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: Wrong Answer)

let rec gcd m n =
  if m = n then m
  else if m > n then gcd n m
  else gcd (n - m) m

let gcd_of_list ls = 
  let init = List.hd ls in
  List.fold_left (fun acc l -> gcd acc l) init ls

let solve n a =
  let rec inner acc i =
    if i = n - 1 then acc
    else 
      let tmp = ref [] in
      for j = 0 to n - 1 do
        if j <> i then tmp := a.(j)::!tmp;
      done;
      inner (max acc @@ gcd_of_list !tmp) (i + 1)
  in inner 0 0

let _ =
  let n = Scanf.scanf "%d\n" (fun n -> n) in
  let a = Array.make n 0 in
  for i = 0 to n - 1 do
    Scanf.scanf (if i <> n - 1 then "%d " else "%d\n") (fun a' -> a.(i) <- a')
  done;
  solve n a
  |> print_int