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