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 Fortran (gfortran v4.8.4) (judge verdict: Time Limit Exceeded)

integer n
integer(16),allocatable,dimension(:)::A
integer(16) gcd,ans
read*,n
allocate(A(n))
read*,A

ans=1
do i=1,N
  gcd=A(mod(i,N)+1)
  do j=1,N
    if(i==j)cycle
    do
      if(mod(A(j),gcd)==0)exit
      gcd= abs(A(j)-gcd)
    end do
  end do
  ans=max(ans,gcd)
end do
print"(I0)",ans
end