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;

int gcd(int a, int b) {
	for (; b; swap(a, b))
		a %= b;
	return a;
}
int a[111111], b[111111];
int main() {
	int n, m = 0;
	cin >> n;
	for (int i = 0; i < n; i++) {
		scanf("%d", a + i);
		b[i + 1] = gcd(b[i], a[i]);
	}
	for (int i = n; i--;)
		a[i] = gcd(a[i], a[i + 1]);
	for (int i = 0; i < n; i++)
		m = max(m, gcd(a[i + 1], b[i]));
	cout << m << endl;
	return 0;
}
