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
#abc125c

def gcd(a,b):
 while b:
  a,b=b,a%b
 return a

n=int(raw_input())
a=map(int,raw_input().split())
res=0
x=[0]*(n+1)
y=[0]*(n+1)
for i in range(n):
 x[i+1]=gcd(x[i],a[i])
 y[i+1]=gcd(y[i],a[n-i-1])
for i in range(n):
 res=max(gcd(x[i],y[n-i-1]),res)
print res
