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
#include<stdio.h>
int gcd(int a,int b){
    if(a%b==0)return b;
    return gcd(b,a%b);
}
int main(void){
    int i,n,a;
    scanf("%d",&n);
    int ary[n];
    for(int i=0;i<n;i++)scanf("%d",&ary[i]);
    int l[n],r[n];
    l[0]=0;
    r[n-1]=0;
    for(i=1;i<n;i++){
        l[i]=gcd(l[i-1],ary[i-1]);
        r[n-i-1]=gcd(r[n-i],ary[n-i]);
    }
    int max=r[0];
    for(i=1;i<n;i++){
        a=gcd(r[i],l[i]);
        if(a>max)max=a;
    }
    printf("%d\n",max);
    return 0;
}