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 x,int y){
    if(x==0)return y;
    return gcd(y%x,x);
}

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