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 gcd(a) {
    var f = (a, b) => b ? f(b, a % b) : a;
    var ans = a[0];
    for (var i = 1; i < a.length; i++) {
        if (a[i] > 0) ans = f(ans, a[i]); 
    }
    return ans;
}
function Main(input) {
    let cin = new Inputer(input);
    let N = cin.getInt();
    let A = cin.getIntArray(N);
    let max = 0;
    for (let n = 0; n < N; n++) {
        let c = A[n]; A[n] = 0;
        let w = gcd(A);
        if (max < w) max = w;
        A[n] = c;
    }
    console.log(max);
}
class Inputer{constructor(t){if(typeof t=='undefined')throw new Error('引数（stdin）を省略できません！');this.cnt=0,this.items=t.split(/\n|\s/)}getInt(){return this.items[this.cnt++]-0}getIntArray(t){if(typeof t=='undefined')throw new Error('引数（1以上）を省略できません！');let r=new Array(t);for(let e=0;e<t;e++)r[e]=this.getInt();return r}getStr(){return this.items[this.cnt++]}getStrArray(t){if(typeof t=='undefined')throw new Error('引数（1以上）を省略できません！');let r=new Array(t);for(let e=0;e<t;e++)r[e]=this.getStr();return r}}
if (typeof window == "undefined") Main(require("fs").readFileSync("/dev/stdin", "utf8"));