#include <bits/stdc++.h>
using namespace std;

void solve() {
    int n; cin >> n;
    set<int> st1;
    for (int i = 0; i < n; i++) {
        int x; cin >> x;
        st1.insert(x);
    }
    for (int k = 1; k <= 1024; k++) {
        set<int> st2;
        for (auto s : st1)
            st2.insert(s ^ k);
        if (st1 == st2) {
            cout << k << "\n";
            return;
        }
    }
    cout << -1 << "\n";
}

int main() {
    int t; cin >> t;
    while (t--) solve();
}