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<bits/stdc++.h>
using namespace std;
int gcd(int x,int y){return (x%y==0?y:gcd(y,x%y));}
int main(){
  int N;cin>>N;
  vector<int>A(N);for(int i=0;i<N;i++)cin>>A[i];
  vector<int>R(N),L(N);L[0]=A[0];R[N-1]=A[N-1];
  for(int i=1;i<N;i++)L[i]=gcd(L[i-1],A[i]);
  for(int i=N-2;i>=0;i--)R[i]=gcd(R[i+1],A[i]);
  int M=0;
  for(int i=0;i<N;i++){
    if(i==0) M=max(M,R[1]);
    else if(i==N-1)M=max(M,L[N-2]);
    else M=max(M,gcd(L[i-1],R[i+1]));
  }
  cout<<M<<endl;
}