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
a = input()
l = map(int, raw_input().split())

def make_divisors(n):
    divisors = []
    for i in range(1, int(n**0.5)+1):
        if n % i == 0:
            divisors.append(i)
            if i != n // i:
                divisors.append(n//i)

    divisors.sort()
    return divisors

def gcd(l):
	l = sorted(l, reverse=True)
	l1 = make_divisors(l[0])
	l2 = make_divisors(l[1])
	l_mix = list(set(l1 + l2))
	l_mix = sorted(l_mix)
	r = 0
	for i in l_mix:
		f = 0
		for j in l:
			if j % i != 0:
				f += 1
			if f > 1:
				break
		if f <= 1:
			r = i
	return r 

print gcd(l)