+ Time Limit: 2 seconds
+ Memory Limit: 256 MB
----------
You are given an array of $n \geq 3$ integers. You must remove exactly two elements. The *beauty* of the remaining array is defined as the greatest common divisor (GCD) of all its elements.
Your task is to maximize this beauty and output its value.
# Input
The first line contains an integer $t$ the number of test cases.
$$1 \leq t \leq 10^4$$
The first line of each test contains an integer $n$ the size of the array.
$$3 \leq n \leq 3 \times 10^5$$
The second line contains $n$ integers $a_1, a_2, \dots, a_n\,\,$.
$$1 \leq a_i \leq 10^8$$
It is guaranteed that the sum of $n$ over all test cases does not exceed $3 \times 10^5$.
# Output
For each test case print a single integer, the maximum possible beauty after removing exactly two elements.
# Examples
### Sample Input 1
```
3
5
21 36 39 12 54
4
30 40 50 60
3
78 97 56
```
### Sample Output 1
```
6
30
97
```