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(a, b):
	while b != 0:
		a, b = b, a % b
	return a

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