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: Accepted)

def rec(n, arr)
  div = (2..(n**0.5).to_i).find { |i| n % i == 0 }
  return arr << n if div.nil?

  rec(n / div, arr << div)
end

gets
as = gets.split.map(&:to_i)

gcd = as.inject(:gcd)
as.map! { |a| a / gcd }

divisor = rec(as[0], []).sort.uniq
ans_without_a0 = as[1..-1].inject(:gcd)

deletes = []
divisor.each do |i|
  tmp = as.select { |a| a % i != 0 }
  deletes << tmp[0] if tmp.size == 1
end

ans = 1
deletes.each do |d|
  as_tmp = as.dup
  as_tmp.delete(d)
  ans = [as_tmp.inject(:gcd), ans].max
end
puts [ans, ans_without_a0].max * gcd