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)

--{-# LANGUAGE OverloadedStrings #-}
--{-# LANGUAGE OverloadedLists   #-}
{-# LANGUAGE BangPatterns      #-} --引数に!
{-# LANGUAGE MultiWayIf        #-}
{-# LANGUAGE TupleSections     #-}

import Data.Bits
import Data.Maybe (fromJust)
import Data.List
import qualified Data.Vector.Unboxed as V
import Control.Monad
import qualified Data.ByteString.Lazy.Char8 as B

type Ans = Int

solve :: Int -> [Int] -> Ans
solve n as = maximum $ sub 0
  where
    lgcd = V.fromList $ scanl1 gcd as
    rgcd = V.fromList $ scanr1 gcd as
    sub :: Int -> [Int]
    sub 0 = rgcd V.! 1 : (sub 1)
    sub i | i == n-1 = [lgcd V.! (n-2)]
          | otherwise = gcd (lgcd V.! (i-1)) (rgcd V.! (i+1)) : (sub (i+1))



readBInt :: B.ByteString -> Int
readBInt = fst . fromJust . B.readInt

main0 :: B.ByteString -> Ans
main0 cont =
   let remLines0 = map (map readBInt . B.words) (B.lines cont)
       [n]:remLines1 = remLines0
       as = head remLines1
       in solve n as

main :: IO ()
main = print . main0 =<< B.getContents