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
N = int(raw_input())
A = map(int, raw_input().split())

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

L = [0,]* (N+1)
for i in range(0, N-1):
    L[i+1] = gcd(L[i], A[i])

R = [0,] * (N+1)
for i in range(N-1, 0, -1):
    R[i] = gcd(R[i+1], A[i])

M = list()
for i in xrange(N):
    M.append(gcd(L[i], R[i+1]))

print max(M)