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(x,y):
	return gcd(y,x%y) if y else x
n,a,b,c=int(input()),list(map(int,input().split())),[],[]
for i in range(n):
	b.append(gcd(b[i-1],a[i-1]) if i else 0)
	c.append(gcd(c[i-1],a[n-i]) if i else 0)
print(max([gcd(b[i],c[n-i-1]) for i in range(n)]))