#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <functional>
#include <cmath>
#include <iomanip>
#include <stack>
#include <queue>
#include <numeric>
#include <map>
#include <unordered_map>
#include <set>
#include <fstream>
#include <chrono>
#include <random>
#include <bitset>
//#include <atcoder/all>
#define rep(i,n) for(int i=0;i<(n);i++)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) ((int)(x).size())
#define pb push_back
using ll = long long;
using namespace std;
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; }
ll gcd(ll a, ll b) {return b?gcd(b,a%b):a;}
ll lcm(ll a, ll b) {return a/gcd(a,b)*b;}

int main(){
  int N; cin >> N;
  vector<ll> A(N);
  vector<ll> B(N);
  rep(i,N) cin >> A[i];
  rep(i,N) cin >> B[i];
  vector<pair<ll,int>> V;
  rep(i,N){
    V.pb({A[i],i});
    V.pb({B[i],i});
    V.pb({(A[i]+B[i])/2,i});
  }
  sort(all(V));
  ll ans = 1LL<<60;
  vector<int> cnt(N,0);
  int c = 0;
  ll lo = 0, hi = 0;
  int l=0,r=0;
  for(;r<sz(V);r++){
    hi = V[r].first;
    cnt[V[r].second]++;
    if(cnt[V[r].second]==1) c++;
    while(c==N && cnt[V[l].second]>1){
      cnt[V[l].second]--;
      l++;
      lo = V[l].first;
    }
    if(c==N) chmin(ans,hi-lo);
  }
  cout << ans << endl;
  return 0;
}