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.to_i
as = gets.split.map(&:to_i)

l = Array.new(n+1)
r = Array.new(n+1)
l[0] = 0
r[n] = 0
(1..n).each do |i|
  l[i] = l[i-1].gcd(as[i-1])
  # r[i] = l[i-1].gcd(as[i-1])
end

(n-1).downto(0).each do |i|
  r[i] = r[i+1].gcd(as[i])
end

ms = Array.new(n)
ans = []
(0..n-1).each do |i|
  ans << l[i].gcd(r[i+1])
end

puts ans.max