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.*;
class Main{

public static void main(String args[]){
Scanner sc=new Scanner(System.in);
int n=sc.nextInt();
long a[]=new long[n];
long f[]=new long[n];
long b[]=new long[n];
for(int i=0;i<n;i++) a[i]=Long.parseLong(sc.next());
for(int i=0;i<n;i++){
if(i==0){
f[i]=a[i];
b[n-i-1]=a[n-i-1];
}
else{
f[i]=gcd(f[i-1], a[i]);
b[n-i-1]=gcd(b[n-i], a[n-i-1]);
}
}
long ans=1;
for(int i=0;i<n;i++){
if(i==0) ans=Math.max(ans, b[i+1]);
else if(i==n-1) ans=Math.max(ans, f[i-1]);
else ans=Math.max(ans, gcd(f[i-1], b[i+1]));
}
System.out.println(ans);
}
static long gcd(long a, long b){
if(a<b) return gcd(b, a);
long r=a%b;
while(r>0){
a=b;
b=r;
r=a%b;
}
return b;
}

}