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
import sys
from fractions import gcd

N=input()
A=map(int, sys.stdin.readline().split())

L=[]
R=[]

for i,a in enumerate(A):
    if i==0:
        L.append(a)
    else:
        L.append( gcd(L[-1],a) )

for i,a in enumerate(A[::-1]):
    if i==0:
        R.append(a)
    else:
        R.append( gcd(R[-1],a) )
R=R[::-1]

ans=float("-inf")
for i in range(N):
    if i==0:
        ans=max(ans,R[i+1])
    elif i==N-1:
        ans=max(ans,L[i-1])
    else:
        ans=max( ans,gcd(L[i-1],R[i+1]) )

print ans
