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
#include <cstdio>
#include <algorithm>
using namespace std;

int a[111111], gf[111111], ge[111111];

int gcd(int x, int y) { return !y ? x : gcd(y, x % y); }

int main(void)
{
	int n, i, ans = 0;

	scanf("%d" ,&n);
	for (i = 1; i <= n; i++)
	{
		scanf("%d" ,&a[i]);
		gf[i] = gcd(gf[i - 1], a[i]);
	}
	for(i = n; i >= 1; i--)
		ge[i] = gcd(ge[i + 1], a[i]);

	for (i = 1; i <= n; i++)
		ans = max(ans, gcd(gf[i - 1], ge[i + 1]));

	printf("%d" ,ans);
	return 0;
}