#include <iostream>
#include <algorithm>
#include <vector>
#include <deque>
#include <queue>
#include <set>
#include <map>
#include <limits>
#include <cmath>
#include <iomanip>
#include <functional>
#include <random>
#include <set>
#include <atcoder/string>
#include <unordered_map>
#include <climits>
#include <atcoder/lazysegtree>

using namespace std;
using ll = long long;
using namespace atcoder;

ll value(vector<ll> &A,vector<ll> &B,ll maxC)
{
    ll N = A.size();
    ll minC = numeric_limits<ll>::max();
    for(int i = 0;i < N;i++){
        if (B[i] <= maxC){
            minC = min(minC,B[i]);
            continue;
        }
        if ( (A[i] + B[i])/2 <= maxC){
            minC = min(minC,(A[i] + B[i])/2);
            continue;
        }
        if (A[i] <= maxC){
            minC = min(minC,A[i]);
            continue;
        }
        return numeric_limits<ll>::max();
    }
    return maxC - minC;
}


ll three_search(vector<ll> &A,vector<ll> &B,ll l,ll r)
{
    // cout << l << "~" << r << endl;
    if (l + 2 >= r)
    {
        vector<pair<ll, ll>> values;
        for (int i = l; i < r; i++)
        {
            values.push_back({value(A,B, i), i});
        }
        sort(values.begin(), values.end());
        return values.front().second;
    }
    else
    {
        ll t1 = (2 * l + r) / 3;
        ll t2 = (l + 2 * r) / 3;
        ll t1_value = value(A,B, t1);
        ll t2_value = value(A,B, t2);
        if (t1_value <= t2_value)
        {
            return three_search(A,B, l, t2);
        }
        else
        {
            return three_search(A,B, t1, r);
        }
    }
}

int solve()
{
    ll N;
    cin >> N;
    vector<ll> A(N);
    vector<ll> B(N);
    for(int i = 0;i < N;i++){
        cin >> A[i];
    }
    for(int i = 0;i < N;i++){
        cin >> B[i];
        if (A[i] > B[i]){
            swap(A[i],B[i]);
        }
    }

    ll maxC = three_search(A,B,0,1e10);
    cout << value(A,B,maxC) << endl;
    return 0;
}
int main()
{
    // ll T;
    // cin >> T;
    // while (T--)
    // {
        solve();
    // }
    // cout << flush;
    return 0;
}