You are given an array $A$ of $N$ integers. Now there is another integer $X$ which is unknown but you know its properties. The properties of the unknown number are:

$1$. It is an integer.

$2$. If you subtract all the elements of the array $A$ individually from the number $X$ and add all the differences then it adds to $0$.

Your goal is to find the number $X$.

Input
The first line contains an integer $T$ denoting the total number of test cases.
The first line of each test case contains an integer $N$ as input.
Next line of each test case contains $N$ space separated integers.

Output
In the output you need to print the number $X$ if it exists or else you need to print $-1$. 

Constraints
$1 \le T \le 10$
$1 \le N \le 10^5$
$1 \le A[i] \le 10^9$