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=int(input())
A=list(map(int,input().split()))

L,R=[0]*n,[0]*n
L[0],R[-1]=A[0],A[-1]

from fractions import gcd

for i in range(1,n):
    L[i]=gcd(A[i],L[i-1])
for i in range(n-2,-1,-1):
    R[i]=gcd(A[i],R[i+1])

ans=max([L[-2],R[1]]+[gcd(L[i-1],R[i+1])for i in range(1,n-1)])
print(ans)