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

int gcd(int a, int b) {
	return b ? gcd(b, a % b) : a;
}

int main() {
	int n; cin >> n;
	vector<int>a(n), l(n), r(n);
	for (auto&& x : a)cin >> x;
	for (int i = 0; i < n - 1; i++)l[i + 1] = gcd(l[i], a[i]);
	for (int i = n - 1; i > 0; i--)r[i - 1] = gcd(r[i], a[i]);

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

	return 0;
}