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: Accepted)

parseInt(x) = parse(Int,x)
function gc(a::Array,m::Int,N::Int)
  if m == 1
    g = gcd(a[2:N])
  elseif m == N
    g = gcd(a[1:(N-1)])
  else
    g = gcd(gcd(a[1:(m-1)]),gcd(a[(m+1):N]))
  end
  return(g)
end

function main()
  N = parseInt(readline())
  a = map(parseInt,split(readline()))
  (b,k) = findmin(a)
  g = gc(a,k,N)
  d = zeros(Int,N)
  for i=1:N
    d[i] = gcd(b,a[i])
  end
  (c,l)=findmin(d)
  h = gc(a,l,N)
  GCD = maximum([g,h])
  println(GCD)
end

main()