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 qualified Data.ByteString.Char8 as B
import           Data.List             (inits, tails)
import           Data.Maybe            (fromJust)

main :: IO ()
main = do
  n <- readLn
  as <- getInts
  print $ solve n as

solve :: Int -> [Int] -> Int
solve _ = maximum . map calcGCD . slice

-- >>> slice "abc"
-- [("", "bc"), ("a", "c"), ("ab", "")]
slice :: [a] -> [([a], [a])]
slice as = [(xs, ys) | (xs, _:ys) <- zip (init (inits as)) (init (tails as)) ]

calcGCD :: ([Int], [Int]) -> Int
calcGCD ([], ys) = gcdAll ys
calcGCD (xs, []) = gcdAll xs
calcGCD (xs, ys) = gcd (gcdAll xs) (gcdAll ys)

gcdAll :: [Int] -> Int
gcdAll = foldr1 gcd

readInts :: B.ByteString -> [Int]
readInts = map (fst . fromJust . B.readInt) . B.words

getInts :: IO [Int]
getInts = readInts <$> B.getLine