# include <bits/stdc++.h>
using namespace std;
using LL = long long;
using ULL = unsigned long long;
const double PI = acos(-1);
template<class T>constexpr T INF() { return ::std::numeric_limits<T>::max(); }
template<class T>constexpr T HINF() { return INF<T>() / 2; }
template <typename T_char>T_char TL(T_char cX) { return tolower(cX); }
template <typename T_char>T_char TU(T_char cX) { return toupper(cX); }
template<class T> bool chmin(T& a,T b) { if(a > b){a = b; return true;} return false; }
template<class T> bool chmax(T& a,T b) { if(a < b){a = b; return true;} return false; }
template<class T> bool is_sqare(T a) { if(floor(sqrt(a)) * floor(sqrt(a)) == a){ return true; }return false; }
int popcnt(unsigned long long n) { int cnt = 0; for (int i = 0; i < 64; i++)if ((n >> i) & 1)cnt++; return cnt; }
int d_sum(LL n) { int ret = 0; while (n > 0) { ret += n % 10; n /= 10; }return ret; }
int d_cnt(LL n) { int ret = 0; while (n > 0) { ret++; n /= 10; }return ret; }
template<class T> using dijk = priority_queue<T, vector<T>, greater<T>>;
# define ALL(qpqpq)           (qpqpq).begin(),(qpqpq).end()
# define UNIQUE(wpwpw)        sort(ALL((wpwpw)));(wpwpw).erase(unique(ALL((wpwpw))),(wpwpw).end())
# define LOWER(epepe)         transform(ALL((epepe)),(epepe).begin(),TL<char>)
# define UPPER(rprpr)         transform(ALL((rprpr)),(rprpr).begin(),TU<char>)
# define REP(i,upupu)         for(LL i = 0, i##_len = (upupu);(i) < (i##_len);(i)++)
# define REPS(i,opopo)        for(LL i = 1, i##_len = (opopo);(i) <= (i##_len);(i)++)
# define len(x)                ((int)(x).size())
# define BIT(n)               (1LL << (n))
# define pb push_back

#ifdef LOCAL
#  include "_debug_print.hpp"
#  define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#  define debug(...) (static_cast<void>(0))
#endif

struct INIT{
    INIT(){
        std::ios::sync_with_stdio(false);
        std::cin.tie(0);
        cout << fixed << setprecision(20);
    }
}INIT;

void solve(){
    int n;
    cin >> n;
    vector<int> a(n), b(n);
    REP(i, n)cin >> a[i];
    REP(i, n)cin >> b[i];
    vector<pair<int, int>> v;
    REP(i, n){
        v.pb({a[i], i});
        v.pb({b[i], i});
        v.pb({(a[i] + b[i]) / 2, i});
    }
    sort(ALL(v));

    LL l = -1, r = HINF<LL>();
    auto check = [&](LL x) -> bool {
        vector<int> ins(n, 0);
        int zeros = n;
        for(int left = 0, right = 0;left < len(v);left++){
            while(right < len(v) && v[right].first <= v[left].first + x){
                if(ins[v[right].second] == 0)zeros--;
                ins[v[right].second]++;
                right++;
            }

            //debug(left, right, ins);

            if(zeros == 0)return true;

            if(ins[v[left].second] == 1)zeros++;
            ins[v[left].second]--;

            //debug(left, right, ins);
        }
        return false;
    };
    while(r - l > 1){
        LL mid = (l + r) / 2;
        //debug(l, r, mid);

        if(check(mid)){
            r = mid;
        }else{
            l = mid;
        }
    }
    cout << r << endl;
}

int main(){
    int t = 1;
    //cin >> t;
    while(t--)solve();
}