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
#coding:utf-8
N=input()
A=map(int,raw_input().split())

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


# L[i]:=gcd(A_0, ..., A_i)
# R[i]:=gcd(A_i, ..., A_{N-1})
L=[0]*N
R=[0]*N

L[0]=A[0]
R[N-1]=A[N-1]
for i,a in enumerate(A):
    if i==0:continue
    L[i]=gcd(L[i-1],a)
for i,a in enumerate(reversed(A)):
    if i==0:continue
    R[N-i-1]=gcd(R[N-i],a)
ans=R[1] 
ans=max(ans,L[N-2])
for i in range(N-1):
    if i==0:continue
    ans=max(ans,gcd(L[i-1],R[i+1]))
print(ans)    


        





