#include <bits/stdc++.h> 
#include <atcoder/all>
#define pub push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (ll i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (ll i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
using namespace std;
using namespace atcoder;
using ll = long long; using dd = double;
using Pll = pair<ll, ll>;
using    vll = vector<   ll>; using   vdd = vector< dd>;
using   vvll = vector<  vll>; using  vvdd = vector<vdd>;
using  vvvll = vector< vvll>; using vvvdd = vector<vvdd>;
using vvvvll = vector<vvvll>;
using  vchar = vector< char>;
using vvchar = vector<vchar>;
using mint = modint998244353;
using mint2 = modint1000000007;
using  vmint = vector< mint>; using  vmint2 = vector< mint2>;
using vvmint = vector<vmint>; using vvmint2 = vector<vmint2>;

constexpr long long INF = (1LL << 60);
constexpr double EPS = 1e-9;
constexpr double PI = 3.141592653589;

//////////////////////////////////////////////////////////

template <typename T>
bool chmax(T& a, const T& b) {
	if (a < b) {
		a = b;  // aをbで更新
		return true;
	}
	return false;
}

template <typename T>
bool chmin(T& a, const T& b) {
	if (a > b) {
		a = b;  // aをbで更新
		return true;
	}
	return false;
}

template <typename T>
T sq(T x) {
	return x * x;
}

std::string zfill(int n, const int width)
{
	std::stringstream ss;
	ss << std::setw(width) << std::setfill('0') << n;
	return ss.str();
}

int main() {
	//cout << fixed << setprecision(10);
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	

	ll N; cin >> N;
	vll A(N), B(N), C(N);
	rep(i, N) {
		cin >> A[i];
	}
	rep(i, N) {
		cin >> B[i];
		C[i] = (A[i] + B[i]) / 2;
	}
	vector<Pll> K;
	rep(i, N) {
		K.pub({ A[i],i });
		K.pub({ B[i],i });
		K.pub({ C[i],i });
	}
	sort(ALL(K));
	vll cnt(N, 0);
	ll now = 0;
	ll l = 0, r = -1;
	ll ans = INF;
	while (true) {
		if (now < N) {
			r++;
			if (r == 3 * N) {
				break;
			}
			cnt[K[r].second]++;
			if (cnt[K[r].second] == 1) {
				now++;
			}
			if (now == N) {
				chmin(ans, K[r].first - K[l].first);
			}
		}
		else {
			cnt[K[l].second]--;
			if (cnt[K[l].second] == 0) {
				now--;
			}
			l++;
			if (now == N) {
				chmin(ans, K[r].first - K[l].first);
			}
		}
	}
	cout << ans << endl;
}