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 a, int b){
    return b==0 ? a : gcd(b, a%b);
}

int main(){
    int N, A[100001];
    cin >> N;
    for(int i=1; i<=N; i++) cin >> A[i];

    int L[100002] = {0}, R[100002] = {0};
    for(int i=1; i<=N; i++) L[i] = gcd(A[i], L[i-1]);
    for(int i=N; i>=1; i--) R[i] = gcd(A[i], R[i+1]);

    int ans = 0;
    for(int i=0; i<=N; i++) ans = max(ans, gcd(L[i-1], R[i+1]));
    cout << ans << endl;
    return 0;
}
