/*For today, you happen to be the defeated. But what will you become tomorrow?*/

#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace __gnu_pbds;
using namespace std;

#define dbg if(debugg)
#define F first 
#define S second 

bool debugg = false;

template <typename T>
using order_set = tree<T, null_type,less<T>, rb_tree_tag,tree_order_statistics_node_update>;

template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());  

const int N = 100005;
vector<int>divisors[N];
void sieve()
{
    for(int i = 1; i < N; i ++){
        for(int j = i; j < N; j += i){
            divisors[j].push_back(i);
        }
    }
}
int cnt[N], tot[N];
void solve()
{
    
    int n;
    cin >> n;
    vector<int>v(n);
    int gd = 0;
    memset(cnt, 0, sizeof(cnt));
    memset(tot, 0, sizeof(tot));
    for(int i = 0; i < n; i ++){
        cin >> v[i];
        gd = __gcd(gd, v[i]);
        cnt[v[i]] += 1;
    }

    for(int i = 1; i < N; i ++){
        for(int j = i; j < N; j += i){
            tot[i] += cnt[j];
        }
    }
    int ans = 2 * gd;
    for(int itr = 0; itr < 50; itr ++){
        int x = v[rng() % n], y = v[rng() % n];
        for(int i : divisors[x]){
            for(int j : divisors[y]){
                
                if(i == j) continue;
                int lm = i * j / __gcd(i, j);
                if(lm >= N) lm = 0;
                if(tot[i] + tot[j] - tot[lm] != n) continue;
                int p = tot[i], q = tot[j];
                if(max(p, q) >= ((n + 1) / 2)){
                    if(min(p, q) >= (n / 2)){
                        ans = max(ans, i + j);
                    }
                }
                
            }
        }
    }

    cout << ans << '\n';
}



int32_t main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);

    int t  = 1;
    cin>>t;

    sieve();

    while(t--){

        solve();

    }

    return 0;

}