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
n=int(input())
a=list(map(int,input().split()))

import fractions as math

l=[0]
r=[0]
for i in range(n-1):
  li=math.gcd(l[i],a[i])
  l.append(li)
  ri=math.gcd(r[i],a[n-i-1])
  r.append(ri)
m=[]
for i in range(n):
  mi=math.gcd(l[i],r[n-i-1])
  m.append(mi)

print(max(m))