#include <stdio.h>
#include <vector>
#include <algorithm>
#include <map>
#include <set>
#define MAX (int)2e9 + 1

int x[200010],y[200010];
std::vector<int> index;
std::map<int,int> hash;
std::set< std::pair<int,int> > S;
std::vector<int> V[200010];
int main()
{
	int a;
	scanf("%d",&a);
	for(int i=1;i<=a;i++) scanf("%d",&x[i]);
	for(int i=1;i<=a;i++) scanf("%d",&y[i]);
	
	for(int i=1;i<=a;i++)
	{
		V[i].push_back(x[i]);
		V[i].push_back(y[i]);
		V[i].push_back((x[i]+y[i])/2);
		V[i].push_back(MAX);
		std::sort(V[i].begin(),V[i].end());
		std::reverse(V[i].begin(),V[i].end());
		S.insert(std::make_pair(V[i].back(),i));
	}
	for(int i=1;i<=a;i++) for(int j=0;j<V[i].size();j++) index.push_back(V[i][j]);
	std::sort(index.begin(),index.end());
	index.erase(std::unique(index.begin(),index.end()),index.end());
	
	int ans = MAX;
	for(int i=0;i<index.size();i++)
	{
		int limit = index[i];
		while(!S.empty())
		{
			std::set< std::pair<int,int> > ::iterator it = S.begin();
			int val = (it->first), ind = (it->second);
			if(val<limit)
			{
				S.erase(it);
				V[ind].pop_back();
				S.insert(std::make_pair(V[ind].back(),ind));
			}
			else break;
		}
		std::set< std::pair<int,int> > ::iterator it = S.end();
		it--;
		int val = (it->first);
		if(val>=MAX) break;
		ans = ans<val-limit?ans:val-limit;
	}
	printf("%d",ans);
}