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: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>

int compare_int(const void *a,const void *b){
	return *(long long*)a-*(long long*)b;
}

long long gcd(long long a,long long b){
	if(a%b==0)return b;
	return gcd(b,a%b);
}

int main(){
	int n,i;
	long long a[100000];
	scanf("%d",&n);
	for(i=0;i<n;i++)scanf("%lld",&a[i]);
	if(n==2){
		printf("%lld\n",(a[0]>a[1]?a[0]:a[1]));
		return 0;
	}
	qsort(a,n,sizeof(long long),compare_int);
	long long aa=a[0],at=a[1];
	for(i=2;i<n;i++)aa=gcd(aa,a[i]);
	for(i=2;i<n;i++)at=gcd(a[i],at);
	printf("%lld\n",(aa>at?aa:at));
	return 0;
}