#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
pii segA[600008];
pii segB[600008];
int ind[600008];
int pref_add[600008];
int pref_add2[600008];
vector<pll> vsort;
int n;
void calc_seg(vl& arr, vl& A, pii* seg, ll x)
{
int l2 = 0;
int r2 = n-1;
rep(j,siz(vsort))
{
int i = vsort[j].ss;
while(l2 != n && arr[i]-A[l2] > x) l2++;
if(l2 != n) seg[i].ff = l2;
else seg[i].ff = n;
}
for(int j = siz(vsort)-1; j >= 0; j--)
{
int i = vsort[j].ss;
while(r2 != -1 && A[r2]-arr[i] > x) r2--;
if(r2 != -1) seg[i].ss = r2;
else seg[i].ss = -1;
}
}
void calc_add(int* add)
{
//A
rep(i,n)
{
int l = n;
int r = n*2-1;
int nxt_less = n*2;
while(l <= r)
{
int mid = (l+r)/2;
if(ind[mid] < ind[i])
{
nxt_less = mid;
r = mid-1;
}
else
{
l = mid+1;
}
}
if(segA[i].ff > segA[i].ss) continue;
int ile = nxt_less-n;
if(i >= segA[i].ff && i-ile <= segA[i].ss)
{
add[max(0,i-segA[i].ss)]++;
add[min({i+1,ile+1,i-segA[i].ff+1})]--;
}
if(ile <= i && i-ile >= segA[i].ff && i-ile <= segA[i].ss)
{
add[ile+1]++;
add[i+1]--;
}
}
//B
rep(i,n)
{
int l = i+n+1;
int r = n*2-1;
int nxt_less = n*2;
while(l <= r)
{
int mid = (l+r)/2;
if(ind[mid] < ind[i])
{
nxt_less = mid;
r = mid-1;
}
else
{
l = mid+1;
}
}
if(segB[i].ff > segB[i].ss) continue;
int ile = nxt_less-(i+n+1);
if(i+n*2-nxt_less >= segB[i].ff && i+n*2-nxt_less <= segB[i].ss)
{
add[i+1]++;
add[i+1+ile]--;
}
bool was = 0;
if(i+n*2-nxt_less >= segB[i].ff && i+n*2-nxt_less <= segB[i].ss)
{
was = 1;
add[i+1+ile]++;
}
else if(i+n*2-nxt_less >= segB[i].ff)
{
add[i+1+ile+(i+n*2-nxt_less-segB[i].ss)]++;
was = 1;
}
if(was)
{
add[min(n+1,i+1+ile+(i+n*2-nxt_less-segB[i].ff)+1)]--;
}
}
}
bool check(vl& arr, vl& A, vl& B, ll x)
{
calc_seg(arr,A,segA,x);
calc_seg(arr,B,segB,x);
rep(i,n*2) if((segA[i].ff == n || segA[i].ss == -1) && (segB[i].ff == n || segB[i].ss == -1)) return 0;
rep(i,n*2+1)
{
pref_add[i] = 0;
pref_add2[i] = 0;
}
calc_add(pref_add);
reverse(ind,ind+n*2);
reverse(segA,segA+n*2);
reverse(segB,segB+n*2);
calc_add(pref_add2);
reverse(ind,ind+n*2);
reverse(segA,segA+n*2);
reverse(segB,segB+n*2);
rep2(i,-1,n) pref_add[n-i] -= pref_add2[i+1];
int cnt = 0;
rep(i,n+1)
{
cnt += pref_add[i];
if(cnt == n*2) return 1;
}
return 0;
}
int main()
{
ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
//random_start();
cin >> n;
vl arr(n*2);
rep(i,n*2) cin >> arr[i];
rep(i,n*2) vsort.pb({(ll)arr[i]*(ll)(1e9+1)+(i < n ? i : n*2-i),i});
sort(all(vsort));
rep(i,n*2) ind[vsort[i].ss] = i+1;
vl B(n),C(n);
rep(i,n) cin >> B[i];
rep(i,n) cin >> C[i];
sort(all(B));
sort(all(C));
ll l = 0;
ll r = 1e9;
ll ans = -1;
while(l <= r)
{
ll mid = (l+r)/2;
if(check(arr,B,C,mid)||check(arr,C,B,mid))
{
ans = mid;
r = mid-1;
}
else
{
l = mid+1;
}
}
cout << ans << "\n";
}
