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

int n;
int pre[500000], suf[500000], a[500000];

int main()
{
	cin >> n;
	for (int i = 1; i <= n; i++) cin >> a[i];
	for (int i = 1; i <= n; i++) pre[i] = gcd(pre[i -1], a[i]);
	for (int i = n; i >= 1; i--) suf[i] = gcd(suf[i +1], a[i]);
	int ans = 1;
	for (int i = 1; i <= n; i++)
	    ans = max(ans, gcd(pre[i - 1], suf[i + 1]));
	 cout << ans;
}