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
from fractions import gcd

n = int(raw_input())
L = map(int, raw_input().split())

D1 = [0]*n
D2 = [0]*n

for i in xrange(1, n):
    D1[i] = gcd(D1[i-1], L[i-1])

for i in xrange(n-2, -1, -1):
    D2[i] = gcd(D2[i+1], L[i+1])

M = [None]*n

for i in xrange(n):
    M[i] = gcd(D1[i], D2[i])

print max(M)