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 <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
int gcd(int x, int y) {
	if (y == 0) return x;
	return gcd(y, x%y);
}

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