The Factor

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)


There is a sequence of $n$ positive integers. Fancycoder is addicted to learn their product, but this product may be extremely huge! However, it is lucky that FancyCoder only needs to find out one factor of this huge product: the smallest factor that contains more than 2 factors(including itself; i.e. 4 has 3 factors so that it is a qualified factor). You need to find it out and print it. As we know, there may be none of such factors; in this occasion, please print -1 instead.


The first line contains one integer $T \ (1 \le T \le 15)$, which represents the number of testcases.

For each testcase, there are two lines:

1. The first line contains one integer denoting the value of $n \ (1 \le n \le 100)$.

2. The second line contains $n$ integers $a_1, \ldots ,a_n\ (1 \le a_1, \ldots ,a_n \le 2\times 10^9)$, which denote these $n$ positive integers.


Print $T$ answers in $T$ lines.

Sample Input

2 3 1 2 3 5 6 6 6 6 6

Sample Output

6 4




BestCoder Round #54 (div.2)