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: Wrong Answer)

program ccc
implicit none

integer(8) :: n, i, one, two, g, dumy, res1, res2
integer(8),dimension(1) :: l
integer(8),allocatable,dimension(:) :: a, gg

read*, n
allocate(a(n))
allocate(gg(n))
read*, a

one=a(1)
gg(1)=one
do i=2,n
one=a(1)
two=a(i)
call gcd(one,two,g)
gg(i)=g
end do

l=minloc(gg)
gg(l)=one
l=minloc(gg)
res1=gg(l(1))

dumy=a(1)
a(1)=a(2)
a(2)=dumy

one=a(1)
gg(1)=one
do i=2,n
one=a(1)
two=a(i)
call gcd(one,two,g)
gg(i)=g
end do

l=minloc(gg)
gg(l)=one
l=minloc(gg)
res2=gg(l(1))

write(*,'(i0)') max(res1,res2)

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