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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner; 

public class Main {
  public static void main (String[] args) {
    Scanner in = new Scanner(System.in);

    while (in.hasNext()) {
      int N = in.nextInt();
      int[] A = new int[N];
 
      for (int i = 0; i < A.length; ++i) {
        A[i] = in.nextInt();
      }

      int[] gcdBefore = new int[N];
      gcdBefore[0] = 0;
//      gcdBefore[1] = A[0];
      for (int i = 1; i < gcdBefore.length; ++i) {
        gcdBefore[i] = gcd(gcdBefore[i - 1], A[i - 1]);
      }

      int[] gcdAfter = new int[N];
      gcdAfter[gcdAfter.length - 1] = 0;
 //     gcdAfter[gcdAfter.length - 2] = A[A.length - 1];
      for (int i = gcdAfter.length - 2; i >= 0; --i) {
        gcdAfter[i] = gcd(gcdAfter[i + 1], A[i + 1]);
      }

      int ans = -1;
      for (int i = 0; i < A.length; ++i) {
        ans = Math.max(ans, gcd(gcdBefore[i], gcdAfter[i]));
      }

      System.out.println(ans);
    }
  }

  private static int gcd (int a, int b) {
    return b == 0 ? a : gcd(b, a % b);
  }
}