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);
		// 入力1をnに入れる
		int n = sc.nextInt();

		int[] a = new int[n];

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

		// 累積GCDの左右
		int[] left = new int[n+1];
		int[] right = new int[n+1];
		int[] middle = new int[n];

	    for (int i = 0; i < n; ++i) left[i+1] = gcd(left[i], a[i]);
	    for (int i = n-1; i >= 0; --i) right[i] = gcd(right[i+1], a[i]);

	    // 集計
		int ans = 1;
	    for (int i=0;i<n;++i) {
	    	// 更新
	    	middle[i]  = gcd(left[i], right[i+1]);
	    	ans = Math.max(ans, middle[i]);
	    }

		System.out.println(ans);
	}


	public static int gcd(int a, int b) {
		return b != 0 ? gcd(b, a % b) : a;
	}
}