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
from fractions import gcd
n=int(input())
c=list(map(int,input().split()))
a=[c[0]]
b=[c[-1]]
for i in c[1:]:
    a.append(gcd(a[-1],i))
for i in c[:-1][::-1]:
    b.append(gcd(b[-1],i))
b=b[::-1]+[a[-2]]
a=[b[1]]+a
k=1
for i in range(n):
    k=max(k,gcd(a[i],b[i+1]))
print(k)