#include<iostream>
#include<set>
#include<algorithm>
#include<vector>
#include<string>
#include<set>
#include<map>
#include<numeric>
#include<queue>
#include<cmath>
using namespace std;
typedef long long ll;
const ll INF=1LL<<60;
typedef pair<ll,ll> P;
typedef pair<ll,P> PP;

const ll MOD=998244353;
const double PI=acos(-1);


int main(){
    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<vector<ll>> C(5,vector<ll>(N));

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

    //C[i][1]<=C[i][2]<=C[i][3]
    for(int i=0;i<N;i++){
        C[i][0]=-INF;
        C[i][1]=A[i];
        C[i][2]=(A[i]+B[i])/2;
        C[i][3]=B[i];
        C[i][4]=INF;
    }

    vector<ll> mini;
    for(int i=0;i<N;i++){
        for(int j=1;j<=3;j++){
            mini.push_back(C[i][j]);
        }
    }

    sort(mini.begin(),mini.end());//C[i][j]が小さい順に

    priority_queue<PP,vector<PP>,greater<PP>> pq;
    for(int i=0;i<N;i++){
        //C[i][0]の値(-INF), index, 次に見るべきインデックス
        pq.emplace(make_pair(C[i][0],make_pair(i,0)));
    }

    ll ans=INF;

    ll nowmaxi=-INF;

    for(ll e:mini){//C[i][j]が小さい順
        ll nowmini=e;

        while(!pq.empty() && pq.top().first< nowmini){
            auto [v,p]=pq.top();
            pq.pop();
            p.second++;
            if(p.second<=4){
            v=C[p.first][p.second];
            pq.push(make_pair(v,p));

            nowmaxi=max(nowmaxi,v);
            }
        }

        ans=min(ans,nowmaxi-nowmini);
    }

    cout<<ans<<endl;

    

}