax(mx, (a[idx]+b[idx])/2);
        }
        for(int idx: indices[1][i]){
            chmax(mx, b[idx]);
        }
        for(int idx: indices[2][i]){
            chmax(mx, inf);
        }
    }
    cout << ans << endl;
}