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: Accepted)

// inputに入力データ全体が入る
function Main(input) {
    // 1行目がinput[0], 2行目がinput[1], …に入る
    input = input.split("\n");
    // 数値の配列を作る
    const numList0 = input[0].split(' ').map(x => parseInt(x, 10));
    const N = numList0[0];
    const aList = input[1].split(' ').map(x => parseInt(x, 10));

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

    const lList = [0];
    const rList = [0];
    var newL = 0;
    var newR = 0;
    for (var i = 0; i < N; i++) {
        newL = gcd(newL, aList[i]);
        lList.push(newL);
        newR = gcd(newR, aList[N - i - 1]);
        rList.unshift(newR);
    }

    var max = 0;
    for (var i = 0; i < N; i++) {
        var result = gcd(lList[i], rList[i + 1]);
        max = Math.max(max, result);
    }

    console.log(max);
}

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