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

//#define int long long
#define ld long double
#define ll long long
#define st first
#define nd second
#define pb push_back
#define eb emplace_back
#define sz(x) (int)(x).size()
#define all(x) begin(x),end(x)
#define FOR(i,l,r) for(int i = (l); i <= (r); i++)
#define ROF(i,r,l) for (int i = (r); i >= (l); i--)

auto& operator<<(auto&o, pair<auto,auto>p) {
	return o << "("  << p.st << ", " << p.nd << ")";
}
auto operator<<(auto&o, auto x)->decltype(end(x), o) {
	o << "{"; int i =0; for (auto e : x) o << ","+!i++ << e; 
	return o << "}";
}
#ifdef LOCAL
#define debug(x...) cerr << "[" #x "]: ", [](auto...$) { \
	((cerr << $ << "; "), ...) << endl; }(x)
#else
#define debug(...) {}
#endif

#define rep(i, a, b) for (int i = (a); i < (b); i++)
using pii = pair<int, int>;
using vi = vector<int>;

const int inf = 1e9 + 7;

const int N=2007;
ll lc[N][N];

ll a[N];
vector<int>G[N*N+N];
ll val[N*N+N];

void edge(int u,int v)
{
	G[u].pb(v);
	G[v].pb(u);
}

int vis[N*N+N], czas = 1;
int match[N*N+N];
bool dfs(int u, int good) {
	if (vis[u] == czas)
		return false;
	vis[u] = czas;
	
	for (int v : G[u]) if (v <= good) {
		if (match[v] == 0) {
			match[v] = u;
			match[u] = v;
			return true;
		}
	}
	
	for (int v : G[u]) if (v <= good) {
		if (dfs(match[v], good)) {
			match[v] = u;
			match[u] = v;
			return true;
		}
	}
	
	return false;
}

signed main() {
	cin.tie(0)->sync_with_stdio(0);
	int tt;
	cin>>tt;
	while(tt--)
	{
		int n;
		cin>>n;
		vector<pair<ll,int>>V;
		FOR(i,1,n) cin>>a[i];
		FOR(i,1,n) 
		{
			FOR(j,i+1,n)
			{
				lc[i][j]=a[i]*a[j]/__gcd(a[i],a[j]);
				lc[j][i]=lc[i][j];
			}
		}
		FOR(i,1,n)
		{
			
			vector<pair<ll,int>>X;
			FOR(j,1,n) X.pb({(ll)a[i]*(ll)j,1});
			FOR(j,1,n) if(i!=j) X.pb({lc[i][j],-1});
			sort(all(X));
			int cnt=0;
			for(auto [t,k]:X)
			{
				if(k==-1) cnt++;
				else 
				{
					V.pb({t,i});
					cnt--;
				}
				if(cnt<0) break;
			}
		}
		sort(all(V));
		int it=1;
		edge(V[0].nd,n+1);
		val[1]=V[0].st;
		int now = 0;
		FOR(i,1,sz(V)-1) 
		{
			if(V[i].st!=V[i-1].st)
			{
				it++;
				val[it]=V[i].st;
			}
			edge(V[i].nd,n+it);
		}
		FOR(i, 1, it) {
			now++;
			if (match[n+i] == 0 && !dfs(n+i, n+i)) {
				czas++;
				if (!dfs(n+i, n+i)) {
					now--;
					// nie udalo sie znalesc matchingu
				}
			}
			if (now == n) {
				cout<<val[i]<<endl;
				break;
			}
		}
		czas++;
		FOR(i,0,n*n+n) {
			G[i].clear();
			match[i] = 0;
			vis[i] = 0;
		}
	}

	return 0;
}