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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

module Main where
import Data.List
import qualified Data.Vector as V

main :: IO()
main = do    
  n <- (read <$> getLine) :: IO Int
  a <- (fmap read <$> words <$> getLine) :: IO [Int]
  let l = V.fromList $ scanl' gcd 0 a
  let r = V.fromList $ reverse $ scanl' gcd 0 (reverse a)
 
  --print $ foldl max 0 $
  --  fmap (\i-> gcd (l V.! i) (r V.! (i+1))) [0..(n-1)]
        
  --print $ maximum $
  --  zipWith gcd l r

  print $ foldl max 0 $
     [ gcd (l V.! i) (r V.! (i + 1)) | i <- [0 .. ((fromIntegral n) - 1)] ]