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)

integer n
integer(16),allocatable,dimension(:)::a,l,r
integer ans
read*,n
allocate(a(n),L(0:N),R(1:N+1) )
read*,a

l(1)=a(1)
do i=2,N
  l(i)=getgcd( l(i-1),a(i) )
end do

r(N)=a(N)
do i=N-1,1,-1
  r(i)=getgcd( r(i+1),a(i) )
end do
l(0)=r(2)
r(N+1)=l(N-1)
ans=1
do i=1,N
  ans=max(ans,getgcd(l(i-1),r(i+1) ) )
end do

print"(I0)",ans
contains
pure function getgcd(a,b)
integer(16),intent(in)::a,b
integer(16) getgcd
integer(16) s,t
s=a+b
getgcd=b

t=mod(a+b,b)
do while(t/=0)
  s=getgcd
  getgcd=t
  t=mod(s,getgcd)
end do
end function getgcd
end