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: Time Limit Exceeded)

import           Data.List -- sort
import           Control.Monad -- replicateM

readInt = read <$> getLine :: IO Integer
arrayInt = map read . words <$> getLine :: IO [Integer]
writeln x = putStrLn $ unwords x :: IO ()

main = do
    n <- readInt
    a <- arrayInt
    let l = scanl' gcd 0 a
    let r = reverse $ scanl' gcd 0 (reverse a)

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