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>

int main(){
	int i,j;
	int n;
	int a[100000];
	int good,koho,tujo=0,min=1000000001,max;
	scanf("%d",&n);
	for(i=0;i<n;i++){
		scanf("%d",a+i);
		if(a[0]!=a[i]){
			tujo=1;
		}
	}
	if(!tujo){
		printf("%d\n",a[0]);
		return 0;
	}
	for(i=0;i<n;i++){
		if(min>a[i]){
			min=a[i];
		}
		if(max<a[i]){
			max=a[i];
		}
	}
	max/=2;
	for(i=2;i<=min;i++){
		if(i>max){
			i=min;
		}
		good=0;
		for(j=0;j<n;j++){
			if(a[j]<i){
				break;
			}else if(a[j]%i==0){
				good++;
			}
		}
		if((n-good)<=1){
			koho=i;
		}
	}
	printf("%d\n",koho);
	return 0;
}