Problem:
Score : 300 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, written on the blackboard.

You will choose one of them and replace it with an integer of your choice between 1 and 10^9 (inclusive), possibly the same as the integer originally written.

Find the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Output

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible greatest common divisor of the N integers on the blackboard after your move.

Sample Input 1

3
7 6 8

Sample Output 1

2

If we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.

Sample Input 2

3
12 15 18

Sample Output 2

6

Sample Input 3

2
1000000000 1000000000

Sample Output 3

1000000000

We can replace an integer with itself.

Solution in Julia (0.5.0) (judge verdict: Runtime Error)

parseInt(x) = parse(Int,x)
function main()
	n = map(parseInt, split(readline()))[1]
    a = map(parseInt, split(readline()))
  gl = zeros(Int,1,n)
  gr = zeros(Int,1,n)
  for i = 1 : n-1	
  	gl[i+1] = gcd(gl[i],a[i])
    gr[i+1] = gcd(gr[i],a[end -i +1])
  end
  g = zeros(Int,n)
  for i = 1 : n
    g[i] = gcd(gl[i],gr[i])
  end
    println(Int64(maximum(g)))
end
main()