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 fractions import gcd
n = int(input())
*A, = map(int, input().split())
L = [0]*n
R = [0]*n
for i in range(n-1):
    L[i] = gcd(L[i-1], A[i])
    R[n-1-i] = gcd(R[(n-i)%n], A[n-1-i])
B = [gcd(L[i-1], R[(i+1)%n]) for i in range(n)]
print(max(B))