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)

"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 max = p.reduce(function (p, c) {
    return p > c ? p : c;
  });
  var div = p.map(function (e) {
    return divisor(e);
  });

  var _loop = function _loop(i) {
    var count = 0;
    div.forEach(function (d) {
      if (d.indexOf(i) >= 0) count++;
    });
    if (count >= div.length - 1) {
      console.log(i);
      return "break";
    }
  };

  for (var i = max; i > 1; i--) {
    var _ret = _loop(i);

    if (_ret === "break") break;
  }
}
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"));