#include<iostream>
#include<vector>
#include<algorithm>
#include<cstring>
#include<cassert>
#include<cmath>
#include<ctime>
#include<iomanip>
#include<numeric>
#include<stack>
#include<queue>
#include<map>
#include<unordered_map>
#include<set>
#include<unordered_set>
#include<bitset>
#include<random>
using namespace std;
template<int m> struct modint
{
	private:
	unsigned int value;
	static constexpr int mod() {return m;}

	public:
	constexpr modint(const long long x = 0) noexcept
	{
		long long y = x;
		if(y < 0 || y >= mod())
		{
			y %= mod();
			if(y < 0) y += mod();
		}
		value = (unsigned int)y;
	}
	constexpr unsigned int val() noexcept {return value;}
	constexpr modint &operator+=(const modint &other) noexcept
	{
		value += other.value;
		if(value >= mod()) value -= mod();
		return *this;
	}
	constexpr modint &operator-=(const modint &other) noexcept
	{
		unsigned int x = value;
		if(x < other.value) x += mod();
		x -= other.value;
		value = x;
		return *this;
	}
	constexpr modint &operator*=(const modint &other) noexcept
	{
		unsigned long long x = value;
		x *= other.value;
		value = (unsigned int) (x % mod());
		return *this;
	}
	constexpr modint &operator/=(const modint &other) noexcept
	{
		return *this *= other.inverse();
	}
	constexpr modint inverse() const noexcept
	{
		assert(value);
		long long a = value,b = mod(),x = 1,y = 0;
		while(b)
		{
			long long q = a/b;
			a -= q*b; swap(a,b);
			x -= q*y; swap(x,y);
		}
		return modint(x);
	}
	constexpr modint power(long long N) const noexcept
	{
		assert(N >= 0);
		modint p = *this,ret = 1;
		while(N)
		{
			if(N & 1) ret *= p;
			p *= p;
			N >>= 1;
		}
		return ret;
	}
	constexpr modint operator+() {return *this;}
	constexpr modint operator-() {return modint() - *this;}
	constexpr modint &operator++(int) noexcept {return *this += 1;}
	constexpr modint &operator--(int) noexcept {return *this -= 1;}
	friend modint operator+(const modint& lhs, const modint& rhs) {return modint(lhs) += rhs;}
	friend modint operator-(const modint& lhs, const modint& rhs) {return modint(lhs) -= rhs;}
	friend modint operator*(const modint& lhs, const modint& rhs) {return modint(lhs) *= rhs;}
	friend modint operator/(const modint& lhs, const modint& rhs) {return modint(lhs) /= rhs;}
	friend ostream &operator<<(ostream &os,const modint &x) {return os << x.value;}
};
//using mint = modint<998244353>;
using mint = modint<1000000007>;
int N,A[2 << 17],B[2 << 17],cnt[2 << 17],P[2 << 17][3];
void solve()
{
	cin >> N;
	for(int i = 0;i < N;i++) cin >> A[i];
	for(int i = 0;i < N;i++) cin >> B[i];
	vector<int> V;
	map<int,multiset<int>> mp;
	V.reserve(3*N);
	int mx = -1;
	for(int i = 0;i < N;i++)
	{
		V.push_back(A[i]);
		V.push_back(B[i]);
		V.push_back((A[i]+B[i])/2);
		P[i][0] = A[i],P[i][1] = B[i],P[i][2] = (A[i]+B[i])/2;
		sort(P[i],P[i]+3);
		mp[A[i]].insert(i);
		mp[B[i]].insert(i);
		mp[(A[i]+B[i])/2].insert(i);
		mx = max(mx,min(min(A[i],B[i]),(A[i]+B[i])/2));
	}
	sort(V.begin(),V.end());
	V.erase(unique(V.begin(),V.end()),V.end());
	int ans = mx-V[0];
	for(int i = 1;i+1 < (int)V.size();i++)
	{
		bool fin = false;
		for(int id:mp[V[i-1]])
		{
			if(++cnt[id] == 3)
			{
				fin = true;
				break;
			}
			mx = max(mx,P[id][cnt[id]]);
		}
		if(fin) break;

		ans = min(ans,mx-V[i]);
	}

	cout << ans << endl;
}
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int tt = 1;
	//cin >> tt;
	while(tt--) solve();
}