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: Wrong Answer)

n = gets.chomp.to_i
a = gets.chomp.split.map(&:to_i).sort

stack = []
2.times do |j|
  i = 1
  while i <= a[j] / i
    if a[j] % i == 0
      stack << i if !stack.include?(i)
      stack << a[0] / i if !stack.include?(a[0] / i)
    end
    i += 1
  end
end

stack.sort.reverse.each do |i|
  cnt = 0
  n.times do |j|
    cnt += 1 if a[j] % i != 0
  end
  if cnt <= 1
    puts i
    exit
  end
end