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: Time Limit Exceeded)

// inputに入力データ全体が入る
function Main(input) {
  lines = input.split("\n")
  n = lines[0] * 1
  a = lines[1].split(' ').map(Number)
  ans = 0
  max = 0
  if (n == 2) {
    ans = Math.max(a[0], a[1])
  } else {
    for(var i = 0; i < a.length; i++) {
      if (i == 0) {
        g = a[1]
      } else {
        g = a[0]
      } 
      for(var j = 0; j < a.length; j++) {
        if (g <= max) {
          break;
        }
        if (j == i) continue;
        g = gcd(a[j], g)
      }
      if (g > max) {
        max = g
      }
    }
  }
  if (max) {
    ans = max
  }
  console.log(ans);
}

function gcd(a, b) {
  if (b == 0) {
    return a;
  }
  return gcd(b, a % b)
}

//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));