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 Maxn 100010
int n, a[Maxn], S_g[Maxn], P_g[Maxn], Ans;

inline int gcd(int x, int y) { if (!y) return x; return gcd(y, x%y); }
int main()
{
	scanf("%d", &n);
	for (int i=1; i<=n; i++) scanf("%d", &a[i]);
	S_g[1]=a[1]; for (int i=2; i<=n; i++) S_g[i]=gcd(S_g[i-1], a[i]);
	P_g[n]=a[n]; for (int i=n-1; i>=1; i--) P_g[i]=gcd(P_g[i+1], a[i]);
	for (int i=1; i<=n; i++) Ans = max(Ans, gcd(S_g[i-1], P_g[i+1])); 
	printf("%d\n", Ans);
}