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 numpy as np

N=int(input())
A=[int(c) for c in input().split()]

#A=np.array(A)






#大きい方から
for i in range(sorted(A)[1],1,-1):
#	if(np.sum(A%i==0)>=N-1):
	
	#check
	b=0
	j=0
	while(b<2):
		if(j==N):
			print(i)
			exit()
		if(A[j]%i!=0):
			b+=1
		j+=1
print(1)
