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: Accepted)

program ccc
implicit none

integer(8) :: n, i, one, two, gl, gr, g, res
integer(8),allocatable,dimension(:) :: a, l, r

read*, n
allocate(a(n),l(0:n+1),r(0:n+1))
read*, a

l=0
r=0
l(1)=a(1)
r(n)=a(n)

do i=2,n
one=l(i-1)
two=a(i)
call gcd(one,two,gl)
l(i)=gl
end do

do i=n-1,1,-1
one=r(i+1)
two=a(i)
call gcd(one,two,gr)
r(i)=gr
end do

res=0
g=0
do i=1,n
gl=l(i-1)
gr=r(i+1)
if(gl==0) gl=gr
if(gr==0) gr=gl
call gcd(gl,gr,g)
res=max(res,g)
end do

write(*,'(i0)') res

end program

subroutine gcd(a,b,ans)
integer(8) :: a, b, aa, bb, m, ans

aa=max(a,b)
bb=min(a,b)
a=aa
b=bb
m=1

do while(m/=0)
 m=mod(a,b)
 a=b
 b=m
end do
ans=a
end subroutine gcd