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 math import gcd

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

if N==2:
    print(max(A))
else:
    r1=max(gcd(A[0],A[1]),gcd(A[1],A[2]),gcd(A[2],A[0]))
    a=gcd(A[2],gcd(A[0],A[1]))

    for i in range(3,N):
        r1=max(gcd(A[i],r1),a)
        a=gcd(a,A[i])
    print(r1)