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
from collections import deque

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

L=deque()

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

R=deque()

for i in range(N-1,-1,-1):
	if i==N-1:
		R.appendleft(A[i])
	else:
		R.appendleft( gcd(A[i],R[0]) )

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

print ans
