#include <bits/stdc++.h>
using namespace std;
#define int long long
#define INF (int)1e18
#define f first
#define s second

mt19937_64 RNG(chrono::steady_clock::now().time_since_epoch().count());
const int N = 2e5 + 69;
int a[N], b[N], c[N];
int seg[4*N];
int n;

void Build(int l, int r, int pos){
    if (l==r) {
        seg[pos] = a[l];
        return;
    }
    
    int mid = (l+r)/2;
    Build(l, mid, pos*2);
    Build(mid + 1, r, pos*2 + 1);
    
    seg[pos] = max(seg[pos * 2], seg[pos * 2 + 1]);
}

void Update(int l, int r, int pos, int qp){
    if (l==r){
        seg[pos] = min(a[l], min(b[l], c[l]));
        return;
    }
    
    int mid = (l+r)/2;
    if (qp <= mid) Update(l, mid, pos*2, qp);
    else Update(mid + 1, r, pos*2 + 1, qp);
    
    seg[pos] = max(seg[pos * 2], seg[pos * 2 + 1]);
}

void Solve() 
{
    cin>>n;
    for (int i=1; i<=n; i++)
    cin>>a[i];
    for (int i=1; i<=n; i++){
        cin>>c[i];
        if (a[i] > c[i]) swap(a[i], c[i]);
        b[i] = (a[i] + c[i])/2;
    }
    
    Build(1, n, 1);
    
    vector <pair<int, pair<int, int>>> v;
    
    for (int i=1; i<=n; i++){
        v.push_back({a[i], {i, 1}});
        v.push_back({b[i], {i, 2}});
        v.push_back({c[i], {i, 3}});
    }
    
    sort(v.begin(), v.end());
    int ans = INF;
    for (auto x: v){
        ans = min(seg[1] - x.f, ans);
        if (x.s.s == 1){
            a[x.s.f] = INF;
        } else if (x.s.s == 2){
            b[x.s.f] = INF;
        } else c[x.s.f] = INF;
        
        Update(1, n, 1, x.s.f);
    }
    
    cout<<ans<<"\n";
}

int32_t main() 
{
    auto begin = std::chrono::high_resolution_clock::now();
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    int t = 1;
   // cin >> t;
    for(int i = 1; i <= t; i++) 
    {
        //cout << "Case #" << i << ": ";
        Solve();
    }
    auto end = std::chrono::high_resolution_clock::now();
    auto elapsed = std::chrono::duration_cast<std::chrono::nanoseconds>(end - begin);
    cerr << "Time measured: " << elapsed.count() * 1e-9 << " seconds.\n"; 
    return 0;
}