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 commonDiv (num1,num2) {
    "use strict";
  if(num1 < num2){
      let tmp = num1;
        num1 = num2;
        num2 = tmp;
  }
  let num3 = num1 % num2;
  if(num3 === 0) {
      return num2;
  } else {
      return commonDiv(num2, num3);
  }

}

function Main(input) {
    "use strict";
    const els = input.split('\n');
    const number = els[0];
    const values = els[1].split(' ');
    let output;
    let results = [];


    for (let i = 0; i < number-1 ; i++) {
        results.push(commonDiv(parseInt(values[i],10), parseInt(values[i+1],10)));
    }
    results.push(commonDiv(parseInt(values[0],10), parseInt(values[number-1],10)));

    let min = Math.min.apply(null, results);
    const newResults = results.filter(n => n != min);

    if(values.length === 2){
        output = commonDiv(parseInt(values[0],10), parseInt(values[1],10));
        console.log(output);
        return;
    }

    if(newResults.length === 0){
        output = min;
        console.log(output);
        return;
    }

    output = Math.min.apply(null,newResults);

    console.log(output);
}

Main(require('fs').readFileSync('/dev/stdin', 'utf-8'));