+ 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 ```