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[] A;

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();

		A = new int[N];
		for(int i = 0; i < N ; i++) {
			A[i] = sc.nextInt();
		}

		sc.close();

		int[] M = new int[N];
		int[] L = new int[N];
		int[] R = new int[N];

		L[0] = A[0];
		for(int i = 1; i < N; i++) {
			L[i] = gcd(L[i-1],A[i]);
			//System.out.println("L[" + i + "]: " + L[i]);
		}

		R[N-1] = A[N-1];
		for(int i = N-2 ; i >=0 ; i--) {
			R[i] = gcd(R[i+1],A[i]);
			//System.out.println("R[" + i + "]: " + R[i]);
		}


		int answer = Math.max(L[N-2], R[1]);
		for(int i = 1 ; i < N-1 ; i++) {;
			answer = Math.max(answer, gcd(L[i-1], R[i+1]));
		}

		System.out.println(answer);
	}


	public static int gcd(int a, int b) {
		int tmp;
		if(b > a) {
			tmp = a;
			a = b;
			b = tmp;
		}

		if(b == 0) {
			return a;
		}

	    int r = -1;
	    do{
	        r = a % b;
	        a = b;
	        b = r;
	    }while (r != 0);

	    return a;
	}

}
