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;
#define rp(i,n) for(int i=0;i<(n);++i)

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);

	rp(n,N) cin>>A[n];

	rp(l,N-1){
		int r = N - l - 2;
		L[l+1] = gcd(L[l], A[l]);
		R[r] = gcd(R[r+1], A[r+1]);
	}

	int maxi = 1;
	rp(n,N) maxi = max(maxi, gcd(L[n], R[n]));
	cout<< maxi <<endl;
}