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 <iostream>

using namespace std;

int n;
int a[100005];
int l[100005], r[100005];

int gcd(int a, int b)
{
	if(b==0) return a;
	return gcd(b, a%b);
}

int main(void)
{
	cin >> n;
	for(int i = 1; i<= n; i++ ) cin >> a[i];

	for(int i = 1; i <= n; i++) l[i] = gcd(l[i-1], a[i]);
	for(int i = n; i >= 1; i--) r[i] = gcd(r[i+1], a[i]);

	int ans = 0;
	for(int i = 1; i <= n; i++){
		ans = max(ans, gcd(l[i-1], r[i+1]));
	}
	cout << ans << endl;
	return 0;
}