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
// C - GCD on Blackboard
#include <bits/stdc++.h>
using namespace std;

int gcd(int a, int b){return b? gcd(b, a%b): a;}

int main(){
	int N; cin>>N;
	vector<int> A(N), L(N), R(N);

	for(int n=0; n<N; ++n) cin>>A[n];
	for(int n=0; n<=N-1-1; ++n) L[n+1] = gcd(L[n], A[n]);
	for(int n=N-1-1; n>=0; --n) R[n] = gcd(R[n+1], A[n+1]);

	int maxi = 0;
	for(int n=0; n<N; ++n) maxi = max(maxi, gcd(L[n], R[n]));
	cout<< maxi <<endl;
}