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
# solution
import io
from fractions import gcd

data=int(input())
array=list(map(int,input().split()))
k=[0]
l=[0]
for i in range(data-1):
    k.append(gcd(k[i],array[i]))
    l.append(gcd(l[i],array[data-i-1]))
ans=0
for i in range(data):
    ans=max(ans,gcd(k[i],l[data-i-1]))
print(ans)
