A. Biggest Field
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are a farmer and you want to create the biggest field possible to make your farm.

You are given certain side lengths, you need to find what is the largest square field and the largest rectangle field you can make using the side lengths.

Print $$$-1$$$ if making a particular field is not possible.

A Square field cannot be a Rectangular Field

Input

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 500$$$) — the number of testcases

  • The first line contains a single integer $$$n$$$ ($$$1 \leq n \leq 2*10^5$$$) — the size of the array.
  • The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \leq a_i \leq 10^9$$$) — the initial values of the array.

It is guaranteed that the sum of all $$$n$$$ across all test cases does not exceed $$$2*10^5$$$.

Output

For each test, print two integers, the biggest square area and biggest rectangle area possible

Example
Input
3
8
1 1 1 1 2 2 2 2
8
1 1 2 2 2 2 3 3
8
1 2 3 4 5 5 5 5
Output
4 2
4 6
25 -1