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 args = input.split('\n');
  var n = args.shift();
  var a = args.shift().split(' ').map(m => parseInt(m)).sort((a, b) => a - b);
  var minimum = a.shift();
  var a1 = a.map(m => euclid(minimum, m)).sort((a, b) => a - b)[a.length === 1 ? 0 : 1];
  minimum = a.shift();
  var a2 = 0;
  if (a.length > 0) {
    a2 = a.map(m => euclid(minimum, m)).sort((a, b) => a - b)[0];
  }
  console.log(a1 > a2 ? a1 : a2);
}

function euclid(u, v) {
  var r = 0;
  while (0 !== v) {
    r = u % v;
    u = v ;
    v = r;
  }
  return u;
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));