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 collections

def gcd(u,v):
	if v:
		return gcd(v, u % v)
	else:
		return u

n = int(raw_input())
elems = map(int , raw_input().split(' '))
dpp = [ None ] * len(elems)
dps = [ None ] * len(elems)
dpp[0] = elems[0]
for i in range(1,len(elems)): 
	dpp[i] = gcd(elems[i], dpp[i-1])
dps[len(elems) -1]  = elems[-1]
for i in range(len(elems) - 2, -1, -1): 
	dps[i] = gcd(elems[i], dps[i+1])
r = 0
for i in range(len(elems)):
	u,v = dpp[i-1] if i-1 >= 0 else -1, dps[i+1] if i+1 < len(elems) else -1
	r  = max(r, gcd(u,v) if u != -1 and v != -1 else max(u,v))
print r

