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
    else:
        return gcd(b, a%b)

def solve():
    N = int(raw_input())
    arr = [int(_) for _ in raw_input().split()]
    left = [0] * (N + 1)
    right = [0] * (N + 1)
    left[0] = 0
    right[N] = 0
    for i in range(1, N+1):
        left[i] = gcd(left[i - 1], arr[i - 1])
    for i in range(N - 1, 0, -1):
        right[i] = gcd(right[i + 1], arr[i])
    max_gcd = 0
    for i in range(N):
        max_gcd = max(max_gcd, gcd(left[i], right[i+1]))
    print str(max_gcd)

if __name__ == '__main__':
    solve()
