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 N,r,tmp;
   int max = 1;
   scanf("%d",&N);
   int A[N];
   for(int i = 0; i < N; i++) {
      scanf("%d",&A[i]);
   }
   for(int i = 0; i < N-1; i++) {
      for(int j = i+1; j < N; j++) {
         if(A[i] < A[j]) {
            tmp = A[i];
            A[i] = A[j];
            A[j] = tmp;
         }
         r = A[i] % A[j];
         while(r != 0) {
            A[i] = A[j];
            A[j] = r;
            r = A[i] % A[j];
         }
         if(max < A[j]) {
            max = A[j];
         }
      }
   }
   for(int i = 0; i < N ; i++) {
      if(A[i] % max != 0) {
         A[i] = max;
      }
   }
   printf("%d\n",max);
}