Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3
7 6 8

Sample Output 1

2

If we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.

Sample Input 2

3
12 15 18

Sample Output 2

6

Sample Input 3

2
1000000000 1000000000

Sample Output 3

1000000000

We can replace an integer with itself.

Solution in Lua (5.3.2) (judge verdict: Time Limit Exceeded)

function gcd(x, y, z)
	return x<z and z or y == 0 and x or gcd(y, x % y, z)
end
n = io.read"*n"
a = {}
for i=1,n do
	a[i] = io.read"*n"
end
r=0
for i=1,n do
	t = {table.unpack(a)}
	t[i] = a[i+1] or a[i-1]
	for j=1,n-1 do
		t[1] = gcd(t[1], t[j+1], r)
	end
	r = t[1]
end
print(r)