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 {
	public static int gcd(int a, int b) {
		int tmp;
		while(b!=0) {
			tmp=b;
			b=a%b;
			a=tmp;
		}
		return a;
	}
	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[] preGCD = new int[n+1];
		preGCD[0]=0;
		int[] postGCD = new int[n+1];
		postGCD[0]=0;
		for(int i=0, tmp=a[0]; i<n; i++) {
			tmp=gcd(tmp, a[i]);
			preGCD[i] = tmp;
//			System.out.println(preGCD[i]);
		}
		for(int i=0, tmp=a[n-1]; i<n; i++) {
			tmp=gcd(tmp, a[n-1-i]);
			postGCD[n-1-i] = tmp;
//			System.out.println(postGCD[n-1-i]);
		}
		int ans=Math.max(preGCD[n-2], postGCD[1]);
		for(int i=0+1, tmp; i<n-1; i++) {
			tmp=gcd(preGCD[i-1], postGCD[i+1]);
			ans = Math.max(ans, tmp);
		}
		System.out.println(ans);
	}
}