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;
const int maxn=100007;
int gcd(int a,int b){
    return b==0?a:gcd(b,a%b);
}
int sum1[maxn],sum2[maxn],a[maxn];
int main(){
    int ans=0;
    int n;cin>>n;for(int i=1;i<=n;i++) cin>>a[i];
    for(int i=1;i<=n;i++) sum1[i]=gcd(sum1[i-1],a[i]);
    for(int i=n;i;i--) sum2[i]=gcd(sum2[i+1],a[i]);
    for(int i=1;i<=n;i++) ans=max(ans,gcd(sum1[i-1],sum2[i+1]));
    cout<<ans;
    return 0;
}
