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)

'use strict'

function Main(input) {
    input = input.split("\n")
    let N = parseInt(input[0])
    let numbers = input[1].split(' ').map(str => parseInt(str, 10))

    const gcd = (x, y) => {
      while(y) {
        var t = y;
        y = x % y;
        x = t;
      }
      return x;      
    }

    let max = 1
    for(let i = 0; i < N; i++) {
      let g = numbers[i+1] || numbers[i-1]

      for(let j = 0; j < N; j++) {
        if(j === i) {
          continue;
        }
        g = gcd(g, numbers[j])
    
        if(g <= max) {
          break;
        }    
      }
       max = Math.max(max, g)
    }
   
    console.log(max)
}

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