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.

Examples

Input

3
7 6 8


Output

2


Input

3
12 15 18


Output

6


Input

2
1000000000 1000000000


Output

1000000000
n,*a=map(int,open(0).read().split())
b=a[::-1]
from math import gcd
L=[0]
R=[0]
for i in range(n-1):
  L.append(gcd(L[-1],a[i]))
  R.append(gcd(R[-1],b[i]))
ans=0
R=R[::-1]
#print(L,R)
for i in range(0,n-1+1):
  tmp=gcd(L[i],R[i])
  ans=max(ans,tmp)
print(ans)
  