Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3
7 6 8

Sample Output 1

2

If we replace 7 with 4, the greatest common divisor of the three integers on the blackboard will be 2, which is the maximum possible value.

Sample Input 2

3
12 15 18

Sample Output 2

6

Sample Input 3

2
1000000000 1000000000

Sample Output 3

1000000000

We can replace an integer with itself.

Solution in C (GCC 5.4.1) (judge verdict: Runtime Error)

#include<stdio.h>


int max(int a,int b){

  if(a>b){
    return a;
  }else{
    return b;
  }

}

int gcd(int a,int b){
  int r,tmp;
  if(a<b){
    tmp=a;
    a=b;
    b=tmp;
  }
  r=a%b;
  while(r!=0){
  a=b;
  b=r;
  r=a%b;
}

  return b;
}

int main(void){
  int n;
  int a[12000];
  int i;
  int ans=0;
  int p[12000];
  int q[12000];
  int tmpg;
  int tmpt;
  int tmps;

  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%d",&a[i]);
  }

  p[0]=a[0];
  tmpg=a[0];

  for(i=1;i<n-1;i++){
    tmpg=gcd(a[i],tmpg);
    p[i]=tmpg;
  }
  q[n-1]=a[n-1];
  tmpt=a[n-1];

  for(i=(n-2);i>0;i--){
    tmpt=gcd(a[i],tmpt);
    q[i]=tmpt;
    }





  ans=max(p[n-2],q[1]);


  for(i=1;i<n-1;i++){
      tmps=gcd(p[i-1],q[i+1]);
      if(tmps>ans){
        ans=tmps;
      }
  }


  printf("%d\n",ans);

  return 0;
}