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
main :: IO()
main = do
  _ <- getLine
  a <- map read . words <$> getLine
  print $ slv a

slv :: [Integer] -> Integer
slv a | length a == 2 = maximum a
      | otherwise = proc (cycle a) (length a - 2) (length a) 0
 
proc :: [Integer] -> Int -> Int -> Integer -> Integer
proc _ _ 0 ret = ret
proc (a:as) len n ret = proc as len (n-1) (max ret gcds)
  where gcds = foldl (gcd) a (take len as)