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;

long long gcd(long long x,long long y){
	if(x<y) swap(x,y);
	while(x%y!=0){
		x=x%y; swap(x,y);
	}
	return y;
}


int main() {
	long long n,i,j,ans;
	cin >> n;
	vector<long long> a(n),l(n),r(n);
	for(i=0; i<n; i++){
		cin >> a[i];
	}
	l[0]=a[0]; r[n-1]=a[n-1];
	for(i=1; i<n; i++){
		l[i]=gcd(l[i-1],a[i]);
		r[n-i-1]=gcd(r[n-i],a[n-i-1]);
	}
	ans=max(r[1],l[n-2]);
	for(i=1; i<n-1; i++){
		ans=max(gcd(l[i-1],r[i+1]),ans);
	}
	cout << ans;
}