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.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();

		long a[] = new long[n];


		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();

		}
		Arrays.sort(a);
		long ans = 1;
		int cd = 0;
		for (long i = a[1]; i >=0; i=i-1) {
			for (int j = 0; j < n; j++) {
				if (a[j] % i != 0) {
					cd++;
					//System.out.println("cd" + i + " " + cd);
				}
				if(cd>=2){
					break;
				}
			}
			//System.out.println("sd#"+cd);


				if (cd <=1) {
					ans = i ;
					break;
				}
			cd = 0;
		}
		System.out.println(ans);
	}
}
