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)


DMAX=17

def func(x,n)
    return if n==1
    gcds=[]
    (n/2).times do |i|
        gcds[i]=x[-1][2*i].gcd(x[-1][2*i+1])
    end
    x << gcds
    func(x,n/2)
end

def func2(x,i,level,temp)
    return if level==DMAX
    t=(i>>DMAX-level-1) ^ 1
    temp << x[DMAX-level-1][t]
    func2(x,i,level+1,temp)
end

N=gets.to_i
A=gets.split.map(&:to_i)
A2=Array.new(2**DMAX,A[-1])
A.each_with_index do |a,i|
    A2[i]=a
end
x=Array.new
x << A2
func(x,2**DMAX)
p x
max=0
N.times do |i|
    temp=[]
    func2(x,i,0,temp)
    g=temp.inject(&:gcd)
    max=g if max<g
end
puts max