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)

open Printf open Scanf
open Array

let rec gcd m n = match m,n with | m,0 -> m | m,n -> gcd n (m mod n)

let print_array f a = Array.iter (fun v -> printf "%s " @@ f v) a; print_newline ()

let () = scanf " %d" @@ fun n ->
  let a = init n (fun _ -> scanf " %d" @@ fun v -> v) in
  let lr = make n a.(0) in
  let rl = make n a.(n-1) in
  for i=1 to n-1 do
    lr.(i) <- gcd lr.(i-1) a.(i)
  done;
  for i=n-2 downto 0 do
    rl.(i) <- gcd rl.(i+1) a.(i)
  done;
  (* print_array string_of_int lr;
  print_array string_of_int rl; *)
  init n (fun i ->
    let w =
      if i=0 then rl.(1)
      else if i=n-1 then lr.(n-2)
      else gcd rl.(i+1) lr.(i-1)
    in w)
  |> fold_left max 0
  |> print_int