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.Arrays;
import java.util.Scanner;

public class Main {
	Scanner sc = new Scanner(System.in);
	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
	}

	private void solve() {
		int n = nextInt();
		long[]a = new long [n];
		for(int i=0;i<n;i++)a[i]=nextLong();
		long[] L = new long[n+1];
		long[] R = new long[n+1];
		long[] res = new long[n];

		for (int i=0;i<n;i++)L[i+1]=gcd(L[i],a[i]);
		for (int i=n;i>0;i--)R[i-1]=gcd(R[i],a[i-1]);
		for (int i=0;i<n;i++)res[i]=gcd(L[i],R[i+1]);
		Arrays.sort(res);
		System.out.println(res[n-1]);
	}

	static long gcd(long m,long n) {
		if (m<n) return gcd(n,m);
		if (n==0)return m;
		return gcd(n,m%n);
	}

	private int nextInt() {
		return Integer.parseInt(sc.next());
	}
	private long nextLong() {
		return Long.parseLong(sc.next());
	}

}
