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)

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

sort_arr = arr.uniq.sort
ans = sort_arr[1] || sort_arr[0]
while ans > 1 do
  fail_count = 0
  arr.each do |num|
    fail_count += 1 if num % ans != 0
    break if fail_count >= 2
  end
  break if fail_count < 2

  if ans == sort_arr[1]
    ans = sort_arr[0]
  else
    ans -= 1
  end
end
puts ans