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 void main(String args[]) {

		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] a = new int[N+1];
		int[] gcd_order = new int[N+2];
		int[] gcd_reverse = new int[N+2];

		// 1~N
		gcd_order[0] = 0;
		int max_gcd = 0;
		for(int i=1;i<N+1;i++) {
			a[i] = sc.nextInt();
			gcd_order[i] = gcd(a[i],gcd_order[i-1]);
		}

		gcd_reverse[N+1] = 0;
		gcd_reverse[N] = gcd(a[N],0);
		max_gcd = gcd_order[N];

		for(int i=N-1;i>=0;i--) {
			gcd_reverse[i] = gcd(a[i],gcd_reverse[i+1]);
			int gcd = gcd(gcd_order[i], gcd_reverse[i+2]);
			max_gcd = Math.max(max_gcd, gcd);
		}

		System.out.println((int)max_gcd);
	}

	//整数a,bの最大公約数
	public static int gcd(int a,int b) {
		if(b == 0) return a;
		else return gcd(b,a%b);
	}

}
