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 <algorithm>
#include <vector>

using namespace std;

int main() {
	int n; cin >> n;
	vector<int> a(n);
	for (int i = 0; i < n; ++i) cin >> a[i];
	sort(a.begin(), a.end());
	int ans;
	if (n == 2) ans = a[1];
	else {
		for (int i = a[1]; i > 0; --i) {
			int flag = 0;
			for (int j = 0; j < n; ++j) {
				if (a[j] % i) flag++;
				if (flag > 1) break;
			}
			if (flag < 2) {
				ans = i;
				break;
			}
		}
	}
	cout << ans << endl;

	return 0;
}