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.Array

gcdlist'::Int->[Int]->Int
gcdlist' n [] = n
gcdlist' n (x:xs) = gcdlist' (gcd n x) xs

gcdlist::[Int]->Int
gcdlist ls = gcdlist' (head ls) (tail ls)

gen_ar::Int->[Int]->Array Int Int
gen_ar n ls = listArray (1,n) ls

gcd_dropping::Array Int Int -> Int -> Int
gcd_dropping ar i =gcdlist [ar!j |j <- ((filter (i/=)) (indices ar))]

solver::Int->[Int]->Int
solver n ls = maximum [gcd_dropping (gen_ar n ls) i |i<-[1..n]]

main::IO()
main=do
  n<-return.read=<<getLine
  ls<-return.map read.words=<<getLine
  print (solver n ls)