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

		int[] L = new int[N+2];
		int[] R = new int[N+2];
		L[0] = 0;
		R[N+1] = 0;
		for(int i = 0;i < N;i++) {
			L[i+1] = gcd(L[i],A[i]);
		}
		for(int i = N;i > 0;i--) {
			R[i] = gcd(R[i+1],A[i]);
		}
		int[] M = new int[N+1];
		int max = 0;
		for(int i = 0;i < N;i++) {
			M[i] = gcd(L[i],R[i+1]);
			max = Math.max(max, M[i]);
		}
		System.out.println(max);
	}

	private static int gcd(int a, int b) {
		if(b == 0) {
			return a;
		}else if(a == 0) {
			return b;
		}
		return gcd(b,a%b);
	}
}
