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";

var _constants = require("constants");

var hasN = true; // has N *only* line
var type = "b";
// a: 2D split
// b: space split
// c: line split
// z: other (only source)
function main(N, p, s) {
  // N, processed data, source
  var div = [];
  for (var i = 0; i < p.length; i++) {
    div.push(divisor(p[i]));
  }
  var a = new Set();
  div.forEach(function (e) {
    return e.forEach(function (z) {
      return a.add(z);
    });
  });
  var x = Array.from(a).sort(function (c, d) {
    return c - d;
  });
  var m = 1;
  for (var _i = x.length - 1; _i >= 0; _i--) {
    var count = 0;
    for (var j = 0; j < div.length; j++) {
      if (div[j].indexOf(x[_i]) >= 0) count++;
      if (j - count > 1) break;
    }
    if (count >= div.length - 1) {
      m = x[_i];
      break;
    }
  }
  console.log(m);
}
function common(a) {
  var line = a.split('\n').slice(0, a.split('\n').length - 1);
  if (hasN) var N = Number(line.shift());
  switch (type) {
    case "a":
      main(N, line.map(function (e) {
        return e.split(' ').map(function (ee) {
          return Number(ee);
        });
      }), a);
      break;
    case "b":
      main(N, line[0].split(' ').map(function (e) {
        return Number(e);
      }), a);
      break;
    case "c":
      main(N, line, a);
      break;
    case "z":
      main(N, null, a);
  }
}
function divisor(num) {
  var results = [];
  for (var i = 2; i <= num; i++) {
    if (num % i == 0) {
      results.push(i);
    }
  }
  return results;
}
common(require("fs").readFileSync("/dev/stdin", "utf8"));