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)

io = STDIN
n=io.gets.to_i
a=io.gets.split.map(&:to_i)
lar=Array.new(n) #left gcd累計
rar=Array.new(n) #right gcd累計
lar[0]=a[0]
(1...n).each do |i|
  lar[i]=lar[i-1].gcd(a[i])
end
rar[-1] = a[-1]
(n-2).downto(0).each do |i|
  rar[i]=a[i].gcd(rar[i+1])
end
ar= [
lar[-2],
(1..n-2).map{ |i|lar[i-1].gcd(rar[i+1])},
rar[1]
]
p ar.flatten.max