A12629. Almost All Divisors

We guessed some integer number $x$ . You are given a list of almost all its divisors. Almost all means that there are all divisors except $1$ and $x$ in the list.

Your task is to find the minimum possible integer $x$ that can be the guessed number, or say that the input data is contradictory and it is impossible to find such number.

You have to answer $t$ independent queries.

The first line of the input contains one integer $t$ ( $1 \le t \le 25$ ) — the number of queries. Then $t$ queries follow.

The first line of the query contains one integer $n$ ( $1 \le n \le 300$ ) — the number of divisors in the list.

The second line of the query contains $n$ integers $d_1, d_2, \dots, d_n$ ( $2 \le d_i \le 10^6$ ), where $d_i$ is the $i$ -th divisor of the guessed number. It is guaranteed that all values $d_i$ are distinct.

For each query print the answer to it.

If the input data in the query is contradictory and it is impossible to find such number $x$ that the given list of divisors is the list of almost all its divisors, print -1. Otherwise print the minimum possible $x$ .