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(input())
A = list(map(int, raw_input().split()))

def gcd(m,n):
    return m if n == 0 else gcd(n, m%n)

L = [0] * (N+1)
R = [0] * (N+1)

# L: list
# boundary: L[0] = 0, L[N-1] = 0
# L[i]: previous (i-1)-th gcd value, i = [0, ..., N-2]
for i in range(N-1):
    L[i+1] = gcd(L[i], A[i])

# R: list
# boundary: R[0] = 0, R[N-1] = 0
# R[i]: last (N-i)-th gcd value, i = [N-1, ..., 1]
for i in range(N-1, 0, -1):
    R[i] = gcd(R[i+1], A[i])

max_gcd = 0
for i in range(N):
    if gcd(L[i], R[i+1]) > max_gcd:
        max_gcd = gcd(L[i], R[i+1])

print '{}'.format(max_gcd)
