#include <bits/stdc++.h>
#include <atcoder/all>
// url 
#define rep(i,a,b) for(int i=a;i<b;i++)
#define rrep(i,a,b) for(int i=b-1;i>=a;i--)
#define all(x) (x).begin(),(x).end()
#define pb(x) push_back(x);
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a = b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a = b; return 1; } return 0; }
typedef long long ll;
typedef long double lld;
using namespace std;
using namespace atcoder;
using mint = static_modint<998244353>;
// using mint = static_modint<1000000007>;
const ll mod=998244353;
//const ll mod=1e9+7;
int dx[4]={1,0,-1,0};
int dy[4]={0,1,0,-1};
const string zton="0123456789";
const string atoz="abcdefghijklmnopqrstuvwxyz";
const string ATOZ="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const ll inf=(1ll<<60);
// const int inf=(1<<30);
lld dist(lld x1,lld x2,lld y1,lld y2){
    lld res=(x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);
    res=sqrt(abs(res));
    return res;
}
lld arg(lld x,lld y){
    const lld eps=1e-8;
    lld res=0;
    if(abs(x)+abs(y)<=eps)return 0.0;
    else if(abs(x)<=eps){
        if(y>=0.0)return (M_PI/2);
        else return (M_PI/2+M_PI);
    }
    else if(abs(y)<=eps){
        if(x>=0.0)return 0.0;
        else return M_PI;
    }
    res=atan2(abs(y),abs(x));
    if(x<=0&&y>=0)res=(M_PI-res);
    else if(x<=0&&y<=0)res+=(M_PI);
    else if(x>=0&&y<=0)res=(M_PI*2-res);
    return res;
}
ll gcd(ll a,ll b){
    if(a==0||b==0)return a+b;
    ll r;
    r=a%b;
    if(r==0){
        return b;
    }
    else{
        return gcd(b,r);
    }
}
typedef pair<ll,int> P;
using S = long long;
using F = long long;

const S INF = 8e18;
const F ID = 8e18;

S op(S a, S b){ return std::min(a, b); }
S e(){ return INF; }
S mapping(F f, S x){ return (f == ID ? x : f); }
F composition(F f, F g){ return (f == ID ? g : f); }
F id(){ return ID; }
int main(void){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int N;cin >> N;
    ll A[N];
    rep(i,0,N)cin >> A[i];
    ll B[N];
    rep(i,0,N){
        cin >> B[i];
        if(A[i]>B[i]){
            swap(A[i],B[i]);
        }
    }
    P p[N*3];
    rep(i,0,N){
        p[i*3]=P(A[i],i);
        p[i*3+1]=P(B[i],i);
        p[i*3+2]=P((A[i]+B[i])/2,i);
    }
    sort(p,p+N*3);
    reverse(p,p+N*3);
    int cnt[N];fill(cnt,cnt+N,0);
    std::vector<S> v(N);
    atcoder::lazy_segtree<S, op, e, F, mapping, composition, id> seg(v);
    rep(i,0,N){
        seg.set(i,B[i]);
    }
    ll ans=inf;
    rep(i,0,N*3){
        int idx=p[i].second;
        ll m=seg.all_prod();
        if(m!=-1){
            chmin(ans,p[i].first-m);
        }
        cnt[idx]++;
        if(cnt[idx]==1){
            seg.set(idx,(A[idx]+B[idx])/2);
        }
        else if(cnt[idx]==2){
            seg.set(idx,A[idx]);
        }
        else{
            seg.set(idx,-1);
        }
    }
    cout << ans << endl;
}