快读是复制粘贴的，复杂度应该正确（看题解了），本地随机数据大概跑300ms

#pragma GCC optimize(2)
#include<bits/stdc++.h>
#define int long long
using namespace std;
template <typename T> inline void read(T &a)
{
	a=0;T w=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){a=(a<<3)+(a<<1)+(ch^48);ch=getchar();}
	a*=w;
}
int t, p[300005], a[300005];
int e[5000005] = {0};
int gcd(int a, int b){
	if(a % b == 0)
	return b;
	return gcd(b, a % b);
}
int f[25][300005];
signed main(){
//	freopen("E.in", "r", stdin);
//	freopen("E.out", "w", stdout);
	read(t);
	int now = 1;
	e[1] = 1;
	p[1] = 1;
	for(int i = 2; now < 300004; i ++){
		if(e[i])
		continue;
		e[i] = 1;
		p[++now] = i;
		for(int j = i; i * j <= 5000000; j ++)
		e[i * j] = 1; 
	}
	while(t --){
		int n, t = 1;
		read(n);
		for(int i = 1; i <= n; i ++){
			read(a[i]);
//			a[i] = i;
			if(a[i] != 1)
			t = 0;
		}
		if(t){
			printf("2\n");
			continue;
		}
//		a[i] = 1;
		for(int i = 1; i <= n; i ++)
		f[0][i] = a[i];
		for(int j = 1; j <= 19; j ++){
			for(int i = 1; i <= n - (1 << (j)) + 1; i ++){
				if(f[j - 1][i] == -1 || f[j - 1][i + (1 << (j - 1))] == -1)
				f[j][i] = -1;
				else
				f[j][i] = f[j - 1][i] * f[j - 1][i + (1 << (j - 1))] / gcd(f[j - 1][i], f[j - 1][i + (1 << (j - 1))]);
				if(f[j][i] > p[n + 1])
				f[j][i] = -1;
			}
		}
		map<int, bool> e;
		for(int i = 1; i <= n; i ++){
			int sum = a[i];
			if(sum >= p[n + 1])
			continue;
			e[sum] = 1;
			for(int j = i + 1; j <= n; j ++){
				sum = sum * a[j] / gcd(sum, a[j]);
				if(sum >= p[n + 1])
				break;
				e[sum] = 1;
				
				int t = j;
				for(int k = 19; k >= 0; k --){
					if(t + (1 << k) - 1 <= n && f[k][t] != -1 && sum * f[k][t] / gcd(sum, f[k][t]) == sum)
					t += (1 << k) - 1;
				}
				j = t;
			}
		}
		int x = 1;
		while(e.find(x) != e.end())
		x ++;
//		for(int i = 1; i <= n; i ++)
//		printf("%lld ", a[i]);
		printf("%lld\n", x);
	}
	return 0;
}