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: Time Limit Exceeded)

#include <stdio.h>
#define max(x,y) ((x)>(y)?(x):(y))
#define min(x,y) ((x)<(y)?(x):(y))
#define FOR(i,m,n) for(i=m;i<n;i++)

int main(void)
{
	long long a,b[100010],i,j,c=0,d=0,e=0;
	scanf("%lld",&a);
	for(i=0;i<a;i++){
		scanf("%lld",&b[i]);
	}
	e=b[1];
	if(a==2){
		c=b[1];
	}else if(c==0){
		for(i=e;i>0;i--){
			for(j=0;j<a;j++){
				if(b[j]%i!=0){
					d++;
				}
			}
			if(d<2){
				c=i;
				break;
			}
			if(i==2) i=i/2;
			d=0;
		}
	}
	printf("%lld\n",c);
	return 0;
}