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: Time Limit Exceeded)

open Batteries
(* a と b の最大公約数を返す関数 *)
let rec gcd a b =
  match b with
  | 0 -> a
  | _ -> gcd b (a mod b)
(* 素数かどうか *)
let is_prime n =
  let rec judge n' i =
    match i with
    | i when n' < i * i -> true
    | i -> if n' mod i = 0 then false else judge n' (i+1)
  in judge n 2
let n = read_int ()
let a = read_line () |> String.split_on_char ' ' |> List.map int_of_string
let get_gcd l =
  let rec loop lst hd = 
    match lst with
    | [] -> hd
    | first :: rest -> gcd first (loop rest hd)
  in loop (List.tl l) (List.hd l)

let rec loop old lst =
  match lst with
  | [] -> min_int
  | first :: rest ->
    max (get_gcd @@ old @ rest) (loop (first::old) (rest))

let _ = Printf.printf "%d\n" @@ loop [] a