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.Scanner;
public class Main {
	
	private static int gcd(int a, int  b) {
		int  temp = 0;

		if(a == 0) {
			return b;
		}
		if(b == 0) {
			return a;
		}
		if(a != 0 && b != 0) {
		while (a % b != 0){
			temp = a;
			a = b;
			b = temp % b;
		}
		}
		return b;
	}

	public static void main(String[] args) {
		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 []l = new int [n+1];
		int []r = new int [n+1];
		l[0] = 0;
		r[n] = 0;
		
		for(int i = 0; i < n ; i++) {
			l[i+1] = gcd(l[i],a[i]);
		}
		for(int j = n-1; j>=0; j--) {
			r[j] = gcd(r[j+1],a[j]);
		}
		int max = 1;
		
		for(int i = 0 ; i < n ; i++) {
			int p = gcd(l[i],r[i+1]);
			if(max < p)
				max = Math.max(max, p);
		}
		System.out.println(max);
		
		}
	}

