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
import math

n = int(input())
a = list(map(int,input().split()))
L = [0]*(n+1)
R = [0]*(n+1)
for i in range(n):
    L[i+1] = math.gcd(L[i], a[i])
    R[-2-i] = math.gcd(R[-1-i], a[-1-i])
    
ans = 0
for i in range(n):
    G = math.gcd(L[i], R[i+1])
    ans = max(ans, G)
print(ans)
