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>
#define rep(i,n) for(int i=0; i<(n); i++)
using namespace std;
const int MX = 100005;
int n, a[MX], d[MX], rd[MX], ans;
int gcd(int a, int b){
	if(a < b) swap(a,b);
	for(;b;swap(a,b)) a %= b;
	return a;
}
int main(){
	scanf("%d", &n);
	rep(i,n){
		scanf("%d", a+i);
		d[i+1] = gcd(d[i], a[i]);
	}
	for(int i = n-1; i >= 0; i--){
		rd[i] = gcd(rd[i+1], a[i+1]);
		ans = max(ans,gcd(d[i], rd[i]));
	}
	printf("%d\n", ans);
}