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 = Integer.parseInt(sc.next());

		long[] A = new long[N];
		long[] L = new long[N];
		long[] R = new long[N];

		for(int i = 0;i<N;i++) {
			A[i]=Long.parseLong(sc.next());
		}

		long w = A[0];
		for(int i=0;i<N-1;i++){
			w = GCD(w,A[i]);
			L[i] = w;
		}
		w = A[N-1];
		for(int i=N-1;i>=0;i--){
			w = GCD(w,A[i]);
			R[i] = w;
		}
		long max = 0;
		long tmp = 0;

		for(int i=0;i<N;i++) {
			if(i==0) {
				tmp = R[i+1];
			}else if(i==N-1) {
				tmp = L[i-1];
			}else {
				tmp = GCD(L[i-1],R[i+1]);
			}

			if(max<tmp) {
				max=tmp;
			}
		}

		System.out.println(max);
		sc.close();
	}
	static long GCD(long a,long b) {
		if(a>b) {
			long tmp;
	        while ((tmp = a % b) != 0) {
	            a = b;
	            b = tmp;
	        }
	        return b;
		}else {
			long tmp;
	        while ((tmp = b % a) != 0) {
	            b = a;
	            a = tmp;
	        }
	        return a;
		}
	}
}