For two integers $$$x$$$ and $$$y$$$ ($$$x,y\ge 2$$$), we will say that $$$x$$$ is a generator of $$$y$$$ if and only if $$$x$$$ can be transformed to $$$y$$$ by performing the following operation some number of times (possibly zero):

Choose a divisor $$$d$$$ ($$$d\ge 2$$$) of $$$x$$$, then increase $$$x$$$ by $$$d$$$.

For example,

$$$3$$$ is a generator of $$$8$$$ since we can perform the following operations: $$$3 \xrightarrow{d = 3} 6 \xrightarrow{d = 2} 8$$$;
$$$4$$$ is a generator of $$$10$$$ since we can perform the following operations: $$$4 \xrightarrow{d = 4} 8 \xrightarrow{d = 2} 10$$$;
$$$5$$$ is not a generator of $$$6$$$ since we cannot transform $$$5$$$ into $$$6$$$ with the operation above.

Now, Kevin gives you an array $$$a$$$ consisting of $$$n$$$ pairwise distinct integers ($$$a_i\ge 2$$$).

You have to find an integer $$$x\ge 2$$$ such that for each $$$1\le i\le n$$$, $$$x$$$ is a generator of $$$a_i$$$, or determine that such an integer does not exist.

Input

Each test contains multiple test cases. The first line of the input contains a single integer $$$t$$$ ($$$1\le t\le 10^4$$$) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1\le n\le 10^5$$$) — the length of the array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$2\le a_i\le 4\cdot 10^5$$$) — the elements in the array $$$a$$$. It is guaranteed that the elements are pairwise distinct.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, output a single integer $$$x$$$ — the integer you found. Print $$$-1$$$ if there does not exist a valid $$$x$$$.

If there are multiple answers, you may output any of them.

Note

In the first test case, for $$$x=2$$$:

$$$2$$$ is a generator of $$$8$$$, since we can perform the following operations: $$$2 \xrightarrow{d = 2} 4 \xrightarrow{d = 4} 8$$$;
$$$2$$$ is a generator of $$$9$$$, since we can perform the following operations: $$$2 \xrightarrow{d = 2} 4 \xrightarrow{d = 2} 6 \xrightarrow{d = 3} 9$$$.
$$$2$$$ is a generator of $$$10$$$, since we can perform the following operations: $$$2 \xrightarrow{d = 2} 4 \xrightarrow{d = 2} 6 \xrightarrow{d = 2} 8 \xrightarrow{d = 2} 10$$$.

In the second test case, it can be proven that it is impossible to find a common generator of the four integers.

Common Generator

Examples