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 OCaml (4.02.3) (judge verdict: Accepted)

let rec gcd a b = if b = 0 then a else gcd b (a mod b)
let () =
  Scanf.scanf "%d" @@ fun n ->
  let a = Array.init n (fun _ -> Scanf.scanf " %d" ((+) 0)) in
  let l = Array.init n (fun i -> a.(i)) in
  for i = 1 to n-1 do l.(i) <- gcd a.(i) l.(i-1) done;

  let r = Array.init n (fun i -> a.(i)) in
  for i = n-2 downto 0 do r.(i) <- gcd a.(i) r.(i+1) done;

  Array.init n (fun i -> 
    if i = 0 then r.(1) else if i = n-1 then l.(n-2)
    else gcd l.(i-1) r.(i+1))
  |> Array.fold_left max 0
  |> Printf.printf "%d\n"