//████████╗██╗███╗░░██╗ ██╗░░░░░███████╗
//╚══██╔══╝██║████╗░██║ ██║░░░░░██╔════╝
//░░░██║░░░██║██╔██╗██║ ██║░░░░░█████╗░░
//░░░██║░░░██║██║╚████║ ██║░░░░░██╔══╝░░
//░░░██║░░░██║██║░╚███║ ███████╗███████╗
//░░░╚═╝░░░╚═╝╚═╝░░╚══╝ ╚══════╝╚══════╝
// __________________
// | ________________ |
// || ____ ||
// || /\ | ||
// || /__\ | ||
// || / \ |____ ||
// ||________________||
// |__________________|
// \###################\
// \###################\
// \ ____ \
// \_______\___\_______\
// An AC a day keeps the doctor away.
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
template<class T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define vt vector
#define all(x) begin(x), end(x)
#define allr(x) rbegin(x), rend(x)
#define ub upper_bound
#define lb lower_bound
#define db double
#define ld long db
#define ll int64_t
#define vll vt<ll>
#define vvll vt<vll>
#define pll pair<ll, ll>
#define vpll vt<pll>
#define vc vt<char>
#define vvc vt<vc>
#define vi vt<int>
#define vvi vt<vi>
#define vvvi vt<vvi>
#define pii pair<int, int>
#define vpii vt<pii>
#define vs vt<string>
#define vvs vt<vs>
#define vb vt<bool>
#define vvb vt<vb>
#define vvpii vt<vpii>
#define vd vt<db>
#define ar(x) array<int, x>
#define var(x) vt<ar(x)>
#define pq priority_queue
#define mset(m, v) memset(m, v, sizeof(m))
#define pb push_back
#define ff first
#define ss second
#define sv string_view
#define MP make_pair
#define MT make_tuple
#define rsz resize
#define sum(x) accumulate(all(x), 0LL)
#define srt(x) sort(all(x))
#define srtR(x) sort(allr(x))
#define srtU(x) sort(all(x)), (x).erase(unique(all(x)), (x).end())
#define SORTED(x) is_sorted(all(x))
#define rev(x) reverse(all(x))
#define gcd(a, b) __gcd(a, b)
#define lcm(a, b) (a * b) / gcd(a, b)
#define MAX(a) *max_element(all(a))
#define MIN(a) *min_element(all(a))
//SGT DEFINE
#define lc i * 2 + 1
#define rc i * 2 + 2
#define lp lc, left, middle
#define rp rc, middle + 1, right
#define entireTree 0, 0, n - 1
#define midPoint left + (right - left) / 2
#define pushDown push(i, left, right)
#define iterator int i, int left, int right
#define IOS ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
struct custom {
static const uint64_t C = 0x9e3779b97f4a7c15; const uint32_t RANDOM = std::chrono::steady_clock::now().time_since_epoch().count();
size_t operator()(uint64_t x) const { return __builtin_bswap64((x ^ RANDOM) * C); }
size_t operator()(const std::string& s) const { size_t hash = std::hash<std::string>{}(s); return hash ^ RANDOM; } };
template <class K, class V> using umap = std::unordered_map<K, V, custom>; template <class K> using uset = std::unordered_set<K, custom>;
template<typename T1, typename T2>
std::ostream& operator<<(std::ostream& o, const std::pair<T1, T2>& p) { return o << "{" << p.ff << " , " << p.ss << "}"; }
auto operator<<(auto &o, const auto &x) -> decltype(end(x), o) {
o << "{"; int i = 0; for (const auto &e : x) { if (i++) o << " , "; o << e; } return o << "}";
}
template <typename T1, typename T2> istream &operator>>(istream& in, pair<T1, T2>& input) { return in >> input.ff >> input.ss; }
template <typename T> istream &operator>>(istream &in, vector<T> &v) { for (auto &el : v) in >> el; return in; }
template<typename K, typename V>
auto operator<<(std::ostream &o, const std::map<K, V> &m) -> std::ostream& {
o << "{"; int i = 0;
for (const auto &[key, value] : m) { if (i++) o << " , "; o << key << " : " << value; }
return o << "}";
}
template<typename T> vt<T> uniqued(vt<T> arr) { srtU(arr); return arr; }
#ifdef LOCAL
#define debug(x...) debug_out(#x, x)
void debug_out(const char* names) { std::cerr << std::endl; }
template <typename T, typename... Args>
void debug_out(const char* names, T value, Args... args) {
const char* comma = strchr(names, ',');
std::cerr << "[" << (comma ? std::string(names, comma) : names) << " = " << value << "]";
if (sizeof...(args)) { std::cerr << ", "; debug_out(comma + 1, args...); }
else { std::cerr << std::endl; }
}
#define startClock clock_t tStart = clock();
#define endClock std::cout << std::fixed << std::setprecision(10) << "\nTime Taken: " << (double)(clock() - tStart) / CLOCKS_PER_SEC << " seconds" << std::endl;
#else
#define debug(...)
#define startClock
#define endClock
#endif
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
#define eps 1e-9
#define M_PI 3.14159265358979323846
const static ll INF = 1LL << 60;
const static int inf = 1e9 + 33;
const static int MK = 20;
const static int MX = 2e6 + 5;
const static int MOD = 1e9 + 7;
int pct(int x) { return __builtin_popcountll(x); }
const vvi dirs = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}, {1, 1}, {-1, -1}, {1, -1}, {-1, 1}}; // UP, DOWN, LEFT, RIGHT
int modExpo(ll base, ll exp, ll mod) { ll res = 1; base %= mod; while(exp) { if(exp & 1) res = (res * base) % mod; base = (base * base) % mod; exp >>= 1; } return res; }
void solve() {
int n; cin >> n;
vi a(n); cin >> a;
srt(a);
int m = MAX(a) + 1;
vi freq(m);
for(auto& it : a) freq[it]++;
vi divisor;
int M = (n + 1) / 2;
for(int i = 2; i < m; i++) {
int cnt = 0;
for(int j = i; j < m; j += i) {
cnt += freq[j];
}
if(cnt >= n - M) divisor.pb(i);
}
if(divisor.empty()) {
cout << 2 << endl;
return;
}
auto generate = [](vi& A, int g) -> void {
int n = A.size();
for(int i = 0; i < min(30, n); i++) {
int id = i, mx = 0;
for(int j = i; j < n; j++) {
int curr = gcd(g, A[j]);
if(curr > mx) {
mx = curr;
id = j;
}
}
swap(A[i], A[id]);
g = gcd(g, A[i]);
}
};
ll res = 0;
for(auto& x : divisor) {
vi A;
int c = 0, g = 0;
for(auto& it : a) {
if(it % x == 0 && A.size() < n - M) A.pb(it);
else g = gcd(g, it);
}
res = max(res, (ll)x + g);
}
cout << res << endl;
}
signed main() {
IOS;
startClock
//generatePrime();
int t = 1;
cin >> t;
for(int i = 1; i <= t; i++) {
//cout << "Case #" << i << ": ";
solve();
}
//endClock
return 0;
}
//███████████████████████████████████████████████████████████████████████████████████████████████████████
//█░░░░░░░░░░░░░░█░░░░░░██████████░░░░░░█░░░░░░░░░░░░███░░░░░░░░░░█░░░░░░██████████░░░░░░█░░░░░░░░░░░░░░█
//█░░▄▀▄▀▄▀▄▀▄▀░░█░░▄▀░░░░░░░░░░██░░▄▀░░█░░▄▀▄▀▄▀▄▀░░░░█░░▄▀▄▀▄▀░░█░░▄▀░░░░░░░░░░██░░▄▀░░█░░▄▀▄▀▄▀▄▀▄▀░░█
//█░░▄▀░░░░░░░░░░█░░▄▀▄▀▄▀▄▀▄▀░░██░░▄▀░░█░░▄▀░░░░▄▀▄▀░░█░░░░▄▀░░░░█░░▄▀▄▀▄▀▄▀▄▀░░██░░▄▀░░█░░▄▀░░░░░░░░░░█
//█░░▄▀░░█████████░░▄▀░░░░░░▄▀░░██░░▄▀░░█░░▄▀░░██░░▄▀░░███░░▄▀░░███░░▄▀░░░░░░▄▀░░██░░▄▀░░█░░▄▀░░█████████
//█░░▄▀░░░░░░░░░░█░░▄▀░░██░░▄▀░░██░░▄▀░░█░░▄▀░░██░░▄▀░░███░░▄▀░░███░░▄▀░░██░░▄▀░░██░░▄▀░░█░░▄▀░░█████████
//█░░▄▀▄▀▄▀▄▀▄▀░░█░░▄▀░░██░░▄▀░░██░░▄▀░░█░░▄▀░░██░░▄▀░░███░░▄▀░░███░░▄▀░░██░░▄▀░░██░░▄▀░░█░░▄▀░░██░░░░░░█
//█░░▄▀░░░░░░░░░░█░░▄▀░░██░░▄▀░░██░░▄▀░░█░░▄▀░░██░░▄▀░░███░░▄▀░░███░░▄▀░░██░░▄▀░░██░░▄▀░░█░░▄▀░░██░░▄▀░░█
//█░░▄▀░░█████████░░▄▀░░██░░▄▀░░░░░░▄▀░░█░░▄▀░░██░░▄▀░░███░░▄▀░░███░░▄▀░░██░░▄▀░░░░░░▄▀░░█░░▄▀░░██░░▄▀░░█
//█░░▄▀░░░░░░░░░░█░░▄▀░░██░░▄▀▄▀▄▀▄▀▄▀░░█░░▄▀░░░░▄▀▄▀░░█░░░░▄▀░░░░█░░▄▀░░██░░▄▀▄▀▄▀▄▀▄▀░░█░░▄▀░░░░░░▄▀░░█
//█░░▄▀▄▀▄▀▄▀▄▀░░█░░▄▀░░██░░░░░░░░░░▄▀░░█░░▄▀▄▀▄▀▄▀░░░░█░░▄▀▄▀▄▀░░█░░▄▀░░██░░░░░░░░░░▄▀░░█░░▄▀▄▀▄▀▄▀▄▀░░█
//█░░░░░░░░░░░░░░█░░░░░░██████████░░░░░░█░░░░░░░░░░░░███░░░░░░░░░░█░░░░░░██████████░░░░░░█░░░░░░░░░░░░░░█
//███████████████████████████████████████████████████████████████████████████████████████████████████████
tin.le LV 4
judge
