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: Time Limit Exceeded)


def gcd(a,b)
  gcd(b,a) if b > a
  return b if (r = a % b) == 0
  gcd(b,r)
end

def gcd_a(x)
  return x[0] if x.size == 1
  (x[1..-1]).inject(x[0]) {|r, n| gcd(r,n) }
end

N = gets.chomp.to_i
A = gets.chomp.split.map(&:to_i)
if N > 1 then
  m = 1
  (0..(N-1)).each do |i|
    p = A.dup
    p.delete_at(i)
    q = gcd_a(p)
    m = q if m < q
  end
  puts m
else
  puts A[0]
end