#include <bits/stdc++.h>
#include <atcoder/all>

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

using namespace std;
using namespace atcoder;

#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define repll(i, n) for (long long i = 0; i < (long long)(n); i++)
#define rep2(i, n, m) for (int i = n; i < (int)(m); i++)
#define repll2(i, n, m) for (long long i = n; i < (long long)(m); i++)
#define all(v) v.begin(),v.end()
using ll=long long;
using ld=long double;
using vi=vector<int>;
using vvi=vector<vi>;
using vvvi=vector<vvi>;
using vl=vector<ll>;
using vvl=vector<vl>;
using vvvl=vector<vvl>;
using vld=vector<ld>;
using vvld=vector<vld>;

int dx[8]={1,0,-1,0,1,1,-1,-1};
int dy[8]={0,1,0,-1,1,-1,1,-1};

const double PI = acos(-1);
//const ll MOD=1e9+7;
//const ll MOD=998244353;
const ll INF=(1LL<<60);
const int INF2=(1<<30);
//using mint=modint1000000007;
//using mint=modint998244353;

int main() {
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int n;cin>>n;
    set<ll> val;
    vl a(n,0),b(n,0);
    rep(i,n)cin>>a[i];
    rep(i,n)cin>>b[i];
    rep(i,n)val.insert(a[i]);
    rep(i,n)val.insert(b[i]);
    rep(i,n)val.insert((a[i]+b[i])/2);
    ll sz=val.size();
    map<ll,ll> val_to_index;
    vl index_to_val(sz,0);
    int now=0;
    for(auto ite=val.begin();ite!=val.end();ite++){
        val_to_index[*ite]=now;
        index_to_val[now]=*ite;
        now++;
    }
    vvi index_to_index(sz);
    //index_to_val[i]にあたる値を持っている添字
    rep(i,n){
        int index=val_to_index[a[i]];
        index_to_index[index].push_back(i);
        index=val_to_index[b[i]];
        index_to_index[index].push_back(i);
        index=val_to_index[(a[i]+b[i])/2];
        index_to_index[index].push_back(i);
    }
    ll ans=INF;
    int left=0,right=-1;
    int f=0;
    vi cnt(n,0);
    int c=0;
    while(1){
        if(f==0){
            right++;
            if(right==sz)break;
            int v=index_to_val[right];
            for(auto i:index_to_index[right]){
                cnt[i]++;
                if(cnt[i]==1){
                    c++;
                    if(c==n)f=1;
                }
            }
        }
        else{
            for(auto i:index_to_index[left]){
                cnt[i]--;
                if(cnt[i]==0){
                    c--;
                    f=0;
                }
            }
            left++;
        }
        if(f){
            ll u=index_to_val[left],v=index_to_val[right];
            ans=min(ans,v-u);
        }
    }
    cout<<ans<<endl;
    return 0;
}