Equalizing Array

Problem Description

Polycarp has an array $a_1, a_2, \dots, a_n$ of length $n$ ($n$ is even). Polycarp is also given a positive integer $k$, and he begins performing the following operation on the array $a$: choose an index $i\ (1 \leq i \leq n)$ and subtract $k$ from $a_i$.

After Polycarp performs several operations (possibly $0$), all numbers in the array $a$ become equal. Find the largest such $k$; if $k$ can be arbitrarily large, output $-1$.

Input Format

The first line contains an integer $t$, the number of test cases.

Each test case consists of two lines. The first line contains an even integer $n$. The second line contains $n$ integers $a_1, a_2, \dots, a_n$.

Output Format

For each test case, output one integer $k\ (k \geq 1)$ on a separate line — the largest value Polycarp can use to operate on the array — or $-1$ if $k$ can be arbitrarily large.

Sample Input

3
6
1 5 3 1 1 5
8
-1 0 1 -1 0 1 -1 0
4
100 -1000 -1000 -1000

Sample Output

2
1
1100

Constraints

For all data, $1 \leq t \leq 10$, $4 \leq n \leq 40$ ($n$ is even), $-10^6 \leq a_i \leq 10^6$, and the sum of $n$ does not exceed $100$.