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

L=[0]*(N+2)
R=[0]*(N+2)

for i in range(1,N+1):
	L[i]=gcd(L[i-1],A[i-1])

for i in range(N)[::-1]:
	R[i]=gcd(R[i+1],A[i])

A=[gcd(L[i],R[i+1]) for i in range(N+1)]

print(max(A))