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)

"use strict";

// read lines from stdin
const input = require("fs")
  .readFileSync("/dev/stdin", "utf8")
  .split("\n");

const N = parseInt(input[0], 10);
const A = input[1].split(" ").map((val) => parseInt(val, 10));

const gcd = (a, b) => (b ? gcd(b, a % b) : a);

if (N === 2) {
  console.log(Math.max(A[0], A[1]));
  return;
}

let sumFromL = [];
let sumFromR = [];

sumFromL[0] = A[0];
for (let i = 1; i < N; i++) {
  sumFromL[i] = gcd(sumFromL[i - 1], A[i]);
}

sumFromR[N - 1] = A[N - 1];
for (let i = N - 2; i >= 0; i--) {
  sumFromR[i] = gcd(sumFromR[i + 1], A[i]);
}

let gcds = [];
for (let i = 0; i < N; i++) {
  gcds[i] = gcd(sumFromL[i - 1] || 0, sumFromR[i + 1] || 0);
}

console.log(Math.max(...gcds));