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.math.BigInteger;
import java.util.Arrays;
import java.util.Scanner;

public class Main{
	
	public static void main(String[] args)
	{
		new Main().run();
	}
	
	public void run()
	{
		Scanner file = new Scanner(System.in);
		int N = file.nextInt();
		int[] ints = new int[N];
		for(int i = 0;i<N;i++)
			ints[i] = file.nextInt();
		int[] before = new int[N];
		int[] after = new int[N];
		before[0] = ints[0];
		after[after.length - 1] = ints[ints.length - 1];
		for(int i = 1;i<ints.length;i++)
		{
			before[i] = gcd(before[i-1],ints[i]);
			after[after.length-i-1] = gcd(after[after.length-i],ints[ints.length-i-1]);
		}
		
		int best = 0;
		
		for(int i = 1;i<ints.length-1;i++)
			best = Math.max(best,gcd(before[i-1],after[i+1]));
		best = Math.max(best, after[1]);
		best = Math.max(best,before[ints.length-2]);
		System.out.println(best);
	}
	
	int gcd(int a, int b)
	{
		return BigInteger.valueOf(a).gcd(BigInteger.valueOf(b)).intValue();
	}
	
}
