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 < (int)(n); i++)
using namespace std;

int gcd(int x, int y) {return (y?gcd(y,x%y):x);}

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