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>

int gcd(a, b){
  if(a == 0 || b == 0) return a + b;
  if(b > a) return gcd(b, a);
  return gcd(b, a % b);
}

void update(int i, int x, int *seg, int k){
  seg[k - 1 + i] = x;
  while(k > 0){
    for(int j = 0; j < k/2; j++){
      seg[(k - 1 + 2 * j)/2] = gcd(seg[k - 1 + 2 * j], seg[k + 2 * j]);
    }
    k /= 2;
  }
  return;
}

int
main(int artc, char *argv[])
{
  int n;
  scanf("%d", &n);
  int k = 1;
  while(n > k) k *= 2;
  int seg[500000] = {};
  for(int i = 0; i < n; i++){
    scanf("%d", &seg[k - 1 + i]);
  }

  int ans = 0; int temp;
  for(int i = 0; i < n; i++){
    temp = seg[k - 1 + i];
    update(i, 0, seg, k);
    ans = (ans > seg[0] ? ans : seg[0]);
    update(i, temp, seg, k);
  }

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

  return 0;
}