We define a Euclid algorithm sequence of length $$$k$$$ ($$$k \geq 2$$$) for two positive integers $$$x \geq y$$$ as the following sequence of positive integers:

$$$a_1, a_2, \ldots, a_k$$$, where $$$a_1 = x$$$, $$$a_2 = y$$$, and for any $$$i$$$ ($$$1 \leq i \leq k - 2$$$), the equality $$$a_{i + 2} = (a_i \bmod a_{i + 1})$$$ holds$$$^{\text{∗}}$$$.

For example, for $$$x = 13, y = 8, k = 4$$$, the corresponding Euclid algorithm sequence is $$$a = [13, 8, 5, 3]$$$. ($$$a_3 = 13 \bmod 8 = 5$$$, $$$a_4 = 8 \bmod 5 = 3$$$).

You are given a sequence $$$b_1, b_2, \ldots, b_n$$$. You need to determine whether it is possible to permute its elements so that it becomes a Euclid algorithm sequence for some two positive integers $$$x \geq y$$$.

$$$^{\text{∗}}$$$$$$x \bmod y$$$ denotes the remainder when $$$x$$$ is divided by $$$y$$$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 500$$$). The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$2 \leq n \leq 100$$$) — the size of the sequence.

The second line of each test case contains $$$n$$$ integers $$$b_1, b_2, \ldots, b_n$$$ ($$$1 \leq b_i \leq 10^9$$$) — the sequence $$$b$$$.

Output

For each test case, if it is possible to permute the elements of sequence $$$b$$$ so that there exists a suitable pair of positive integers $$$x \geq y$$$, output $$$x, y$$$ on a separate line. Otherwise, output $$$-1$$$ on a separate line.

If there are several suitable pairs $$$x, y$$$, you may output any of them.

Note

In the first test case, the pair ($$$1, 1$$$) is suitable: for $$$x = 1, y = 1, k = 2$$$, $$$a_1 = x = 1, a_2 = y = 1$$$, and the sequence $$$a = [1, 1] = b$$$ is obtained.

In the third test case, it can be shown that no suitable pair ($$$x, y$$$) exists.

In the fourth test case, the pair ($$$6, 4$$$) is suitable: for $$$x = 6, y = 4, k = 3$$$, $$$a_1 = x = 6, a_2 = y = 4, a_3 = (a_1 \bmod a_2) = (6 \bmod 4) = 2$$$, and the sequence $$$a = [6, 4, 2] = b$$$ is obtained.

Euclid, Sequence and Two Numbers

Examples