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
import java.util.*;
import java.io.*;

import static java.lang.System.in;

public class Main {
    static long[][] selfCon, selfUncon;
    static long mod = 1000000000+7;
    static int n;
    public static void main(String[] args) throws FileNotFoundException {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        for(int i=0;i<n;i++) a[i]=sc.nextInt();
        int[] left = new int[n], right = new int[n];

        left[0]=a[0];right[n-1]=a[n-1];
        for(int i=1;i<n;i++) left[i]=gcd(left[i-1],a[i]);
        for(int i=n-2;i>=0;i--) right[i] = gcd(right[i+1],a[i]);
        int ans = Math.max(right[1],left[n-2]);
        for(int i=1;i<n-1;i++){
            int cur = gcd(left[i-1],right[i+1]);
            ans = Math.max(cur,ans);
        }
        System.out.println(ans);
    }
    static int gcd(int a, int b){
        int c;
        if(a<b){
            c = a;
            a = b; b = c;
        }
        while(a%b!=0){
            c = a%b;
            a = b; b = c;
        }
        return b;
    }
}
