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 main()
  N = readline() |> parseInt
  # A = readdlm(STDIN, Int)
  A = map(parseInt, split(readline()))

  a_gcd = Array{Int}(N)
  a_gcd[1] = A[1]
  for i in 2:N
    a_gcd[i] = gcd(a_gcd[i - 1], A[i])
  end

  a_gcd_r = Array{Int}(N)
  a_gcd_r[end] = A[end]
  for i in N-1:-1:1
    a_gcd_r[i] = gcd(a_gcd_r[i + 1], A[i])
  end

  a = map(1:N) do i
    if i == 1
      a_gcd_r[2]
    elseif i == N
      a_gcd[end - 1]
    else
      gcd(a_gcd[i - 1], a_gcd_r[i + 1])
    end
  end
  # println(a)
  result = maximum(a)

  println(result)
end

main()