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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

require "set"

n = gets.chomp.to_i
arr = gets.chomp.split(" ").map(&:to_i)

yakusu_arr = []
n.times do |t|
  yakusu_arr << Set.new
end

(1..Math.sqrt(arr.max).to_i).each do |t|
  arr.each_with_index do |a, i|
    if a % t == 0 then
      yakusu_arr[i] << t
      yakusu_arr[i] << a / t
    end
  end
end

max = 0
n.times do |i|
  p = yakusu_arr.select.with_index{|set, j| i != j}.reduce(&:&)
  max = p.max if p.max > max
end

puts max