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();
		
		int[] A = new int[N];
		int[] B = new int[N];
		
		for(int i = 0; i < N; i++) {
			A[i] = sc.nextInt();
			B[i] = A[i];
		}
		
		Arrays.sort(A);
		
		int Y = yaku(A[0], A[1]);
		int check = 1;
				
		for(int i = 2; i < N; i++) {
			if(yaku(Y, A[i]) < Y) {
				Y = yaku(Y, A[i]);
				check = i;
			} else {
				Y = yaku(Y, A[i]);
			}
		}
		
		A[check] = A[0];
		int Y1 = yaku(A[0], A[1]);
		
		for(int i = 2; i < N; i++) {
			Y1 = yaku(Y1, A[i]);
		}
		
		Arrays.sort(B);
		
		B[0] = B[1];
		int Z = yaku(B[0], B[1]);
		
		for(int i = 2; i < N; i++) {
			Z = yaku(Z, B[i]);
		}
	
		System.out.println(Math.max(Y1, Z));
	}
	
	public static int yaku(int a, int b) {
		if(b == 0) {
			return a;
		}
		return yaku(b, a % b);
	}
}