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: Wrong Answer)

import java.util.*;
class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = Integer.parseInt(sc.next());
        int[] a = new int[N];
        for(int i = 0; i<N; i++) {
            a[i] = Integer.parseInt(sc.next());
        }
        if(N==2) {
            System.out.println(Math.max(a[0],a[1]));
            return;
        }
        int ans = 0;
        int gcda = a[0];
        int min = Integer.MAX_VALUE;
        int minI = 0;
        int preMinI = 0;
        for(int i = 0; i<N; i++) {
            gcda = gcd(gcda,a[i]);
            if(min > gcda) {
                min = gcda;
                preMinI = minI;
                minI = i;
            }
        }
        //        System.out.println(minI);
        gcda = a[0];
        for(int i = 0; i<N; i++) {
            if(minI == 0 && i == minI) {
                gcda = a[1];
                continue;
            }
            if(i == minI)continue;
            gcda = gcd(gcda, a[i]);
        }
        ans = gcda;

        for(int i = 0; i<N; i++) {
            if(preMinI == 0 && i == preMinI) {
                gcda = a[1];
                continue;
            }
            if(i == preMinI)continue;
            gcda = gcd(gcda, a[i]);
        }


        System.out.println(Math.max(ans, gcda));
    }

    public static int gcd(int a, int b) {
        if(b==0)return a;
        return gcd(b, a%b);
    }
}