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):
  while(y): 
       x, y = y, x % y   
  return x 

def solve():
  n = int(raw_input())
  a = map(int, raw_input().split())
  left = [0] * (n + 1)
  right = [0] * (n + 1)
  for i in range(1,n + 1):
    left[i] = gcd(left[i - 1], a[i - 1])
  for i in range(n - 1, 0, -1):
    right[i] = gcd(right[i + 1], a[i])
  max_gcd = 0
  for i in range(n):
    max_gcd = max(max_gcd, gcd(left[i], right[i + 1]))
  print max_gcd
        
if __name__ == '__main__':
    solve()