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)

let
  n = parse(Int, readline())
  black_board_numbers = map(x -> parse(Int, x), split(readline()))

  left_gcd = zeros(Int, n - 1)
  right_gcd = zeros(Int, n - 1)

  left_gcd[1] = black_board_numbers[1]
  right_gcd[1] = black_board_numbers[n]

  for i = 2:n - 1
    left_gcd[i] = gcd(left_gcd[i - 1], black_board_numbers[i])
    right_gcd[i] = gcd(right_gcd[i - 1], black_board_numbers[n - i + 1])
  end
  
  max_gcd = max(left_gcd[n - 1], right_gcd[n - 1])

  for i = 2:n - 1
    max_gcd = max(max_gcd, gcd(left_gcd[i - 1], right_gcd[n - i]))
  end
  
  println(max_gcd)
end