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)

require'prime'
n=gets.to_i
A=gets.split.map &:to_i
B=[1]*n
r=A.reduce:gcd
A.map!{|a|a/r}
M=A.max
Prime.each{|p|
	break if p>M
	f=true
	while f
		x=nil
		c=0
		n.times{|i|
			if A[i]%p==0
				A[i]/=p
				x=i
				c+=1
			end
		}
		if c==n-1
			B[x]*=p
		else
			f=false
		end
	end
}
p B.max*r