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 ll long long
#define rep(i,n) for(ll (i)=0;(i)<(n);(i)++)
using namespace std;

ll gcd(ll a, ll b) {
    if(b == 0)return a;
    return gcd(b,a%b);
}

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