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: Time Limit Exceeded)

parseInt(x) = parse(Int,x)

function main()
  N = parseInt(readline())
  a = map(parseInt,split(readline()))
  b = zeros(Int,N)
  c = 1
  d = 1
  b[1] = gcd(a[2:N])
  for i = 2:(N-1)
    c = gcd(a[1:(i-1)])
    d = gcd(a[(i+1):N])
    b[i] = gcd(c,d)
  end
  b[N]=gcd(a[1:(N-1)])
  GCD = maximum(b)
  println(GCD)
end

main()