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 = input()

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

B = []
C = []

for i in A:
    if i not in B:
        B.append(i)
    elif i not in C:
        C.append(i)

def gcd(x,y):
    if y == 0:
        return x
    return gcd(y,x%y)

ans = 0;
for i in range(len(B)):
    res = 0
    for j in range(len(B)):
        if B[i] not in C:
            if i == j:
                continue
        res = gcd(res,B[j])
    ans = max(ans,res)
        

if ans == 0:
    if len(B) == 1:
        print B[0]
    else:
        print 1
else:
    print ans