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 main() {
	int n; int gcd;
	cin >> n;
	vector<int>num(n);
	for (int i = 0; i < n; i++) {
		cin >> num[i];
	}

	sort(num.begin(), num.end());

	for (int i = num[1]; i > 0; i--) {
		int sum = 0;
		for (int j = 0; j < n; j++) {
			if (num[j] % i == 0) {
				sum++;
			}
		}
		if (sum >= n - 1) {
			gcd = i;
			break;
		}
	}
	cout << gcd;

}