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)

class Array
  def gcd
    self.inject{|a,b| a.gcd(b)}
  end
end

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

array = []
now_b = 0
n.times do |i|
  b = a.dup
  x = b[i]
  if i == n-1
    b = [b[i]]
  else
    b = b.slice(i+1..n-1)
  end
  late_b = b.gcd
  array.push(late_b.gcd(now_b))
  if i == 0
    now_b = x
  else
    now_b = x.gcd(now_b)
  end
end

p array.max