#include <bits/stdc++.h>
using namespace std;
#define FORE(i,a,b) for(int i = a; i <= b; ++i)
#define FORD(i,a,b) for(int i = a; i >= b; --i)
#define FOR(i,a,b) for(int i = a; i < b; ++i)
#define pb push_back
#define endl '\n'
#define ll long long
#define X first
#define Y second
const int MAXN = 1e5 * 5;
const int base = 1e9 + 7;
const int N = 55000;
int t,n;
int ans;
int a[N];
int gcd(int a,int b)
{
if (b == 0) return a;
else return gcd(b,a%b);
}
void upd(int d)
{
if (d <= ans) return;
int gcd1 = a[1];
int gcd2 = 0;
FORE(i,2,n)
{
if (a[i]%d == 0) gcd1 = gcd(gcd1 , a[i]);
else
{
if (gcd2 == 0) gcd2 = a[i];
else gcd2 = gcd(gcd2 , a[i]);
}
if (gcd2 && min(gcd1 , gcd2) <= ans) return;
}
if (gcd2 == 0) gcd2 = gcd1;
ans = max(ans , min(gcd1 , gcd2));
}
int main()
{
ios_base::sync_with_stdio(0); cin.tie(0);
//freopen("vo17lan.inp" , "r" , stdin);
//freopen("vo17lan.out" , "w" , stdout);
cin>>t;
while(t--)
{
cin>>n;
FORE(i,1,n) cin>>a[i];
sort(a+1,a+n+1);
ans = 1;
int xx = sqrt(a[1]);
FORD(d,xx,2)
if (a[1]%d == 0)
{
upd(d);
upd(a[1]/d);
}
upd(a[1]);
cout<<ans<<endl;
}
return 0;
}
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