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.*;
public class Main {
		
		public static int gcd(int a, int b) {
			return b == 0 ? a: gcd(b, a % b);
		}

		public static void main(String[] args) {
			Scanner sc = new Scanner(System.in);
			int N = sc.nextInt();
			int[] A = new int[N];
			int ans = 0;
			for(int i = 0; i < N; i++)
				A[i] = Integer.parseInt(sc.next());
			int[] L = new int[N+1];
			int[] R = new int[N+1];
			for(int i = 0; i < N; i++)
				L[i+1] = gcd(L[i],A[i]);
			for(int i = N-1; i > 0; i--)
				R[i] = gcd(R[i+1], A[i]);
			for(int i = 0; i < N; i++)
				ans = Math.max(ans, gcd(L[i],R[i+1]));
			System.out.println(ans);
		}

	}
