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
def gcd(a,b):
	while b:
		a,b=b,a%b
	return a
n=int(input())
l = list(map(int, input().split()))
ans=1;
m=[0]*(n+1)
o=[0]*(n+1)
for i in range(n):
	m[i+1]=gcd(m[i],l[i])
	o[i+1]=gcd(o[i],l[n-i-1])
for i in range(n):
	ans=max(gcd(m[i],o[n-i-1]),ans)
print(ans)