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)

def gcd(a, b)
  return b if (r = a % b).zero?
  gcd(b, r)
end
n = gets.chomp.to_i
as = gets.split.map(&:to_i)
if as.size == 2
  ans = as.max
else
  one_ans = gcd(as[0],as[1])
  two_ans = gcd(as[0],as[2])
  three_ans = gcd(as[1],as[2])
  one_count = 0
  two_count = 0
  three_count = 0
  as.each do |num|
    one_count += 1   if num % one_ans == 0
    two_count += 1   if num % two_ans == 0
    three_count += 1 if num % three_ans == 0
  end
  one_ans_next   = one_count   == (n - 1) ? one_ans : 1
  two_ans_next   = two_count   == (n - 1) ? two_ans : 1
  three_ans_next = three_count == (n - 1) ? three_ans : 1
  ans = [one_ans_next, two_ans_next, three_ans_next].max
end
puts ans