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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function Main(input) {
	var inputArr = input.split("\n");
	var n = parseInt(inputArr[0]);
	var a = inputArr[1].split(" ");
    var max = 0;
  
    var b = a.filter(function (x, i, self) {
            return self.indexOf(x) === i;
        });
    var c = a.filter(function (x, i, self) {
            return self.indexOf(x) !== self.lastIndexOf(x);
        });
	for (var i = 0; i < n ; i++) {
      var ai = b.concat();
      ai.splice(i, 1);
      var g = gcd(ai);
      if (g > max) {
        max = g;
      }
    }
    console.log(max) ;
}
function gcd() {
  	var arg = arguments[0];
    var f = (a, b) => b ? f(b, a % b) : a;
    var ans = arg[0];
    for (var i = 1; i < arg.length; i++) {
        ans = f(ans, arg[i]); 
    }
    return ans 
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));