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 collections import deque
from fractions import gcd
n=int(input())
a=list(map(int,input().split()));g=a[-1]
b=deque([a[0]])
for num in reversed(a[1:]):
	g=gcd(g,num)
	b.appendleft(g)
m=b[0];gg=a[0]
for i,j in enumerate(a[:n-1]):
	gg=gcd(gg,j)
	m=max(m,gcd(gg,b[i+1]))
print(m)