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.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int n = sc.nextInt();
		int[] a = new int[n];
		for(int i = 0; i < n; i++){
		    a[i] = sc.nextInt();
		}
		// 計算
		int result = 0;
		int[] l = new int[n];
		int[] r = new int[n];
		int[] g = new int[n];
		for(int i = 0; i < n; i++){
		    if(i == 0){
		        l[i] = a[i];
		    }else{
		        l[i] = gcd(l[i-1], a[i]);
		    }
		}
		for(int i = n - 1; i >= 0; i--){
		    if(i == n - 1){
		        r[i] = a[i];
		    }else{
		        r[i] = gcd(r[i+1], a[i]);
		    }
		}
		for(int i = 0; i < n; i++){
		    int now = 0;
		    if(i == 0){
		        now = r[i+1];
		    }else if(i == n - 1){
		        now = l[i-1];
		    }else{
		        now = gcd(l[i-1], r[i+1]);
		    }
		    result = max(result, now);
		}
		
		// 出力
        System.out.println(result);
	}

	static int gcd(int x, int y){
	    if(x < y){
	        int temp = x;
	        x = y;
	        y = temp;
	    }
	    if(y == 0) return x;
	    if(x%y == 0) return y;
	    return gcd(y , x%y);
	}
}