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):
    if b == 0:
        return a
    g = gcd(b, a % b)
    return g

n = input()
a_list = map(int, raw_input().split())

gs1 = [None] * n
gs1[0] = a_list[0]
for i in xrange(1, n):
    gs1[i] = gcd(gs1[i - 1], a_list[i])

gs2 = [None] * n
gs2[n - 1] = a_list[n - 1]
for i in reversed(xrange(n - 1)):
    gs2[i] = gcd(gs2[i + 1], a_list[i])

max_g = 0
for exclude in xrange(n):
    if exclude == 0:
        g = gs2[1]
    elif exclude == n - 1:
        g = gs1[n - 2]
    else:
        g = gcd(gs1[exclude - 1], gs2[exclude + 1])
    if g > max_g:
        max_g = g
print(max_g)
