#include <bits/stdc++.h>

using namespace std;

/*const int MAXN = 5010;
int a[MAXN], b[MAXN], N;

bool check (int K) {
    cerr << "BS " << K << endl;
    multiset<int> A, B;
    for (int i = 1; i <= N; i++) {
        A.insert(a[i]);
        B.insert(b[i]);
    }
    while (!A.empty()) {
        int minA = *A.begin();
        int minB = *B.begin();

        if (minA < minB) {
            auto x = B.lower_bound(minA+K);
            if (x == B.end()) return false;
            cerr << 'A' << minA << ' ' << *x << endl;
            A.erase(A.begin());
            B.erase(x);
        } else {
            auto x = A.lower_bound(minB+K);
            if (x == A.end()) return false;
            cerr << 'B' << minB << ' ' << *x << endl;
            A.erase(x);
            B.erase(B.begin());
        }
    }
    return true;
}

int main() {
    ios::sync_with_stdio(false); cin.tie(0);
    int t; cin >> t;
    while(t--) {
        cin >> N;
        for (int i = 1; i <= N; i++) {
            cin >> a[i];
        }
        for (int i = 1; i <= N; i++) {
            cin >> b[i];
        }
        sort(a+1, a+1+N);
        sort(b+1, b+1+N);

        int l = 0, r = 1000000000, rez = 0;
        while (l <= r) {
            int mid = (l+r)/2;
            if (check(mid)) {
                l = mid+1;
                rez = mid;
            } else {
                r = mid-1;
            }
        }
        cout << rez << '\n';
    }
    return 0;
}*/

int n;
int a[5003];
int b[5003];

int levi[5003];
int desni[5003];

bool moze(int s)
{
    int p=0,q=0;
    for (;p<n;p++)
    {
        while (q<n && b[q]-a[p]<s) q++;
        desni[p]=q;
    }

    p=0,q=-1;
    for (;p<n;p++)
    {
        while (q+1<n && a[p]-b[q+1]>=s) q++;
        levi[p]=q;
    }

    for (int i=0;i<n;i++)
        for (int j=i+1;j<n;j++)
        {
            int najde=desni[i];
            int najle=levi[j];
            if (najle>=najde) continue;
            int nemoze=najde-najle-1;
            if (j-i+1 > n-nemoze) return false;
        }
    
    return true;
}

int main()
{
    ios::sync_with_stdio(false); cin.tie(0);

    int t; cin>>t;
    while (t--)
    {
        cin>>n;
        for (int i=0;i<n;i++) cin>>a[i];
        for (int i=0;i<n;i++) cin>>b[i];
        sort(a,a+n);
        sort(b,b+n);

        int l=0,r=1'000'000'007;
        while (r-l>1)
        {
            int mid=(l+r)/2;
            if (moze(mid)) l=mid;
            else r=mid;
        }

        cout<<l<<"\n";
    }
}