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 <cstdio>
#include <algorithm>
using namespace std;
int N, A[100002], L[100002], R[100002], ans;
int gcd(int a, int b) {
  if(b == 0) return a;
  return gcd(b, a%b);
}
int main() {
  scanf("%d", &N);
  for(int i = 1; i <= N; ++i) scanf("%d", &A[i]);
  for(int i = 1; i <= N; ++i) {
    L[i] = gcd(L[i-1], A[i]);
    R[N-i+1] = gcd(R[N-i+2], A[N-i+1]);
  }
  for(int i = 1; i <= N; ++i) {
    ans = max(ans, gcd(L[i-1], R[i+1]));
  }
  printf("%d\n", ans);
}