p03061 AtCoder Beginner Contest 125 - GCD on Blackboard
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
```python
from fractions import gcd
n=int(input())
a=list(map(int,input().split()))
l=[0]*(n+1)
r=[0]*(n+1)
for i in range(n):
    l[i+1]=gcd(l[i],a[i])
for i in range(n-1,-1,-1):
    r[i]=gcd(r[i+1],a[i])
ans=l[-1]
for i in range(n):
    ans=max(ans,gcd(l[i],r[i+1]))
print(ans)
    
```