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
try:
    from fractions import gcd
except:
    from math import gcd
from itertools import accumulate
N=int(input())
A=[int(i) for i in input().split()]
l=[0]+list(accumulate(A,gcd))
g=list(reversed(list(accumulate(reversed(A),gcd))))+[0]

print(max([gcd(l[i-1],g[i]) for i in range(1,N+1)]))