# All are Same solution codeforces

This problem is a simplified version of D2, but it has significant differences, so read the whole statement.

Polycarp has an array of \$\$\$n\$\$\$ (\$\$\$n\$\$\$ is even) integers \$\$\$a_1, a_2, \dots, a_n\$\$\$. Polycarp conceived of a positive integer \$\$\$k\$\$\$. After that, Polycarp began performing the following operations on the array: take an index \$\$\$i\$\$\$ (\$\$\$1 \le i \le n\$\$\$) and reduce the number \$\$\$a_i\$\$\$ by \$\$\$k\$\$\$.

## All are Same solution codeforces

After Polycarp performed some (possibly zero) number of such operations, it turned out that all numbers in the array became the same. Find the maximum \$\$\$k\$\$\$ at which such a situation is possible, or print \$\$\$-1\$\$\$ if such a number can be arbitrarily large.

### Input All are Same solution codeforces

The first line contains one integer \$\$\$t\$\$\$ (\$\$\$1 \le t \le 10\$\$\$) — the number of test cases. Then \$\$\$t\$\$\$ test cases follow.

Each test case consists of two lines. The first line contains an even integer \$\$\$n\$\$\$ (\$\$\$4 \le n \le 40\$\$\$). The second line contains \$\$\$n\$\$\$ integers \$\$\$a_1, a_2, \dots a_n\$\$\$ (\$\$\$-10^6 \le a_i \le 10^6\$\$\$).

It is guaranteed that the sum of all \$\$\$n\$\$\$ specified in the given test cases does not exceed \$\$\$100\$\$\$.

## Output All are Same solution codeforces

For each test case output on a separate line an integer \$\$\$k\$\$\$ (\$\$\$k \ge 1\$\$\$) — the maximum possible number that Polycarp used in operations on the array, or \$\$\$-1\$\$\$, if such a number can be arbitrarily large.

Example
input

### Copy All are Same solution codeforces

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

```2
1
1100```