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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;

public class HelloWorld
{    
    static long[] A;
    static long N;
    static long[] left;
    static long[] right;
    
    static public void Main ()
    {
        //
        N = long.Parse(Console.ReadLine());
        A = Console.ReadLine().Split().Select(a => long.Parse(a)).ToArray();
        left = new long[N];
        for(int i = 0;i < N;i++){
          left[i] = -1;
        }
        left[0] = A[0];
        right = new long[N];
        for(int i = 0;i < N;i++){
          right[i] = -1;
        }
        right[N-1] = A[N-1];
      
        var ans = 1L;
        //Console.WriteLine(String.Join(" ",right));
        for(int i = 0;i < N;i++){
            
            long l = 1;
            long r = 1;
            
            //左のループ
            if(i != 0){
                l = lgcd(i-1);
            }

            //右のループ
            if(i != N-1){
                r = rgcd(i+1);
            }
          // Console.WriteLine(l+" "+r);
            var tmp = GCD(l,r);
         // Console.WriteLine("sss"+tmp);
            if(i == 0){
                tmp = rgcd(1);
              //Console.WriteLine("sss"+tmp);
            }
            if(i == N-1){
                tmp = lgcd(N-2);
              //Console.WriteLine("sss"+tmp);
            }
            
            ans = Math.Max(ans,tmp);
        }
       // Console.WriteLine(String.Join(" ",right));
       // Console.WriteLine(String.Join(" ",left));
        Console.WriteLine(ans);
        
    }
    
    static long lgcd(long n){
        if(n == 0){
          return left[0];
        }else if(left[n] != -1){
          return left[n];
        }else{
          left[n] = GCD(left[n-1],A[n]);
          return left[n];
        }
    }
    
    
    static long rgcd(long n){
      if(n == N-1){
        return right[N-1];
      }else if(right[n] != -1){
        return right[n];
      }else{
        right[n] = GCD(right[n+1],A[n]);
        return right[n];
      }
    }
    
    static long GCDP(long s ,long g){
        var res = A[s];
        for(long i = s+1;i <= g;i++){
            res = GCD(res,A[i]);
        }
        
        return res;
    }
    
    static long GCD(long A,long B){
        if(A < B){
            GCD(B,A);
        }
        
        long r = A%B;
        while(A%B != 0){
            r = A%B;
            A=B;
            B=r;
        }
        return B;
    }
    
}